最終版: 2022/8/8“日本数学会2022 年度秋季総合分科会

英 文

サ

マ

リ

2022 年 9 月
於

北海道大学

集

2022 日 本 数 学 会
秋季総合分科会プログラム期

日2022 年 9 月 13 日（ 火 ）〜 9 月 16 日（ 金 ）会場

北海道大学高等教育推進機構
北 海 道 札 幌 市 北 区 北 17 条 西 8 丁 目

連 絡 先北海道大学大学院理学研究院数学部門〒060-0810
北 海 道 札 幌 市 北 区 北 10 条 西 8 丁 目
E-mail hokudai22sept mathsoc jp
一般社団法人

日 本 数 学 会

第 I 会場

第 II 会場

第 III 会場

第 IV 会場

第 V 会場

第 VI 会場

第 VII 会場

第 VIII 会場

第 IX 会場

E208

E310

N304

N2

E301

N1

N302

E214

E308

函数解析学 函数方程式論 統 計 数 学 代 数 学 応 用 数 学 幾 何 学 トポロジー 函 数 論 無限可積分系
10:00〜11:45

9:45〜12:00
14:15〜16:45

9:30〜11:50

13 日
（火）

9:30〜12:00 10:00〜11:45 9:30〜11:45 9:30〜12:00 9:30〜12:00
14:15〜16:45 14:15〜15:25 14:15〜16:15 14:20〜18:00 14:15〜15:15

企画特別講演

9:30〜12:00

13:00〜14:00

特別講演 特別講演 特別講演 特別講演 特別講演 特別講演

特別講演 特別講演

14:15〜15:15 17:00〜18:00 14:15〜15:15 17:00〜18:00 15:45〜16:45 16:30〜17:30
15:30〜16:30

15:30〜16:30 14:15〜15:15

函数解析学 函数方程式論 統 計 数 学 代 数 学 応 用 数 学
9:30〜12:00

9:45〜12:00

9:30〜11:30

14 日 特 別 講 演 特 別 講 演（水） 13:15〜14:15 13:30〜14:30

幾 何 学・
トポロジー

9:30〜12:00 10:00〜11:45
13:00〜14:15

函 数 論 無限可積分系
9:30〜12:00

9:30〜10:50

特別講演

特別講演

特別講演 特別講演

13:00〜14:00

10:30〜11:30
13:15〜14:15

13:30〜14:30 11:00〜12:00

日 本 数 学 会 賞 授 賞 式（高等教育推進機構 大講堂） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:00〜15:30)
〃
総
合
講
演（
） 日 本 数 学 会 賞 秋 季 賞 受 賞 者 · · · · · · · · · · · · (15:50〜16:50)
佐 伯
修 (九 大 I M I) · · · · · · · · · · · · (17:10〜18:10)

函数解析学 函数方程式論 統 計 数 学 代 数 学 応 用 数 学 幾 何 学 トポロジー 実 函 数 論
15 日
（木）

9:30〜12:00 9:45〜12:00
14:15〜16:00 14:15〜16:45

9:30〜12:00

数学基礎論
および歴史

9:30〜11:30 9:30〜12:00 9:30〜11:45 9:30〜12:00 9:30〜11:30 10:35〜12:00
14:15〜17:15 14:15〜16:45 14:15〜16:15 15:40〜18:00 14:15〜16:20 14:45〜16:15

企画特別講演

13:00〜14:00

特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演
16:15〜17:15 17:00〜18:00 14:25〜15:25 17:30〜18:30 17:00〜18:00 16:30〜17:30 14:20〜15:20 16:40〜17:40 16:30〜17:30
15:45〜16:45函数方程式論 統 計 数 学 代 数 学 応 用 数 学 幾 何 学 トポロジー 実 函 数 論
16 日
（金）

数学基礎論
および歴史

9:45〜12:00 9:30〜12:00 9:30〜12:00 9:30〜12:00 9:30〜12:00 9:30〜12:00 9:30〜11:50 10:30〜12:00
14:15〜16:45 14:25〜16:50 14:15〜17:00 14:15〜16:10 14:15〜16:30 15:40〜17:00 14:15〜16:20 14:15〜15:55

企画特別講演

13:00〜14:00

特別講演

特別講演 特別講演

特別講演 特別講演 特別講演

17:00〜18:00

17:15〜18:15 16:25〜17:25

14:20〜15:20 16:40〜17:40 16:25〜17:25

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3

目次
総合講演

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

企画特別講演1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

数学基礎論および歴史 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

代数学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

幾何学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

函数論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

実函数論

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

函数解析学 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

統計数学

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

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4

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
応用数学

85

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

トポロジー . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112

9 月 15 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

9 月 16 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

116

無限可積分系. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

120

9 月 13 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

120

9 月 14 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

122

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1

総合講演

総 合

講

演

9 月 14 日（水） 総合講演会場
2022 年度日本数学会賞秋季賞受賞講演
日本数学会賞秋季賞受賞者· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:50〜16:50)
Autumn Prize Winner
佐 伯

修 (九 大 I M I )Osamu Saeki(Kyushu Univ.)

ジェネリックな可微分写像の大域的特異点論 · · · · · · · · · · · · · (17:10〜18:10)

Global singularity theory of generic differentiable maps

概 要 One of the most popular methods to study the topological structure of a given differentiable manifold

is to use Morse functions. Such functions can be regarded as generic differentiable maps into the real line.
Then, what happens if we consider generic maps into general dimensional Euclidean spaces or manifolds?
This might have been a motivation of Whitney or Thom around the middle of the 20th century for studying
singularities of differentiable maps between manifolds. In this talk, following such an idea, the speaker willsurvey some studies of structures of manifolds by using generic differentiable maps, and some global studies
of generic differentiable maps with singularities themselves, including recent developments.

最終版: 2022/8/8
企画特別講演

企

画

特

別

講

2

演

9 月 13 日（火）第 IV 会場
梅 田

亨 (阪 公 大 数 学 研) [ Capelli 恒等式の過去・現在・未来 · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Tôru Umeda (Osaka Metro. Univ.)

The Capelli identities, past, present, and the future

概 要 The Capelli identities have been useful tools in the classical invariant theory. A notable use, aside

from the works by Capelli himsels, is seen in the famous book by Hermann Weyl, The Classical Groups.
But, their representation theoretic meaning were not so clear, and acturally clarified, for example, by Roger
Howe’s paper ”Remarks on Classical Inveriant Theory”. Also, some generalization were given by a paper byHowe-Umeda around 1990. Since then, many investigations came up in many directions.
I would like to explain, for geneneral audience, the basic ideas to look at these identities, including the proofs.
We have still some open problems relating them. I will give some hints to grasp those problems. Also, there
are many interesting facts, especially in relation to hypergeometric series.
I am afraid that I could have time to explain all those things. I will pick up some charming side of Capelli
identities as far as possible.
第 VI 会場
柳 原

宏 ( 山 口 大 工)Hiroshi Yanagihara (Yamaguchi Univ.)

解析的普遍被覆写像に関するレブナー理論 · · · · · · · · · · · · · · · (13:00〜14:00)

Loewner theory on analytic universal covering maps

概 要 The classical Loewner theory deals with time evolution of univalent functions ft in the unit disk D.

Therefore each image domain Ωt := ft (D) is necessary simply connected, i.e., Ωt has no holes. In thistalk, instead of univalent functions, we consider evolution families of analytic universal covering maps, andgeneralize Loewner theory. In this case we show that the connectivity order of Ω t (= the number of holes inΩt ) is non decreasing in t.
総合講演会場
特別招待講演 (台湾数学会)
Jungkai Chen (国 立 台 湾 大)

Jungkai Chen (Nat. Taiwan Univ.)

Explicit birational geometry of threefolds, after Mori, Kawamata and Kawakita · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)
Explicit birational geometry of threefolds, after Mori, Kawamata and Kawakita

概 要 One of the highlights of modern algebraic geometry is the minimal model program in dimension three,thanks to the work of Mori, Kawamata, Kollar, Reid, Shokurov, and many others. After that, there arethen many more works to understand 3fold MMP explicitly. Other than above-mentioned mathematicians,
main contributors along this direction includes Hayakawa, Kawakita, Tziolas, and Prokhorov. In this talk,we will present some results and expectations in understanding and classifying birational maps in 3fold
MMP. Particularly, we will explain ideas toward the classification of divisorial contractions to curves. If time
permits, we will also demonstrate some geometric applications.

9 月 15 日（木）第 IV 会場
小 澤

徹 (早 大 理 工) [ 非線型分散方程式に関する修正エネルギー法 · · · · · · · · · · · · · (13:00〜14:00)

Tohru Ozawa (Waseda Univ.)

Modified Energy Method for Nonlinear Dispersive Equations

概 要 We introduce the modified energy method for the proof of the existence of strong solutions to the

Cauchy problem for nonlinear dispersive equations such as nonlinear Schrödinger equations, coupled KleinGordon-Schrödinger equations, and the Zakharov system.

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3

企画特別講演

第 VI 会場青 嶋

誠 (筑波大数理物質)

Makoto Aoshima (Univ. of Tsukuba)

高次元現象の統計数理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Statistical mathematics for high-dimensional phenomena

概 要 The theory of conventional statistics does not hold for high-dimensional data such as genomes. Whenthe number of dimensions exceeds the number of samples, various high-dimensional phenomena appear as
a curse of dimensionality, which hinders the establishment of the theory. Our research group pioneered thetheory and methodology of high-dimensional statistical analysis and developed statistical mathematics forhigh-dimensional phenomena. In this talk, we explain various high-dimensional phenomena and introduce
statistical mathematics to deal with high-dimensional data at high speed and with high accuracy even forsmall samples of only a few tens. As practical examples, we give analysis examples of next-generation
sequencing data with millions of dimensions and the latest high-dimensional data in space physics andadvanced materials. Papers and analysis tools related to this talk are available from the following site:
https://www.math.tsukuba.ac.jp/ aoshima-lab/jp/

9 月 16 日（金）第 IV 会場
田 中

公 ( 東 大 数 理)

Hiromu Tanaka (Univ. of Tokyo)

極小モデル理論について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

On minimal model program

概 要 Minimal model program is classification theory of algebraic varieties. It is based on the theory ofalgebraic surfaces established in the early 20th century. The 3-dimensional minimal model program wascompleted in the 1980s, however its main conjecture for the general case still remains to be an open problem.
In this talk, we overview the current status of the minimal model program.
第 VI 会場
本 田

Ko Honda

公 (

UCLA

)

(UCLA)

Contact structures, convex hypersurfaces, and open book decompositions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)
Contact structures, convex hypersurfaces, and open book decompositions

概 要 Contact structures, alongside symplectic structures (their even-dimensional siblings), play a central

role in modern geometry and have many connections to dynamical systems, low-dimensional topology,
representation theory, algebraic geometry, and mathematical physics.
This talk is concerned with the fundamental question of how to decompose contact manifolds, especiallyin higher dimensions, into smaller, easier-to-understand pieces. The key result — a highly nontrivial one— is to perturb a given hypersurface in a contact manifold into a nice hypersurface called a ”convex”
hypersurface. (This was already possible for contact 3-manifolds and was successfully applied to many
classifications problems.) We also explain the relationship to open book decompositions as articulated by
Emmanuel Giroux about 20 years ago. This is joint work with Yang Huang and also with Joseph Breen.

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数学基礎論および歴史

数 学

基

礎

論

9 月 15 日（木）

お

よ

び

歴

4

史

第 IX 会場

10:35〜12:00
1 只 木 孝 太 郎 ( 中 部 大 工)

Kohtaro Tadaki (Chubu Univ.)

アルゴリズム的ランダムネスによる量子情報理論の精密化 VI · · · · · · · · · 15

A refinement of quantum information theory by algorithmic randomnessVI

概 要 The notion of probability plays a crucial role in quantum mechanics. It appears as the Born rule.

In modern mathematics which describes quantum mechanics, however, probability theory means nothingother than measure theory, and therefore any operational characterization of the notion of probability is
still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness,
we presented an operational refinement of the Born rule, called the principle of typicality, for specifying
the property of the results of quantum measurements in an operational way. In this talk, we refine andreformulate the Holevo–Schumacher–Westmoreland theorem based on the principle of typicality, in order todemonstrate how properly our framework works in practical problems in quantum mechanics.
2 宮 部 賢 志 ( 明 大 理 工)
Kenshi Miyabe(Meiji Univ.)

実閉体を成す弱計算可能実数の部分族 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Subclasses of weakly computable reals that form real closed fields

概 要 We give some examples of subclasses of weakly computable reals that form real closed fields. Someknown examples are the class of computable reals, that of weakly computable reals, and that of non-random
weakly computable reals. We extend these results by introducing strong Solovay reducibility.
3 池 田 宏 一 郎 ( 法 政 大 経 営)
Koichiro Ikeda(Hosei Univ.)

On regular generic structures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On regular generic structures

概 要 A generic structure M is said to be regular, if whenever A is a finite set of M and a ∈ M , thena ∈ acl(A) implies d(a/A) = 0. Known generic structures are regular, and we do not have any example ofnon-regular generic structures. In this talk, we want to explain that various properties of generic structures
can be simply expressed in regular generic structures, and that known examples of generic structures areusually regular.
4 桔 梗 宏 孝 (神戸大システム情報)
Hirotaka Kikyo(Kobe Univ.)log 風関数で定義されるジェネリック構造について · · · · · · · · · · · · · · · · · · 15
On generic structures defined by log-like functions概 要 Hrushovski introduced log-like functions in his 1988 paper to refute a conjecture by Lachlan. He

defined classes Kf depending on log-like functions f defined using some approximation of some real number.
The class (Kf , <) has the free amalgamation property and the one point graph is closed in any non-empty
graph belonging to Kf for the original f . We can modify the definition of the log-like functions in theway that the classes have the free amalgamation property while the one point graph may not be closed inother graphs in the class. Still, the generic structures of the class will have model complete theories if f isunbounded, and the automorphism group of the generic structure will be simple if the real number used todefine f is a rational number.

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5

数学基礎論および歴史

5 坪 井 明 人 (筑波大⋆)Akito Tsuboi (Univ. of Tsukuba⋆)

Some comments on the difference between forking and dividing · · · · · · 10
Some comments on the difference between forking and dividing

概 要 The two notions dividing and forking are important in model theory, especially in stability theory.

By definition, dividing is clearly a stronger condition than forking. But Shelah has shown that they are thesame in stable theories. Kim and Pillay showed the equivalence in the case of simple theories. Of course,
there are some examples that show the difference. One of the best known has the strict order property.
However, this example is not satisfactory, because a simple theory does not have the strict order property.
We give a (possibly) new example, which may be of interest.
14:15〜14:30

数学基礎論および歴史分科会総会

14:45〜16:15
6 津 久 浦 健 太 (筑波大数理物質)

Kenta Tsukuura (Univ. of Tsukuba)

Huge cardinal and Prikry forcing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Huge cardinal and Prikry forcing

概 要 The models of many kinds of saturated ideals over the successor of regular cardinals are known andhave been used to solve some questions for combinatorics on the successors of regular cardinals, for example,
polarized partition relations, reflection principle for graph chromatic number, and Chang’s conjecture. Ourinterest is accomplishing these on the successors of singular cardinals. Using a huge cardinal, we can obtainsome models in which the successor of large cardinals carries a saturated ideal and satisfies some of the
combinatorial properties. Then we can define Prikry forcing, which is a forcing that changes a large cardinal
into a singular cardinal. In this talk, we see that Prikry forcing preserves the centeredness of ideals but kills
the layeredness. We also investigate some of the polarized partition relations and the reflection principle
for graph chromatic number after Prikry forcing.
7 後 藤 達 哉 (神戸大システム情報)
Tatsuya Goto

(Kobe Univ.)

測度 0 集合の和集合に関する Goldstern の原理 · · · · · · · · · · · · · · · · · · · · · 15

Goldstern’s principle about unions of measure 0 sets

概 要 In his 1993 paper, Martin Goldstern showed that the union of a family of Lebesgue measure zero setsthat is parametrized by ω ω and is increasing has also Lebesgue measure zero provided that the sets are
uniformly analytic. Our aim is to study to what extent we can drop the analytic assumption. We showthat Goldstern’s principle for the pointclass of all subsets is independent from ZFC. Also we prove thatGoldstern’s principle for the pointclass of all subsets holds both under ZF + AD and in Solovay models.
8 D. A. Mejı́a( 静 岡 大 理)

Diego A. Mejı́a (Shizuoka Univ.)

強測度ゼロ集合のイデアルに関連する基数不変量 · · · · · · · · · · · · · · · · · · · 15

Cardinal characteristics associated with the ideal of strong measure zerosets

概 要 We prove new results about the combinatorics of strong measure zero sets of reals, particularly underhypothesis involving cardinal characteristics. Expanding results of Yorioka (2002) and Cardona (2022),
we show that cov(M) = d = λ implies cof(SN ) > λ where SN denotes the strong measure zero ideal.
Moreover, under further assumptions with λ regular, we guarantee that cof(SN ) > dλ .
We use this result to force in ZFC that the four cardinal characteristics (additivity, covering, uniformity
and cofinality) associated with SN are pairwise different. Previous recent work with Cardona and RiveraMadrid proves partial results, but it was unknown how to force the additivity smaller than everything else.
We now overcome this obstacle by using forcings with finitely additive measures. This is a joint work withJörg Brendle and Miguel Cardona.

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数学基礎論および歴史

9 宮 内
凛 ( 早 大 理 工)
薄 葉 季 路 ( 早 大 理 工)
Rin Miyauchi (Waseda Univ.)
Toshimichi Usuba (Waseda Univ.)

6

The continuum function on the countable unions of countable sets · · · 15
The continuum function on the countable unions of countable sets

概 要 We construct a model of ZF in which the following hold: 1. For every cardinal ℵα , there is a countable

union of countable setsSn An and a surjection from P (for every countable union of countable sets
10 池 上 大 祐 (芝 浦 工 大 工)
Daisuke Ikegami(Shibaura Inst. of Tech.)S

Sn An ) onto ℵα , and 2.

There is a set X such thatSn An , there is no surjection from P ( n An ) onto X.

Preservation of AD via forcings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Preservation of AD via forcings

概 要 It is well-known that forcings preserve ZFC, i.e., any set generic extension of any model of ZFC isagain a model of ZFC. How about the Axiom of Determinacy (AD) under ZF? It is not difficult to see that
Cohen forcing always destroys AD, i.e., any set generic extension of a model of ZF+AD via Cohen forcing
is not a model of AD. Actually it is open whether there is a forcing which adds a new real while preserving
AD.
In this talk, we present several results on preservation and non-preservation of AD via forcings. This is
joint work with Nam Trang.
16:30〜17:30

特別講演
河 井 達 治 (北陸先端大情報)

Real numbers from a point-free perspective(JAIST)

Real numbers from a point-free perspective

Tatsuji Kawai

概 要 We take another look at real numbers from the viewpoint of point-free topology. The intuitionisticpresentation of real numbers by a spread leads to a unique representation of a real number called regular
ideal. Regular ideals form the models of a certain geometric theory; thus the point-free space associated withthis theory provides us with a novel notion of real numbers. As applications of this point-free real numbers,
we give point-free proofs of the intermediate value theorem and Brouwer’s fixed-point theorem. These
point-free proofs make the finitary aspect of these theorems more explicit than their point-set counterparts.

9 月 16 日（金）第 IX 会場

10:30〜12:00
11 関

隆 宏 (新潟大経営戦略本部)

Takahiro Seki

(Niigata Univ.)

制限された weakening と contraction を持つ結合則を持たない部分構造
論理の可換性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Commutativity of non-associative substructural logics with restricted
weakening and contraction

概 要 It is well-known that the associative substructural logic FLcw , obtained from FL by adding bothcontraction and weakening rules, derives exchange rule. In this talk, we consider the commutativity resultin non-associative substructural logics with weakening, contraction, restricted weakening and restricted
contraction axioms.

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7

数学基礎論および歴史

12 加 藤鹿 島

裕 (東工大情報理工)
亮 (東工大情報理工)

Yutaka KatōRyo Kashima(Tokyo Tech)(Tokyo Tech)

証明可能性論理 GLS の意味論とカット除去 · · · · · · · · · · · · · · · · · · · · · · · · 15

Semantics and cut-elimination for the provability modal logic GLS

概 要 Solovay (1976) introduced a modal logic GLS and proved the arithmetic completeness of GLS withrespect to the standard model of PA. Kushida (2020) introduced a sequent calculus of GLS and proved thecut-elimination theorem. Our study attempt to construct a Kripke semantics of GLS and prove soundnessof GLS and completeness of cut-free GLS, which gives an alternative proof of the cut-elimination theorem.
13 大 川 裕 矢 (千 葉 大 理)
Yuya Okawa(Chiba Univ.)

解釈可能性論理 IL の部分論理に対する simplified Veltman frame による
完全性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Simplified Veltman frames for sublogics of the interpretability logic IL

概 要 Visser proved that the interpretability logic IL is sound and complete with respect to a correspondingclass of simplified Veltman frames and is not complete with respect to a corresponding class of finite
simplified Veltman frames. Ignatiev introduced the conservativity logic CL which is a sublogic of IL, andhe proved that CL is sound and complete with respect to a corresponding class of simplified Veltman frames.
On the other hand, Ignatiev proposed the problem whether CL is complete with respect to a correspondingclass of finite simplified Veltman frames or not.
We investigate the completeness with respect to (finite) simplified Veltman frames for several sublogics ofIL. Then, we solve Ignatiev’s problem affirmatively.
14 鈴 木 信 行 (静 岡 大 理)

Nobu-Yuki Suzuki (Shizuoka Univ.)

冠頭標準形定理が成り立つ中間述語論理についての注意 · · · · · · · · · · · · · 15

Remarks on intermediate predicate logics enjoying prenex normal form
theorem概 要 The prenex normal form theorem (PNFT) is a well-known metatheorem on classical predicate logic.

It is said to characteristically express the behavior of quantifiers in classical predicate logic. We consider
PNFT in the framework of intermediate predicate logics, and make some remarks.
15 堀
弘 昌 ( 名 大 情 報)
中 澤 巧 爾 ( 名 大 情 報)龍 田
真 ( 国 立 情 報 学 研)
Hiromasa Hori (Nagoya Univ.)
Koji Nakazawa (Nagoya Univ.)
Makoto Tatsuta(Nat. Inst. of Informatics)

命題論理に対する無限証明体系と循環証明体系の証明能力同等性 · · · · · · 15

Equivalence of infinite and cyclic proof systems for propositional logics

概 要 It is proved that the provabilities of infinite proof system and cyclic proof system are equivalent forsome propositional logics: the propositional LK with inductively defined propositions, the propositional LK
with fixed point operators, and the proof system for the linear temporal logic with fixed point operators.

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数学基礎論および歴史

8

14:15〜15:55
16 田 中 紀 子 (愛知県立旭丘高)
Noriko Tanaka(Aichi Prefectural Asahigaoka High School)

戦中戦後の京都における特別科学教育学級 · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Experimental Class for Science Education in Kyoto in the near endof the World War II

概 要 Following a decision of the Ministry of Education, “the Experimental Classes for Science Education”

were formed in four cities of Japan in the near end of the World War II. The one of the Experimental classes
were established in the Kyoto-Prefectural Kyoto First Secondary School, one each in the 3rd, 2nd and 1st
year. In addition to the actual management of the class, the content of the lessons and the pupils’careers
after the class are described. I will once again shed light on the Experimental Class for Science Education,and make use of a part of science and technology education in Japan in the future.
17 脇

克 志 ( 山 形 大 理)

Katsushi Waki (Yamagata Univ.)

和算書内の図形領域抽出 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Extraction of graphic regions within WASAN books

概 要 Two pre-processes that have been carried out to extract the graphic regions in the WASAN books

are described. First, an evaluation of the recognition accuracy of the first pre-process, the extraction ofimportant characters by character recognition, is presented. Next, the results of the shape area using theHough transform are presented. Finally, the expected improvement in accuracy by combining the two
pre-processing methods and future issues are explained.
18 真 島 秀 行 (お茶の水女大⋆)Hideyuki Majima (Ochanomizu Univ.

⋆)

関孝和, 建部賢弘の円周率の近似計算の理論的意味づけ · · · · · · · · · · · · · · 15

Theoretical meaning of the calculation of Pi used by Seki Takakazu andTakebe Katahiro

概 要 We will give some theoretical meaning on culculation of the number Pi by Seki Takakazu. Seki foundthe so-called Aitken’s delta-sequenced process in his theory, but there were some errors in his calculationand he only claimed that his approximate number of Pi was a bit less than 3.14159265359. Katahiro Takebe
followed Seki’s method and discovered another method of calculation of Pi.
19 森 本 光 生(四日市大関孝和数学研・上智大⋆)
Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)『関算四伝書』について (2) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the Sekisan Shidensho (2)概 要 In the Sekisan Shidensho, there is the list of private library of the Yamaji, masters of Seki’s wasan

school. There are 175 items in this list, most of which are related with wasan but a few are important
Chinese books on mathematics imported by the 8th shogun Yoshimune. We shall present a preliminary talkon this Yamaji List ad discuss how the books or materials in the list are treated in the Sekisan Shidensho
itself.
20 小 川束(四日市大関孝和数学研)

Tsukane Ogawa (Yokkaichi Univ.)

岡之只『妙矩集』における帰納的方法論 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Inductive methodology in the ‘Myouku Shu’ written by Oka Yukitada

概 要 The ‘Myouku shu’ written by Oka Yukitada (1791–?) is a kind of formula collection in Edo period.

The word ‘Yuzuri Koshi’ appears in the proofs of formulae 20, 21, and 23 in the book, but its meaning is
not obvious so far. It could be seen as a term related to inductive reasoning, it is more appropriate to think
it as an analogy. Oka was interested in whether similar results could be obtained by analogy in generalisinga problem. I will illustrate this with some examples.

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9

数学基礎論および歴史

21 田 村誠(大阪産大全学教育機構)

Makoto Tamura (Osaka Sangyo Univ.)

開帯従立方について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the solution of cubic equations in China

概 要 “Jigu Suanjing (Continuation of Ancient Mathematics)” written shortly after 626 deals with cubic

equations, but does not explain how to solve them. However, the book shows correct solutions to many
cubic equations, it is natural to consider that the method had been established before the book appeared.
In this talk, we consider the difference between calculating cube roots and solving cubic equations, and anumeric solution according to the text proposed by Qian Baocong.
16:00〜16:15

歴史部門懇談会

16:25〜17:25

特別講演

ハラルドクマレ (ド イ ツ 日 本 研)

小倉金之助のヒストリオグラフィーにおける「民間数学者」の再評価

Harald Kuemmerle(German Inst. for Japanese Stud.)A re-evaluation of “civil mathematicians” in Ogura Kinnosuke’s historiography

概 要 In his historical research on mathematics since the Meiji period, Ogura Kinnosuke assigns “civil

mathematicians” (minkan sugakusha) a role that was important but limited in scope. For example, in his
Meiji sugakushi no kiso koji, he judges that although they did important translation work until the 1880s,
their role was limited to publishing popularizing literature and test-taking journals after this. A systematic
study of his statements on civil mathematicians and their context helps to highlight their relevance. As
Ogura also referred to himself as a civil mathematician, studying his biography also gives important insights.
Doing so, the study of mathematics in the Meiji period from the perspective of knowledge circulation throughjournals becomes possible and allows for international contextualization.

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代数学

代 数
9 月 13 日（火）10

学第 IV 会場

9:30〜12:00
潟大⋆)
1 田 島 慎 一 (新小 原 功 任 ( 金 沢 大 理 工)
照 井章 (筑波大数理物質)

一般固有空間と Jordan 鎖の厳密で効率的な計算 (1) · · · · · · · · · · · · · · · · · 10

Shinichi Tajima (Niigata Univ.⋆)
Katsuyoshi Ohara (Kanazawa Univ.)
Akira Terui (Univ. of Tsukuba)

Efficient symbolic computation of Jordan chains and generalized eigenspaces(1)

概 要 An efficient method for computing Jordan chains of a matrix of integers or rational numbers by exact

computation is proposed. A Jordan–Krylov basis, special generators in the sense of Krylov subspace, ofa certain subspace over rational numbers is introduced. It is shown that computation of Jordan chains is
reduced to a Jordan–Krylov basis. In this theory, the Krylov subspace is effectively used.
潟大⋆)2 田 島 慎 一 (新小 原 功 任 ( 金 沢 大 理 工)
照 井章 (筑波大数理物質)

一般固有空間と Jordan 鎖の厳密で効率的な計算 (2) · · · · · · · · · · · · · · · · · 10

Shinichi Tajima (Niigata Univ.⋆)
Katsuyoshi Ohara (Kanazawa Univ.)
Akira Terui (Univ. of Tsukuba)

Efficient symbolic computation of Jordan chains and generalized eigenspaces(2)

概 要 An efficient method for computing Jordan chains of a matrix of integers or rational numbers by exact

computation is proposed. A Jordan–Krylov basis, special generators in the sense of Krylov subspace, of acertain subspace over rational numbers is introduced. Efficient computation of both a Jordan–Krylov basis
and Jordan chains is given.
3 松 下 光 虹 ( 阪 大 情 報)
Koji Matsushita (Osaka Univ.)

整凸多面体のトーリック環の因子類群のねじれ自由性 · · · · · · · · · · · · · · · 13

Torsionfreeness for divisor class groups of toric rings of integral polytopes

概 要 In this talk, we give some sufficient conditions for Cl(k[P ]) to be torsionfree, where Cl(k[P ]) denotes

the divisor class group of the toric ring k[P ] of an integral polytope P . We prove that Cl(k[P ]) is torsionfree
if P is compressed, and Cl(k[P ]) is torsionfree if P is a (0, 1)-polytope which has at most dim P + 2 facets.
Moreover, we characterize the toric rings of (0, 1)-polytopes in the case Cl(k[P ]) ∼
= Z.
4 宮 下

空 (阪 大 情 報) [ Levelness versus nearly Gorensteinness of homogeneous domains · · · · · 13

Sora Miyashita (Osaka Univ.)

Levelness versus nearly Gorensteinness of homogeneous domains

概 要 Levelness and nearly Gorensteinness are well-studied properties on graded rings as a generalized

notion of Gorensteinness. In this presentation, we talk about the strength of these properties. Under some
additional conditions, we proved that every nearly Gorenstein domain is level. We also talk about nearly
Gorenstein Stanley–Reisner rings of low-dimensional simplicial complexes.
5 宮 崎 充 弘 ( 京 都 教 育 大)
Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)

Almost Gorenstein property of the Ehrhart ring of the stable set polytope of a cycle graph and Hibi–Tsuchiya’s conjecture · · · · · · · · · · · · · · · 13
Almost Gorenstein property of the Ehrhart ring of the stable set polytope of a cycle graph and Hibi–Tsuchiya’s conjecture

概 要 Let G = (V, E) be a cycle graph. We show that the Ehrhart ring of the stable set polytope of G isalmost Gorenstein. Further, we show that the conjecture of Hibi–Tsuchiya is true.

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11

代数学

6 柴 田 孝 祐 ( 米 子 工 高 専)
柳 川 浩 二 (関西大システム理工)
Kohsuke Shibata(Yonago Nat. Coll. of Tech.)
Kohji Yanagawa (Kansai Univ.)

Minimal free resolutions of Specht ideals for (n − d, d) · · · · · · · · · · · · · · 13
Minimal free resolutions of Specht ideals for (n − d, d)Sp

概 要 For a partition λ of a positive integer n, let Iλbe the ideal of R = K[x1 , . . . , xn ] generated by all

Specht polynomials of shape λ. It is known that if R/IλSp is Cohen–Macaulay then λ is of the form either(n − d, 1, . . . , 1), (n − d, d), or (d, d, 1), and it is also known that the converse is true if char(K) = 0.
Sp
In this talk, we construct minimal free resolutions of R/I(n−d,d), when char(K) = 0 by using Specht modules

and operations on Young diagrams.
7 吉 田 健 一 ( 日 大 文 理)
奥 間 智 弘 ( 山 形 大 理)
渡 辺 敬 一 ( 日 大 文 理)

Ken-ichi Yoshida (Nihon Univ.)
Tomohiro Okuma (Yamagata Univ.)
Kei-ichi Watanabe (Nihon Univ.)

Gorensteinness for normal tangent cones of elliptic ideals · · · · · · · · · · · · 13

Gorensteinness for normal tangent cones of elliptic ideals

概 要 Throughout this talk, let (A,m) be a 2-dimensional excellent normal local domain containing an

algebraically closed field, and let I be an m-primary integrally closed ideal. An ideal I is called an elliptic
ideal if the normal reduction number 2. In this talk, we discuss the Gorensteinness for normal tangent
cones. In particular, we give a criterion for Gorensteinness in the case of elliptic ideals.
8 遠 藤 直 樹 ( 明 大 政 治 経 済)
後 藤 四 郎 ( 明 大 理 工)
Naoki Endo
Shiro Goto

(Meiji Univ.)(Meiji Univ.)

Reflexive modules over the endomorphism algebras of reflexive trace
ideals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Reflexive modules over the endomorphism algebras of reflexive trace
ideals概 要 In this talk, we investigate the behavior of reflexive modules over the endomorphism algebras ofreflexive trace ideals in one-dimensional Cohen–Macaulay local rings. The main result generalizes both of
the results of S. Goto, N. Matsuoka, and T. T. Phuong and T. Kobayashi regarding the Gorensteinnessof the endomorphism algebra of the maximal ideal. We also explore the question of when the base ringhas only finitely many isomorphism classes of indecomposable reflexive modules. We will show that thefiniteness of the isomorphism classes implies the ring is analytically unramified and has only finitely many
Ulrich ideals.
9 神 代 真 也 ( 小 山 工 高 専)
Shinya Kumashiro(Oyama Nat. Coll. of Tech.)

正準加群のトレースの colength の上限 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Upper bound on the colength of the trace of the canonical module

概 要 We study upper bounds of the colength of the trace of the canonical module in one-dimensional

Cohen–Macaulay rings. We answer two questions posed by Herzog–Hibi–Stamate and Kobayashi.
14:15〜16:45
10 百 合 草 寿 哉 (東 北 大 理)

Toshiya Yurikusa (Tohoku Univ.)

Acyclic cluster algebras with dense g-vector fans · · · · · · · · · · · · · · · · · · · 10
Acyclic cluster algebras with dense g-vector fans

概 要 The g-vector fans play an important role in studying cluster algebras and silting theory. We showthat a connected acyclic cluster algebra has a dense g-vector fan if and only if it is either finite type oraffine type. As an application, we also show that a finite dimensional, connected, hereditary algebra overan algebraically closed field has a dense g-vector fan if and only if it is Morita equivalent to the path algebraof a quiver of Dynkin or extended Dynkin type.

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代数学

11 後 藤 悠 一 朗 (阪Yuichiro Goto

大理)

(Osaka Univ.)

12

擬遺伝構造の連結性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Connectedness of quasi-hereditary structures概 要 Dlab and Ringel showed that algebras being quasi-hereditary in all orders for indices of primitive

idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra
is again quasi-hereditary. As a matter of fact, we consider permutations of indices, and if the algebra withpermuted indices is quasi-hereditary, then we say that this permutation gives a quasi-hereditary structure.
In this talk, we consider those which we call connectedness of quasi-hereditary structures. For two permutations s, s′ giving quasi-hereditary structures, the definition of connectedness for s, s′ is provided that there
exists a decomposition s′ s−1 = sl · · · s2 s1 into adjacent transpositions such that each product sk · · · s2 s1 s for
0 < k < l also gives a quasi-hereditary structure. We then show that any two quasi-hereditary structures
are connected.
12 臼 井智 ( 東 京 理 大 理)

Satoshi Usui (Tokyo Univ. of Sci.)

特異圏における終局周期加群の特徴づけとその応用 · · · · · · · · · · · · · · · · · 13

Characterization of eventually periodic modules in the singularity categories, and its application

概 要 The singularity category of a ring makes only the modules of finite projective dimension vanish among

all modules. Hence, the singularity category is expected to capture some homological properties of modules
of infinite projective dimension. In this talk, we focus on eventually periodic modules among those of
infinite projective dimension and characterize them by using morphisms in the singularity categories. As anapplication, we show that, for the class of finite dimensional algebras over a field, being eventually periodic
is invariant under singular equivalence of Morita type with level.
13 浅 芝 秀 人(静岡大理・京大高等研・阪公大数学研)
E. G. Escolar (神戸大人間発達環境)
中 島
健(岡山大AI・数理データサイエンスセンター)
吉 脇 理 雄 ( 阪 公 大 数 学 研)
Hideto Asashiba(Shizuoka Univ./Kyoto Univ./Osaka Metro. Univ.)
Emerson Gaw Escolar (Kobe Univ.)
Ken Nakashima (Okayama Univ.)
Michio Yoshiwaki (Osaka Metro. Univ.)

Approximation by interval-decomposables and interval resolutions of 2D
persistence modules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Approximation by interval-decomposables and interval resolutions of 2D
persistence modules

概 要 In the field of topological data analysis, two-parameter persistence can be studied using the represen-tation theory of the 2d commutative grid, the tensor product of two An -type quivers. In a previous work, we
studied interval approximations using restrictions to subquivers of intervals and Möbius inversion, related tothe idea of the generalized rank invariant. In this work, we consider the homological approximations using
the interval representations, and show that the interval global dimension is finite for the 2d commutativegrid, and that it is equal to the maximum of the interval dimensions of the Auslander–Reiten translatesof the interval representations. Furthermore, by a suitable modification of our interval approximation, we
provide a formula linking the two conceptions of approximation.
14 大 関 一 秀 (山 口 大 創 成)Kazuho Ozeki (Yamaguchi Univ.)

The first Hilbert coefficient of stretched ideals · · · · · · · · · · · · · · · · · · · · · 13
The first Hilbert coefficient of stretched ideals

概 要 In this talk we explore the almost Cohen–Macaulayness of the associated graded ring of stretchedm-primary ideals with small first Hilbert coefficient in a Cohen–Macaulay local ring (A, m). In particular,
we explore the structure of stretched m-primary ideals satisfying the equality e1 (I) = e0 (I) − `A (A/I) + 4
where e0 (I) and e1 (I) denotes the multiplicity and the first Hilbert coefficient respectively.

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代数学

15 足 立 崇 英 (山口大国際総合)
榎 本 悠 久 ( 阪 公 大 理)
塚 本 真 由 ( 山 口 大 創 成)

Takahide Adachi (Yamaguchi Univ.)
Haruhisa Enomoto(Osaka Metro. Univ.)
Mayu Tsukamoto (Yamaguchi Univ.)

Generalization of HRS-tilt · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Generalization of HRS-tilt

概 要 Beilinson, Bernstein and Deligne introduced the notion of t-structures on triangulated categories. As aremarkable property of t-structures, various abelian categories inside triangulated categories can be realized
as hearts of t-structures. Happel, Reiten and Smalø provided a construction of new t-structures throughtorsion pairs in the heart of a given t-structure. This construction is called the HRS-tilt. In this talk,
we introduce t-structures on an extriangulated category, which is a common generalization of triangulated
categories and exact categories, and give a generalization of the HRS-tilt.
16 松 野 仁 樹 (静 岡 大 自 然)

Masaki Matsuno (Shizuoka Univ.)

3 次元 Sklyanin 代数の twisted algebra の分類 · · · · · · · · · · · · · · · · · · · · · · 13
The classification of twisted algebras of 3-dimensional Sklyanin algebras

概 要 A twisting system is one of the major tools to study graded algebras, however, it is often difficult toconstruct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In thistalk, we show that a twisted algebra of a geometric algebra is determined by a certain automorphism of its
point scheme. As an application, we explain the classification of twisted algebras of 3-dimensional Sklyanin
algebras up to graded algebra isomorphism.
17 Haigang Hu (静岡大創造科学技術)
毛 利
出 ( 静 岡 大 理)
Haigang Hu
Izuru Mori

(Shizuoka Univ.)(Shizuoka Univ.)

Quantum quadratic complete intersections · · · · · · · · · · · · · · · · · · · · · · · · 13
Quantum quadratic complete intersections

概 要 The purpose of this research is to define and classify noncommutative analogues of quadratic complete

intersections. We say that S/(f1 , ..., fr ) is a quantum (resp. Clifford) quadratic complete intersection if S
is an n-dimensional Calabi–Yau (resp. Clifford) quantum polynomial algebra, and f1 , ..., fr ∈ S2 a regularsequence of central elements. The main result in this talk is that there is a natural one-to-one correspondence
between the set of isomorphism classes of (commutative) quadratic complete intersections and the set of
isomorphism classes of Clifford quadratic complete intersections. We also give a complete classification ofquantum quadratic complete intersections for n = 3 and r = 1, 2, 3.
18 塚 本 真 由 (山 口 大 創 成)
足 立 崇 英 (山口大国際総合)

Mayu Tsukamoto (Yamaguchi Univ.)
Takahide Adachi (Yamaguchi Univ.)

Extriangulated 圏の余ねじれ対と準傾部分圏 · · · · · · · · · · · · · · · · · · · · · · · 13
Cotorsion pairs and silting subcategories in extriangulated categories

概 要 The notion of co-t-structures on a triangulated category was introduced as an analog of t-structures.

While the heart of a t-structure becomes an abelian category, the coheart of a co-t-structure becomes a
so-called presiltiing subcategory. Bondarko and Mendoza–Santiago–Saenz–Souto gave a bijection between
bounded co-t-structures and silting subcategories in a triangulated category. In this talk, we generalize theirresult. Namely, we provide a bijection between bounded hereditary cotorsion pairs and silting subcategories
in an extriangulated category. Moreover, we show that our result recovers a bijection between contravariantly
finite resolving subcategories and basic tilting modules for a finite dimensional algebra with finite global
dimension.

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代数学

17:00〜18:00
A. Chan特別講演( 名 大 多 元 数 理)

Algebras associated to surface dissections and their tilting theory(Nagoya Univ.)

Algebras associated to surface dissections and their tilting theory

Aaron Chan

14

概 要 We are interested in two particular classes of finite-dimensional algebras. One is called Brauer graphalgebra and the other is called gentle algebra. The former class has its origin traced back to the dawnof modular representation theory of finite groups, whereas the latter grew out of the studies of quiver
representations for quivers of Dynkin type A and of affine Dynkin type A. Recent advances in homologicalmirror symmetry and cluster algebras arising from Teichmuller theory reveals a new approach to studying
the homological algebra of gentle algebras. Namely, each gentle algebra can be associated to a dissectionof some topological surface with vertices (marked points) on the boundary, and by doing so, one caninterpret the representation theory and homological behaviour of a gentle algebra in terms of the topology
or geometry of the associated dissected surface. In this talk, we will survey this connection as well as how
such a connection can be exploited in the same way for Brauer graph algebras. We will also survey results on
how this algebra-vs-topology connection gives us classification of objects (such as silting/tilting complexes
and t-structures) that are used to study equivalences between the derived categories for these algebras.

9 月 14 日（水）第 IV 会場

9:30〜12:00
19 C. Reyes-Bustos(NTT 基礎数学研究センタ)
Cid Reyes-Bustos(NTT Inst. for Funda. Math.)

Spectra and Ihara zeta function of group-subgroup pair graphs · · · · · · 10
Spectra and Ihara zeta function of group-subgroup pair graphs

概 要 Group-subgroup pair graphs (or pair-graphs) are a non-regular generalization of Cayley graphs forgroup-subgroup pairs that maintain the properties of Cayley graphs to a certain extent. In particular, when
the subgroup is abelian, the eigenvalues are expressed in terms of sums of irreducible characters of thesubgroup. We present a new proof for the formulas of the spectrum and new formulas for the Laplacianand signless Laplacian spectra of pair-graphs, along with formulas for the Ihara zeta function in terms of thesubgroup characters. In addition, we consider examples and applications for several families of non-regulargraphs described by pair-graphs and compare with their regular analogs.
20 𠮷 野 聖 人 (東 北 大 情 報)

Kiyoto Yoshino (Tohoku Univ.)

共通角度 arccos(1/3) の等角直線族 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Equiangular lines with common angle arccos(1/3)

概 要 I discuss sets of equiangular lines with common angle arccos(1/3), or equivalently, Seidel matrices

with largest eigenvalue at most 3 by using switching roots. The switching roots were introduced to give
integral lattices corresponding to sets of equiangular lines. When the common angle of a set of equiangularlines is arccos(1/3), the corresponding lattice is a root lattice. From this correspondence, the maximal setsof equiangular lines with common angle arccos(1/3) were classified. As an application, I explain why the
numbers of sets of n equiangular lines with common angle arccos(1/3) in dimension 7 are almost symmetricalaround n = 14.

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15

代数学

21 L. Speyer(沖縄科学技術大)

Liron Speyer(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Schurian-infinite blocks of type A Hecke algebras · · · · · · · · · · · · · · · · · · · 13
Schurian-infinite blocks of type A Hecke algebras

概 要 For any algebra A over an algebraically closed field F, we say that an A-module M is Schurian if

EndA (M ) ∼= F. We say that A is Schurian-finite if there are only finitely many isomorphism classes of
Schurian A-modules, and Schurian-infinite otherwise. I will present recent joint work with Susumu Ariki

in which we determined that many blocks of type A Hecke algebras are Schurian-infinite. A wide variety
of techniques were employed in this project—I will give more details on those required for our results
concerning the principal blocks.
22 小 境 雄 太 (東 京 理 大 理)

Yuta Kozakai (Tokyo Univ. of Sci.)

巡回ブロックを被覆するブロック上の傾複体について · · · · · · · · · · · · · · · 10

On tilting complexes over blocks covering cyclic blocks

概 要 Let p be a prime number, k an algebraically closed field of characteristic p, G a finite group, and N anormal subgroup of G having a p-power index in G. Moreover let b be a block of kN with a cyclic defectgroup and B be the unique block of kG covering b. We show that the block B is a tilting-discrete algebra.
Moreover we show that the set of all tilting complexes over B is isomorphic to that over b as partiallyordered sets.
23 藤 田 直 樹 (熊 本 大 先 端)

Naoki Fujita (Kumamoto Univ.)

