最終版: 2023/2/17“日本数学会
2023 年度年会

英 文

サ

マ

リ

2023 年 3 月
於

中央大学

集

2023 日 本 数 学 会
年会プログラム期日

2023 年 3 月 15 日（ 水 ）〜 3 月 18 日（ 土 ）会場

中 央 大 学 理 工 学 部
東 京 都 文 京 区 春 日 1–13–27

連 絡 先

中 央 大 学 理 工 学 部 数 学 科〒112-8551
東 京 都 文 京 区 春 日 1–13–27
E-mail chuo23mar mathsoc jp
一般社団法人15 日（水）

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

5 号館 5 階5533 教室

5 号館 3 階5333 教室

5 号館 3 階5335 教室

5 号館 3 階
5336 教室

5 号館 2 階5233 教室

5 号館 2 階5234 教室

5 号館 2 階
5235 教室

5 号館 2 階
5236 教室

5 号館 1 階
5138 教室

代 数 学 幾 何 学 トポロジー 函数方程式論 函 数 論 函数解析学 応 用 数 学 統 計 数 学

数学基礎論
および歴史

9:00〜12:00 9:30〜11:40 9:30〜12:00 9:30〜12:00
14:15〜14:50 14:15〜16:00 15:40〜17:30 14:15〜16:15

9:30〜11:45

企画特別講演

9:30〜12:00 9:50〜11:50 10:00〜11:30 9:30〜10:15
14:15〜16:15 14:15〜15:25
14:30〜16:45

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
15:00〜16:00 16:15〜17:15 14:20〜15:20 16:30〜17:30 14:15〜15:15 16:30〜17:30 15:45〜16:45 14:15〜15:15 10:30〜11:30
16:15〜17:15
15:30〜16:30
15:30〜16:30 17:00〜18:00

代 数 学 幾 何 学 トポロジー 函数方程式論 函 数 論 函数解析学 応 用 数 学 統 計 数 学
9:10〜12:00
13:00〜14:10

16 日
（木）

9:30〜12:00

9:30〜12:00
13:00〜14:00

9:15〜12:00

9:30〜11:45

9:30〜12:00 10:00〜11:45 10:20〜11:10
13:00〜14:10

特別講演

特別講演 特別講演 特別講演

13:00〜14:00

13:00〜14:00 13:00〜14:00 13:10〜14:10

数学基礎論
および歴史
9:15〜12:15

日 本 数 学 会 賞 授 賞 式（5 号館 5 階 5534 教室） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30〜15:05)
〃
総
合
講
演（
） 日 本 数 学 会 賞 春 季 賞 受 賞 者 · · · · · · · · · · · · (15:20〜16:20)
大⋆) · · · · · · · · · · · · (16:35〜17:35)
日 比 孝 之 (阪代 数 学 幾 何 学 トポロジー 函数方程式論 実 函 数 論 函数解析学 応 用 数 学 統 計 数 学 無限可積分系
9:00〜12:00

17 日
（金）

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

企画特別講演

9:50〜11:35

9:45〜10:45

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
14:40〜15:40 15:10〜16:10 14:20〜15:20 16:30〜17:30 15:40〜16:40 15:45〜16:45 16:45〜17:45 14:25〜15:25 11:00〜12:00
16:00〜17:00
17:00〜18:00
15:40〜16:40

18 日
（土）

代 数 学

函数方程式論 実 函 数 論

応 用 数 学 統 計 数 学 無限可積分系

9:15〜12:00
14:15〜16:45

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

9:50〜11:50 10:00〜11:10 10:00〜10:45
14:15〜15:05

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

16:30〜17:30 17:00〜18:00

15:20〜16:20

11:00〜12:00

最終版: 2023/2/17

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

5

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

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

11

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

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

25

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

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

33

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

実函数論

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

57

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

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

66

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

統計数学

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

76

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

最終版: 2023/2/17

4

応用数学

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

84

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

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

98

3 月 15 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

3 月 16 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104

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

107

3 月 17 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107

3 月 18 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

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1

総合講演

総 合

講

演

3 月 16 日（木） 総合講演会場
2023 年度日本数学会賞春季賞受賞講演
日本数学会賞春季賞受賞者· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:20〜16:20)
Spring Prize Winner
日 比 孝 之 (阪大⋆)Takayuki Hibi (Osaka Univ.

⋆)

多面体と単項式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16:35〜17:35)

Polytopes and Monomials

概 要 The theory of convex polytopes, which has its origins in Euler’s theorem (1752) and Pick’s formula(1899), is one of the traditional areas of combinatorics. It underwent a dramatic change in trend around1970. Backed by the trend from abstract to concrete, a fascinating contact of convex polytopes with
commutative algebra was discovered, and a bridge was built from the abstract theory of commutative
algebra to the concrete theory of convex polytopes. The bridge simultaneously fostered a movement toreimport combinatorial techniques back into commutative algebra, inviting the birth of the rich soil of socalled “commutative algebra and combinatorics” from the mid-1980s, which led to a historic developmentof commutative algebra for monomial ideals. Later, in the 1990s, with the rapid development of computers
and the evolution of software, the theory of convex polytopes took on the color of computational algebra
and benefited from Gröbner bases, which is a treasure trove of techniques. This plenary talk will overview
the trends in convex polytopes and commutative algebra in the last half-century since 1970 and furthermore
report on current of study for reflexive polytopes and Castelnuovo polytopes.

最終版: 2023/2/17
企画特別講演

企

画

特

別

講

2

演

3 月 15 日（水）第 I 会場
特別招待講演 (日本応用数理学会)
吉 田 真 紀 (情報通信研究機構) NewSpace セキュリティ —民間事業者による宇宙開発のための暗号理論— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)
Maki Yoshida
NewSpace security —Cryptography for space development(Nat. Inst. Information Comm. Tech.) by private companies—
概 要 In the recent NewSpace era, many small satellites have been launched on various academic or commercial

missions. A low cost yet highly secure wireless communication has been desired for small satellites and small
launch vehicles, for protecting their critical commands and valuable data transmissions. I would like to first
explain requirements that are indispensable in such context and whether the various types of cryptography
used in existing network systems satisfy them or not. I will then show our approach and results that establish
high security and low implementation cost. The latest flight test conducted on July 31, 2021 achieves
successful downlink transmission of 34Mbytes at a practical effective bandwidth of 512kbps.
第 VI 会場
横 山 啓 太 ( 東 北 大 理)

自然数論のモデルと逆数学 · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Keita Yokoyama (Tohoku Univ.)

Models of arithmetic and reverse mathematics

概 要 Reverse mathematics is an ongoing program in the field of mathematical logic whose aim is to classify

mathematical theorems by their logical strengths. Then, how can we say that one theorem τ is logicallydifferent from another theorem σ? One way to show this is to construct a mathematical structure which
satisfies τ (together with some basic axioms) but not σ. In this talk, I will introduce several types of structures(models) of axioms for the natural number systems (arithmetic) and show some examples of classifications ofmathematical theorems from the viewpoints of model theory.

3 月 17 日（金）第 I 会場平 岡 裕 章 ( 京 大 高 等 研)

パーシステントホモロジー: 理論と応用 · · · · · · · · · · · · · · · · · (13:00〜14:00)

Yasuaki Hiraoka (Kyoto Univ.)

Persistent homology: theory and application

概 要 Topological data analysis (TDA) has emerged in this century and shed new light on data science.

A particularly important tool in TDA is persistent homology, which can provide useful information about”shape of data” in a multi-scale way. Much of the development of theoretical research on persistent homology
has been motivated by applications. This talk will survey the progress of persistent homology from theperspective of both mathematical and applied research.

最終版: 2023/2/17

3

企画特別講演

第 III 会場
石 橋

典 ( 東 北 大 理)

Tsukasa Ishibashi (Tohoku Univ.)クラスター代数と曲面のトポロジー · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Cluster algebras and the topology of surfaces

概 要 Since its foundation by Fomin–Zelevinsky (2001), the study of cluster algebras has been developed withfruitful connections with various areas of mathematics, such as topology, representation theory, integrable
systems, mirror symmetry, and so on. It focuses on a common combinatorial structure, called clustertransformations, which typically arises as coordinate transformations on a certain space, such as the decorated
Teichmueller space of Penner (1987). Its geometric aspect is formulated as cluster varieties by Fock–Goncharov(2006). One of the motivating examples is the moduli space of decorated (twisted) G-local systems on amarked surface, which includes the decorated Teichmueller space in the case G=SL(2).
In this talk, I would like to talk on the interplay between the cluster algebras and the topology of surfaces,with a focus on the geometry and cluster structure of the moduli space mentioned above. I also mention
recent developments on its quantization via the quantum cluster algebra and the relation to the skein theory.
第 V 会場小 川 卓 克 (東 北 大 理) ♭ 端点最大正則性と臨界型非線型問題への応用 · · · · · · · · · · · · · (13:00〜14:00)

Takayoshi Ogawa (Tohoku Univ.)

End point maximal regularity and its application to a criticalnonlinear problem

概 要 Maximal regularity for the abstract Cauchy problem of evolution equations is well developed in theLebesgue-Bochner space Lρ (I; X), where 1 < ρ < ∞, I is a time interval and X is the UMD Banach
space. If X is UMD then it is necessarily reflexive and maximal regularity in non-reflexive Banach spaces
is depending on each setting. In this talk, we consider the end-point case ρ = 1 in the homogeneous Besovsspace X = Ḃp,1(Rn+ ) in the half Euclidean space. We then apply it to the initial boundary value problem ofsome nonlinear evolution equations such as the Navier-Stokes equations.

3 月 18 日（土）第 III 会場
山 崎 雅 人 (東 大 I P M U )可積分系とチャーン=サイモンズ理論 · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Masahito Yamazaki (Univ. of Tokyo)

Integrability and Chern-Simons Theory

概 要 Integrable models, which are ”exactly solvable”, lie at the intersections of many different topics/areas

in mathematics and physics. However, many of the existing results are gradually built up through decadesof research, and often involve trials and errors. This makes it newcomers (including myself) to learn thesubject. One might therefore hope to find a new conceptual framework for understanding integrable models
from scratch. In this lecture, I will discuss recent developments (in collaboration with Kevin Costelloand Edward Witten, among others) in understanding integrable models from the perspective of the ”fourdimensional Chern-Simons theory.” This is a precise analog to Witten’s explanation of knot invariants fromthe three-dimensional Chern-Simons theory, but is based mostly on perturbative methods of quantum field
theory, which can be formulated mathematically. If time allows, I will also discuss more recent developments
concerning affine Yangians (and quantum toroidal algebras) and five-dimensional version of the Chern-Simons
theory. The developments covered in this lecture give rise to many new mathematical structures, many ofwhich are yet to be fully studied in mathematics.

最終版: 2023/2/17
企画特別講演

第 VI 会場
浅 芝 秀 人(静岡大⋆・京大高等研・阪公大数学研)

Hideto Asashiba(Shizuoka Univ.⋆/Kyoto Univ./Osaka Metro. Univ.)

4

クイバー表現のパーシステンス加群への応用: 区間加群による近似と分解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Applications of quiver representations to persistence modules: approximations and resolutions by interval modules

概 要 In topological data analysis, an input datum is given as a point cloud P , which is a set of points in Rd

for some positive integer d. Then for each r with 0 ≤ r ≤ d an r-th persistent homology H r (P ) of P over a
field k is calculated, which is a representation of an equi-oriented type An quiver Q for some positive integer nover the field k. By Gabriel’s theorem, the “interval” representations VI (I := [a, b], 1 ≤ a ≤ b ≤ n) of Q form
a complete list of indecomposable representations of Q. For each representation M of Q, let dM (I) be themultiplicity of VI in the indecomposable decomposition of M . Then dM := (dM (I))I is a complete invariant
up to isomorphisms of M by the Krull–Schmidt Theorem. The family (H r (P ))0≤r≤d contains information on
P valuable in applications, which is analyzed by the the persistence diagrams dH r (P ) of H r (P ) (0 ≤ r ≤ d).
When P varies with another parameter, say, time, it yields a 2D persistence module. In general, persistence
modules M are understood as modules over the path algebra (or category) A of an acyclic quiver Q with fullcommutativity relations. (Thus A is regarded as the incidence algebra of a poset.) We deal only with thecase where Q is a finite quiver. Unlike the 1-parameter case, there are an infinite number of indecomposablesin the general case, which makes it difficult to use dM in real time. The interval representation above isgeneralized as an interval module VI consisting of k and the identity of k as a representation of Q whose
support I forms a connected and convex subquiver of Q. Instead of using dM , we use approximations of Mby (direct sums of) interval modules in two senses.

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5

数学基礎論および歴史

数 学

基

礎

論

3 月 15 日（水）

お

よ

び

歴

史

第 IX 会場

9:30〜10:15
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列が満たす実効的大数の法則とその収束速度限界· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An effectivization of the law of large numbers for algorithmically random
sequences and its absolute speed limit of convergence

概 要 In this talk, we show that the law of large numbers can be effectivized for an arbitrary Schnorr random

infinite sequence, with respect to an arbitrary computable Bernoulli measure. Actually, we show that an
absolute speed limit of convergence in this effectivization exists and it equals 2 in a certain sense.
2 鈴 木 悠 大 ( 東 北 大 理)
横 山 啓 太 ( 東 北 大 理)
Yudai Suzuki (Tohoku Univ.)
Keita Yokoyama (Tohoku Univ.)

On the Weihrauch degrees between Cωω and ATR · · · · · · · · · · · · · · · · · · 15
On the Weihrauch degrees between Cωω and ATR

概 要 A binary relation over the Cantor space 2ω is called a Weihrauch problem. In this talk, we introduce

ω-model reflection for Weihrauch problems and show that the ω-model reflection of ATR2 gives an upperbound for problems provable from ATR0 in the context of reverse mathematics. We also consider thecomplexity of the existence of fixed point for monotone operators (FP) and its variations (LFP) from theviewpoint of Weihrauch degrees. We will show that LFPs form a linear hierarchy between the ω-model
reflection of ATR2 and Cωω .
10:30〜11:30
藤 原

特別講演
誠 ( 東 京 理 大 理)

Makoto Fujiwara (Tokyo Univ. of Sci.)

半直観主義算術の階層と保存拡大定理

Hierarchy of semi-classical arithmetic and conservative extension theorems

概 要 It is well-known that classical arithmetic PA is Π2 -conservative over intuitionistic arithmetic HA.

Using a generalized negative translation, we relativize this result with respect to theories of semi-classicalarithmetic, which lie in-between PA and HA. In particular, it follows from our main result that PA isΠk+2 -conservative over HA + Σk -LEM where Σk -LEM is the low-of-excluded-middle scheme for formulasof Σk form. In addition, we show that this conservation theorem is optimal in the sense that for any
semi-classical arithmetic T, if PA is Πk+2 -conservative over T, then T proves Σk -LEM. In the same manner,
we also characterize conservation theorems for other well-studied classes of formulas by fragments of classicalaxioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmeticalhierarchy of classical principles. This is a joint work with Taishi Kurahashi.

最終版: 2023/2/17
数学基礎論および歴史

14:15〜14:30

6

歴史部門懇談会

14:30〜16:45
誠(大阪産大全学教育機構)
張 替 俊 夫
(大阪産大全学教育機構)『緝古算経』の方程式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Makoto Tamura (Osaka Sangyo Univ.)
Toshio Harikae (Osaka Sangyo Univ.)

On the equations of “Continuation of Ancient Mathematics”

3 田 村

概 要 “Continuation of Ancient Mathematics” was written by early Tang dynasty calendarist and mathe-

matician Wang Xiaotong some time after the year 626, and is known as the oldest extant book solving cubic
equations. In this talk, we list up its equations and mention the features of them.
4 張 替 俊 夫
(大阪産大全学教育機構)
田 村誠(大阪産大全学教育機構)

Toshio Harikae (Osaka Sangyo Univ.)
Makoto Tamura (Osaka Sangyo Univ.)『緝古算経』の逸文の復元について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On restration of lost chinese text in Continuation of Ancient Mathematics

概 要 “Continuation of Ancient Mathematics” was written by early Tang dynasty calendarist and mathe-

matician Wang Xiaotong some time after the year 626, and was listed as one of the Ten Computational
Canons compiled during Tang dynasty. The aim of this talk is to provide a restration of lost chinese text
in “Continuation of Ancient Mathematics.”
5 脇

克 志 ( 山 形 大 理)

Katsushi Waki (Yamagata Univ.)

和算書内図形領域抽出の精度評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Evaluation of the accuracy of extracting graphic regions in a WASAN
book

概 要 In this presentation, we first present a workflow for extracting graphic regions in a WASAN book,which is necessary for creating a WASAN database, using the Hough transform, and evaluate the accuracyof the extraction. In the latter half of the presentation, we will show how the character “now,” which isthe starting point of the graphic problem, is extracted using artificial intelligence and used to determine thegraphic region for the rectangular combined region, which is a candidate for the graphic region.
6 小 川

束(四日市大関孝和数学研)

Tsukane Ogawa (Yokkaichi Univ.)

岡之只『妙矩集』における数学思想の独立性に関する問題 · · · · · · · · · · · 15

Problems related to the uniqueness of mathematical thought in Oka
Yukitada’s Collection of Exquisite Formulae

概 要 I present some arguments and summarize the current state of affairs regarding the originality of themathematical thought of Oka Tadayuki (1791-?), that is, whether his mathematical methods and ideas wereunique to him or not. In particular, I suggest that his use of the term “pole” is one clue, even though no
new historical documents have been discovered at present.
7 真 島 秀 行 (お茶の水女大⋆)Hideyuki Majima (Ochanomizu Univ.

⋆)“Seki Takakazu, his life and bibliography” 補遺 · · · · · · · · · · · · · · · · · · · · 15
Supplement to the paper “Seki Takakazu, his life and bibliography”

概 要 We will talk about some episodes concerning to the discovery of Seki Takakazu’s carrer in the Kofu

clan.

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7

数学基礎論および歴史

8 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 by Seki Takakazu andTakebe Katahiro

概 要 We will give some theoretical meaning on the calculation of the number Pi by Seki Takakazu andTakebe Katahiro. Seki found the so-called Aitken’s delta-sequenced process in his theory, but there weresome errors in his calculation and he only claimed that his approximate number of Pi was a little bit lessthan 3.14159265359. Takebe Katahiro followed Seki’s method and discovered another method of calculationof Pi.
9 真 島 秀 行 (お茶の水女大⋆)Hideyuki Majima (Ochanomizu Univ.

⋆)

2022 年, 関孝和没後 314 年,「綴術算経」序から 300 年 · · · · · · · · · · · · · · · 15
The year 2022, the memorial 314th year of Seki Takakazu and the 300th
anniversary of “Takebe Katahiro’s Tetsujjutsu-Sankei”

概 要 The author talked about the works of SEKI Takakazu (?-1708), and TAKEBE Katahiro (1664-1739)

on Pi. In this time, we propose to build a stone monument near his tomb in Jorinji Temple, because of his
significant work concerning to Pi.
10 田 中 紀 子 (愛知県立旭丘高)
大⋆)
松 原
望 (東
Noriko Tanaka(Aichi Prefectural Asahigaoka High School)
Nozomu Matsubara (Univ. of Tokyo⋆)

不規則な運動に対する確率的表現についての一考察 · · · · · · · · · · · · · · · · · 15

A study on stochastic representations for random motion

概 要 Regarding the random motion, including Brownian motion, Kiyoshi Ito et al. constructed a proba-bilistic representation, based on P. Levy’s point of view. D. Mumford wrote “The Dawning of the Age of
Stochasticity”, the basic object of study in probability is the random variable and he argues that it shouldbe treated as a basic construct, like spaces, groups and functions, and it is artificial and unnatural to define
it in terms of measure theory. This time, based on D. Mumford’s article, we discuss stochasticity based on
its historical background.

最終版: 2023/2/17
数学基礎論および歴史

17:00〜18:00

8

特別講演

小 林 龍 彦(前橋工科大⋆・四日市大関孝和数学研)

新『関孝和全集』の編集を終えて

Tatsuhiko Kobayashi(Maebashi Inst. of Tech.⋆ /Yokkaichi Univ.)

Finishing the editing of the new Seki Takakazu’s Collected Works概 要 Seki Takakazu’s life and his mathematical achievements were published in the Takakazu Seki’s Collected

Works (Osaka Kyouiku Tosho, 1974), edited by Akira Hirayama and others. In the compilation of historicalsources, it is natural to check the content of the descriptions in the documents, but issues relating totheir history and the authenticity of the sources must also be carefully considered. The collected works
by Akira Hirayama and others was carefully compiled based on detailed research. However, a detailed
examination of the documents included in this collected works reveals that the compilation was not based on
sufficient historical criticism. In June 2023, a new edition of the Seki Takakazu’s Collected Works, edited by
Kenji Ueno, Tsukane Ogawa, Tatsuhiko Kobayashi and Kenichi Sato will be published by Iwanami Shoten,
publishers. The new collected works consists of three volumes with approximately 4000 pages. Volume
1 introduces Seki’s life and his mathematical achievements based on new historical documents discovered.
Volume 2 is a collection of transliteration from books and manuscripts which written in classical Chinese
relating to Seki’s mathematical achievements. In preparing these, the editors conducted a comprehensive
survey of relevant sources scattered throughout Japan, and then collated the different editions. Volume 3
is a collection of historical documents related to Seki’s research on calendrical calculations and his life. In
addition, the book contains the writings of his disciples, various records and statements by contemporary
mathematicians. Many aspects of Seki Takakazu’s life and his biography remain unclear. For this reason,
genealogical records relating to the Seki family and him have been included. In this lecture we will introduce
the editorial policy of the new Seki Takakazu’s Collected Works, how the authenticity of Seki’s writings was
judged etc.

3 月 16 日（木）第 IX 会場

9:15〜12:15
11 薄 葉 季 路 (早 大 理 工)

Toshimichi Usuba (Waseda Univ.)

Monotinicity of ultrafilter numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Monotinicity of ultrafilter numbers

概 要 We consider monotonicity of ultrafilter numbers of infinite cardinals. We show that if there are

cardinals λ < κ with u(κ) < u(λ), then there is an inner model of a large cardinal. Hence the failure ofmonotinicity of ultrafilter numbers has large cardinal strength.
12 竹 内 耕 太 (筑波大数理物質)

Kota Takeuchi (Univ. of Tsukuba)

On the indivisibility of metric structures · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the indivisibility of metric structures

概 要 An ifinite L-structure M is said to be indivisible if for any patition M = X0 t X1 there is i < 2such that Xi contains an isomorphic copy of M . Many important structures, such as infinite sets, randomgarphs, countable dense linear order, in model theory has this property. Recently, many structures withmetrics are studied by model theorists using continuous model theory. So it seems that investigating theindivisibility of metric structures are interseting from the point of view of continuous logic. In this talk we
discuss about the indivisibility of Urysohn universal spaces, which was proven by Sauer.

最終版: 2023/2/17

9

数学基礎論および歴史

13 桔 梗 宏 孝 (神戸大システム情報)
Hirotaka Kikyo(Kobe Univ.)

Hrushovski の擬平面の構造について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the structure of Hrushovski’s pseudoplanes

概 要 We discuss the structure of Hrushovski’s pseudoplanes. In the definition of the Hrushovski’s pseudo-planes associated to an irrational number α, good approximations kn /dn of α from the above are introduced.
For each n, a tree Bn with kn nodes, dn edges and dn + 1 vertices is introduced. Bn is a biminimal zeroextension of the set of its leaves. Let B∞ be the union of all Bn . Let M be the Hrushovski’s pseudoplane
associated to α. Let Dn < M be a copy of Bn in M . Let a be a node of Dn and Fn the set of leaves of Dn .
The closure of the orbit of a over Fn will be whole M . Let D∞ < M be a copy of B∞ and let be the set ofleaves of D∞ . Let a be a node of D∞ . We discuss the non-superstability of M by considering the type ofa over some finite subset F of F∞ and also discuss on the orbit of a over F∞ .
14 坪 井 明 人 (筑波大⋆)Akito Tsuboi (Univ. of Tsukuba⋆)

Ramsey’s theorem and coheir sequences · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Ramsey’s theorem and coheir sequences

概 要 Ramsey’s theorem is very easy to prove. However, its relation to the notion of coheir sequences, whichis quite important in model theory, has not been discussed much. Here we present a result that illustrates
the relationship between the two.
( 東 北 大 理)
15 L. Pacheco(
田 中 一 之 東 北 大 理)

Leonardo Pacheco (Tohoku Univ.)
Kazuyuki Tanaka (Tohoku Univ.)