既約表現の essential 基底と Newton–Okounkov 凸体 · · · · · · · · · · · · · · · · · 13

Essential bases of irreducible representations and Newton–Okounkov
bodies概 要 An essential basis is a basis of a finite-dimensional irreducible representation of a semisimple Liealgebra, which was introduced by Fang–Fourier–Littelmann as a generalization of an FFLV basis. In
this talk, we slightly generalize the notion of an essential basis, and discuss an explicit description of its
parametrizing set. To give such description, the notion of a Newton–Okounkov body is useful. In this talk,
we focus on a specific (generalized) essential basis, and see that the corresponding Newton–Okounkov body
is a marked chain-order polytope. This result connects previous realizations of Gelfand–Tsetlin polytopes
and FFLV polytopes as Newton–Okounkov bodies in a uniform way.
24 柴 田 大 樹 (岡 山 理 大 理)
若 尾 亮 太 ( 岡 山 理 大 理)

Taiki Shibata (Okayama Univ. of Sci.)
Ryota Wakao (Okayama Univ. of Sci.)

低次元 pointed ホップ・スーパー代数の分類について · · · · · · · · · · · · · · · 10

On classification of pointed Hopf superalgebras of low dimension

概 要 In this talk, we will discuss structure on Hopf superalgebras of low dimension. Using known results

on classification of Hopf algebras and the “bosonization technique”, we obtain the following two results.
Let p be an odd prime. (1) There are no non-trivial Hopf superalgebras of dimension p. (2) There exists
only one isomorphism class of pointed Hopf superalgebras of dimension p2 .
25 栗 原 大 武 (山 口 大 創 成)
東 谷 章 弘 ( 阪 大 情 報)

Hirotake Kurihara (Yamaguchi Univ.)
Akihiro Higashitani (Osaka Univ.)

有限一般化アレキサンダーカンドルの新しい不変量とその応用 · · · · · · · · 13

New invariants for finite generalized Alexander quandles and their application

概 要 Quandle is an algebraic system with one binary operation, but it is quite different from a group.

In our talk, we investigate a special kind of quandles, called generalized Alexander quandles, which aredefined by groups together with their group automorphisms. We give new quandle invariants for generalizedAlexander quandles. Moreover, we give an equivalent condition of the quandle isomorphic property among
special generalized Alexander quandles.

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代数学

26 清 水 健 一(芝浦工大システム理工)
Kenichi Shimizu(Shibaura Inst. of Tech.)16

双対テンソル圏の中山関手の公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

A formula of the Nakayama functor of the dual tensor category

概 要 The Nakayama functor for a finite abelian category plays an important role in recent study of finite

tensor categories and their modules. Given a finite tensor category C and a finite left C-module category,∗the dual of C with respect to M, denote by CM, is defined as the category of linear right exact left C-module∗
endofunctors on M. In this talk, an explicit formula of the Nakayama functor of CM
will be given.

27 鍋 島 克 輔 (東 京 理 大 理)潟
大⋆)田 島 慎 一 (新Katsusuke Nabeshima(Tokyo Univ. of Sci.)
Shinichi Tajima (Niigata Univ.⋆)

ゼロ次元イデアルのネター作用素について · · · · · · · · · · · · · · · · · · · · · · · · · 13

On Noetherian operators of zero-dimensional ideals

概 要 We consider the relations between a zero-dimensional ideal and its Noetherian operators. Upon uti-

lizing the theory of holonomic D-modules, we present a new method for computing Noetherian operators
associated to a zero-dimensional ideal. An effective algorithm that consists mainly of linear algebra techniques is proposed for computing them. Moreover, as applications, new computation methods of polynomial
ideals are discussed by utilizing the Noetherian operators.
13:00〜14:00

特別講演
元 良 直 輝 (東 大 I P M U )Feigin–Semikhatov 双対性について

Naoki Genra (Univ. of Tokyo)

Feigin–Semikhatov duality

概 要 W-algebras are a family of vertex (super)algebras defined by the quantized Drinfeld–Sokolov reductionsof affine Lie (super)algebras. They include the Virasoro algebra, Super Virasoro algebra, N=2 superconformal algebras and so on, important algebras related to (super)symmetries in (super) conformal field
theory. We talk about Feigin–Semikhatov duality, which is dualities between subregular W-algebras andprincipal W-superalgebras, super analogs of Feigin–Frenkel duality and generalizations of Kazama–Suzuki
cosets correspondences. The Feigin–Semikhatov duality gives rise to correspondences of fusion rules of dual
W-(super)algebras in rational cases, and the induced coset functors imply equivalences between blocks ofthe module categories in general levels. This is joint work with Thomas Creutzig, Shigenori Nakatsuka and
Ryo Sato.

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代数学

9 月 15 日（木）第 IV 会場

9:30〜11:30
28 岩 見 智 宏 (九 工 大 工) [ Strong approximation property related to three-dimensional Miyaoka–
Yau type inequality with the associated third Chern classes · · · · · · · · · 13

Tomohiro Iwami (Kyushu Inst. of Tech.)

Strong approximation property related to three-dimensional Miyaoka–
Yau type inequality with the associated third Chern classes

概 要 For an three-dimesnional extremal neighborhood (X, C) ⊂ C4 of type A, S. Mori proved the existenceof three-dimesional flip via “2-game” for 0-dimensional supports of general members of | − KX |([M88]).
Based on [M88], for an extended (X, Cs ) with Cs not necessary irreducible nor reduced ([I2019Mar]),the author had found three-dimesional Miyaoka–Yau type inequality (M Y )3,c3 with the associated c3([I2018Mar, I2019Sep]), (M Y )3,c3 with the differential operators ([I2020Sep]) and so on, moreover introduce
an interemdiate Jacobians ([I2022Mar et al]). Continueing to [I2022Mar], as its Part II, the author willreport: 1) to introduce valuations of “continuous” diffrential operators related to (M Y )3,c3 , 2) to construct“quaterion algebra” data along the above 1) as adele, and 3) to discuss strong apporoximation for 2) inorder to determine (exponential) periods of (M Y )3,c3 .
29 大 橋亮 (横浜国大環境情報)

Ryo Ohashi (Yokohama Nat. Univ.)

Fast enumeration of superspecial hyperelliptic curves of genus 4 with
automorphism group V4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Fast enumeration of superspecial hyperelliptic curves of genus 4 with
automorphism group V4

概 要 In arithmetic and algebraic geometry, superspecial curves have been studied as one of the mostimportant objects, with practical applications to cryptography and coding theory. The enumeration of
those curves is a central problem, but if g ≥ 4 it is not even known whether a superspecial curve of genus
g exists in general characteristic p > 0. In this paper, we propose an algorithm with complexity Õ(p3 )to enumerate superspecial hyperelliptic curves of genus 4 with automorphism group V4 . By executing thealgorithm over Magma, we enumerate those curves over Fp for p up to 200. We also succeeded in finding a
superspecial hyperelliptic curve of genus 4 in every characteristic p with 19 ≤ p < 7000.
30 那 須 弘 和 (東 海 大 理)
Hirokazu Nasu

(Tokai Univ.)

3 次元多様体上の曲線の第 1 変形障害について · · · · · · · · · · · · · · · · · · · · · 13
On the primary obstructions to deforming curves on a threefold

概 要 In Theorem 3.3 of Internat. J. Math. 28(13) (2017) 1750099, I gave a sufficient condition for a firstorder deformation of a curve on a projective threefold to be primarily obstructed. However the statementof the theorem is false as it stands. In this talk, I will make a correction to the theorem and will give its
reformulation.
31 那 須 弘 和 (東 海 大 理)
Hirokazu Nasu

(Tokai Univ.)

Obstructions to deforming space curves lying on a smooth cubic surface· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Obstructions to deforming space curves lying on a smooth cubic surface

概 要 In 1980s, J. O. Kleppe gave a conjecture concerning maximal families of space curves lying on asmooth cubic surface. Later, the conjecture was modified by Ph. Ellia by a counterexample. I will talkabout a recent progress on the conjecture. I will also give a sufficient condition for curves lying on a smoothcubic surface to be obstructed in P3 in terms of lines on the surface.

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代数学

32 東 谷 章 弘 (阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)

18

グラスマン多様体の matching field による 2 つのトーリック退化の組合
せ的変異同値性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Combinatorial mutation equivalence of two toric degenerations of Grassmannians arising from matching fields

概 要 Matching fields are used for the construction of toric degenerations of Grassmannians. Whenever amatching field gives rise to a toric degeneration, the associated polytope of the toric variety coincides withthe matching field polytope. In this talk, we study combinatorial mutation equivalences of two certain
matching field polytopes, which correspond to order polytopes and chain polytopes of Grassmannian posets.
33 川 口良 ( 奈 良 県 立 医 大)

Ryo Kawaguchi (Nara Medical Univ.)

偏極トーリック多様体の第 i 断面幾何種数の下限 · · · · · · · · · · · · · · · · · · · 13

A lower bound for the ith sectional geometric genus of polarized toricvarieties

概 要 The sectional genus is one of the fundamental invariants in the study of polarized varieties, and isextended to the notion of ith sectional geometric genus. The ith sectional geometric genus has an upperbound proved by Y. Fukuma, and a conjectured lower bound which has not yet been completely proven.
This lower bound, however, is trivial in the case of polarized toric varieties. In this talk, we provide a newlower bound for the ith sectional geometric genus of polarized toric varieties resulting from the theory of
Ehrhart h-vector of polytopes.
34 吉 川翔 ( 理 化 学 研)

Shou Yoshikawa(RIKEN)

Quasi-F -splitting · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Quasi-F -splitting

概 要 Yobuko recently introduced the notion of quasi-F -splitting and F -split heights, which generalize andquantify the notion of Frobenius-splitting, and proved that F -split heights coincide with Artin–Mazur
heights for Calabi–Yau varieties. In this talk, I will introduce a generalization of Fedder’s criterion for
F -splitting and the theory of F -splittings in the context of birational geometry. The talk is based on joint
work with Tatsuro Kawakami, Teppei Takamatsu, Hiromu Tanaka, Jakub Witaszek and Fuetaro Yobuto.
11:30〜12:00

代数学分科会総会

14:15〜17:15
35 永 野 中 行 (金 沢 大 自 然)

Atsuhira Nagano (Kanazawa Univ.)

クンマー曲面族を含むある K3 曲面族について · · · · · · · · · · · · · · · · · · · · · 13

A family of lattice polarized K3 surfaces which contains the family ofKummer surfaces

概 要 The speaker will introduce a family of lattice polarized K3 surfaces which contains the family ofKummer surfaces derived from principally polarized Abelian surfaces. Also, he will introduce a relation
between the period mapping of this family, theta functions and invariants of a complex reflection group.
36 御 子 柴 尚 希 (東京電機大理工)Naoki Mikoshiba (Tokyo Denki Univ.)

Dn 型のアーベル多様体上の Hodge サイクル · · · · · · · · · · · · · · · · · · · · · · · 13
Hodge cycles on abelian varieties of Dn -type

概 要 Let Kn /Q be a Galois CM-filed with Gn = Gal(Kn /Q) ∼= Dn ⟨ρ⟩,where Dn denotes the dihedral groupof degree 2n and ρ the complex conjugation. Let S ⊂ Gn be an arbitrary CM-type,and let AS be the abelianvariety of CM-type such that EndQ (AS ) ∼= Kn and its CM-type is given by S. Let Hg(As ) denote the
Hodge group of AS . It is known that Hg(AS ) is an algebraic torus and dimHg(AS ) ≤ dimAS = 2n. When
dimHg(AS ) = 2n, AS is said to be non-degenerate, and the Hodge ring of AS is known to be generated byits divisor classes. In this talk we classify the CM-type S for which the abelian variety AS is degenerate.

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19

代数学

37 三 浦 真 人 (京 大 数 理 研)
Makoto Miura(Kyoto Univ.)

Calabi–Yau 超曲面の幾何転移 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Geometric transitions for Calabi–Yau hypersurfaces

概 要 Geometric transition is a process of connecting two smooth Calabi–Yau 3-folds by a birational

contraction followed by a complex smoothing. It has attracted the interest of both mathematicians andphysicists, since it may give the right notion to connect moduli spaces of Calabi–Yau 3-folds. For Calabi–Yau
hypersurfaces in toric varieties, a well-known idea of constructing geometric transitions is the use of nested
reflexive polytopes. In this talk, I will report the current situation of this approach.
38 川 谷 康 太 郎 (阪公大理・大和大理工)
Kotaro Kawatani(Osaka Metro. Univ./Yamato Univ.)

線形圏の安定性条件の非存在 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Non-existence of stability conditions on linear triangulated categories

概 要 We discuss the non-existence of Bridgeland stability conditions on an R-linear triangulated category.

39 松 井 紘 樹 (徳島大社会産業理工)

Hiroki Matsui (Tokushima Univ.)

導来圏のスペクトラムと代数多様体の復元問題 · · · · · · · · · · · · · · · · · · · · · 13

Spectra of derived categories and reconstruction of algebraic varieties

概 要 Recently, I have introduced the notion of prime thick subcategories of a given triangulated category T

and of the spectrum Spec(T ) as the set of prime thick subcategories of T together with a certain topology.
In this talk, using the spectrum, we will give an alternative proof of the Bondal–Orlov–Ballard reconstruction
theorem. Also, I will give the similar reconstruction result for quasi-affine varieties.
40 奥 山 真 吾 (香 川 高 専)
Shingo Okuyama(Kagawa Nat. Coll. of Tech.)

偏加法的な環と F1 上の偏群スキーム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Partially additive rings and partial group schemes over F1

概 要 We develop an elementary theory of partially additive rings as a foundation of F1 -geometry. Our

approach is so concrete that an analog of classical algebraic geometry is established straightforwardly. As
applications, (1) we construct a kind of group scheme GLn whose value at a commutative ring R is thegroup of n × n invertible matrices over R and at F1 is the n-th symmetric group, and (2) we construct a
projective space Pn as a kind of scheme and count the number of points of Pn (Fq ) for q = 1 or q = pn apower of a rational prime, then we explain a reason of number 1 in the subscript of F1 even though it has
two elements.
工大)
41 中 島 規 博 (名辻 栄 周 平 ( 北 教 大 旭 川)
Norihiro Nakashima(Nagoya Inst. of Tech.)
Shuhei Tsujie (Hokkaido Univ. of Edu.)

A 型拡張 Shi 配置と A 型拡張 Catalan 配置が遺伝的自由配置であるための条件 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Conditions for the extended Shi arrangements and the extended Catalanarrangements to be hereditarily free

概 要 In this talk, we prove that the cone of the extended Catalan arrangement of type A is always

hereditarily free, while we determine the dimension that the cone of the extended Shi arrangement of type
A is hereditarily free. For this purpose, we define a class of arrangements which contains the extended Shi
and Catalan arrangement of type A and which closed under restriction, using digraphs with vertex weights.

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代数学

42 南

範 彦 (名工大)Norihiko Minami(Nagoya Inst. of Tech.)

20

幾何学的附値に対する 1 型の局所一意化定理 · · · · · · · · · · · · · · · · · · · · · · · 13

A type 1 local uniformization theorem for arbitrary geometric valuations

概 要 A geometric valuation is a special kind of Abhyankar valuation. A rank 1 geometric valuation is also

called a divisorial valuation, which admits for any base field with arbitrary characteristic the so-called type1 local uniformization, realizing its valuation ring as the local ring at its center, thanks to a 1939 classicaltheorem of Zariski. Motivated by my own effort to construct a birational subsheaf for any unramified sheaf
in the sense of Morel, I shall report a generalization of such a type 1 local uniformization theorem forarbitrary geometric valuation.
43 南

範 彦 (名工大)Norihiko Minami(Nagoya Inst. of Tech.)

レトラクト (−i)-有理性への双有理モチーフの 2 つの応用 · · · · · · · · · · · · 13

Two applications of the birational motive to the retract (−i)-rationality

概 要 The birational motives of Kahn–Sujatha and Rost is applied to study the following two types of

implications of the retract (−i)-rationality of a smooth projective variety: (1) in terms of an arbitraryP1 -invariant Nisnevich sheaf with transfer. (2) in terms of the Bloch–Srinivas type decomposition of the
diagonal.
44 島 田 了 輔 (東 大 数 理)

Ryosuke Shimada (Univ. of Tokyo)

On some simple geometric structure of affine Deligne–Lusztig varieties
for GLn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
On some simple geometric structure of affine Deligne–Lusztig varieties
for GLn

概 要 We study the geometric structure of affine Deligne–Lusztig varieties Xλ (b) for GLn and b basic.

Motivated by the work of Görtz–He–Nie and Chan–Ivanov, we consider a new condition on a cocharacter
λ. If this is satisfied, then Xλ (b) is the disjoint union of classical Deligne–Lusztig varieties times finitedimensional affine spaces.
17:30〜18:30
岸 本

特別講演
崇 (埼 玉 大 理) [ Equivariant completions of vector groups into Fano varieties

Takashi Kishimoto (Saitama Univ.)

Equivariant completions of vector groups into Fano varieties

概 要 It is well known that the structure as toric variety on a given projective variety is uniquely determined(if there exists at all), and it can be interpreted by means of complete fans. In contrast with toric varieties,
namely, equivariant completions of algebraic tori, we are instead interested in equivariant completions ofvector groups into projective varieties, especially into Fano varieties. Different from torus embeddings, theequivariant completions of vector groups do not have an explicit interpretation except for projective spaces,
meanwhile certain varieties admit several non-isomorphic structures as equivariant vector group completions.
In the talk, we will devote ourselves mainly to equivariant vector group completions into (forms of) quintic
del Pezzo varieties and an observation of their automorphism groups. This is based on the joint work with
Adrien Dubouloz and Pedro Montero.

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21

代数学

9 月 16 日（金）第 IV 会場

9:30〜12:00
45 中 野伸 ( 学 習 院 大 理)
加藤虎太郎

Shin Nakano (Gakushuin Univ.)
Kotaro Kato

5 次巡回体のイデアル類群について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On ideal class groups of quintic cyclic fields

概 要 We give an infinite family of quintic cyclic fields with class number divisible by any prime less than

10000.
46 木 村 藍 貴 (東 北 大 理)
Aiki Kimura(Tohoku Univ.)

多重ゼータ値の導分関係式から生成される双対関係式の全体について · · 13

The duality relations derived from the derivation relations for multiple
zeta values

概 要 The duality relations are a basic family of relations for multiple zeta values. The extended double

shuffle relations (EDSR) are one of the families expected to generate all linear relations among multiple
zeta values, but it remains unclear whether all the duality relations can be derived from EDSR. In this talk,we consider two families of relations generated by the duality and the derivation relations, and characterize
explicitly the intersection of them. Here the derivation relations are specializations of EDSR.
47 武 田渉 ( 東 京 理 大 理)
大 野 泰 生 ( 東 北 大 理)
中 筋 麻 貴 ( 上 智 大 理 工)

Wataru Takeda (Tokyo Univ. of Sci.)(Tohoku Univ.)
Yasuo Ohno
Maki Nakasuji (Sophia Univ.)

Schur 多重ゼータ値の一般化双対公式の複素補間 · · · · · · · · · · · · · · · · · · · · 13

An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions

概 要 One of the important research subjects in the study of multiple zeta functions is to clarify thelinear relations and functional equations among them. Among many relations, the duality formula and its
generalization are important families for both Euler–Zagier type and Schur type multiple zeta values. In
this talk, following the method of previous works for multiple zeta values of Euler–Zagier type, we givean interpolation of the sums in the generalized duality formula, called Ohno relation, for Schur multiple
zeta values. Moreover, we prove that the Ohno relation for Schur multiple zeta values is valid for complex
numbers.
48 川 﨑 菜 穂 (東 北 大 理)

Naho Kawasaki (Tohoku Univ.)

荒川–金子型と Euler–Zagier 型, 2 つの多重ゼータ関数の関係の明示式 · 10

An explicit formula of the relation between multiple zeta functions of
Arakawa–Kaneko and Euler–Zagier types

概 要 Multiple zeta functions of Arakawa–Kaneko and Euler–Zagier types are known as generalizations of

the Riemann zeta function. In 2018, Kaneko and Tsumura proved the existence of functional equations
between these multiple zeta functions. In this talk, we give the functional equations explicitly.
49 小 野 雅 隆 (早 大 G E C)
山 本 修 司 ( 東 大 数 理)
Masataka Ono (Waseda Univ.)
Shuji Yamamoto (Univ. of Tokyo)

一般の整数点における金子–Zagier 予想 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Kaneko–Zagier conjecture for general integer indices

概 要 Finite multiple zeta values and symmetric multiple zeta values are defined for positive integer indices.

Kaneko and Zagier conjectured that they satisfy the same algebraic relations. In this talk, we generalize
Kaneko–Zagier conjecture for general integer indices and prove that the generalized conjecture is deduced
from the original one.

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代数学

50 小 林 弘 京 (名 大 多 元 数 理)

Hirotaka Kobayashi (Nagoya Univ.)

22

On an entire function derived from higher derivatives of Hardy’s Zfunction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
On an entire function derived from higher derivatives of Hardy’s Zfunction

概 要 In 2012, Matsuoka showed that the zeros of Z (k+1) (t) are interlaced with the zeros of Z (k) (t) for t > Twith sufficiently large T under the Riemann Hypothesis, where Z (k) (t) is the kth derivative of Hardy’s
Z-function associated with the Riemann ζ-function. We introduce a generalisation of Riemann’s ξ-function
derived from higher derivatives of Hardy’s Z-function to try to make the proof of his result simpler. Our
proof is based on the proof of special case k = 1 by H. M. Edwards and J. Mozer.
51 井 上 翔 太 (東 工 大 理)
( Univ. Bonn )Junxian Li
Shota Inoue
Junxian Li(Tokyo Tech)(Univ. Bonn)

臨界線上での L 関数の同時値分布 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Joint value distribution of L-functions on the critical line

概 要 The independence of L-functions is firstly mentioned by Selberg. Later Bombieri and Hejhal estab-lished the independence by showing the joint central limit theorem of L-functions on the critical line. In
this talk, we discuss the large deviations in the central limit theorem of Bombieri and Hejhal. Our results
have some consequences for moments of L-functions. For example, our results lead to a relation between
the moment of the Riemann zeta-function and of the minimum of the Riemann zeta-function and Dirichlet
L-functions. This is a joint work with Junxian Li (Universität Bonn).
52 峰

正 博 ( 上 智 大 理 工)

Masahiro Mine (Sophia Univ.)

Hurwitz ゼータ関数に対するディスクレパンシー評価と Mahler の分類· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Discrepancy estimates for the Hurwitz zeta-functions and Mahler’s classification

概 要 In this talk, we consider the speed of the convergence of the limit theorem for the value-distributionof the Hurwitz zeta-functions. The estimates of the speed are sometimes called the discrepancy estimates.
We prove several discrepancy estimates for the Hurwitz zeta-functions under a certain condition on theparameters, which is based on Mahler’s classification of transcendental numbers.
53 遠 藤 健 太 (名 大 多 元 数 理)
Kenta Endo

(Nagoya Univ.)

Riemann ゼータ関数の対数の反復積分の普遍性定理 · · · · · · · · · · · · · · · · · 13
Universality theorem for the iterated integrals of the logarithm of the
Riemann zeta-function

概 要 In 1975, Voronin proved the universality theorem for the Riemann zeta-function. In this talk, we

generalized this theorem to the iterated integrals of the logarithm of the Riemann zeta-function on someline parallel to the real axis.
14:15〜17:00
54 行 田 康 晃 (東 大 数 理)

Yasuaki Gyoda (Univ. of Tokyo)(x + y)2 + (y + z)2 + (z + x)2 = 12xyz の正整数解と一般化マルコフ団代数· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Positive integer solutions to (x + y)2 + (y + z)2 + (z + x)2 = 12xyz andgeneralized markov cluster algebra

概 要 We give a specific way of describing positive integer solutions of a Diophantine equation (x + y)2 +(y + z)2 + (z + x)2 = 12xyz and introduce a generalized cluster pattern behind it.

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23

代数学

55 飯 高茂 (学 習 院 大⋆)布中)齋 藤 之 理 (麻Shigeru Iitaka (Gakushuin Univ.⋆)
Yukimasa Saito(Azabu Junior High School)

完全数の一般化について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Generalization of perfect numbers

概 要 By P we denote an odd prime, which plays Base of perfect numbers. For a = P e , P = P − 1 satisfies

P σ(a) = P e+1 − 1 = aP − 1. Let m denote translation parameter, and let h(̸= P ) (another odd prime)
denote multiplier.
32

P σ(α) + (P − h)P 2 ϕ(α) = P P α(2P − h) − mP − h(P − 2)P is established.
The number α which satisfies the above equality is said to be σφ perfect number, which is a kind ofGeneralization of perfect numbers.
56 井 川 祥 彰
デビカバネルジー(Indraprastha Inst. of Information Tech. Delhi)
南 出
真 ( 山 口 大 理)
谷 川 好 男Tadaaki Igawa
Debika Banerjee(Indraprastha Inst. of Information Tech. Delhi)
Makoto Minamide (Yamaguchi Univ.)
Yoshio Tanigawa

モジュラー群の合同部分群の指数の平均について · · · · · · · · · · · · · · · · · · · 10

On averages of indexes of congruence subgroups in the modular group

概 要 We shall consider averages of indexes of congruence subgroups in the modular group, and deduce someresults on error terms of them.
57 田 島 凌 太 (九 大 J G M I)
Ryota Tajima (Kyushu Univ.)

Shadow が虚数乗法を持つモックモジュラー形式の p 進的な性質について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A p-adic property of mock modular forms whose shadows have complex
multiplication

概 要 Let f be a mock modular form and g denote the shadow of f . Then there exists a unique p-adic numberα(f ) and we can obtain a p-adic modular form from f and α(f ). When g has complex multipulication by
K and p is split in K, it is known that α(f ) is not zero. On the other hand, we don’t know much aboutα(f ) for an inert prime p. The speaker proved that α(f ) is not zero when p is inert in K under certain
conditions. In this talk, I will explain the result.
58 境

優 一
(久留米工大基幹教育センター)
永 友 清 和D. Zagier(Max Plank Inst. for Math.)

Modular linear differential equations and generalized Rankin–Cohenbrackets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Yuichi Sakai (Kurume Inst. of Tech.)
Kiyokazu Nagatomo
Don Zagier (Max Plank Inst. for Math.)

Modular linear differential equations and generalized Rankin–Cohenbrackets

概 要 We show that all modular linear differential operators can be described in terms of Rankin–Cohenbrackets and a modified Rankin–Cohen bracket found by Kaneko and Koike. We give more uniform
descriptions of MLDEs in terms of an extension of Rankin–Cohen brackets.

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代数学

24

Folding 型の連分数展開によって生成される級数の無理測度 · · · · · · · · · · 1359 D. Duverney (Baggio Eng. School)
黒 沢
健 ( 東 京 理 大 理)
大⋆)塩 川 宇 賢 (慶Daniel Duverney (Baggio Eng. School)
Takeshi Kurosawa (Tokyo Univ. of Sci.)
Iekata Shiokawa (Keio Univ.⋆)

Irrationality exponents of certain series generated by continued fraction
with folding lemma

概 要 Let xn be a certain fast converging sequence of rational numbers greater than one. We give theirrationality exponents of reciprocal sums of xn using a continued-fraction expansion with the folding
lemma.
単項式指数をもつ空隙級数の線形独立性について · · · · · · · · · · · · · · · · · · · 1060 村 上 慎 太 郎 (弘 前 大 理 工)
立 谷 洋 平 ( 弘 前 大 理 工)

Shintaro Murakami (Hirosaki Univ.)
Yohei Tachiya (Hirosaki Univ.)

Linear independence of certain gap series with monomial exponents

概 要 Let (i, j) ∈ N × N≥2 and Si,j be an infinite subset of positive integers including all prime numbers insome arithmetic progression. In this talk, we show the linear independence over Q of the numbers
1,

X ai,j (n)
,
binj
n∈S

(i, j) ∈ N × N≥2 ,i,jwhere b ≥ 2 is an integer and ai,j (n) are bounded nonzero integer-valued functions on Si,j . Our theorem
generalizes a result of V. Kumar.
61 齋 藤 耕 太 (筑波大数理物質)
武 田渉 ( 東 京 理 大 理)
Kota Saito (Univ. of Tsukuba)
Wataru Takeda (Tokyo Univ. of Sci.)

素数表現定数の集合の位相的性質と代数的独立性 · · · · · · · · · · · · · · · · · · · 12

Topological properties and algebraic independence of sets of primerepresenting constants

概 要 Let (ck )∞k=1 be a sequence of positive integers. We investigate the set of A > 1 such that the integer

part of Ac1 ···ck is always a prime number for every positive integer k. Let W(ck ) be this set. The firstgoal of this talk is to determine the topological structure of W(ck ). Under some conditions on (ck )∞k=1 , wereveal that W(ck ) ∩ [0, a] is homeomorphic to the Cantor middle third set for some a. The second goal is to
propose an algebraically independent subset of W(ck ) if ck is rapidly increasing. As a corollary, we disclosethat the minimum of W(k) is transcendental.
62 井 手 春 希 (慶 大 理 工)
田 中 孝 明 ( 慶 大 理 工)
(Keio Univ.)
Haruki Ide(
Taka-aki Tanaka Keio Univ.)

Algebraic independence properties of certain entire functions with many
variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Algebraic independence properties of certain entire functions with many
variables

概 要 Some entire functions of one variable are known to have the property that the values of their derivativesof any order at any nonzero distinct algebraic numbers are algebraically independent. On the other hand,
there are very few results on the algebraic independence of the values of the partial derivatives of a given
entire function of several variables at distinct algebraic points. In this talk we construct an entire function
with arbitrary number of variables having the following property: The infinite set consisting of all the valuesof all its partial derivatives of any orders at all algebraic points is algebraically independent.

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25

代数学

63 井 手 春 希 (慶 大 理 工)
(Keio Univ.)

Haruki Ide

Algebraic independence results for certain families of analytic functions
generated by linear recurrences · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Algebraic independence results for certain families of analytic functions
generated by linear recurrences

概 要 For certain families of entire functions of one variable defined by power series and infinite products,

we show the algebraic independence of the values of their derivatives at distinct algebraic numbers. Thisis obtained as a corollary to the algebraic independence result on the values of the partial derivatives of acertain family of entire functions of two variables.
64 隈 部哲 (九 大 J G M I )Satoshi Kumabe (Kyushu Univ.)

Appell の超幾何関数の Supercongruence · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Supercongruences for fourth Appell function

概 要 In this talk, we give a congruence relation, called supercongruence, for a hypergeometric function of

two variables. There are some congruence relations between a truncation of a hypergeometric series and ap-adic unit modulo a power of a prime number p. If we give an additional assumption, some of them holdmodulo higher power of p. Then such congruences are called supercongruence. The purpose of this talk is
to give a supercongruence relation for Appell’s function F4 .
17:15〜18:15
川 島

特別講演
誠 ( 日 大 生 産 工)

Makoto Kawashima (Nihon Univ.)

ジーゲルの G 関数の数論的性質について

On arithmetic properties of the Siegel G-functions

概 要 The Grothendieck period conjecture predicts that all the algebraic relations among the periods of asmooth algebraic variety over a number field are only due to its geometric structure. Following the definition
by C. L. Siegel, the G-function is a certain class of power series with algebraic coefficients, satisfying a linear
differential equation, whose typical example is the polylogarithmic function. It is conjectured by Bombieriand Dwork that the ring of the values of G-functions at algebraic points exactly coincides with the ring of
periods of the varieties above. Their observation thus suggests us to study the values of the G-functions atalgebraic points together with the transcendence or the irrationality, to approach the period conjecture.
Relying on this background, we are motivated to construct Pade approximation of the values of G-functions,which is one of efficient tools to investigate such an arithmetic property. It is worth mentioning that R.
Apery succeeded in proving the irrationality of ζ(3) by Pade approximation, however, for a given number,
it is in general crucial and very difficult whether we can construct Pade approximation of the number in an
explicit way.
In this talk, we focus on the generalized hypergeometric G-functions and our explicit construction of Padeapproximation. We give a survey of our recent progress on arithmetic properties of the values of thefunctions, including the linear independence criteria, which have been unknown.

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幾何学

幾 何
9 月 13 日（火）26

学第 VI 会場

9:30〜11:45
1 大 野
優 (北
小 林 真 平 (北大大理) [ 多次元正規分布の甘利–Chenstov の α 接続の特徴づけ · · · · · · · · · · · · · · · 15
理)

(Hokkaido Univ.)
Yu OhnoShimpei Kobayashi (Hokkaido Univ.)

A characterization of the alpha-connections on the statistical manifoldof multivariate normal distributions

概 要 In this talk, we show that the statistical manifold of multivariate normal distribution admits solvable

Lie group structure. In addition, we give a characterization of Amari–Chenstov α-connections of it.
2 藤 井

忍 (千歳科学技術大理工)

Shinobu Fujii(Chitose Inst. of Sci. and Tech.)

対称 Clifford 系に付随する部分空間配置 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Subspace arrangements associated with symmetric Clifford systems

概 要 A symmetric Clifford system is a finite set of real symmetric matrices satisfying some relations. In

this talk, we define subspace arrangements associated with symmetric Clifford systems which are named
Clifford arrangements. Moreover, we show several properties of Clifford arrangements.
3 森 本 真 弘 ( 阪 公 大 数 学 研)
Masahiro Morimoto(Osaka Metro. Univ.)

Hermann 作用から誘導される path 群作用の軌道の幾何学 · · · · · · · · · · · 15
Geometry of orbits of path group actions induced by Hermann actions

概 要 It is known that an isometric action of a Lie group on a compact symmetric space gives rise to aproper Fredholm action of a path group on a path space via the gauge transformations. In this talk, I
will introduce my recent results concerning the principal curvatures and the austere property of orbits ofpath group actions induced by Hermann actions. Here a submanifold is called austere if the set of principal
curvatures in the direction of each normal vector is invariant under the multiplication by minus one. The
results greatly extend the author’s previous result in the case of the standard sphere and show that there
exist a larger number of infinite dimensional austere submanifolds in Hilbert spaces.
4 馬 場 蔵 人 ( 東 京 理 大 理 工)
井 川
治 (京都工繊大基盤)

Kurando Baba (Tokyo Univ. of Sci.)
Osamu Ikawa (Kyoto Inst. Tech.)

コンパクト対称三対の標準形と二重佐武図形 · · · · · · · · · · · · · · · · · · · · · · · 15

Double Satake diagrams and canonical forms in compact symmetric
triads with applications to Hermann actions

概 要 We show that there exists a representative with good properties in the isomorphism class of a compact

symmetric triad. We call such a representative a canonical form of the compact symmetric triads. In orderto study the geometry of Hermann actions, it is sufficient to consider ones obtained from canonical forms.
We also show that canonical forms give sections of Hermann actions.
5 杉 本 恭 司 ( 東 京 理 大 理 工)

Kyoji Sugimoto (Tokyo Univ. of Sci.)

Para-real forms of para-Hermitian symmetric spaces and real forms ofpseudo-Hermitian symmetric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Para-real forms of para-Hermitian symmetric spaces and real forms ofpseudo-Hermitian symmetric spaces

概 要 We show that each of the pseudo-Riemannian symmetric R-space associated with a non-degenerate

Jordan triple system and a real form of an effective simple irreducible pseudo-Hermitian symmetric spacecan be realized as a para-real form of an effective semisimple para-Hermitian symmetric space of hyperbolic
orbit type.

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27

幾何学

6 大 野 走 馬 ( 早 大 理 工)
Soma Ohno(Waseda Univ.)

Nearly parallel G2 多様体上のキリングスピノールの無限小変形 · · · · · · 15
Infinitesimal deformations of Killing spinors on nearly parallel G2 manifolds

概 要 Manifolds admitting Killing spinors are Einstein manifolds. Thus, a deformation of a Killing spinor

entails a deformation of Einstein metrics. In this time, we study infinitesimal deformations of Killingspinors on nearly parallel G2 manifolds. Furthermore, since there is a one-to-one correspondence between
nearly parallel G2 structures and Killing spinors on 7-dimensional spin manifolds, our results imply that
we investigate an infinitesimal deformation of nearly parallel G2 structures. Applying the same technique,we identify that the space of the Rarita–Schwinger fields coincides with a subspace of the eigenspace of the
Laplacian.
7 坂 根 由 昌 (阪 大 情 報⋆)
Yusuke Sakane (Osaka Univ.⋆)

SU(N ) 上の naturally reductive でないアインシュタイン計量について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On non-naturally reductive Einstein metrics on SU(N )概 要 We discuss non-naturally reductive Einstein metrics on special unitary group SU (k1 + (p − 1)k) via

the generalized flag manifold SU (k1 + (p − 1)k)/S(U (k1 ) × U (k) × · · · × U (k)). We show that, if k1 > k|{z}
and p ≥ 3, there exist at least two such Einstein metrics.

p−1

14:15〜16:15
8 軸 丸 芳 揮 (九 大 I M I )Yoshiki Jikumaru (Kyushu Univ.)

建築曲面設計における吊り下げ曲面について · · · · · · · · · · · · · · · · · · · · · · · 15

Geometry of hanging membranes in architectural surface design

概 要 A hanging chain (catenary) is a naturally generated curve by its weight, and a reversed hanging chain

resists gravity with pure compression stress states. In the architectural field, an analogy for the surface caseis known as hanging membranes, however, no effective formulation applicable to the membrane structure is
known. In this presentation, we introduce a mathematical formulation of the hanging membranes compatible
with the mechanics of the membrane structure, variational characterization, shape generation by appropriate
discretization, and structural analysis of hanging membranes in the architectural surface design. This study
is based on the joint work with Prof. Yohei Yokosuka (Kagoshima University).
9 金 田伸 (広島大先進理工)

Shin Kaneda (Hiroshima Univ.)

向き付け不可能な極大曲面とその特異点について · · · · · · · · · · · · · · · · · · · 15

Nonorientable maximal surfaces and their singular points

概 要 We construct new nonorientable maximal surfaces and study their singular points.

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幾何学

10 秋 山 梨 佳 (都 立 大 理)
酒 井 高 司 ( 都 立 大 理)
佐藤雄一郎
(工学院大学習支援センター・都立大理)

Rika Akiyama (Tokyo Metro. Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Yuichiro Sato
(Kogakuin Univ./Tokyo Metro. Univ.)

28

Riemann 空間形内の Chern–Federer 部分多様体 · · · · · · · · · · · · · · · · · · · · 15

Chern–Federer submanifolds in Riemannian space forms

概 要 By using an idea of integral geometry, we define integral invariants of the second fundamental formof a map between Riemannian manifolds and construct an S 1 -family of energy functionals including thebienergy functional. In this talk, we introduce the Chern–Federer energy functional, whose Euler–Lagrange
equation is a second-order partial differential equation. For an isometric immersion into a Riemannian space
form, we give a necessary and sufficient condition to be a Chern–Federer map. Considering this condition,
there is an obstruction for the domain manifold. In addition, we show some examples of Chern–Federer
submanifolds in Riemannian space forms, where a Chern–Federer submanifold is the image of an isometricimmersion which is a Chern–Federer map.
11 清 原 悠 貴 (北小 林 真 平 (北

大

理)

大

理)

Hirotaka Kiyohara (Hokkaido Univ.)
Shimpei Kobayashi (Hokkaido Univ.)

3 次元 Heisenberg 群の時間的曲面の極小性の特徴付け · · · · · · · · · · · · · · · 15
Characterization of minimality of timelike minimal surfaces in the threedimensional Heisenberg group

概 要 It is known that the minimality of non-vertical surfaces in the three-dimensional Heisenberg groupwith the left-invariant Riemannian metric is characterized by the non-conformal harmonic maps into thehyperbolic plane, and then the minimality can be denoted by the integrable systems. We show that
non-vertical timelike minimal surfaces in the three-dimensional Heisenberg group with the left-invariant
Lorentzian metric are characterized by the non-conformal Lorentz harmonic maps into the de Sitter twosphere.
12 赤 嶺 新 太 郎 (日 大 生 物 資 源)
藤 野 弘 基 ( 名 大 高 等 研)

Shintaro Akamine (Nihon Univ.)
Hiroki Fujino (Nagoya Univ.)

Krust の定理の拡張と極小曲面の変形について · · · · · · · · · · · · · · · · · · · · · 15
Extension of Krust theorem and deformations of minimal surfaces

概 要 In the minimal surface theory, the Krust theorem asserts that if a minimal surface in the Euclidean

3-space is the graph of a function over a convex domain, then each surface of its associated family is also agraph. The same is true for maximal surfaces in the Minkowski 3-space. In this talk, we prove a Krust-type
theorem for a deformation family including various important deformation of minimal and maximal surfaces
such as the associated family and the Lopez–Ros deformation and the Calabi-type correspondence. We also
prove another Krust-type theorem which does not assume the convexity assumption. The results are proved
based on the recent progress of planar harmonic mapping theory.

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29

幾何学

13 Pham Hoang Ha(Hanoi National Univ.)
川 上
裕 ( 金 沢 大 理 工)
渡 邉 元 嗣 ( 高 岡 支 援 学 校)
Pham Hoang Ha(Hanoi National Univ.)
Yu Kawakami (Kanazawa Univ.)
Mototsugu Watanabe(Takaoka special support school)

有限全曲率完備極小曲面のガウス写像の完全分岐値数について · · · · · · · · 15

On the total weight of a number of totally ramified values of the Gaussmap of a complete minimal surface with finite total curvature

概 要 We give a new example of algebraic minimal surface whose Gauss map has two omitted values and one

totally ramified value of order 2. Thus, the total weight of a number of totally ramified value of its Gauss
map equals 2.5. Moreover, we study a more precise estimate for the total weight of a number of totally
ramified value of the Gauss map of an algebraic minimal surface which has genus 0 in Euclidean 4-space.
16:30〜17:30

特別講演
國 分 雅 敏 ( 東 京 電 機 大 工)

Flat fronts in hyperbolic three-space and related topics

Masatoshi Kokubu (Tokyo Denki Univ.)

Flat fronts in hyperbolic three-space and related topics

概 要 Recent works about flat fronts and related topics will be introduced after a brief overview. It is

known that a complete flat surface immersed in hyperbolic 3-space H 3 is either a horosphere or a hyperbolic
circular cylinder. However, if the condition is weakened so that surfaces are not necessarily immersed, thenthere are many ‘complete flat surfaces’, properly speaking, weakly complete flat fronts. The word ‘front’comes from a wavefront which means a mapping which have a Legendrian lift to the projective cotangent
bundle of the target space. In early 2000s, M. Umehara, K. Yamada and I started to study flat fronts.
After that, W. Rossman and K. Saji joined and our research was advanced. There are still some interesting
problems that I am working on.

9 月 14 日（水）10:10〜10:25

第 VI 会場

2022 年度日本数学会幾何学賞授賞式

10:30〜11:30

2022 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
入 江
博 (茨 城 大 理) 3 次元対称凸体の Mahler 予想の解決
柴 田 将 敬 ( 名 城 大 理 工)
Hiroshi Iriyeh (Ibaraki Univ.)
Masataka Shibata (Meijo Univ.)

A solution of Mahler’s conjecture of three dimensional symmetric convex
bodies概 要 We have proved Mahler’s conjecture concerning the volume product of three dimensional centrally

symmetric convex bodies in R3 . In this talk, we give an outline of its proof and also provide its applications
and recent developments.
13:15〜14:15
桑 垣

2022 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
大理) [ 層量子化の幾何と代数解析
樹 (京Tatsuki Kuwagaki (Kyoto Univ.)

Geometry and algebraic analysis of sheaf quantization

概 要 Sheaf quantization is a way of quantizing Lagrangian submanifolds. The concept is quite rich anduseful to study symplectic geometry, algebraic analysis, and etc. In this talk, I will give an introduction to
the concept.

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幾何学

9 月 15 日（木）30

第 VI 会場

9:30〜11:45
14 五 明納 谷

工 ( 名 大 多 元 数 理)
信 ( 名 大 多 元 数 理)

Takumi Gomyou (Nagoya Univ.)
Shin Nayatani (Nagoya Univ.)

有限グラフの第 1 固有値の最大化と Nadirashvili 型定理 · · · · · · · · · · · · · 15

Maximization of the first eigenvalue of a finite graph and Nadirashvilitype theorem

概 要 Given an edge-length parameter on a finite graph, we construct a vertex-weight and an edge-weightfrom it and define the corresponding graph Laplacian. We consider a maximization of the first nonzero
eigenvalue of the graph Laplacian over all edge-length parameters subject to a normalization. We obtaina Nadirashvili-type theorem which describes the maximizing edge-length parameter in terms of the first
eigenfunctions of the corresponding Laplacian.
15 永 野 哲 也 (長 崎 県 立 大)

Tetsuya Nagano (Univ. of Nagasaki)

フィンスラー空間の非可逆測地線の乖離を測る量 · · · · · · · · · · · · · · · · · · · 15

The study to quantify of the estrangement for non-reversible geodesics
in Finsler space

概 要 The purpose of this article is to quantify the estrangement of non-reversible geodesics in Finsler

space.In the paper [2], it is shown that the images of non-reversible geodesics which go to opposite direction
are different from each other.Then the estrangement degree for the purpose of quantifying of the extent ofbranching for non-reversible geodesics are defined in this time.Finally, a proposition that if some conditions
are satisfied, then the indicatrix on the tangent space of the point is closed is shown for the estrangement
degree as the application.
16 辻

寛 (阪

Hiroshi Tsuji

大理)(Osaka Univ.)

Blaschke–Santaló 不等式と inverse Santaló 不等式への熱によるアプロー
チ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Blaschke–Santaló inequality and inverse Santaló inequality via heat semigroup

概 要 We will discuss the Blaschke–Santaló inequality and inverse Santaló inequality which are well known

in convex geometry. A key ingredient in our talk is the smoothing property of Ornstein–Uhlenbeck
semigroup, namely Gaussian hypercontractivity. Our first result is to make a new connection between the
Blaschke–Santaló inequality and the reverse hypercontractivity. In particular, we give a new proof of theBlaschke–Santaló inequality via an improvement of the reverse hypercontractivity. Our second result is to
give the forward hypercontractivity with a special exponent, which is naturally motivated from our first
result. As a corollary, it enables us to obtain some stability type estimate of the inverse Santaló inequality.
This talk is based on a joint work with Neal Bez (Saitama University) and Shohei Nakamura (Osaka
University).
17 浅 香猛 ( 東 大 数 理)
狩 野 隼 輔 (東北大RACMaS)
石 橋
典 ( 東 北 大 理)
Takeru Asaka (Univ. of Tokyo)
Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Tohoku Univ.)

Earthquake theorem for cluster algebras of finite type · · · · · · · · · · · · · · 15

Earthquake theorem for cluster algebras of finite type

概 要 Eathquake maps give important flows on the Teichmuller spaces. We calculate earthquake maps interms of shear coordinates, which are examples of cluster X-variables in the cluster algebra. In this talk,We define an analogue of earthquake maps for any cluster algebras of finite type and prove a similar result
to the Thurston’s earthquake theorem.

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31

幾何学

18 狩 野 隼 輔 (東北大RACMaS)浅 香
猛 ( 東 大 数 理)
石 橋
典 ( 東 北 大 理)

Shunsuke Kano (Tohoku Univ.)
Takeru Asaka (Univ. of Tokyo)
Tsukasa Ishibashi (Tohoku Univ.)

Asymptotic behavior of earthquake maps for cluster algebras of finite
type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic behavior of earthquake maps for cluster algebras of finite
type

概 要 We defined an “earthquake map” for a cluster manifold of finite type as an analogue of the Thurston’searthquake map for a closed surface. Moreover, we proved an analogue of the Thurston’s earthquake theorem
for a cluster manifold of finite type, namely, we gave a homeomorphism between the tropicalized cluster
manifold and the cluster manifold via the earthquake map. In this talk, we observe how the Fock–Goncharov
fan, which lies in the tropicalized cluster manifold, behaves under the earthquake map. In particular, we
discuss its asymptotic behavior in a certain sense.
19 バラルリホラモン(立命館大総合科学技術研究機構)
野 沢
啓 ( 立 命 館 大 理 工)
J. A. Álvarez López(サンチアゴ・デ・コンポステラ大)( ビ ー ゴ 大)
C. MeniñoRamón Barral Lijó (Ritsumeikan Univ.)
Hiraku Nozawa (Ritsumeikan Univ.)
Jesús Antonio Álvarez López(Univ. of Santiago de Compostela)
Carlos Meniño (Univ. de Vigo)

Leaves of chaotic, compact foliated spaces · · · · · · · · · · · · · · · · · · · · · · · · · 15

Leaves of chaotic, compact foliated spaces

概 要 The main topic of this talk will be the relation between chaotic dynamics in foliated spaces and thegeometry of the leaves. A compact foliated space is chaotic if it has a dense leaf and the set of compact
leaves is dense. We will study the metric, differentiable and topological realization of manifolds as dense
leaves without holonomy in compact, chaotic foliated spaces.
20 児 玉 悠 弥 (都 立 大 理)

Yuya Kodama (Tokyo Metro. Univ.)

Lodha–Moore 群の一般化について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A generalization of the Lodha–Moore group

概 要 In this talk, I state the new group obtained by generalizing the Lodha–Moore group. The Lodha–

Moore group is known as a nonamenable finitely presented group similar to the Thompson group F . Since
the Lodha–Moore group is defined by using infinite binary words, it can be generalized into “n-ary”. After
I give a short definition of the Lodha–Moore group, I will state the definition of the generalized one and theresults for “expected” properties.
14:15〜16:15
21 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

距離関数の空間の稠密部分集合について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On dense subsets in spaces of metrics

概 要 In spaces of metrics, we investigate topological distributions of the doubling property, the uniform dis-connectedness, and the uniform perfectness, which are the quasi-symmetrically invariant properties appearing
in the David–Semmes theorem. We show that the set of all doubling metrics and the set of all uniformly
disconnected metrics are dense in spaces of metrics on finite-dimensional and zero-dimensional compact
metrizable spaces, respectively. Conversely, this denseness of the sets implies the finite-dimensionality, zerodimensionality, and the compactness of metrizable spaces. We also determine the topological distributionof the set of all uniformly perfect metrics in the space of metrics on the Cantor set.

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幾何学

22 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)32

グロモフ・ハウスドルフ距離の分岐測地線 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Branching geodesics of the Gromov–Hausdorff distance概 要 We first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected

spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces
equipped with the Gromov–Hausdorff distance. We then construct branching geodesics of the Gromov–
Hausdorff distance continuously parameterized by the Hilbert cube, passing through or avoiding sets of all
spaces satisfying some of the three properties shown above, and passing through the sets of all infinitedimensional spaces and the set of all Cantor metric spaces. From our results, we observe that the sets
explained above are geodesic spaces and infinite-dimensional.
23 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

フラクタル次元とヒルベルト立方体のグロモフ・ハウスドルフ空間への位相的埋め込み · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Fractal dimensions and topological embeddings of the Hilbert cube into
the Gromov–Hausdorff space

概 要 We show that for all four non-negative real numbers, there exists a Cantor ultrametric space whose

Hausdorff dimension, packing dimension, upper box dimension, and Assouad dimension are equal to given
four numbers, respectively. By constructing topological embeddings of the Hilbert cube into the Gromov–
Hausdorff space, we prove that the set of all compact metric spaces possessing prescribed topologicaldimension, Hausdorff dimension, packing dimension, upper box dimension, and Assouad dimension, andthe set of all compact ultrametric spaces are path-connected and have infinite topological dimension. Thisobservation on ultrametrics provides another proof of Qiu’s theorem stating that the ratio of the Archimedean
and non-Archimedean Gromov–Hausdorff distances is unbounded.
24 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Boju–Funar type theorems via m-Bakry–Émery Ricci curvature withm ⩽ 1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Boju–Funar type theorems via m-Bakry–Émery Ricci curvature withm⩽1

概 要 We establish some Boju–Funar type compactness criteria for complete Riemannian manifolds byassuming that the m-Bakry–Émery Ricci curvature with m ⩽ 1 tends slowly to zero as the distance from afixed point goes to infinity. Our results largely improve previous Boju–Funar type compactness criteria forcomplete Riemannian manifolds via m-Bakry–Émery Ricci curvature established by the author. The key
ingredient is a modification of the second variation formula in terms of the m-Bakry–Émery Ricci curvature
with m ⩽ 1.
25 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Bonnet–Myers type theorems via m-Bakry–Émery Ricci curvature with
ε-range · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bonnet–Myers type theorems via m-Bakry–Émery Ricci curvature with
ε-range概 要 Inspired by recent works by Y. Lu, E. Minguzzi, and S. Ohta and by K. Kuwae and Y. Sakurai, we givevarious compactness criteria for complete Riemannian manifolds via m-Bakry–Émery Ricci curvature with
ε-range. Our results generalize a Bonnet–Myers type theorem by Y. Lu, E. Minguzzi, and S. Ohta as well as
an Ambrose type theorem by K. Kuwae and Y. Sakurai via m-Bakry–Émery Ricci curvature with ε-range.
The key ingredients in proving our results are Riccati inequalities obtained from Bochner–Weitzenböck
formulas via m-Bakry–Émery Ricci curvature with ε-range.

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33

幾何学

26 深 谷 友 宏 (都 立 大 理)

Tomohiro Fukaya (Tokyo Metro. Univ.)

Busemann 空間の位相的分解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A topological product decomposition of Busemann space

概 要 We show that a Busemann space X which is covered by parallel bi-infinite geodesics is homeomorphic

to a product of another Busemann space Y and the real line. We also show that a semi-simple isometry on
X preserving the foliation by parallel geodesics canonically induces a semi-simple isometry on Y .
16:30〜17:30

特別講演
近 藤 剛 史 ( 鹿 児 島 大 理)

CAT(0) 空間に対する Coxeter 群の非線形スペクトルギャップ

Takefumi Kondo (Kagoshima Univ.)

Nonlinear spectral gaps of Coxeter groups with respect to CAT(0) spaces

概 要 Nonlinear spectral gap is an invariant defined for a pair of a finite graph and a metric space andplays important roles in geometric group theory and metric geometry. Pansu calculated the exact values ofnonlinear spectral gaps of cycles and generalized triangles with respect to CAT(0) spaces by applying the
Wirtinger inequalities for finite cyclic groups proved by Gromov. However, no example of exact calculation
was known other than Pansu’s results.
In this talk, we discuss variants of the Wirtinger inequalities for finite irreducible Coxeter groups and its
application to calculations of nonlinear spectral gaps of Coxeter groups. This contains a nonlinear analogueof computations of spectral gaps of Coxeter groups by Kassabov and Ivrissimtzis–Peyerimhoff.
This is a joint work with Tetsu Toyoda and Takato Uehara.

9 月 16 日（金）第 VI 会場

9:30〜12:00
27 南

範 彦 (名工大)Norihiko Minami(Nagoya Inst. of Tech.)

単線織性と有理連結性を補完する階層構造のコホモロジー的特徴付け · · 15

Cohomological characterization of the hierarchical structures interpolating the uniruledness and the rationally connectedness

概 要 For a complex projective manifold, Bouchsom–Demailly–Paun–Peternell (J. Algebraic Geom. 2013)

characterized its uniruledness by the non peudoeffectiveness of its canonical divisor. Furthermore, Campana–
Demailly–Peternell (London Math. Soc. Lecture Note ser., 417, 2015) gave a cohomological characterizationof rationally-connectedness. In this talk, I shall report these characterizations can be interpolated to givesome cohomological characterization of the hierarchical structures interpolating the uniruledness and therationally connectedness.
[
28 土 井護
四 ッ 谷 直 仁 ( 香 川 大 教 育)
Mamoru Doi
Naoto Yotsutani (Kagawa Univ.)

自明な標準束をもつ単純正規交叉複素曲面の微分幾何学的大域スムージ
ングの応用について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On applications of differential geometric global smoothings of simple
normal crossing complex surfaces with trivial canonical bundle

概 要 Let X be a simple normal crossing compact complex surface with trivial canonical bundle which

includes at most triple intersections. In our recent article [DY22], we have proved that if X is d-semistable,
then there exists a family of smoothings in a differential geometric sense. As an important application, weshall provide several examples of d-semistable simple normal crossing complex surfaces with trivial canonicalbundle including triple points, which are smoothable to K3 surfaces.

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幾何学

29 四 ッ 谷 直 仁 (香 川 大 教 育)

Naoto Yotsutani (Kagawa Univ.)

34

Diffeomorphism classes of the doubling Calabi–Yau threefolds · · · · · · · 15
Diffeomorphism classes of the doubling Calabi–Yau threefolds

概 要 In our previous work (New York J. Math. 20 (2014) 1–33), we have constructed Calabi–Yau 3-folds

by a differential-geometric gluing method using Fano 3-folds with their smooth anticanonical K3 divisors,which are called the doubling Calabi–Yau 3-folds. In this talk, we show that any two of the doubling
Calabi–Yau 3-folds with Picard number 2 are not diffeomorphic to each other when the underling Fano
3-folds are distinct.
大理)
30 松 坂 公 暉 (北秦 泉 寺 雅 夫 ( 岡 山 大 自 然)

Koki Matsuzaka (Hokkaido Univ.)
Masao Jinzenji (Okayama Univ.)

Period integrals and intersection numbers of moduli space of quasimaps
in the case of Calabi–Yau hypersurface in CP N −1 · · · · · · · · · · · · · · · · · · 15
Period integrals and intersection numbers of moduli space of quasimaps
in the case of Calabi–Yau hypersurface in CP N −1

概 要 In mirror symmetry, period integrals are used in the computation of genus 0 Gromov–Witten invariants.

Jinzenji introduced moduli space of quasimaps instead of moduli space of stable maps, and intersection
numbers of it. In the case of Calabi–Yau Hypersurface in CP N −1 , Jinzenji also showed that there are
gp0,2 (N, d) andsome relations between intersection numbers w(Oha Ohb )0,d of moduli space of quasimaps M
corresponding Gromov–Witten invariants ⟨Oha Ohb ⟩0,d . In this talk, we derived the expressions of period
gp0,2 (N, d).
integrals and Givental’s I function as generating function of intersection numbers of M
31 渡 邊 祐 太 (東 大 数 理)

Yuta Watanabe (Univ. of Tokyo)

特異エルミート計量を伴う正則ベクトル束に対する Bogomolov–Sommese
型消滅定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Bogomolov–Sommese type vanishing theorem for holomorphic vector
bundles equipped with positive singular Hermitian metrics

概 要 We introduce the Bogomolov–Sommese type vanishing theorem involving multiplier ideal sheaves for

big line bundles. We define a dual Nakano semi-positivity of singular Hermitian metrics with L2 -estimatesand obtain the vanishing theorem which is a generalization of the Bogomolov–Sommese type vanishingtheorem to holomorphic vector bundles.
32 川 村 昌 也 (香 川 高 専)
Masaya Kawamura(Kagawa Nat. Coll. of Tech.)

疑負曲率を持つコンパクト概エルミート多様体と概エルミート曲率流 · · 15

Compact almost Hermitian manifolds with quasi-negative curvature andthe almost Hermitian curvature flow

概 要 In this talk, we introduce a result that the non-positivity of the first Chern–Ricci curvature can bepreserved along the almost Hermitian curvature flow, if the initial almost Hermitian metric has the Griffiths
non-positive Chern curvature. We have shown that as an application, if additionally the first Chern–Ricci
curvature of the initial metric is negative at some point, then the almost complex structure of a compact
non-quasi-Kähler almost Hermitian manifold equipped with such a metric cannot be integrable.

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35

幾何学

33 田 内 大 渡 (九 大 I M I)
米 田
剛 ( 一 橋 大 経 済)
L. A. Lichtenfelz (Wake Forest Univ.)
Taito Tauchi (Kyushu Univ.)
Tsuyoshi Yoneda (Hitotsubashi Univ.)
Leandro A. Lichtenfelz(Wake Forest Univ.)

Existence of a conjugate point in the incompressible Euler flow on athree-dimensional ellipsoid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence of a conjugate point in the incompressible Euler flow on athree-dimensional ellipsoid

概 要 The existence of a conjugate point on the volume-preserving diffeomorphism group of a compact

Riemannian manifold M is related to the Lagrangian stability of a solution of the incompressible Euler
equation on M . The Misiolek curvature is a reasonable criterion for the existence of a conjugate point on thevolume-preserving diffeomorphism group corresponding to a stationary solution of the incompressible Euler
equation. In this talk, we introduce a class of stationary solutions on an arbitrary Riemannian manifold
whose behavior is nice with respect to the Misiolek curvature and give a positivity result of the Misiolek
curvature for solutions belonging to this class. Moreover, we also show the existence of a conjugate point in
the three-dimensional ellipsoid case as its corollary.
34 浅 野 知 紘 (金 沢 大 理 工)池祐 一 ( 東 大 情 報 理 工)

Tomohiro Asano (Kanazawa Univ.)(Univ. of Tokyo)
Yuichi Ike

層の導来インターリービング距離の完備性と C 0 シンプレクティック幾何· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Completeness of derived interleaving distances for sheaves and C 0 symplectic geometry

概 要 We show the completeness of a derived category of sheaves with respect to the interleaving distance andconstruct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik–Schnirelmanntheory in the microlocal theory of sheaves. With these new tools, we prove an Arnold-type theorem for theimage of the zero-section under a Hamiltonian homeomorphism.
14:15〜16:30
35 佐 古 彰 史 (東 京 理 大 理)

Akifumi Sako (Tokyo Univ. of Sci.)

量子化全体の圏を用いた逆問題へのアプローチ · · · · · · · · · · · · · · · · · · · · · 15

Category of quantizations and its application to inverse problem

概 要 We introduce a category composed of all quantizations of all Poisson algebras. By the category, we

can treat in a unified way the various quantizations for all Poisson algebras and develop a new classicallimit formulation. This formulation proposes a new method for the inverse problem, that is, the problemof finding the classical limit from a quantized space. Equivalence of quantizations is defined by using thiscategory, and the conditions under which the two quantizations are equivalent are investigated. Two typesof classical limits are defined as the limits in the context of category theory, and they are determined bygiving a sequence of objects. Using these classical limits, we discuss the inverse problem of determining theclassical limit from some noncommutative Lie algebra. We present a method to obtain this classical limit
from the principle of least action by using matrix regularization.
36 鹿 俣 尚 志 (東 京 理 大 理)
佐 古 彰 史 ( 東 京 理 大 理)
Naoyuki Kanomata(Tokyo Univ. of Sci.)
Akifumi Sako (Tokyo Univ. of Sci.)

Φ32 有限行列模型における多点相関関数の厳密解 · · · · · · · · · · · · · · · · · · · · 15
Exact solution of the multipoint correlation function in the Φ32 finite
matrix model

概 要 We find the exact solutions of the Φ32 finite matrix model (Grosse–Wulkenhaar model). In the Φ32
B
finite matrix model, multipoint correlation functions are expressed as G|a11 ...a1N |...|aB. It is known
1 ...aN |1

B

B
that any G|a11 ...a1N |...|aB
can be expressed using G|a1 |...|an | type n-point functions. Thus we focus on
1 ...aN |1

B

rigorous calculations of G|a1 |...|an | . The formula for G|a1 |...|an | is obtained, and it is achieved by using thepartition function Z[J] calculated by the Harish-Chandra–Itzykson–Zuber integral.

最終版: 2022/8/8
幾何学

37 池 田 憲 明 (立 命 館 大 理 工)
廣 田 祐 士 ( 麻 布 大 獣 医)

Noriaki Ikeda (Ritsumeikan Univ.)(Azabu Univ.)
Yuji Hirota

36

Homotopy momentum sections on pre-multisymplectic manifold · · · · · · 15
Homotopy momentum sections on pre-multisymplectic manifold

概 要 We introduce a notion of a homotopy momentum section on a Lie algebroid over a pre-multisymplectic

manifold. A homotopy momentum section is a generalization of the momentum map with a Lie group
action and the momentum section on a pre-symplectic manifold, and is also a generalization of thehomotopy momentum map on a multisymplectic manifold.
38 濱 中 翔 太(三菱電機先端技術総合研)
Shota Hamanaka(Mitsubishi Electric Corp. Adv. Tech. R&D Center)

全スカラー曲率に対する C 0 , C 1 極限定理 · · · · · · · · · · · · · · · · · · · · · · · · · 15

C 0 , C 1 limit theorems for total scalar curvatures

概 要 We give some C 0 or C 1 limit theorems for total scalar curvatures. More precisely, we show that thelower bound of the total scalar curvatures on a closed manifold is preserved under the C 0 or C 1 convergenceof the Riemannain metrics under some assumptions. Moreover, we give some counterexamples to the above
theorems on an open manifold.
39 藤 井 知 輝 (東 京 理 大 理)

Tomoki Fujii (Tokyo Univ. of Sci.)

逆平均曲率流のグラフトランスレーティングソリトンと等径関数 · · · · · · 15

Graphical translating solitons for the inverse mean curvature flow andisoparametric functions

概 要 In this talk, we consider a translating soliton for the inverse mean curvature flow given as the graph ofa function over some domain of a Riemannian manifold whose level sets give isoparametric foliation. The
translating soliton is the graph of a function which is a composition of an isoparametric function and asolution of a certain ordinary differential equation. In particular, in case where the Riemannian manifold isthe sphere, we classify the shape of such translating solitons.
40 國 川 慶 太 (宇 都 宮 大 教 育)
櫻 井 陽 平 ( 埼 玉 大 理 工)

Keita Kunikawa (Utsunomiya Univ.)
Yohei Sakurai (Saitama Univ.)

Super Ricci flow に沿った Bamler–Zhang 型熱核評価 · · · · · · · · · · · · · · · · 15
Gaussian heat kernel estimates of Bamler–Zhang type along super Ricciflow

概 要 Bamler–Zhang have developed geometric analysis on Ricci flow with scalar curvature bound. A partof their work can be extended to more general geometric flows. In this talk, we show Gaussian heat kernel
estimates of Bamler–Zhang type along super Ricci flow with non-negative differential quantity.
41 近 藤Kei Kondo

慶 ( 岡 山 大 理)

(Okayama Univ.)

リプシッツ関数に関するレーブの球面定理 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Reeb’s sphere theorem for Lipschitz functions

概 要 We show the Reeb sphere theorem for Lipschitz functions, i.e., if a closed Riemannian manifold

admits a Lipschitz function with exactly two singular points in the sense of Clarke, then the manifold ishomeomorphic to the sphere.

最終版: 2022/8/8

37

函数論

函

数

9 月 13 日（火）論第 VIII 会場

9:30〜12:00
1 植 木 誠 一 郎 ( 横 浜 国 大 工)

Sei-Ichiro Ueki (Yokohama Nat. Univ.)

解析的 Besov 型 Bergman–Orlicz 空間の等距離写像 · · · · · · · · · · · · · · · · · 15

Isometries of analytic Besov-type Bergman–Orlicz spaces

概 要 We consider isometries of the analytic Besov-type Bergman–Orlicz space on the open unit disk. We

describe the form of linear isometries of this space. Furthermore, we give the characterization for a subjective
multiplicative isometry.
2 米 田 力 生 (金沢大人間社会)

Rikio Yoneda (Kanazawa Univ.)

調和なシンボルを持つベルグマン空間上の可逆なテープリッツ作用素 · · 15

Invertibility of Toeplitz operators on the Bergman spaces with harmonic
symbols

概 要 We give the sufficient conditions ensuring the invertibility of Toeplitz operators on the Bergman spaces

with harmonic symbols.
3 深 作 亮 也 ( 九 大 数 理)潟大⋆)田 島 慎 一 (新Ryoya Fukasaku (Kyushu Univ.)
Shinichi Tajima (Niigata Univ.⋆)

効率的な一変数留数計算アルゴリズム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Efficient algorithms for computing univariate residues

概 要 We introduce a new algorithm for computing univariate residues, which is based on the theories of

local cohomology classes and differential operators. In addition, we compare the algorithm with existingalgorithms.
4 綾 野 孝 則 ( 阪 公 大 数 学 研)

Takanori Ayano (Osaka Metro. Univ.)

テレスコピック曲線のシグマ関数のべき級数展開の Hurwitz 整性 · · · · · 15

Hurwitz integrality of the power series expansion of the sigma function
for the telescopic curves

概 要 The elliptic sigma function, which is defined and studied by Weierstrass, is generalized to themultivariable sigma functions associated with the higher genus curves. The coefficients of the power series
expansion of the sigma function around the origin are included in the ring generated by the coefficients ofthe defining equations of an algebraic curve over the rationals. From this algebraic property, when a curvedegenerates to a singular curve, the sigma function has a limit. Y. Onishi proved more precise property,
i.e., the Hurwitz integrality of the power series expansion of the sigma function for the (n, s) curves. In thistalk, we will generalize this result to the telescopic curves, which contain the (n, s) curves as special cases.
5 M. S. Alam (Univ. of Barishal)
須 川 敏 幸 ( 東 北 大 情 報)

Md Shafiul Alam (Univ. of Barishal)
Toshiyuki Sugawa (Tohoku Univ.)

一般化モジュラー方程式の解の幾何的導出について · · · · · · · · · · · · · · · · · 15

On geometric deduction of the solutions to generalized modular equations

概 要 Ramanujan presented without proof many remarkable formulae for the solutions to generalized modular

equations. Much later, proofs of the formulae were provided by making use of highly nontrivial identities
for theta series and hypergeometric functions. We offer a geometric approach to the proof of those formulae.
We emphasize that our proofs are geometric and independent of such identities.

最終版: 2022/8/8
函数論

6 小 森 洋 平 ( 早 大 教 育)
Yohei Komori (Waseda Univ.)

38

Angle parameters for hyperelliptic Riemann surfaces · · · · · · · · · · · · · · · · 10
Angle parameters for hyperelliptic Riemann surfaces

概 要 We show that any hyperelliptic Riemann surface can be parametrized by means of 4g-2 angles between

simple closed geodesics.
7 松 田

凌 (京

Ryo Matsuda

大理)(Kyoto Univ.)

Z 作用を持つ Riemann 面の Techüller 空間の測地線の構成について · · · 15
Geodesics on the Teichmüller space of a Riemann surface with Z action

概 要 Let R be a Riemann surface of infinite analytic type. We give sufficient conditions for extremality of

Beltrami coefficients on R. Next, we apply these results to a discussion of geodesics in Teichmüller spaces.
In particular, we explain a construction of a Beltrami coefficient µ0 in Teich(C \ Z) satisfying the following
conditions: |µ0 |(z) = ∥µ0 ∥ (a.e.z) and there exists a family of geodesics {γλ }λ∈D from [0] to [µ0 ] withcomplex analytic parameter, where D is an open set in l∞ . This means that we cannot exclude condition|µ0 |(z) = ∥µ0 ∥, which is one of the necessary and sufficient conditions for the unique existence of a geodesic
given by Earle–Kra–Krushkaĺ.
8 正 井 秀 俊 ( 東 工 大 理)
グレッグマックシェーン( Inst. Fourier )Hidetoshi Masai (Tokyo Tech)
Greg McShane (Inst. Fourier)

4 点穴あき球面のタイヒミュラー測地線に沿った複素変形 · · · · · · · · · · · · 15

Deformation of complex structures on 4 punctured sphere along a Teichmüller geodesic

概 要 Some pictures and movies of complex structures on the 4 punctured sphere, and the mathematics

behind them will be presented.
9 松 崎 克 彦 ( 早 大 教 育)
Huaying Wei(Jiangsu Normal Univ.)

Katsuhiko Matsuzaki (Waseda Univ.)
Huaying Wei (Jiangsu Normal Univ.)

Chordal Loewner chains and Teichmüller spaces on the half-plane · · · · 15

Chordal Loewner chains and Teichmüller spaces on the half-plane

概 要 We consider a univalent analytic function f on the half-plane satisfying the condition that the supre-

mum norm of its (pre-)Schwarzian derivative vanishes on the boundary. Under certain extra assumptions
on f , we show that there exists a chordal Loewner chain initiated from f until some finite time, and thisLoewner chain defines a quasiconformal extension of f over the boundary such that its complex dilatation
is given explicitly in terms of the (pre-)Schwarzian derivative in some neighborhood of the boundary. Asan application of this quasiconformal extension, we complete the characterization of an element of the
VMO-Teichmüller space on the half-plane using the vanishing Carleson measure condition induced by the(pre-)Schwarzian derivative.
14:15〜15:15
10 堀 口 俊 二
Shunji Horiguchi

Extended Mandelbrot sets of f (z) = (z m + c)n · · · · · · · · · · · · · · · · · · · · · 15
Extended Mandelbrot sets of f (z) = (z m + c)n

概 要 In section 1, we extend the Mandelbrot set M(2,c,1) of f(z)=z*z+c to M(m,c,n) of g(z)=(z**m+c)**n,

and show that the extend Mandelbrot is connected,closed set. Nest we show that the outlines of M(m,c,n)related to M(1,c,mn) are same. In section 2, we give definitions of fractals. In section 3, we give 6 examples
of extended Mandelbrot sets which are fractals.

最終版: 2022/8/8

39

函数論

11 渡 邉 天 鵬 (京大理)Takayuki Watanabe (Kyoto Univ.)

On the stochastic bifurcations regarding random iterations of polynomials of the form z 2 + cn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the stochastic bifurcations regarding random iterations of polynomials of the form z 2 + cn

概 要 In this talk, we consider random iterations of polynomial maps z 2 + cn where cn are complex-valued

independent random variables following the uniform distribution on the closed disk with center c andradius r. The aim of this paper is twofold. First, we investigate the bifurcation of our proposed random
iterations and give quantitative estimates of bifurcation parameters. Second, we apply the estimates to the(dis)connectedness of random Julia sets. In particular, we prove that for the central parameter c = −1,
almost every random Julia set is totally disconnected with much smaller radial parameters r than expected.
12 奥 山 裕 介 (京都工繊大基盤)

Yûsuke Okuyama (Kyoto Inst. Tech.)

Uniform perfectness in non-archimedean dynamics · · · · · · · · · · · · · · · · · 15
Uniform perfectness in non-archimedean dynamics

概 要 The notion of uniform perfectness of subsets in C (or P1 ) plays an important role in complex analysis,complex dynamics, and (complex) potential theory. In this talk, we will introduce a non-archimedeancounterpart to this important notion, and give a few applications of it in non-archimedan dynamics andpotential theory on the Berkovich projective line.
13 奥 山 裕 介 (京都工繊大基盤)

Yûsuke Okuyama (Kyoto Inst. Tech.)

Reduction, quantization, and degeneration in non-archimedean and complex dynamics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Reduction, quantization, and degeneration in non-archimedean and complex dynamics

概 要 For a family of (complex) rational functions on P1 of degree d > 1 holomorphically parametrized byD∗ and meromorphically parametrized by D, when this family degenerates at the puncture t = 0 for D∗ , thefamily of the equilibrium measures of each rational functions converges weakly as t → 0. In this talk, wewill complement a key computation in the proof of the above DeMarco–Faber’s degenerating limit theorem,
which is in terms of reduction and quantization of non-archimedean dynamics on the Berkovich projectiveline.

最終版: 2022/8/8
函数論

特別講演
藤 解 和 也 ( 金 沢 大 理 工)

値分布論からの Stothers–Mason の定理再訪

Kazuya Tohge (Kanazawa Univ.)

Revisiting the Stothers–Mason theorem with Nevanlinna40

15:30〜16:30

概 要 By the Stothers–Mason theorem we mean the abc inequality for complex polynomials stating: three

relatively prime and non-constant polynomials a, b and c satisfy the relation a + b = c only if each of theirdegree is at most the number of distinct roots of the product abc minus one. It is well known that this estimate
is sharp with many examples and applies to polynomial or rational solutions of Fermat-type equations as for
Davemport’s theorem, naturally. One can bring Picard’s Little Theorem over to the observation of a + b = c
so that some of the known generalizations of the Stothers–Mason theorem are stated in Nevanlinna’s value
distribution theory of meromorphic functions on the complex plane. Then it is obvious that Wronskian
plays an essential role in order to count the number of distinct roots of the abc. In this talk, we change
this way of counting and see that another type of abc inequalities is available with another operation thandifferentiation. In other words, we introduce a new radical based on a judgment of multiple roots in adifferent angle. When one observes the multiplicity as the repletion number of roots with a fixed stride, theoperation is, of course, the shift or difference operator. We give the abc inequality in this setting and apply
it for the corresponding Fermat or Davemport type estimates as well as for some known generalizations of
the Stothers–Mason theorem. All those discussions proceed in parallel to the usual differential setting where
Casoratian replaces Wronskian as a matter of course. Some of their extremal solutions can be exchanged insome translation rule. But we have found no indication of a possible geometric approach in the difference
setting, yet. Hence this talk is all about complex functions of one variable and not about integers but avery naı̈ve experiment. This is based on a joint work with K. Ishizaki, R. Korhonen, and N. Li.

9 月 14 日（水）第 VIII 会場

9:30〜12:00
14 八 木 拓 己 (京 大 人 間 環 境)
Takumi Yagi

(Kyoto Univ.)

半放物固定点を持つ 2 次エノン写像の摂動 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Perturbations of quadratic Hénon maps with a semi-parabolic fixedpoint

概 要 We consider a family of dissipative quadratic complex Hénon maps Ha,t with a ∈ Dδ and t ∈ [0, 1],

where δ > 0. Suppose that Ha,t has a fixed point qa,t ∈ C2 , depending continuously on a and t, with
one eigenvalue λt such that λt → λ = exp(2πip/q), (p, q) ∈ Z × N as t → 0. Let λt /λ be expressed byexp(Lt + iθt ) and θt → 0 as t → 0. We prove that the Julia sets J and J + depend continuously on t if
θt2 /Lt log(|θt /Lt |) → 0 as t → 0. We see that Ha,t is hyperbolic if θt = O(Lt ) and Lt ̸= 0. Moreover, {Ha,t }is J-stable if θt = O(Lt ) and Lt ≥ 0.
15 小 川 智 史 (阪 公 大 理)

Satoshi Ogawa (Osaka Metro. Univ.)

S 1 束の構造を持つあるレビ平坦面周りの線形化 · · · · · · · · · · · · · · · · · · · · 15
Linearization along a certain Levi-flat hypersurface with a S 1 -bundle
structure

概 要 We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained bysuspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficientcondition to obtain a normal form as a geometrical analogue of Arnol’d’s linearization theorem.

最終版: 2022/8/8

41

函数論

16 本 田 竜 広 (専 修 大 商)
濱 田 英 隆 ( 九 州 産 大 理 工)

Tatsuhiro Honda (Senshu Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)

Composition operators from the α-Bloch space into the β-Bloch spacein several complex variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Composition operators from the α-Bloch space into the β-Bloch spacein several complex variables

概 要 In this talk, we first give a necessary and sufficient condition for the composition operator Cφ fromthe α-Bloch space into the β-Bloch space to be bounded. Next, we discuss a necessary condition for Cφ to
be compact.
17 野 口 潤 次 郎 (東大⋆・東工大⋆)
Junjiro Noguchi(Univ. of Tokyo⋆ / Tokyo Tech⋆)

On analytic Ax–Schanuel — I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On analytic Ax–Schanuel — I

概 要 We give another proof of analytic Ax–Schanuel theorem for semi-abelian varieties by means of

Nevanlinna theory. It was motivated by Schanuel’s Conjecture, which implies the algebraic independence ofe and π as a special case. The Ax–Schanuel Theorem is a formal functional version of Schanuel’s Conjecture
and was proved by Ax 1971 by making use of Kolchin’s differential algebra. Here we give another proofof the analytic Ax–Schanuel Theorem by means of the Log Bloch–Ochiai Theorem and some estimate ofintegrals of log-differentials.
18 野 口 潤 次 郎 (東大⋆・東工大⋆)
Junjiro Noguchi(Univ. of Tokyo⋆ / Tokyo Tech⋆)

On analytic Ax–Schanuel — II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On analytic Ax–Schanuel — II

概 要 The purpose is to explore Nevanlinna theory of the entire curve ed
xpf := (exp f, f ) : C → A × Lie(A)associated with an entire curve f : C → Lie(A), where A is a semi-abelian variety. In particular, we prove a
2nd Main Theorem for ed
xpf and its k-jet lifts with truncated counting functions at level one. We give some
applications to a problem of a type raised by S. Lang and the unicity. The results clarify a relationshipbetween the problems of Ax–Schanuel type and Nevanlinna theory.
19 松 本 佳 彦 (阪大理)

Yoshihiko Matsumoto (Osaka Univ.)

CR Killing 作用素と Bernstein–Gelfand–Gelfand 構成 · · · · · · · · · · · · · · · 15
CR Killing operator and the Bernstein–Gelfand–Gelfand construction

概 要 What we call the CR Killing operator D on a contact manifold (M, H) equipped with a compatible

almost CR structure J (also known as a strictly pseudoconvex partially integrable almost CR manifold) is
the linear differential operator describing trivial deformations of J. We report our recent finding that D canalso be found as the first operator in the so-called Bernstein–Gelfand–Gelfand sequence. More precisely, D
is the first BGG operator induced by a modified tractor connection introduced by Čap, not by the normal
tractor connection, of the adjoint tractor bundle.
20 松 本 和 子 (東 京 理 大 理 工)
Kazuko Matsumoto(Tokyo Univ. of Sci.)

C 2 -写像に対する Hartogs の正則性定理と q-convex function に対する最大値の原理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hartogs’ analyticity theorem for C 2 -mappings and maximum principle
for q-convex functions

概 要 In this talk, we show that a C 2 -mapping from an open subset in Cq to Ck is holomorphic if its graphis pseudoconcave of order q. This is an extension of Hartogs’ analyticity theorem. The proof is given using
the characterization of pseudoconcave sets of order q by local maximum principle for q-convex functions.

最終版: 2022/8/8函数論( Univ. of Crete )21 I. D. Platis
孫
立 杰 ( 山 口 大 創 成)

Ioannis D. Platis (Univ. of Crete)(Yamaguchi Univ.)
Lijie Sun42

ハイゼンベルク群のケーラー錐について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the Kähler cone of the Heisenberg group

概 要 We review the Sasakian structure of the Heisenberg group and the Kähler structure of its Kähler cone.

The latter provides the horospherical model of the complex hyperbolic plane, which is known as Siegel
domain. We study the geometric properties of the Kähler manifolds, such as its curvature, geodesics. The
Kähler manifolds and the complex hyperbolic plane are neither biholomorphic nor isometric; however, we
prove that there exist subbundles of their respective (1,0) tangent spaces such that the horospherical tangent
map is a holomorphic isometry when restricted to those subbundles. This is a joint work with Ioannis D.
Platis.
22 大 沢 健 夫 (名 大 多 元 数 理) [ Existence theorems on complex manifolds which are complete at infinity· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Takeo Ohsawa (Nagoya Univ.)

Existence theorems on complex manifolds which are complete at infinity

概 要 A complex manifold is said to be complete Kähler at infinity if it admits a complete metric whose

fundamental form is closed outside a compact subset. A large amount of locally pseudoconvex domains havethis property. It is expected that basic existence theorems on strongly pseudoconvex manifolds for coherent
analytic sheaves have natural generalizations for locally free sheaves with approriate curvature conditions
on such manifolds. Affirmative results in this direction will be shown.
13:30〜14:30

特別講演
潟
田 島 慎 一 (新大⋆)Shinichi Tajima (Niigata Univ.

⋆)

特異点の複素解析, 代数解析とアルゴリズム

Complex and algebraic analysis of singularities, and algorithms

概 要 We consider complex analytic properties of singularities. In this talk, we show that the use of local

cohomology and Grothendieck local duality allow us to construct a new approach for studying singularities.
As applications, we present several algorithms for computing complex analytic invariants of singularities.
We study in particular non-isolated hypersurface singularities. By using Gröbner basis on Poincaré–
Birkhoff–Witt algebra, we give a method for computing b-functions and holonomic D-modules associatedto non-isolated hypersurface singularities. We study the structure of holonomic D-modules and give some
applications to singularity theory.

最終版: 2022/8/843函数方程式論函 数

方9 月 13 日（火）

程

式

論

第 II 会場

9:45〜12:00
1 塚 本 一 郎 (東 洋 大 理 工) [ x′′ = ±eαλt x1+α の直線に漸近する解の解析的表示 · · · · · · · · · · · · · · · · · · 10

Ichiro Tsukamoto (Toyo Univ.)

On asymptotically linear solutions of x′′ = ±eαλt x1+α

概 要 As already known, the differential equations denoted in the title have solutions asymptotic to linear

functions as t tends to −∞. In this talk, we get the asymptotic expansions of these in terms of Hukuhara’s
theory of a Briot–Bouquet differential equation.
2 安 達 駿 弥 ( 熊 本 大 自 然)

Shunya Adachi (Kumamoto Univ.)

2 階 Fuchs 型微分方程式のモノドロミー不変 Hermite 形式 · · · · · · · · · · · 10
Monodromy invariant Hermitian forms for second order Fuchsian differential equations

概 要 In our previous work, we characterized the conditions for the monodromy of second order Fuchsiandifferential equations with four singularities to have an invariant Hermitian form. In this talk, we relax
the assumption regarding the number of singularities. Namely, we consider the existence of monodromy
invariant Hermitian form when the number of singularities is arbitrary. As a result, we give a criterion for
the existence of monodromy invariant Hermitian forms in terms of monodromy variety.
3 間 野 修 平 ( 統 計 数 理 研)
高 山 信 毅 ( 神 戸 大 理)

Shuhei Mano (Inst. of Stat. Math.)
Nobuki Takayama (Kobe Univ.)

コーダルグラフが定める行列が導く GKZ 超幾何多項式の特殊値における和公式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A sum formula of GKZ-hypergeometric polynomials with matrices associated with chordal graphs at specific values

概 要 The graphical toric model is an important and interesting model in statistics. The normalizing

constant of the probability function is a multi-variable polynomial and satisfies a GKZ hypergeometricholonomic system. Sundberg (1975) obtained a closed form expression of the special value of the polynomial
when the graph is chordal. He derived it by using a factorization of the probability measure. From the
GKZ point of view, the polynomial has an Euler type integral representation. We will give a proof for theformula by the integral representation.
4 佐 々 木 真 二 ( 芝 浦 工 大 建 築)

Shinji Sasaki (Shibaura Inst. of Tech.)

二重変わり点における WKB 解析的変換の Borel 総和可能性 · · · · · · · · · 10

Borel summability of WKB-theoretic transformation near a double turning point

概 要 We consider the one-dimensional stationary Schödinger equation with a double turning point. Near

the double turning point, the equation is WKB-theoretically transformed to the canonical equation (thedegenerate Weber equation). Following the result of Kamimoto–Koike (2011) near a simple turning point,
we give Borel summability of the transformation near a double turning point, so that we obtain theconnection formula from the canonical equation via the transformation.

最終版: 2022/8/8函数方程式論畿
大⋆)5 青 木 貴 史 (近鈴 木 貴 雄 ( 近 畿 大 理 工)
内 田 匠 風 ( 近 畿 大 理 工)

Takashi Aoki
Takao Suzuki
Shofu Uchida(Kinki Univ.⋆)(Kinki Univ.)(Kinki Univ.)

44

Exact WKB analysis for the Pearcey system with a large parameter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Exact WKB analysis for the Pearcey system with a large parameter

概 要 The Pearcey system is an extension of the Airy equation for multi variables. In this talk, we showthat the Borel transform of WKB solutions for the Pearcey system can be written as linear combinations ofalgebraic functions.
6 吉 野 正 史 ( 広 島 大 理)

Masafumi Yoshino (Hiroshima Univ.)

Movable singular point of solution of some Hamiltonian system · · · · · · 10
Movable singular point of solution of some Hamiltonian system

概 要 In this talk we study the solution of the Hamiltonian system with two movable singular points. We

solve the Hamiltonian system by transforming it to a certain simpler Hamiltonian system by virtue of thehomology equation and the global Borel summability method for PDEs.
7 石 橋 和 葵 ( 広 島 商 船 高 専)
Kazuki Ishibashi(Hiroshima Nat. Coll. of Maritime Tech.)

比例微分制御を利用した減衰付き線形微分方程式の非振動定理 · · · · · · · · 10

A nonoscillation theorem for damped linear differential equations witha proportional derivative controller

概 要 The proportional derivative controller of a differential operator is commonly referred to as theconformable derivative. In this talk, we present a nonoscillation theorem for damped linear differential
equations with a differential operator using the conformable derivative of control theory. The proof of thenonoscillation theorem utilizes the Riccati inequality corresponding to the equation considered.
8 小川原弘士(熊本大数理科学総合教育センター)

Hiroshi Ogawara (Kumamoto Univ.)

2 階線形 q 差分方程式の解の微分超越性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Differential transcendence of solutions for second order linear q difference equations

概 要 We investigate differential transcendence of solutions for second order linear q difference equations

based on a criterion of Nishioka.
9 橋 詰 雅 斗 ( 広 島 大 理)
猪 奥 倫 左 ( 東 北 大 理)

Masato Hashizume (Hiroshima Univ.)
Norisuke Ioku (Tohoku Univ.)

Moser–Trudinger 不等式のべき乗近似 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A power type approximation of the Moser–Trudinger inequality

概 要 The Moser–Trudinger inequality is considered to be a limiting case of the Sobolev inequality in theframework of Orlicz spaces. However, the Moser–Trudinger inequality is not obtained via a direct limiting
procedure. In this talk, we consider a Sobolev type inequality and some properties of the inequality. In
particular, we show that the Carleson–Chang limit on the Moser–Trudinger inequality is derived by thelimiting procedure for the concentration level of the Sobolev type inequality.

最終版: 2022/8/845函数方程式論10 宇 佐 美 広 介 (岐 阜 大 工)
媛
大⋆)
内 藤
学 (愛
Hiroyuki Usami (Gifu Univ.)
Manabu Naito (Ehime Univ.⋆)

摂動された半分線形常微分方程式の解の存在と漸近挙動について · · · · · · 10

On the existence and asymptotic behavior of solutions of perturbed
half-linear ordinary differential equations

概 要 Perturbed half-linear ordinary differential equations are considered near the infinity. When theperturbed term is identically zero, every nontrivial solutions of the equation behaves like exponentialfunctions near the infinity. We show that, if the perturbed term is small enough, every nontrivial solutionof the equation still behaves like exponential functions.
14:15〜16:45
11 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

Oscillatory bifurcation problems for ODEs with logarithmic nonlinearity· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Oscillatory bifurcation problems for ODEs with logarithmic nonlinearity

概 要 We consider the asymptotic behavior of the bifurcation curve of nonlinear ODEs with logarithmic andoscillatory terms. It is well known that the bifurcation curve λ is a continuous function of the maximum
norm α = ∥uλ ∥∞ of the solution uλ corresponding to λ. Moreover, it is parameterized by α such asp
λ = λ(α). Our goal is to obtain the asymptotic formula for λ(α) as α → ∞.
12 森
竜 樹 ( 武 蔵 野 大 工)
大理)
田 﨑 創 平 (北
(
崎
大⋆)
辻 川
亨 宮
谷
大⋆)
四 ツ 谷 晶 二 (龍Tatsuki Mori (Musashino Univ.)
Sohei Tasaki (Hokkaido Univ.)
Tohru Tsujikawa (Univ. of Miyazaki⋆)
Shoji Yotsutani (Ryukoku Univ.⋆)

Secondary bifurcation and the direction of bifurcation of stationary solutions to a phase field model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Secondary bifurcation and the direction of bifurcation of stationary solutions to a phase field model

概 要 We are concerned with bifurcation diagrams of stationary solutions to a phase field model proposed

by Fix and followed by Caginalp. We obtained all global bifurcation diagrams of stationary solutions,which include the secondary bifurcation from odd symmetric solutions. In this talk, we clarify the directionof bifurcation after the secondary bifurcation. The direction of bifurcation is crucial for investigating thestability/instability of solutions.
13 梶 木 屋 龍 治(大阪電通大共通教育機構)
Ryuji Kajikiya(Osaka Electro-Comm. Univ.)

劣線形 Moore–Nehari 方程式の解の分岐 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Bifurcation of solutions for the sublinear Moore–Nehari differential equation

概 要 We study the bifurcation of symmetric nodal solutions for the sublinear Moore–Nehari equation. Here

we call a solution symmetric if it is even or odd. For a nonnegative integer n, we call a solution n-nodal if
it has exactly n zeros in (−1, 1). We denote the unique n-nodal symmetric solution by un (x, λ). We provethat if n is even, un (x, λ) does not bifurcate, however if n is odd, it bifurcates at a certain point and abifurcation branch consists of asymmetric solutions.