Fixed-points in epistemic logic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Fixed-points in epistemic logic

概 要 The µ-calculus is an extension of modal logic by least and greatest fixed-point operators. Its alternation

hierarchy characterizes formulas by the entanglement of their fixed point operators. While the alternation
hierarchy is usually strict, in many settings it may collapse. We study the consequences of the strictness
or the collapse in epistemic logic. We show that different axioms for knowledge imply in different numbersof possible degrees of ignorance. We also show that if we consider two or more agents simultaneously, thealternation hierarchy is strict.
16 倉 橋 太 志 (神戸大システム情報)

Taishi Kurahashi (Kobe Univ.)Friedman–Goldfarb–Harrington の定理の拡張 · · · · · · · · · · · · · · · · · · · · · · 15
Extensions of the Friedman–Goldfarb–Harrington theorem

概 要 We investigate the Friedman–Goldfarb–Harrington theorem. In the frameworks of classical and modal

propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH theorem.
17 倉 橋 太 志 (神戸大システム情報)
小 暮 晏 佳 ( 金 沢 大 理 工)

Taishi Kurahashi (Kobe Univ.)
Haruka Kogure (Kanazawa Univ.)

単調性を満たす証明可能性述語の様相論理 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Monotonic modal logics of provability predicates

概 要 We investigate modal logical aspects of provability predicates Pr T (x) satisfying the following condition:

M: If T ` φ → ψ, then T ` PrT (⌜φ⌝) → PrT (⌜ψ⌝).
We proved the arithmetical completeness theorems for monotonic modal logics MN, MN4, MNP, MNP4, and
MND with respect to provability predicates satisfying the condition M.

最終版: 2023/2/17
数学基礎論および歴史

18 岩 田 荘 平 (神戸大システム情報)
Sohei Iwata(Kobe Univ.)

10

Sacchetti の論理のカット除去可能性について · · · · · · · · · · · · · · · · · · · · · · 15
The cut-elimination theorem for Sacchetti’s logics

概 要 Sacchetti showed the modal logics wGLn (Here wGLn is obtained from the provability logic GL byreplacing the axiom □(□A → A) → □A by an weaker one □(□n A → A) → □A.) have the fixed-pointproperty. Moreover, these logics also have desirable properties (for instance, the Lyndon interpolation
property, arithmetical completeness, effective constructibility of fixed-points, etc.). We investigate them inthe point of view of proof theory. We introduce sequent calculi for wGLn and give a purely syntactical
proof of the cut-elimination property for these calculi.
19 大 川 裕 矢 (千 葉 大 理)
岩 田 荘 平 (神戸大システム情報)
倉 橋 太 志 (神戸大システム情報)(Chiba Univ.)
Yuya Okawa(Kobe Univ.)
Sohei Iwata
Taishi Kurahashi (Kobe Univ.)

様相論理 IL− (P) について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The logic IL− (P)概 要 The logic IL− (P) is obtained by adding the persistence principle P : A▷B → □(A▷B) to the sublogic

IL− of the basic interpretability logic IL. We investigate IL− (P) from several perspectives. Firstly, weshow that IL− (P) has a weak version of fixed-point property. Secondly, we show that IL− (P) is a natural
basis for some relational semantics. Thirdly, we introduce a system of sequent calculus for IL− (P), andprove the cut-elimination theorem for it. Finally, we show that IL− (P) is sound and complete with respect
to a suitable arithmetical semantics.
12:15〜12:30

数学基礎論および歴史分科会総会

最終版: 2023/2/17

11

代数学

代

数

3 月 15 日（水）学
第 I 会場

9:00〜12:00
1 丹 原 大 介

♭ 長方形の条件をみたす R2 の直線図形について · · · · · · · · · · · · · · · · · · · · · 10

Daisuke Tambara

A linear figure in the Cartesian plane satisfying a condition of rectangle

概 要 We say a subset X of the Cartesian plane R2 satisfies the rectangle condition if for any points (x1 , y1 ),(x1 , y2 ), (x2 , y1 ) of X the point (x2 , y2 ) also belongs to X. We are interested in what restrictions on the
shape of X the condition imposes. We consider the case where X is a linear figure in the sense that X
is a finite union of segments and points. Our result is about the shape of a connected component of X
satisfying the rectangle condition.
2 安 部 利 之 ( 愛 媛 大 教 育)
Toshiyuki Abe (Ehime Univ.)

原田予想 II とグラム行列式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Harada’s conjecture II and Gramian determinants

概 要 We consider Harada’s conjeture II for finite groups G. The conjecture states that the number h(G)defined as a ratio of the product of all sizes of conjugacy classes and thay of all irreducible degrees of G is
an ineteger. We see that the square h(G)2 is given as a quotient of Gramian determinat for suitable basis of
the center of the group algebra CG by a product of all sizes of centeralizers of representatives of conjugacy
classes. We generalize h(G)2 to numbers µϕ (G) associated to a pair of (Z, ϕ) of central subgroup Z and its
irreducible character ϕ, and give a factrozation theorem of h(G)2 to of these numbers µϕ (G) for fixed Z.
We will show some examples.
3 田 邊 顕 一 朗 (東京都市大共通教育)

Kenichiro Tanabe (Tokyo City Univ.)

非退化偶格子に付随する頂点代数の不変部分代数のフュージョン則 · · · · 15

Fusion rules for the fixed point subalgebra of the vertex algebra associated with a non-degenerate and non-positive definite even lattice by anautomorphism of order 2

概 要 Let VL be the vertex algebra associated with a non-degenerate and non-positive definite even lattice L

and VL+ the fixed point subalgebra of VL under the action of the automorphism induced from the −1-isometryof L. We determine the fusion rules for weak VL+ -modules.
4 鈴 木 武 史 ( 岡 山 大 理)
豊 澤 由 貴Takeshi Suzuki (Okayama Univ.)
Yoshitaka Toyosawa

Cylindric skew Young 図のフック長公式について · · · · · · · · · · · · · · · · · · · 15
On hook formulas for cylindric skew diagrams

概 要 We present a conjectual hook formula concerning the number of the standard tableaux on “cylindric”

skew diagrams. Our formula can be seen as an extension of Naruse’s hook formula for skew diagrams.
Moreover, we prove our conjecture in several cases.
5 吉 井豊 ( 茨 城 大 教 育)

Yutaka Yoshii (Ibaraki Univ.)

単純代数群の超代数のある部分代数に関するいくつかの結果 · · · · · · · · · · 10

Some results on certain subalgebras of the hyperalgebra of a simple
algebraic group

概 要 Let G be a simply connected simple algebraic group defined over a field Fp of p elements, where p is aprime number. Then G is associated an Fp -algebra U which is called a hyperalgebra. We give some resultson certain Fp -subalgebras of U .

最終版: 2023/2/17
代数学

6 後 藤 悠 一 朗 (阪Yuichiro Goto

大理)

(Osaka Univ.)

12

擬遺伝構造の個数に関して · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A remark on the number of quasi-hereditary structures概 要 Dlab and Ringel showed that algebras being quasi-hereditary in all total 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. We say that two total orders are equivalent if they induce the same set of standard
modules. As a matter of fact, if an equivalence class of orders make an algebra be quasi-hereditary, thenwe call this class a quasi-hereditary structure. Flores, Kimura and Rognerud gave the counting method of
the number of quasi-hereditary structures on path algebras of Dynkin quivers. In this talk, I give a similar
result for path algebras of the quivers Q. Here Q is a quiver whose underlying graph is gotten by adding asingle vertex to type An and a single edge between the new vertex and a vertex originally in An .
7 宮 本 賢 伍 ( 茨 城 大 工)王
起 (Tsinghua Univ.)

Kengo Miyamoto (Ibaraki Univ.)(Tsinghua Univ.)
Qi Wang多項式増大型の対称代数の τ -傾有限性について · · · · · · · · · · · · · · · · · · · · · 15

On τ -tilting finiteness of symmetric algebras of polynomial growth

概 要 In this talk, we report on the τ -tilting finiteness of finite dimensional symmetric algebras of polynomial

growth over an algebraically closed field. It is known that τ -tilting finiteness is preserved under Morita
equivalence, but usually not preserved under derived equivalence. However, we have not found any examplesof symmetric algebras which do not preserve τ -tilting finiteness under derived equivalence. In this talk, any
symmetric algebras of polynomial growth preserve τ -tilting finiteness under derived equivalence.
8 淺 井 聡 太 ( 阪 大 情 報)
伊 山
修 ( 東 大 数 理)
(Osaka Univ.)
Sota Asai
Osamu Iyama (Univ. of Tokyo)

実 Grothendieck 群の元の rigid 部分 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The rigid parts of the elements of the real Grothendieck groups

概 要 Let A be a finite-dimensional algebra over a field K. For any complex X in the homotopy category

Kb (projA) of the complexes over the category of finitely generated projective modules, we can naturally
define the rigid part of X as the maximum presilting direct summand of X. In our study, we found thatthe rigid part of each element θ in the real Grothendieck group K0 (projA)R , which can be identified with an
Euclidean space, is also well-defined. In this talk, I will talk about some key properties to prove our result.
9 佐 藤 眞 久
(愛知大地域政策・山梨大⋆)
Masahisa Sato
(Aichi Univ./Univ. of Yamanashi⋆)

中山 (東屋) の補題の拡張について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On generalized Nakayama–Azumaya’s Lemma

概 要 Let R be a ring and J(R) its Jacobson radical. We prove the following lemma. Generalized Nakayama–

Azumaya’s Lemma “Let M be a direct summand of a direct sum of finitely generated right R-modules. If
M satisfies MJ(R) = M, then M = 0.”This unifies the following known results; “Let M be a finitely generated module or a projective module. If
MJ(R)=M, then M=0.”
As an aplication of this lemma, we show existence of a maximal submodule for some kind of modules.

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13

代数学

10 中 村力 ( 三 重 大 教 育)(Czech Acad. of Sci.)
M. Hrbek
J. Šťovı́ček(Charles Univ. in Prague)

Tsutomu Nakamura (Mie Univ.)
Michal Hrbek (Czech Acad. of Sci.)
Jan Šťovı́ček (Charles Univ. in Prague)

Large tilting complexes and homomorphic images of Cohen–Macaulayrings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Large tilting complexes and homomorphic images of Cohen–Macaulayrings

概 要 Tilting theory plays a central role in representation theory of algebras. Making mutation operations

possible, the notion of tilting objects was extended to silting objects. While they are usually assumed
to be compact objects in triangulated categories, the definitions have been naturally extended to possibly
non-compact objects. In this talk, we give a concrete way to construct (possibly non-compact) silting
objects and cosilting objects in the unbounded derived category of a commutative noetherian ring R by
using strictly increasing functions from Spec R to the integers. Then we discuss when they are tilting objects
and cotilting objects. Finally, we relate our construction of (co)tilting objects with a question when R is ahomomorphic image of a Cohen–Macaulay ring.
11 東 谷 章 弘 (阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)

同変 Ehrhart 理論における効果性予想とそのある種の反例 · · · · · · · · · · · 15

Effectiveness conjecture on equivariant Ehrhart theory and a kind of its
counterexample

概 要 Equivariant Ehrhart theory discusses lattice polytopes admitting a finite group action ρ. Note that thecase where ρ is trivial corresponds to the usual Ehrhart theory. Since every lattice polytope admits a trivialgroup action, we can recover the usual Ehrhart theory. In the equivariant Ehrhart theory, the effectivenessconjecture is one of the central problems. This predicts the following: for any lattice polytope P , if theH ∗ -series of P , which is a formal power series appearing in the equivariant Ehrhart series, becomes just a
polynomial, then the H ∗ -series becomes effective, i.e., the coefficients really become some representations.
In this talk, we give a kind of a counterexample of this conjecture.
14:15〜14:50
12 黒 田 匡 迪 (日 本 文 理 大 工)
三 井 健 太 郎 ( 神 戸 大 理)
Masamichi Kuroda(Nippon Bunri Univ.)
Kentaro Mitsui (Kobe Univ.)

単項 GAPN 関数の分類について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the classification of monomial GAPN functions

概 要 Perfect nonlinear (PN) functions and almost PN (APN) functions over finite fields of characteristic p

have high nonlinearity. When p = 2, they have been widely studied due to their applications to cryptography
and coding theory. Recently, generalized APN (GAPN) functions were defined as an algebraic generalizationof APN functions in characteristic 2 to odd characteristic p > 2 and they have been studied. In this talk,
we introduce some results of the study for the classification of monomial GAPN functions.

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代数学

13 山 形颯 ( 福 岡 大 理)

So Yamagata (Fukuoka Univ.)

14

r-set の分類と超平面配置が non-very generic となるための十分条件について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On classification of r-sets and a sufficient condition for non-very genericity of arrangements

概 要 Manin and Schechtman introduced a family of arrangements of hyperplanes generalizing classicalbraid arrangements, which they called the discriminantal arrangements. Athanasiadis proved a conjecture
by Bayer and Brandt providing a full description of the combinatorics of discriminantal arrangements in thecase of very generic arrangements. Libgober and Settepanella described a sufficient geometric condition forgiven arrangements to be non very generic in terms of the notion of dependency for a certain arrangement.
Settepanella and the author generalized the notion of dependency introducing r-sets and KT -vector sets,
and provided a sufficient condition for non very genericity but still not convenient to verify by hand. In thistalk we give a classification of the r-sets, and a more explicit and tractable condition for non very genericity.
15:00〜16:00

特別講演
藤 田 直 樹 ( 熊 本 大 先 端)シューベルト・カルキュラスと凸多面体

Naoki Fujita (Kumamoto Univ.)

Schubert calculus and convex polytopes

概 要 A goal of Schubert calculus is to compute the structure constants of the cohomology ring of a flag

variety with respect to the basis consisting of Schubert classes. One approach to such computation is torealize Schubert classes as concrete combinatorial objects such as Schubert polynomials. In type A case,monomials in a Schubert polynomial are naturally parametrized by specific faces of a Gelfand–Tsetlin
polytope. These faces are called reduced Kogan faces and appear as the limit of a semi-toric degenerationof a Schubert variety. Since the Gelfand–Tsetlin polytope is a Newton–Okounkov body of the flag variety,
Newton–Okounkov bodies and induced toric degenerations are expected to give a generalization of theories
in Schubert calculus to more general projective varieties. Such generalization has partially developed in thecase of flag varieties in different Lie types. In this talk, some fundamental objects in Schubert calculus will
be explained from the viewpoints of convex polytopes and of Kashiwara crystal bases. We also discuss theirgeneralization to more general projective varieties.
16:15〜17:15

特別講演
松 井 紘 樹 (徳島大社会産業理工) ♭ 三角圏のスペクトラムとスキームの復元問題

Hiroki Matsui (Tokushima Univ.)

Spectra of triangulated categories and reconstruction of schemes fromtheir derived categories

概 要 For a given noetherian scheme X, it is natural to ask whether we can reconstruct X from its perfectderived category Dpf (X) or not. This reconstruction problem has been well studied so far in algebraic
geometry. It is known that we cannot reconstruct X from the triangulated category structure of Dpf (X).
For example, Mukai proved that for an abelian variety A, the perfect derived categories of A and A∨ areequivalent as triangulated categories. On the other hand, Balmer proved that we can reconstruct X fromits perfect derived category using its tensor triangulated category structure. For this, Balmer defined theringed space Spec⊗ (T ) for a given tensor triangulated category T , which is called the Balmer spectrum of T .
Using Balmer spectra, Balmer developed tensor triangular geometry and as an application, he proved thatthe Balmer spectrum of Dpf (X) is isomorphic to X as ringed spaces. In this sense, X can be reconstructedfrom the tensor triangulated category structure of Dpf (X).
In this talk, I will introduce another ringed space Spec△ (T ) for a given triangulated category T without
using tensor structure to develop a “tensor-free” analog of tensor triangular geometry. We call Spec △ (T ) the
spectrum of T . Using the spectra of derived categories, we will prove several reconstruction results. Amongthem, we will give an alternative and algebraic proof of Bondal-Orlov-Ballard reconstruction theorem.

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15

代数学

3 月 16 日（木）第 I 会場

9:10〜12:00
14 大 竹 優 也 (名 大 多 元 数 理)
Yuya Otake(Nagoya Univ.)

n 球加群と n 捩れ自由加群の安定圏 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stable categories of n-spherical modules and n-torisonfree modules

概 要 Auslander and Bridger introduced the notions of n-spherical modules and n-torsionfree modules. In

this talk, we study the stable category of n-spherical modules. Moreover, we introduce the notion of n-Gspherical modules as a G-analogue and give similar results for the stable category of n-G-spherical modules.
As an application, we prove that if R is a Gorenstein local ring of Krull dimension d > 0, then there exists
a stable equivalence between the category of (d − 1)-torsionfree R-modules and the category of d-sphericalmodules relative to the local cohomology functor.
15 石 塚伶 ( 東 工 大 理)
下 元 数 馬 ( 日 大 文 理)
(Tokyo Tech)Ryo Ishizuka
Kazuma Shimomoto (Nihon Univ.)

混標数における perfectoid almost Cohen–Macaulay 代数の明示的構成· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An explicit construction of perfectoid almost Cohen–Macaulay algebrain mixed characteristic

概 要 The existence and properties of non-Noetherian algebras over a given Noetherian ring play importantroles in commutative algebra. Properties of such algebras are, for example, perfectoid and almost Cohen–
Macaulay. In positive characteristic, the perfect closure has these properties. In this talk, we construct ananalog of the perfect closure in mixed characteristic and show that it has the same properties.
16 伊 城 慎 之 介 (日 大 総 合 基 礎)

Shinnosuke Ishiro (Nihon Univ.)

The canonical module of a local log-regular ring · · · · · · · · · · · · · · · · · · · 15
The canonical module of a local log-regular ring概 要 Local log-regular rings are a certain class of Cohen–Macaulay rings that are treated in logarithmic

geometry. This class has similar properties to those toric rings. From this perspective, I determined theform of the canonical module of a local-log regular ring. As an application, we gave the Gorenstein criterionof this class of rings. In this talk, we introduce these results.
17 松 下 光 虹 (阪 大 情 報)
Koji Matsushita (Osaka Univ.)

トーリック環の conic 因子的イデアルと安定集合環への応用 · · · · · · · · · · 15

Conic divisorial ideals of toric rings and applications to stable set rings

概 要 Conic divisorial ideals of toric rings play important roles in the theory of non-commutative algebraic

geometry as well as commutative algebra. In this talk, we introduce an idea to determine a region
representing conic classes in the divisor class group of a toric ring and a description of the conic divisorial
ideals of stable set rings of perfect graphs.
18 石 原 侑 樹 (東 京 理 大 理)

Yuki Ishihara (Tokyo Univ. of Sci.)

パラメータ付きのイデアル操作の計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Computation of ideal operations with parameters

概 要 Ideal is one of the fundamental concepts in Commutative Algebra and Algebraic Geometry. For one

or more ideals, we consider ideal operations that generate new ideals from them, e.g., the ideal intersection√
I ∩ J, the ideal quotient I : J, the saturation I : J ∞ , the radical I, etc., where I and J are ideals in thepolynomial ring C[x1 , . . . , xn ]. In this talk, we consider several algorithms to compute ideal operations withparameters by using Comprehensive Gröbner Systems. In addition, we present an algorithm for “feasible”
parameterized primary decomposition by utilizing those operations.

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代数学

19 服 部 京 平 (新 潟 大 自 然)
小 島 秀 雄 ( 新 潟 大 自 然)
Kyohei Hattori (Niigata Univ.)
Hideo Kojima (Niigata Univ.)

16

Rings of nilpotent elements of monomial derivations on polynomial rings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Rings of nilpotent elements of monomial derivations on polynomial rings

概 要 In this talk, we give a classification of Nil D of monomial derivations D on the polynomial ringR[x, y] over a UFD R containing Q. Furthermore, as its application, we show that the minimal number ofgenerators of kernels of derivations on the polynomial ring R[x, y, z] as a R-algebra is unbound.
20 木 村 海 渡 (名 大 多 元 数 理)
Kaito Kimura (Nagoya Univ.)加群の局所化の漸近深度 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Asymptotic depths of localizations of modules

概 要 Let R be a commutative Noetherian ring, I an ideal of R, and M a finitely generated R-module. The

asymptotic behavior of the quotient modules M/I n M of M is an actively studied subject in commutative
algebra. In this talk, we consider the existence of an integer k such that for all integers n ≥ k and all prime
ideals p of R, the depth of (M/I n M )p is equal to the depth of (M/I k M )p .
21 遠 藤 直 樹 (明 大 政 治 経 済)
Naoki Endo

(Meiji Univ.)

On the stratification of one-dimensional Cohen–Macaulay rings · · · · · · 15
On the stratification of one-dimensional Cohen–Macaulay rings

概 要 The aim of this talk is to discover a good candidate for natural generalizations both of almost

Gorenstein and 2-almost Gorenstein rings from the point of view of Sally modules of canonical ideals. Even
though our results are at this moment restricted within the case of dimension one, we expect that a higher
dimensional notion might be possible after suitable modifications.
22 奥 間 智 弘 (山 形 大 理)
吉 田 健 一 ( 日 大 文 理)
渡 辺 敬 一(日大文理・明大研究・知財)

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

The core of ideals in minimally elliptic singularities · · · · · · · · · · · · · · · · · 15

The core of ideals in minimally elliptic singularities

概 要 A two-dimensional normal local domain is called a minimally elliptic singularity if it is Gorenstein

and its geometric genus is one. For an m-primary integrally closed ideal I in a minimally elliptic singularity(A, m), we represent its core using a cycle on a resolution of the singularity.
23 吉 田 健 一 (日 大 文 理)
奥 間 智 弘 ( 山 形 大 理)
渡 辺 敬 一(日大文理・明大研究・知財)

Gorensteinness for normal tangent cones of the maximal ideals in Brieskorn
hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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

Gorensteinness for normal tangent cones of the maximal ideals in Brieskorn
hypersurfaces

概 要 Let (A, m) be a two-dimensional excellent normal local domain containing an algebraically closed field.

The graded ring defined by all integal closures of powers of an ideal I of A is called the normal tangent coneof I. We classify all Brieskorn hypersurfaces for which the normal tangent cone of the maximal ideal m is
to be Gorenstein.

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17

代数学

13:00〜14:10
24 是 枝 由 統 (広 島 大 理)

Yoshimune Koreeda (Hiroshima Univ.)

標数 2 の D41 型曲面特異点のジェットスキーム上のファイバー · · · · · · · · 13

Jet scheme of a singular surface of type D41 in characteristic 2

概 要 Let k be an algebraically closed field, X a variety over k and m a nonnegative integer. There is aspace Xm over X, called the jet scheme of X of order m, parameterizing m-th jets on X. The fiber overthe singular locus of X is called the singular fiber. In this talk, we assume k is of characteristic 2 and X isa singular surface of type D41 . For m  0, we give the irreducible decomposition of the singular fiber of X
and determine the maximal elements among the intersections of two different irreducible components.
25 赤 池 広 都 (阪大理) ♭ 楕円曲面上巡回被覆ファイバー曲面の自己同型群の位数の上界について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Hiroto Akaike(Osaka Univ.)

Bounds for the order of automorphism groups of cyclic covering fibrations of an elliptic surface

概 要 In this talk, we show upper bounds for the order of automorphism groups of primitive cyclic covering

fibrations of an elliptic surface. The upper bound is an explicit function in the genus of the base curve, thecovering degree and the square of relative canonical divisor.
26 舛 谷 亮 祐 (都 立 大 理)

Ryosuke Masuya (Tokyo Metro. Univ.)

平面 4 次曲線の弱二重接線と有理楕円曲面について · · · · · · · · · · · · · · · · · 13

On weak-bitangents for plane quartics and rational elliptic surfaces

概 要 It is well-known that a smooth plane quartic has twenty-eight bitangents. We consider weak-bitangents

which are generalizations on bitangents for a reduced quartic. We study weak-bitangents from the viewpointof rational elliptic surfaces attached to reduced quartics. In particular, we consider an analogy of syzygetic
triads. As a result, we can give new proofs for some classical results on certain singular plane quartics andtheir bitangents.
27 山 口樹 (東 大 数 理) ♭ Big Cohen–Macaulay test ideals in equal characteristic zero via ultraproducts · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Tatsuki Yamaguchi (Univ. of Tokyo)

Big Cohen–Macaulay test ideals in equal characteristic zero via ultraproducts

概 要 Schoutens constructed big Cohen–Macaulay (BCM) algebras in equal characteristic zero using ultra-

products. In this talk, we show that BCM test ideals with respect to Schoutens’ BCM algebras coincide withmultiplier ideals, which define the non-klt loci of normal varieties. As an application, we study singularitiesof pure subrings.

3 月 17 日（金）第 I 会場

9:00〜12:00
28 桜 井真 ( 開 智 学 園)

Makoto Sakurai (Kaichi Gakuen)

カイラル共形場の次元と準連接層 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Dimensions of chiral conformal fields and quasi-coherent sheaves

概 要 The so-called AGT correspondence between 4d gauge theories and 2d conformal field theories wasunder discussion. However, despite much effort by mathematicians (and some physicists), the scope of results
is limited, although it is sophisticated. In this report, I will deliver a trial to synthesize the mathematical
literature of Beilinson and Drinfeld and some of the more “natural” physics for formulae of “anomalies.”
Several conventional definitions of “dimensions” will be briefly reviewed. Then I will seek a correct notionof dimensions for chiral fields in the context of S-duality and the geometrical dimension. Some more efforts
will be on the (non-)quasi-coherent sheaves for chiral algebra theories and D-modules.

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代数学

29 岩 見 智 宏 (九 工 大 工)

Tomohiro Iwami (Kyushu Inst. of Tech.)

18

Majorana double solids for three-dimensional Miyaoka–Yau type inequality with the associated third Chern classes · · · · · · · · · · · · · · · · · · · · 13
Majorana double solids for three-dimensional Miyaoka–Yau type inequality with the associated third Chern classes

概 要 Based on S. Mori’s proof for an three-dimesnional extremal neighborhood (X, C) ⊂ C4 of type A in theexistence of three-dimensional flips, for an extended extremal nbd (X, Cs ) with Cs not necessary irreducible
nor reduced ([I2019Mar]), the author found three-dimesional Miyaoka–Yau type inequality (M Y )3,c3 with theassociated c3 ([I2018Mar, I2019Sep]), (M Y )3,c3 with the differential operators ([I2020Sep]) and related ones,f
moreover introduced an interemdiate Jacobians IJ(X,Cs ) ([I2022Mar]) and found its strong approximation
for its Z-structure ([I2022Sep]). In this talk, as sequel to [I2022Sep], the author will report: a) to showfprecise form of strong approximation for IJ(X,Cs ) via the differential operators, b) to give slightly extended
diagonal decomposition ([Bloch–Srinivas 1983]) to introduce real/Majorana spinor by a), and c) to constructZ-structure by gluing this underlying real structure via b) regarding to integral Hodge conjeture, in order
to discuss alternative to [Artin–Mumford 1972].
30 髙 橋 優 太 (中 大 理 工)
渡 邉
究 ( 中 大 理 工)
Yuta Takahashi (Chuo Univ.)
Kiwamu Watanabe (Chuo Univ.)

正標数におけるネフ接束をもつ 4 次元ファノ多様体の分類 · · · · · · · · · · · 13

Fano 4-folds with nef tangent bundle in positive characteristic

概 要 In characteristic 0, the Campana–Peternell conjecture claims that the only smooth Fano variety with

nef tangent bundle should be homogeneous. In this talk, we present the positive characteristic version of
the Campana–Peternell conjecture. In particular, we give a result for Fano 4-folds with nef tangent bundle
and Picard number greater than one.
31 吉 野 太 郎 (東 大 数 理)
Taro Yoshino (Univ. of Tokyo)

On the degree of irrationality of complete intersections · · · · · · · · · · · · · · 13
On the degree of irrationality of complete intersections

概 要 This is joint work with Lucas Braune. We obtain a lower bound of the degree of irrationality of very

general complete intersections over the complex field from the recent results of Braune and Chen–Stapleton.
For combining these results, we make a minor adjustment of Chen–Stapleton’s method using the trace mapof differential modules.
32 水 野 雄 貴 (早 大 理 工)
Yuki Mizuno(Waseda Univ.)

Some examples of noncommutative projective Calabi–Yau schemes · · · 13
Some examples of noncommutative projective Calabi–Yau schemes

概 要 We construct some examples of noncommutative projective Calabi–Yau schemes by using noncom-

mutative Segre products and quantum weighted hypersurfaces. We also compare them with commutative
Calabi–Yau varieties and examples by Kanazawa.
33 星
明 考 ( 新 潟 大 理)
大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classification for algebraic tori (I) · · · · · · · · · · · · · · · · · · · · · · · 13
Birational classification for algebraic tori (I)

概 要 We give a stably birational classification for algebraic k-tori of dimensions 3 and 4 over a field k.

34 星
明 考 ( 新 潟 大 理)
大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classification for algebraic tori (II) · · · · · · · · · · · · · · · · · · · · · · 13
Birational classification for algebraic tori (II)概 要 We give a stably birational classification for algebraic k-tori of dimensions 3 and 4 over a field k.

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19

代数学

35 助 永 真 之 (広島大先進理工)

Masayuki Sukenaga (Hiroshima Univ.)

トロピカル平面曲線の交わりの実現問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Tropical lifting problem for the intersection of plane curves

概 要 Let D be a tropical divisor in the intersection of two tropical plane curves. We study when it can berealized as the tropicalization of the intersection of two algebraic curves. When a graph theoretic condition
determined by these tropical curves is satisfied, we can algorithmically find algebraic curves such that thetropicalization of their intersection is D.
36 天 野 通 大 (明星大)Michio Amano (Meisei Univ.)

Witt vectors のある準同型写像の核について II · · · · · · · · · · · · · · · · · · · · · 10
On kernels of certain homomorphisms of Witt vectors, II

概 要 Let W (A) be a Witt group over A and let W n (A) be the product of n of W (A). T. Sekiguchi and

N. Suwa have constructed a certain endomorphism Un of W n (A) related to the deformation group schemefrom the additive group scheme to the multiplicative group scheme. We study the equality of kernels ofcertain homomorphisms related to Un .
37 川 辺 大 貴 (東 北 大 理)
Daiki Kawabe (Tohoku Univ.)

Chow motives of genus one fibrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Chow motives of genus one fibrations

概 要 Genus 1 fibrations play a central role in the classification of surfaces. Let f : X → C be a genus 1

fibration from a surface to a curve. Then there is a Jacobian genus 1 fibration j : J → C that satisfies
some good properties. In this talk, we prove that the motive of X is isomorphic to the motive of J. As anapplication, we prove motivic finite-dimensionality for surfaces not of general type with geometric genus 0.
This can be regarded as a generalization of Bloch–Kas–Lieberman’s result to arbitrary characteristic.
38 安 藤 哲 哉 (千 葉 大 理)
Tetsuya Ando

(Chiba Univ.)

4 変数 4 次対称 extremal 不等式と K3 曲面 · · · · · · · · · · · · · · · · · · · · · · · · · 13
Symmetric quartic extremal inequalities of four variables and K3 surfaces

概 要 Let P4,4 be the convex cone of quartic homogeneous polynomials of four variables which is positive

semidefinite. We present a family of symmetric elements of P4,4 . Let f be a such polynomial. Then zero
locus of f in the complex 3-dimensional projective space is a K3 surface which has 10 real A1 type rational
double points.
39 寄 崎 恵 美 子 (都 立 大 理)
坂 内 真 三 ( 岡 山 理 大 理)
徳 永 浩 雄 ( 都 立 大 理)

Emiko Yorisaki (Tokyo Metro. Univ.)
Shinzo Bannai (Okayama Univ. of Sci.)
Hiro-o Tokunaga (Tokyo Metro. Univ.)

Ramified and Split models of rational elliptic surfaces and bitangent
lines for a quartic curve · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Ramified and Split models of rational elliptic surfaces and bitangent
lines for a quartic curve

概 要 We introduce the notion of ramified and split models of elliptic surfaces. We consider how these twomodels are related. In particular, we apply our consideration to rational elliptic surfaces which arise assmooth models of double covers of the projective plane branched along quartics. As a result, we determine
the number of concurrent bitangent lines for irreducible quartics with at most nodes.

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代数学

14:15〜14:30

202023 年度 (第 26 回) 日本数学会代数学賞授与式

14:40〜15:40

2023 年度 (第 26 回) 日本数学会代数学賞受賞特別講演
權 業 善 範 (東 大 数 理) 高次元極小モデル理論の構築とその応用について

Yoshinori Gongyo (Univ. of Tokyo)

On higher dimensional minimal model theory and its applications

概 要 I will report what I am going on projects related to the minimal model program. First, I will

discuss some new invariants for studies of Fano varieties. We call it the “total index”, which is naturalinvariant mixing Shokurov’s complexities and the usual Fano index. In this study, the Birkar generalizedpair naturally appears. Using this invariant, I propose some conjecture for the characterization of the
product of projective spaces, which is some variant of Mukai’s type conjecture. The methods are to use thelocal–global method from singularities rather than studies of rational curves. To study this conjecture, thenon-vanishing conjecture and characterization of toric varieties are involved. Second, I will explain what I
consider recently on the mainstream of the minimal model theory.
16:00〜17:00
若 槻

2023 年度 (第 26 回) 日本数学会代数学賞受賞特別講演
聡 ( 金 沢 大 理 工)

Satoshi Wakatsuki (Kanazawa Univ.)

跡公式とその応用

Trace formulas and their applications

概 要 The trace formula is one of the main tools in the study of automorphic forms, and its theory has been

greatly developed by many researchers (Selberg, Arthur, etc.). The trace formula plays an important roleeven today, such as the classification of automorphic representations by stable trace formulas and the studyof automorphic periods by relative trace formulas. In this talk, I will give an overview of trace formulas andtheir applications. After that, I will introduce my recent research on asymptotic behaviors for dimensionsof spaces of automorphic forms.

3 月 18 日（土）第 I 会場

9:15〜12:00
40 飯 高茂 (学 習 院 大⋆)

Shigeru Iitaka (Gakushuin Univ.

⋆)

第 2 種スーパー完全数と完全数 80 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Super perfect numbers of the second kind

概 要 Let m denote translation parameter, and let h denote an odd prime.

Defining A to be σ(a) + m if hσ(A) = 2a(h + 1) − h2 + mh then a is said to be super perfect numbers of thesecond kind. A is called a partner of a.
41 小 林 雅 人 (神 奈 川 大 工)

Masato Kobayashi (Kanagawa Univ.)

約数和関数のバランス · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Balance for the divisor sum function

概 要 Let us say finite A ⊆ N is balanced if

XXn∈A d|n,d odd

d=

X

X

d.

n∈A d|n,d, even

For example, {1, 2}, {1, 3, 4}, {3, 6, 8, 9} are balanced. For each natural number N , does there exist abalanced set A of the cardinality N ? I solved this problem affirmatively in June 2022 with Ramanujan’s
theta function and Jacobi’s triple product idenitity. In this talk, I wish to show details of this.

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21

代数学

42 金 堂 優 哉 (名 大 多 元 数 理)
Yuya Kanado(Nagoya Univ.)

The relation between a generalized Fibonacci sequence and the lengthof Cunningham chains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
The relation between a generalized Fibonacci sequence and the lengthof Cunningham chains概 要 Let p be a prime number and α ≥ 3 be an integer. In this talk, a generalized Fibonacci sequence

Fα = (Fn )n∈Z is defined as F0 = 0, F1 = 1, Fn+2 = αFn+1 + Fn (n ∈ Z), and Fα σ(n) =P

d|n,0<d∈Fα d iscalled the divisor function on Fα . Then we obtain that for two prime numbers p and q the fact p = 2q + 1
or 2q − 1 is equivalent to Fα σ(Fα σ(Fp )) = Fα σ(Fq ) for some α.
43 栗 野 俊 一 (日 大 経 済)
中 野 正 俊 (気仙沼高等技術専)

Shun-ichi Kurino (Nihon Univ.)
Masatoshi Nakano(Kesennuma Coll. of Tech.)

The error term in the prime number theorem under the RH · · · · · · · · · 10
The error term in the prime number theorem under the RH√

概 要 We propose the conjecture that the error term in the prime number theorem under the RH is o( x).

44 杉 山 真 吾 (日 大 理 工)
アデイルマスリアジャヤ( 九 大 数 理)

Shingo Sugiyama (Nihon Univ.)
Ade Irma Suriajaya (Kyushu Univ.)

Dirichlet L 関数の族の重み付き零点密度について · · · · · · · · · · · · · · · · · · · 10

On a weighted density of zeros of Dirichlet L-functions in a family

概 要 Katz and Sarnak suggested a relation between zeros of L-functions in a family and eigenvalues ofrandom matrices in a compact matrix group. In this talk, we consider the analogous conjecture weighted by
L-values and verify this conjecture in the case of the family of Dirichlet L-functions attached to nontrivial
Dirichlet characters of a prime modulus. This is a joint work with Ade Irma Suriajaya (Kyushu University).
45 橋 本 康 史 (琉 球 大 理)
Yasufumi Hashimoto(Univ. of Ryukyus)

セルバーグゼータ関数に関する普遍性定理 · · · · · · · · · · · · · · · · · · · · · · · · · 13

Universality theorem for the Selberg zeta function

概 要 In 2013, Drungilas et al. proposed the universality theorem for the Selberg zeta function associatedwith the modular group, which is (probably) the first universality theorem for the zeta function of the orderof more than one. Recently in 2021, Mishou extended it by proving the joint universality theorem for thetuple of Selberg zeta functions associated with principal congruence subgroups. In this talk, we present
the universality theorem (and joint universality theorem) for the Selberg zeta function associated with (notnecessarily congruence) subgroup of the modular group. We also note that our universality theorems areavailable in wider regions than the regions given in the previous works.
46 篠 原健 ( 名 大 多 元 数 理)

Takeshi Shinohara (Nagoya Univ.)

On shuffle product of desingularized multiple zeta functions · · · · · · · · · 13
On shuffle product of desingularized multiple zeta functions

概 要 Furusho, Komori, Matsumoto, and Tsumura introduced the desingularized multiple zeta functions toresolve all singularities of multiple zeta functions (MZF for short). It is a natural question to ask how muchdesingularized MZFs retain the properties of MZFs. As one of the answers, we show that special values ofdesingularized MZFs at positive integer points satisfy the shuffle product that holds among special valuesof MZFs at positive integer points.

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代数学

47 加 藤 正 輝 (富 山 高 専)
Masaki Kato(Toyama Nat. Coll. of Tech.)22

ルート系のゼータ函数の q-類似について · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

On q-analogues of zeta functions of root systems

概 要 Komori, Matsumoto and Tsumura introduced zeta functions ζr (s, ∆) associated with root systems∆. In this talk, we introduce q-analogues of functions ζr (s, ∆), denoted by ζr (s, a, ∆; q). We establish
q-extensions of the following properties satisfied by ζr (s, ∆): (a) Integral representations of sums of zetafunctions which have Weyl group symmetries. (b) Explicit expressions of Witten volume formulas. (c)Functional relations including Witten volume formulas. We also introduce elliptic analogues of ζr (s, a, ∆; q),denoted by ζr (s, a, β, ∆; p, q), and investigate their basis properties. To extend the properties (a) and (b)to ζr (s, a, β, ∆; p, q), the factorization formulas of Poincaré polynomials, established by Macdonald, plays
important roles.
48 峰

正 博 ( 上 智 大 理 工)

Masahiro Mine (Sophia Univ.)

2 次無理数をパラメータに持つ Hurwitz ゼータ関数に対する弱い稠密性
定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Weak denseness theorem for the Hurwitz zeta-function with quadratic
irrational parameter

概 要 In this talk, we consider the value-distribution of the Hurwitz zeta-function with algebraic irrationalparameter. The main result is that any complex number can be approximated by values of the Hurwitz
zeta-function for arbitrary quadratic irrational parameters but with finite exceptions.
49 中 井 啓 太 (名 大 多 元 数 理)
Keita Nakai(Nagoya Univ.)

対数をとった Selberg クラスの L 関数の反復積分の普遍性定理 · · · · · · · · 10

Universality for the iterated integrals for the logarithm of L-functionsin the Selberg class

概 要 In 1975, Voronin proved the Universality theorem for the Riemann zeta-function and in 2022, Endo

generalized this theorem for the iterated integrals for the logarithm of the Riemann zeta-function. In thistalk, we give a more generalization of this theorem for the iterated integrals for the logarithm of L-functionsin the Selberg class.
50 杉 山 和 成 (千 葉 工 大)
Kazunari Sugiyama(Chiba Inst. of Tech.)Siegel ゼータ関数の保型性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
The modularity of Siegel’s zeta functions

概 要 Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic

properties such as analytic continuations and functional equations. We discuss the modularity of Siegel’s
zeta functions on the basis of converse theorems.
14:15〜16:45
51 武 田渉 ( 東 京 理 大 理)
中 筋 麻 貴 (上智大理工・東北大理)
山 﨑 義 徳 ( 愛 媛 大 理)

Wataru Takeda (Tokyo Univ. of Sci.)
Maki Nakasuji(Sophia Univ. / Tohoku Univ.)
Yoshinori Yamasaki (Ehime Univ.)

Quadratic relations for 9th variation Schur functions involving Plücker
relations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Quadratic relations for 9th variation Schur functions involving Plücker
relations

概 要 The 9th variation of Schur polynomial is known to satisfy determinant formulas such as Jacobi–Trudi,

Gambelli, and Hamel–Goulden identities. In this talk, we apply the Plücker relations to these identities.
These relations are known to give algebraic dependencies among the determinants of the various minorsof an arbitrary matrix. Applying them to the n × n minors of an n × 2n matrix, we give some quadratic
relations between the 9th variation of Schur polynomials.

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23

代数学

52 渋 川 元 樹 (神 戸 大 理)
後 藤 良 彰 ( 小 樽 商 大)

Genki Shibukawa (Kobe Univ.)
Yoshiaki Goto
(Otaru Univ. of Commerce)

Some monotonic properties of special values of the bivariate complete
homogeneous symmetric polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Some monotonic properties of special values of the bivariate complete
homogeneous symmetric polynomials

概 要 We prove some monotonic properties of special values of the bivariate complete homogeneous symmetricpolynomials.
53 星
明 考 ( 新 潟 大 理)
金 井 和 貴 ( 新 潟 大 自 然)大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Kazuki Kanai (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Hasse norm principle for M11 extensions · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Hasse norm principle for M11 extensions

概 要 Let k be a field and T be an algebraic k-torus. In 1969, over a global field k, Voskresenskii provedthat there exists an exact sequence 0 → A(T ) → H 1 (k, Pic X)∨ → Sha(T ) → 0 where A(T ) is the kernel of
the weak approximation of T , Sha(T ) is the Shafarevich–Tate group of T , X is a smooth k-compactificationof T , Pic X is the Picard group of X = X ×k k. On the other hand, in 1963, Ono proved that for the norm
(1)

one torus T = RK/k (Gm ) of K/k, Sha(T ) = 0 if and only if the Hasse norm principle holds for K/k. We(1)determine H 1 (k, Pic X) for norm one tori T = RK/k (Gm ) when the Galois group Gal(L/k) of the Galois
closure L/k of K/k is isomorphic to the Mathieu group M11 of degree 11. We also give a necessary andsufficient condition for the Hasse norm principle for such extensions K/k with Gal(L/k) ' M11 .
54 伊 吹 山 知 義 (阪大⋆)Tomoyoshi Ibukiyama (Osaka Univ.⋆)

符号付きパラモジュラー形式の次元公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Dimensions of paramodular forms with involutions

概 要 Paramodular forms are a part of Siegel modular forms. For degree two case, they are important for

Shimura–Taniyama conjecture for abelian surfaces and the new form theory of Roberts and Schmidt. Here
we give explicit dimension formulas for paramodular forms of any vector valued weight det3 Sym(j) withk ≥ 3 of prime level p with fixed sign of the Atkin–Lehner involution. It is known that such forms havea good correspondence with certain algebraic modular forms up to endoscopic part and old forms. We
calculate dimensions of the corresponding algebraic modular forms and apply it to paramodular case.
55 伊 吹 山 知 義 (阪大⋆)Tomoyoshi Ibukiyama (Osaka Univ.⋆)

ジーゲル保型形式上の微分作用素とラプラス変換 · · · · · · · · · · · · · · · · · · · 13

Differential operators on Siegel modular forms and Laplace transforms

概 要 The talk has two aims. One is to give a new special basis of the polynomial ring C[T ] in components

of n × n symmetric matrix T . The basis P (T ) is characterized by the action of P (∂Z ) on det(CZ + D)s ,where ∂Z is the matrix of partial derivatives of the variable of the Siegel upper half space and det(CZ + D) isthe automorphy factor. Everything is described explicitly. For example, the basis is obtained as coefficientsof certain explicitly described generating series. The second aim is to apply this to the so-called pullback
formula of the Siegel Eisenstein series of degree 2n and determine all appearing constants.

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代数学

56 境

優 一
(久留米工大基幹教育センター)

Yuichi Sakai (Kurume Inst. of Tech.)24

On modular-form solutions of a certain modular linear differential equations for cocompact groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
On modular-form solutions of a certain modular linear differential equations for cocompact groups

概 要 In this talk, we give a modular linear differential equation of second order for a cocompact groupof discriminant 6, and we also give its solutions. Furthermore we prove a relation between supersingularpolynomials and certain polynomials derived from solutions of the modular linear differential equation.
57 杉 山 真 吾 (日 大 理 工)
佐 久 川 憲 児 ( 信 州 大 教 育)

Shingo Sugiyama (Nihon Univ.)
Kenji Sakugawa (Shinshu Univ.)

Hilbert 保型形式と Siegel 保型形式の Hecke 固有値の代数的整数性 · · · · 10
Integrality of Hecke eigenvalues of Hilbert and Siegel modular forms

概 要 In this talk, we prove the integrality of Hecke eigenvalues of Hilbert modular forms and Siegel modular

forms in a general setting. As applications, we estimate the degrees of Hecke fields of cuspidal automorphic
representations of GL(2d) with a prime number d and Sp(2n).
58 加 藤 裕 基 (宇 部 工 高 専)

Yuki Kato (Ube Nat. Coll. of Tech.)Almost mathematics and its algebraic K-theory from non-unital algebras viewpoint · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Almost mathematics and its algebraic K-theory from non-unital algebras viewpoint

概 要 While almost mathematics has various applications to arithmetic geometry, Quillen mentioned linear

algebra over non-unital rings which is the same as almost mathematics introduced by Faltings; and Gabberand Ramero. Quillen’s work is more conceptional in the sense of using categorical language: in his work,
almost mathematics is characterized as bilocalization of an abelian category of modules. By using thetheory of bilocalization, we define the derived category (or stable ∞-category) of almost perfect complexes,
enabling us to obtain the K-theory of almost modules. Furthermore, by modifying K-theory of almost
algebra, we prove that the modified K-groups decompose into the almost algebraic K-theory and the almost
acyclic part of them. The main result of almost K-theory is that the almost K-theory of A is represented
by the modified K-theory of the corresponding the idempotent non-unital algebra.
59 南

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

任意のモチビック一般コホモロジー論に対する SBNR ((stably birationalized) unramified sheaf) と Gersten 型分解 · · · · · · · · · · · · · · · · · · · · · · · · · 13

SBNR (stably birationalized unramified sheaf) and Gersten type resolution for any motivic generalized cohomology theory

概 要 Suppose the base field is perfect. Then, for any generalized motivic cohomology theory, I shall discuss

its Zariski sheafifcation which turns out to be unramified in Morel’s sense and a Nisnevich sheaf in thisparticular case.
Amongst of all, I shall emphasize the existence of its Gersten type resolution as Zariski sheaves and its
SBNR - stably birationalized Nisnevich subsheaf of the unramified sheaf.
60 南

範 彦 (名工大) ♭ Integral Hodge 予想反例の高次余次元非有理性 · · · · · · · · · · · · · · · · · · · · · 13

Norihiko Minami(Nagoya Inst. of Tech.)Higher codimensional irrationality of counter examples of the integral
Hodge conjecture

概 要 Some necessary condition for a non-singular complex projective manifold X to be a counter-example

for the codimension k integral Hodge conjecture Z 2k (X) 6= 0 is given.
Our necessary condition is stated as codimension ck irrationality for some ck , which grows as k increases.
This may suggest that counter-examples to the integral Hodge conjecture become ubiquitous as k increases.

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25

幾何学

幾

何

3 月 15 日（水）学
第 II 会場

9:30〜11:40
1 キヨヴスキアントニ(沖縄科学技術大)Antoni Kijowski(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Asymptotically mean value harmonic functions · · · · · · · · · · · · · · · · · · · · 15
Asymptotically mean value harmonic functions

概 要 The Blaschke–Privaloff–Zaremba theorem gives rise to a recently investigated concept of the asymptotic

mean value harmonic function on a metric measure space X. For a function u ∈ L1loc (X) define the rlaplacian of u as:
uBr (x) − u(x)∆r u(x) :=,r2
where uBr (x) stands for the mean-value of u over a ball Br (x). We say that u is amv-harmonic if its
r-laplacian converges to 0 in an appropriate sense as r → 0. In my talk I will present known results focusing
on regularity, blow ups and characterization of these functions in the following settings: weighted Euclidean
domains, Carnot groups and RCD spaces.
2 横 田 滋 亮 ( 東 北 大 理)

Shigeaki Yokota (Tohoku Univ.)