最終版: 2022/8/8函数方程式論14 長 田 祐 輝 (都 立 大 理)

Yuki Osada (Tokyo Metro. Univ.)46

3 波相互作用をもつ非線形シュレディンガー方程式系に対する特異摂動問
題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A singular perturbation problem for a nonlinear Schrödinger systemwith three wave interaction

概 要 In this talk, we consider the locations of spikes of ground states for the following nonlinear Schrödinger

system with three wave interaction

2
p−1


−ε ∆u1 + V1 (x)u1 = |u1 | u1 + γu2 u3−ε2 ∆u2 + V2 (x)u2 = |u2 |p−1 u2 + γu1 u3−ε2 ∆u + V (x)u = |u |p−1 u + γu u
3

3

3

3

3

1 2

in RN ,
in RN ,
in RN

as ε → +0, where N ≤ 5, 2 ≤ p < 2∗ − 1, 2∗ = ∞ (N ≤ 2), 2∗ = 2N/(N − 2) (N ≥ 3), ε, γ > 0. Moreprecisely, we define a function ρ, where the spikes are trapped at the minimum points of ρ(V1 (x), V2 (x), V3 (x))
under certain conditions.
15 田 中敏 ( 東 北 大 理)衛
大)渡 辺 宏 太 郎 (防塩 路 直 樹 ( 横 浜 国 大 工)Satoshi Tanaka (Tohoku Univ.)
Kotaro Watanabe(Nat. Defense Acad. of Japan)
Naoki Shioji (Yokohama Nat. Univ.)

Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the 3-sphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Existence and multiplicity of positive solutions to the scalar-field equation on large annuli in the 3-sphere概 要 A Dirichlet problem for the scalar-field equation on an annular domain in the unit 3-sphere isconsidered. The existence and multiplicity of positive solutions are shown.
16 内 藤 雄 基 (広 島 大 理)
宮 本 安 人 ( 東 大 数 理)
Yuki Naito (Hiroshima Univ.)
Yasuhito Miyamoto (Univ. of Tokyo)

Singular solutions for semilinear elliptic equations with general supercritical growth · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Singular solutions for semilinear elliptic equations with general supercritical growth

概 要 A positive radial singular solution for ∆u+f (u) = 0 with a general supercritical growth is constructed.

An exact asymptotic expansion as well as its uniqueness in the space of radial functions are also established.
These results can be applied to the bifurcation problem ∆u + λf (u) = 0 on a ball. Our method can treat awide class of nonlinearities in a unified way, e.g., up log u, exp(up ) and exp(· · · exp(u) · · · ) as well as up andeu . Main technical tools are intrinsic transformations for semilinear elliptic equations and ODE techniques.
17 井 上 順 平 (早 大 理 工)
Jumpei Inoue (Waseda Univ.)

ロジスティック方程式のディリクレ問題における最適棲息分布 · · · · · · · · 10

On the optimal habitat profile for the Dirichlet problem of a logistic
equation

概 要 This talk is concerned with the stationary problem for a diffusive logistic equation with the ho-mogeneous Dirichlet boundary condition. Relating to the corresponding Neumann problem, Wei-Ming Ni
proposed a question as follows: Maximizing the ratio of the total masses of species to resources. For thisquestion, Bai, He and Li showed that the supremum of the ratio is 3 in the one dimensional case, and the
speaker and Kuto showed that the supremum is infinity in the multi-dimensional ball. In this talk, we show
the same results still hold true for the Dirichlet problem.

最終版: 2022/8/847函数方程式論18 北 野 修 平 (早 大 理 工)
Shuhei Kitano (Waseda Univ.)

完全非線形積分方程式における W σ,p 評価 · · · · · · · · · · · · · · · · · · · · · · · · · 10

W σ,p a priori estimates for fully nonlinear integral equations

概 要 In this talk, we discuss W σ,p estimates for a class of fully nonlinear integral equations of order σ,which are analogues of W 2,p estimates by Caffarelli. We also obtain ABP maximum principles, which are
improvements of estimates proved by Guillen and Schwab, depending only on Lp norms of inhomogeneousterms.
19 北 野 修 平 (早 大 理 工)
Shuhei Kitano (Waseda Univ.)

非有界非斉次項を伴う完全非線形積分方程式における ABP 最大値原理· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

ABP maximum principles for fully nonlinear integral equations withunbounded inhomogeneous terms

概 要 ABP maximum principles for integral equations have been investigated by Caffarelli–Silvestre andGuillen–Schwab, but strictly depends on the boundness of inhomogeneous terms. We present an improved
ABP maximum principle when the order of equation is close to 2, by using a new iteration method.
20 藤 田 安 啓 (富 山 大 理)
山 口 範 和 ( 富 山 大 教 育)
A. Siconolfi(Sapienza Univ. di Roma)

Yasuhiro Fujita (Univ. of Toyama)
Norikazu Yamaguchi (Univ. of Toyama)
Antonio Siconolfi(Sapienza Univ. di Roma)

Hamilton–Jacobi flow と初期値の至る所微分不可能性 · · · · · · · · · · · · · · · 10

Hamilton–Jacobi flows and nowhere differentiablity of initial data

概 要 In this talk, we report that nowhere differentaiblity of initial data can be derived from specific assump-

tions on the Hamilton–Jacobi flow issued from these data. This is a sort of inverse problem. The results ofthis talk can be seen in an electronic version of Mathematische Annalen, https://doi.org/10.1007/s00208021-02353-w, Open Access.
21 鈴 木貴 (阪 大 M M D S )Takashi Suzuki (Osaka Univ.)

領域変動に関する固有値の微分可能性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Differentiability of eigenvalues concerning domain perturbations

概 要 We show the first and the second differentiability of the eigenvalues of Laplacian concerning general

perturbation of Lipschitz domains provided with mixed boundary conditions, particularly, for multiple
eigenvalues. This property is valid if the order of eigenvalues is changed and the derivatives are characterized
by the other eigenvalues on finite dimensional spaces. Joint work with Takuya Tsuchiya.
17:00〜18:00

特別講演
山 川 大 亮 ( 東 京 理 大 理)

Daisuke Yamakawa(Tokyo Univ. of Sci.)

モノドロミー保存変形の幾何学と対称性

Geometry and symmetry of isomonodromic deformations

概 要 Isomonodromic deformations are some nice deformations of linear ordinary differential equations withmeromorphic coefficients and are governed by nonlinear differential equations, called the isomonodromy
equations. The most famous examples of isomonodromy equations are the Painlevé equations. I will
give an overview of some topics on isomonodromic deformations relating to the algebraic and symplectic
geometry.

最終版: 2022/8/8函数方程式論

9 月 14 日（水）48

第 II 会場

9:45〜12:00
22 廣 瀬 和 也 (北
浜 向
直 (北

大

理)

大

理)

Kazuya Hirose (Hokkaido Univ.)
Nao Hamamuki (Hokkaido Univ.)

A dynamical approach to lower gradient estimates for viscosity solutionsof Hamilton–Jacobi equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A dynamical approach to lower gradient estimates for viscosity solutionsof Hamilton–Jacobi equations

概 要 In this talk, we present a new approach to deriving lower bounds for gradients of a viscosity solution

to a Hamilton–Jacobi equation when the Hamiltonian is convex. For the proof, we study solutions to theapproximate Hamiltonian systems. Moreover, we compare our results with the previous work by O. Ley(2001). We show that our results give better and optimal estimates in several senses.
23 三 栖 邦 康 (北大理)Kuniyasu Misu (Hokkaido Univ.)

平均曲率流方程式の障害物問題の解の漸近挙動 —ゲーム理論的アプロー
チ— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A game-theoretic approach to the asymptotic behavior of solutions toan obstacle problem for the mean curvature flow equation

概 要 We consider the asymptotic behavior of solutions to an obstacle problem for the mean curvature flow

equation by using a game-theoretic approximation, which we extend from that of Kohn and Serfaty (2006).
We prove that moving curves governed by the mean curvature flow converge in time to the boundary of theconvex hull of obstacles under some assumptions on the initial curves and obstacles. In these proofs, we
utilize the properties of the game trajectories given by very elementary game strategies.
24 森 龍 之 介 (明 大 M I M S)
富 松 瑛 太 ( 東 工 大 理)
利 根 川 吉 廣 ( 東 工 大 理)
Ryunosuke Mori (Meiji Univ.)
Eita Tomimatsu (Tokyo Tech)
Yoshihiro Tonegawa (Tokyo Tech)

移流項付き一般化平均曲率流に対する強解について · · · · · · · · · · · · · · · · · 10

On a strong solution to a generalized mean curvature flow with a transport term in the sense of Brakke’s formulation

概 要 Suppose that a family of k-dimensional surfaces in Rn evolves by the generalized mean curvature flow

with a given transport vector u in the sense of Brakke’s formulation of velocity. When the flow is locallyclose to a time-dependent k-dimensional plane in a weak sense of measure in space-time, it is represented
as a graph of a C 1,α function over the plane. On the other hand, it is not known if the graph satisfies thecorresponding PDE pointwise in general. For this problem, when k = n − 1 and the distributional time
derivative of the graph is a signed Radon measure, it is proved that the graph satisfies the PDE pointwise.
An application to a short-time existence theorem for a surface evolution problem is given.
25 高 棹 圭 介(京大理・京大白眉センター)
Keisuke Takasao(Kyoto Univ. / Kyoto Univ.)

任意の空間次元における体積保存平均曲率流方程式の弱解の存在について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Existence of weak solution to volume preserving mean curvature flow inall dimensions

概 要 We consider the weak solution to the volume preserving mean curvature flow. In 2016, Mugnai, Seis,and Spadaro proved the existence of the weak solution (flat flow) by the minimizing movement scheme. In
addition, they also showed that the flat flow is the distributional solution under the reasonable assumption
for the convergence of the approximate solution. In this talk, we prove the existence of the weak solution
called L2 -flow via the phase field method without the assumption. We also show that the weak solution isthe distributional solution for a short time, under an assumption for initial data.

最終版: 2022/8/849函数方程式論26 伊 藤涼 ( 神 奈 川 大 理)
二 宮 広 和 ( 明 大 総 合 数 理)
(Kanagawa Univ.)
Ryo ItoHirokazu Ninomiya (Meiji Univ.)

反応拡散方程式の非有界な進行波解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Unbounded traveling wave solutions for reaction-diffusion equations

概 要 We discuss the existence of unbounded traveling wave solutions for one dimensional reaction-diffusion

equations with several type of nonlinearities. It is well known that in the monostable nonlinearity case there
exist traveling wave solutions connecting two zero points. The idea of this study is varying the one zero
point. We consider the question: what happens when one of the zero point goes to infinity? The purposeof this study is to construct a theory of unbounded traveling wave solutions and to reconsider the classicaltheory of traveling wave solutions from new viewpoint introduced in this study.
27 市 田Yu Ichida

優 ( 明 大 理 工)

(Meiji Univ.)

相空間のコンパクト化に基づくある走化性方程式系の球対称定常解 · · · · 10

Radially symmetric stationary solutions for certain chemotaxis systems
based on compactification in phase space

概 要 This talk reports results on the existence, shapes, and asymptotic behavior of positive radiallysymmetric stationary solutions for several models (the simplest parabolic-elliptic Keller–Segel model andthe simplest attraction-repulsion chemotaxis system) of chemotaxis in higher dimensions, using a methodthat combines classical results from the continuous dynamical systems theory and Poincaré–Lyapunov
compactification. The key to the discussion is to derive a scalar equation by using a transformation on the
averaged mass for the equation satisfied by the radially symmetric stationary solution and to investigate theinfinity dynamics as geometric information for the two-dimensional ordinary differential equations derived
from it.
28 井 上 順 平 (早 大 理 工)
久 藤 衡 介 ( 早 大 理 工)
佐 藤
誉 ( 早 大 理 工)
Jumpei Inoue (Waseda Univ.)
Kousuke Kuto (Waseda Univ.)
Homare Sato (Waseda Univ.)

Full cross-diffusion limit in the stationary SKT model with Dirichletboundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Full cross-diffusion limit in the stationary SKT model with Dirichletboundary conditions

概 要 This talk is concerned with positive steady-states of the Shigesada–Kawasaki–Teramoto model withhomogeneous Dirichlet boundary conditions. A main result reveals that the asymptotic behavior of positive
steady-states as both cross-diffusion terms tend to infinity can be classified into two types. Furthermore,each type is characterized by the limiting system. Concerning one of two limiting systems, we obtain the
global bifurcation structure.
29 塚 本 悠 暉 (明大研究・知財)Yuki Tsukamoto (Meiji Univ.)

ある反応拡散近似の収束性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A convergence of reaction-diffusion approximation

概 要 We consider a singular limit problem called the fast reaction limit. This problem has been studied

extensively when the reaction terms of each component are the same function in a two-component system.
However, it is not fully understood how solutions behave in problems with different reaction terms. In thistalk, we will consider the problem where the reaction term is represented by a power term. We proved thatthe initial interface instantly vanishes and the function converges to a function satisfying the heat equation.

最終版: 2022/8/8函数方程式論5030 石 井 裕 太 (茨 城 工 高 専)

Y 字グラフにおける Gierer–Meinhardt モデルの多重ピーク解の存在と安定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Yuta Ishii (Ibaraki Nat. Coll. of Tech.)

The existence and stability of multi-peak solutions to the Gierer–Meinhardt
model on Y -shaped metric graph概 要 In this talk, we consider the existence and the stability of two-peak solutions to the Gierer–Meinhardt

model with heterogeneity in front of nonlinear terms on Y -shaped metric graphs. In particular, we explainthat the location, amplitude, and stability of spikes are decided by the interaction of the heterogeneity
function with the geometry of the graph, represented by the associated Green’s function. Also, to investigate
the effect of the geometry of the graph in details, we consider the non-heterogeneity function case, comparing
the corresponding previous works of the one-dimensional interval case.
31 石 井 裕 太 (茨 城 工 高 専)

Yuta Ishii (Ibaraki Nat. Coll. of Tech.)

スターグラフにおける Schnakenberg モデルの多重ピーク解の存在と安定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The existence and stability of multi-peak solutions to the Schnakenberg
model on star shaped metric graph概 要 In this talk, we explain the results on the existence and the stability of N -peak solutions to the

Schnakenberg model with heterogeneity in front of nonlinear terms on star shaped metric graphs. The
location, amplitude, and stability of spikes are decided by the effects of the heterogeneity function andthe geometry of the graph represented by the associated Green’s function. Also, by considering nonheterogeneity function case, we describe the effects of the geometry of a star graph on N -peak solution indetails. Moreover, we give the classification of the lengths of segments in the case that spikes are arranged
on segments one by one.
13:30〜14:30

特別講演
柴 田 将 敬 ( 名 城 大 理 工)

Masataka Shibata (Meijo Univ.)

H 1 臨界項を持つ準線形楕円型方程式の正値解の漸近挙動
Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with H 1 -critical growth

概 要 We consider a quasilinear elliptic equation −∆u − κu∆(u2 ) = up − u in RN , where N ≥ 3, p > 1,

κ > 0. The equation appears in the study of standing waves of a modified Schrödinger equation. In thistalk, we focus on the case of p + 1 = 2∗ (H 1 -critical case) and discuss the asymptotic behavior of positive
solutions.

9 月 15 日（木）第 II 会場

9:45〜12:00
32 池 田 幸 太 (明 大 総 合 数 理)
Kota Ikeda(Meiji Univ.)

樟脳粒の集団運動における一様流の安定性解析 · · · · · · · · · · · · · · · · · · · · · 10

Stability analysis of a uniform flow in a mathematical model of camphorboats

概 要 Various collective motions of camphor boats, called jamming, clustering, and swarming state observedin a one-dimensional circuit, have been studied. It is expected that the center manifold theories proposed inprevious works are useful for the analysis of the collective motion of camphor boats. In my previous work,
we have developed a new theory for a system with Dirac’s delta functions in L2 -framework. In this talk, wewill examine the stability analysis in the reduced system and numerically show that the uniform flow canbe destabilized even if the length of the circuit is large.

最終版: 2022/8/851函数方程式論33 兼 子 裕 大 (日 本 女 大 理)
松 澤
寛 ( 神 奈 川 大 理)
山 田 義 雄 ( 早 大 理 工)

Yuki Kaneko (Japan Women’s Univ.)
Hiroshi Matsuzawa (Kanagawa Univ.)
Yoshio Yamada (Waseda Univ.)

Positive bistable 項を伴う反応拡散方程式の自由境界問題に対する球対称解の漸近挙動 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic behaviors of radially symmetric solutions for a free boundary problem of a reaction-diffusion equation with positive bistable nonlinearity

概 要 We consider a free boundary problem for a reaction-diffusion equation with positive bistable non-linearity under a radially symmetric environment. This problem may be applied to model the spreadingof biological species, where unknown functions are population density and spreading front of the species.
In this talk, we will classify the asymptotic behaviors of solutions into four cases: Big spreading, Small
spreading, Transition and Vanishing, and give some sufficient conditions for each dynamical behavior. We
will also discuss the spreading speed of the free boundary.
34 水 上 雅 昭 (京 都 教 育 大)
田 中 悠 也 ( 東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)
Masaaki Mizukami(Kyoto Univ. of Edu.)
Yuya Tanaka (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Occurrence of blow-up phenomena by chemotactic effects in a twospecies chemotaxis-competition model · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Occurrence of blow-up phenomena by chemotactic effects in a twospecies chemotaxis-competition model

概 要 This talk deals with occurrence of blow-up phenomena in a diffusive Lotka–Volterra competition

model with chemotaxis. In 2012 Tello–Winkler (Nonlinearity; 2012: 25; 1413–1425) proposed a diffusive
Lotka–Volterra competition model having chemotaxis terms. As to this model, boundedness of solutions
was obtained under conditions that chemotactic effect is small by e.g. Tello–Winkler (2012) and Mizukami(Math. Methods Appl. Sci.; 2018; 41; 234–249). However, blow-up of solutions has not been derived yet.
The purpose of this talk is to discuss whether solutions blow up.
( 東 北 大 理)
35 F. Salin
赤 木 剛 朗 ( 東 北 大 理)
Florian Salin
Goro Akagi(Tohoku Univ.)(Tohoku Univ.)

Existence of energy solutions to fractional nonlinear diffusion equations
posed on bounded domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Existence of energy solutions to fractional nonlinear diffusion equations
posed on bounded domains

概 要 This talk is concerned with existence and uniqueness of energy solutions to the Cauchy–Dirichletproblem posed on bounded domains for nonlinear diffusion equations involving the so-called restricted
fractional Laplacians.
36 オーヘーダヒ (東 北 大 理)
岩 渕
司 ( 東 北 大 理)

Dáithı́ Ó hAodha (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

表面準地衡方程式の解の最適な減衰評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The optimal decay estimate of solutions to the surface quasi-geostrophic
equation

概 要 We construct a linear approximation of the solution to the Surface Quasi-Geostrophic Equation in

two-dimensional Euclidean space, and obtain a convergence rate, in the Lebesgue norm, between the solution
and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution
is bounded sharply by the same function of time.

最終版: 2022/8/8函数方程式論37 岩 渕
司 ( 東 北 大 理)
R. Farwig(ダルムシュタット工科大)

Tsukasa Iwabuchi (Tohoku Univ.)
Reinhard Farwig (TU Darmstadt)

52

Semigroups generated by fractional Laplacian and Sobolev spaces on
arbitrary domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Semigroups generated by fractional Laplacian and Sobolev spaces on
arbitrary domains

概 要 We show several estimates of the semigroup generated by the fractional Dirichlet Laplacian on anarbitrary domain of Rd . We also describe a procedure to introduce Sobolev spaces associated with the
Dirichlet Laplacian.
38 上 村豊 (東 京 海 洋 大⋆) [ エネルギー依存逆散乱と爆発ソリトン · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.⋆)Energy dependent inverse scattering and exploding soliton

概 要 An inverse scattering method is established for finding soliton solutions of a hierarchy generalising theKdV hierarchy. The soliton solutions become generically exploding solitons.
39 山 崎 陽 平 (九 大 数 理)
前 田 昌 也 ( 千 葉 大 理)

Yohei Yamazaki (Kyushu Univ.)
Masaya Maeda (Chiba Univ.)

Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Center stable manifold for ground states of nonlinear Schrödinger equations with internal modes

概 要 We study the dynamics of solutions of nonlinear Schrödinger equation near unstable ground states.

The existence of the local center stable manifold around ground states and the asymptotic stability for thesolutions on the manifold is proved. The novelty of our result is that we allow the existence of internal
modes.
40 木 下 智 晴 (早 大 理 工)

Tomoharu Kinoshita (Waseda Univ.)

Infinitely many solutions for nonlinear Schrödinger equations underBerestycki–Lions condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Infinitely many solutions for nonlinear Schrödinger equations underBerestycki–Lions condition

概 要 In this talk, we study the existence and multiplicity of solutions of the nonlinear Schrodinger equatios

under Berestycki–Lions condition. For this purpose, we apply a new deformation lemma argument under a
new version of the Palais–Smale condition.
大
理)
41 林
雅 行 (京深 谷 法 良 ( 東 京 理 大 理)
戍 亥 隆 恭(阪大理・ブリティッシュコロンビア大)Masayuki Hayashi (Kyoto Univ.)
Noriyoshi Fukaya (Tokyo Univ. of Sci.)
Takahisa Inui
(Osaka Univ./Univ. of British Columbia)

Traveling waves for a nonlinear Schrödinger system with quadratic interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Traveling waves for a nonlinear Schrödinger system with quadratic interaction

概 要 We study traveling wave solutions for a system of nonlinear Schrödinger equations with quadraticinteraction. For the non mass-resonance case, the system has no specific symmetry such as Galilean or
pseudo-conformal symmetry, which is of particular interest. We construct traveling wave solutions by
variational methods, and also show global existence for oscillating large data as an application.

最終版: 2022/8/853函数方程式論

14:15〜16:45
42 加 藤Isao Kato

勲 (京

大

理)

(Kyoto Univ.)

Ill-posedness for the half wave Schrödinger equation · · · · · · · · · · · · · · · · 10
Ill-posedness for the half wave Schrödinger equation

概 要 We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu (2017). There

are some well-posedness results for the equation, however there is no ill-posedness result. We focus on thescale critical space and obtain the ill-posedness in the super-critical or the critical space under certain
condition. The proof in the super-critical space is based on the argument established by Christ, Colliander
and Tao (2003). For the critical space, we use the standing wave solution, which was proved the existenceby Bahri, Ibrahim and Kikuchi (2021).
43 中 橋渉 ( 東 京 理 大 理)
加 藤 圭 一 ( 東 京 理 大 理)

Wataru Nakahashi (Tokyo Univ. of Sci.)
Keiichi Kato (Tokyo Univ. of Sci.)

Non-smoothness of the fundamental solutions of Schrödinger equationsin three dimensions with super-quadratic potential · · · · · · · · · · · · · · · · · 10
Non-smoothness of the fundamental solutions of Schrödinger equationsin three dimensions with super-quadratic potential

概 要 We consider non-smoothness of the fundamental solution for the initial value problem of the

Schrödinger equations with super-quadratic scalar potential. One dimensional case was studied by K.
Yajima (1996). The purpose of this talk is to show the case which spatial dimension is three and scalarpotential is radical.
44 松 井 直 己 (東 京 理 大 理)

Naoki Matsui (Tokyo Univ. of Sci.)

Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrödinger
equations with potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrödinger
equations with potentials

概 要 It is known that all the subcritical mass solutions of the nonlinear Schrödinger equation with L2 -critical power-type nonlinear terms and small perturbation terms are bounded time global solutions. On
the other hand, in the critical mass case, blow-up solutions may exist. In this talk, I treat an equation withthe power-type nonlinear terms with inhomogenity and a potential including a growing one as a smaller
perturbation term, and state that there exists a critical mass blow-up solution for this equation.
45 佐 川 侑 司 (千 葉 工 大 工)
Chunhua Li ( Yanbian Univ. )西 井 良 徳 ( 東 京 理 大 理)
砂 川 秀 明 ( 阪 公 大 理)

Yuji Sagawa (Chiba Inst. of Tech.)
Chunhua Li (Yanbian Univ.)
Yoshinori Nishii (Tokyo Univ. of Sci.)
Hideaki Sunagawa(Osaka Metro. Univ.)

Upper and lower L2 -decay bounds for a class of derivative nonlinear
Schrödinger equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Upper and lower L2 -decay bounds for a class of derivative nonlinear
Schrödinger equations

概 要 We consider the initial value problem for cubic derivative nonlinear Schroedinger equations possessing

weakly dissipative structure in one space dimension. We show that the small data solution decays likeO(-1/4 power of (log t)) in L2 as t tends to infinity. Furthermore, we find that this L2-decay rate is optimalby giving a lower estimate of the same order.

最終版: 2022/8/8函数方程式論54

46 佐 藤 拓 也 (東 北 大 理) [ Optimal L2 -decay of solutions to dissipative nonlinear Schrödinger equa北直 泰 (熊 本 大 先 端) tions with a critical cubic nonlinearity · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Takuya Sato (Tohoku Univ.)
Naoyasu Kita (Kumamoto Univ.)

Optimal L2 -decay of solutions to dissipative nonlinear Schrödinger equations with a critical cubic nonlinearity

概 要 We consider the optimality of L2 -decay of solutions to the Cauchy problem of dissipative nonlinear

Schrödinger equations with a long-range nonlinearity. We show that the L2 -norms of any global solutions
do not decay more rapidly than (log t)−1/2 , and we also prove that there exists a solution decaying just at
the rate of (log t)−1/2 in L2 . This talk is based on the joint work with Professor Naoyasu Kita (Kumamoto
University).
47 平 良 晃 一 (立 命 館 大 理 工)

Kouichi Taira (Ritsumeikan Univ.)

Strichartz estimates for Schrödinger equations with slowly decreasing
potentials in dimension two · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Strichartz estimates for Schrödinger equations with slowly decreasing
potentials in dimension two

概 要 In this talk, we introduce a result on the Strichartz estimates for Schrödinger equations with slowly

decreasing potentials in dimension two. It is a generalization of a recent result by Mizutani. Ingredients ofthe proof are Kato’s perturbation method, resolvent estimates near zero energy and Hardy’s inequality.
48 鈴 木 敏 行 (神 奈 川 大 工)

Toshiyuki Suzuki (Kanagawa Univ.)

Nonlinear Schrödinger equations with some singular electromagnetic potentials of the critical scailing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Nonlinear Schrödinger equations with some singular electromagnetic potentials of the critical scailing

概 要 We consider the Cauchy problems for nonlinear Schrödinger equations with the singular electro-

magnetic field. Here the electric potential V and the magnetic potential A satisfy V (µx) = µ−2 V (x),A(µx) = µ−1 A(x), and x · A(x) = 0. The main result is the unique existence of the solution to thesemilinear problems under the condition that P := (−i ∇ + A)2 + A is nonnegative and selfadjoint in thesense of Friedrichs extension.
49 宮 﨑 隼 人 (香 川 大 教 育)
川 本 昌 紀 ( 愛 媛 大 理 工)

時間減衰する調和振動子を持つ臨界斉次型非線形シュレディンガー方程
式における長距離散乱について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Hayato Miyazaki (Kagawa Univ.)
Masaki Kawamoto (Ehime Univ.)

Long-range scattering for a critical homogeneous type nonlinear Schrödinger
equation with time-decaying harmonic potentials

概 要 We consider the final state problem for a homogeneous type nonlinear Schrödinger equation with

time-decaying harmonic potential. The nonlinearity has the critical order and is not necessarily the form ofa polynomial. In the case of the gauge-invariant nonlinearity, Kawamoto proves that the equation admits
a nontrivial solution that behaves like a free solution with a logarithmic phase correction. In this talk, we
extend his result into the case with the general homogeneous nonlinearity by the technique due to the Fourier
series expansion introduced by Masaki and Miyazaki. To prove the main result, we develop a factorization
identity for the propagator and require a little stronger decay condition for the Fourier coefficients arisingfrom the harmonic potential.

最終版: 2022/8/855函数方程式論50 A. H. Ardila(Univ. Federal de Minas Gerais)
浜 野
大 ( 早 大 理 工)
池 田 正 弘(理化学研 AIP・慶大理工)Alex Hernandez Ardila(Univ. Federal de Minas Gerais)
Masaru Hamano (Waseda Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

Global dynamics of mass-energy threshold for NLS with an inversepower potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Global dynamics of mass-energy threshold for NLS with an inversepower potential

概 要 In this talk, we treat a nonlinear Schrödinger equation with an inverse-power potential. In particular,

we consider global dynamics of mass-energy threshold for the equation. Here, mass-energy threshold implies
solutions, whom the product of its mass and energy is equal to that of the ground state to a nonlinear
Schrödiger equation without the potential. We prove that if a virial functional of initial data is positive,then the solution scatters and if a virial functional of initial data is negative and “the initial data is radialor has finite variance”, then the solution blow-up in finite time.
大理)
51 水 谷 治 哉 (阪( 華 中 師 範 大)
Zijun Wan
Xiaohua Yao (華 中 師 範 大)

Haruya Mizutani (Osaka Univ.)
Zijun Wan
(Central China Normal Univ.)
Xiaohua Yao(Central China Normal Univ.)

1 次元 4 階 Schrödinger 作用素に対する波動作用素の Lp 有界性 · · · · · · · 10

The Lp -boundedness of wave operators for fourth-order Schrödinger operators in one space dimension

概 要 Some recent progress on the Lp -boundedness properties of the wave operators for fourth-order

Schrödinger operators in one space dimension will be discussed. For instance, we will provide someconditions on the potential and spectrum of the Hamiltonian such that the wave operators are boundedon the weighted Lp spaces for any non-endpoint p and of weighted weak-type (1,1) with general even
Muckenhoupt weights.
52 中 里 亮 介 (早 大 理 工) [ Hall 効果を考慮した量子プラズマ MHD モデルの時間大域適切性と時間減衰評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ryosuke Nakasato (Waseda Univ.)

Global well-posedness and time-decay of solutions for the compressible
quantum MHD model with Hall effect概 要 We consider the initial value problem for the compressible quantum MHD system with Hall effect inthe whole space R3 . Because the quantum MHD system is equipped with the correction term similar to theKorteweg stress tensor, the solution of its problem is expected to satisfy some good properties, for instance,
the L1 -maximal regularity of the density. In this talk, we shall state the existence of global-in-time solutions
in a critical Lp framework and Lp -Lp/2 type decay estimates for global solutions.

最終版: 2022/8/8函数方程式論特別講演
菊 池 弘 明 ( 津 田 塾 大 学 芸)

56

17:00〜18:00

Hiroaki Kikuchi (Tsuda Coll.)

空間 3 次元における二重べき非線形シュレディンガー方程式の基底状態

Ground state of double power nonlinear Schrödinger equations in threespace dimensions

概 要 In this talk, we consider minimization problem related to the double power nonlinear Schrödinger

equations involving the Sobolev critical exponent in three space dimensions. In four and higher spacedimensions, it is known that for any frequency and any power of the subcritical nonlinearity, there exists
a ground state. In contrast to those cases, when the space dimension is three and the subcritical poweris three or less, we can show that there exists a threshold frequency, above which no ground state exists,
and below which the ground state exists. If time permits, I will also explain about several properties of theground state and global dynamics of solutions to the nonlinear Schrödinger equations. Main part of thistalk is based on a joint work with Takafumi Akahori (Shizuoka Univ.), Slim Ibrahim (Univ. of Victoria)
and Hayato Nawa (Meiji Univ.).

9 月 16 日（金）第 II 会場

9:45〜12:00
53 森

直 文
(東京海洋大海洋資源環境)
岡 田 真 理 ( 山 口 大 創 成)
川 島 秀 一 ( 早 大 理 工)
Naofumi Mori
(Tokyo Univ. of Marine Sci. and Tech.)Mari Okada (Yamaguchi Univ.)
Shuichi Kawashima (Waseda Univ.)

Decay property for symmetric hyperbolic system with memory-type diffusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Decay property for symmetric hyperbolic system with memory-type diffusion

概 要 We consider the decay property for symmetric hyperbolic systems with memory-type diffusion. Under

the structural condition (called Craftsmanship condition) we prove that the system is uniformly dissipative
and the solutions satisfy the corresponding decay property. Our proof is based on a technical energy methodin the Fourier space which makes use of the properties of strongly positive definite kernels.
54 森

直 文
(東京海洋大海洋資源環境)
岡 田 真 理 ( 山 口 大 創 成)
川 島 秀 一 ( 早 大 理 工)
Naofumi Mori
(Tokyo Univ. of Marine Sci. and Tech.)Mari Okada (Yamaguchi Univ.)
Shuichi Kawashima (Waseda Univ.)

Decay property for symmetric hyperbolic system with memory-type relaxation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Decay property for symmetric hyperbolic system with memory-type relaxation

概 要 We consider the decay property for a symmetric hyperbolic system with memory-type relaxation. We

assume that the memory kernel is a strongly positive definite kernel and prove that the system has the
decay property of regularity-loss type. Our proof is based on a technical energy method in the Fourier
space which makes use of the structural condition (called Craftsmanship condition or Condition (K)) andthe modified properties of strongly positive definite kernels.

最終版: 2022/8/857函数方程式論55 北 村 駿 介 (東 北 大 理) [ 空間 1 次元における特性方向による重み付き微分型半線形波動方程式の古典解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Shunsuke Kitamura (Tohoku Univ.)

Semilinear wave equations of derivative type with characteristic weights
in one space dimension

概 要 In this talk, we discuss about the initial value problems for semilinear wave equations of derivative

type with characteristic weights in one space dimension. The lifespan estimates of classical solutions arequite different from those for nonlinearity of unknown functions itself in the almost global existence case byinteraction of characteristic weights.
56 佐々木多希子 (武蔵野大工・東北大理)
Takiko Sasaki(Musashino Univ./Tohoku Univ.)

異なる伝播速度をもつ半線形波動方程式系の爆発曲線の特異性について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Singularity of a blow-up curve for systems of semilinear wave equations
with different propagation speeds

概 要 In this talk, we consider a blow-up curve for systems of semilinear wave equations with different

propagation speeds in one space dimension. The blow-up curve has been studied from the view point of
its differentiability and singularity. In 2012, Merle and Zaag considered a single wave equation and showedthat there are cases that its blow-up curve is not differentiable if the sign of the solution changes. They also
showed that the blow-up curve near the singular point is characterized by the propagation speed. However,
it is not known that the blow-up curve for systems of semilinear wave equations with different propagation
speeds has a singular point or not. In this talk, we show that the blow-up curve has a singular point undersuitable initial conditions.
57 若 杉 勇 太 (広島大先進理工)側 島 基 宏 ( 東 京 理 大 理 工)

Yuta Wakasugi (Hiroshima Univ.)
Motohiro Sobajima(Tokyo Univ. of Sci.)

Asymptotic expansion of solutions to the wave equation with spacedependent damping · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic expansion of solutions to the wave equation with spacedependent damping

概 要 We study the large time behavior of solutions to the wave equation with space-dependent damping inan exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded interms of solutions of corresponding parabolic equations. The main idea to obtain the asymptotic expansion
is the decomposition of the solution of the damped wave equation into the solution of the corresponding
parabolic problem and the time derivative of the solution of the damped wave equation with certain
inhomogeneous term and initial data.
58 谷 口 晃 一 (東 北 大 A I M R)
池 田 正 弘(理化学研 AIP・慶大理工)
若 杉 勇 太 (広島大先進理工)

Koichi Taniguchi (Tohoku Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Yuta Wakasugi (Hiroshima Univ.)

On global existence and asymptotic behavior for nonlinear damped wave
equations on measure spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On global existence and asymptotic behavior for nonlinear damped wave
equations on measure spaces

概 要 This talk is concerned with the nonlinear damped wave equation on a measure space with a self-adjoint

operator, instead of the standard Laplace operator. Under a certain decay estimate on the corresponding
heat semigroup, we establish the linear estimates which generalize the so-called Matsumura estimates, andprove the small data global existence and asymptotic behavior of solutions to the damped wave equation
based on the linear estimates. Our approach is based on a direct spectral analysis analogous to the Fourier
analysis.

最終版: 2022/8/8函数方程式論59 石 垣 祐 輔 (東 工 大 理)
上 田 好 寛 ( 神 戸 大 海 事)
Yusuke Ishigaki (Tokyo Tech)
Yoshihiro Ueda (Kobe Univ.)

58

Asymptotic stability of stationary solutions to outflow problem for compressible viscoelastic system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic stability of stationary solutions to outflow problem for compressible viscoelastic system

概 要 This talk is concerned with the stability of stationary solutions to the outflow problem for compressible

viscoelastic system in the one-dimensional half space. We classify the existence of stationary solutions bydetermining suitable conditions for several parameters, such as the Mach number and propagation speed ofelastic wave. We next establish the stability result and convergence rate toward the stationary solutions
under the small initial perturbation.
60 上 田 好 寛 (神 戸 大 海 事)
M. A. Jorge Silva(State Univ. of Londrina)
Yoshihiro Ueda (Kobe Univ.)
Marcio Antonio Jorge Silva(State Univ. of Londrina)

Memory effects on the stability of viscoelastic Timoshenko systems · · · 10

Memory effects on the stability of viscoelastic Timoshenko systems

概 要 In this talk, we investigate new classes of viscoelastic Timoshenko–Ehrenfest systems under thepresence of full or partial memory effects in one-dimensional whole space. Our achievements rely on recent
approaches to the theory of dissipative structure for systems of partial differential equations by featuring
optimal pointwise estimates in the Fourier space and explicit energy decay rates depending on the viscoelastic
damping coupling.
61 福 田 一 貴 (信 州 大 工)
池 田 正 弘(理化学研 AIP・慶大理工)
Ikki Fukuda (Shinshu Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

BBM–Burgers 方程式の初期値問題の解の漸近挙動 · · · · · · · · · · · · · · · · · · 10

Asymptotic behavior of solutions to the Cauchy problem for the BBM–
Burgers equation

概 要 In this talk, we consider the asymptotic behavior of the solutions to the Cauchy problem for theBBM–Burgers equation. We prove that the solution to this problem converges to the self-similar solution to
the Burgers equation. Moreover, we construct the appropriate second asymptotic profiles of the solutions
depending on the initial data. Based on that discussion, we investigate the effect of the initial data on theasymptotic behavior of the solutions, and derive the optimal asymptotic rate to the self-similar solution.
Especially, the main novelty of this study is that the second asymptotic profiles of the solutions with slowly
decaying data, whose case has not been studied, are obtained.
62 大 縄 将 史 (東京海洋大海洋環境)
鈴 木 政 尋 ( 名 工 大 工)
Masashi Ohnawa(Tokyo Univ. of Marine Sci. and Tech.)
Masahiro Suzuki (Nagoya Inst. of Tech.)

摩擦の影響を受ける河川流の漸近安定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Asymptotic stability of river flows subject to friction

概 要 We consider stationary flows around weirs in rivers modeled by one-dimensional shallow water equation

with friction. Waters enter weirs at subcritical states, and are accelerated beyond critical states flowing
down weirs, and return to subcritical states discontinuously due to the gentle slope downstream of weirs. We
focus on the discontinuous transition from supercritical states to subcritical states, and claim the asymptotic
stability of the stationary shock wave whatever large the strength of the shock or the gradient of the bed
elevation may be.

最終版: 2022/8/859函数方程式論

14:15〜16:45
63 牧 野

哲 (山

口

大⋆)

Tetu Makino (Yamaguchi Univ.⋆)

回転する地球大気の運動方程式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the equation of motion of the rotating atmosphere of the Earth

概 要 Even the simplest model of motions of the atmosphere of the Earth has not yet been analyzed inmathematically rigorous manner. We present few fundamental properties of the solutions governed by thecompressible Euler equations.
64 濱 本 直 樹 (阪 公 大 理)

Naoki Hamamoto (Osaka Metro. Univ.)

退化構造を伴う不確定性原理不等式のソレノイダル場に対する高次元拡張について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Higher-dimensional extension of uncertainty principle inequality with adegenerate structure for solenoidal fields
RR

概 要 We show the functional inequality RN |∇u|2 dx RN |x × u|2 dx ≥ CN

R
RN

|u|2 dx

2for vector fields uunder the condition divu = 0. This is a degenarated version of Heisenberg’s uncertainty principle inequality
for vector fields, here the sharp constant number CN can be positive and computable by considering u in
the class of solenoidal fields.
65 鶴 見 裕 之 (京前 川 泰 則 (京

大

理)

大

理)

Hiroyuki Tsurumi (Kyoto Univ.)
Yasunori Maekawa (Kyoto Univ.)

Existence of the 2D stationary Navier–Stokes flow on the whole planearound a radial flow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Existence of the 2D stationary Navier–Stokes flow on the whole planearound a radial flow

概 要 We consider the stationary Navier–Stokes equations on the whole plane R2 . We show that for a given

small and smooth external force around a radial flow, there exists a classical solution decaying like |x|−1 .
In our result, it is not necessary to impose any symmetric conditions on external forces.
工大)
66 鈴 木 政 尋 (名高 山 正 宏 ( 慶 大 理 工)

Masahiro Suzuki (Nagoya Inst. of Tech.)
Masahiro Takayama (Keio Univ.)

Vlasov–Poisson 方程式の定常解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stationary solutions of the Vlasov–Poisson system

概 要 The purpose of this talk is to mathematically investigate the formation of a plasma sheath, and toanalyze the Bohm criterions which are required for the formation. Bohm derived originally the (hydrodynamic) Bohm criterion from the Euler–Poisson system. Boyd and Thompson proposed the (kinetic) Bohm
criterion from kinetic point of view, and then Riemann derived it from the Vlasov–Poisson system. We
study the solvability of boundary value problems of the Vlasov–Poisson system. On the process, we seethat the kinetic Bohm criterion is a necessary condition for the solvability. Furthermore, the hydrodynamic
criterion can be derived from the kinetic criterion. It is of great interest to find the relation between thesolutions of the Vlasov–Poisson and Euler–Poisson systems. To clarify the relation, we also investigate thedelta mass limit of solutions of the Vlasov–Poisson system.
67 米 田 慧 司 (九 大 数 理)髙 田了 ( 東 大 数 理)
Keiji Yoneda (Kyushu Univ.)
Ryo Takada (Univ. of Tokyo)

Global solutions for the rotating magnetohydrodynamics system in thescaling critical Sobolev space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Global solutions for the rotating magnetohydrodynamics system in thescaling critical Sobolev space

概 要 We consider the initial value problem for the incompressible magnetohydrodynamics system with the

Coriolis force in the 3D whole space. We prove the global in time existence and the uniqueness of solutions
for large initial data in the scaling critical Sobolev space when the speed of rotation is sufficiently high. Inorder to control the large magnetic fields, we introduce a modified linear solution for the velocity, and show
its smallness in a suitable space-time norm by means of the dispersive effect of the Coriolis force.

最終版: 2022/8/8函数方程式論68 青 木 基 記 (東 北 大 理)
岩 渕
司 ( 東 北 大 理)

Motofumi Aoki (Tohoku Univ.)
Iwabuchi Tsukasa (Tohoku Univ.)60

A sufficient condition for the energy conservation law of compressible
Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A sufficient condition for the energy conservation law of compressible
Navier–Stokes equations

概 要 We consider the energy conservation law for two and three-dimensional compressible Navier–Stokes

equations. We study a sufficient condition for the density, velocity and pressure such that a weak solutionof the full system of compressible Navier–Stokes equations conserves the total energy which is constructedby the kinetic energy, the elastic potential and the heat contribution. Moreover, we generalize the result of
the energy conservation law for the motion of the ideal gas.
69 武 内 太 貴 (早 大 理 工)
Taiki Takeuchi (Waseda Univ.)

On the local well-posedness and inviscid limits for the Keller–Segel–
Navier–Stokes system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the local well-posedness and inviscid limits for the Keller–Segel–
Navier–Stokes system

概 要 We consider the Cauchy problem for the Keller–Segel–Navier–Stokes system of parabolic-elliptic typein RN , N ≥ 3. We show the local well-posedness for the system with initial data in Sobolev spaces, where
the solutions are uniformly bounded with respect to the viscosity. In addition, we also obtain inviscid limitsof the above system. The proof is mainly based on the a priori estimates independent of the viscosity
combined with the method of Kato–Lai (1984) and the commutator estimate of Kato–Ponce (1988).
70 大 石 健 太 (早 大 理 工)
柴 田 良 弘 ( 早 大 理 工)
(Waseda Univ.)
Kenta Oishi
Yoshihiro Shibata (Waseda Univ.)

非有界領域における Navier–Stokes 方程式の自由境界問題の時間大域適切性と解の減衰について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the global well-posedness and decay for a free boundary problem of
the Navier–Stokes equation in unbounded domains

概 要 A free boundary problem for the incompressible Navier–Stokes equations in unbounded domains is

considered. We obtain a sufficient condition for the Lp -Lq decay estimate of the Stokes semigroup to prove
the global well-posedness of the problem. This result improves the result in exterior domains by Shibata
when N ≥ 4, where N stands for the dimension of the space. The novelty is that the compactness of theboundary is not needed. We also develop the global well-posedness in the half space with N ≥ 3. This is a
joint work with Professor Yoshihiro Shibata (Waseda University).
71 渡 邊 圭 市 (早 大 理 工)

Keiichi Watanabe (Waseda Univ.)

Stability of stationary solutions to a free boundary problem of theNavier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stability of stationary solutions to a free boundary problem of theNavier–Stokes equations

概 要 We consider the stability of the equilibrium figure of uniformly rotating viscous incompressible fluidin R3 with surface tension, where the equilibrium figure is rotationally symmetric about a certain axis. It is
proved that this stability result can be characterized by the positivity of the second variation of the energyfunctional associated with the equation that determines an equilibrium figure, provided that initial data
are close to an equilibrium state. The solution converges exponentially to an equilibrium. The proof isinspired by a series of papers due to Shibata, but a new orthogonal condition is introduced in order to show
the exponential stability of an associated analytic C0 -semigroup. If a value of initial angular momentum issmall, the steady-state is determined uniquely.

最終版: 2022/8/861函数方程式論72 藤 井 幹 大 (九 大 数 理)
渡 邊 圭 市 ( 早 大 理 工)
Mikihiro Fujii (Kyushu Univ.)
Keiichi Watanabe (Waseda Univ.)

Compressible Navier–Stokes–Coriolis system in critical Besov spaces · · 10
Compressible Navier–Stokes–Coriolis system in critical Besov spaces

概 要 We consider the three dimensional compressible Navier–Stokes equations with the Coriolis force andprove the long-time existence of a unique strong solution. More precisely, we show that for any 0 < T < ∞and arbitrary large initial data in the scaling critical Besov spaces, the solution uniquely exists on [0, T ]provided that the Rosbby and Mach numbers are sufficiently small. To the best of our knowledge, ourresult is the first contribution to the well-posedness of the compressible Navier–Stokes–Coriolis system in
the whole space R3 . The key ingredient of our analysis is to establish the dispersive estimates despite acomplicated structure of the linearized system due to the anisotropy of the Coriolis force.
73 梶 原 直 人 (岐 阜 大 工)
Naoto Kajiwara(Gifu Univ.)

Maximal regularity for the Stokes equations with various boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Maximal regularity for the Stokes equations with various boundary conditions

概 要 It is known that resolvent esimates and maximal regularity are important topics for linear parabolic

evolution equations. We prove these estimates for the Stokes equations with various boundary conditions
in a unite way. The method is applied for Dirichlet, Neumann and Robin boundary although the talk ispresented only main ideas. The basis is to obtain a suitable form of the solution. Then we use a useful
sufficient condition to use Fourier multiplier theorem and Lq -Lq -boundedness in the half space. Since thesymbols are R-bounded for λ, we can get maximal regularity at the same time.
17:00〜18:00

特別講演

寺 澤 祐 高 (名 大 多 元 数 理) [ 二層流の非局所拡散界面モデルの弱解およびその局所漸近Yutaka Terasawa (Nagoya Univ.)

Weak solutions of nonlocal diffuse interface model for two-phase flows
and those local asymptotics

概 要 We talk on existence of weak solutions for local and nonlocal diffuse interface models for two-phaseflows and nonlocal-to-local asymptotics of them, some of which are the speaker’s recent results. The talkis based on joint works with Helmut Abels (Regensburg Univ., Germany). Diffuse interface models for
two-phase flows describe the behavior of a mixture of two kinds of fluids such as water and oil. The fluids
are macroscopically immiscible, but the model takes a partial mixing on a small length scale measured bya small parameter into account. A classical diffuse interface model treating fluids with the same densities
and different viscosities is due to Hohenberg and Halperin (1977). More recently, a model treating fluidswith different densities were introduced by Abels, Garcke and Gruen (2012). This is a coupled system of
the Navier–Stokes equations and the Cahn–Hilliard equations. If the chemical potential contains a elliptic
operator acting on a order parameter, which is a concentration difference of two fluids, it is called a local
model and if the chemical potential contains a nonlocal operator, it is called a nonlocal model. Frigeri (2015)
proved the existence of weak solutions for some nonlocal diffuse interface model with different densities. We
review his result and method of proof. We next explain the speaker’s result with Abels (2020) on existenceof weak solution for another nonlocal diffuse interface model containing some kind of fractional Laplacian.
We moreover explain the speaker’s recent result with Abels (2022) on convergence of weak solutions for thenonlocal model with a small parameter to weak solutions for the local model when the small parameter
tends to zero. The proof is based on a corresponding result in the case of a single Cahn–Hilliard equation
by Davoli, Scarpa and Trussardi (2021).

最終版: 2022/8/8
実函数論

実

函

数

9 月 15 日（木）62

論第 VIII 会場

9:30〜11:30
1 水 口 洋 康 (関西大システム理工)

Hiroyasu Mizuguchi (Kansai Univ.)

ある幾何学的定数の下限値について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the lower bound of a geometric constant in normed linear space

概 要 To describe the geometry of normed space, many geometric constants have been investigated. Amongthem, there are two geometric constants related to Minkowski ellipses. Here we study the lower bound of
one of them. We also consider Birkhoff orthogonality. This generalized orthogonality is not symmetric ingeneral. A two-dimensional normed plane in which Birkhoff orthogonality is symmetric is called Radon
plane. An inequality had shown in Radon planes will be proved in general spaces.
2 青 山 耕 治 ( 千 葉 大 社 会)
Koji Aoyama(Chiba Univ.)

吸引点と擬非拡大拡張 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A quasinonexpansive extension of a mapping with an attractive point

概 要 We show that, under appropriate conditions, there exists a quasinonexpansive extension of a mappingwith an attractive point in the sense of Takahashi and Takeuchi (2011) such that the fixed point set of theextension equals the attractive point set of the given mapping. Then using the quasinonexpansive extension,
we establish some convergence theorems for approximating attractive points of a generalized hybrid mappingin the sense of Kocourek, Takahashi, and Yao (2010).
3 木 村 泰 紀 ( 東 邦 大 理)
Yasunori Kimura (Toho Univ.)

完備測地距離空間における不動点近似法の比較 · · · · · · · · · · · · · · · · · · · · · 15

Comparison of approximation methods of fixed points for a complete
geodesic space

概 要 In this talk, we compare several types of approximation methods of a fixed point of a mapping definedon a complete geodesic space. In particular, one can see that some projection methods are related to thosegenerated by convex combinations. We also show a new approximation method convergent to a fixed pointof a mapping defined on a complete geodesic space.
4 河 邊
淳 ( 信 州 大 工)
山 田 直 貴Jun Kawabe (Shinshu Univ.)
Naoki Yamada

Choquet 積分が定める Lorentz 空間の完備性 · · · · · · · · · · · · · · · · · · · · · · · 15
The completeness of the Lorentz spaces defined by the Choquet integral

概 要 In this talk, the Choquet–Lorentz spaces are defined for a nonadditive measure µ and the completenessof the spaces is investigated. A new characteristic of nonadditive measures, called property (C), is introduced
to establish the Cauchy criterion for convergence in µ-measure of measurable functions. This criterion anda suitable convergence theorem of the Choquet integral provide instruments for showing the completenessof the Choquet–Lorentz spaces.
5 齋 藤 洋 樹 ( 日 大 理 工)
田 中
仁 ( 筑 波 技 術 大)
(Nihon Univ.)
Hiroki Saito
Hitoshi Tanaka(Tsukuba Univ. of Tech.)

Choquet integrals, Hausdorff content and sparse operator · · · · · · · · · · · 15
Choquet integrals, Hausdorff content and sparse operator

概 要 In this talk, we show that the sparse operators are not weak (1, 1) on the Choquet space with theHausdorff content. In view of this result, we define a variant of the Orlicz–Morrey–Choquet space, andprove that the sparse operator maps Choquet space to the Orlicz–Morrey–Choquet space.

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63

実函数論

6 齋 藤 洋 樹 ( 日 大 理 工)
Hiroki Saito(Nihon Univ.)

A note on embedding inequalities for weighted Sobolev and Besov space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A note on embedding inequalities for weighted Sobolev and Besov space

概 要 In this talk, we establish two embedding inequalities for the weighted Sobolev space and the weighted

homogeneous endpoint Besov space by using the weighted Hausdorff capacity. To do this, we shall determine
the dual spaces of weighted Choquet and weighted homogeneous Besov spaces.
14:15〜16:20
7 岡 本

潤 (京 大 A S H B i )Jun Okamoto(Kyoto Univ.)

On a singular limit of the Kobayashi–Warren–Carter energy · · · · · · · · · 15
On a singular limit of the Kobayashi–Warren–Carter energy

概 要 We consider the singular limit problem of a single-well Modica–Mortola energy and the Kobayashi–

Warren–Carter energy. In this study, we introduce a finer topology of sliced graph convergence of functions
into the function space and derive the singular limit of a single-well Modica–Mortola energy and the
Kobayashi–Warren–Carter energy energies in the sense of Gamma-convergence. The energy functional
obtained as this singular limit is also shown to have the remarkable property of a minimizing function thatis concave concerning the strength of jumps of a function.
8 筒 井 容 平 (京大理)Youhei Tsutsui (Kyoto Univ.)

Rearrangements, medians and their maximal functions · · · · · · · · · · · · · · 15
Rearrangements, medians and their maximal functions

概 要 We give an exact expression of the set of all medians with non-increasing rearrangements. After that,

we consider fractional maximal functions with rearrangements and medians instead of integral averages, anddiscuss their boundedness on Lorentz spaces.
9 川 澄 亮 太 ( 中 大 理 工)
Ryota Kawasumi (Chuo Univ.)

Pointwise multipliers on Orlicz–Morrey spaces of the second kind · · · · 15
Pointwise multipliers on Orlicz–Morrey spaces of the second kind

概 要 In this talk we give the characterization of pointwise multipliers on Orlicz–Morrey spaces of the second

kind. Orlicz–Morrey spaces of the second kind was first studied by Sawano, Sugano and Tanaka in 2012 andare difference from Orlicz–Morrey spaces of the first kind which was first studied by Nakai in 2004. To dothis we first prove a generalized Hölder’s inequality for the Orlicz–Morrey spaces of the second kind. Next,
to characterize the pointwise multipliers, we use the fact that all pointwise multipliers from a Orlicz–Morrey
space of the second kind to another Orlicz–Morrey space of the second kind are bounded operators.
10 宮 崎 洋 一 (日大歯)Yoichi Miyazaki (Nihon Univ.)

BMO ノルムを含む対数型 Sobolev 不等式の改良 · · · · · · · · · · · · · · · · · · · · 15
Improvement of the logarithmic Sobolev inequalities with BMO norm

概 要 In this talk we show that the inequalitiesno∥f ∥L∞ ≤ C 1 + ∥f ∥BM O log+ (∥f ∥Lp + ∥(−∆)s/2 f ∥Lq ) ,no∥f ∥L∞ ≤ C 1 + ∥f ∥Lp + ∥f ∥BM O log+ ∥(−∆)s/2 f ∥Lqhold if f ∈ Lp (Rn ) and (−∆)s/2 f ∈ Lq (Rn ) for 1 ≤ p < ∞, 1 < q < ∞ and n/q < s < ∞. These inequalities
improve the results obtained by Kozono–Taniuchi (2000) and Kozono–Wadade (2008). The proof is basedon Muramatu’s integral formula.

最終版: 2022/8/8
実函数論

11 至 田 直 人 (阪

大

理)

64

m
Boundedness of bilinear pseudo-differential operators with BS0,0
sym-

bols on Sobolev spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Naoto Shida(Osaka Univ.)mBoundedness of bilinear pseudo-differential operators with BS0,0
symbols on Sobolev spaces

概 要 We consider bilinear pseudo-differential operators with symbols in the bilinear Hömander classes S0,0 .

In particular, we discuss the boundedness of these operators on Sobolev spaces by using symbolic calculus
and some boundedness results for bilinear pseudo-differential operators with symbols in more general classes
than the bilinear Hömander classes on Lebesgue spaces. In contrast to the linear case, we need some
restrictions on the exponents of Sobolev spaces to assure the boundedness, and we also discuss the necessityof these restrictions.
12 原

宇 信 ( 北 大 情 報)

Takanobu Hara (Hokkaido Univ.)

特異楕円型問題と Sobolev 型の埋め込みについて · · · · · · · · · · · · · · · · · · · 15

On singular elliptic problems and Sobolev type embeddings

概 要 We discuss model semilinear elliptic equations of the type −div(A(x)∇u) = f u−λ in Ω, where Ω is abounded domain in RN , A ∈ L∞ (Ω)N ×N is a coercive matrix, 0 < λ ≤ 1 and f is a nonnegative Radon
measure on Ω. We consider various properties of positive H01 (Ω)-solutions in relation to the corresponding
Sobolev type embedding.
16:40〜17:40

特別講演
飯 田 毅 士 ( 福 島 工 高 専)

Takeshi Iida
(Fukushima Nat. Coll. of Tech.)

Lp 空間と Morrey 空間上の Orlicz 極大作用素について
Orlicz maximal operators on Lp and Morrey spaces

概 要 In this talk, we deal with boundedness for Orlicz maximal operators and Orlicz-fractional maximal

operators on Lp spaces and Morrey spaces. Next, we define and classify Orlicz–Morrey spaces into threekinds. Then, we study the boundedness of the Orlicz maximal operator and the Orlicz-fractional maximal
operator on the second kind of the Orlicz–Morrey space, which we plan to focus our study on the second
kind of the Orlicz–Morrey space.

9 月 16 日（金）第 VIII 会場

9:30〜11:50
13 赤 川 佳 穂 (岐 阜 工 高 専)
加 納 理 成 ( 高 知 大 教 育)
深 尾 武 史 ( 京 都 教 育 大)
Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)(Kochi Univ.)
Risei Kano
Fukao Takeshi (Kyoto Univ. of Edu.)

ある完全塑性モデルの閾値関数のなめらかさについて · · · · · · · · · · · · · · · 15

Time-dependence of the thereshold function in a perfect plasticity model

概 要 This paper discusses the time-dependence of the threshold function in the perfect plasticity model.

In physical terms, it is natural that the threshold function depends on some unknown variable. Therefore,
it is meaningful to discuss the well-posedness under the weaker assumption of time-dependence.

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実函数論

14 千 代 祐 太 朗 (東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

Yutaro Chiyo (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Stabilization in a quasilinear attraction-repulsion chemotaxis system:
balanced case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Stabilization in a quasilinear attraction-repulsion chemotaxis system:
balanced case

概 要 This talk deals with global existence, boundedness and stabilization in a quasilinear parabolic-elliptic-

elliptic attraction-repulsion chemotaxis system. Boundedness and blow-up in this system have been classified
by the sizes of the effects of the attraction and repulsion (Z. Angew. Math. Phys.; 2022; 73; Paper No.
61). More precisely, in the case that the effect of the attraction is stronger than the one of the repulsion,boundedness has been shown. Also, in the opposite case, blow-up has been obtained. However, the casethat the effects of the attraction and repulsion are balanced has been excluded. The purpose of this talk isto prove boundedness and stabilization in the balanced case.
15 小 杉 千 春 (日 本 女 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)

Chiharu Kosugi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

圧縮性弾性体の伸縮運動を表す初期値境界値問題の時間無限大における解の挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A large time behavior of solutions to initial and boundary value problems for compressible elastic curves

概 要 We talk about a large time behavior of the solutions to the initial and boundary value problem forthe beam equation with the viscosity term and the nonlinear stress function having a singularity. We havealready shown the existence and uniqueness of weak solutions. Moreover, thanks to the estimate of lower
bounds for the strain, we also proved the existence of strong solutions. In this talk, for a solution u, we
prove that the ω - limit of the orbit {u(t)|t ≥ 0} is not empty and included in the set of steady solutions.
Also, we give an example in which the solutions of the steady problem are not uniquely determined.
16 久 保 田 翔 大 (神 奈 川 大 工)
白 川
健 ( 千 葉 大 教 育)

Shodai Kubota (Kanagawa Univ.)
Ken Shirakawa (Chiba Univ.)

結晶粒界運動を記述する KWC システムに対する時間周期解 · · · · · · · · · 15

Periodic solutions for KWC type systems of grain boundary motions

概 要 In this talk, we consider the periodic solutions for the parabolic PDE systems, denoted by (S). Eachsystem (S) is associated with the phase-field model of grain boundary motion, proposed by [Kobayashi etal.; Phys. D, 140 (2000), 141–150]. Under suitable assumptions, the existence of the periodic solution to
the system (S) will be reported as the main theorem of this talk.
17 香 川 渓 一 郎 (早 大 理 工)大⋆)大 谷 光 春 (早Keiichiro Kagawa (Waseda Univ.)Ôtani Mitsuharu (Waseda Univ.⋆)

Existence of solutions for initial value problem of viscous Cahn–Hilliard
equation with dynamic boundary condition · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence of solutions for initial value problem of viscous Cahn–Hilliard
equation with dynamic boundary condition

概 要 In 2011, Goldstein, Miranville, and Schimperna proposed the Cahn–Hilliard model with dynamic

boundary condition (GMS model). In 2015, Colli and Fukao showed the existence of the solutions to theinitial value problem of the GMS model. They considered the nonlinear terms appearing in the interiorand surface equations as the sum of the monotone term and the global Lipschitz term and assume that thecondition (A) where the interior monotone term is controlled by the surface monotone term holds. In thistalk, we focus on the existence of solutions to the initial value problem with viscous terms. We extend theglobal Lipschitz term to apply to a wider class of nonlinear functions and assume that the restriction (A) or
the growth rate on the inner monotone term holds.

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実函数論

18 喜 多 航 佑 (早 大 理 工)
大 谷 光 春 ( 早 大 理 工)
Kosuke Kita (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

66

Existence and nonexistence of global solutions to nonlinear diffusion
equations on a bounded domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence and nonexistence of global solutions to nonlinear diffusion
equations on a bounded domain

概 要 This talk is devoted to studying the existence and nonexistence of global solutions to nonlinear diffusion

equations with nonlinear boundary conditions. In the whole space, it is well known that the critical Fujita
exponent exists, which gives the threshold that divides the existence of global solutions. On the other hand,
there is no such a critical exponent in the case of a bounded domain. However, we show that the thresholdphenomenon, controlled according to boundary conditions, can occur in a bounded domain.
19 黒 田 隆 徳 (早 大 理 工)
大 谷 光 春 ( 早 大 理 工)
T. Cazenave (Sorbonne Univ.)

Existence and non-existence of stationary solutions of the complex Ginzburg–
Landau equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Takanori Kuroda (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)
Thierry Cazenave (Sorbonne Univ.)

Existence and non-existence of stationary solutions of the complex Ginzburg–
Landau equations

概 要 In this talk, we study the stationary problem for the complex Ginzburg–Landau equations (CGL) on

bounded domain Ω:−(λ + iα)∆u − (κ + iβ)|u|q−2 u = 0,u|∂Ω = 0,

where q > 2, λ, κ > 0 and α, β ∈ R. Since multiplying (CGL) by u, we may prove the non-existence of weak
nontrivial solutions when α/λ ̸= β/κ, we consider the case where α/λ = β/κ. Our results can be formulated
as follows: when N = 1, then there exists no non-constant phase classical solution; when N ≥ 2 and let q
be Sobolev sub-critical, then there exists a non-constant phase solution for some domains; when N ≥ 2 andlet q be Sobolev critical or super-critical, then there exists no nontrivial classical solution including constantphase solutions on star-shaped domains.
20 来 間 俊 介 (東 京 理 大 理)

Shunsuke Kurima (Tokyo Univ. of Sci.)

Convergence of a singular nonlocal phase field system of conserved type
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Convergence of a singular nonlocal phase field system of conserved type

概 要 This talk deals with convergence of a singular nonlocal phase field system of conserved type. Colli–

K. (2020) have proved existence of solutions to a singular phase field system of conserved type. On theother hand, Davoli–Scarpa–Trussardi (2021) have studied nonlocal-to-local convergence of Cahn–Hilliard
equations. In this talk we focus on nonlocal-to-local convergence of singular nonlocal phase field systems ofconserved type.

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67

実函数論

14:15〜16:20
21 池 田 正 弘(理化学研 AIP・慶大理工)内 田俊 ( 大 分 大 理 工)
深 尾 武 史 ( 京 都 教 育 大)

Masahiro Ikeda (RIKEN/Keio Univ.)(Oita Univ.)
Shun Uchida
Takeshi Fukao (Kyoto Univ. of Edu.)

Heat equation on the hypergraph containing vertices with given data
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Heat equation on the hypergraph containing vertices with given data

概 要 Hypergraph G is the triplet consisting of a finite set V , a family E ⊂ 2V , and w : E → (0, ∞).

We are concerned with an ODE governed by some nonlinear set-valued operator defined on RV , whichis called “hypergraph Laplacian”. This ODE can be interpreted as a model of “heat” diffusion in the
network represented by hypergraph. In this talk, we consider the case where the heat at some vertices of
the hypergraph is given, and discuss the existence of solution and the continuous dependence of solution on
given data.
22 熊 崎 耕 太 (長 崎 大 教 育)

Kota Kumazaki (Nagasaki Univ.)

多孔質媒体内の拡散物質の浸透を表すある自由境界問題の解の時間大域的挙動 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Large time behavior of a solution to a free boundary problem describing
the penetration of diffusant into rubber

概 要 In this talk, we consider a one-dimensional free boundary problem describing the penetration ofdiffusant into rubber. In this problem, the free boundary represents the front of the diffusant region and its
growth rate is given by an ordinary differential equation including the effect of breaking the growth of the
diffusant region. In the previous result, we showed the existence and uniqueness of a local solution to our
problem. In this talk, we discuss the existence and uniqueness of a global solution to the problem and thelarge-time behavior of a solution as time goes to infinity.
23 渡 邉紘 ( 大 分 大 理 工)

Hiroshi Watanabe (Oita Univ.)

放物型・双曲型単独保存則のエントロピー解に対する時間減衰評価 · · · · 15

Decay estimates for entropy solutions to scalar parabolic-hyperbolic conservation laws

概 要 We consider one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation laws.

The equation has both properties of hyperbolic equations and those of parabolic equations. Accordingly, it
is difficult to investigate the regularity and the behavior of solutions to (CP). In this talk, we prove decay
estimates for entropy solutions to (CP). To see this, we modify Oleinik type entropy estimates for them.
大理)
24 黒 田 紘 敏 (北M. Lasica(Polish Acad. of Sci.・東大数理)儀 我 美 一 ( 東 大 数 理)

Hirotoshi Kuroda (Hokkaido Univ.)
Michal Lasica(Polish Acad. of Sci./Univ. of Tokyo)
Yoshikazu Giga (Univ. of Tokyo)

全空間における 4 階の全変動流方程式の球対称解 · · · · · · · · · · · · · · · · · · · 15

Radial solutions to the fourth-order total variation flow in Rn

概 要 In this talk we consider the fourth-order total variation flow equation in Rn . We characterize thesolution in terms of what is called the Cahn–Hoffman vector field, based on a duality argument, andintroduce a notion of calibrability of a set in our fourth-order setting. This notion is related to whether acharacteristic function preserves its form throughout the evolution. It turns out that all balls are calibrable.
However, unlike in the second-order total variation flow, the outside of a ball is calibrable if and only ifn ̸= 2. If n ̸= 2, all annuli are calibrable, while in the case n = 2, if an annulus is too thick, it is notcalibrable.

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実函数論

25 深 尾 武 史 (京 都 教 育 大)
P. Colli(Univ. degli Studi di Pavia)
L. Scarpa(Politecnico di Milano)

Takeshi Fukao (Kyoto Univ. of Edu.)
Pierluigi Colli(Univ. degli Studi di Pavia)
Luca Scarpa (Politecnico di Milano)

68

前方後方動的境界条件を持つ Cahn–Hilliard 方程式に対する粘性消滅法· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Cahn–Hilliard equation with forward-backward dynamic boundary
condition via vanishing viscosity

概 要 An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn–Hilliard

type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus
obtaining a forward-backward dynamic boundary condition at the limit. This is done in a very general
setting, with nonlinear terms admitting maximal monotone graphs both in the bulk and on the boundary.
The two graphs are related by a growth condition, with the boundary graph that dominates the otherone. It turns out that in the limiting procedure the solution of the problem looses some regularity and thelimit equation has to be properly interpreted in the sense of a subdifferential inclusion. However, the limit
problem is still well-posed since a continuous dependence estimate can be proved.
26 白 川健 ( 千 葉 大 教 育)久 保 田 翔 大 ( 神 奈 川 大 工)
Ken Shirakawa (Chiba Univ.)
Shodai Kubota (Kanagawa Univ.)

Optimal inner-heat controls of Warren–Kobayashi–Lobkovsky–Carter
type systems under higher dimensional settings · · · · · · · · · · · · · · · · · · · · 15
Optimal inner-heat controls of Warren–Kobayashi–Lobkovsky–Carter
type systems under higher dimensional settings

概 要 In this talk, we deal with the optimal control problem motivated by grain boundary motion in 2 or 3

dimensional space. In this light, the regularized version of the phase-field model, proposed by [Warren etal.; Acta Materialia, 51 (2003), 6035–6058], is adopted as the corresponding state system. Under suitable
assumptions, the well-posedness of state system, and the existence and necessary condition for the optimal
control will be presented as the main results of this talk.
27 山 崎 教 昭 (神 奈 川 大 工)葉大⋆)剣 持 信 幸 (千白 川
健 ( 千 葉 大 教 育)

Noriaki Yamazaki (Kanagawa Univ.)
Nobuyuki Kenmochi (Chiba Univ.⋆)
Ken shirakawa (Chiba Univ.)

Singular optimal control problems for doubly nonlinear evolution inclusions with quasi-variational structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Singular optimal control problems for doubly nonlinear evolution inclusions with quasi-variational structure

概 要 In this talk we consider singular optimal control problems for abstract doubly quasi-variational

evolution inclusions governed by time-dependent subdifferentials with the unknown-dependent constraints.
Then, we show the existence of optimal control for our problems. Also, we apply our abstract results toquasi-variational inequalities with time-dependent gradient constraints.

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69

実函数論

16:40〜17:40

特別講演
水 上 雅 昭 ( 京 都 教 育 大)

ある chemotaxis-consumption 系の解の存在と挙動について

Masaaki Mizukami(Kyoto Univ. of Edu.)

Global existence and asymptotic behavior in some chemotaxis-consumption
system概 要 In the study of the chemotaxis systems asymptotic behavior of solutions is one of the important

themes; mainly it is shown that solutions converge to constant steady states in the previous works. For
example, Tao–Winkler (2012) considered a chemotaxis-consumption system, and derived that solutionsof the problem converge to constant steady states. However, this result does not describe some patternformation of species suggested by Tuval et.al. (2005). Here one of the reasons is the boundary condition
for the oxygen in the problem; in the previous works the boundary conditions is the Neumann boundary
condition, even though that suggested in Tuval et, al. is a Robin-type boundary conditions. Thus, thistalk considers a chemotaxis-consumption system under realistic boundary conditions for the oxygen. The
purpose of this talk is to show that solutions of the problem converge to non-constant steady states.

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函数解析学

函

数

解

9 月 13 日（火）

析

70

学

第 I 会場

10:00〜11:45
1 岩 田 順 敬 (関西大化学生命工)
Yoritaka Iwata (Kansai Univ.)

2 次および 3 次の非線形性に由来する非線形半群の生成 · · · · · · · · · · · · · · 15
Generation of nolinear semigroup associated with second or third ordernonlinearity

概 要 Nonlinear abstract evolution equations in a Banach space X:du(t)= A2 (t)(u(t) + ū)(u(t) − ū),dt
du(t)= A3 (t)u(t)(u(t) + ū)(u(t) − ū)dt
are systematically studied by the logarithmic representation of operators. In conclusion representations forthe nonlinear semigroup are obtained.
2 佐 々 木 格 (信 州 大 理) [ A general theory of diagonalization by Bogoliubov transformations · · · 15
Itaru Sasaki(Shinshu Univ.)

A general theory of diagonalization by Bogoliubov transformations

概 要 It is believed that quantum field models whose interactions are quadratic can be diagonalized by

Bogoliubov transformations. However, in many cases, the construction of the Bogoliubov transformation
was complicated. Here we construct Bogoliubov transformations that explicitly diagonalize a wide class ofquadratic Hamiltonians. For relativistic particles, the resulting one-particle Hamitltonians turn out to be
the square root of non-relativistic Schrodinger operators with trace class perturbation.
3 川 本 昌 紀 ( 愛 媛 大 理 工)
石 田 敦 英 ( 東 京 理 大 教 養)

Masaki Kawamoto (Ehime Univ.)
Atsuhide Ishida (Tokyo Univ. of Sci.)

臨界係数を持つ時間減衰調和振動子に対する波動作用素の存在・非存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence and nonexistence of wave operators for critical time-decaying
harmonic oscillator

概 要 The critical time-decaying harmonic oscillator decelerate a quantum particle but whose probability ofthe position growth like t1/2 log t. Because of its log growth term, the threshold of the decay order of thepotential, in order to exist the wave operators, can not be characterized only by the polynomial decay rate.
Hence we give the log-weight in x to the potential and the characterize the threshold using growth order oflog-weight.
4 廣 島 文 生 ( 九 大 数 理)大理)
寺 西 功 哲 (北Fumio Hiroshima (Kyushu Univ.)
Noriaki Teranishi (Hokkaido Univ.)

1 次元調和振動子に付随した時間作用素の行列表現 · · · · · · · · · · · · · · · · · · 15
Matrix representation of time operators of 1D harmonic oscillator

概 要 A time operator of the one-dimensional harmonic oscillator is rigorously constructed in the sense of

sesqui-linear form, and the continuous limit of the time operator is shown. Finally a matrix representationof the time operator and its analytic continuation are given.

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71

函数解析学

大
理)
5 寺 西 功 哲 (北廣 島 文 生 ( 九 大 数 理)

Noriaki Teranishi (Hokkaido Univ.)
Fumio Hiroshima (Kyushu Univ.)

調和振動子における phase 作用素の一般化 · · · · · · · · · · · · · · · · · · · · · · · · · 15

A genralization of the phase operator

概 要 We study about time operators of the quantum harmonic oscillator H. It is known that H is unitaryequivarent to the number operator N + 1/2 on `2 (N). We construct time operators of N and show that a
relation between the phase operator and Galapon’s time operator.
6 P. Exner(Czech Tech. Univ.・Czech Acad. of Sci.)
中 村
周 ( 学 習 院 大 理)
只 野 之 英 ( 東 京 理 大 理)
Pavel Exner(Czech Tech. Univ./Czech Acad. of Sci.)
Shu Nakamura (Gakushuin Univ.)
Yukihide Tadano (Tokyo Univ. of Sci.)

Continuum limit of the lattice quantum graph Hamiltonian · · · · · · · · · 15

Continuum limit of the lattice quantum graph Hamiltonian

概 要 We consider a continuum limit problem of quantum graph Hamiltonians, that is, Schödinger operators

defined on metric graphs. We show that the quantum graph Hamiltonian on the ν-dimensional squarelattice `Zν with its mesh size ` converges as the continuum limit (` → 0) to the corresponding Schrödinger
operator on Rν in the sense of norm resolvent convergence.
14:15〜15:15

特別講演
梅 田 陽 子 ( 城 西 大 理)

A unified family of PJ -hierarchies (J=I,II,IV,34) with a large parameter(Josai Univ.)

A unified family of PJ -hierarchies (J=I,II,IV,34) with a large parameter

Youko Umeta

概 要 The exact WKB analysis is a very effective method in studying both linear and non-linear differential

equations which contain a large parameter in an appropriate way. We study the common structures between
PJ -hierarchies(J=I,II,IV,34) with a large parameter from a view point of the exact WKB analysis. The firstpart is the result concerning the Stokes geometry for a unified family of PJ -hierarchies(J=I,II,IV,34) with alarge parameter. We study the relation between the Stokes geometry of the system of non-linear ordinary
differential equations and that of its underlying Lax pair. In the second part, we construct instanton-type
solutions with sufficiently many free parameters which can describe the Stokes phenomenon of the Borel
sum of a 0-parameter solution.

9 月 14 日（水）第 I 会場

9:30〜12:00
7 伊 師 英 之 ( 阪 公 大 理)

Hideyuki Ishi (Osaka Metro. Univ.)

色付き等質グラフからの等質錐の構成 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Construction of homogeneous cones from colored homogeneous graphs

概 要 We show that the cone of positive definite symmetric matrices of a specific form defined from anundirected simple graph satisfying certain conditions and a subgroup of the automorphism group of thegraph is a homogeneous cone. In this way, we can construct many examples of homogeneous cones. We
mention some applications of integral formulas over the homogeneous cone to mathematical statistics. Thisis joint work with Piotr Graczyk (University of Angers) and Bartosz Kolodziejek (Warsaw University ofTechnology).

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函数解析学

8 中 島 秀 斗 ( 統 計 数 理 研)

Hideto Nakashima (Inst. of Stat. Math.)72

Sub-Hankel 行列式に付随する概均質ベクトル空間の b-関数と不変微分作
用素について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On b-functions and invariant differential operators of prehomogeneous
vector spaces associated with sub-Hankel determinants

概 要 In this talk, we give an explicit formula of Capelli-type identity of invariant differential operators on

a prehomogeneous vector space associated with sub-Hankel determinants. Moreover, an explicit formula ofmultivariate b-functions with respect to relatively invariant functions is also given.
9 西 山
享 ( 青 学 大 理 工)
L. Fresse(IECL, Univ. Lorraine)

Kyo Nishiyama (Aoyama Gakuin Univ.)
Lucas Fresse (IECL, Univ. Lorraine)

二重旗多様体上の Steinberg 理論と RSK 対応 · · · · · · · · · · · · · · · · · · · · · · 15

Steinberg theory for double flag varieties and RSK correspondence

概 要 Let G be a connected reductive algebraic group, and K its symmetric subgroup. By the double flag

variety of G/K, we mean a product of flag varieties of G and K. For a double flag variety associated with thesymmetric space of type AIII, we establish two kinds of generalized Steinberg maps, which sends conormal
bundles of K-orbits to nilpotent K-orbits in the Lie algebra of K and in the tangent space of the symmetricspace respectively. We described the Steinberg maps combinatorially, which generalize the classical RSK
correspondence for permutations.
10 西 山享 ( 青 学 大 理 工)
L. Fresse(IECL, Univ. Lorraine)

Kyo Nishiyama (Aoyama Gakuin Univ.)
Lucas Fresse (IECL, Univ. Lorraine)

二重旗多様体上の軌道空間へのヘッケ環の作用 · · · · · · · · · · · · · · · · · · · · · 15

Action of a Hecke algebra on the space of orbits on a double flag variety

概 要 Consider a connected reductive algebraic group G and its symmetric subgroup K. Let X = K/BK ×

G/P be a double flag variety of finite type, where BK is a Borel subgroup of K, and P a parabolic subgroupof G. A general argument shows that the orbit space C X/K inherits a natural action of the Hecke algebra
H = H (K, BK ) of double cosets via convolutions. However, to find out the explicit structure of the Hecke
module is a quite different problem. We will clarify the explicit action of H on C X/K in combinatorial
way using graphs for the double flag variety of type AIII.
11 笹 木 集 夢 (東 海 大 理)
Atsumu Sasaki(Tokai Univ.)

Invariant measures on non-symmetric reductive spherical homogeneous
spaces of rank-one type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Invariant measures on non-symmetric reductive spherical homogeneous
spaces of rank-one type

概 要 We give a description of invariant measures on non-symmetric reductive spherical homogeneous spacesof rank-one type. For this, we revisit a Cartan decomposition for a spherical homogeneous space andconsider the set of restricted roots associated to this decomposition. The idea of our description of invariant
measures is similar to that for semisimple symmetric spaces.

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73

函数解析学

12 甘 中 一 輝 (理 化 学 研) [ 3 次元コンパクト反ド・ジッター多様体の安定固有値の重複度 · · · · · · · · 15
Kazuki Kannaka(RIKEN)

Multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds

概 要 A Lorentzian manifold has an intrinsic second-order differential operator called the Laplacian as in a

Riemannian manifold. However, the Laplacian is no longer an elliptic but a hyperbolic differential operator,
and there are non-smooth eigenfunctions in general.
A Lorentzian manifold with negative constant sectional curvature is called an anti-de Sitter manifold, andespecially in the 3-dimensional case, its rich deformation theory is known to exist. In this talk, I will discuss
quantitative results on the behavior of multiplicities of eigenvalues of the Laplacian in the 3-dimensionalcase when deforming anti-de Sitter structures.
13 田 森 宥 好 (北大理)Hiroyoshi Tamori (Hokkaido Univ.)

On the existence of a nonzero linear period · · · · · · · · · · · · · · · · · · · · · · · · 15
On the existence of a nonzero linear period

概 要 Let D be a quaternion algebra over R, G = GLn (D) and H = GLn (C) regarded as a subgroupof G. For a character χ on C× , we say that an irreducible representation π of G is χH -distinguished if
HomH (π, χ ◦ detH ) ̸= 0. We compute the root number of a χH -distinguished representation π twisted by
the representation induced from χ, and prove an Archimedean analogue of the conjecture by Prasad and
Takloo-Bighash. The proof is based on the analysis of the contribution of H-orbits in a flag manifold of G on
the Schwartz homology of principal series representations. Moreover, we prove that the Schwartz homology
H∗ (H, π) is finite-dimensional for a general reductive symmetric pair (G, H) and a Casselman-Wallach
representation of G. This is a joint work with Miyu Suzuki (Kanazawa Univ.).
14 C. Reyes-Bustos(NTT 基礎数学研究センタ)
若 山 正 人(NTT基礎数学研究センタ・九大⋆)
Cid Reyes-Bustos(NTT Inst. for Funda. Math.)
Masato Wakayama(NTT Inst. for Funda. Math./Kyushu Univ.⋆)

Shifted non-commutative harmonic oscillators · · · · · · · · · · · · · · · · · · · · · 15

Shifted non-commutative harmonic oscillators

概 要 The non-commutative harmonic oscillator (NCHO) is a generalization of the quantum harmonic

oscillator that is related with the physical model called the quantum Rabi model via a confluence process
on their respective ODE pictures. A generalization of the QRM, called the asymmetric QRM, has a rich
structure in its hidden symmetry including a far-reaching conjecture relating its spectrum with algebraic
geometry. In this talk we define a generalization of the the NCHO, called the η-shifted NCHO, related
to the AQRM via a confluence process and give its basic properties. In addition we show how the finite
eigenvalues of the η-NCHO converge to the degenerate eigenvalues of the AQRM via the confluence process.
13:15〜14:15
跡 部

特別講演
大
発 (北

理) [ Local newforms for unramified odd unitary groups

Hiraku Atobe (Hokkaido Univ.)

Local newforms for unramified odd unitary groups

概 要 In this talk, we introduce a family of compact open subgroups of unramified odd unitary groups

over a p-adic field, and explain that for any irreducible generic representation, the subspaces fixed by thesecompact subgroups give a specific vector called a local newform, which is uniquely determined up to a scalarmultiple. This is an analogue of a well-known result of Jacquet–Piatetskii–Shapiro–Shalika for the case ofgeneral linear groups. For the proof, we establish the fundamental lemma for our compact groups. This isa joint work with Masao Oi in Kyoto University and Seidai Yasuda in Hokkaido University.

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函数解析学

9 月 15 日（木）74

第 I 会場

9:30〜12:00
15 古 市茂 ( 日 大 文 理)

Shigeru Furuichi (Nihon Univ.)

対数平均に関連した不等式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On inequalities related to logarithmic mean

概 要 After reviewing the ordering among some weighted means including the weighted logarithmic mean,

we state some operator inequalities related to logarithmic mean. We also give some inequalities for thenested means. In addition, we show the natural generalization of Zou–Jiang with weighted mean. Finally,
considering the geometric bridge between the arithmetic mean and the geometric mean, we study someunitarily invariant norm inequalities.
16 瀬 尾 祐 貴 (大阪教育大教育)
平 松
空 ( 泉 大 津 高)
Yuki Seo (Osaka Kyoiku Univ.)
Sora Hiramatsu(Osaka Prefectural Izumiohtsu High School)

Karcher 幾何平均と正規化行列式について · · · · · · · · · · · · · · · · · · · · · · · · · 15
Karcher mean and normalized determinant

概 要 As a natural generalization of the Fuglede–Kadison determinant, there is an attempt to extend theconcept of the determinant to vector states. In this talk, we present the normalized determinant for a state
on a von Neumann algebra, and by virtue of the Specht ratio, we show a variant of determinant identity of
Karcher mean for the normalized determinant of positive invertible operators on a separable Hilbert space.
17 内 山充(島根大⋆・立命館大総合科学技術研究機構)
Mitsuru Uchiyama(Shimane Univ.⋆ /Ritsumeikan Univ.)

Symmetric matrix means · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Symmetric matrix means

概 要 Let A and B be linearly independent positive definite matrices and σ a symmetric operator mean but

the arithmetic mean. We show that AσB is a linear combination of A and B if and only if A−1 B has justtwo different eigenvalues. Moreover, we get similar results for three-variable symmetric means.
18 宇 田 川 陽 一 (立 命 館 大 理 工)
大 坂 博 幸 ( 立 命 館 大 理 工)
山 崎 丈 明 ( 東 洋 大 理 工)
(Indian Inst. Tech.)
G. Ramesh

Yoichi Udagawa (Ritsumeikan Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)
Takeaki Yamazaki (Toyo Univ.)
Gola Ramesh (Indian Inst. Tech.)

Stability of AN -property for the induced Aluthge transformations · · · 15

Stability of AN -property for the induced Aluthge transformations

概 要 Let H be a Hilbert space. An operator T ∈ B(H) is AN (H)-operator if and only if there exists a unit

vector x ∈ B(H) such that ∥T |M x∥ = ∥T |M ∥ for any closed subspace M ⊆ H. In this talk, we shall discussstability of An-property. Especially, we shall introduce that if T ∈ AN (H), then the induced Aluthgetransformation of T ∈ AN (H). Moreover, we shall consider the iteration of mean transformation.

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75

函数解析学

19 大 坂 博 幸 (立 命 館 大 理 工)
G. Ramesh(Indian Inst. of Tech. Hyderabad)

Hiroyuki Osaka (Ritsumeikan Univ.)
Golla Ramesh(Indian Inst. of Tech. Hyderabad)

On a subclass of norm attaining operators · · · · · · · · · · · · · · · · · · · · · · · · 15

On a subclass of norm attaining operators

概 要 A bounded linear operator T : H1 → H2 , where H1 , H2 are Hilbert spaces, is said to be norm attaining

if there exists a unit vector x ∈ H such that ∥T x∥ = ∥T ∥ and absolutely norm attaining (or AN -operator) if
T |M : M → H2 is norm attaining for every closed subspace M of H. Let RT denote the set of all reducing
subspaces of T . Define β(H) := {T ∈ B(H) : T |M : M → M is norm attaining ∀ M ∈ RT }. In this talkwe present a structure theorem for operators in β(H).
20 羽 鳥

理 (新

潟

大⋆)

Osamu Hatori (Niigata Univ.

⋆)

The complex Mazur–Ulam property for extremely C-regular spaces · · · 15
The complex Mazur–Ulam property for extremely C-regular spaces

概 要 We exhibit a sufficient condition for the complex Mazur–Ulam property. In particular, we show thata uniformly closed extremely C-regular space has the complex Mazur–Ulam property.
21 大 井 志 穂 (新 潟 大 理)
(Niigata Univ.)

Shiho OiC ∗ 環に値をとるリプシッツ環上の Jordan ∗ 準同型写像 · · · · · · · · · · · · · 15
Jordan ∗-homomorphisms on Banach algebras of vector-valued Lipschitz
maps

概 要 In this talk, we consider Jordan ∗-homomorphisms on Banach ∗-algebras of all Lipschitz maps froma compact metric space into a unital C ∗ -algebra. We show that every Jordan ∗-homomorphism on thespace is represented as a weighted composition operator by using the irreducible representations of a unitalC ∗ -algebra. Our results generalize previous works on algebra ∗-homomorphisms on the space of all Lipschitz
maps from a compact metric space into a unital C ∗ -algebra.
22 森

迪 也 (理化学研iTHEMS)

Michiya Mori

(RIKEN)

Lattice isomorphisms between projection lattices of von Neumann algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Lattice isomorphisms between projection lattices of von Neumann algebras

概 要 Let M, N be von Neumann algebras, and P(M ), P(N ) their projection lattices. I will explain thatevery lattice isomorphism from P(M ) onto P(N ) can be described by means of a ring isomorphism between
the algebras of locally measurable operators if M has no direct summands of type I1 and I2 . If M has
no finite type I direct summands, then every ring isomorphism between the algebras of locally measurable
operators of M and N is similar to a real ∗ -isomorphism.
14:15〜16:00
23 井 上寛 ( 九 州 産 大 経 済)

Hiroshi Inoue (Kyushu Sangyo Univ.)

An unbounded generalization of Tomita’s observable algebras · · · · · · · · 15
An unbounded generalization of Tomita’s observable algebras

概 要 In this talk I shall introduce the basic theory of Tomita’s observable algebras and build the basic theoryof unbounded Tomita’s observable algebras which are related to unbounded operator algebras, especiallyunbounded Tomita-Takesaki theory, operator algebras on Krein spaces, studies of positive linear functionals
on ∗-algebras and so on.

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函数解析学

24 磯 野 優 介 (京 大 数 理 研)
Yusuke Isono(Kyoto Univ.)

76

Pointwise inner automorphisms of almost periodic factors · · · · · · · · · · · 15
Pointwise inner automorphisms of almost periodic factors

概 要 We prove that a large class of nonamenable almost periodic type III1 factors M , including all McDuff

factors that tensorially absorb the Araki–Woods factor R∞ of type III1 and all free Araki–Woods factors,
satisfy Haagerup–Størmer’s conjecture (1988): any pointwise inner automorphism of M is the compositionof an inner and a modular automorphism. This is joint work with C. Houdayer.
25 武 石 拓 也 (京都工繊大基盤)( Univ. Glasgow )C. Bruce

Takuya Takeishi (Kyoto Inst. Tech.)
Christopher Bruce (Univ. Glasgow)

Constructing number field isomorphisms from *-isomorphisms of certain
crossed product C*-algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Constructing number field isomorphisms from *-isomorphisms of certain
crossed product C*-algebras

概 要 We prove that the class of crossed product C*-algebras associated with the action of the multiplicative

group of a number field on its ring of finite adeles is rigid in the following explicit sense: Given any*-isomorphism between two such C*-algebras, we construct an isomorphism between the underlying number
fields. As an application, we prove an analogue of the Neukirch–Uchida theorem using topological fullgroups, which gives a new class of discrete groups associated with number fields whose abstract isomorphismclass completely characterises the number field.
26 𠮷 田 啓 佑 (北大教育推進機構)

Keisuke Yoshida (Hokkaido Univ.)