Geometric data set の幾何学 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Geometry of geometric data set

概 要 Gromov originated a geometric theory of metric measure spaces based on the phenomenon of con-centration of measure and the theory of the collapsing of Riemannian manifolds; Pestov pointed out theconnection of Gromov’s theory with the curse of dimensionality in statistics. To improve time complexity,
Hanika, Schneider, Stumme proposed to generalize metric measure space to ‘geometric data set’. The
total set of the metric measure spaces has two natural distance functions, the observable and box distancefunctions, and their topological properties are well known, but the properties of the total set of the geometricdata set are almost unknown. In this talk, we extend these results of metric measure space to the total setof geometric data sets.
3 数 川 大 輔 ( 九 大 数 理)
中 島 啓 貴 (東 北 大 I E H E )塩 谷
隆 ( 東 北 大 理)

Daisuke Kazukawa (Kyushu Univ.)
Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)

測度距離空間全体の位相的性質について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Topological aspects of the space of metric measure spaces

概 要 Gromov introduced two distance functions, the box distance and the observable distance, on the spaceof isomorphism classes of metric measure spaces and developed the convergence theory of metric measurespaces. We investigate several topological properties on the space equipped with these distance functions
toward a deep understanding of convergence theory.

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幾何学

4 数 川 大 輔 ( 九 大 数 理)
中 島 啓 貴 (東 北 大 I E H E )塩 谷
隆 ( 東 北 大 理)

Daisuke Kazukawa (Kyushu Univ.)
Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)26

測度距離空間全体のスケーリング作用に関する主束構造について · · · · · · 10

Principal bundle structure of the space of metric measure spaces

概 要 We study the topological structure of the space X of isomorphism classes of metric measure spaces

equipped with the box or concentration topologies. We consider the scale-change action of the multiplicative
group R+ of positive real numbers on X , which has a one-point metric measure space, say ∗, as only one fixed
point. We prove that the R+ -action on X \{∗} admits the structure of nontrivial and locally trivial principal
R+ -bundle over the quotient space. A similar statement is obtained for the pyramidal compactification of X ,where we completely determine the structure of the fixed-point set of the R+ -action on the compactification.
5 松 家 拓 稔 ( 都 立 大 理)

Takumi Matsuka (Tokyo Metro. Univ.)

距離空間の自由積と粗バウム・コンヌ予想 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Free products of metric spaces and the coarse Baum–Connes conjecture

概 要 We introduce the notion of free products of metric spaces. When X and Y are coarsely convex, thefree product X ∗ Y is coarsely convex. In particular, the free product X ∗ Y satisfies the coarse Baum–
Connes conjecture. This talk is based on a ongoing joint work with Tomohiro Fukaya (Tokyo Metropolitan
University).
6 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

グロモフ・ハウスドルフ空間の中の連結空間 · · · · · · · · · · · · · · · · · · · · · · · 15

Continua in the Gromov–Hausdorff space

概 要 We first prove that for all compact metrizable spaces, there exists a topological embedding of thecompact metrizable space into each of the sets of compact metric spaces which are connected, path-connected,
geodesic, or CAT(0), in the Gromov–Hausdorff space with finite prescribed values. As its application, weshow that the sets prescribed above are path-connected and their non-empty open subsets have infinite
topological dimension. By the same method, we also prove that the set of all proper CAT(0) spaces ispath-connected and its non-empty open subsets have infinite topological dimension with respect to thepointed Gromov–Hausdorff distance.
7 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

グロモフ・ハウスドルフ空間の中の木 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Metric trees in the Gromov–Hausdorff space

概 要 Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topologicalembedding of the compact metrizable space into the set of all metric trees in the Gromov–Hausdorff spacewith finite prescribed values. As its application, we show that the set of all metric trees is path-connected
and its all non-empty open subsets have infinite topological dimension.
14:15〜16:00
8 米 村 拳 太 郎 ( 九 大 数 理)

Kentaro Yonemura (Kyushu Univ.)

多様体構造を持つカンドルの Lie 群への埋め込み · · · · · · · · · · · · · · · · · · · 10

Embedding smooth quandles in Lie groups

概 要 We deal with embedding smooth quandles in Lie groups in this talk.

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27

幾何学

9 佐 々 木 優 ( 東 京 工 高 専)

Yuuki Sasaki (Tokyo Nat. Coll. of Tech.)

結合的グラスマン多様体の部分多様体 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Some submanifolds of the associative Grassmann manifold

概 要 We construct a totally complex immersion from almost complex submanifolds of the 6-dimensional

sphere into the associative Grassmann manifold. Also, as an analogy of almost complex immersions weconstruct a CR immersion from 3-dimensional CR submanifolds of the 6-dimensional sphere into theassociative Grassmann manifold. Moreover, in the associative Grassmann manifold we show that many
orbits of the action of the isotropy subgroup of the isometry group are the image of some CR immersions.
10 木 村 太 郎 (鶴 岡 工 高 専)
間 下 克 哉 ( 法 政 大 理 工)
Taro Kimura(Nat. Inst. of Tech., Tsuruoka Coll.)
Katsuya Mashimo (Hosei Univ.)

Biharmonic Cartan embeddings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Biharmonic Cartan embeddings

概 要 In this talk, we determine all the proper biharmonic submanifolds in compact Lie groups which are

the image of Cartan embeddings defined by automorphism of order 4. Moreover we show that if the Cartan
embedding defined by automorphism of order 3 is biharmonic, then it is harmonic.
11 井 川治 (京都工繊大工芸)
間 下 克 哉 ( 法 政 大 理 工)

Osamu Ikawa (Kyoto Inst. Tech.)
Katsuya Mashimo (Hosei Univ.)Spin(8) の triality automorphism から誘導される σ 作用の軌道の幾何学· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The geometry of orbits of σ-action induced by triality automorphism ofSpin(8)

概 要 The universal covering group Spin(8) of the special orthogonal group SO(8) has an outer automorphism

σ of order 3 called the triality automorphism. From this σ, the action of Spin(8) on Spin(8) itself, called
the σ-action, is determined. This action is a hyperpolar action of cohomogeneity (= codimension of
maximum-dimensional orbit) 2. We report on the orbit space and properties of orbits of this action.
12 塚 田 和 美 (お茶の水女大⋆)Kazumi Tsukada (Ochanomizu Univ.

⋆)

Lie 球面幾何学の複素化と実グラスマン多様体の全複素部分多様体 · · · · 15
The complexification of Lie sphere geometry and totally complex submanifolds of the real Grassmann manifold

概 要 The real Grassmann manifold Gr4 (Rn ) of all 4-dimensional subspaces in Rn is known to have thequaternionic Kähler structure. We consider the set H2 (C n ) of all 2-dimensional complex subspaces in C nthat are isotropic with respect to the standard complex inner product. H2 (C n ) is a complex manifoldof dimension 2n − 7 and has the holomorphic contact structure. The natural projection of H2 (C n ) onto
Gr4 (Rn ) is a twistor fibration. Through H2 (C n ), we show the relation between the geometry regarded as
the complexification of Lie sphere geometry and that of totally complex submanifolds of Gr4 (Rn ).
13 坂 根 由 昌 (阪大⋆)Yusuke Sakane (Osaka Univ.⋆)

コンパクト等質空間上のアインシュタイン計量の存在・非存在について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence and non-existence of Einstein metrics on compact homogeneous manifolds

概 要 The study of existence and non-existence of Einstein metrics on G/H is started by Wang and Ziller

in 1986. More general results for non-existence are obtained by Böhm in 2005. One of his results is that
G/H = SU (n + k1 + · · · + kp )/S(SO(n)U (1) × U (k1 ) × · · · × U (kp )) (where SO(n)U (1) ⊂ U (n)) does not
admit G-invariant Einstein metrics, if n > (k1 + · · · + kp )2 + 2. He has obtained the results by considering“traceless” part of Ricci tensor. For G/H = SO(2n + k1 + · · · + kp )/SO(n)U (1) × SO(k1 ) × · · · × SO(kp )(where SO(n)U (1) ⊂ U (n) ⊂ SO(2n)), we can not apply his method directly. In this talk, we will show
that, if n ≥ 5(k1 + · · · + kp ) (ki ≥ 3), G/H does not admit G-invariant Einstein metrics. We also discuss
existence of Einstein metrics for compact homogeneous manifolds G/H above.

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幾何学

特別講演
多 羅 間 大 輔 ( 立 命 館 大 理 工)

半単純 Lie 群上の可積分測地流について

Daisuke Tarama (Ritsumeikan Univ.)

On integrable geodesic flows over a semi-simple Lie group28

16:15〜17:15

概 要 This talk deals with the geodesic flow of a semi-simple Lie group equipped with a left-invariant metric.

After a short review over the geometric settings for general left-invariant Hamiltonian systems on the
cotangent bundle to a Lie group, a class of left-invariant metrics is considered on a semi-simple Lie group,
following Mishchenko and Fomenko. These metrics have been known to give rise to completely integrable
geodesic flows since late 1970’s. It is however rather recent that their equilibrium points are studied mostly
on the basis of techniques in symplectic/Poisson geometry. In the talk, these developments are briefly
reviewed. Then, as a main result, the classification of Williamson types of relative equilibrium points for alarge subclass of above integrable geodesic flows is explained in terms of root systems. Related studies andremaining problems are also mentioned.

3 月 16 日（木）第 II 会場

9:30〜12:00
14 川 村 昌 也 (香 川 高 専)
Masaya Kawamura(Kagawa Nat. Coll. of Tech.)

コンパクト概 Hermitian 多様体上の k-th Gauduchon 計量について · · · · 15

On a k-th Gauduchon metric on compact almost Hermitian manifolds

概 要 In this talk, we introduce some results about k-th Gauduchon metrics on compact almost Hermitian

manifolds. We have shown that if both the conformally k-th Gauduchon condition and the conformallysemi-Kähler condition are satisfied, then it becomes conformally quasi-Kähler. Also, we characterize thek-th Gauduchon condition and by applying its characterization, we have shown some geometric conditions
for negative Kodaira dimension on compact almost Hermitian manifolds.
15 宮 武 夏 雄 (九 大 I M I)大理)
糟 谷 久 矢 (阪Natsuo Miyatake (Kyushu Univ.)
Hisashi Kasuya (Osaka Univ.)

Uniformization of compact Sasakian manifolds using basic Higgs bundles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Uniformization of compact Sasakian manifolds using basic Higgs bundles

概 要 Simpson introduced the notion of uniformizing variation of Hodge structure (VHS) and showed thatthe universal covering of a compact Kähler manifold is isomorphic to a bounded symmetric domain if andonly if there exists a uniformizing VHS on the Kähler manifold. In this talk, on compact Sasakian manifolds,
we consider an analogy of this. We can formulate an analogy of the uniformizing VHS also on compact
Sasakian manifolds. However, even if there exists a uniformizing VHS on a compact Sasakian manifold, theconstructed map collapses all the points on each leaf of the foliation of the universal covering into one pointand can never be an isomorphism. I will explain how to properly take the lift of this map and construct anisomorphism from the universal covering to a homogeneous space.

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29

幾何学

16 宮 武 夏 雄 (九 大 I M I)

Natsuo Miyatake (Kyushu Univ.)

正則ではない Higgs 場を持つ Higgs 束の Donaldson 汎関数の対角形の計量全体への制限 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Restriction of Donaldson’s functional to diagonal metrics on Higgs bundles with not-holomorphic Higgs filelds

概 要 A Higgs bundle over a compact Kähler manifold X is the pair (E, θ) consisting of a holomorphic

vector bundle E → X and a holomorphic section θ of EndE ⊗V1,0satisfying θ ∧ θ = 0. The holomorphic

section θ is called a Higgs field. Usually, Higgs fields are assumed to be holomorphic. However, in this talk,I will consider Higgs bundles with not holomorphic Higgs fields. I will suppose that the holomorphic vector
bundle E decomposes into a direct sum of holomorphic line bundles, and I will give some necessary andsufficient conditions for Donaldson’s functional to attain a minimum over diagonal metrics concerning thedecomposition. I will also slightly extend the theorem for not-holomorphic splittings of the vector bundle.
17 宮 武 夏 雄 (九 大 I M I)

Natsuo Miyatake (Kyushu Univ.)

巡回 Higgs 束の Hermitian–Einstein 方程式の拡張とその放物型方程式とDirichlet 問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Some generalizations of the Hermitian–Einstein equation of cyclic Higgs
bundles and their parabolic equations and the Dirichlet problem

概 要 In this talk, I will introduce some generalizations of the Hermitian–Einstein equation of cyclic Higgs

bundles on Riemann surfaces. For such generalized equations, I will show the existence and the uniquenessof the time-global solution of the parabolic equations and I will also show the existence and the uniquenessof the solution to the Dirichlet problem.
18 松 坂 公 暉 (北大教育推進機構)
秦 泉 寺 雅 夫 ( 岡 山 大 自 然)

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

Recursion relation on moduli space of quasimaps in the case of Calabi–
Yau hypersurface in CP N −1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Recursion relation on moduli space of quasimaps in the case of Calabi–
Yau hypersurface in CP N −1

概 要 In computing of B-model in classical mirror symmetry, Picard–Fuchs equation is very important. In

the case of Calabi–Yau hypersurface in CP N −1 , its solutions are used in a mirror map, and it is known that a
gp0,2 (N, d) of quasimaps fromgenerating function of intersection numbers w(OhN −3 Oh0 )0,d of moduli space M
CP 1 with 2 marked points to CP N −1 coincides with the mirror map. In our previous work, we proved thatthe solutions are written by using a term d · w(σj (OhN −2−j )Oh−1 )0,d + w(σj−1 (OhN −1−j )Oh−1 )0,d , where σjcorresponds to the Mumford–Morita–Miller class. In this talk, we see that the above term can be obtained
gp0,2|1 (N, d) of quasimaps from CP 1 with 2 + 1 marked points
from a recursion relation on moduli space M
to CP N −1 .
19 小 林 和 志 (阪大理)Kazushi Kobayashi (Osaka Univ.)

ある gerbe による複素トーラスの変形とホモロジー的ミラー対称性 · · · · 15

A gerby deformation of complex tori and the homological mirror symmetry

概 要 Let (X, X̌) be a mirror pair of a complex torus X and its mirror partner X̌. This mirror pair is

described as the trivial special Lagrangian torus fibrations X → B and X̌ → B on the same base space B
by SYZ construction. Then, we can associate a holomorphic line bundle E(s, L) → X to a pair (s, L) of a
Lagrangian section s of X̌ → B and a unitary local system L along it. In this talk, we first construct the
deformation XG of X by a certain flat gerbe G and its mirror partner X̌G from the mirror pair (X, X̌), anddiscuss deformations of objects E(s, L) and (s, L) over the deformed mirror pair (XG , X̌G ).

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幾何学

20 中 西 隼 斗 (千葉大融合理工)

Hayato Nakanishi (Chiba Univ.)30

モースホモトピーを用いたトーリックファノ曲面のホモロジー的ミラー
対称性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Homological mirror symmetry of toric Fano surfaces via Morse homotopy

概 要 Strominger–Yau–Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations.

We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homologicalmirror symmetry, where we consider Morse homotopy of the moment polytope instead of the Fukaya
category.
21 山 本 悠 登 (Yuto Yamamoto

IBS-CGP)(IBS-CGP)

超曲面の周期積分とトロピカル幾何学 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Period integrals of hypersurfaces via tropical geometry

概 要 Let {Zt }t be a one-parameter family of complex toric hypersurfaces of dimension d ≥ 1. We computeasymptotics of period integrals for {Zt }t by applying the method of Abouzaid–Ganatra–Iritani–Sheridan,
which uses tropical geometry. As integrands, we consider Poincaré residues of meromorphic (d + 1)-forms on
the ambient toric variety, which have poles along the hypersurface Zt . The cycles over which we integratethem are spheres and tori which correspond to tropical (0, d)-cycles and (d, 0)-cycles on the tropicalizationof {Zt }t respectively.
13:00〜14:00

特別講演

橋 本 義 規 (阪 公 大 理) ♭ 因子に沿って錐的特異点をもつ 定スカラー曲率 Kähler 計量についての最近の進展
Yoshinori Hashimoto
Recent developments on constant scalar curvature Kähler metrics with
(Osaka Metro. Univ.) cone singularities along a divisor
概 要 We present some recent results concerning constant scalar curvature Kähler metrics with cone singu-

larities along a divisor, henceforth abbreviated as cscK cone metrics. One of the main results is that theexistence of cscK cone metrics implies various stability conditions of the underlying pair of the manifold andthe divisor, including G-uniform K-stability and K-polystability. We also prove that any Kähler manifold
admits a cscK cone metric if the divisor is a generic member of the linear system defined by a sufficiently
large multiple of the polarisation, and point out an analogy to the twisted constant scalar curvature Kähler
metrics. This talk is based on a joint work with Takahiro Aoi and Kai Zheng.

3 月 17 日（金）第 II 会場

9:30〜11:40
22 泉

宏 明 (広島

大)Hiroaki Izumi (Hiroshima Univ.)

ゲーム理論の意義と概日リズムの定式化 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Significance of game theory and formulization of in-phase and anti-phasecircadian rhythms

概 要 In this paper, we explain the significance of game theory, which frees a system of differential equations

from the spell of integrability conditions. Also using it, we present the system of equations of in-phaseand anti-phase circadian rhythms from the viewpoint of variational principle. In addition, the generalformulization of the mathematical structure of phase transition and synchronization is carried out.

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31

幾何学

23 軸 丸 芳 揮 (九 大 I M I)大工)
早 川 健 太 郎 (京
(
大
工)
林
和 希 京
梶 原 健 司 (九 大 I M I )横 須 賀 洋 平 ( 鹿 児 島 大 理 工)

Yoshiki Jikumaru (Kyushu Univ.)
Kentaro Hayakawa (Kyoto Univ.)
Kazuki Hayashi (Kyoto Univ.)
Kenji Kajiwara (Kyushu Univ.)
Yohei Yokosuka (Kagoshima Univ.)

可積分幾何に基づく Michell トラス型構造と離散対数型美的曲線 · · · · · · 15

On the Michell truss-like structure and discrete log-aesthetic curves
based on integrable geometry

概 要 The truss structure minimizing the product of axial forces and lengths for a given load and a

support condition is called Michell truss, which is classically known in the field of structural mechanics.
In this presentation, we have an analytical construction of Michell truss-like structure described by adiscrete holomorphic function (discrete conformal map) in the context of discrete integrable systems.
The validity of the structure is demonstrated by the result of structural analysis. Moreover, we show
the truss structure is composed of so-called discrete log-aesthetic curves. This structure connects threeobjects (discrete holomorphic functions, discrete log-aesthetic curves, and classical truss structures) having
completely different origins which were achieved through the collaboration of mathematics and architecture.
24 陶 山 芳 彦 (福 岡 大 理)
松 浦
望 ( 久 留 米 工 大 工)

Yoshihiko Suyama (Fukuoka Univ.)
Nozomu Matsuura(Kurume Inst. of Tech.)

Generic で共形平坦な超曲面内の曲率曲面の拡張と近似 · · · · · · · · · · · · · · 15
Extension and approximation of curvature surfaces in generic conformally flat hypersurfaces

概 要 We talk about curvature surfaces of generic conformally flat analytic-hypersurfaces in the Euclidean

4-space.
25 石 渡聡 ( 山 形 大 理)
河 備 浩 司 ( 慶 大 経 済)

Satoshi Ishiwata (Yamagata Univ.)
Hiroshi Kawabi (Keio Univ.)

リーマン多様体上の非対称拡散過程の離散近似 · · · · · · · · · · · · · · · · · · · · · 10

A discretization of a non-symmetric diffusion on a Riemannian manifold

概 要 In this talk, we give a graph discretized approximation of the diffusion for a Schrödinger operator withdrift on a complete Riemannian manifold.
26 張頁 (沖縄科学技術大)

Ye Zhang(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Gradient estimates for the heat semigroup on step-two Carnot groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Gradient estimates for the heat semigroup on step-two Carnot groups

概 要 It is well-known that we can characterize the lower bound of the Ricci curvature by the bound for thegradient of the heat semigroup. However, on a nonabelian nilpotent Lie group endowed with a left-invariant
Riemannian metric, there exists a direction of strictly negative Ricci curvature. This implies the gradientbound has exponential growth. In this talk, I will present how to improve the gradient bound to theconstant in the setting of step-two Carnot groups on which the H.-Q. Li inequality holds.

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幾何学

27 武 富 雄 一 郎 (阪 公 大 理)
Yuichiro Taketomi(Osaka Metro. Univ.)

32

リーマン計量の moduli 空間の極大元について · · · · · · · · · · · · · · · · · · · · · · 15

A maximal element of a moduli space of Riemannian metrics

概 要 For a given smooth manifold X, we consider the moduli space of Riemannian metrics on X up toisometry and scaling. One can define a preorder on the moduli space by the size of isometry groups. We
call a Riemannian metric that attains a maximal element with respect to the preorder a maximal metric.
Maximal metrics give nice examples of self-similar solutions for various metric evolution equations such as
the Ricci flow. In this talk, we construct many examples of maximal metrics on Euclidean spaces.
28 松 本 佳 彦 (阪大理)

Yoshihiko Matsumoto (Osaka Univ.)

写像の繰り込みエネルギーと共形測地線 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Renormalized energy of maps and conformal geodesics

概 要 We introduce a certain renormalized energy of maps between asymptotically hyperbolic Einsteinmanifolds. Then, it is used to give a holographic description of conformal geodesics on the boundary at
infinity, in a way deeply inspired by a work of Fine and Herfray on renormalized area minimization andconformal geodesics.
14:15〜14:55
29 雪 田 友 成 (早 大 教 育)

Tomoshige Yukita (Waseda Univ.)

On nerves and growth rates of 2-dimensional Coxeter systems · · · · · · · 15
On nerves and growth rates of 2-dimensional Coxeter systems

概 要 For a Coxeter system (Γ, S), the nerve L(Γ, S) is a simplicial complex defined via the structure offinite parabolic subgroups of Γ. The dimension of (Γ, S) is defined by dim L(Γ, S) + 1. In this talk, we
consider the relationship between the combinatorial structure of L(Γ, S) and the arithmetic properties of
the growth rate of (Γ, S). We show that the growth rate of a 2-dimensional Coxeter system (Γ, S) withvanishing (resp. positive) Euler characteristic χ(L(Γ, S)) is a Salem (resp. Pisot) number. This is a joint
work with Naomi Bredon.
30 牛 島顕 (兵庫県立大国際商経)

Akira Ushijima (Univ. of Hyogo)

ケーリー・クライン幾何学としての双曲平面でのチェバの定理とメネラ
ウスの定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ceva’s and Menelaus’ theorems in the hyperbolic plane as Cayley–Klein
geometry

概 要 Using the construction of the hyperbolic plane as Cayley–Klein geometry, we will demonstrate how

to obtain Ceva’s and Menelaus’ theorems in the hyperbolic plane from their corresponding theorems in thereal projective plane.
15:10〜16:10

特別講演

H. Seshadri(Indian Inst. of Sci., Bangalore)

正の双正則断面曲率を持つケーラー多様体の直径についてHarish Seshadri(Indian Inst. of Sci., Bangalore)

On the diameter of Kähler manifolds with positive bisectional curvature

概 要 I will discuss the Kähler analogues of the classical Bishop volume inequality and Myers–Bonnet

diameter bound for Riemannian manifolds. In particular, I will outline the proof of diameter rigidity(an analogue of Cheng’s theorem in the Riemannian case) for compact Kähler n-manifolds (M, ω) withbisectional curvature BK ≥ 1. It is known from the work of Li–Wang that diam (M ) ≤ diam (CP n ) forsuch manifolds, where CP n is endowed the Fubini–Study metric. In joint work with V. Datar, we provedthat if diam (M ) = diam (CP n ), then M is isometric to CP n .

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33

函数論

函

数

3 月 15 日（水）論第 V 会場

9:30〜11:45
1 齋 藤 三 郎 (群馬大⋆・再生核研)
Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Complex analysis and theory of reproducing kernels · · · · · · · · · · · · · · · · 10
Complex analysis and theory of reproducing kernels

概 要 The theory of reproducing kernels is very fundamental, beautiful and will have many applicationsin analysis, numerical analysis and data sciences. Based on a draft paper, I would like to give a global
viewpoint for the relation of complex analysis and the theory of reproducing kernels. I listed the basic
references on the topics.
2 齋 藤 三 郎 (群馬大⋆・再生核研)
Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Complex analysis and division by zero calculus · · · · · · · · · · · · · · · · · · · · 15
Complex analysis and division by zero calculus

概 要 Based on a draft book manuscript, I would like to introduce the basic and essential relations ofcomplex analysis and division by zero calculus. Basic references are cited in the references.
3 綾 野 孝 則 ( 阪 公 大 数 学 研)
V. M. Buchstaber(Steklov Inst. of Math.)