Non-commutative topological entropy for some Exel–Laca algebras · · · 15
Non-commutative topological entropy for some Exel–Laca algebras

概 要 In this talk, I will discuss non-commutative entropy for the canonical ucp (unital completely positive)

maps on Exel–Laca algebras associated to some infinite 0-1 matrices. In the first half of the talk, I showthat one can define the canonical ucp maps on Exel–Laca algebras associated to some infinite 0-1 matrices.
In particular, we see that we have the canonical ucp map on the Exel–Laca algebras associated with therenewal shift. In the last half of the talk, I show an evaluation of the non-commutative entropy for thecanonical ucp map on the Exel–Laca algebras associated with the renewal shift.
27 梶 原毅 (岡山大環境理工)大⋆)
綿 谷 安 男 (九Tsuyoshi Kajiwara (Okayama Univ.)
Yasuo Watatani (Kyushu Univ.⋆)

自己相似写像の直積に付随する C*環のコア · · · · · · · · · · · · · · · · · · · · · · · · 15

Cores of the C*-algebras associated with self-similar maps

概 要 In this talk, we report that the products of self-similar sets which satisfies simple condition arecontained in the class where we can do matrix representation, analysis of the restriction of model traces tothe finite core, and the structure of primitive ideals of the cores.
大⋆)28 綿 谷 安 男 (九渚勝
(千葉大理・立命館大理工)

Yasuo Watatani (Kyushu Univ.⋆)
Masaru Nagisa(Chiba Univ./Ritsumeikan Univ.)

C*-環の間の非線型正写像と行列環上の非線形トレースと majorization 理
論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Non-linear positive maps on C*-algebras, non-linear traces on matrix
algebras and majorization theory

概 要 We study non-linear monotone positive maps on C*-algebras. In this talk we consider non-linear

and non-commutative integration theory. Choquet integrals and Sugeno integrals are studied as non-linear
integrals in non-additive measure theory. We introduce non-linear traces of Choquet type and Sugeno
type on matrix algebras and characterize these non-linear traces of Choquet type and Sugeno type bypartial additivity called comonotonic additivity and comonotonic F-additivity respectively. We study aclose relation among non-linear traces of Choquet type, majorization and unitarily invariant norms and2-positivity.

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77

函数解析学

16:15〜17:15

特別講演
大鈴 木 悠 平 (北理) [ 非可換従順作用

Yuhei Suzuki (Hokkaido Univ.)

Non-commutative amenable actions

概 要 Recently amenability of C*-dynamical systems attracted much attention. This is a consequence of mydiscovery of amenable actions on simple C*-algebras. The characterizations/formulations of amenability ofC*-dynamical systems had been unclear for a long time (> 30 years?), but Ozawa and I recently settled
it. This allows us to give a functorial construction of amenable actions on Kirchberg algebras. A recent
highlight on this subject may be my observation that amenability of actions is the genuine ingredient forthe classification of C*-dynamical systems. In particular, interestingly, the well-known dichotomy in von
Neumann algebra theory (Ocneanu, Jones, Popa, Brothier–Vaes etc) fails in the C*-algebra realm. Notably
an ultimate classification theorem was recently established by Gabe–Szabo in the purely infinite case.
Partly joint work with Ozawa. If time permits, I also explain my latest work, which gives amenable actions
on tracial simple C*-algebras. This example clarifies/motivates an ultimate goal in classification theory ofC*-algebras.

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統計数学

統

計

9 月 13 日（火）

数

78

学
第 III 会場

9:30〜11:50
1 河 本 野 恵 (北大理)

Noe Kawamoto (Hokkaido Univ.)

Spread-out limit of the critical points for lattice trees and lattice animals
in dimensions d > 8 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Spread-out limit of the critical points for lattice trees and lattice animals
in dimensions d > 8

概 要 A spread-out lattice animal(LA) is a finite connected set of edges in {{x, y} ⊂ Zd : 0 < ||x − y|| ≤ L}.

A lattice tree(LT) is a LA with no loops. Both models are the statistical-mechanical models for branchedpolymers. Let χp be the susceptibility which is a sum of the generating function of LT or LA containing
the origin and x, with fugacity p/|Λ|, where |Λ| is the degree of a vertex. There exists the critical point
pc of χp in the sense that χp diverges if p is bigger than pc and χp is finite otherwise. As the previous
research, Penrose (JSP, 77 (1994): 3-15) proved that pc = 1/e + O(L−2d/7 log L) for both models for alld ≥ 1. We show that pc = 1/e + CL−d + O(L−d−1 ) for all d > 8, where the non-universal constant C has therandom-walk representation. This talk is based on the joint research with Prof. Sakai at Hokkaido univ.
2 中 川 雄 太 ( 京 大 人 間 環 境)
Yuta Nakagawa (Kyoto Univ.)

ギブス点過程に関するランダムシュレディンガー作用素の状態密度 · · · · 15

Density of states for random Schrödinger operators associated with
Gibbs point processes

概 要 We consider the Schrödinger operator for the field generated by a non-negative single-site potential

and a realization of a point process. If the point process is a Poisson point process, it is known that the
integrated density of states (IDS) for the Schrödinger operator decays exponentially near its spectral loweredge. In this talk, we consider a pairwise interaction Gibbs point process and compare the asymptotic
behavior of the IDS with that of the case of a Poisson point process.
3 河 備 浩 司 ( 慶 大 経 済)
星 野 壮 登 ( 阪 大 基 礎 工)大理)
楠 岡 誠 一 郎 (京Hiroshi Kawabi (Keio Univ.)
Masato Hoshino (Osaka Univ.)
Seiichiro Kusuoka (Kyoto Univ.)

Stochastic quantization associated with the exp(Φ)2 -quantum field model
driven by the space-time white noise · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Stochastic quantization associated with the exp(Φ)2 -quantum field model
driven by the space-time white noise

概 要 We consider a quantum field model with exponential interactions on the two-dimensional torus, whichis called the exp(Φ)2 -quantum field model or Hoegh–Krohn’s model. In this talk, we discuss the stochastic
quantization of this model. Combining key properties of Gaussian multiplicative chaos with a method
for singular SPDEs, we construct a unique time-global solution to the corresponding parabolic stochastic√
quantization equation in the full L1 -regime |α| < 8π of the charge parameter α. We also identify thesolution with an infinite dimensional diffusion process constructed by the Dirichlet form approach.
4 濱 名 裕 治 (筑波大数理物質)

Yuji Hamana (Univ. of Tsukuba)

Square-root doundaries for Bessel processes · · · · · · · · · · · · · · · · · · · · · · · 10
Square-root doundaries for Bessel processes

概 要 We consider the hitting times of a Bessel process to a square-root boundary and obtain the explicit

form of the distribution function of the hitting time by means of zeros of the confluent hypergeometricfunction with respect to the first parameter.

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79

統計数学

5 簗 島
瞬 ( 都 立 大 理)
石 谷 謙 介 ( 都 立 大 理)

Shun Yanashima (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

On the weak convergence of conditioned Bessel bridges · · · · · · · · · · · · · 15
On the weak convergence of conditioned Bessel bridges

概 要 The purpose of this presentation is to introduce the construction of a stochastic process called “δ-dimensional Bessel house-moving” and its properties. δ-dimensional Bessel house-moving is a δ-dimensional
Bessel process hitting a fixed point at t = 1 for the first time. We show that this process can be obtained as
the weak limit of δ-dimensional Bessel bridges conditioned from above. Applying this weak convergence, wegive the decomposition formula for its distribution and the Radon–Nikodym density for the distribution of
the Bessel house-moving with respect to the one of the Bessel process. We also study sample path propertiesof the Bessel house-moving.
6 松 本 裕 行 ( 青 学 大 理 工)
Hiroyuki Matsumoto(Aoyama Gakuin Univ.)

Laplacian and Brownian motion on positive definite matrices, revisited· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Laplacian and Brownian motion on positive definite matrices, revisited概 要 We show explicit expression for the Laplace–Beltrami operator on the symmetric space of positive

definite matrices by using the Iwasawa coordinate, and study the corresponding diffusion process and its
largest and smallest eigenvalues.
7 笹 谷 晃 平 ( 京 大 数 理 研)
Kôhei Sasaya(Kyoto Univ.)

Some relation between spectral dimension and Ahlfors regular conformal
dimension of resistance metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Some relation between spectral dimension and Ahlfors regular conformal
dimension of resistance metrics

概 要 The spectral dimension dS of a metric space is an exponent associated with the asymptotic behaviorof the heat kernel of the standard Dirichlet form and Brownian motion on the space. The Ahlfors regularconformal dimension dimAR of the metric space is a quasisymmetric invariant, where quasisymmetry is awell-studied property of homeomorphisms between metric spaces. For (generalized) Sierpiński carpets or
Sierpiński gaskets, Kigami showed that dimAR ≤ dS < 2 or dimAR ≥ dS ≥ 2 holds, in 2020. In this lecture,
we give an appropriate extension of this results to the framework of resistance forms. We also show that
another simple extension, which is to be expected, does not hold in the framework in general.
8 梶 野 直 孝 ( 京 大 数 理 研)
Naotaka Kajino (Kyoto Univ.)

On singularity of energy measures for symmetric diffusions with full
off-diagonal heat kernel estimates II: Some borderline examples · · · · · · 15
On singularity of energy measures for symmetric diffusions with full
off-diagonal heat kernel estimates II: Some borderline examples

概 要 We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular

Sierpiński gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichletform. We prove that any fractal K in this family satisfies the full off-diagonal heat kernel estimates withsome space-time scale function ΨK and the singularity of the associated energy measures with respect tothe canonical volume measure (uniform distribution) on K, and also that the decay rate of r−2 ΨK (r) to 0
as r ↓ 0 can be made arbitrarily slow by suitable choices of K. These results together support [Ann. Probab.
48 (2020), no. 6, 2920–2951, Conjecture 2.15] stating that the full off-diagonal heat kernel estimates withspace-time scale function Ψ satisfying limr↓0 r−2 Ψ(r) = 0 imply the singularity of the energy measures.

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統計数学

80

14:15〜15:15

2021 年度 (第 20 回) 日本数学会解析学賞受賞特別講演
香 取 眞 理 (中 大 理 工) 多重シュラム・レヴナー発展とダイソンのブラウン運動模型

Makoto Katori(Chuo Univ.)

Multiple Schramm–Loewner evolution and Dyson’s Brownian motion
model

概 要 Schramm–Loewner evolution (SLE) is a stochastic extension of the classical Loewner theory in complex

analysis on a simply connected proper domain of C such that the driving function of the Loewner chain ofconformal maps is given by a one-dimensional stochastic process. Here we assume that the domain is theupper-half complex-plane H and the driving process runs on R. It was proved that the SLE driven by atime changed Brownian motion on R, (Bκt )t≥0 , κ > 0, determines a one-parameter family of probability
laws of a random continuous curve in H connecting 0 and ∞, and that this family, denoted by SLEκ ,κ > 0, covers all probability laws of such curves having the conformal invariance and the domain Markov
property. In probability theory and statistical physics, the SLE κ has been playing a central role in studying
critical phenomena associated with continuous phase transitions and fractal geometries in two dimensions.
Therefore, it is natural to generalize the SLE theory to describe random multiple curves in H driven by aninteracting particle system on R. The problem is that the requirement of the conformal invariance and thedomain Markov property is not sufficient to determine a ‘canonical’ family of multiple SLEs. Motivated by
the recent work by Sheffield on the quantum gravity zipper and a series of papers by Miller and Sheffieldon the imaginary geometry, we employ the coupling of Gaussian free fields (GFFs) and multiple SLEs. We
show that a multiple SLE is correctly coupled with a certain GFF if and only if the driving particle system
is given by Dyson’s Brownian motion model studied in random matrix theory. Dyson’s Brownian motion
model is also a one-parameter (β > 0) family of one-dimensional log-gases. The coupling is achieved if
and only if β = 8/κ. The present study on the GFF/multiple SLE coupling enables us to clarify the basic
properties of the constructed multiple SLE (e.g., continuity of multiple SLE curves, ‘phase transitions’ atκ = 4 and 8). Moreover, we expect that a notion of conformal invariance of SLE will enrich the study ofrandom matrix theory via the present results on the trinity of the GFF, the multiple SLE, and Dyson’s
Brownian motion model. The present talk is based on a joint work with Shinji Koshida (Aalto University).
15:30〜16:30

特別講演
大長 谷 部 高 広 (北理)Takahiro Hasebe (Hokkaido Univ.)

Loewner chains, Markov processes and non-commutative stochastic processes
Loewner chains, Markov processes and non-commutative stochastic processes

概 要 The notion of Loewner chain is a one-parameter family of univalent holomorphic self-maps of a domain

with certain properties. It played a key role in some problems on univalent functions, especially in the deBranges’ proof of Bieberbach’s conjecture in 1985. Loewner chains have found another application to thetheory of SLE around 2000. Later, reverse evolution families (more general than Loewner chains) began to
be used in free probability and then in monotone probability. More recently, (temporally inhomogeneous)branching processes are analyzed with the help of reverse evolution families. This talk summarizes recent
work of the speaker concerning some of the above mentioned topics, in which additive processes, a certainclass of Markov processes, branching processes and non-commutative stochastic processes are involved. Oneof the general purposes of this work is to make a dictionary between different fields or objects. For example,
the Laplace exponents of a branching process form a reverse evolution family. Then some basic properties(e.g. having finite first moment) of the branching process can be translated into some basic properties ofreverse evolution families that were formerly developed independently in complex analysis. The presentation
will be based on joint work with Uwe Franz, Sebastian Schleissinger, Ikkei Hotta, Pavel Gumenyuk andJose-Luis Perez.

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81

統計数学

9 月 14 日（水）第 III 会場

9:30〜11:30
9 平 井 祐 紀 (京Yuki Hirai

大理)(Kyoto Univ.)

Linear integral equations with additive noise in the pathwise Itô calculus· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Linear integral equations with additive noise in the pathwise Itô calculus

概 要 The Itô–Föllmer calculus, pioneered by Föllmer (1981), is a deterministic counterpart of classical Itô’s

stochastic calculus. In this talk, we treat linear integral equations with additive noise in the frameworkof the Itô–Föllmer calculus in Banach spaces. We interpret the term ‘noise’ as a càdlàg path that has
quadratic variation along a sequence of partitions. We give a solution to such an equation by the variationof constants formula and study the regularity of the solution path using that representation. As anapplication, we consider a purely pathwise approach to the HJM term structure model of bond markets.
10 濵 口 雄 史 (阪 大 基 礎 工)

Yushi Hamaguchi (Osaka Univ.)

線形確率ヴォルテラ積分方程式のカオス展開 · · · · · · · · · · · · · · · · · · · · · · · 15

Chaos expansions for linear stochastic Volterra integral equations

概 要 We consider a general class of linear stochastic Volterra integral equations with singular kernels. Bymeans of the Wiener–Itô chaos expansion approach, we define suitable classes of stochastic Volterra kernels
and introduce a new notion of the product for adapted L2 -processes. Observing the algebraic properties ofstochastic Volterra kernels, we obtain a variation of constants formula which gives an explicit expression for
the Wiener–Itô chaos expansion of the solution to a general class of linear SVIEs.
11 中 田 寿 夫 (福 岡 教 育 大)

Toshio Nakata (Fukuoka Univ. of Edu.)

超重裾分布に関する大偏差 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Large deviations for super-heavy tailed distributions

概 要 In this talk, we study large deviations for sums of independent and identically distributed randomvariables (random walks) with nonnegative super-heavy tailed distributions. While Hu and Nyrhinen (2004)
gave results for heavy tailed distributions, our result is an improvement of one of theirs for super-heavy tailed
ones. Moreover, we apply it to the log-Pareto distribution and the distribution for the super-Petersburg
game.
12 小 川 重 義 (立 命 館 大 理 工)

Shigeyoshi Ogawa (Ritsumeikan Univ.)

非因果的確率積分に対する平均値定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Mean value theorems for the noncausal stochastic integral

概 要 In the classical calulus the statement called mean value theorem for the integral is well known. We

are now concerned with the validity of a similar statement for the stochastic integrals. The aim of the talkis to show that we can establish mean value theorems as exact formulae when limited to the noncausal
Rbstochastic integral (also called ogawa integral) of the form a f (Xt )d∗ Wt , where Wt is Brownain motion andRb
Xt an Itô process, causal or not. We also discsuss the case of Itô integral a f (Xt )d0 Wt , moreover such agenuin noncausal case where the process Xt is noncausal. Whole discussions are developed in the frameworkof the noncausal stochastic calculus. hence for the related materials and basic facts we would refer to themonograph “Noncausal Stochastic Calculus” by Ogawa, S., (2017, Springer).

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統計数学

13 植 田 優 基 (北 教 大 旭 川)大理)
長 谷 部 高 広 (北(野 場
啓 統 計 数 理 研)
佐 久 間 紀 佳 ( 名 古 屋 市 大 理)

Yuki Ueda (Hokkaido Univ. of Edu.)
Takahiro Hasebe (Hokkaido Univ.)
Kei Noba (Inst. of Stat. Math.)
Noriyoshi Sakuma (Nagoya City Univ.)

82

Regularity results on the class of Boolean selfdecomposable distributions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Regularity results on the class of Boolean selfdecomposable distributions

概 要 Khintchine introcuded the class L of limit distributions of certain independent triangular arrays. This

class contains the class of stable distributions as a subset. In 1937, Lévy characterized the class L as follows:
A probability measure µ on R is in the class L if and only if µ is selfdecomposable. In non-commutative
probability theory, notions of independence of random variables are classified into five ones: tensor, free,
Boolean, monotone and anti-monotone independence. The concept of selfdecomposability is also formulated
for each notion of independence. In this talk, we focus on Boolean version of the class of selfdecomposable
distributions and investigate general regularity results on the class of Boolean selfdecomposable distributions.
14 臼 杵 峻 亮 (京大理)Shunsuke Usuki (Kyoto Univ.)×a × b 作用に関する経験測度とその irregular set 及びエントロピーとの関係について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
×a and ×b empirical measures, the irregular set and entropy

概 要 For integers a and b ≥ 2 which are multiplicatively independent, let Ta and Tb be multiplication by aand b on R/Z. It is known that the only Ta , Tb -invariant and ergodic measure with positive entropy of Ta or
Tb is the Lebesgue measure. In this talk, we consider the empirical measures with respect to Ta , Tb -action
and show that the set of x such that the empirical measures of x do not converge to any measure has
Hausdorff dimension 1 and the set of x such that the empirical measures accumulate to some invariant
measure with small entropy has small Hausdorff dimension. Furthermore, we obtain some equidistribution
result about the Ta , Tb -orbit of x in the complement of a set of Hausdorff dimension 0.
大理)
15 中 島 由 人 (京
(
慶
大
理
工)
高 橋 博 樹Yuto Nakajima (Kyoto Univ.)
Hiroki Takahashi (Keio Univ.)

準正則連分数展開が定める無理数集合のハウスドルフ次元について · · · · 15

Hausdorff dimension of sets with restricted, slowly growing partial quotients in the semi-regular continued fraction

概 要 We describe the Hausdorff dimension of sets of irrational numbers whose partial quotients in thesemi-regular continued fraction expansion obey certain restrictions and growth conditions. To prove ourresults, we construct non-autonomous iterated function systems well-adapted to the given restrictions andgrowth conditions, and then apply the dimension theory developed by Rempe-Gillen and Urbański.
11:30〜12:00

統計数学分科会総会

9 月 15 日（木）第 III 会場

9:30〜12:00
16 藤 田 敏 治 (九 工 大 工)
Toshiharu Fujita(Kyushu Inst. of Tech.)

確率環境下における合流型決定過程について —再帰的解法に関する考察—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On recursive methods for converging decision process in stochastic environment

概 要 The goal of this study is to solve the stochastic decision process models with a converging transition

system. In this presentation, a simple example will be discussed and some recursive equations will bederived by using dynamic programming technique.

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83

統計数学

17 田 中 輝 雄 (広 島 市 大 情 報)

Teruo Tanaka (Hiroshima City Univ.)

最適停止問題の預言者の不等式 —比の評価— · · · · · · · · · · · · · · · · · · · · · · 10

Prophet inequalities for finite stage multiparameter optimal stopping
problems

概 要 We consider the optimal stopping problem for discrete time multiparameter stochastic processes. In

the classical optimal stopping problems, the comparisons between the expected reward of a player withcomplete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet
inequalities, have been studied by many authors. We shall study the prophet inequalities for optimal
stopping problems for finite stage multiparameter stochastic processes.
18 地
栗
藤
宮

嵜 頌 子 ( 大 阪 工 大 情 報)
府大⋆)木 進 二 (阪
波
大⋆)
原
良 (筑
本 暢 子 ( 東 京 理 大 理 工)

Shoko Chisaki (Osaka Inst. of Tech.)Shinji Kuriki (Osaka Pref. Univ.⋆)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

Optimality of spanning bipartite block designs · · · · · · · · · · · · · · · · · · · · · 10

Optimality of spanning bipartite block designs

概 要 It is usually to design an experiment using treatments and its blocks in the design of experiments.

Consider a set of edges of a complete bipartite graph as a treatments set and suppose the treatments havea structure. Then, we proposed a spanning bipartite block design (SBBD) to achieve better estimation
accuracy. In this talk, using an SBBD as a statistical model, we discuss the optimality of how small
the variance of the estimator was. And we prove that the variances of all estimators are equal (variancebalanced). We also show the goodness of SBBD by the simulation.
19 矢
上
篠
吉
田

萩
原
田
本
畑

隆 哉 ( 東 京 理 大 理 工)
歩 夢 ( 東 京 理 大 理 工)
覚 ( 横 浜 市 大 医)拓 矢 ( 中 外 製 薬)
耕 治 ( 東 京 理 大 理 工)

Ryuya Yahagi (Tokyo Univ. of Sci.)
Ayumu Uehara (Tokyo Univ. of Sci.)
Satoru Shinoda (Yokohama City Univ.)
Takuya Yoshimoto(Chugai Pharmaceutical Co.)
Kouji Tahata (Tokyo Univ. of Sci.)

多元分割表における周辺累積非同等モデルの一般化 · · · · · · · · · · · · · · · · · 15

The generalization of marginal cumulative inhomogeneity model for
multi-way contingency tables

概 要 For multi-way contingency tables, Bhapkar and Darroch (1990) considered the marginal symmetry

model for order h. Yoshimoto et al. (2020) proposed the marginal cumulative logistic model for order h asa model of an inhomogeneity for marginal cumulative probability for order h. This presentation proposes a
generalized marginal cumulative inhomogeneity model for order h. It also gives the decomposition of themarginal symmetry model for order h into the generalized marginal cumulative inhomogeneity model fororder h, the marginal moment equality model for order h and the marginal symmetry model for order h − 1.
20 佃

康 司 ( 九 大 数 理)

Koji Tsukuda (Kyushu Univ.)

Pitman 分割の長さの漸近挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the asymptotic behavior of the length of a Pitman partition

概 要 The Pitman sampling formula is a multivariate discrete distribution with three parameters, anda Pitman partition is a random partition whose law is given by the Pitman sampling formula. This
presentation discusses the asymptotic behavior of the length of a Pitman partition under a two-parameter
asymptotic regime. In particular, convergence in probability is shown and evaluated.

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統計数学

21 宮 田 庸 一 (高 崎 経 大 経 済)
塩 濱 敬 之 ( 南 山 大 理 工)
阿 部 俊 弘 ( 法 政 大 経 済)
Yoichi Miyata(Takasaki City Univ. of Econ.)
Takayuki Shiohama (Nanzan Univ.)(Hosei Univ.)
Toshihiro Abe84

正弦関数摂動分布族のある拡張について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On an extension of the family of sine-skew circular distributions

概 要 The sine skewed circular distribution is a circular probability model that can be asymmetric inshape and that has the advantage that the sine and cosine moments can be written in explicit forms, andgeneration of random numbers can be easily implemented. In contrast, this distribution is difficult to belargely asymmetric near the modes of the distributions. In this talk, we use the framework of Ley and
Verdebout to propose a new family of probability distributions, that can give stronger asymmetry aroundthe mode than the sine skewed circular distribution. We also show that a subfamily of extended sine-skewed
wrapped Cauchy distributions, and a subfamily of von Mise distributions are identifiable with respect toparameters.
22 赤 間 陽 二 (東 北 大 理)
フスナキラティアティナ
( 東 北 大 理)

A dichotomous behavior of Guttman–Kaiser criterion from equi-correlated
normal population · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yohji Akama (Tohoku Univ.)
Atina Husnaqilati (Tohoku Univ.)

A dichotomous behavior of Guttman–Kaiser criterion from equi-correlated
normal population

概 要 In high-dimensional statistics, a famous eigenvalue-greater-than-one rule (GK rule) assesses the numberof significant components/factors of inferences principal component analysis and exploratory factor analysis.
Psychologists and simulation study report: if the dimension p is small, when a common correlation coefficientamong the p variables is r, GK rule assessment is very small (r > 0), and p/2 (r = 0). For the sample size n,
we establish this dichotomy for large p but small p/n and equi-correlated normal population, by proving: asn, p → ∞, p/n → c > 0, the spectral distribution of the sample correlation matrix goes to Marčenko-Pastur
distribution scaled by 1 − r
23 赤 間 陽 二 (東 北 大 理)
Yohji Akama(Tohoku Univ.)

Shrinkage of eigenvalue distributions of sample correlation matrix formed
from equi-correlated normal population · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Shrinkage of eigenvalue distributions of sample correlation matrix formed
from equi-correlated normal population

概 要 From a p-dimensional normal population with all the correlation coefficient between variables beinga fixed, nonnegative constant r < 1, we draw a sample of size n and form a sample correlation matrix
R. Suppose p, n → ∞, p/n → c > 0. The eigenvalue distribution of R almost surely converges weakly to
Marčenko-Pastur distribution Fc (x/(1 − r)) of scale parameter 1 − r and index c (A. and A. Husnaqilati, Adichotomous behavior of Guttman–Kaiser criterion from equi-correlated normal population, preprint, 2022).
For the largest eigenvalue λ of R, we aim to prove λ/p converges to r almost surely, to explain a shrinkage
phenomenon (Laloux et al. Random matrix theory and financial correlations, Int. J. Theor. Appl. Finance,2000): the histogram of eigenvalues of a sample correlation matrix R of stock market fits the density of
Fp/n (x/(1 − λ/p)).

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85

統計数学

12:10〜12:45

2021 年度 (第 20 回)・2022 年度 (第 21 回) 日本数学会解析学賞授賞式

14:25〜15:25

特別講演
伊 森 晋 平 (広島大先進理工)

Shinpei Imori (Hiroshima Univ.)

高次元多変量線形回帰モデルにおける変数選択について

Variable selection in high-dimensional multivariate linear regression models

概 要 Recently, there are advances in variable selection for high-dimensional multivariate linear regression

models, where the dimension of response variables and the sample size are large. In this talk, we consider
the asymptotic properties of variable selection procedures including model selection consistency (i.e., theselection probability of the true model goes to one with the sample size tending to infinity) and efficiency(i.e., a loss or risk function of the selected model is similar to that of the best model). The propertiesof variable selection procedures in high-dimensional situations are not always the same as those derived
in low-dimension. We consider a situation that each response variable does not need to use the same
explanatory variables. This condition yields more flexible variable selection frameworks.
15:45〜16:45

特別講演
後 藤 佑 一 ( 九 大 数 理)

Yuichi Goto

(Kyushu Univ.)

Integrated copula spectrum with applications to tests for time-reversibility
and tail symmetry
Integrated copula spectrum with applications to tests for time-reversibility
and tail symmetry

概 要 The spectral density plays a pivotal role in time series analysis. Since the classical spectral density isdefined as the Fourier transform of autocovariance functions, it fails to capture the distributional features.
To overcome this drawback, we consider the spectral density based on copula and show the weak convergenceof integrated copula spectra. This result combined with the subsampling procedure enables us to construct
uniform confidence bands, a test for time-reversibility, and a test for tail symmetry. This talk is basedon joint work with T. Kley (Georg-August-Univ. Gottingen), R. Van Hecke (Ruhr-Univ. Bochum), S.
Volgushev (Univ. of Toronto), H. Dette (Ruhr-Univ. Bochum), and M. Hallin (Univ. libre de Bruxelles).

9 月 16 日（金）第 III 会場

9:30〜12:00
24 種 市 信 裕 (北 教 大 札 幌)
関 谷 祐 里 ( 北 教 大 釧 路)
外 山
淳 ( 数 学 利 用 研)
Nobuhiro Taneichi(Hokkaido Univ. of Edu.)
Yuri Sekiya (Hokkaido Univ. of Edu.)
Jun Toyama(Inst. for Pract. Appl. of Math.)

漸近展開に基づく 3-way 分割表における条件付独立性検定統計量の改良· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Improvement of the test statistics for conditional independence in 3-way
contingency table based on asymptotic expansion

概 要 We derived an expression of asymptotic expansion for the distribution of test statistics based on

fai-divergence which include power divergence family of statistics for conditional independence in 3-way J x
K x L contingency table. The expansion consists of continuous and discrete terms. Continuous terms meanterms of multivariate Edgeworth expansion. Using the continuous terms of the expansion, we constructedtransformations that improve the speed of convergence to the chi-square asymptotic distribution of the test
statistics. When the statistics are power divergence family of statistics as a special case, performance of thetransformed statistics was investigated by Monte Carlo simulation.

最終版: 2022/8/8
統計数学

25 米 永 航 志 朗 (北 大 経 済)
鈴 川 晶 夫 ( 北 大 経 済)

Koshiro Yonenaga (Hokkaido Univ.)
Akio Suzukawa (Hokkaido Univ.)

86

ウィッシャート行列と正規ベクトルの積の高次モーメント · · · · · · · · · · · 15Higher order moments of the product of a Wishart matrix and a normal
vector

概 要 In this report, we consider the distribution of the product of a Wishart matrix and a normal vector with

uncommon covariance matrices. We provide the stochastic representation which reduces the computationalburden for the generation of realizations of the product. Based on the stochastic representation of the
product, the density function and higher order moments of the product are derived. In a numericalillustration, we investigate some properties of the distribution of the product; in particular, skewness
and kurtosis are computed for various values of the parameters of the product. We further suggest the
Edgeworth type expansions of the product, and we observe that the suggested approximations provide agood performance for moderately large degrees of freedom of a Wishart matrix.
26 八 木 文 香 (東 京 理 大 理)
瀬 尾
隆 ( 東 京 理 大 理)

Ayaka Yagi (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

Multivariate pairwise comparisons among mean vectors with monotone
missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Multivariate pairwise comparisons among mean vectors with monotone
missing data

概 要 We consider the approximate simultaneous confidence intervals for pairwise comparisons among mean

vectors with monotone missing data. On the test for mean vectors, for example, Yagi and Seo (2017) andYagi et al. (2018) discussed the simplified T 2 -type test statistic Te2 to test the equality of two mean vectors.
Further, they proposed the approximate simultaneous confidence intervals for pairwise comparisons among2
mean vectors using the approximate upper percentile of the Tmax
-type test statistic based on Te2 . In thistalk, we give the T 2 -type statistic based on a partially modified Te2 and derive an approximate upper
max

percentile for it. By using this approximate upper percentile, an approximate simultaneous confidence
interval is given.
27 中 山 優 吾 (京 大 情 報)
矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)
Yugo Nakayama (Kyoto Univ.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

高次元主成分分析における頑健性について · · · · · · · · · · · · · · · · · · · · · · · · · 15

Robustness in high-dimensional principal component analysis

概 要 In this talk, we discuss the robustness of principal component analysis (PCA) for high-dimensional,

low-sample-size (HDLSS) data. PCA has been studied extensively in the framework of HDLSS. It should be
noted that conventional PCA is strongly influenced by outliers. On the other hand, Locantore et al. (1999,
Test) and Visuri et al. (2000, JSPI) proposed robust PCA based on a spatial sign covariance matrix. The
work of Zhou and Marron (2015, EJS) showed asymptotic properties of robust PCA in the HDLSS setting
under Gaussian. In this talk, we evaluate both conventional PCA and robust PCA under non-Gaussianwith some outliers and compare their performance using numerical simulations and microarray datasets.

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87

統計数学

28 栗 木哲 ( 統 計 数 理 研)
松 原 隆 彦(高エネルギー加速器研究機構)

Satoshi Kuriki (Inst. of Stat. Math.)
Takahiko Matsubara(High Energy Accelerator Res. Organ.)

中心極限確率場に対する期待ミンコフスキー汎関数の漸近展開 · · · · · · · · 15

Asymptotic expansion of the expected Minkowski functional for isotropic
central limit random fields

概 要 The Minkowski functionals, including the Euler characteristic statistics, are standard tools for mor-

phological analysis in cosmology. Motivated by cosmological research, we examine the Minkowski functionalof the excursion set for an isotropic central limit random field, the k-point correlation functions (kth order
cumulants) of which have the same structure as that assumed in cosmic research. We derive the asymptotic
expansions of the expected Euler characteristic density incorporating skewness and kurtosis, which is abuilding block of the Minkowski functional. The resulting formula reveals the types of non-Gaussianitythat cannot be captured by the Minkowski functionals. As an example, we consider an isotropic chi-squarerandom field, and confirm that the asymptotic expansion precisely approximates the true Euler characteristic
density.
29 山 田 隆 行 (島根大総合理工)

Takayuki Yamada (Shimane Univ.)

High-dimensional asymptotic expansion of the null distribution for testing complete independence of normal random variables · · · · · · · · · · · · · 10
High-dimensional asymptotic expansion of the null distribution for testing complete independence of normal random variables

概 要 Testing the null hypothesis that all elements of observation vector are independent has been studied.

Schott (2005) proposed the testing statistic and gave the limiting null distribution under high-dimensional
asymptotic framework that the sample size n and the dimensionality p go to infinity together while p/nconverges to a positive constant. We give a one-term asymptotic expansion of the null distribution asmin{n, p} tends toward infinity. In addition, we derive a correction of the critical point for Schott (2005)’s
test based on this expansion. The finite sample size and dimensionality performance for attained significancelevel is evaluated in a simulation study and the results are compared to those of Schott (2005)’s test.
30 江 頭 健 斗 (筑波大数理物質)
矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)

Kento Egashira (Univ. of Tsukuba)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

階層的クラスタリングの高次元漸近的振舞い · · · · · · · · · · · · · · · · · · · · · · · 15

High-dimensional asymptotic behaviors of hierarchical clustering

概 要 Three asymptotic behaviors of hierarchical clustering are investigated under several settings frommoderate dimension to high-dimension, low-sample size (HDLSS). However, it is considered that conditions
required are strict for HDLSS data. Given this background, this presentation focuses on HDLSS settings
and we give the asymptotic properties of hierarchical clustering under practical settings. Lastly, numericalsimulations are given and we discuss the performance of the hierarchical clustering for HDLSS data.

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統計数学

31 増 田 弘 毅 (九大数理・東大数理)
Hiroki Masuda(Kyushu Univ. / Univ. of Tokyo)

88

BIC-type model selection for locally stable regression · · · · · · · · · · · · · · · 15
BIC-type model selection for locally stable regression

概 要 We consider a class of non-ergodic dynamic regression models partially driven by a locally stable

Levy process, specified by the characteristics: constant activity index, parametric trend coefficient, andparametric scale coefficient. Assuming that the process is observed at high frequency and the activity index
is unknown, we derive the stochastic expansion of the marginal quasi-likelihood to formulate a Schwarz-typemodel selection of the trend and scale coefficients. The modeling is essentially based on the conditional
stable quasi-likelihood function.
14:25〜16:50( 早 大 理 工)
32 Yujie Xue
谷 口 正 信 ( 早 大 理 工)
(Waseda Univ.)
Yujie Xue
Masanobu Taniguchi (Waseda Univ.)

A new generalized estimator for autoregressive coefficient which improves MLE uniformly · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A new generalized estimator for autoregressive coefficient which improves MLE uniformly

概 要 For the first order autoregressive model, in Ochi (1983), a generalized estimator of the coefficientwith two constants was introduced, which includes Daniels’s estimator, least-squares estimator and Durbin’s
estimator. From Fujikoshi and Ochi (1984), compared with a third-order approximated estimator of
maximum likelihood estimator, it was shown that approximated estimator of maximum likelihood estimatoris better than Ochi’s estimator in the third-order sense if we modify the both estimators to be third-order
asymptotically median unbiased. In this paper, we propose a new estimator based on Ochi (1983) which
improves the MLE uniformly in the sense of the third-order mean square error without bias-adjustments.
33 藤 森洸 ( 信 州 大 経 法)
後 藤 佑 一 ( 九 大 数 理)
劉言 ( 早 大 理 工)
谷 口 正 信 ( 早 大 理 工)
Kou Fujimori (Shinshu Univ.)(Kyushu Univ.)
Yuichi Goto(
Waseda Univ.)
Yan Liu
Masanobu Taniguchi (Waseda Univ.)

The Lasso-based principal component analysis for high-dimensional stationary time series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Lasso-based principal component analysis for high-dimensional stationary time series

概 要 In this talk, we discuss the Lasso-based principal component analysis for high-dimensional stationary

processes. This problem is motivated by the observation that the standard principal component analysis
performs poorly when the dimension of the data is large with sparse eigenvector. We deal with stationary
time series under suitable mixing conditions and establish the rate of convergence of the Lasso-type
estimators of the first eigenvector. We also elucidate the theoretical rate for choosing the tuning parameterin the Lasso-type estimators. The performance of the sparse principal component analysis is demonstrated
by numerical simulations.

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89

統計数学

34 劉
ト ウ ( 早 大 理 工)
( 早 大 理 工)
Yujie Xue
谷 口 正 信 ( 早 大 理 工)
(Waseda Univ.)
Tong Liu(Waseda Univ.)
Yujie Xue
Masanobu Taniguchi (Waseda Univ.)

Characterization of time series models by various divergences · · · · · · · · 10

Characterization of time series models by various divergences

概 要 In this talk, we characterize representative time series models which best fit under the given constraints

in the sense of maximizing three divergences. First, we show an another understanding of the characterizationof the maximum entropy spectral distribution via Durbin–Levinson algorithm. Next, we characterize thespectral distribution which maximizes the minimum linear interpolation error, when autocovariances withfinite number of lags of a stationary process are known. Lastly, when a finite number of generalized
autocovariance values (Proietti & Lauti (2015)) are given, we show that the exponential model introduced
by Bloomfield (1973) minimizes the divergence of the integral of power spectral measure.
35 明 石 郁 哉 (東 大 経 済)Fumiya Akashi (Univ. of Tokyo)

多変量自己回帰モデルに対する一般化経験尤度法を用いた頑健な推測理論の構成 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Robust statistical inference for vector autoregressive models by smoothed
generalized empirical likelihood method

概 要 In this talk, we develop the generalized empirical likelihood (GEL) method for vector autoregressivemodels. The models in this talk involve infinite variance processes, and the distribution of the error term
is nonparametric. Motivated by a concept of the spatial median vector, we consider the spatial median
regression-based moment function and its smoothed version. We also consider the weighted version of the
moment function, and the proposed GEL estimator has asymptotic normality regardless of whether themodel has finite or infinite variance. A feasible testing procedure for a possively nonlinear restriction of
the coefficients is proposed, and some simulation experiments illustrate the finite sample performance of the
proposed methods.
36 劉
Yan Liu

言 ( 早 大 理 工)

(Waseda Univ.)

A minimum contrast estimation for spectral densities of multivariate
time series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A minimum contrast estimation for spectral densities of multivariate
time series

概 要 In this talk, we introduce a new class of minimum contrast estimators for spectral densities ofmultivariate time series. Previous studies have shown the efficiency of the Whittle estimator, which was
originally designed for parameter estimation of Gaussian processes. It is thought of as a special form of
the minimum contrast estimator in time series analysis. For univariate time series, the estimator has been
generalized to several classes of minimum contrast estimators. However, the generalization was limited in
the sense of univariate time series. We focused on the multivariate time series and introduce a new classof the minimum contrast estimators. We study asymptotic distributions of minimum contrast estimators.
The asymptotic properties will be illustrated by our simulation studies.

最終版: 2022/8/8
統計数学

37 仲 北 祥 悟 (東 大 総 合 文 化)
今 泉 允 聡 ( 東 大 総 合 文 化)

Shogo Nakakita (Univ. of Tokyo)
Masaaki Imaizumi (Univ. of Tokyo)

90

過剰パラメータを伴う線形時系列モデルと良性過適合 · · · · · · · · · · · · · · · 15

Benign overfitting in overparameterized linear time series models

概 要 We consider a linear regression model with overparameterization, in which the number of features

exceeds the sample size. When the model is with overparameterization and without regularization, there
exist interpolators which fit all the training data and achieve zero training error. It is known that the excess
risk of an interpolator can be convergent to zero if the eigenvalues of the covariance of the features decay
moderately and the i.i.d. assumption for training data holds. We show that a similar result can hold even
if the features and noises are dependent processes by showing upper bounds for the excess risk. We also
examine how the dependence structures appear in those upper bounds.
38 前 園 宜 彦 (中 大 理 工) [ カーネル型確率点推定の平均二乗誤差について · · · · · · · · · · · · · · · · · · · · · 10
中 村 広 大 ( 中 大 理 工)

Yoshihiko Maesono (Chuo Univ.)
Koudai Nakamura (Chuo Univ.)

On mean squared error of kernel quantile estimator

概 要 In this talk we study asymptotic properties of quantile estimators which are based on the empirical

distrubution function and kernel type estimator. We show that the kernel quantile estimator has smallmean squared error in many case.
39 柿 沢 佳 秀 (北 大 経 済)

Yoshihide Kakizawa (Hokkaido Univ.)

非対称カーネルを用いた確率密度関数の微分推定について · · · · · · · · · · · 15

Asymmetric kernel density derivative estimation

概 要 The usual approximation (near the origin x = 0) of a certain smooth function u as the convolution

integral does not hold when u(0) ̸= 0, and, even for the case u(0) = 0, the order of the approximation(near the origin x = 0) is slower when u′ (0) ̸= 0. For the data supported on [0, ∞) or [0, 1], this boundary
bias problem is one of the interests. Instead of the location-scale kernel k((x − ·)/h)/h (e.g. Rosenblatt),
we focus on an application of an asymmetric kernel to solve the boundary bias problem. In this talk, we
consider estimating the density derivative for the nonnegative data, using the asymmetric kernel method.
40 駒 場敦 ( 山 梨 大 医)城 野 悠 志 ( 山 梨 大 医)中 本 和 典 ( 山 梨 大 医)Atsushi Komaba (Univ. of Yamanashi)
Hisashi Johno (Univ. of Yamanashi)
Kazunori Nakamoto(Univ. of Yamanashi)

2 標本 Kolmogorov–Smirnov 検定の拡張 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An extension of the two-sample Kolmogorov–Smirnov test

概 要 Here we propose a new nonparametric framework for two-sample testing, named as the OVL-q(q = 1, 2, . . .). This can be regarded as a natural extension of the Smirnov test, which is eqivalent to the
OVL-1. We specifically focus on the OVL-2, implement its fast algorithm, and show its superiority overother statistical tests in some experiments. The system to perform the OVL-1 and OVL-2 developed here
can be used on-line at https://fiveseven-lambda.github.io/ovl-test.

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91

応用数学

応 用
9 月 13 日（火）数学
第 V 会場

10:00〜11:45
1 松 本 直 己 (慶 大 D M C )山 本 真 基 ( 成 蹊 大 理 工)
山 崎 将 仁 ( 成 蹊 大 理 工)

Naoki Matsumoto (Keio Univ.)
Masaki Yamamoto (Seikei Univ.)
Masahito Yamazaki (Seikei Univ.)

The minimum number of vertices of graphs containing two monochromatic triangles for any edge 2-coloring · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The minimum number of vertices of graphs containing two monochromatic triangles for any edge 2-coloring

概 要 The simplest problem in graph theoretic Ramsey theory is to ask for the minimum number of verticesof complete graphs Kn such that there is one monochromatic triangle for any edge 2-coloring. It is wellknown that the answer is six and so every graph with K6 satisfies the same property. From this fact, it isnatural to ask for a structure of graphs with such a property that does not contain K6 , which was posedby Erdős and Hajnal. Graham answered this question by constructing a minimal graph with the condition,
which is on eight vertices and called the Graham graph. In this talk, we introduce a generalization of thisstudy focusing on the number of monochromatic triangles and our result about the minimum number ofvertices of graphs containing two monochromatic triangles for any edge 2-coloring.
2 大野由美子(横浜国大研究推進機構)
松 本 直 己 (慶 大 D M C )Yumiko Ohno (Yokohama Nat. Univ.)
Naoki Matsumoto (Keio Univ.)

キャタピラの achromatic number と pseudoachromatic number の差について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The difference between the achromatic number and the pseudoachroamtic
number of caterpillars

概 要 A complete k-coloring (resp., a pseudocomplete k-coloring) is a proper coloring (resp., a not necessarily

proper coloring) such that each pair of colors appears on at least one edge. The achromatic number (resp.,
the pseudoachromatic number) of a graph G is the largest number k such that G has a complete k-coloring(resp., a pseudocomplete k-coloring).
Hedetniemi conjectured that the difference between the achromatic number and the pseudoachromatic
number is at most 1 for every tree. A caterpillar is a tree such that the set of vertices of degree at least two
induces a path. In this talk, we shall show that Hedetniemi’s conjecture holds for a caterpillar satisfying
certain conditions.
3 永 並 健 吾 ( 成 蹊 大 理 工)
中 本 敦 浩 (横浜国大環境情報)
小 関 健 太 (横浜国大環境情報)(Seikei Univ.)
Kengo Enami
Atsuhiro Nakamoto(Yokohama Nat. Univ.)
Kenta Ozeki (Yokohama Nat. Univ.)

Surface immersions and projective planar graphs · · · · · · · · · · · · · · · · · · · 15

Surface immersions and projective planar graphs

概 要 Let G and H be 4-regular graphs embedded on a surface F 2 . A pair of edges in G is consecutive if

these edges induced a cousecutive part of a facial walk. We say that G contains H as a surface immersion
if H can be obtained from G by repeatedly splitting off pairs of consecutive edges. We prove that for any
4-regular graph H embedded on the projective plane, there exists an integer N = N (H) such that every
4-regular graph of dual width at least N contains H as a surface immersion.

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応用数学

4 森 田 英 章 ( 室 蘭 工 大 工)
石 川 彩 香 ( 横 浜 国 大 理 工)

Hideaki Morita (Muroran Inst. of Tech.)Ayaka Ishikawa (Yokohama Nat. Univ.)

92

グラフゼータ函数の伊原表示について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the Ihara expression for graps zeta functions

概 要 We consider a determinant expression of graph zeta functions, which is called the Ihara expression, forfinite digraphs. Digraphs allow multi-arcs and multi-loops. We will see that graph zeta functions have the
Ihara expression in the case where the inverse arc is given uniquely for each arc if it exists in this general
setting.
5 石 川 彩 香 ( 横 浜 国 大 理 工)
森 田 英 章 ( 室 蘭 工 大 工)Ayaka Ishikawa (Yokohama Nat. Univ.)
Hideaki Morita (Muroran Inst. of Tech.)