Takanori Ayano (Osaka Metro. Univ.)
Victor M. Buchstaber(Steklov Inst. of Math.)

種数 3 の超楕円関数と楕円関数の間の関係式 · · · · · · · · · · · · · · · · · · · · · · · 15

A relationship between hyperelliptic functions of genus 3 and elliptic
functions

概 要 In the nineteenth century, the reductions of hyperelliptic integrals to elliptic integrals were studied

actively and many examples of the reductions were obtained. They are closely related to coverings ofcurves, split Jacobians, and automorphism groups of curves. This knowledge is applied to the isogeny-based
cryptography. In our previous work, by using this knowledge, we derived the relationships between thehyperelliptic functions of genus 2 and the elliptic functions when the curve of genus 2 admits a morphism ofdegree 2 to an elliptic curve. In this talk, we will derive a relationship between the hyperelliptic functionsof genus 3 and the elliptic functions when the hyperelliptic curve of genus 3 admits a morphism of degree 2
to an elliptic curve.
4 杉 山 真 吾 ( 日 大 理 工)

Shingo Sugiyama (Nihon Univ.)

同変関数の存在と Schwarz 微分 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The existence of equivariant functions and the Schwarzian derivative

概 要 Equivariant functions associated to a 2-dimensional representation of a Fuchsian group was introducedby Saber and Sebbar. They are regarded as a generalization of automorphic functions. We prove theexistence of equivariant functions associated to any generic 2-dimensional representation of any Fuchsiangroup. We prove such existence by using the Schwarzian derivative.

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函数論

5 山 岸 義 和 (龍谷大先端理工)上 薗 拓 郎(マースネットワークス)
須 志 田 隆 道 (サレジオ工高専)

Yoshikazu Yamagishi (Ryukoku Univ.)
Takuro Uezono (Mars Networks Corp.)
Takamichi Sushida (Salesian Polytech.)34

回転対称性を加えた対数螺旋格子上の円充填とボロノイ分割 · · · · · · · · · · 10

Voronoi tiling and circle packing on spiral lattices with rotational symmetry

概 要 It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational

symmetry is graph-theoretically dual to the bifurcation diagram of Voronoi tessellations, by using the relative
metric. If the rotation parameter (called divergence angle) is badly approximable, then the aspect ratioof the quadrilateral Voronoi cells is bounded. If the divergence angle is linearly equivalent to the golden
section, then the shape of the quadrilateral cells tend to square as the plastochron ratio tends to 1.
6 熊 谷

駿 ( 東 北 大 情 報)

Shun Kumagai (Tohoku Univ.)

折り紙のボロノイ分解について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Voronoi decomposition of origamis

概 要 The Edwards–Sanderson–Schmidt method uses the Voronoi decomposition to present an excellent

criterion for the equivalence class and the Veech group of a finite translation surface. The key argument of
their method includes a complicated combinatorial structure. An origami is a typical example of a translation
surface defined combinatorially. This talk discusses the Voronoi decomposition of a half-translation versionof origami.
7 馬 場 伸 平 (阪Shinpei Baba

大理)

(Osaka Univ.)

Bending maps of Teichmüller spaces and character varieties · · · · · · · · · 15
Bending maps of Teichmüller spaces and character varieties

概 要 The space holomorphic quadratic differentials on a compact Riemann surface is a complex vector

space. By the holonomy map of complex projective structures, this vector space properly embeds into thePSL(2, C)-character variety of the base surface. We construct certain analogues of such an embedding fromthe viewpoint of Thurston’s parametrization of complex projective structures.
8 小 森 洋 平 ( 早 大 教 育)
Yohei Komori (Waseda Univ.)

Applications of canonical polygons of Zieschang–Vogt–Coldewey · · · · · 15
Applications of canonical polygons of Zieschang–Vogt–Coldewey

概 要 As applications of canonical polygons of Zieschang–Vogt–Coldewey, we will show that (1) 6g-6 angles

between geodesics on Riemann surfaces of genus g globally parametrize Teichmuller space of genus gsurfaces. (2) Mapping classes of genus 2 surface can be represented by the cut and paste argument ofcanonical polygons.
9 木 坂 正 史 ( 京 大 人 間 環 境)
Masashi Kisaka (Kyoto Univ.)

Polynomial-like mappings and transcendental entire functions with irrationally indifferent fixed points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Polynomial-like mappings and transcendental entire functions with irrationally indifferent fixed points

概 要 In this talk, by using the theory of polynomial-like mappings, we construct various kinds of transcen-

dental entire functions with irrationally indifferent fixed points. This talk is based on the joint work withHiroto Naba.

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35

函数論

14:15〜15:15

特別講演
中 西 敏 浩 (島根大総合理工)

おもに種数 2 のタイヒミュラー空間とクライン群について

Toshihiro Nakanishi (Shimane Univ.)

Teichmüller space of the genus two surface and Kleinian groups

概 要 In this talk the Teichmüller space is a deformation space of marked Fuchsian groups of finite type, inmost cases, genus two Fuchsian groups. We deal with (1) trace functions as parameters for a Teichmüller
space, (2) matrix representation of the genus two surface group, (3) mapping classes represented by rationaltransformations. These materials are used to produce some examples of Kleinian groups related to surface
groups.
15:30〜16:30

2022 年度 (第 21 回) 日本数学会解析学賞受賞特別講演
松 崎 克 彦 (早 大 教 育) 絶対連続タイヒミュラー空間の曲線と関数空間

Katsuhiko Matsuzaki (Waseda Univ.)

Curves and function spaces of absolutely continuous Teichmüller spaces

概 要 The universal Teichmüller space is the total space containing all quasiconformal Teichmüller spaces

and it can be regarded as the space of normalized quasisymmetric functions f on the real line. According to
the regularity of these functions f , there are two different directions of subspaces included in the universal
Teichmüller space: Teichmüller spaces of Riemann surfaces are typically in the direction of totally singular
f , and Teichmüller spaces of function spaces are absolutely continuous f .
Teichmüller spaces can be represented by quasisymmetric homeomorphisms mentioned above, and in otherways, they can be represented by the complex dilatations of quasiconformal mappings, the Schwarzian or
pre-Schwarzian derivatives of conformal mappings, and the quasicircles given as the images of the circle.
Fundamental studies of particular Teichmüller spaces are composed by the investigation of the relationshipbetween these different representations and structures. In addition, if we deal with absolutely continuous
Teichmüller spaces, the derivative f ′ or log f ′ defines the corresponding function spaces, and by using them,
we can introduce simpler structures to these Teichmüller spaces.
In this talk, we exhibit several important examples of absolutely continuous Teichmüller spaces and explain
how the identification of different representations works. The examples include Weil–Petersson Teichmüller
spaces, BMO Teichmüller spaces and the space of chord-arc curves between them. One technical tool is thesimultaneous uniformization imported from the theory of quasifuchsian spaces. We represent the space ofparticular quasicircles by the product of the corresponding Teichmüller spaces and consider biholomorphic
correspondence between this parameter space and the complex function space. Furthermore, we apply
this method to see (dis)continuous dependence of the Riemann mapping parametrizations of the family of
Weil–Petersson curves and chord-arc curves to their arc-length parametrizations.

3 月 16 日（木）第 V 会場

9:30〜11:45
10 上 野 康 平 (大Kohei Ueno

同大)(Daido Univ.)

Dynamics of superattracting skew products · · · · · · · · · · · · · · · · · · · · · · · 15
Dynamics of superattracting skew products

概 要 We consider the dynamics of a holomorphic skew product with a superattracting fixed point. We

proved that it is generally conjugate to a monomial map on an invariant wedge whose closure contains
the fixed point. In this talk we provide several kinds of plurisubharmonic functions on the complement ofspecific fibers in the attracting basin, which describe the vertical dynamics well.

最終版: 2023/2/17
函数論

11 Shaolin Chen
(Hengyang Normal Univ.)
濱 田 英 隆 ( 九 州 産 大 理 工)
Jian-Feng Zhu ( Huaqiao Univ. )Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Jian-Feng Zhu (Huaqiao Univ.)

36

Lipschitz constant of harmonic Bloch functions and composition operators on Bloch and Hardy type spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Lipschitz constant of harmonic Bloch functions and composition operators on Bloch and Hardy type spaces

概 要 The main purpose of this talk is to discuss Hardy type spaces, Bloch type spaces and the composition

operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz
continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudo-hyperbolic
metric, which gives an answer to an open problem. Then some classes of composition operators on Blochand Hardy type spaces will be investigated. The obtained results improve and extend some corresponding
known results.
12 濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
G. Kohr(Babeş-Bolyai Univ)
M. Kohr
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)
Mirela Kohr (Babeş-Bolyai Univ)

Fekete–Szegö problem for univalent mappings in one and higher dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Fekete–Szegö problem for univalent mappings in one and higher dimensions

概 要 In this talk, we will give the Fekete–Szegö inequality for the mappings f in various subclasses ofnormalized univalent mappings which are the first elements of g-Loewner chains on the unit disc U in C
and also on the unit ball B of a complex Banach space. As an application, we give the estimation of
the third coefficient for f under the condition that the second coefficient of f is zero. This result gives ageneralization of the estimation of the third coefficient for odd univalent functions on the unit disc U. We
also give the Fekete–Szegö inequality for the images of the first elements of g-Loewner chains on U under
the Roper–Suffridge type extension operators.
13 濱 田 英 隆 (九 州 産 大 理 工)
(Babeş-Bolyai Univ.)
G. Kohr
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Loewner PDE in infinite dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Loewner PDE in infinite dimensions

概 要 In this talk, we generalize the existence and uniqueness result for the solutions of the Loewner partial

differential equation (Loewner PDE) from Cn to the case of separable reflexive complex Banach spaces.

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37

函数論

14 Shaolin Chen
(Hengyang Normal Univ.)
濱 田 英 隆 ( 九 州 産 大 理 工)

Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)

Some sharp Schwarz–Pick type estimates and their applications of harmonic and pluriharmonic functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Some sharp Schwarz–Pick type estimates and their applications of harmonic and pluriharmonic functions

概 要 The purpose of this talk is to study the Schwarz–Pick type inequalities for harmonic or pluriharmonic

functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of thenorm of harmonic functions from the Euclidean unit ball in Rn into the unit ball of the real ℓp space. Next,
we give several sharp Schwarz–Pick type inequalities for pluriharmonic functions from the Euclidean unit
ball in Cn or from the unit polydisc in Cn into the unit ball of the ℓp space. Furthermore, we establish
some sharp coefficient type Schwarz–Pick inequalities for pluriharmonic functions defined in the ℓp space.
Finally, we use the obtained Schwarz–Pick type inequalities to discuss the Schwarz–Pick type lemmas ofarbitrary order and the Bohr phenomenon of harmonic or pluriharmonic functions.
15 Shaolin Chen
(Hengyang Normal Univ.)
濱 田 英 隆 ( 九 州 産 大 理 工)
S. Ponnusamy(Indian Inst. of Tech. Madras)
R. Vijayakumar(Indian Inst. of Tech. Madras)

Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Saminathan Ponnusamy(Indian Inst. of Tech. Madras)
Ramakrishnan Vijayakumar(Indian Inst. of Tech. Madras)

Schwarz type lemmas and their applications in Banach spaces · · · · · · · 15

Schwarz type lemmas and their applications in Banach spaces

概 要 The main purpose of this talk is to develop some methods to investigate the Schwarz type lemmasof holomorphic mappings and pluriharmonic mappings in Banach spaces. Initially, we extend the classicalSchwarz lemmas of holomorphic mappings to Banach spaces, and then we apply to establish a sharp
Bloch type theorem for pluriharmonic mappings on homogeneous unit balls of Cn and to obtain somesharp boundary Schwarz type lemmas for holomorphic mappings in Banach spaces. Next, we improve andgeneralize the classical Schwarz lemmas of planar harmonic mappings into the sharp forms of Banach spaces
and give some applications to sharp boundary Schwarz type lemmas for pluriharmonic mappings in Banach
spaces. Finally, we give some sharp Schwarz-Pick type estimates of pluriharmonic mappings in JB ∗ -triples.
16 渡 邊 祐 太 (東 大 数 理)

Yuta Watanabe (Univ. of Tokyo)

乗数イデアル層で捩じれた対数的微分形式の層に対する L2 -型 Dolbeault
同型と消滅定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

L2 -type Dolbeault isomorphisms and vanishing theorems for logarithmic
sheaves twisted by multiplier ideal sheaves

概 要 In this speech, we first establish an L2 -type Dolbeault isomorphism for the sheaf of logarithmic

differential forms twisted by the multiplier ideal sheaf. By using this isomorphism and L2 -estimatesequipped with a singular Hermitian metric, we obtain logarithmic vanishing theorems involving multiplierideal sheaves on compact Kähler manifolds with simple normal crossing divisors.

最終版: 2023/2/17
函数論

3817 大 沢 健 夫 (名 大 多 元 数 理) ♭ On the Levi problem on Kähler manifolds under the negativity of canonical bundles on the boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Takeo Ohsawa (Nagoya Univ.)

On the Levi problem on Kähler manifolds under the negativity of canonical bundles on the boundary

概 要 It is proved that a bounded smooth pseudoconvex domain D in a Kähler manifold M can be mapped

onto a locally closed analytic set in a complex number space holomorphically and properly with connected
fibers if the caninical bundle of M is negative on a neighborhood of the boundary of D. A similar result
holds for Zariski open domains of compact manifolds.
13:00〜14:00
阿 部

特別講演
誠 (広島大先進理工)

Makoto Abe (Hiroshima Univ.)

Stein 多様体上の岡・Grauert の原理をみたす領域について
Domains over a Stein manifold satisfying the Oka–Grauert principle

概 要 We discuss the pseudoconvexity and the Steinness of a complex manifold or a complex space undersome conditions. Among others, we announce the recent joint research with Sugiyama on the Steinness ofa domain over a Stein manifold that satisfies the Oka–Grauert principle for a complex Lie group of positive
dimension and some additional cohomological conditions.

最終版: 2023/2/1739函数方程式論函 数

方3 月 15 日（水）

程

式

論

第 IV 会場

9:30〜12:00
1 竹 井 優 美 子 ( 茨 城 工 高 専)
Yumiko Takei(Ibaraki Nat. Coll. of Tech.)(1, 1, 1, 2)-超幾何微分方程式の Voros 係数の位相的漸化式による表示とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On the expression of Voros coefficients for the hypergeometric differential equation of type (1,1,1,2) in terms of the topological recursion, andits applications

概 要 Voros coefficients are important objects in the exact WKB analysis for the global study of solutions ofdifferential equations. In this talk I will report that the Voros coefficients for the hypergeometric differential
equation of type (1,1,1,2) are given by the generating functions of free energies defined in terms of Eynard
and Orantin’s topological recursion.
2 松 原 宰 栄 ( 熊 本 大 先 端)
後 藤 良 彰 ( 小 樽 商 大)
Saiei-Jaeyeong Matsubara-Heo(Kumamoto Univ.)
Yoshiaki Goto
(Otaru Univ. of Commerce)

The signature of the invariant hermitian form for a regular holonomic
GKZ system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
The signature of the invariant hermitian form for a regular holonomic
GKZ system

概 要 Frits Beukers and Carlos Verschoor conjectured that the signature of the monodromy invariant

hermitian form for a regular holonomic GKZ system has an explicit formula. We prove that this conjectureis true, by computing the intersection matrix of the twisted homology group associated to Euler type integral
representation of a solution to GKZ system.
3 伊 藤 秀 一 ( 神 奈 川 大 工)

Hidekazu Ito (Kanagawa Univ.)

シンプレクティック写像族のバーコフ標準化とハミルトン系の超可積分性· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Birkhoff normalization of a family of symplectic maps and superintegrability of Hamiltonian systems

概 要 Integrability of a Hamiltonian system is defined by the existence of sufficiently many (Poisson-commuting) integrals. The Liouville–Arnold theorem gives description of the orbit structure near a compact
regular level set of those integrals, however, is not valid near singularities of those integrals. The aim of thistalk is to clarify the orbit structure of a super (noncommutatively) integrable system near singularities of
its integrals. For this purpose, Birkhoff normalization for a family of symplectic maps plays a key role. We
show that there exists a convergent Birkhoff normalization if a family of 2n-dimensional analytic symplectic
maps has n + q integrals near a fixed point of resonance degree q.
4 上 村

豊 (東 京 海 洋 大⋆) ♭ エネルギー依存逆散乱の 2 成分ソリトン · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.⋆)Two-component solitons via an energy dependent inverse scattering

概 要 An extended KdV hierarchy is discussed. Based upon an inverse scattering method on an energy

dependent Schroedinger operator, soliton solutions in the hierarchy are constructed in a unified manner.

最終版: 2023/2/17函数方程式論5 畑
裕 貴 ( 阪 府 大 理)
松 永 秀 章 ( 阪 公 大 理)
Yuki Hata (Osaka Pref. Univ.)
Hideaki Matsunaga(Osaka Metro. Univ.)

40

2 つの時間遅れをもつ線形微分方程式の漸近安定性 · · · · · · · · · · · · · · · · · · 12
Asymptotic stability in a linear differential equation with two delays

概 要 This study is devoted to the investigation of the effect of delays on the asymptotic stability of a linear

differential equation with two delays x′ (t) = −ax(t) − bx(t − τ ) − cx(t − 2τ ), t ≥ 0, where a, b, and c arereal numbers and τ > 0. We establish some explicit conditions for the zero solution of the equation to be
asymptotically stable.
6 鬼 塚 政 一 ( 岡 山 理 大 理)
Masakazu Onitsuka(Okayama Univ. of Sci.)

On Ulam stability of two-dimensional linear differential systems · · · · · · 10
On Ulam stability of two-dimensional linear differential systems

概 要 The main purpose of this talk is to classify the Ulam stability of the linear differential equationu′ = Au, where A is a real-valued constant 2 × 2 matrix. The best Ulam constant is obtained for somespecial cases of A.
7 宇 佐 美 広 介 ( 岐 阜 大 工)
Hiroyuki Usami(Gifu Univ.)

非線形項に単調性等を仮定しない常微分方程式の正値解の非存在定理について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Study on nonexistence results of positive solutions of ODEs without
assuming monotonicities on nonlinear terms

概 要 Sufficient conditions for the existence of positive solutions of quasilinear ODEs are given. Usually,such results are proved under the monotonicity conditions of nonlinear terms. However, in this talk we will
give such results without assuming monotonicities on nonlinear terms.
8 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

Global and asymptotic behaviors of bifurcation curves of one-dimensional
nonlocal elliptic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Global and asymptotic behaviors of bifurcation curves of one-dimensional
nonlocal elliptic equations

概 要 We consider the global behavior of the bifurcation curves and solution curves of one-dimensional

nonlocal elliptic eigenvalue problems. We know that the bifurcation curve λ is a continuous function of the
maximum norm α = kuλ k∞ such as λ(α). Here, uλ is the positive solution associated with λ. Our purpose
here is to establish the asymptotic formulas for λ(α) and uλ as λ → ∞.
9 濱 本 直 樹 ( 阪 公 大 理)

Naoki Hamamoto (Osaka Metro. Univ.)

The Poincaré constant for curl-free vector fields on a ball · · · · · · · · · · · 12
The Poincaré constant for curl-free vector fields on a ball

概 要 We investigate the best value of the constant in classical Poincaré inequality

ZZ|∇u|2 dx ≥ C
BN|u|2 dx
BNfor a class of vector fields u with u|∂B N = 0 on the unit ball B N ⊂ RN which are subject to the curl-freeconstraint. We find that the best value of C turns out to be the square of the first zero of Bessel functionof the (N/2)-th order.

最終版: 2023/2/1741函数方程式論10 齋 藤 三 郎 (群馬大⋆・再生核研)
Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Functional equations and theory of reproducing kernels · · · · · · · · · · · · · 10
Functional equations and theory of reproducing kernels

概 要 By a survey paper, we shall introduce the basic relations of functional equations and the theory of

reproducing kernels, globally, as a summary of the topics. In particular, I would like to introduce typicalresults with their principles in some concrete way based on the draft paper.
The general theory of reproducing kernels will give the basic tool of these widespread problems.
11 齋 藤 三 郎 (群馬大⋆・再生核研)
Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Representations of quotients g/f =h in terms of g=fh · · · · · · · · · · · · · · · 12
Representations of quotients g/f =h in terms of g=fh

概 要 We are considering the simple functional equation hf=g. By the paper (REPRESENTATIONS OFQUOTIENTS g/f = h IN TERMS OF g = fh, International Journal of Reproducing Kernels Vol. 2 No. 1(2023)), we shall introduce quotients g/f of general functions f and g in some deep and natural meanings, ina natural setting.
14:15〜16:15
12 堀 内 利 郎 (茨 城 大 理)

Toshio Horiuchi (Ibaraki Univ.)

On general Caffarelli–Kohn–Nirenberg type inequalities involving nondoubling weights · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On general Caffarelli–Kohn–Nirenberg type inequalities involving nondoubling weights

概 要 By introducing W (R+ ) = P (R+ ) ∪ Q(R+ ) = ∪a∈[0,∞] Wa (R+ ) as a class of weight functions, wewill establish the Caffarelli–Kohn–Nirenberg type inequalities for p ≥ 1 involving non-doubling weights
in W (R+ ). The classical Caffarelli–Kohn–Nirenberg type inequalities are categorized into non-critical andcritical cases, and it is known that there is some kind of mysterious relationship between them. Interestingly
the new framework in this treatise allows them to be integrated and reveals the meaning of mysterious
relationships. A function w(t) on (0, ∞) is said to be a doubling weight if there exists a positive number
C such that we have C −1 w(t) ≤ w(2t) ≤ Cw(t)(0 < t < ∞), where C is independent of each t ∈ (0, ∞).

When w(t) does not possess this property, w(t) is said to be a non-doubling weight in the talk.
13 梶 木 屋 龍 治(大阪電通大共通教育機構)
Ryuji Kajikiya(Osaka Electro-Comm. Univ.)

Boundedness of critical points in the symmetric mountain pass lemma· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Boundedness of critical points in the symmetric mountain pass lemma

概 要 We study the boundedness of critical points defined by the symmetric mountain pass lemma. We

construct three types of functionals, which have an unbounded sequence of critical values. For the first one,the set of all critical points is bounded and the set of critical values is unbounded. The second one hasboth an unbounded sequence and a bounded sequence of critical points. For the last one, the set of criticalpoints is countably infinite and unbounded.
14 赤 木 剛 朗 (東 北 大 理)
宮 川 寛 基 ( 東 北 大 理)
(Tohoku Univ.)
Goro Akagi
Hiroki Miyakawa (Tohoku Univ.)

Maximal regularity of distributional solutions to degenerate elliptic systems for locally integrable data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Maximal regularity of distributional solutions to degenerate elliptic systems for locally integrable data

概 要 This talk is concerned with degenerate elliptic equations involving the p-Laplacian and absorption in

unbounded domains. Main results consist of the existence of distributional solutions and their maximal
regularity (estimates) for locally integrable forcing terms beyond the duality.

最終版: 2023/2/17函数方程式論15 赤 木 剛 朗 (東 北 大 理)
佐 藤 光 汰 朗 ( 東 北 大 理)
Goro Akagi
Kotaro Sato

(Tohoku Univ.)(Tohoku Univ.)

42

On some quasistatic evolution equation arising from fracture mechanics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On some quasistatic evolution equation arising from fracture mechanics

概 要 This talk deals with some quasistatic evolution equation, which relates fracture mechanics and is also

written as an evolutionary variational inequality. The main result of this talk is concerned with the existenceof strong solutions complying with three qualitative properties, that is, irreversibility, unilateral equilibriumand energy conservation, which were originally proposed in a phase-field model for brittle fracture.
16 岡

大 将 (東大工)Tomoyuki Oka (Univ. of Tokyo)

Corrector results for space-time homogenization of fast diffusion equations without assumptions for smoothness of coefficients · · · · · · · · · · · · 12
Corrector results for space-time homogenization of fast diffusion equations without assumptions for smoothness of coefficients概 要 In this talk, we shall discuss a space-time homogenization problem for fast diffusion equations withperiodically oscillating (in space and time) coefficients. The main purpose of this talk is to present a
corrector result, i.e., strong convergence of gradient of the solution with a corrector term. The proof isbased on the unfolding method and the strong two-scale convergence theory.
17 鈴 木貴 (阪 大 M M D S )Takashi Suzuki (Osaka Univ.)

ブラウン粒子気体モデルの数学解析 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Mathematical analysis for Brownian particle gas

概 要 We study Streater’s model on Brownian particle gas in statistical mechanics on bounded domain in

Rn . If n ≤ 2, there is a solution global in time, provided that the entropy production is bounded.
18 谷 口 晃 一 (東 北 大 A I M R)
工
大)
千 頭
昇 (名
池 田 正 弘(理化学研 AIP・慶大理工)
S. Tayachi(Univ. de Tunis El Manar)

Koichi Taniguchi (Tohoku Univ.)
Noboru Chikami (Nagoya Inst. of Tech.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Slim Tayachi (Univ. de Tunis El Manar)

Hardy–Hénon 型半線型熱方程式の解の無条件一意性と非一意性 · · · · · · 10

Unconditional uniqueness and non-uniqueness of solutions for Hardy–
Hénon parabolic equations

概 要 In this talk we study the problems of uniqueness for Hardy–Hénon parabolic equations, which aresemilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénontype) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ the weighted
Lorentz spaces as the solution space. The purpose of this talk is to prove unconditional uniqueness andnon-uniqueness for Hardy–Hénon parabolic equations in the weighted Lorentz spaces.
19 下 條 昌 彦 (都 立 大 理)
Jong Shenq Guo (Tamkang Univ.)
大工)
Amy Ai-Ling Poh (東Masahiko Shimojo(Tokyo Metro. Univ.)
Jong Shenq Guo (Tamkang Univ.)
Amy Ai-Ling Poh (Univ. of Tokyo)

Spreading behavior of an SIR model with non-local dispersal · · · · · · · · 10

Spreading behavior of an SIR model with non-local dispersal

概 要 We explain a Liouville type of theorem on the positive bounded entire solution of a class of reaction-diffusion systems with nonlocal dispersal. Some application from epidemiology is also given.

最終版: 2023/2/1743函数方程式論20 下 條 昌 彦 (都 立 大 理)
Jong Shenq Guo (Tamkang Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong Shenq Guo (Tamkang Univ.)

Spreading behavior of a predator-prey system with fractional Laplacian· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Spreading behavior of a predator-prey system with fractional Laplacian

概 要 We establish a Liouville theorem on the positive bounded entire solution of a class of reaction-diffusion systems with fractional diffusion. As an application, we investigate the spreading phenomena of apredator-prey system with fractional diffusion. More precisely, by a suitable limiting argument along with
the Liouville-type theorem, we prove that the solution converges to the unique positive co-existence statebehind the spreading front.
16:30〜17:30
池 畠

2022 年度 (第 21 回) 日本数学会解析学賞受賞特別講演
優 (広 島 大 工) 時間領域における囲い込み法の展開

Masaru Ikehata (Hiroshima Univ.)

Development of the time domain enclosure method

概 要 This talk is concerned with a reconstruction method in inverse problems formulated by using thesolutions of various partial differential equations. Such equations are called the governing equations and theobservation data are described by the solutions. The object to be reconstructed or extracted from the datais the discontinuity such as obstacles, inclusions, cracks etc.
The probe and enclosure methods are general ideas to extract information about unknown discontinuity
embedded in a known background medium from the observation data. The data are given by the far field
pattern of the scattered field, the Dirichlet-to-Neumann map or its partial knowledge at the boundary of themedium. The methods were introduced by the speaker and it has already been passed more than twenty
years. The methods have been applied to several inverse problems, e.g., an inverse boundary value problem
related to EIT(electrical impedance tomography), elasticity and inverse obstacle scattering problems ofacoustic wave at a fixed wave number, whose governing equations are time-independent.
The next challenge and interest of the speaker were to extend the enclosure method to cover inverse
problems governed by time-dependent PDEs. However, as a result of research over the last ten years, it
has been found that the enclosure method is also effective for various time-dependent PDEs, such as theheat equation, the wave equation, a system of equations in thermoelasticity, the Maxwell system and quite
recently the fractional diffusion equation.
This talk will give a brief history of probe and enclosure method and then describe some of recent
developments of enclosure methods in the time domain.

3 月 16 日（木）第 IV 会場

9:15〜12:00
21 水 上 雅 昭 (京 都 教 育 大)
田 中 悠 也 ( 東 京 理 大 理)
Masaaki Mizukami(Kyoto Univ. of Edu.)
Yuya Tanaka (Tokyo Univ. of Sci.)

Non-simultaneous blow-up in a two-species chemotaxis-competition modelwith single production · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Non-simultaneous blow-up in a two-species chemotaxis-competition modelwith single production

概 要 In a two-species chemotaxis-competition model, blow-up of solutions was shown in a previous paper.

In this model, the production term seems to promote blow-up phenomena; this implies that the lack of the
production term makes the solution likely to be bounded. Thus, it is expected that the model without oneof the production terms has a solution such that the species which does not produce the chemical substanceremains bounded, whereas the other species blows up. The purpose of this paper is to prove that thisconjecture is true.

最終版: 2023/2/17函数方程式論

22 田 中 悠 也 (東 京 理 大 理)

Yuya Tanaka (Tokyo Univ. of Sci.)

44

Finite-time blow-up in a degenerate parabolic–elliptic Keller–Segel system with logistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Finite-time blow-up in a degenerate parabolic–elliptic Keller–Segel system with logistic source

概 要 This talk deals with a degenerate parabolic–elliptic Keller–Segel system with logistic source. In thecase of nondegenerate diffusion, Black, Fuest and Lankeit (Z. Angew. Math. Phys.; 2021; 72; no. 96, 23
pp.) obtained a condition such that finite-time blow-up occurs. The purpose of this talk is to show that
finite-time blow-up occurs also in the case of degenerate diffusion.
23 千 代 祐 太 朗 (東 京 理 大 理)
水 上 雅 昭 (京都教育大教育)

Yutaro Chiyo (Tokyo Univ. of Sci.)
Masaaki Mizukami(Kyoto Univ. of Edu.)

Boundedness of solutions to a chemotaxis system for tumor angiogenesis· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Boundedness of solutions to a chemotaxis system for tumor angiogenesis

概 要 This talk deals with a chemotaxis system for tumor angiogenesis. When the third equation is simplified

by the elliptic one and the sensitivity functions are constants, global existence and boundedness were proved
by Tao and Winkler (Nonlinear Analysis; 2021; 112324; 16 pp). However, the case that the sensitivity
functions are not constants and the third equation is parabolic seems not to have been studied yet. The
purpose of this talk is to establish global existence and boundedness in a fully parabolic chemotaxis system
for tumor angiogenesis with sensitivity functions.
24 勝 呂 剛 志 (京 大 数 理 研) ♭ 放物-楕円型 Keller–Segel 系の初期値問題の一様局所可積分空間における適切性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Takeshi Suguro (Kyoto Univ.)

Well-posedness of the Cauchy problem of a parabolic-elliptic Keller–
Segel system in uniformly local spaces

概 要 We consider the Cauchy problem of the parabolic-elliptic Keller–Segel system on Euclidean space.

This system is one of the diffusion equation involving a nonlocal term. It is interesting whether this problem
is well-posed in function spaces containing the non-decaying function. We show that the Cauchy problem
of a Keller–Segel system is well-posed in uniformly local Lebesgue spaces.
25 細 野 竜 也 (東 北 大 理) ♭ Global existence of solutions to the 4D attraction-repulsion chemotaxis
小 川 卓 克 (東 北 大 理) system and applications of Brezis–Merle inequality · · · · · · · · · · · · · · · · · 12

Tatsuya Hosono (Tohoku Univ.)
Takayoshi Ogawa (Tohoku Univ.)

Global existence of solutions to the 4D attraction-repulsion chemotaxis
system and applications of Brezis–Merle inequality

概 要 We consider the Cauchy problem for an attraction-repulsion chemotaxis system in the four spacedimension. One of main topics in the study of such a system is the presence of L1 threshold. In fact,
the critical mass phenomenon called 8π-problem is well-known in the 2-dimensional setting. In this talk,using the Brezis–Merle type inequality and rearrangement arguments, we will show that the solution exists
globally in time when the initial mass is less than 4-dimensional L1 threshold value (8π)2 .
26 田 代 紀 一 (東 工 大 理)
Kiichi Tashiro(Tokyo Tech)

Elliptic regularization による適切な一般化平均曲率流の構成について · 10
On the construction of canonical generalized mean curvature flow byelliptic regularization

概 要 In this talk, we consider a generalized mean curvature flow constructed by elliptic regularization.

Elliptic regularization is a method invented by Tom Ilmanen to construct an approximation of the generalized
mean curvature flow using real analytic functional. We will show that the area change of the region movedby this flow is given by equality using the generalized mean curvature. The key to the proof is to establish
approximate velocity and estimate it in L2 .

最終版: 2023/2/1745函数方程式論27 三 浦 達 哉 (東 工 大 理)
吉 澤 研 介 (九 大 I M I )Tatsuya Miura (Tokyo Tech)
Kensuke Yoshizawa (Kyushu Univ.)

Complete classification of planar p-elasticae · · · · · · · · · · · · · · · · · · · · · · · 12
Complete classification of planar p-elasticae

概 要 Euler’s elastica is defined by a critical point of the total squared curvature under the fixed length

constraint, and its Lp -counterpart is called p-elastica. In our talk, we completely classify all p-elasticae inthe plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new
types of p-elliptic functions which streamline the whole argument and result. As an application we alsoclassify all closed planar p-elasticae.
28 長 澤 壯 之 (埼 玉 大 理 工)

Takeyuki Nagasawa (Saitama Univ.)

非局所曲率流の存在時間の下界評価と爆発レート · · · · · · · · · · · · · · · · · · · 10

A lower estimate of the life-span and a blow-up rate for non-local curvature flows for plane curves

概 要 Several non-local curvature flows for plane curves with general rotation number are considered here.

The flows include the area-preserving flow and the length-preserving flow. Previously, we showed sufficientconditions for finite-time blow-up, and gave an upper bound of the blow-up time. Here, we give estimatesfor solutions including at least two important applications. As the first one, it gives a lower bound of thelife span, which is a lower bound of the blow-up time for blow-up solutions. Secondly, our estimate also
improves the blow-up rate of blow-up solutions.
29 三 浦 達 彦 (弘 前 大 理 工)

Tatsu-Hiko Miura (Hirosaki Univ.)

Error estimate for classical solutions to the heat equation in a moving
thin domain and its limit equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Error estimate for classical solutions to the heat equation in a moving
thin domain and its limit equation

概 要 We consider the Neumann type problem of the heat equation in a moving thin domain around a given

closed moving hypersurface. Our main result is an estimate in the sup-norm for the difference of a classicalsolution to the heat equation in the moving thin domain and a classical solution to a limit equation on
the moving hypersurface which appears in the thin-film limit of the heat equation. To prove that error
estimate, we construct a suitable approximate solution to the heat equation from a classical solution to thelimit equation and then estimate the difference of a classical solution and the approximate one to the heat
equation based on the maximum principle.
30 二 宮 広 和 (明 大 総 合 数 理)

Hirokazu Ninomiya (Meiji Univ.)

等拡散によるパターン形成の例 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Example of pattern formation by equal diffusion

概 要 In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium of somekinetic system is destabilized by diffusion. In the case of two-component reaction-diffusion systems, however,the diffusion coefficients should be different. Conversely, there exist several chemical models that produce
the stable patterns even though the diffusion coefficients are equal. To study the pattern formation by equal
diffusion, this talk presents an example of a kinetic system with a asymptotically stable equilibrium, while
the corresponding reaction-diffusion system has a family of unstable stationary solutions that is arbitrarilyclose to the homogeneous stationary solution.

最終版: 2023/2/17函数方程式論31 二 宮 広 和 (明 大 総 合 数 理)

Hirokazu Ninomiya (Meiji Univ.)46

非一様場における面積保存曲率流のダイナミクス · · · · · · · · · · · · · · · · · · · 12

Dynamics of area-preserving curvature flow of a convex plane curve in
an inhomogeneous medium

概 要 In 1986, Gage studied the area-preserving curvature flows in a two-dimensional homogeneous medium.

He showed that an initially convex closed curve remains convex and converges to a circle as time goes toinfinity. However, in many applications, the medium is not homogeneous. In this talk, we consider the area
preserving flow in an inhomogeneous medium when the area enclosed by the interface is small. The reduced
equation of its center will be explained.
13:00〜14:00

特別講演
長 澤 壯 之 ( 埼 玉 大 理 工)Möbius エネルギーの分解と波動写像

Takeyuki Nagasawa (Saitama Univ.)

The decomposition of the Möbius energies and wave maps

概 要 The Möbius energy for knots is known as a functional invariant under Möbius transformations. Thereis an energy for links having the same properties. For the energies for knots and two-component links,
there exists a Möbius invariant decomposition, that is, each decomposed part is still invariant under Möbiustransformations.
Recently, the author found two new expressions of decomposition using Gauss maps of knots and links. One
is an “indirect expression”, the other is a “direct expression.”
Using the indirect expression, we can regard the decomposition as the parallelogram law of the Möbius
energy. Furthermore, the cosine formula of the Möbois energy for knots is generalized to decomposedenergies.
It has been known that the first decomposed energy relates to an energy of fractional harmonic maps. We
can see from the direct expression that the second one does to an energy of wave maps. As an application,
we show the existence or non-existence of knots and links which Gauss maps are wave maps.

3 月 17 日（金）第 IV 会場

9:30〜12:00
32 佐 藤 洋 平 (埼 玉 大 理 工)
Yohei Sato

(Saitama Univ.)

斥力的連立シュレディンガー方程式の偶対称基底状態 · · · · · · · · · · · · · · · 12

Even ground state for nonlinear Schrödinger systems with repulsive interaction

概 要 It is known that the nonlinear Schrödinger systems with repulsive interaction has no ground states.

Here ground state means a positive solution that attains a minimizing problem on the Nehari set withtwo constrains. On the other hand, when the minimizing problem is restricted to even functions, one calls
a positive minimizer as an even ground state. We show the existence of even ground states of nonlinear
Schrödinger systems with repulsive interaction. The keys of the proof are estimates of minimizing level anda classificaton of Palais-Smale sequences of even functions. In particular, the case N = 1 requires moredetailed estimates than N = 2, 3.

最終版: 2023/2/1747函数方程式論33 平 山 浩 之 (宮 崎 大 教 育)
池 田 正 弘(理化学研 AIP・慶大理工)

Hiroyuki Hirayama (Univ. of Miyazaki)
Masahiro Ikeda (RIKEN/Keio Univ.)

微分型の非線形項を持つ非線形シュレディンガー方程式系の基底状態の存在と安定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Existence and stability of ground states for the system of nonlinear
Schrödinger equations with derivative nonlinearity

概 要 We consider the Cauchy problem of the system of nonlinear Schrödinger equations with derivative

nonlinearlity. The well-posedness of this system in the Sobolev space H 1 is obtained by the previous works.
But the long time behavior of the solution of this system is not well known. In this talk, we prove theexistence of ground state solutions of this system. Furthermore, for 1 dimensional case, we also prove thestability of ground states by using the variational method.
34 深 谷 法 良 (東 京 理 大 理)林
雅 行 (ピサ大・早大理工)

Noriyoshi Fukaya (Tokyo Univ. of Sci.)
Masayuki Hayashi(Univ. di Pisa / Waseda Univ.)

1 次元における二重べき型非線形シュレディンガー方程式の定常解の不安
定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Instability of stationary solutions for double power nonlinear Schrödinger
equations in one dimension

概 要 We consider a double power nonlinear Schrödinger equation in one dimension and L2 -subcritical setting.

The equation has the algebraically decaying stationary solution ϕ0 as well as exponentially decaying standing
waves eiωt ϕω (x) with positive frequency. It is known from the general theory that the standing wave withpositive frequency is stable if M ′ (ω) > 0 and unstable if M ′ (ω) < 0, where M (ω) := 21 kϕω k2L2 . In this talkwe prove the instability of the stationary solution under the condition M ′ (0) := limω↓0 M ′ (ω) ∈ [−∞, 0).
The key in the proof is the costruction of the one-sided derivative of ω 7→ ϕω at ω = 0, which is effectively
used to construct the unstable direction.
35 佐 川 侑 司 (千 葉 工 大 工)
佐 藤 拓 也 ( 東 北 大 理)
川 上 翔 汰 ( 埼 玉 大 理 工)

Yuji Sagawa (Chiba Inst. of Tech.)Takuya Sato (Tohoku Univ.)
Shota Kawakami (Saitama Univ.)

調和ポテンシャル付き非線形シュレディンガー方程式に対する小さな初期値の有限時間爆発解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Finite time blow up solutions to the nonlinear Schrödinger equation
with harmonic potential for arbitrary small initial data

概 要 We construct finite time blow up solutions to the power type nonlinear Schrödinger equation withharmonic potential for arbitrary small initial data in the positive time direction. We simultaneously observethat those solutions exist globally in time and its mass decays in the negative time direction. This part isan improvement of the previous work by Antonelli, Carles and Sparber.
36 平 山 浩 之 (宮 崎 大 教 育)木 下 真 也 ( 埼 玉 大 理 工)
大
理)
岡 本
葵 (阪

Hiroyuki Hirayama (Univ. of Miyazaki)
Shinya Kinoshita (Saitama Univ.)
Mamoru Okamoto (Osaka Univ.)

2 次の非線形項をもつ 2 次元非線形 Schrödinger 方程式の角度正則性を課した Sobolev 空間での適切性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Well-posedness of the Cauchy problem for the two dimensional quadratic
nonlinear Schrödinger equation with angular regularity

概 要 We consider the Cauchy problem for the two dimensional nonlinear Schrödinger equation with thequadratic nonlinearity |u|2 . In the Sobolev space H s (R2 ), it is known that s = − 41 is the threshold for the
Cauchy problem to be well-posed. We prove the well-posedness in H s (R2 ) for − 12 < s < − 14 by assumingsome angular regularity on initial data.

最終版: 2023/2/17函数方程式論48

37 津 原駿 (東 北 大 理) ♭ 4 次元 Sobolev 臨界の連立非線型 Schrödinger 方程式系の時間大域適切性
小 川 卓 克 (東 北 大 理) について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Shun Tsuhara (Tohoku Univ.)
Takayoshi Ogawa (Tohoku Univ.)

Global well-posedness for the Sobolev critical nonlinear Schrödinger system in four space dimensions

概 要 We consider the Cauchy problem of the system of nonlinear Schrödinger equations with cubic non-linearity in four space dimensions. We prove the existence of the ground state solution and the global
well-posedness for the system below the ground state solution under the mass resonance condition. We
also show that the ground state solution is written by Aubin–Talenti function. The proof of the gloval
well-posedness result is following the well-known results due to Kenig–Merle (2006).
38 佐 藤 拓 也 (東 北 大 理) ♭ The initial boundary value problem of nonlinear Schrödinger equations
林
仲 夫 (東 北 大 理) with a nonlinear Neumann boundary condition · · · · · · · · · · · · · · · · · · · · 12
小 川 卓 克 ( 東 北 大 理)
Takuya Sato (Tohoku Univ.)
Nakao Hayashi (Tohoku Univ.)
Takayoshi Ogawa (Tohoku Univ.)

The initial boundary value problem of nonlinear Schrödinger equations
with a nonlinear Neumann boundary condition

概 要 We consider the initial-boundary value problem of the nonlinear Schrödinger equation on the half linewith a nonlinear Neumann boundary condition. After establishing the boundary Srtichartz estimate in L2 ,we consider the time local well-posedness of the problem in the lower regularity spaces as L2 .
39 長 田 祐 輝 (都 立 大 理)

Yuki Osada (Tokyo Metro. Univ.)

非対称ポテンシャルの下での 3 波相互作用をもつ非線形シュレディンガー方程式系の minimizer の存在 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Existence of a minimizer for a nonlinear Schrödinger system with three
wave interaction under non-symmetric potentials

概 要 In this talk, we show the existence of a minimizer for the L2 -constrained minimization problem

associated with a nonlinear Schrödinger system with three wave interaction without assuming symmetry forpotentials by using interaction estimates.
40 池 田 正 弘(理化学研 AIP・慶大理工)
戍 亥 隆 恭(阪大理・ブリティッシュコロンビア大)浜 野
大 ( 早 大 理 工)
清 水 一 慶 ( 阪 大 基 礎 工)

Masahiro Ikeda (RIKEN/Keio Univ.)
Takahisa Inui
(Osaka Univ./Univ. of British Columbia)
Masaru Hamano (Waseda Univ.)(Osaka Univ.)
Ikkei Shimizu

Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph概 要 We consider the nonlinear Schrödinger equations on the star graph with the Kirchhoff boundary andthe repulsive Dirac delta boundary at the origin. In this talk, we show scattering-blowup dichotomy result
below the mass-energy of the ground state on the real line. The proof of the scattering part is basedon a concentration compactness and rigidity argument. Our main contribution is to give a linear profile
decomposition on the star graph by using a new idea of decomposition of functions on the star graph.

最終版: 2023/2/1749函数方程式論41 川 上 隼 平 (京大理)Jumpei Kawakami (Kyoto Univ.)

Averaging of strong magnetic nonlinear Schrödinger equations in energy
space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Averaging of strong magnetic nonlinear Schrödinger equations in energy
space

概 要 We consider nonlinear Schrödinger equation with strong magnetic field in 3-dimension. To analyze

this, R L. Frank, F. Méhats, C. Sparber derived two nonlinear Schrödinger type models. One model isderived by spatial scaling and the other model is obtained by averaging the aforesaid spatial scaled modelin time. We study these two models in energy space and obtain global solutions for some cases. We also
prove that the time averaged model is energy-critical when this model has the nonic nonlinear power.
Furthermore, we improve the previous result that the solution to the spatial scaled model converges to thesolution to the time averaged model.
14:15〜16:15
42 石 塚 健 二 郎 (京 大 数 理 研)

Kenjiro Ishizuka (Kyoto Univ.)

ポテンシャルのついた非線形消散クライン・ゴルドン 方程式の漸近挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Long-time asymptotics of the one-dimensional damped nonlinear Klein–
Gordon equation with a potential

概 要 In this talk, we consider the one-dimensional nonlinear focusing damped Klein–Gordon equation witha potential. When a potential is good conditon, it follows from standard arguments that the Cauchy
problem for this equation is locally well-posed in the energy space. When a potential is zero, Cote–Martel–
Yuan (2021) proved the full soliton resolution. Anywaw we consider soliton resolution for this equation.
Especially we will mainly talk the case that a potential is a repulsive delta potential.
43 眞 﨑聡 ( 阪 大 基 礎 工)
瀬 片 純 市 ( 九 大 数 理)
瓜 屋 航 太 ( 岡 山 理 大 理)
Satoshi Masaki (Osaka Univ.)
Jun-ichi Segata (Kyushu Univ.)
Kota Uriya (Okayama Univ. of Sci.)

3 次非線形方程式系の分類について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

On classification of cubic nonlinear systems

概 要 In this talk, we introduce the classification of cubic nonlinear systems. The critical ingredient is tointroduce a matrix representation of a system. It turns out that the rank of the matrix is an invariant
quantity that describes the number of linearly independent conserved quantities. We give a classification ofsystems that have two distinct conserved quantities.
44 眞 﨑聡 (阪 大 基 礎 工) ♭ 複素数値 3 次非線形方程式系の分類について · · · · · · · · · · · · · · · · · · · · · · · 12

Satoshi Masaki (Osaka Univ.)

On classification of complex-valued cubic nonlinear systems

概 要 In this talk, we introduce the classification of complex-valued gauge-invariant cubic systems. The

critical ingredient is the matrix-vector representation of a system. This clarifies the effect of the changeof variables and describes the systems’ Hamiltonian structure. In particular, the rank of the matrix part
denotes the number of the conserved quantities, and hence reflects the system’s complexity. We show theclassification of systems that have only one conserved quantity.

最終版: 2023/2/17函数方程式論5045 津 田 谷 公 利 (弘 前 大 理 工) ♭ Blow up of solutions of semilinear wave equations with time-dependent
若 杉 勇 太 (広島大先進理工) damping · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Kimitoshi Tsutaya (Hirosaki Univ.)
Yuta Wakasugi (Hiroshima Univ.)