有向グラフの逆辺に関する注意 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A remark on inverse arcs in finite digraphs

概 要 We consider the Ihara expression of graph zeta functions for finite digraphs, which allow multi-arcs

and multi-loops. The existence of Ihara expression depends on a way we assign the set of inverse arcs foreach arc. In this talk, we will see an example of the way which does not appear in the classical cases.
6 佐
今
小
田

藤
巖 ( 小 山 工 高 専)
野 紀 雄 ( 横 浜 国 大 工)松尭 (産業数理研究所Calc)
村 駿 也 ( 横 浜 国 大 理 工)

Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Takashi Komatsu(Math. Res. Inst. Calc for Industry)
Shunya Tamura (Yokohama Nat. Univ.)

Generalized Grover/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A generalized Grover/Zeta correspondence

概 要 We introduce a generalized Grover matrix of a graph and present an explicit formula for its character-istic polynomial. Next, we define a zeta function and a generalized zeta function of a graph G with respect
to its generalized Grover matrix and present explicit formulas for their zeta functions for a vertex-transitivegraph. As applications, we express the limit on the generalized zeta functions of a family of finite vertextransitive regular graphs by an integral. Furthermore, we give the limit on the generalized zeta functions ofa family of finite tori as an integral expression.
14:15〜15:25
7 小 田 切 真 輔 (秀明大学校教師)

Shinsuke Odagiri (Shumei Univ.)

極大鎖多面体の面とガイド付き王冠構造 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Faces of maximal chain polytopes and guided crown structure

概 要 For a finite ordered set P , we define the maximal chain polyhedron M (P ) as the convex hull of all the

points in RP corresponding to maximal chains. Let C be a set of maximal chains, and consider the convex
hull of corresponding points in RP . We will show that the obtained polytope is a face of M (P ) if and only
if C does not have an incomplete guided crown structure. Using this result, we calculate the dimension of
the maximal chain polytope when P = m × n.

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93

応用数学

8 奈 良 知 惠 (明 大 M I M S )伊 藤 仁 一 (椙山女学園大教育))
MIT
E. Demaine ((Meiji Univ.)
Chie Nara
Jin-ichi Itoh (Sugiyama Jogakuen Univ.)(MIT)
Erik Demaine

多面体的多様体の連続的平坦化: 可算無限個の折り目付 · · · · · · · · · · · · · 15

Continuous flattening of all polyhedral manifolds using countably infinite creases

概 要 We report results by joint-work with Z. Abel, M. Demaine, J. Ku, and J. Lynch: any finite polyhedral

manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding
self-crossing, answering an open problem proposed in 2001, if we extend standard folding models to allow
for countable infinite creases, and the area of the manifold that needs to support moving creases can bemade arbitrary small.
9 神 吉 知 博 ( 松 江 工 高 専)
名 倉
誠 (大阪電通大基礎理工)大 谷 信 一 (関東学院大理工)
Tomohiro Kamiyoshi(Matsue Coll. of Tech.)
Makoto Nagura(Osaka Electro-Comm. Univ.)
Otani Shin-ich (Kanto Gakuin Univ.)

指数型 extended Riordan array と統一スターリング数について · · · · · · · 10

On exponential extended Riordan arrays and unified Stirling numbers

概 要 We propose the notion of extended Riordan array, permitted negative indices, of exponential type byusing the Roman factorial. In this context, we will establish a fundamental theory of the unified Stirlingnumbers that were introduced by Hsu and Shiue. As a consequence, we give a luminous explanation for thereciprocity law among those numbers that was discovered by Choi, et al. and Maltenfort. Moreover, ourmethods reveal that some interesting numbers appear in a certain part of the exponential extended array,
although the numbers in the area had been regarded as zero until now.
10 川 端 大 輝 (阪 府 大 理)
丸 田 辰 哉 ( 阪 公 大 理)

Daiki Kawabata (Osaka Pref. Univ.)
Tatsuya Maruta (Osaka Metro. Univ.)

On the achievement of the Griesmer bound · · · · · · · · · · · · · · · · · · · · · · · · 15
On the achievement of the Griesmer bound概 要 An [n, k, d]q code is a linear code of length n, dimension k and minimum weight d over the field oforder q. The Griesmer bound gives a lower bound on the length n of an [n, k, d]q code. It is known that
the Griesmer bound is attained for all sufficiently large d for fixed q and k. We pose a conjecture on the
problem to find Dq,k , the largest value of d such that the Griesmer bound is not attained for fixed q and k.
And we give some new results on the conjecture.

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応用数学

15:45〜16:45 特別講演
早 水 桃 子 ( 早 大 理 工)進化の系統樹と系統ネットワークに関する組合せ論

Momoko Hayamizu (Waseda Univ.)

Combinatorics of phylogenetic trees and networks

94

概 要 Since the time of Charles Darwin, phylogenetic trees have been widely used as a model of evolution todescribe the branching history of how the various organisms on Earth arrived at the present day from theircommon ancestor. On the other hand, reconstructing phylogeny from biological data often requires the useof more general graphs called phylogenetic networks to represent both branching and merging. However,existing theorems and algorithms concerning phylogenetic trees do not work as they are for phylogenetic
networks in general. Indeed, as the mathematical biologist Joel E. Cohen stressed in a 2004 essay, theparadigm shift from evolutionary trees to networks is regarded as one of the biological challenges that could
stimulate, and benefit from, major innovations in mathematics. Particularly active in this direction arestudies of combinatorics aimed at elucidating the mathematical and computational properties of phylogenetic
networks. In this talk, in an attempt to introduce the field of combinatorial phylogenetics, I will present an
overview of my research results on the structure of phylogenetic networks, together with related studies andsome open problems.

9 月 14 日（水）10:00〜11:45
11 東 谷 章 弘 (阪 大 情 報)
上 山 健 太 ( 弘 前 大 教 育)

Akihiro Higashitani (Osaka Univ.)
Kenta Ueyama (Hirosaki Univ.)

第 V 会場グラフのスイッチングと付随する単体的複体による (±1) 歪多項式環の分類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classification of (±1)-skew polynomial rings by switching of graphs andits associated simplicial complexes

概 要 Classifying skew polynomial rings is important in noncommutative algebraic geometry because a skew

polynomial ring can be regarded as a noncommutative version of the homogeneous coordinate ring of the
projective space. In this talk, we focus on (±1)-skew polynomial rings. For this case, we prove that theclassification of (±1)-skew polynomial rings up to equivalence of their graded module categories can becompletely done by using the switching of graphs and the simplicial complexes associated to switchingequivalence classes.
12 辻 栄 周 平 (北 教 大 旭 川)
Tan Nhat Tran (Ruhr Univ. Bochum)

Shuhei Tsujie (Hokkaido Univ. of Edu.)
Tan Nhat Tran (Ruhr Univ. Bochum)

強弦グラフの辺ラベルによる特徴づけ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A characterization of strongly chordal graphs by edge-labeling概 要 Stanley showed that a graphic arrangement is free if and only if the corresponding graph is chordal.

The class of MAT-free arrangements is an important subclass of free arrangements. We proved that agraphic arrangement is MAT-free if and only if the corresponding graph is strongly chordal. To prove thiswe gave a characterization of strongly chordal graphs by edge-labeling.
13 尾 白 典 文 (豊 田 工 大 工)
松 井
一 ( 豊 田 工 大 工)

Norifumi Ojiro (Toyota Tech. Inst.)
Hajime Matsui (Toyota Tech. Inst.)

テンソル積によって得られる有理整数剰余環上の符号に対する最小ユー
クリッド重み · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Minimum Euclidean weights for codes over rational integer quotientrings via tensor products

概 要 In this research, we explain that any Zm -code can be uniquely represented by a certain integer

coefficient square matrix called a reduced generator matrix. Then we show that the Kronecker productof the reduced generator matrices Gi for Zmi -code Ci of length li with i = 1, 2 is the reduced generator
matrix for a Zm1 m2 -code C3 of length l1 l2 . As the main result, we give a theorem to calculate the minimum
Euclidean weight of C3 from those of C1 and C2 .

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95

応用数学

14 吉 田 建 一(お茶の水女大ソフトマター教育研究センター)
児 玉 大 樹(東北大AIMR・理化学研iTHEMS)

Ken’ichi Yoshida (Ochanomizu Univ.)
Hiroki Kodama(Tohoku Univ. / RIKEN)

ネットワークによる弾塑性のモデル化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A mathematical model of network elastoplasticity

概 要 A thermoplastic elastomer (TPE) is a polymeric material with rubber elasticity and is removable athigh temperatures. In this talk, we present results of modeling the elastoplastic deformation of a TPE byusing a network represented as a periodic graph. A TPE consists of a soft domain, which exhibits rubber
elasticity, and hard domains, which act as cross-links. This structure can be represented as a graph. We
introduce the tension tensor for a periodically realized graph, which induces the stress and the elasticity.
The hard domains of a TPE are less robust than the cross-links of vulcanized rubber. We express this as
local moves of a graph, which induce the plasticity in elongation.
15 齋 藤渓 ( 神 奈 川 大 工)
瀬 川 悦 生 (横浜国大環境情報)(Kanagawa Univ.)
Kei Saito
Etsuo Segawa (Yokohama Nat. Univ.)

連続時間版 Szegedy walk のスペクトル解析 · · · · · · · · · · · · · · · · · · · · · · · · 15

Spectral analysis for continuous-time Szegedy walks

概 要 The time evolution of continuous-time quantum walks are defined by the Scrödinger equations whilethat of discrete-time walks are defined by the product of coin and shift operators. Strauch (2006) gives aconnection between continuous-time and discrete-time walks by taking a continuous limit for one-dimensionalmodel. The methods in the paper are difficult to apply to graphs more complex than one-dimensional lattice.
By defining split-step quantum walks on the graph, we have led to similar results for Szegedy walks on
more general graphs, which we call continuous version of Szegedy walk. In this talk, we will report on themethod to deriving such a continuous walk and the spectral analysis of its Hamiltonian.
16 寺 田 知 幸(横浜国大理工・金沢工大)
井 手 勇 介 ( 日 大 文 理)
今 野 紀 雄 ( 横 浜 国 大 工)
Tomoyuki Terada(Yokohama Nat. Univ./Kanazawa Inst. of Tech.)(Nihon Univ.)
Yusuke Ide(
YokohamaNat. Univ.)
Norio Konno

パスグラフ上の Szegedy walk に対する確率測度 · · · · · · · · · · · · · · · · · · · · 15

Probability measure for the Szegedy walk on the path graph概 要 In this talk, we consider a spectral analysis of the Szegedy walk on the path graph. Here, we havederived an explicit formula for the probability measure of the walker by using eigenvalues and eigenvectorsof the Jacobi matrix related to the birth and death chain.
13:00〜14:15
17 藤 田 慎 也(横浜市大データサイエンス)

Shinya Fujita (Yokohama City Univ.)

中心グラフの支配数に着目したグラフの分類について · · · · · · · · · · · · · · · 10Classification of graphs in terms of the domination number of central
graphs概 要 For a graph G, the central graph C(G) is the graph constructed from G by subdividing each edge of

G with one vertex and also by adding an edge to every pair of non-adjacent vertices in G. In this talk, wegive a new classification of graphs in terms of the domination number of central graphs.

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応用数学

18 安 藤清 ( 国 立 情 報 学 研)

Kiyoshi Ando (Nat. Inst. of Informatics)

96

Properly contractible edges and properly liftable vertices in a 4-connected
graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Properly contractible edges and properly liftable vertices in a 4-connectedgraph

概 要 We focus on the distribution of properly contractible edges and properly liftable vertices in a minimally

4-connected graph G. Let Ec∗ (G) and L∗ (G) denote the set of properly 4-contractible edges of G and theset of properly 2k-liftable vertices of G, respectively.
Theorem 2

Let G be a minimally 4-connected graph. Then,P

2|Ec∗ (G)| + |L∗ (G)| ≥ 3|U4K1 (G)| + 2|U2K1 ∪K2 (G)| +H∈A′ |UH (G)|.

′

where A is the set of graphs on four vertices with at least two edges whose maximum degree is less than 3,
and UH (G) = {x ∈ V4 (G) | G[NG (x)] ∼= H}.
19 斎 藤明 ( 日 大 文 理)
出 川 慎 悟 ( 日 大 文 理)
(Nihon Univ.)
Akira Saito
Shingo Degawa (Nihon Univ.)

Secure domination in C5 -free graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Secure domination in C5 -free graphs

概 要 A dominating set X in a graph G is said to be secure if for each v ∈ V (G) − X, there exists a vertex


x in NG (v) ∩ X such that X − {x} ∪ {v} is a dominating set. The order of a smallest secure dominating

set is called a secure domination number and denoted by γs (G). For a connected graph H, G is said tobe H-free if G does not contain an induced subgraph isomorphic to H. In this talk, we report that every
C5 -free graph satisfies γs (G) ≤ α(G), where α(G) is the independence number of G. This result unites andextends several known bounds of γs (G) in terms of α(G).
20 斎 藤明 ( 日 大 文 理)
藤 波 大 弥 (総合研究大複合)(Nihon Univ.)
Akira Saito
Hiroya Fijinami(Grad. Univ. for Adv. Stud.)

Relative length of triangle-free graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Relative length of triangle-free graphs

概 要 For a 2-connected graph G, the difference of the orders of a longest path and a longest cycle iscalled the relative length of G and denoted by diff(G). In 2008, Paulusma and Yoshimoto proved thatevery 2-connected triangle-free graph G of order n with σ4 (G) ≥ n + 2 satisfies diff(G) ≤ 1, where σ4 (G)is the minimum value of the sums of degrees of four independent vertices in G. We conjecture that every
2-connected triangle-free graph G of order n with σ4 (G) ≥ s satisfies diff(G) ≤ n + 3 − s. The result by
Paulusma and Yoshimoto corresponds to the case s = n + 2. We verify the conjecture for s = n + 1.

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97

応用数学

9 月 15 日（木）第 V 会場

9:30〜12:00
21 江 藤 徳 宏 (東 大 数 理)
Tokuhiro Eto (Univ. of Tokyo)

On a discrete scheme for the Mullins–Sekerka flow and its fine properties· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On a discrete scheme for the Mullins–Sekerka flow and its fine properties

概 要 The Mullins–Sekerka problem is numerically solved by the charge simulation method at the first time.

In this scheme, an evolving curve in the plane R2 is imitated by a regular polygon. An evolving law isdiscretized by the forward Euler method. An optimal rate between the time step and the number of verticesof the polygon is revealed by means of a careful calculation. A particular contribution of the study is toclarify the possibility to handle the case where an evolving interface touches the boundary of a container.
To our best knowledge, there have been no researches to treat numerically the Mullins–Sekerka problem
with boundary contact angle condition.
22 松 井 一 徳 (成 蹊 大 理 工)

Kazunori Matsui (Seikei Univ.)

Navier–Stokes 方程式に対する rotation form と Lagrange–Galerkin 法 · 15
The rotation form and the Lagrange–Galerkin method for the Navier–Stokes equations

概 要 The advection term in the Navier–Stokes equations can be written in several ways. One of them isthe rotation form. The rotation form is easy to conserve the total kinetic energy when discretized. On theother hand, the Lagrange–Galerkin (LG) method is a powerful numerical method for flow problems becauseof its robustness for convection-dominated problems and symmetry of the resulting matrix. The LG method
uses that the sum of the time derivative and advection terms is the material derivative. In this talk, we
propose a LG scheme for the rotation form Navier–Stokes equations, where the nonlinear term is different
from the advection term.
23 剱 持 智 哉 (名大工)Tomoya Kemmochi (Nagoya Univ.)

Stokes 作用素の有限要素近似に対する Lp リゾルベント評価 · · · · · · · · · · 15
Lp -resolvent estimates for finite element approximation of the Stokes
operator

概 要 In this study, we consider finite element approximation of the Stokes resolvent problem. For parabolic

problems, finite element approximation of a priori estimates, such as resolvent estimates, analyticity ofsemigroups, and maximal regularity, are well-studied. Moreover, these estimates are applied to error
estimates for finite element methods to nonlinear problems. However, studies in this direction has not beendeveloped for the Stokes case. As a starting point of the study, we present the Lp -resolvent estimate for thefinite element approximation of the Stokes resolvent problem.
24 小 山 大 介 (電通大情報理工)
Daisuke Koyama(Univ. of Electro-Comm.)

重調和問題に対する IP 法と HJ 法の間の事前差異評価 · · · · · · · · · · · · · · · 15

An a priori difference estimate between the IP method and the HJ
method for the biharmonic problem

概 要 An interior penalty (IP) method for the biharmonic problem is studied. An a priori difference estimate

between the IP method and the HJ method is derived. From the difference estimate and the a priori error
estimate of the Herrmann–Johnson (HJ) method, an a priori error estimate of the IP method is obtained.
It is shown that the error estimate of the IP method is the same as that of the HJ method by taking apenalty parameter of O(1/h), where h is the mesh size parameter. Further it is shown that the number of
iterations of a naive linear solver for the IP method is independent of the penalty parameter.

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応用数学

25 渡 部 善 隆(九大情報基盤研究開発センター)

Yoshitaka Watanabe (Kyushu Univ.)

98

精度保証付き数値計算による Proudman–Johnson 方程式の定常解の存在
別証 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Another numerical verification proof of steady-state solutions for the
Proudman–Johnson equation

概 要 This talk presents a computer-assisted proof of the existence of steady-state solutions for the

Proudman–Johnson equation which is a representative of the two-dimensional fluid flow. The proposed
approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and it is anotherproof by Miyaji–Okamoto (2019). Verification results show their validity.
26 藤 原 宏 志 (京 大 情 報)
西 田 孝 明 (京 大 情 報⋆)

Hiroshi Fujiwara (Kyoto Univ.)
Takaaki Nishida (Kyoto Univ.⋆)

Heat convections in the horizontal layer with non-uniform heat supply.
Stommel model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Heat convections in the horizontal layer with non-uniform heat supply.
Stommel model

概 要 Stommel (1950) considered a model of thermal convection in horizontally long liquid layer with

non-uniform heat supply under gravity. He obtained approximate solutions by asymptotic expansion of
the equations with respect to a dimension-less parameter and showed its picture of contour line of thestream function and isothermal line. It may be considered as a simplest model to indicate thermal effecton the ocean current. Here we have an existence theorem of stationary solutions for the model undersome assumptions and obtain several figures of contour line of the stream function and isothermal line bynumerical computations, which show the above meaning of the model. Some of the computations are outof the existence theorem.
大理)
27 坂 上 貴 之 (京V. S. Krishnamurthy(Indian Inst. of Tech. Hyderabad)

Takashi Sakajo (Kyoto Univ.)
Vikas S. Krishnamurthy(Indian Inst. of Tech. Hyderabad)

Quantized point vortex equilibria with a Liouville-type background vorticity on a curved torus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Quantized point vortex equilibria with a Liouville-type background vorticity on a curved torus

概 要 An analytic formula of solutions to a modified Liouville equation on a curved torus is presented. Ityields point vortex equilibria with strengths quantized by 2π in a background smooth Liouville-type vorticity
field, which is a model of quantized vortex crystals appearing superfluids and Bose–Einstein–Condensates(BEC). We show that appropriate choices of the loxodromic function in the solution lead to stationary
vortex patterns with point vortices of identical strengths. We also find solutions continuously dependent
on a parameter, such that the point vortices remain fixed whereas the smooth background vorticity changes
with the parameter. We investigate how non-constant curvature and a handle structure of the torus affectthe topological flow structures. This talk is based on joint work with Dr. V. S. Krishnamurthy at Indian
Institute of Technology Hyderabad.
28 清 水 雄 貴 (東 大 数 理)
米 田
剛 ( 一 橋 大 経 済)

Yuuki Shimizu (Univ. of Tokyo)
Tsuyoshi Yoneda (Hitotsubashi Univ.)

三次元 Euler 流の渦伸長に対する幾何学的特徴づけ · · · · · · · · · · · · · · · · · 15

Locality of vortex stretching for the 3D Euler equations

概 要 We discuss what kind of large-scale stationary flow stretch small-scale vortex blob in alignment withstraining direction in 3D incompressible Euler flow.

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99

応用数学

29 奥 村 真 善 美 (北 大 電 子 研)
小 林 康 明 ( 北 大 電 子 研)
長 山 雅 晴 ( 北 大 電 子 研)
藤 原 裕 展 ( 理 化 学 研)
安 ヶ 平 祐 介 ( 北 大 電 子 研)
大 野 航 太 ( 中 大 理 工)

Makoto Okumura (Hokkaido Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Masaharu Nagayama (Hokkaido Univ.)
Hironobu Fujiwara (RIKEN)
Yasugahira Yusuke (Hokkaido Univ.)(Chuo Univ.)
Kota Ohno塑性変形可能な基底膜モデルを用いた毛包のシリンダー構造の再現 · · · · 15

Reproduction of the cylinder structure of hair follicles using a plastic
deformable basement membrane model

概 要 As an appendage of the skin, a hair follicle is the source of the hair. The hair follicle is crucial for

maintaining the epidermis and hair tissue homeostasis and for repairing damaged tissue. We have been
attempting to design a mathematical model that reproduces the cylinder structure of the hair follicle.
Although we have reproduced the cylinder shape of the hair follicle to some extent in the mathematicalmodel, there are still significant differences from the actual experimental results. Thus, we aim to reproduce
the cylinder structure closer to the experimental results by improving the mathematical model. In thispresentation, we present the results.
14:15〜16:45
30 高 橋 淳 一 (高 知 大 理 工)
大 森 祥 輔 ( 早 大 理 工)

Junichi Takahashi (Kochi Univ.)
Shosuke Ohmori (Waseda Univ.)

η 対称性を持つ非エルミート量子系における Rigged Hilbert 空間の構築· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Construction of Rigged Hilbert space for non-Hermitian quantum system with η symmetry

概 要 Non-Hermitian quantum systems with η symmetry have been widely studied because of their interesting

features. On the other hand, the rigged Hilbert space is a set of linear phase spaces introduced to justify
the description of brackets in quantum mechanics and can be obtained by expanding the Hilbert space toincorporate superfunctions such as delta functions. It is known that ordinary Hermite quantum mechanics
is formulated in this space, but it is unclear whether it can be a mathematical foundation space for systems
that go beyond conventional quantum theory, such as non-Hermite quantum systems. In this talk, we showthat RHS formulation is possible for η symmetric non-Hermitian quantum systems.
31 甲 斐 大 貴 (阪 市 大 理)

Hirotaka Kai (Osaka City Univ.)

Path-properties of jump-diffusion processes on Riemannian manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Path-properties of jump-diffusion processes on Riemannian manifolds

概 要 It is natural to construct Lévy processes on Riemannian manifolds and study their properties. We

focus on the jump-diffusion process which is given by projecting the solution of the Marcus-type stochastic
differential equation on the orthonormal frame bundle. The generator of the jump-diffusion process is similar
to the one of the Lévy process on Euclidian space. In this talk, we will discuss irreducibility, transienceand conservativeness. In order to grasp the behavior of the paths of the jump-diffusion process, we will
introduce some nice upper and lower estimates.

最終版: 2022/8/8
応用数学

32 岩 上
爲
真
毛
岩
岡
光
近
神
渡

聡
(アースライズカンパニー)賀 雅 彦(アースライズカンパニー)田 将 英(アースライズカンパニー)
利 道 明(アースライズカンパニー)
上 義 隆(アースライズカンパニー)
本 尚 己(アースライズカンパニー)
井 英 視(アースライズカンパニー)
森 秀 高 (岡山大環境生命)
山大)保 秀 司 (岡辺 雅 二
(岡山大⋆・岡山大環境生命)

Satoshi Iwakami(Earth Rise Company, Inc.)
Masahiko Tamega(Earth Rise Company, Inc.)
Masahide Sanada(Earth Rise Company, Inc.)
Michiaki Mohri(Earth Rise Company, Inc.)
Yoshitaka Iwakami(Earth Rise Company, Inc.)
Naoki Okamoto(Earth Rise Company, Inc.)
Eishi Mitsui (Earth Rise Company, Inc.)
Hidetaka Chikamori (Okayama Univ.)
Shuji Jimbo (Okayama Univ.)
Masaji Watanabe(Okayama Univ.⋆ /Okayama Univ.)

100

測位データと音響測深機データから水面下の地形を作成するための数理的手法の考察 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Study of mathematical techniques for constructing underwater topography from positioning data and echo sounder data

概 要 Disastrous heavy rain events are expected to occur more frequently as climate change progresses, and

it is important to update information on water areas such as rivers, reservoirs and coastal waters. This study
focuses on construction of underwater topographic surfaces from positioning data and echo sounder data.
Longitude and latitude components of ellipsoidal coordinates recorded by a GPS receiver are transformed torectangular coordinates, and combined with vertical components including depth data recorded by an echosounder unit. So generated underwater topographic data are introduced into construction of an underwater
topographic surface which is defined as a piecewise linear function over a triangular mesh.

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応用数学

101

大
理)
33 劉
恩 豪 (京井 元 佑 介 ( 京 大 高 等 研)
平 岡 裕 章 ( 京 大 高 等 研)

(Kyoto Univ.)
Enhao Liu
Yusuke Imoto (Kyoto Univ.)
Yasuaki Hiraoka (Kyoto Univ.)

Curse of dimensionality in persistence diagrams · · · · · · · · · · · · · · · · · · · · 15

Curse of dimensionality in persistence diagrams

概 要 High dimension low sample size (HDLSS) data brings difficulties in statistical analysis. In this talk,we will first show the asymptotic behavior of persistence diagrams of high dimensional random data. As aresult of the asymptotic behavior, we show the unreliability of using observed persistence diagrams in reality
due to the presence of high dimensional noise, indicating the existence of curse of dimensionality (CoD) in
persistence diagrams. Finally, we claim that simple application of principal component analysis (PCA) is
not sufficient to completely eliminate the curse of dimensionality in persistence diagrams
34 岡宏 枝 ( 龍 谷 大 理 工)

Hiroe Oka

(Ryukoku Univ.)

Equilibria and their stability in networks with steep sigmoidal nonlinearities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Equilibria and their stability in networks with steep sigmoidal nonlinearities

概 要 Equilibria of continuous differential equation models of network dynamics is investigated. The motiva-tion comes from gene regulatory networks where each directed edge represents either down- or up-regulation,and is modeled by a sigmoidal nonlinear function. We show that the existenceand stability of equilibria of asigmoidal system are determined by a combinatorial analysis of the limiting switching system with piecewise
constant nonlinearities.
35 矢 ヶ 崎 一 幸 (京 大 情 報)

Kazuyuki Yagasaki (Kyoto Univ.)

Some recent results on nonintegrability of dynamical systems · · · · · · · · 15
Some recent results on nonintegrability of dynamical systems

概 要 In this talk, we briefly review some recent results on nonintegrability of dynamical systems: Nearly

integrable systems, time-periodic perturbations of single-degree-of-freedom Hamiltonian systems and theSEIR epidemic model. A generalized version due to Ayoul and Zung of the Morales–Ramis and Morales–
Ramis–Simó theories were used to obtain these results. A perturbation approach was also used for the firsttwo results.
36 矢 ヶ 崎 一 幸 (京 大 情 報)

Kazuyuki Yagasaki (Kyoto Univ.)

Nonintegrability of three- and four-dimensional dynamical systems neardegenerate equilibria · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nonintegrability of three- and four-dimensional dynamical systems neardegenerate equilibria

概 要 In this talk, we review a recent result on nonintegrability of three- and four-dimensional dynamicalsystems near degenerate equilibria. We assume that the origin x = 0 is an equilibrium and the Jacobianmatrix of the vector field at x = 0 has (I) a zero and pair of purely imaginary eigenvalues, λ = 0, ±iω (ω > 0),in the three-dimensional case or (II) two pairs of purely imaginary eigenvalues, ±iωj (ωj > 0), j = 1, 2,
with ω1 /ω2 ̸∈ Q in the four-dimensional case. Our results also imply that three- and four-dimensional
systems exhibiting fold-Hopf and double-Hopf bifurcations, respectively, are real-analytically nonintegrable
in general.

最終版: 2022/8/8
応用数学

37 梶 原 唯 加 (京 大 情 報)
金英 子
(阪大全学教育推進機構)
柴 山 允 瑠 ( 京 大 情 報)
Yuika Kajihara (Kyoto Univ.)(Osaka Univ.)
Eiko Kin
Mitsuru Shibayama (Kyoto Univ.)102

平面 2n 体問題の周期解における braid type · · · · · · · · · · · · · · · · · · · · · · · · 15

Braid types of periodic solutions in the planar 2n-body problem

概 要 Periodic solutions of the planar n-body problem determine braids through the trajectory of n bodies.

According to the Nielsen–Thurston classification of surface automorphisms, braids fall into three types:
periodic, reducible and pseudo-Anosov. In this talk, we give a way to classify periodic orbits in the planar
2n-body problem through braid types.
38 須 田 智 晴 (慶 大 理 工)
Tomoharu Suda

(Keio Univ.)

Partial maps generated by flows · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Partial maps generated by flows

概 要 The concept of the first-return map is fundamental in studying continuous-time dynamical systems.

Such maps are usually not global and are defined only partially, reflecting the dynamics of the flow. A
question here is whether we can use that partiality to our advantage. In this talk, we consider a generalizationof the first-return map and discuss its applications to the description of dynamics and a reduction of hybrid
systems to flows. This talk is based on arXiv:2205.03794 [math.DS].
17:00〜18:00

特別講演
西 口 純 矢 (東 北 大 A I M R )時間遅れがもたらす無限次元性と超越性

Junya Nishiguchi (Tohoku Univ.)

Infinite-dimensionality and transcendency brought by time-delay

概 要 Time evolutionary systems and their mathematical models with a “time-lag” in causality are col-lectively called time-delay systems. A “time-lag” in such a time-delay system arises, for example, fromthe finiteness of the rate of transmission of information. One can observe various dynamic phenomena as
time-delay systems. A delay diﬀerential equation (DDE), which is a differential equation whose derivativeẋ(t) of an unknown function x = x(t) also depends on the past value of x, is a typical example of atime-delay system as a mathematical model. DDEs are similar in form to ordinary differential equations,however, these equations have infinite-dimensionality and transcendency as their characteristics. In the talk,we share previous studies of time-delay systems and discuss possible future directions from the viewpoint oftheory and applications. For this purpose, the talk will be divided into two parts: 1. Overview of previous
studies of time-delay systems, especially of mathematical studies of DDEs, 2. A recent study by the speakerincluding variation of constants formula for DDEs.

9 月 16 日（金）第 V 会場

9:30〜12:00
39 渡 辺樹 ( 早 大 理 工)

Itsuki Watanabe (Waseda Univ.)

Application of Markov chain approximation method to nonlinear reactiondiffusion equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Application of Markov chain approximation method to nonlinear reactiondiffusion equation

概 要 We consider the hight density scaling limit of the stochastic model for nonlinear diffusion. The

stochastic model can be constructed as a random walk on the discrete torus with a nonlinear diffusion
rates. In this talk, we show that the deterministic limit of the stochastic model is governed by the nonlinear
reaction-diffusion equation by showing the relative compactness and using the continuous mapping theorem.

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103

応用数学

40 江 夏 洋 一 (東 京 理 大 教 養)
M. Banerjee(Indian Inst. of Tech. Kanpur)

Yoichi Enatsu (Tokyo Univ. of Sci.)
Malay Banerjee(Indian Inst. of Tech. Kanpur)

捕食時の種間協力を考慮した被食者-捕食者モデル · · · · · · · · · · · · · · · · · · 15

A prey-predator model describing hunting cooperation

概 要 In this talk, we consider the dynamics of a prey-predator model describing hunting cooperation. By

focusing on coefficients for hunting cooperation and carrying capacity, we investigate the stability of apredator-free equilibrium and coexistence equilibria. In particular, for the case where the carrying capacity
is small, we investigate the condition under which saddle-node bifurcation occurs when the model has two
coexistence equilibria. Some of results are based on a joint work with Malay Banerjee (IIT Kanpur).
41 関 坂 歩 幹 (明大研究・知財)
小 川 知 之 ( 明 大 総 合 数 理)
Ayuki Sekisaka (Meiji Univ.)
Toshiyuki Ogawa (Meiji Univ.)

外来種の侵入可能性を規定する固有値問題 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Eigenvalue problem defining the invasive potential of alien species

概 要 In a competitive system, two species are competing with each other, and the question is whether aninvasive alien species can invade. In this case, the problem of what kind of potentials the eigenvalues exist
in the Strum–Liouville type eigenvalue problem determines the above problem. In this talk, I will present
results obtained for the Strum–Liouville type eigenvalue problem by using a topological index called theMalov index to determine the shape of the potential and the existence of eigenvalues.
42 岩 崎悟 ( 阪 大 情 報)
山 口 勇 太 郎 ( 阪 大 情 報)
Satoru Iwasaki (Osaka Univ.)
Yutaro Yamaguchi (Osaka Univ.)

メトリックグラフ上の Allen–Cahn 方程式における安定定常解集合のパラメータ依存関係 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Parameter dependence of stationary solutions of the Allen–Cahn equations in metric graphs

概 要 We are concerned with stationary solutions of the Allen–Cahn equations in compact metric graphs.

More precisely, we attempt to reveal a parameter dependence of sets of stationary solutions through an edge
labelling problem. In this presentation, we present some numerical simulations for the Allen–Cahn equations
in metric graphs and show that solutions of the edge labeling problem actually reveal the structures ofstationary solutions of the Allen–Cahn equations.
43 関 坂 歩 幹 (明大研究・知財)
山 本 宏 子 (理 化 学 研 A I P )Ayuki Sekisaka (Meiji Univ.)
Hiroko Yamamoto (RIKEN)

シリンダー領域の反応拡散方程式のスペクトル問題と Evans 関数 · · · · · 15

Evans function and spectral problem for a reaction-diffusion equation
in a cylindrical domain

概 要 In this study, we consider the spectral problem for a reaction-diffusion equation of a traveling wave

solution traveling in the cylindrical domain and construct the Evans function. For the boundary conditions,
we consider the periodic and the Robin boundary conditions, respectively, and introduce the results obtained.

最終版: 2022/8/8
応用数学

44 穴 田 浩 一 (早 大 高 等 学 院)
石 渡 哲 哉
(芝浦工大システム理工)
牛 島 健 夫 ( 東 京 理 大 理 工)
Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Takeo Ushijima (Tokyo Univ. of Sci.)

104

曲線短縮問題に現れる準線形放物型偏微分方程式に対する爆発解の上からの評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Upper estimates for blow-up solutions of a quasi-linear parabolic equation in the curve shortening flow

概 要 We consider asymptotic behavior of blow-up solutions to a quasi-linear parabolic equation ut =uδ (uθθ + u) which appears in the classical curve-shortening flow of a closed cardioid-like immersed curvewith a self-crossing point. It is known that this problem has type II blow-up solutions. In this talk, we
provide upper esitimates for blow-up rates of solutions for the case of 2 < δ < 3 and δ = 3.
45 出 原 浩 史 (宮 崎 大 工)
大理)
小 林 俊 介 (京Hirofumi Izuhara (Univ. of Miyazaki)
Shunsuke Kobayashi (Kyoto Univ.)

2 成分反応拡散系のパターン形成: 一様周期解からの分岐を追う · · · · · · 15
Pattern formation in 2-component reaction-diffusion systems

概 要 We consider the pattern formation in 2-component reaction-diffusion systems. Introducing a specificparameter into the 2-component reaction-diffusion systems, the constant steady state is destabilized due toHopf bifurcation, and spatially homogeneous periodic solutions appear. In this talk, we numerically treat abifurcation problem from the spatially homogeneous periodic solutions.
46 長
物
榊
中
小
北

山
部
原
村
林
畑

雅
治
航
健
康
裕

晴 ( 北 大 電 子 研)
徳 ( 阪 公 大 理)也 ( 岡 山 理 大 理)
一 ( 金 沢 大 理 工)
明 ( 北 大 電 子 研)
之 ( 千 葉 大 理)

Masaharu Nagayama (Hokkaido Univ.)
Harunori Monobe (Osaka Metro. Univ.)
Koya Sakakibara(Okayama Univ. of Sci.)
Ken-Ici Nakamura (Kanazawa Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Hiroyuki Kitahata (Chiba Univ.)

自己駆動体運動に対する反応拡散系モデルについて · · · · · · · · · · · · · · · · · 15

Reaction-diffusion model for the self-propelled body

概 要 A self-propelled system is a system that moves by having an action that deforms itself or by having

an action that changes its own motion field. The motion of bacteria and cells, which are living systems,
and the motion of camphor and pentanol droplets, which are non-living systems, are considered to belong
to self-driven systems because they have internal mechanisms that generate motion. We developed a selfpropelled system model based on the Allen–Cahn equation. We combined it with the equation for molecularsurfactant concentration used in previous studies to construct a mathematical model that can handle selfpropelled system motion with shape change. One feature of our mathematical model is that it can represent
deforming self-propelled bodies such as droplets and solid self-propelled bodies such as camphor with asingle parameter.

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105

応用数学

47 桑 村 雅 隆 (神 戸 大 発 達)

Masataka Kuwamura (Kobe Univ.)

細胞の極性化における polarity oscillations と wave-pinning について · 15

Oscillations and wave-pinning in cell polarity formation

概 要 We consider reaction-diffusion systems with bistable nonlinearity and mass conservation, which areuseful for understanding cell polarization. We show that a specific model proposed by [Otsuji et al, PLoS
Comp. Biol. 3 (2007), e108] exhibits four different spatiotemporal patterns including two types of oscillatory
patterns which can be regarded as cell polarity oscillations with the reversal and non-reversal of polarity,
respectively. Moreover, we show the existence and stability of single transition layer in such reactiondiffusion systems under general assumptions by the singular perturbation theory. This result provides a
condition for wave-pinning in cell polarity formation.
14:15〜16:10
48 高 橋正 (甲南大知能情報)
鷲 野 朋 広 ( 甲 南 大 自 然)

Tadashi Takahashi (Konan Univ.)
Tomohiro Washino (Konan Univ.)

学習モデルを用いた現象分析 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Analysis of phenomenon using a learning model

概 要 We consider an initial value of the statistic model and the dynamics of learning changing under the

influence of a critical line in case the true distribution near the singular regions is realizable by the statisticalmodel. Then over-fitting phenomena that a training loss decreases but a validation loss increases have been
observed in case the true distribution on the singularity is realizable by the statistical model. We consider
the phenomenon of dynamics on the learning loss surface using the theory of the learning model.
49 陳鈺
涵 (神戸大システム情報)
松 原
崇 ( 阪 大 基 礎 工)
谷 口 隆 晴 (神戸大システム情報)(Kobe Univ.)
Yuhan Chen
Takashi Matsubara (Osaka Univ.)
Takaharu Yaguchi (Kobe Univ.)

ニューラルシンプレクティック形式と変分原理の両立性について · · · · · · 15

Compatibility of the neural symplectic forms and the variational principle

概 要 In recent years, research on deep learning techniques to formulate models from observed data ofphysical phenomena has been attracting attention. Neural symplectic forms learn the symplectic form
from data using neural networks, thereby providing a method for learning Hamiltonian equations from data
represented in general coordinate systems. However, there has been little research on discretization methods
for simulation using those models. In this presentation, I will talk about a variational principle that leads
to neural symplectic forms. Using this, a numerical method called variational integrator can be designed.

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応用数学

50 徐
百
陳
鈺
松 原
谷 口 隆

歌 (神戸大システム情報)
涵 (神戸大システム情報)
崇 ( 阪 大 基 礎 工)
晴 (神戸大システム情報)(Kobe Univ.)
Baige Xu
(Kobe Univ.)
Yuhan Chen
Takashi Matsubara (Osaka Univ.)
Takaharu Yaguchi (Kobe Univ.)

106

一般化 Dissipative SymODEN の GENERIC 形式 · · · · · · · · · · · · · · · · · · · 15

GENERIC formulation of generalized dissipative SymODEN

概 要 In recent years, methods for learning governing equations of physical phenomena using deep learning

have been studied extensively. Therein Dissipative SymODEN is known as a deep learning model that learns
the port-Hamiltonian dynamics with energy dissipation. On the other hand, the GENERIC formulation
is a framework for describing non-equilibrium thermodynamic systems, including terms of two dynamics,
reversible and irreversible. In this work, by rewriting the dissipative SymODEN models to GNERIC
systems, we propose a deep neural GENERIC model for the port-Hamiltonian dynamics, thereby revealing
the hidden GENERIC structure behind the data.
51 安 田 諒 子 (神戸大システム情報)
松 原
崇 ( 阪 大 基 礎 工)
谷 口 隆 晴 (神戸大システム情報)(Kobe Univ.)
Ryoko Yasuda
Takashi Matsubara (Osaka Univ.)
Takaharu Yaguchi (Kobe Univ.)

神経ネットワーク動画像からのモデリングの試み · · · · · · · · · · · · · · · · · · · 15

Learning differential equation models from neural activity images

概 要 Recently, methods for constructing differential equation models using neural networks have been

attracting much attention. If such methods can be used to learn equations from images, it would be possible
to construct models at a very low cost. Although research on such an approach has been performed, only
simple problems have been considered. In this study, we apply such a technique to construct a model froma real data, i.e., images of a neural activity.
52 磯 部伸 ( 東 大 数 理)

Noboru Isobe (Univ. of Tokyo)

ODE-Net の変分的定式化とその解存在について · · · · · · · · · · · · · · · · · · · · 15
On a variational formulation of ODE-Net and an existence result

概 要 Deep learning has attracted much attention recently because of its interpretation as a variational

problem with differential equations as constraints, or ODE-Net. On the other hand, the existence ofa solution to the problem has been guaranteed only in impractical conditions. Therefore, we use the
Benamou–Brenier formula to prove the existence of ODE-Nets under some reasonable assumptions.
53 長 瀬 准 平 (芝 浦 工 大 理 工)
石 渡 哲 哉
(芝浦工大システム理工)

Jumpei Nagase (Shibaura Inst. of Tech.)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)

連続区分線型関数を活性化関数にもつ深層ニューラルネットワークモデ
ルの等価性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Equivalence of deep neural network models with continuous piecewise
linear functions as activation functions

概 要 Deep learning is one of the leading machine learning methods in recent years. One of the major

research issues in deep learning is the problem of model design, and since many models have been proposed
experimentally, a systematic understanding of models is still insufficient. In this study, we focus on theactivation function among the components of designing a model to interpret a certain model in a unified
manner. Specifically, we show that there is no difference between the widely used ReLU activation function
and similar piecewise linear functions in terms of expressive ability.

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応用数学

大
理)
54 神 野 拓 哉 (東大理)
三 浦 裕 亮 (東(中 井 拳 吾 東京海洋大学術)齊 木 吉 隆 (一橋大経営管理)
末 松
環 ( 理 化 学 研)
高 須 賀 大 輔 (海洋研究開発機構)
米 田
剛 ( 一 橋 大 経 済)

Takuya Jinno (Univ. of Tokyo)
Hiroaki Miura (Univ. of Tokyo)
Kengo Nakai(Tokyo Univ. of Marine Sci. and Tech.)
Yoshitaka Saiki (Hitotsubashi Univ.)(RIKEN)
Tamaki Suematsu
Daisuke Takasuka(Japan Agency for Marine-Earth Sci. and Tech.)Tsuyoshi Yoneda (Hitotsubashi Univ.)

Constructing a data-driven model of intraseasonal weather time-series
using machine learning · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Constructing a data-driven model of intraseasonal weather time-series
using machine learning

概 要 By employing a reservoir computing, a machine learning technique, we construct a data-driven model

for predicting time-series of an index of Madden–Jullian oscillation (MJO). MJO has far reaching influenceon the global weather and is recognized to be one of the most important sources of predictability in an
extended-range weather forecast. Our model has the potential of predicting the MJO for one month. This
successful modelling relies on the the creation of an appropriate training time-series which has relatively low
dimensional deterministic structures by employing a newly created band-pass filter. The usage of the delay
coordinate also contributes to the effective modeling.
16:25〜17:25

特別講演
川 原 田 茜 ( 京 都 教 育 大)

Akane Kawaharada(Kyoto Univ. of Edu.)

セル・オートマトンが生成するフラクタルの特徴付けについて

Characterization of fractals generated by cellular automata

概 要 In this talk, we mainly study linear one-dimensional and two-dimensional elementary cellular automata

that generate symmetrical spatio-temporal patterns. By observing self-similar structures, we count the
number of nonzero states in the spatio-temporal patterns of cellular automata for each time step n ∈ Z≥0 .
This allows us to compute future activities more efficiently than simulating the entire spatio-temporal
patterns. We also normalize the number of nonzero states of the patterns, take the limits, and give onevariable functions for the limit sets. We can obtain a one-variable function for each limit set and show thatthe resulting functions are singular functions, which are non-constant, are continuous everywhere, and havea zero derivative almost everywhere. For Rule 90, a one-dimensional elementary cellular automaton, and a
two-dimensional elementary CA, we show that the resulting functions are Salem’s singular function.

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ト

ポ

ロ

9 月 13 日（火）

ジ

108

ー

第 VII 会場

9:30〜12:00
1 赤 池 祐 次 ( 呉 工 高 専)
友 安 一 夫 ( 都 城 工 高 専)

Yuji Akaike (Kure Nat. Coll. of Tech.)Kazuo Tomoyasu(Miyakonojo Nat. Coll. of Tech.)Higson 型コンパクト化の完全性と剰余の連結性 · · · · · · · · · · · · · · · · · · · · 10
Perfectness of Higson type compactifications and connectedness of remainders

概 要 We study perfectness of Higson type compactifications and give a necessary and sufficient condition

that the subpower and the sublinear Higson compactification of locally connected proper metric space are
perfect. Consequently, we show that the sublinear Higson corona of the half open interval with the usual
metric is an indecomposable continuum.
2 越 野 克 久 ( 神 奈 川 大 工)

Katsuhisa Koshino (Kanagawa Univ.)