Blow up of solutions of semilinear wave equations with time-dependent
damping

概 要 We consider the Cauchy problem for nonlinear wave equations with time-dependent damping. We

show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as
upper bounds of the lifespan of blow-up solutions. We also show the same results for the space derivative
nonlinear term.
46 福 田 一 貴 (信 州 大 工)
平 山 浩 之 ( 宮 崎 大 教 育)
Ikki Fukuda (Shinshu Univ.)
Hiroyuki Hirayama (Univ. of Miyazaki)

一般化 KP–Burgers 方程式の初期値問題の解の長時間挙動と最良な減衰評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Large time behavior and optimal decay estimate for solutions to the
Cauchy problem for the generalized KP–Burgers equation in 2D

概 要 In this talk, we consider the Cauchy problem for the generalized KP–Burgers equation in 2D. This is

one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropic dissipative term.
Under some suitable regularity assumptions on the initial data u0 , especially the condition ∂x−1 u0 ∈ L1 (R2 ),it is known that the solution to this problem decays at the rate of t− 4 in the L∞ -sense. In this study, we7

investigate the more detailed large time behavior of the solution and construct the approximate formula forthe solution at t → ∞. Moreover, we obtain a lower bound of the L∞ -norm of the solution and prove thatthe decay rate t− 4 of the solution given in the previous work to be optimal.
7(Univ. of Victoria)
47 S. Ibrahim
清 水 一 慶 ( 阪 大 基 礎 工)

Slim Ibrahim (Univ. of Victoria)(Osaka Univ.)
Ikkei Shimizu

Phase transition threshold and stability of magnetic skyrmions · · · · · · 12
Phase transition threshold and stability of magnetic skyrmions

概 要 We examine the stability of vortex-like configuration of magnetization in magnetic materials, so-called the magnetic skyrmion. These correspond to critical points of the Landau–Lifshitz energy with the
Dzyaloshinskii–Moriya interactions. In this talk, we prove that there is an explicit critical value of theparameter in the energy above which the skyrmion is unstable, while stable below this threshold. This
mathematically explains the occurrence of phase transition observed in some experiments. We also showthat in the unstable regime, the infimum of energy is not bounded below.
48 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.)

周期境界条件下の浅水波系について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

On the shallow water systems under periodic boundary conditions

概 要 We consider stationary flows over periodic topography modeled by one-dimensional shallow waterequation. We first show the nonexistence of stationary solutions with discontinuities as well as the conditions
on the existence of continuous subsonic/supersonic stationary solutions. We also claim that the subsonicstationary solutions are not asymptotically stable.

最終版: 2023/2/1751函数方程式論49 古 屋 貴 士(島根大数理・データサイエンス教育研究センター)

Takashi Furuya (Shimane Univ.)

Inverse medium scattering problems with Kalman filter techniques · · · 10
Inverse medium scattering problems with Kalman filter techniques

概 要 We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium

from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed andnonlinear, and the iterative optimization method is often adapted. A natural iterative approach to thisproblem is to place all available measurements and mappings into one long vector and mapping, respectively,
and to iteratively solve the linearized large system equation. However, this is computationally expensive
because we must construct the larger system equations when the number of available measurements
increases. In this talk, we propose the reconstruction algorithm based on the Kalman filter, which avoids
the construction of a large system equation and retains the information of past updates.
16:30〜17:30
北特別講演
直 泰 (熊 本 大 工) ♭ 複素係数をもつ非線形シュレーディンガー方程式の解の挙動

Naoyasu Kita (Kumamoto Univ.)

On behaviors of solutions to nonlinear Schrödinger equations with complex coefficient in its nonlinearity

概 要 We consider the Cauchy problem of nonlinear Schrodinger equations. Unlike the conservative system,

the equation contains a complex coefficient in its nonlinearity. The physical background of such a nonconservative system is coming from the optical fiber engineering, where nonlinear Ohm’s law and nonlinear
amplification are applied. My talk consists of two parts. The first part treats a problem of global existence
and asymptotic behavior of solutions without size restriction on the initial data, where Hayashi–Naumkin’s
theory basically contributes to the result. The second part treats a construction of blowing-up solutions.
Combining the former result on asymptotic behavior of solutions, we can obtain blowing-up solutions evenfor small initial data. Recently, the result on the blowing-up solutions has been generalized by Cazenave–
Martel–Zhao, Cazenave–Han–Martel and Kawakami–Machihara. If time permits, these recent progresses
will be also presented.

3 月 18 日（土）第 IV 会場

9:30〜12:00
50 岩 田 直 之 (名 工 大 工)
鈴 木 政 尋 ( 名 工 大 工)

Naoyuki Iwata (Nagoya Inst. of Tech.)
Masahiro Suzuki (Nagoya Inst. of Tech.)

多成分プラズマの Vlasov–Poisson 方程式の定常解 · · · · · · · · · · · · · · · · · · 12

Stationary solutions of the Vlasov–Poisson system for a multicomponent
plasma概 要 In this talk, we mathematically investigate the formation of a plasma sheath, and analyze the Bohm

criterion which is required for the formation. In 1995, Riemann derived the Bohm criterion from thestationary Vlasov–Poisson system which describes the motion of a multicomponent plasma. We study thesolvability of boundary value problems of the system, and show that the Bohm criterion is a necessary
condition but not a sufficient condition for the solvability.

最終版: 2023/2/17函数方程式論工大)51 鈴 木 政 尋 (名高 山 正 宏 ( 慶 大 理 工)
Katherine Zhiyuan Zhang(New York Univ.)

Masahiro Suzuki (Nagoya Inst. of Tech.)
Masahiro Takayama (Keio Univ.)
Katherine Zhiyuan Zhang(New York Univ.)

52

Vlasov–Poisson 方程式の定常解の安定性・不安定性 · · · · · · · · · · · · · · · · · 12

Stability and instability of stationary solutions of the Vlasov–Poisson
system概 要 We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov–Poisson

system on a half-line with the completely absorbing boundary condition. The solvability of the stationary
problem has been established. In this talk, we study the nonlinear stability and instability of these stationary
solutions of the Vlasov–Poisson system.
52 江 口 太 一 (早 大 理 工)
Taichi Eguchi (Waseda Univ.)

Energy equality of MHD system under a weaker condition on magnetic
field · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Energy equality of MHD system under a weaker condition on magneticfield

概 要 We prove the energy equality of MHD system in the space founded by Cheskidov–Constantin

Friedlander–Shvydkoy (2008) and Berselli–Chiodaroli (2020). It is clarified that the energy equality isestablished for a lager class of the magnetic filed than that of velocity field. Our result covers most ofprevious theorems on validity of the energy equality on the Navier–Stokes equations.
53 中 里 亮 介 (早 大 理 工) ♭ Fourier–Herz 空間上でのエネルギー法と Hall 効果を伴う準線形プラズマモデルの漸近安定性への応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Ryosuke Nakasato (Waseda Univ.)

Asymptotic stability for quasi-linear plasma models with Hall effects via
energy methods on Fourier–Herz spaces

概 要 We consider the initial-value problem for the compressible Hall-magnetohydrodynamic system withquantum effects in the 3-dimensional Euclidean space R3 . The aim of this talk is to obtain time-decay
estimates for solutions as a perturbation from a constant equilibrium state (1, 0, B̄) in a critical Lp framework.
Here B̄ ∈ R3 is denoted by constant magnetic fields. To obtain such a result, we establish energy methods
b p introduced by Grünrock (2004). By combining L
b p energy methods and aon Fourier–Herz spaces L
b p -Lb p/2 typetransformation of the momentum equation given by the effective velocity, we will derive the L
time-decay estimate without the smallness requirement of low frequencies for initial data.
54 波 多 間 備 (京 大 数 理 研)
Sonae Hadama (Kyoto Univ.)

Stability of Fermi gas at zero temperature for the Hartree equation · · · 12
Stability of Fermi gas at zero temperature for the Hartree equation

概 要 We consider the Hartree equation describing the time evolution of wave functions of infinitely many

fermions interacting with each other. The Hartree equation can be formulated in terms of the operators
on L2 (Rd ). It has infinitely many stationary solutions, and several authors have studied their stability, forexample, Lewin–Sabin(2014), Chen–Hong–Pavloić(2018), and Collot–de Suzzoni(2020, 2022). However, thestability of Fermi gas at zero temperature, one of the most important stationary solutions from the physics
point of view, was left open. In this talk, we report that it is stable; that is, any small perturbation from
Fermi gas at zero temperature scatters.

最終版: 2023/2/1753函数方程式論55 古 場

一 ( 阪 大 基 礎 工)

(Osaka Univ.)

Hajime Koba

界面流を含む非粘性混相流の数理モデリング · · · · · · · · · · · · · · · · · · · · · · · 10

Mathematical modeling of inviscid multiphase flow system with surfaceflow

概 要 We consider the governing equations for the motion of the inviscid fluids in moving domains andsurface from an energetic point of view. We employ an energetic variational approach to derive multiphaseflow system with surface flow and tension. We make use of the feature of the barotropic fluid to derive thesurface pressure and tension of the compressible fluid in the surface.
56 古 場

一 ( 阪 大 基 礎 工)

(Osaka Univ.)

Hajime Koba

相転移を含む非粘性混相流の数理モデリング · · · · · · · · · · · · · · · · · · · · · · · 10

Mathematical modeling of inviscid multiphase flow system with phasetransition

概 要 We consider the governing equations for the motion of the fluid particles near air-water interface froman energetic point of view. We employ an energetic variational approach to derive inviscid multiphase flow
system with phase transition, where a phase transition means a jump condition. We apply our energetic
variational approach and jump condition to study the dominant equations for the densities of the fluids inmoving domains.
57 古 川賢 ( 理 化 学 研)

Ken Furukawa(RIKEN)

最大正則性のクラスでのプリミティブ方程式のデータ同化 · · · · · · · · · · · 10

Data assimilation of the primitive equations in maximal Lp -Lq settings概 要 We discuss about data assimilation to the primitive equations in maximal Lp -Lq settings in amathematically rigorous way. The primitive equations describe the flow in a thin domain. The equations
combined with some data assimilation methods are used in meteorology and ocean physics for predictions
for phenomena. Our results are that the solution to data assimilation equations of the primitive equations
converges to the solution to the primitive equations in maximal Lp -Lq spaces at t → ∞.
58 野 田慶 ( 京 大 人 間 環 境)

Kei Noda(Kyoto Univ.)

最大正則性に基づく多重線形作用素をもつ方程式の解の時空解析性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Analyticity in space-time of solutions to evolution equations with multilinear operator based on maximal regularity

概 要 In this presentation, we introduce a method to prove space-time analyticity for evolution equations

with nonlinear terms represented by multilinear operators via the parameter trick. By extending the caseof bilinear operators in the previous work, this method is expected to be applicable not only to theNavier–Stokes equations but also to the equations of Fujita type.
59 飯 田 祥 樹 (早 大 理 工)
Yoshiki Iida

(Waseda Univ.)

Energy equality for the 3D inhomogeneous Navier–Stokes equations inLorentz–Besov spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Energy equality for the 3D inhomogeneous Navier–Stokes equations inLorentz–Besov spaces

概 要 We establish the energy equality for Leray–Hopf weak solutions of the 3D incompressible inhomoge-

neous Navier–Stokes equations in Lorentz–Besov spaces. This result may be regarded as an extension ofthat by Cheskidov and Luo (2020).

最終版: 2023/2/17函数方程式論54

14:15〜16:15
60 青 木 基 記 (東 北 大 理)
岩 渕
司 ( 東 北 大 理)

Motofumi Aoki (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

On the ill-posedness for the full system of the compressible Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On the ill-posedness for the full system of the compressible Navier–Stokes equations

概 要 We consider the Cauchy problem for the equations of the ideal gas in the three space dimensions. In

the critical Besov spaces, it is known that the Cauchy problem is uniquely solvable for all 1 < p < 3 andill-posed for all p > 3. We study the threshold case p = 3. We prove that the Cauchy problem is ill-posedby constructing a sequence of the initial data such that the solution map is discontinuous.
61 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.)

Optimality of the decay estimate of solutions to the linearised curl-freecompressible Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Optimality of the decay estimate of solutions to the linearised curl-freecompressible Navier–Stokes equations

概 要 We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov norms.

In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, inthe homogeneous case. We prove that our estimate is optimal in the L∞ -norm by showing that the norm
is bounded from below by the same decay rate. This is the first time such a bound from below has beenobtained for the compressible Navier–Stokes equation.
62 岡 部 考 宏 (阪 大 基 礎 工)
L. Brandolese ( Univ. Lyon 1 )Takahiro Okabe (Osaka Univ.)
Lorenzo Brandolese (Univ. Lyon 1)

Forced rapidly dissipative Navier–Stokes flows · · · · · · · · · · · · · · · · · · · · · 12
Forced rapidly dissipative Navier–Stokes flows

概 要 We consider the asymptotic behavior of the solution to the incompressible Navier–Stokes equation on

the whole space. By an action of a forcing term we control the nonlinear term of the flow and derive a rapid
time decay. This talk is based on the joint work with Lorenzo Brandolese (Univ. Lyon 1).
63 中 塚 智 之 (松 山 大 経 済)
Tomoyuki Nakatsuka(Matsuyama Univ.)

On solvability of the time-periodic problem for the Navier–Stokes equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On solvability of the time-periodic problem for the Navier–Stokes equation

概 要 In this talk, we consider the existence of time-periodic solutions to the Navier–Stokes equation in

the whole space. We decompose periodic solutions into steady and purely periodic parts, and we analyze
the equations they should satisfy. Based on the analysis of the purely periodic solutions represented by
the Fourier transform to the Stokes equation, their additional property can be obtained and we use it toconstruct a time-periodic solution of the Navier–Stokes equation.
64 小 泉 祐 太 (早 大 理 工)
谷 口 透 也 ( 早 大 理 工)
Yuta Koizumi (Waseda Univ.)
Toya Taniguchi (Waseda Univ.)

Convergence of approximating solutions of the Navier–Stokes equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Convergence of approximating solutions of the Navier–Stokes equations

概 要 We show that the approximating solutions {uj }∞j=0 of the Navier–Stokes equations constructed by

Kato (1984) with the initial data u(0) ∈ Lnσ (Rn ) converge to the local strong solution u in the topology of
W 2,n (Rn ) provided the convergence in the scaling invariant norm in Lp (Rn ) with the time weight holds.

最終版: 2023/2/1755函数方程式論65 大 山 広 樹 (九 大 数 理)
米 田 慧 司 ( 九 大 数 理)

Hiroki Ohyama (Kyushu Univ.)
Keiji Yoneda (Kyushu Univ.)

Fast rotation limit for the magnetohydrodynamics equations in a 3D
layer · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Fast rotation limit for the magnetohydrodynamics equations in a 3Dlayer

概 要 We consider the initial value problem for the incompressible magnetohydrodynamics system with the

Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial
data in the scaling invariant space when the speed of rotation is sufficiently high. Moreover, we show thatthe global solution converges to that of the coupled system of the 2D incompressible magnetohydrodynamics
equations and the 3D incompressible Maxwell equations as the rotation speed tends to infinity.
66 江 頭 貴 成 (九 大 数 理)髙 田了 ( 東 大 数 理)

Takanari Egashira (Kyushu Univ.)
Ryo Takada (Univ. of Tokyo)

Large time behavior of solutions to the 3D rotating Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Large time behavior of solutions to the 3D rotating Navier–Stokes equations

概 要 We consider the large time behavior of the solutions for the initial value problem of the Navier–Stokes

equations with the Coriolis force in the three-dimensional whole space. We show the temporal decay
estimates with the dispersion effect of the Coriolis force for the global solutions. Moreover, we prove thelarge time asymptotic expansion of the solutions behaving like the first-order spatial derivatives of theintegral kernel of the corresponding linear solution.
67 藤 井 幹 大 (九 大 数 理)
Mikihiro Fujii (Kyushu Univ.)

Global strong solutions to the compressible Navier–Stokes equation with
the Coriolis force · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Global strong solutions to the compressible Navier–Stokes equation with
the Coriolis force

概 要 In this talk, we consider the global solvability for the compressible Navier–Stokes equation with the

Coriolis force in the scaling critical Besov space. Despite many studies on the weak solutions, the existenceof global strong solutions has been an open problem. Unlike the incompressible case, the Coriolis force
causes the linear solutions to behave like a semigroup {e−t∆ }t>0 , which creates difficulties in nonlinear2

estimates in the low frequency part. In this research, we propose a new idea of the low frequency analysis
and overcome these difficulties.
68 齋 藤 平 和 (電通大情報理工)
Hirokazu Saito(Univ. of Electro-Comm.)

On decay properties of solutions to the two-phase Stokes equations withsurface tension and gravity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On decay properties of solutions to the two-phase Stokes equations withsurface tension and gravityN
概 要 In this talk, we consider the two-phase Stokes equations with surface tension in ṘN = RN
+ ∪ R− andin the presence of a uniform gravitational field acting vertically downward. Let ρ± be positive constants
describing the densities of fluids occupying RN± . It is well-known that the Rayleigh-Taylor instability occurs
when the upper fluid is heavier than the lower one, i.e., when ρ+ > ρ− . On the other hand, this talk aims
to introduce time decay estimates of solutions to the two-phase Stokes equations under the condition thatthe lower fluid is heavier than the upper one, i.e., ρ− > ρ+ .

最終版: 2023/2/17函数方程式論特別講演
大筒 井 容 平 (京56

16:30〜17:30

理) ♭ Convergence to the initial data and weighted estimates for the incom-pressible Navier–Stokes equations
Youhei Tsutsui (Kyoto Univ.)

Convergence to the initial data and weighted estimates for the incompressible Navier–Stokes equations

概 要 We discuss conditions on data for which ensure the solution to the incompressible Navier–Stokes

equations strongly converges to the initial data from weak Ln space on the whole space. We also consider
weighted estimates for the solutions.

最終版: 2023/2/17

57

実函数論

実 函
3 月 17 日（金）数論
第 V 会場

9:00〜11:45
1 豊 田 昌 史 ( 東 邦 大 理)
Masashi Toyoda (Toho Univ.)

ボール空間における不動点定理と Caristi の不動点定理 · · · · · · · · · · · · · · 15

Fixed point theorem in a ball space and Caristi fixed point theorem

概 要 The purpose of this talk is to introduce a fixed point theorem in a ball space, which is proved without

the Axiom of Choice. Moreover, using the fixed point theorem in a ball space, we prove Caristi’s fixed point
theorem. Therefore the proof of Caristi’s fixed point theorem in this paper does not depend on the Axiomof Choice.
2 厚 芝 幸 子 (東京女大現代教養)
Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Convergence theorems for families of monotone nonexpansive mappingsin orderd Banach spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Convergence theorems for families of monotone nonexpansive mappingsin orderd Banach spaces

概 要 In this talk, we prove weak and strong convergence theorems for monotone nonexpansive mappingsand convergence theorems for monotone nonexpansive semigroups in Banach spaces endowed with a partial
order.
3 木 村 泰 紀 ( 東 邦 大 理)
Yasunori Kimura (Toho Univ.)

収縮射影法の類似手法による写像族の共通不動点近似 · · · · · · · · · · · · · · · 15

Approximation of common fixed points by modified shrinking projection
methods

概 要 This study deals with the approximation of fixed points for nonexpansive and other types of mappings.

Using a modified shrinking projection method, we obtain the delta-convergence of generated approximation
sequence to a fixed point of the mapping. We also consider a family of mappings and show a convergence
theorem to their common fixed point.
4 青 山 耕 治 ( 千 葉 大 社 会)
Koji Aoyama(Chiba Univ.)

吸引点に関する平均収束定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mean convergence theorems with respect to attractive points in a Hilbertspace

概 要 We show a mean convergence theorem for a mapping with an attractive point in a Hilbert space by using

a quasinonexpansive extension of the mapping and a mean convergence theorem for a quasinonexpansive
mapping. Then using the theorem, we establish a mean convergence theorem for a λ-hybrid mapping in thesense of Aoyama, Iemoto, Kohosaka, and Takahashi (2010).
5 波 多 野 修 也 ( 中 大 理 工)
Naoya Hatano(Chuo Univ.)

モレー・ローレンツ空間に対する真の埋め込み · · · · · · · · · · · · · · · · · · · · · 15

Proper embedding for Morrey–Lorentz spaces

概 要 The embeddings for Morrey–Lorentz spaces have been previously introduced by Ragusa. This paper

describes the major differences between these embedding types.

最終版: 2023/2/17
実函数論

6 D. I. Hakim(Bandung Inst. of Tech.)
波 多 野 修 也 ( 中 大 理 工)
野 ヶ 山 徹 ( 中 大 理 工)
澤 野 嘉 宏 ( 中 大 理 工)
Denny Ivanal Hakim(Bandung Inst. of Tech.)(Chuo Univ.)
Naoya Hatano
Toru Nogayama (Chuo Univ.)
Yoshihiro Sawano (Chuo Univ.)

58

Bourgain–Morrey spaces and its applications · · · · · · · · · · · · · · · · · · · · · · 15

Bourgain–Morrey spaces and its applications

概 要 In this talk, we introduce the Bourgain–Morrey space which is a one generalization of Morrey spaces.

By using this space, it is showed that we can refine the Strichartz estimate for Schrödinger equations. We
consider some properties of this space from the viewpoints of harmonic analysis and functional analysis.
7 野 ヶ 山 徹 ( 中 大 理 工)
Toru Nogayama (Chuo Univ.)

Complex interpolation for mixed Morrey spaces · · · · · · · · · · · · · · · · · · · · 15
Complex interpolation for mixed Morrey spaces

概 要 In this talk, we consider the complex interpolation for mixed Morrey spaces via the Calderón product.

The mixed Morrey space Mpq⃗ (Rn ) is a function space which is a generalization of Morrey spaces. The
results in this talk are extensions for classical Morrey spaces.
8 谷 口 晃 一 (東 北 大 A I M R )池 田 正 弘(理化学研 AIP・慶大理工)
石 川
勲(愛媛大データサイエンスセンター)

Koichi Taniguchi (Tohoku Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)(Ehime Univ.)
Isao Ishikawa

Besov 空間上の合成作用素の有界性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Boundedness of composition operators on Besov spacess
概 要 In this talk we consider boundedness of composition operators on Besov spaces Bp,qon one dimensional

Euclidean space. The boundedness has been well studied in the lower derivative case 0 < s < 1. In contrast,
there is almost no research on the higher order case s ≥ 1, and many problems remain unsolved. The purposeof this talk is to give necessary and sufficient conditions for the boundedness when s > 1 + 1/p. Similar
results for composition operators on Triebel–Lizorkin spaces are provided.
9 原

宇 信 ( 北 大 情 報)

Takanobu Hara (Hokkaido Univ.)

Strong barriers for weighted quasilinear equations · · · · · · · · · · · · · · · · · · 15
Strong barriers for weighted quasilinear equations

概 要 We construct strong barriers for weighted quasilinear elliptic equations. There are two applications:(i) solvability of Poisson-type equations with boundary singular data, and (ii) a geometric version of Hardy
inequality.
14:15〜15:25
10 川 﨑 敏 治
拡張積分可能関数族と拡張原始関数族の差について · · · · · · · · · · · · · · · · · 15
(玉川大工・千葉大法経・千葉大理)
Toshiharu Kawasaki(Tamagawa Univ./Chiba Univ./Chiba Univ.)

On the difference between the families of extended integrable functions
and extended primitive functions

概 要 In this talk, we discuss the difference between the families of extended integrable functions andextended primitive functions.

最終版: 2023/2/17

59

実函数論

On topologically invariant means and almost convergence · · · · · · · · · · · 15

11 国 定 亮 一
Ryoichi Kunisada

On topologically invariant means and almost convergence

概 要 In this talk, we discuss applications of topologically invariant means and almost convergence for thetheory of analytic functions on the half plane.
12 寺 江 拓 海 (東工大情報理工)室 伏 俊 明 (東工大情報理工)(Tokyo Tech)
Takumi Terae
Toshiaki Murofushi (Tokyo Tech)

非加法的測度論における歪測度の上限増分の一致条件 · · · · · · · · · · · · · · · 15

An equality condition for supremum increments of distorted measuresin non-additive measure theory

概 要 In non-additive measure theory, there exist two definitions of null sets, which are weak null sets andstrong null sets. Several theorems in measure theory such as the Egoroff theorem and the Lebesgue theorem
are described by using the concept of null sets, therefore there exist weak forms and strong forms of these
theorems as definitions in non-additive measure theory. The concept of supremum increment is importantfor studying about the strong forms of them. This paper has an argument that gives a necessary andsufficient condition for two different distorted measures having an equal supremum increment for a simple
case. In addition, we define the concept of strong supremum increments in preparation for generalizing thisargument.
13 岡 崎 悦 明 (ファジィシステム研)
福 田 亮 治 ( 大 分 大 理 工)
本 田 あ お い ( 九 工 大 情 報 工)
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)(Oita Univ.)
Ryoji Fukuda(
Aoi Honda Kyushu Inst. of Tech.)

非加法的測度の定める集合環上の Fréchet–Nikodym 一様位相 · · · · · · · · · 15Fréchet–Nikodym uniformity on a ring determined by a non-additive
measure概 要 Fréchet–Nikodym difference on a measure ring R determined by a non-additive measure µ is definedby µ(A

B). We prove that if µ is quasi-monotone and satisfies (p.g.p)-condition, then the entourages{(A, B) | µ(AB) ≤ ϵ}, ϵ > 0 is a basis of entourages of a uniform structure on the measure ring R.

15:40〜16:40

2022 年度 (第 21 回) 日本数学会解析学賞受賞特別講演
中 井 英 一 (茨 城 大 理) 平均振動量が一様でないカンパナト空間とそれに関連する話題

Eiichi Nakai(Ibaraki Univ.)