Recognizing the topologies on spaces of metrics · · · · · · · · · · · · · · · · · · · · 15
Recognizing the topologies on spaces of metrics

概 要 Given a metrizable space X, let P M (X), M (X), AM (X), and EM (X) be the spaces consisting ofcontinuous bounded pseudometrics, continuous bounded metrics, bounded admissible metrics, and admissible
metrics that can be extended on the one-point compactification of X, which are regarded as subspaces in thespace of real-valued continuous bounded functions on X 2 . In this talk, we shall investigate the topologicaltypes of P M (X), M (X) and AM (X) endowed with the uniform convergence topology, and EM (X) endowedwith the compact-open topology.
3 井 上 雅 照 ( 岡 山 理 大 理)

Masateru Inoue (Okayama Univ. of Sci.)

Morava K 理論の安定余作用素と形式群の自己同型群のファイバー積 · · 10
The stable cooperations of Morava K-Theory and the fiber product ofautomorphism groups of formal group laws

概 要 The Hopf algebra K(n)∗ (K(n)), the stable cooperations of n-th Morava K-theory at an odd prime, iswell-known. Whereas the main part of K(n)∗ (K(n)) corepresents the group-valued functor consisting of theautomorphisms of a formal group law of height n, relations between the whole structure of K(n)∗ (K(n)) andformal group laws have not been investigated well. Firstly, we constitute the fiber product of two naturaltransformations between the automorphism groups of formal group laws, and the corepresenting Hopf
algebra C∗ . Next, we construct a Hopf algebra homomorphism from C∗ to K(n)∗ (K(n)) via Boardman’s
stable comodule algebras. By Yagita’s results and the algebra structure of K(n)∗ (K(n)), we see that thehomomorphism is an isomorphism.
4 松 橋 英 市 (島根大総合理工)大 島 慶 之 ( 島 根 大 自 然)

Eiichi Matsuhashi (Shimane Univ.)
Yoshiyuki Oshima (Shimane Univ.)

いくつかの分解可能連続体およびそれらの超空間 · · · · · · · · · · · · · · · · · · · 15

Some decomposable continua and their hyperspaces

概 要 We show that every irreducible D ∗∗ -continuum is an arc. This gives the negative answer to [1,Question 2]. Also, we prove that being Wilder, being D, being D∗ , and being D∗∗ are Whitney properties.

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109

5 栗
内
若
山

林 勝 彦 ( 信 州 大 理)
藤 貴 仁 (日本工大共通教育)
月
駿 ( 信 州 大 理)
口 俊 博 ( 高 知 大 教 育)

Katsuhiko Kuribayashi (Shinshu Univ.)
Takahito Naito (Nippon Inst. of Tech.)
Shun Wakatsuki (Shinshu Univ.)
Toshihiro Yamaguchi (Kochi Univ.)

Cartan calculi on the free loop spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Cartan calculi on the free loop spaces

概 要 A typical example of a Cartan calculus is the Lie algebra representation of vector fields of a manifold on

the derivation ring of the de Rham complex. In this talk, we investigate Cartan calculus on the Hochschildchain complex of DGAs. It is a Lie algebra representation of the André–Quillen cohomology of a CDGA on
the endomorphism ring of the Hochschild homology in terms of the homotopy Cartan calculi in the sense of
Fiorenza and Kowalzig. Moreover, the representation in the Cartan calculus is interpreted geometrically asa map from the real homotopy group of the monoid of self-homotopy equivalences to the derivation ring on
the loop cohomology.
6 栗
内
若
山

林 勝 彦 ( 信 州 大 理)
藤 貴 仁 (日本工大共通教育)
月
駿 ( 信 州 大 理)
口 俊 博 ( 高 知 大 教 育)

Katsuhiko Kuribayashi (Shinshu Univ.)
Takahito Naito (Nippon Inst. of Tech.)
Shun Wakatsuki (Shinshu Univ.)
Toshihiro Yamaguchi (Kochi Univ.)

BV exactness and string brackets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

BV exactness and string brackets

概 要 The string bracket is a Lie bracket on the S 1 -equivariant homology of the free loop space of an oriented

closed manifold, which is introduced by Chas and Sullivan. In this talk, we explain methods to compute
them when the manifold is BV exact. This method can be applied to many examples, since any rationallyformal space (or more generally a space admitting positive weights) is BV exact. We also give non-examples
of BV exact spaces, which are found by a computer-assisted method.
7 浅 尾 泰 彦 ( 福 岡 大 理)
石 黒 賢 士 ( 福 岡 大 理)
山 縣
真 ( 福 岡 大 理)

Yasuhiko Asao (Fukuoka Univ.)
Kenshi Ishiguro (Fukuoka Univ.)
Makoto Yamagata (Fukuoka Univ.)

Admissible maps and the cohomology of classifying spaces · · · · · · · · · · 10

Admissible maps and the cohomology of classifying spaces

概 要 The admissible map that determines a map between classifying spaces of connected compact Liegroups can be regarded as a matrix. We discuss the diagonalizability of such matrices as well as thetriangularizability, particularly in the case of generalized cyclic matrices. Sometimes a high-dimensional
behavior characterizes the induced homomorphism of the cohomology. We will generalize some previous
results.
8 田 邊 真 郷 ( 北 大 情 報)

Masato Tanabe (Hokkaido Univ.)

Definable な亜群の滑層分割について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Canonical stratification of definable groupoids

概 要 We consider semialgebraic or subanalytic category, or more generally, o-minimal category over R or

X-category. These are examples of ‘tame topology.’ In this talk, we present a structure of a definable Liegroupoid and its orbit space in these categories. Our work is based on M. Shiota’s theory of X-category,and refine and generalize J. N. Mather and V. A. Vassiliev’s results on real algebraic group actions.

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トポロジー

9 山 本 卓 宏 ( 東 京 学 大 教 育)
Takahiro Yamamoto(Tokyo Gakugei Univ.)

110

境界付き曲面上の安定写像のトポロジー · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Topology of stable maps of surfaces with boundary into the plane

概 要 A smooth map of a compact surface with boundary into the plane is called weakly admissible if it

behaves locally like a stable map on a neighbourhood of the boundary. The notions of the half boundary
winding number of a weakly admissible smooth map M → R2 and weakly-admissibly homotopic among
weakly admissible smooth maps M → R2 are introduced. Then, we show that weakly admissible smooth
maps f0 and f1 : M → R2 are weakly-admissibly homotopic if and only if the half boundary winding numberof f0 coincides with that of f1 .
14:20〜18:00
10 地 引 知 栄 (東 工 大 理)
Chihaya Jibiki(Tokyo Tech)

左順序の構成とその性質について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Constructions of left-orderings and investigating their properties

概 要 I show new left orderings of an HNN extension and an countably-generated group. More precisely,

these are left-orderings of Baumslag–Solitar groups and inductive limits of groups and investigate propertiesof them. Our construction is based on the fact that an HNN extension is a semidirect product of an inductive
limit of amalgamated free products with Z. The left ordering on the BS(m, n) is nether Conradian nor
isolated.
11 佐 藤 尚 倫 (早 大 理 工)

Takamichi Sato (Waseda Univ.)

On subgroups of Richard Thompson’s group F · · · · · · · · · · · · · · · · · · · · 15
On subgroups of Richard Thompson’s group F

概 要 The R. Thompson group F has a description as the group of piecewise linear homeomorphisms fromthe closed unit interval onto itself that are differentiable everywhere except at finitely many dyadic rational
numbers and such that on the intervals of differentiability the derivatives are integer powers of 2. We givean algebraic characterization, as subgroups of F , of the stabilizers of finite sets of numbers in the interval(0, 1) under the natural action of F on (0, 1).
12 田 嶌優 (北大理) [ サイクルグラフのマグニチュードホモロジーと Asao–Izumihara 複体のホモトピー型 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yu Tajima(Hokkaido Univ.)

Magnitude homology of cycle graphs and the homotopy type of the
Asao–Izumihara complexes

概 要 The magnitude homology is defined by Hepworth and Willerton as a categorification of the magnitude(an invariant for metric spaces). Recently, Asao and Izumihara introduced CW complexes whose homology
groups are isomorphic to direct summands of graph magnitude homology groups. We prove that the Asao–
Izumihara complex is homotopy equivalent to a wedge of spheres (of various dimensions) for cycle graphswith 2m − 1 (m = 3, 4, · · · ) vertices.
13 田 所 勇 樹 (木 更 津 工 高 専)
逆 井 卓 也 ( 東 大 数 理)
田 中
心 ( 東 京 学 大 教 育)
Yuuki Tadokoro(Kisarazu Nat. Coll. of Tech.)Takuya Sakasai (Univ. of Tokyo)
Kokoro Tanaka (Tokyo Gakugei Univ.)

Minimal generating sets of groups of Kim–Manturov · · · · · · · · · · · · · · · · 10

Minimal generating sets of groups of Kim–Manturov

概 要 Kim and Manturov introduced a certain group derived from triangulations of a surface. Using a

combinatorial group method, we give a minimal generating set of the group.

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111

14 菅 原 朔 見 (北大理)Sakumi Sugawara (Hokkaido Univ.)

超平面配置の Z-局所系係数コホモロジーと CDO 型定理 · · · · · · · · · · · · · 15

Z-local system cohomology of hyperplane arrangements and a CDOtype theorem

概 要 For the complement of a complex hyperplane arrangement, a vanishing theorem of C-local systemcohomology is known, which is first proved by Cohen, Dimca, and Orlik. In this talk, we consider the
Z-local system cohomology for complexified real arrangements and prove a CDO-type theorem for Z-local
system cohomology. The method to calculate the cohomology is based on the minimality of arrangements
and combinatorial descriptions of basis in terms of chambers.
大理)
15 吉 永 正 彦 (阪石 橋
卓 (ARISE analytics)
大理)
菅 原 朔 見 (北Masahiko Yoshinaga (Osaka Univ.)
Suguru Ishibashi (ARISE analytics)
Sakumi Sugawara (Hokkaido Univ.)

20・12 面体配置と関連する二重被覆空間 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The icosidodecahedral arrangement and related double coverings

概 要 The icosidodecahedral arrangement is a plane arrangement in three dimensional space which is closely

related to the icosidodecahedron. The icosidodecahedral arrangement has two peculiar properties. First,
it provides the first example of arrangement such that the first homology of the Milnor fiber has torsion.
Second, it breaks a conjecture by Papadima and Suciu concerning the first Betti number of the Milnor fiber.
In this talk we will discuss the relationship between these two peculiar properties.
16 原 子 秀 一 (東 大 数 理)

Shuichi Harako (Univ. of Tokyo)

Computational results for the symplectic derivation Lie algebras · · · · · 15
Computational results for the symplectic derivation Lie algebras

概 要 The Lie algebras consisting of symplectic derivations on certain algebras are called the symplec-tic derivation Lie algebras. We determine the second homology group of the certain Lie ideal of “thecommutative world” of the symplectic Lie algebras in terms of symplectic modules.
17 Y. Eliashberg (Stanford Univ.)
小 川
竜 ( 東 海 大 理)
吉 安
徹 (京都教育大教育)

Yakov Eliashberg (Stanford Univ.)
Noboru Ogawa (Tokai Univ.)
Toru Yoshiyasu (Kyoto Univ. of Edu.)

Stabilized convex symplectic manifolds are Weinstein · · · · · · · · · · · · · · · 15

Stabilized convex symplectic manifolds are Weinstein

概 要 We show that a stabilized convex symplectic (also called Liouville) manifold with the homotopy typeof a half dimensional CW-complex is symplectomorphic to a flexible Weinstein manifold.
18 林

晋(JST さきがけ・東北大 AIMR)

Shin Hayashi(JST PRESTO / Tohoku Univ.)

An index theorem for quarter-plane Toeplitz operators via extended
symbols · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An index theorem for quarter-plane Toeplitz operators via extended
symbols

概 要 We discuss index theory for some Toeplitz operators on a discrete quarter-plane (called quarter-plane

Toeplitz operators). Duducava employed Gohberg–Krein theory for matrix factorizations and obtained an
index formula in an analytic way. In this talk, we investigate his idea from a geometric point of view.
We discuss Fredholm quarter-plane Toeplitz operators of two-variable rational matrix function symbols andshow that their symbols defined originally on a two-dimensional torus can canonically be extended to somethree-dimensional sphere. Their Fredholm indices are expressed as three-dimensional winding numbers ofextended symbols.

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トポロジー

19 A. Darby(Xi’an Jiaotong-Liverpool Univ.)
黒 木 慎 太 郎 ( 岡 山 理 大 理))
KIAS
Jongbaek Song (Alastair Darby(Xi’an Jiaotong-Liverpool Univ.)
Shintaro Kuroki(Okayama Univ. of Sci.)(KIAS)
Jongbaek Song112

Equivariant cohomology of torus orbifolds · · · · · · · · · · · · · · · · · · · · · · · · · 15

Equivariant cohomology of torus orbifolds

概 要 In this talk, we introduce the calculation of the integral equivariant cohomology, in terms of generatorsand relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. This is
joint work with Alastair Darby and Jongbaek Song.
20 田 村 俊 輔 (津 山 工 高 専)
Shunsuke Tamura(Tsuyama Nat. Coll. of Tech.)

低次元球面上の有限群の odd-Euler-characteristic action について · · · · · 15

On odd-Euler-characteristic actions of finite groups on low-dimensional
spheres概 要 Let G be a finite group, M a smooth manifold with a smooth G-action and M G the G-fixed-point setof the G-action on M . We call the G-action on M an odd-Euler-characteristic action (resp. a one-fixed-point
action) if χ(M G ) ≡ 1 mod 2 (resp. |M G | = 1). The existence of one-fixed-point actions of finite groups on
low-dimensional spheres has been studied by various topologists. In this talk, we will discuss a necessary
condition for the existence of odd-Euler-characteristic actions of finite groups on the sphere S n of dimension
n ≤ 6.

9 月 14 日（水）10:10〜10:25

第 VI 会場

2022 年度日本数学会幾何学賞授賞式

10:30〜11:30

2022 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
入 江
博 (茨 城 大 理) 3 次元対称凸体の Mahler 予想の解決
柴 田 将 敬 ( 名 城 大 理 工)

Hiroshi Iriyeh (Ibaraki Univ.)
Masataka Shibata (Meijo Univ.)

A solution of Mahler’s conjecture of three dimensional symmetric convex
bodies概 要 We have proved Mahler’s conjecture concerning the volume product of three dimensional centrally

symmetric convex bodies in R3 . In this talk, we give an outline of its proof and also provide its applications
and recent developments.
13:15〜14:15
桑 垣

2022 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
大理) [ 層量子化の幾何と代数解析
樹 (京Tatsuki Kuwagaki (Kyoto Univ.)

Geometry and algebraic analysis of sheaf quantization

概 要 Sheaf quantization is a way of quantizing Lagrangian submanifolds. The concept is quite rich anduseful to study symplectic geometry, algebraic analysis, and etc. In this talk, I will give an introduction to
the concept.

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9 月 15 日（木）第 VII 会場

9:30〜12:00
21 大 森 源 城 (東 京 理 大 理 工)
廣 瀬進 ( 東 京 理 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)
Susumu Hirose (Tokyo Univ. of Sci.)

Finite presentations for the balanced superelliptic mapping class groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Finite presentations for the balanced superelliptic mapping class groups

概 要 The balanced superelliptic mapping class group is the normalizer of the transformation group of

the balanced superelliptic covering space in the mapping class group of the total surface. We give finite
presentations for the balanced superelliptic mapping class groups of closed surfaces, surfaces with one
marked point, and surfaces with one boundary component. To give these presentations, we construct finite
presentations for corresponding liftable mapping class groups in a different generating set from Ghaswala–
Winarski’s presentation.
22 大 森 源 城 (東 京 理 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)

The balanced superelliptic mapping class groups is generated by threeelements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
The balanced superelliptic mapping class groups is generated by threeelements

概 要 The balanced superelliptic mapping class group is the normalizer of the transformation group of thebalanced superelliptic covering in the mapping class group of the total surface. We prove that the balanced
superelliptic mapping class groups with either one marked point, one boundary component, or no marked
points and boundary are generated by three elements. To prove this, we also show that its liftable mappingclass groups are also generated by three elements. These generating sets are minimal except for several nomarked points and boundary cases.
23 小 林 竜 馬 (石 川 工 高 専)
Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)

向き付け不可能曲面の写像類群の 4 つの無限表示 · · · · · · · · · · · · · · · · · · · 15

Four infinite presentations for the mapping class group of a non-orientablesurface概 要 Omori and the speaker have given an infinite presentation for the mapping class group of a compact

non-orientable surface. In this work, we give more simple four infinite presentations for this group.
24 小 林 竜 馬 (石 川 工 高 専)
Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)

曲面の基本群の無限表示 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Infinite presentations for fundamental groups of surfaces

概 要 For any finite type connected surface S, we give an infinite presentation of the fundamental group

π1 (S, ∗) of S based at an interior point ∗ ∈ S whose generators are represented by simple loops. When S is
non-orientable, we also give an infinite presentation of the subgroup of π1 (S, ∗) generated by elements which
are represented by loops whose regular neighborhoods are annuli.
25 片 山 拓 弥 (学 習 院 大 理)
大理)
久 野 恵 理 香 (阪Takuya Katayama (Gakushuin Univ.)(Osaka Univ.)
Erika Kuno

ブレイド群の曲面の写像類群へのバーチャル埋め込みについて · · · · · · · · 15

On virtual embeddings of braid groups into mapping class groups of
surfaces

概 要 We give a necessary and sufficient condition for embedding a finite index subgroup of Artin’s braid

group into the mapping class group of a connected orientable surface.

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トポロジー

26 久 野 雄 介 (津 田 塾 大 学 芸)
竹 澤 花 恵 ( 津 田 塾 大 学 芸)
Yusuke Kuno
Kae Takezawa(Tsuda Coll.)(Tsuda Coll.)

114

ファットグラフ複体の Penner のコサイクルについて · · · · · · · · · · · · · · · · 10

On Penner’s cocycle on the fatgraph complex

概 要 The fatgraph complex of an oriented surface is a combinatorial model for the Teichmuller space of thesurface, and it can be used for studying the cohomology of the mapping class group. We consider a certain
1-cocycle on the fatgraph complex introduced by Penner, and we give an explicit cobounding 0-cochain forit.
27 野 崎 雄 太 (広島大先進理工)佐 藤 正 寿 (東京電機大未来)
鈴 木 正 明 ( 明 大 総 合 数 理)
Yuta Nozaki (Hiroshima Univ.)
Masatoshi Sato (Tokyo Denki Univ.)
Masaaki Suzuki (Meiji Univ.)

A non-commutative Reidemeister–Turaev torsion of homology cylinders· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A non-commutative Reidemeister–Turaev torsion of homology cylinders

概 要 We compute the Reidemeister-Turaev torsion of homology cylinders which takes values in the K1 -

ˆd+1\group of the I-adic completion of the group ring Qπ1 Σg,1 , and prove that its reduction to Qπ
1 Σg,1 /I
is a finite-type invariant of degree d. We also show that the 1-loop part of the LMO functor and the
Enomoto-Satoh trace are written by the leading term of our torsion.
28 辻

俊 輔 (明大研究・知財)

Shunsuke Tsuji(Meiji Univ.)

いくつかのスケイン加群におけるデーン・ツィストの公式とその応用 · · 15

Formulas for the actions of Dehn twists in some skein modules and theirapplications

概 要 We give explicit formulas for the actions of the Dehn twists along simple closed curves in a compact

connected oriented surface on the completions of some types of skein modules. Using them, we candefine some “quantum” Johnson homomorphisms and some invariants for integral homology 3-spheres andhomology cylinders.
14:20〜15:20

特別講演

C. Vespa(Univ. of Strasbourg・JSPS)

Eilenberg Mac Lane polynomial functors and their applications

Christine Vespa(Univ. of Strasbourg / JSPS)

Eilenberg Mac Lane polynomial functors and their applications

概 要 In 1954, Eilenberg and Mac Lane introduced the notion of a polynomial functor as a generalization of

additive functors. Fundamental results in representation theory and algebraic topology have been obtainedusing the polynomial functors. Polynomial functors are used both as a tool to measure the complexity ofa functor and to study such functors. In this talk, I will give results on polynomial functors on finitely
generated free groups and present some recent applications.
15:40〜18:00
29 村 上順 ( 早 大 理 工)

Jun Murakami (Waseda Univ.)

結び目群の量子化について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On quantization of knot groups

概 要 By using the plat presentation of a knot, a quantization of the knot group is constructed. The main

tool is the bottom tangle. The relations of the knot group is reformulated as relations of the algebra ofbottom tangles, and the quantization of the knot group is defined as the quotient of the algebra with these
relations.

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トポロジー

30 中 西 康 剛 (神 戸 大 理)
高 木 駿 希Yasutaka Nakanishi (Kobe Univ.)
Shunki Takagi

Differences of Conway polynomials for knots caused by a single passmove · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Differences of Conway polynomials for knots caused by a single passmove

概 要 In this talk, we will characterize Conway polynomials of knots which are transformed into the trivial

knot by a single pass move.
31 秋 田 利 之 (北長 谷 川 蒼 (北

大

理)

大

理)

Toshiyuki Akita (Hokkaido Univ.)
Aoi Hasegawa (Hokkaido Univ.)

カンドルの associated group について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the associated group of a quandle

概 要 The associated groups of quandles play an important role in understanding quandles themselves.

In this talk, we give several explicit descriptions of structure of associated groups by introducing certain
quotient groups of them.
32 水 澤 篤 彦 (早 大 非 常 勤)
小 鳥 居 祐 香 (広島大理・理化学研)

Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii(Hiroshima Univ. / RIKEN)Clasper を用いた 5 成分 link の link-homotopy 類の分類 · · · · · · · · · · · · · 15
A classification of 5-component link-homotopy classes through the clasper
theory概 要 The link-homotopy classes of links are obtained from the link-homotopy classes of string links modulo

the partial conjugations. Yasuhara and Meilhan gave a standard form of the link-homotopy classes ofstring links by using the claspers. In this talk, we calculate the actions of the partial conjugations for the
5-component link-homotopy classes of string links by using the clasper theory and give a new presentationof the link-homotopy classes of 5-component links.
33 沢 辺俊 ( 早 大 理 工)

Shun Sawabe(Waseda Univ.)

On the potential function of the colored Jones polynomial with arbitrarycolors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the potential function of the colored Jones polynomial with arbitrarycolors概 要 In this study, we consider the potential function of the colored Jones polynomial for a link with

arbitrary colors. This potential function has new parameters derived from the colors of the link. When
we fix the new parameters, we can obtain a cone-manifold structure of the complement of a hyperbolic
link from a saddle point of the potential function. Furthermore, when we regard the new parameters as
variables, the derivatives with respect to the new parameters correspond to the completeness conditions.
This correspondence implies that the saddle point of the potential function gives the complete hyperbolic
structure to the link complement.
34 鈴 木 正 明 (明 大 総 合 数 理)
A. T. Tran
(Univ. of Texas at Dallas)
Masaaki Suzuki (Meiji Univ.)
Anh T. Tran (Univ. of Texas at Dallas)

Genera and crossing numbers of 2-bridge knots · · · · · · · · · · · · · · · · · · · · 10

Genera and crossing numbers of 2-bridge knots

概 要 We determine the average genus of all the 2-bridge knots with a given crossing number. As aconsequence, we obtain the oblique asymptote of this value as the crossing number grows.

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トポロジー

35 北 野 晃 朗 (創 価 大 理 工)
野 崎 雄 太 (広島大先進理工)
Teruaki Kitano (Soka Univ.)
Yuta Nozaki (Hiroshima Univ.)

116

Reidemeister torsion の代数的整数性について · · · · · · · · · · · · · · · · · · · · · · 10
Algebraic integrality of Reidemeister torsion

概 要 For a 3-manifold M and an acyclic SL(2, C)-representation ρ of its fundamental group, the Reidemeister

torsion τρ (M ) ∈ C is defined. If there are finitely many conjugacy classes of irreducible representations,then the Reidemeister torsions are known to be algebraic numbers. In this talk we report that any value ofthem is an algebraic integer for a Seifert fibered space under mild conditions, even though there are inifinite
conjugacy classes.
36 北 野 晃 朗 (創 価 大 理 工)
Teruaki Kitano(Soka Univ.)

結び目群の間の全射準同型写像と SL(2; C)-指標多様体について · · · · · · · 10

Epimorphisms between knot groups and the SL(2; C)-character variety

概 要 In this talk we will study to how determine the knot by the SL(2; C)-character variety. This includes

some joint work with Michel Boileau, Steven Sivek, and Raphael Zentner.
37 高 野 暁 弘 (東 大 数 理)

Akihiro Takano (Univ. of Tokyo)

The Long–Moody construction and twisted Alexander invariants · · · · · 15
The Long–Moody construction and twisted Alexander invariants

概 要 The Long–Moody construction is a method of constructing a new representation of the braid groupfrom a representation of the semidirect product of the braid group and the free group. In this talk, we showthat its matrix presentation is described by the Fox derivation, and also a relation with twisted Alexander
invariants.

9 月 16 日（金）第 VII 会場

9:30〜12:00
大理)
38 鎌 田 聖 一 (阪伊 藤 大 貴 ( キ ス テ ム)

Seiichi Kamada (Osaka Univ.)(KISTEM)
Hiroki Ito

ねじれ仮想結び目のねじれ交差彩色とその不変量について · · · · · · · · · · · 10

Twisted intersection colorings and invariants of twisted links

概 要 Twisted links are a generalization of classical links and virtual links. Here we introduce twisted

intersection colorings of a diagram and construct invariants of a twisted link using such colorings. As anapplication, we show that there exist infinitely many pairs of twisted links such that for each pair the twotwisted links are not equivalent but their double coverings are equivalent.
39 鎌 田 直 子 (名 古 屋 市 大 理)

Naoko Kamada (Nagoya City Univ.)

Virtual link diagram とその sublink diagram · · · · · · · · · · · · · · · · · · · · · · · 10
Virtual link diagrams and their sublink diagrams

概 要 Jin and Lee proved the following: Suppose that D1 , . . . , Dn are link diagrams. Given a link L whichis partitioned into sublinks L1 , . . . , Ln admitting diagrams D1 , . . . , Dn respectively, there is a diagram Dof L whose restrictions to L1 , . . . , Ln are isotopic to D1 , . . . , Dn , respectively. In this talk we show that asimilar result does hold for welded links and does not for virtual links.
40 和 田 康 載 (神 戸 大 理)
Kodai Wada

(Kobe Univ.)

仮想結び目のねじれ数と 2k-移動 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Writhes and 2k-moves for virtual knots

概 要 In this talk, we show that if two virtual knots are related by a finite sequence of 2k-moves, then theirn-writhes are congruent modulo k for any nonzero integer n. Moreover, we give a necessary and sufficientcondition for two virtual knots to be equivalent up to 2k-moves and Ξ-moves in terms of their odd writhes.

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117

トポロジー

41 境
圭 一 ( 信 州 大 理)
加 納 早 貴Keiichi Sakai
Saki Kanou(Shinshu Univ.)

The Fox–Hatcher cycle and the Vassiliev invariants · · · · · · · · · · · · · · · · · 15
The Fox–Hatcher cycle and the Vassiliev invariants

概 要 Configuration space integral produces cohomology classes of the space of long knots from graphcocycles, and it is known that, if the graphs are trivalent, then the corresponding cohomology classes areclosely related to the Vassiliev invariants. We give a combinatorial formula for the evaluation of the cocycles
coming from certain non-trivalent graphs over the Fox–Hatcher cycles of the space of framed long knots.
As a corollary we see that some non-trivalent graphs also produce (possibly trivial) Vassiliev invariants.
42 安 部 哲 哉 (立 命 館 大 理 工)
田 神 慶 士 (広島修道大経済)

Tetsuya Abe (Ritsumeikan Univ.)
Keiji Tagami (Hiroshima Shudo Univ.)

Ribbon concordance and the minimality of torus knots · · · · · · · · · · · · · 15
Ribbon concordance and the minimality of torus knots

概 要 Agol proved that ribbon concordance forms a partial ordering on the set of knots in the 3-sphere.

In this talk, we prove that a tight fibered knot, such as a torus knot, is minimal in the partially orderedset. This result gives a supporting evidence of the generalization of the slice-ribbon conjecture proposed byDaemi and Scaduto.
43 谷 口 雄 大 (阪大理)Yuta Taniguchi (Osaka Univ.)

カンドル 2-コサイクルから得られる曲面結び目の不変量の関係 · · · · · · · 15

A relation between surface knot invariants obtained from a quandle 2cocycle

概 要 J. S. Carter, M. Saito and S. Satoh defined an invariant of oriented surface knots using a quandle

2-cocycle θ. In this talk, we relate the surface knot invariant using a quandle 2-cocycle θ to an f -twisted
Alexander matrix, which was introduced by A. Ishii and K. Oshiro, using the Alexander pair associatedwith the quandle 2-cocycle θ. As an application, we determine the second quandle homology group of theknot quandle of 2-knots.
44 安 田 順 平 (阪大理)Jumpei Yasuda (Osaka Univ.)

Plat 指数における曲面絡み目の具体例について · · · · · · · · · · · · · · · · · · · · · 15
Computation of the plat index for surface-links

概 要 A plat form for links is a presentation of a classical link using a braid. We can apply this presentation

to surface-links, using a braided surface instead of a braid, and prove that every surface-link has a platform presentation. Using plat form presentation for surface-links, the plat index is defined as a surface-link
invariant, which is an analogy of the bridge index for links. In this talk, we consider a lower bounds of theplat index for a surface-link by using a symmetric quandle coloring. As an application, we give infinitely
many surface-knots with the plat index m for any positive integer m.
45 磯 島司 ( 東 工 大 理)

Tsukasa Isoshima (Tokyo Tech)

曲面結び目の自明な再接着により得られる trisection · · · · · · · · · · · · · · · · 15

Trisections obtained by trivially regluing surface-knots

概 要 A (relative) trisection of a 4-manifold (with boundary) is a decomposition of the 4-manifold into

three 4-dimensional 1-handlebodies. The complement of a surface-knot S has the standard decomposition
according to a trisection T of a closed 4-manifold X, but it is never a relative trisection. Kim andMiller developed a new technique called a boundary-stabilization, so that the decomposition is a relative
trisection. We study the difference between T and a new trisection of X obtained by boundary-stabilizing
the complement of S when S is a P 2 -knot which is of Kinoshita type.

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トポロジー

46 高 橋 夏 野 (阪 大 情 報)

Natsuya Takahashi (Osaka Univ.)

118

コルクの最小種数の相対トライセクション · · · · · · · · · · · · · · · · · · · · · · · · · 15

Minimal genus relative trisections of corks

概 要 A relative trisection is a decomposition of a smooth 4-manifold with boundary into three 4-dimensional

1-handlebodies. In this talk, we show how to construct minimal genus relative trisections for infinitely manycorks. As an application, we determine the minimal number of binding components of planar open bookdecompositions on the boundaries of these corks.
14:20〜15:20
佐 藤Shin Satoh特別講演
進 ( 神 戸 大 理)

(Kobe Univ.)

2 次元結び目の表の作成に向けて
Toward tabulation of 2-knots

概 要 The crossing number c(k) of a knot k in S 3 is the minimal number of crossings for all diagrams of k.

It has been used to tabulate knots; in fact, c(k) = 0 holds if and only if k is the trivial knot, there is noknot of c(k) = 1, 2, c(k) = 3 holds if and only if k is the trefoil knot, and so on.
A 2-knot is a 2-dimensional sphere embedded in S 4 smoothly. It is presented by a diagram through a
projection onto 3-space with a finite number of branch points and triple points. The minimal number ofbranch points for all diagrams of a 2-knot K is known to be equal to zero. The triple point number t(K)of K is the minimal number of triple points for all diagrams of K. We would like to tabulate 2-knots byusing the triple point number t(K).
We have a great difference between the crossing number and the triple point number: There are infinitely
many 2-knots of t(K) = 0 which are called ribbon. By introducing the notion of ribbon concordance, we
can say that t(K) = 0 if and only if K is ribbon concordant to the trivial 2-knot. It is also known that there
is no 2-knot of t(K) = 1, 2, 3. Our main theorem is that t(K) = 4 if and only if K is ribbon concordant
to the 2-twist-spun trefoil knot. The aim of this talk is to review diagrammatic 2-knot theory and give asketch of our theorem.
15:40〜17:00
47 丹 下 基 生 (筑波大数理物質)
工大)
鈴 木 龍 正 (東Motoo Tange (Univ. of Tsukuba)
Tatsumasa Suzuki (Tokyo Tech)

Pochette surgery of S 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Pochette surgery of S 4

概 要 Iwase and Matsumoto defined a pochette P , which is S 1 × D 3 \S 2 × D 2 and defined a surgery (it iscalled a pochette surgery) around an image P ,→ M in a 4-manifold M . They gave a complete data to
determine the diffeomorphism type of the surgery. We clarify the diffeomorphism type of pochette surgery
for any embedding with trivial cord. As a result we prove that any pochette surgery for embedding withtrivial core sphere gives M or a Gluck surgery. We also show that there exist embeddings P ,→ S 4 with
non-trivial core sphere and non-trivial cord such that the pochette surgery gives S 4 .

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119

トポロジー

[ ある複素曲面特異点の Milnor 束から見出された S 5 から S 3 へのトーラ
48 児 玉 大 樹(東北大 AIMR・理化学研) スファイブレーション · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
大理)
粕 谷 直 彦 (北三 松 佳 彦 ( 中 大 理 工)森
淳 秀 ( 大 阪 歯 大 歯)
Hiroki Kodama(Tohoku Univ. / RIKEN)
Naohiko Kasuya (Hokkaido Univ.)
Yoshihiko Mitsumatsu (Chuo Univ.)
Atsuhide Mori (Osaka Dent. Univ.)

Torus fibrations from S 5 to S 3 found from Milnor fibrations of certain
complex surface singularities

概 要 We explain Tpqr cusp singularities and Milnor fibers Fθ of them. We construct a complex map g on a

Milnor fiber Fθ so that it has p + q + r critical points and the inverse images of regular values are tori T 2 .
We also construct a deformation of the Milnor fiber so that all critical points become Lefschetz type.
49 三 松 佳 彦 (中 大 理 工)大理)粕 谷 直 彦 (北児 玉 大 樹(東北大 AIMR・理化学研)
森
淳 秀 ( 大 阪 歯 大 歯)

Yoshihiko Mitsumatsu (Chuo Univ.)
Naohiko Kasuya (Hokkaido Univ.)
Hiroki Kodama(Tohoku Univ. / RIKEN)
Atsuhide Mori (Osaka Dent. Univ.)

カスプ特異点のミルナーファイバーのレフシェッツファイブレーションと K3 曲面の位相分解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Lefschetz fibration of Milnor fibers of cusp singularities and topologicaldecompositions of the K3 surface

概 要 We explain that the K3 surface admits a smooth topological decomposition into the two Milnor fibersof Tpqr cusp singularities which are dual in the sense of the extended strange duality. Among such 10
decompositions, the pair T237 -T237 gives a particularly good decomposition.
50 三 松 佳 彦 (中 大 理 工)大理)粕 谷 直 彦 (北(森淳 秀 大 阪 歯 大 歯)

Yoshihiko Mitsumatsu (Chuo Univ.)
Naohiko Kasuya (Hokkaido Univ.)
Atsuhide Mori (Osaka Dent. Univ.)

Lefschetz 的臨界点 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Lefschetz-like critical points

概 要 We show the fact that the space of homogeneous quadratic maps from R4 to R2 for which the origin

is the unique critical point has two path connected components, which has the following application. If
the Hessian of a smooth map from a 4-manifold to a 2-manifold at a critical point P is of above typeand belongs to the positive component, then the map is deformed in an arbitrary small neighborhood of P
without creating new critical points so that P is a Lefschetz type critical point.

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無限可積分系

無限

可9 月 13 日（火）

積

分

120

系

第 IX 会場

9:30〜12:00
1 土 谷 洋 平 ( 神 奈 川 工 大)

Yohei Tutiya (Kanagawa Inst. of Tech.)

Periodic ILW equation with discrete Laplacian のテータ関数解 · · · · · · · 10
Theta function solutions for periodic ILW equation with discrete Laplacian

概 要 It will be reported that periodic ILW equation with discrete Laplacian admits theta function solutions

whose genera are greater than two. It will be achieved by conducting a special reduction for theta solutions
for n-component KP equation that requires certain incommensurate relation among three points on compact
Riemann surface.
2 長 尾 秀 人 ( 明 石 工 高 専)

Hidehito Nagao (Akashi Coll. of Tech.)

ある因子化された行列型ラックス形式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A certain factorized matrix Lax form

概 要 It is well known that the q-Painlevé system and its multivariable extension (called q-Garnier system)

are given as a condition for the compatibility of the Lax pair (i.e. a set of a linear equation and its
deformation equation). Recently, a factorized matrix Lax form for the q-Garnier system was obtained
through a similarity reduction of the q-KP hierarchy. In this talk, we discuss an extension of the factorized
matrix Lax form and its relation to other systems.
3 矢 ヶ 崎 一 幸 ( 京 大 情 報)

Kazuyuki Yagasaki (Kyoto Univ.)

Integrability of the two-dimensional Zakharov–Shabat systems by quadrature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Integrability of the two-dimensional Zakharov–Shabat systems by quadrature

概 要 In this talk we consider the two-dimensional Zakharov–Shabat (ZS) systems, which are linear systemsof ordinary differential equations appearing in application of the inverse scattering transform (IST) to
integrable partial differential equations (PDEs) such as the KdV equation, the nonlinear Schrödinger
equation and so on. To obtain solutions to the initial value problems of these PDEs using the IST, we firsthave to solve the ZS systems. In particular, we show under some wide condition that if for any wave number
they can be solved by quadrature, i.e., they are integrable in the meaning of differential Galois theory, thenthe potentials are reflectionless.
4 渋 川 元 樹 ( 神 戸 大 理)
土 見 怜 史 ( 神 戸 大 理)

Genki Shibukawa (Kobe Univ.)
Tsuchimi Satoshi (Kobe Univ.)

A generalization of Zwegers’ µ-function according to the q-Hermite–
Weber difference equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A generalization of Zwegers’ µ-function according to the q-Hermite–
Weber difference equation

概 要 We introduce a one parameter deformation of the Zwegers’ µ-function as the image of q-Borel andq-Laplace transforms of a fundamental solution for the q-Hermite–Weber equation. We further give someformulas of our generalized µ-function, for example, forward and backward shift, translation, symmetry,a difference equation for the new parameter, and q-bilateral hypergeometric expressions. From one pointof view, the continuous q-Hermite polynomials are some special cases of our µ-function, and the Zwegers’µ-function is regarded as a continuous q-Hermite polynomial of “minus degree”.

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121

無限可積分系

5 増 田

哲 ( 青 学 大 理 工)

Tetsu Masuda (Aoyama Gakuin Univ.)

梶原–野海–山田系の付加的対称性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Additional symmetry of Kajiwara–Noumi–Yamada systems

概 要 We present a description of the additional symmetry of the discrete dynamical systems proposedby Kajiwara, Noumi and Yamada, which originally possess the extended affine Weyl group symmetryf (A(1) ) × W
f (A(1) ).
W
m−1

n−1

6 新 井 由 美
(お茶の水女大人間文化)
竹 村 剛 一 (お茶の水女大基幹)
Yumi Arai (Ochanomizu Univ.)
Kouichi Takemura (Ochanomizu Univ.)

On q-middle convolution and q-hypergeometric equations · · · · · · · · · · · 15

On q-middle convolution and q-hypergeometric equations

概 要 We reformulate q-integral transformations associated with the q-middle convolution. We obtainq-integral representations of the variants of the q-hypergeometric equation by applying the q-middle convolution.
7 重 富 尚 太 ( 九 大 数 理)
梶 原 健 司 (九 大 I M I )Shota Shigetomi (Kyushu Univ.)
Kenji Kajiwara (Kyushu Univ.)

カライドサイクルの明示公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An explicit formula of Kaleidocycle

概 要 We construct an explicit formula of Kaleidocycle in terms of elliptic theta function.

8 西 山 雄 太 ( 熊 本 大 先 端)

Yuta Nishiyama (Kumamoto Univ.)

2 被約 Schur 関数と Schur の Q-関数に関する予想について · · · · · · · · · · · 15
On a conjecture on 2-reduced Schur functions and Schur’s Q-functions

概 要 Sato and Mori introduced some families of functions to state about behavior of the solutions of the

KdV equation. Mizukawa, Nakajima and Yamada interpreted them as symmetric functions using 2-reduced
Schur functions and Littlewood–Richardson coefficients. They also made a conjecture that these symmetricfunctions are equal to Schur’s Q-functions up to a scalar. In this talk we prove the conjecture in a special
case and give some consideration on the general case.
9 大 山 陽 介 ( 徳 島 大 理 工)

Yousuke Ohyama (Tokushima Univ.)

A q-analogue of the Euler–Poisson–Darboux equation · · · · · · · · · · · · · · · 15
A q-analogue of the Euler–Poisson–Darboux equation

概 要 We study a q-analogue of the Euler–Poisson–Darboux equation, different from the q-EPD equation

proposed by Koga and Nagatomo in 1995. We show our q-EPD equation has special solutions written bybasic hypergeometric series.
14:15〜15:15
星 野

特別講演
歩 ( 広 島 工 大 工)

Ayumu Hoshino(Hiroshima Inst. of Tech.)

鈎型 C 型 Macdonald 多項式の明示公式と Pieri 型公式

Macdonald polynomials of type C with hook-shape diagrams and Pieri
type formula

概 要 We obtained explicit forms of the Koornwinder polynomials with one-row and one-column diagrams bya series of our studies. In this lecture, we give explicit forms of the Macdonald polynomials of type C with
hook-shape diagrams. Moreover, we present an explicit Pieri type formula for the Macdonald polynomialsof type C with one-row, one-column and hook-shape diagrams.

最終版: 2022/8/8
無限可積分系

9 月 14 日（水）122

第 IX 会場

9:30〜10:50
10 武 中亮 ( 阪 公 大 理)

Ryo Takenaka (Osaka Metro. Univ.)(2)

A2l 型アフィンリー環とフェルミ公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(2)

Affine Lie algebras of type A2l and fermionic formulas(2)

概 要 Vertex algebraic construction of modules for the twisted affine Lie algebra A2

was studied byCalinescu, Lepowsky and Milas. In this talk, we see that such construction will be true for higher rank(2)cases, that is for twisted affine Lie algebras of type A2l . As a consequence, we obtain some fermioniccharacter formulas.
11 渡 邉 英 也 (阪 公 大 数 学 研)

Hideya Watanabe (Osaka Metro. Univ.)

有限型実階数 1 の ı 標準基底について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On ıcanonical bases of finite type of real rank one

概 要 In 2010’s, Huanchen Bao and Weiqiang Wang generalized the theory of canonical basis for quantum

groups to that for ıquantum groups (also known as quantum symmetric pair coideal subalgebras). In thistalk, we focus on the ıquantum groups of real rank one, and show that their canonical bases have a stability
property. Then, we introduce possible applications to integrable system and combinatorial representation
theory.
12 水 野 勇 磨 (千 葉 大 理)
Yuma Mizuno(Chiba Univ.)

Mutations of blowups of toric surfaces and q-Painlevé systems · · · · · · · 15
Mutations of blowups of toric surfaces and q-Painlevé systems

概 要 We provide a relation between the geometric framework for q-Painlevé equations and cluster Poisson

varieties by using toric models of rational surfaces associated with q-Painlevé equations. We introduce thenotion of seeds of q-Painlevé type by the negative semi-definiteness of symmetric bilinear forms associatedwith seeds, and classify the mutation equivalence classes of these seeds. This classification coincides withthe classification of q-Painlevé equations given by Sakai.
13 白 石 勇 貴(阪大インターナショナルカレッジ)
大理)
高 橋 篤 史 (阪池 田 暁 志 ( 城 西 大 理)
大理)
大 谷 拓 己 (阪Yuuki Shiraishi (Osaka Univ.)
Atsushi Takahashi (Osaka Univ.)(Josai Univ.)
Akishi Ikeda
Takumi Otani (Osaka Univ.)`-クロネッカー箙から構成されるフロベニウス多様体 · · · · · · · · · · · · · · · · 15

A Frobenius manifold for `-Kronecker quiver概 要 A Frobenius manifold is a complex manifold whose tangent bundle is a flat family of commutative

Frobenius algebras satisfying certain conditions. In this talk, I will explain that a unique Frobenius manifold,whose intersection form coincides with the Cartan matrix of `-Kronecker quiver K(`), can be constructedfrom the invariant theory of the Weyl group associated to K(`).
14 武 田渉 ( 東 京 理 大 理)
中 筋 麻 貴 ( 上 智 大 理 工)

Wataru Takeda (Tokyo Univ. of Sci.)
Maki Nakasuji (Sophia Univ.)

Schur Q 型多重ゼータ関数の Pfaffian 表示 · · · · · · · · · · · · · · · · · · · · · · · · · 15
Pfaffian expression of the Schur Q type multiple zeta functions

概 要 We introduce Schur P and Q type multiple zeta functions. These functions are defined as sums overcombinatorial objects called shifted Young tableaux. We will show that the Schur Q type multiple zetafunction has a pfaffian expression under an assumption on variables.

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123

無限可積分系

11:00〜12:00

特別講演衛
高 木 太 一 郎 (防大) [ 可積分セルオートマトンの幾何的リフトとその連続極限

Taichiro Takagi(Nat. Defense Acad. of Japan)

A geometric lifting of integrable cellular automata and its continuum
limits概 要 I first explain a method to construct a family of discrete integrable systems with periodic boundary

conditions, which can be regarded as a geometric lifting of a family of integrable cellular automata associatedwith affine type A crystals. By combining an unconventional usage of the matrices for defining the discrete
periodic Toda chain with the Perron-Frobenius theorem, we give a definition of our systems. It is carried out
on the space of real positive dependent variables, without regarding them to be written by subtraction-freerational functions of independent variables.
Next I present two types of systems of differential equations that can be derived from those discrete
integrable systems. One is a kind of extended Lotka–Volterra systems, and the other seems to be generallynew. Both equations have Lax representations associated with what are known as the loop elementary
symmetric functions. I would like to talk about an example of the derivations of the continuous time
Lax equations from a discrete time one, where a novel method of taking a continuum limit by assuming
asymptotic behaviors of the eigenvalues of the Lax matrix in Puiseux series expansions is used.