Generalized Campanato spaces with variable growth condition and related topics

概 要 Generalized Campanato spaces with variable growth condition were introduced by Nakai and Yabuta

in 1985 to characterize the space of pointwise multipliers on BMO(Rn ). This characterization was extended
from Rn to spaces of homogeneous type in 1997, to probability spaces with filtration in 2014, and, to Rn
with non-doubling measures in 2018. On the other hand, this characterization was used by Lerner in 2005
to study the class P(Rn ) of functions p(·) for which the Hardy-Littlewood maximal operator is bounded on
the Lebesgue spaces Lp(·) (Rn ) with variable exponent, and positively solve a conjecture of Deining in 2005
saying that there are discontinuous functions belonging to P(Rn ). Moreover, in 2012 it was discovered by
Nakai and Sawano that the dual of generalized Hardy space H p(·) (Rn ) with variable exponent is a generalizedCampanato space with variable growth condition. In this talk we discuss generalized Campanato spaces
with variable growth condition and related topics.

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実函数論

17:00〜18:00
田 中

特別講演
仁 ( 筑 波 技 術 大)Hitoshi Tanaka(Tsukuba Univ. of Tech.)60

2 進立方体解析・2 進直方体解析
Dyadic cubes analysis, dyadic rectangles analysis

概 要 After reviewing a history of the dyadic cubes analysis, with rectangular doubling weight, a generalized

Hardy–Littlewood–Sobolev inequality for rectangular fractional integral operators is verified. The result isa nice application of M -linear embedding theorem for dyadic ractangles.

3 月 18 日（土）第 V 会場

9:00〜12:00
14 赤 木 剛 朗 (東 北 大 理)
中 島 慶 人 ( 東 北 大 理)
(Tohoku Univ.)
Goro Akagi
Yoshihito Nakajima (Tohoku Univ.)

非整数階時間微分を含む発展方程式の可解性とその応用 · · · · · · · · · · · · · 15

Solvability of evolution equations involving time-fractional derivatives
and applications

概 要 This talk is concerned with local and global in time solvability of abstract evolution equations

involving time-fractional derivatives as well as subdifferential operators. An application to the initialboundary value problem for degenerate parabolic equations involving time-fractional derivatives as well as
blow-up nonlinearity will also be discussed.
15 喜 多 航 佑 (早 大 理 工)
大 谷 光 春 ( 早 大 理 工)
Kosuke Kita (Waseda Univ.)Ôtani Mitsuharu (Waseda Univ.)

Mosco convergence of functionals associated with Laplacian under nonlinear boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Mosco convergence of functionals associated with Laplacian under nonlinear boundary conditions

概 要 This talk is devoted to studying the convergence of functionals associated with Laplacian under

nonlinear boundary conditions and the asymptotic behavior of solutions to nonlinear evolution equations
governed by subdifferential operators of the functionals. To be more precise, we show the continuous
dependence of the solution on the power of the nonlinear term of boundary conditions. The proof is basedon some modifications of the argument of Mosco convergence by Attouch.

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61

実函数論

16 黒 田 隆 徳 (早 大 理 工)
大 谷 光 春 ( 早 大 理 工)

Takanori Kuroda (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

Asymptotic behaviors of complex solutions for the semilinear heat equation with arbitrarily large initial energy · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic behaviors of complex solutions for the semilinear heat equation with arbitrarily large initial energy

概 要 In this talk, we consider the semilinear heat equation (P):ut − ∆u − |u|q−2 u = 0,u(0) = u0

and the semilinear elliptic equation (E), which corresponds to the stationary problem of (P):−∆u − |u|q−2 u = 0,
with the hohogeneous Dirichlet boundary condition in bounded domains Ω ⊂ RN , (N ≥ 3) which areradially symmetric with respect to the first two variables. We seek solutions which takes complex values ofthe following form:uk (x1 , x2 , x̃) = eikθ vk (r, x̃),

(x1 , x2 , x̃) = (r cos θ, r sin θ, x̃) ∈ Ω,k ∈ N.

We show the energy of solutions uk of (E) tends to infinity as k → ∞. Making use of this fact, for initial
data of arbitrarily large energy, we construct two kinds of sets, i.e., stable set W and blow-up set V suchthat if u0 ∈ W (resp. u0 ∈ V ), then u can be continued globally up to (0, ∞) (resp. u blows up in finitetime).
17 小 波 津 晶 平 (東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

Shohei Kohatsu (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Behavior of weak solutions to a Keller–Segel system with gradient dependent chemotactic coefficient · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Behavior of weak solutions to a Keller–Segel system with gradient dependent chemotactic coefficient

概 要 We consider behavior of weak solutions to a Keller–Segel system with gradient dependent chemotactic

coefficient:u = ∆u − χ∇ · (u|∇v|p−2 ∇v),tv = ∆v − v + u,twhere χ > 0, p ∈ (1, ∞).
18 千 代 祐 太 朗 (東 京 理 大 理)

Boundedness and stabilization in a quasilinear attraction-repulsion chemotaxis system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yutaro Chiyo (Tokyo Univ. of Sci.)

Boundedness and stabilization in a quasilinear attraction-repulsion chemotaxis system

概 要 This talk deals with a quasilinear parabolic–parabolic–elliptic attraction-repulsion chemotaxis system.

In the case that the second equation is simplified by the elliptic one, boundedness and stabilization havealready been obtained. The purpose of this talk is to derive boundedness and stabilization in the case thatthe second equation is parabolic.

最終版: 2023/2/17
実函数論(Paderborn Univ.)
19 T. Black
M. Fuest(Leibniz Univ. Hannover)J. Lankeit(Leibniz Univ. Hannover)
水 上 雅 昭 ( 京 都 教 育 大)

Tobias Black (Paderborn Univ.)
Mario Fuest (Leibniz Univ. Hannover)
Johannes Lankeit(Leibniz Univ. Hannover)
Masaaki Mizukami(Kyoto Univ. of Edu.)

62

Possible points of blow-up in a chemotaxis system with environmental
dependent logistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Possible points of blow-up in a chemotaxis system with environmental
dependent logistic source

概 要 We discuss the influence of possible spatial inhomogeneities in the coeffcients of logistic source terms

in parabolic–elliptic chemotaxis-growth systems in two-dimensional smoothly bounded domains. Assumingthat the coeffcient functions is nonnegative, we prove that finite-time blow-up of the classical solution can
only occur in points where the coefficient function is zero.
20 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
Takeshi Fukao (Kyoto Univ. of Edu.)

仮似変分不等式で記述される塑弾性モデルについて · · · · · · · · · · · · · · · · · 15

A quasi-variational inequality in plasticity model

概 要 This paper discusses the a quasi-variational inequality in plasticity model. In phys- ical terms, it isnatural that the threshold function depends on some unknown variable. This model is expected to describe
plastic deformation due to the time-nonlocal depen- dence of the constraint on the unknown function. Thisis a difference from the perfect plasticity model. To prove the existence of a solution of the plastity model,
Banach fixed point theorem is applied, taking care to choose the test function.
21 森 村 晃 子 (日 本 女 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)
Akiko Morimura(Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

多孔質媒体における水分移動モデルの解の存在と一意性について · · · · · · 15

On existence and uniqueness of solutions to the moisture transportmodel in porous materials

概 要 We consider the initial-boundary value problems for nonlinear parabolic equations describing mois-

ture transport in a porous material occupying a one-dimensional interval. Our problem is obtained bysimplification of the model proposed by Green, Dabiri and Weinaug. Precisely, their system consists of two
equations corresponding to conservation law for water in air and liquid regions, and in our problem thewater distribution in air is given. The unknown function of the problem indicates the chemical potential ofwater. Also, we approximate the equation which is type of elliptic-parabolic, originally, as a first step inthis research. The aim of this talk is to establish existence and uniqueness of solutions to the approximate
problem by applying the standard fixed-point argument.

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63

実函数論

22 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強解に対する ω 極限集合について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Omega-limit sets for the strong solutions to initial and boundary value
problems for compressible elastic curves

概 要 We talk about omega-limit sets for strong solutions to the initial and boundary value problem for the

beam equation with the viscosity term and the nonlinear stress function having a singularity. Thanks to the
singularity, we obtained the uniform estimate of lower bounds for the strain, and already proved existence
and uniqueness of weak and strong solutions. By effect of the viscosity, it seems to be natural that thesolution converges to the stationary solution. On this conjecture we show existence of a subsequence of theorbit {u(t)|t ≥ 0} such that it converges to a strong solution to the steady problem. We note that similar
result on the weak solutions was reported at the previous meeting.
23 熊 崎 耕 太 (長 崎 大 教 育)
A. Muntean (Karlstads Univ.)

Kota Kumazaki (Nagasaki Univ.)
Adrian Muntean (Karlstads Univ.)

多孔質媒体の湿潤・乾燥現象を表すマルチスケールモデルについて · · · · 15

A multiscale model describing the wetting-drying phenomenon in porous
materials

概 要 In this talk, we propose a multiscale model describing the wetting-drying phenomenon in porous

materials. This model consists of a diffusion equation for the relative humidity distributed in materials
and a free boundary problem describing the wetting-drying process in microscopic pores. We consider
each microscopic pore as a one-dimensional interval and correspond the interval to each point of materials.
In our previous results, for a given relative humidity we showed the well-posedness of the free boundary
problem. In this talk, we impose a governing equation for the relative humidity and discuss the existence
and uniqueness of a locally-in-time solution of this model.
14:15〜16:30
24 水 野 大 樹 (千 葉 大 教 育)白 川
健 ( 千 葉 大 教 育)
(Chiba Univ.)
Daiki Mizuno
Ken Shirakawa (Chiba Univ.)

擬放物型全変動流の適切性と解の正則性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Well-posedness and regularity results for a class of total variation flows
of pseudo-parabolic types

概 要 In this talk, a class of initial-boundary value problems of total variation flows of pseudo-parabolic types

is considered. Total variation flow has been adopted as governing equation of various nonlinear phenomena,such as grain boundary motion, image denoising, and so on. The principal characteristic of our problem
is in the velocity term of diffusion flux, and the velocity would bring stronger regularity that that as instandard parabolic PDE. Meanwhile, our total variation flow contains singular diffusion, and the singularity
would degenerate the regularity of solution. The objective of this paper will be to clarify the power balance
between these conflicted effects. Consequently, the mathematical results concerned with well-posedness andregularity of solution will be discussed in the Main Theorems of this talk.
25 久 保 田 翔 大 (神 奈 川 大 工)

Shodai Kubota (Kanagawa Univ.)

結晶粒界運動を記述する Warren–Kobayashi–Lobkovsky–Carter 型シス
テムにおける時間周期解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Periodic solutions for Warren– Kobayashi–Lobkovsky–Carter type systems of grain boundary motions

概 要 In this talk, we consider teh 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 [Warren, etal.; Acta Materialia, 51(20): 6035–6058, 2003]. Under suitable assumptions, the existence of the periodic
solution to the system (S) will be reported as the main theorem of this talk.

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実函数論

26 渡 邉
白 川
S. Moll紘 ( 大 分 大 理 工)
健 ( 千 葉 大 教 育)
( Univ. València )Hiroshi Watanabe (Oita Univ.)
Ken Shirakawa (Chiba Univ.)
Salvador Moll (Univ. València)

64

3 次元結晶粒界運動のフェーズフィールドモデルに対する解の存在 · · · · 15

Existence of solutions to a phase-field model of 3D-grain boundary motion

概 要 We consider a phase-field model of 3D-grain boundary motion. The model is based on the three

dimensional Kobayashi–Warren model for the dynamics of polycrystals. To formulate our 3D-model, we
use a quaternion formulation for the orientation variable. In this talk, we obtain existence of solutions
to the L2 -gradient descent flow of the constrained energy functional via several approximating problems.
Moreover, we also obtain an invariance principle for the orientation variable.
27 深 尾 武 史 (京 都 教 育 大)
( Univ. of Pavia )P. Colli
L. Scarpa(Politecnico di Milano)

Takeshi Fukao (Kyoto Univ. of Edu.)
Pierluigi Colli (Univ. of Pavia)
Luca Scarpa (Politecnico di Milano)

前方後方動的境界条件を持つ Cahn–Hilliard 方程式に対する LW モデル
からの接近 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Cahn–Hilliard system of LW model with forward-backward dynamic boundary condition

概 要 For Cahn–Hilliard equations with forward-backward dynamical boundary conditions, we consider thevanishing viscosity approach from LW model. In the previous study, the approach from GMS model was
discussed. The same idea is used for the LW model. Since the regularity of the solution is lowered in thelimit equations, we define a weak solution using the subdifferential with suitable function spaces. In the
LW model unlike the GMS model, it is subject to the mass conservations at the bulk and the boundary,respectively, which makes some difficulty. In this talk, we will especially introduce the idea of the uniform
estimate.
28 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.)

Approximation of singular optimal control problems for doubly quasivariational evolution inclusions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Approximation of singular optimal control problems for doubly quasivariational evolution inclusions

概 要 In this talk, we establish an approximate procedure for singular optimal control problems for ab-

stract doubly quasi-variational evolution inclusions governed by time-dependent subdifferentials with the
unknown-dependent constraints. Indeed, we consider the parameter-dependent state inclusion and its control problems. Then, we show the relationship between the original control problem and its approximateone.

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65

実函数論

29 伊 藤 昭 夫
Akio Ito

Tumor invasion model with quasi-variational structural porous medium
diffusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Tumor invasion model with quasi-variational structural porous medium
diffusion

概 要 We consider an initial-boundary value problem of a tumor invasion of Chaplain–Anderson type, inwhich the coefficient of random motility of tumor cells depends on the extracellular matrix and the diffusion
flux of tumor cells is porous medium type whose power depends upon the extracellular matrix. Form thesepoints of view, the Cauchy problem considered in this talk has a quasi-variational structure and this fact
makes it more difficult and complicate to analyze this model mathematically. The aim of this talk, we givethe global existence of strong solutions by using the general theory, which was established in the paper,
Evolution inclusion on a real Hilbert space with quasi-variational structure for inner products, Journal ofConvex Analysis, 26 (2019), No. 4, 1185–1252.
30 松 本 敏 隆 (静 岡 大 理)
田 中 直 樹 ( 静 岡 大 理)

Toshitaka Matsumoto (Shizuoka Univ.)
Naoki Tanaka (Shizuoka Univ.)

一般化安定性条件の下での線形発展作用素の生成 · · · · · · · · · · · · · · · · · · · 15

Generation of evolution operators under a generalized stability condition

概 要 A generation theorem of a linear evolution operator on a Banach spaces is given under a generalizedstability condition for a difference scheme. The denseness and the time-independence of the domains ofgenerators are not assumed. A differentiablity theorem of an evolution operator is also given.
17:00〜18:00

特別講演
来 間 俊 介 ( 東 京 理 大 理)

フェーズフィールドシステムに対する時間離散化法

Shunsuke Kurima (Tokyo Univ. of Sci.)

Time discretization methods for phase field systems

概 要 The speaker has studied approaches by time discretization to a phase field system of Caginalp typeand a singular phase field system of conserved type with Pierluigi Colli. The time discretization method isa method of capturing the derivative with respect to time with the limit of the difference quotient, and it
has the advantage that evolution equations can be reduced to stationary problems of elliptic equations. In
this talk, for phase field systems with inertial term which has already been proved to have solutions, we will
confirm if we can apply time discretization methods to show existence of solutions and derive error estimates
for the time step. Also, in this talk, for singular nonlocal phase field systems with inertial term which has
not yet been proved to have solutions, we will show existence of solutions by time discretization methods.

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函数解析学

函

数

解

3 月 15 日（水）

析

66

学

第 VI 会場

9:30〜12:00
1 岩 田 順 敬 (関西大化学生命工)
Yoritaka Iwata (Kansai Univ.)

非有界作用素の対数表現による フォン・ノイマン方程式の一般化 · · · · · 15

Generalization of von Neumann equation based on the logarithmic representation of unbounded operators

概 要 In this paper, by replacing the commutator product by the logarithmic representation of unbounded

operators [1-9], the generalized/unbounded version of von Neumann equation is presented. The proposed
equation is general enough to be valid to bounded situations (i.e., classical mechanics). By taking someconcrete examples in the quantum mechanics, the derivation of generalized von Neumann equation is
explained.
2 渡 辺 秀 司 ( 群 馬 大 理 工)

Shuji Watanabe (Gunma Univ.)

超伝導の BCS ギャップ方程式の新たな作用素論的扱いと 2 次相転移への応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A new operator-theoretical treatment of the BCS gap equation of superconductivity and its application to the second-order phase transition

概 要 We give a new operator-theoretical proof of the existence, uniqueness and smoothness of the solution

to the BCS-Bogoliubov gap equation of superconductivity and apply the results to the second-order phasetransition.
畿大⋆)3 青 木 貴 史 (近葉大⋆)石 村 隆 一 (千岡 田 靖 則 ( 千 葉 大 理)

Takashi Aoki (Kindai Univ.⋆)
Ryuichi Ishimura (Chiba Univ.⋆)
Yasunori Okada (Chiba Univ.)

整関数の空間における連続準同型の微分作用素表示 · · · · · · · · · · · · · · · · · 15

Differential operator representations of continuous homomorphisms onsome spaces of entire functions

概 要 The space of entire functions at most of a given order and of normal type (resp. minimal type) is

endowed with a locally convex topology as an inductive limit (resp. projective limit) of Banach spaces.
Continuous endomorphisms of such spaces include differential operators, translations, dilations, etc., andthey can be represented as formal differential operators of infinite order satisfying suitable conditions. We
consider continuous homomorphisms between spaces of entire functions with growth given by proximate
orders instead of orders, and give their differential operator representations. We also reveal the merits oftreating proximate orders and homomorphisms from the view point of inductive and projective descriptions.
4 廣 島 文 生 ( 九 大 数 理)

Fumio Hiroshima (Kyushu Univ.)

並行移動不変なネルソン模型の正値改良性 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Positivity improving for the translation invariant Nelson model

概 要 Let H(P) be the renormalized Nelson Hamiltonian with total momentum P. We show that exp(-TH(P))

is positivity improving for any P.

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67

函数解析学

5 佐
松
泉
井

々
澤
真
村

木
泰
之
航

格 ( 信 州 大 理)
道 ( 信 州 大 教 育)介 ( 信 州 大 理)
太 (長野県富士見高)

Itaru Sasaki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Shinnosuke Izumi (Shinshu Univ.)
Kota Imura(Nagano Pref. Fujimi High School)

Analyticity of the ground state for the pair interaction model · · · · · · · · 15

Analyticity of the ground state for the pair interaction model

概 要 We consider the pair interaction model which is a models in the quantum field theory. In our previous

work, we diagonalize its Hamiltonian by a Bogoliubov transformation. As a consequence, the existence anduniqueness of the ground states are proven. In addition, the explicit formula for the ground state energy
has been given. In this talk, we show that the ground state and the ground state energy are analytic in the
coupling constant. Their radii of convergence are always finite.
6 吉 田 尚 矢 ( 立 命 館 大 理 工)

Naoya Yoshida (Ritsumeikan Univ.)

Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators

概 要 We consider the eigenvalue problem for self-adjoint Dirac operators. It is known that, near an energy

level where the square of the potential makes a simple well, the eigenvalues are approximated by a Bohr–
Sommerfeld type quantization rule. A remarkable difference from the Schroedinger case appears in the
Maslov correction term. This fact was recently found by Hirota (2017) under the analyticity condition of
the potential using a complex WKB method. In this talk, we approach this problem with a microlocal
technique focusing on the asymptotic behavior of the eigenfunction along the characteristic set to generalize
the result to smooth potentials.
7 板 倉 恭 平 ( 東 大 数 理)

Kyohei Itakura (Univ. of Tokyo)

On resonances for inverted harmonic oscillators · · · · · · · · · · · · · · · · · · · · 15
On resonances for inverted harmonic oscillators

概 要 We characterize resonance free domain for semiclassical inverted harmonic oscillators by employing

method of Briet–Combes–Duclos. For fixed non-zero energy E, we assume a certain non-trapping condition;
the whole domain can be split into the classically forbidden region and region where virial is bounded bynegative constant from above. Then we obtain the absence of resonances in a complex neighborhood of E.
8 宇 治 野 広 大 ( 九 大 数 理)
Kota Ujino(Kyushu Univ.)

Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree

概 要 It is known that Schroedinger operators with sparse potentials have singular continuous spectrum.

The graph Laplacian on a sparse tree is identified with one-dimensional discrete Schroedinger operators, andhas singular continuous spectrum. The intermittency function describes the behavior of the time averaged
momentum and gives the upper bound of the Hausdorff dimension of the spectral measure. We show theintermittency function explicitly and give the Hausdorff dimension of the spectral measure for the graphLaplacian on a sparse tree.

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函数解析学

68

9 宇 治 野 広 大 ( 九 大 数 理)

No eigenvectors embedded in the singular continuous spectrum of Schrödinger
operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

(Kyushu Univ.)

No eigenvectors embedded in the singular continuous spectrum of Schrödinger
operators

Kota Ujino

概 要 It is known that the spectrum of Schrödinger operators with sparse potentials consists of singular

continuous spectrum. We give a sufficient condition so that the edge of the singular continuous spectrum
is not an eigenvalue and construct examples with singular continuous spectrum which have no eigenvalues
and which have a single negative eigenvalue.
14:15〜16:15
10 柳 下 浩 紀 (京 都 産 大 理) ♭ 無限次元空間 R∞ 上の Laplace 作用素の変分法的定式化と自己共役性 · · 10

Hiroki Yagisita (Kyoto Sangyo Univ.)

Variational formulation and self-adjointness of Laplace operator in infinite dimensional space R∞

概 要 In a variational method like Lax–Milgram theorem, we define Laplacian on the infinite direct productspace R∞ :=Qn∈N R and show that it is a self-adjoint operator.

Here, the most important thing is to define

Hilbert space that corresponds to Sobolev space H 1 (R∞ ). To do it, we use square root of density introducedby Hormander in context of Fourier integral operator theory. However, here, we use a measure-theoretic
method rather than a geometric method to give a very elementary introduction at least for analyst (inspiredby statistical interpretation of quantum mechanical wave function by Born and Heisenberg) of square rootof density. All in all, only basic knowledge of analysis (as it is quite possible to study undergraduate) is
required.
11 柳 下 浩 紀 (京 都 産 大 理) ♭ R∞ 上の無限次元干渉 Brown 運動に関する解析的半群 · · · · · · · · · · · · · · · 5

Hiroki Yagisita (Kyoto Sangyo Univ.)

Analytic semigroup of infinite dimensional interacting Brownian motion
on R∞

概 要 We define the generator of a holomorphic semigroup for a countably infinite interacting BrownianQ
particle system on a countable direct product space R∞ := n∈N R as a maximal monotone self-adjointP∞
operator k=1 ((− ∂x∂ k + Hk )( ∂x∂ k + Hk )). At first glance, this may seem like a pretty difficult problem, but
it is not too difficult because ∂x∂ k on R∞ can be defined as just a (generalized) partial derivative. The mostimportant thing is to define a H-partial derivative ∂H,k := ∂x∂ k + Hk as a closed operator for a sequence∞{Hk }∞
k=1 of measurable functions whose domain are measurable “subsets” of R . As with the previous

talk, only basic knowledge of analysis (and part of the previous talk) is required.
12 望 月清 (中大理工・都立大⋆)中 澤 秀 夫 ( 日 本 医 大)Kiyoshi Mochizuki(Chuo Univ./Tokyo Metro. Univ.⋆)
Hideo Nakazawa(Nippon Medical School)

摩擦項をもつ磁場中の波動方程式に対する極限振幅の原理 · · · · · · · · · · · 15

The principle of limiting amplitude for dissipative wave equations inmagnetic fields

概 要 The dissipative wave propagation problem with magnetic Laplacian in an exterior domain is consid-

ered.The uniform estimates and Hölder conditions of the resolvent are studied for the reduced wave operator
without dissipation. Based on these results, the validity of the principle of limiting amplitude is proved forwave propagation problem with dissipation. As byproduct, the result by Mizohata–Mochizuki in 1966 are
improved.

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69

函数解析学

13 大 屋 博 一 (サレジオ工高専)

Hirokazu Ohya (Salesian Polytech.)

指数関数を重みにもつ ソボレフ空間の埋め込みに関する一考察 · · · · · · · 15

Embedding properties for some Weighted Sobolev spaces with growing
weight概 要 In this talk we are concerned with the embedding properties for several kind of functional spaces in

RN . We will consider the functional spaces called as Weighted Sobolev space with some weight function. If
we choose some suitable growing functions in the weight functions, we can derive the continuity and compact
embedding for these functional spaces. We also obtain the sufficient conditions for the weight functions toshow the above properties. Our method is mainly owed to usual Sobolev’s inequality.
14 樋 口 健 太 (愛 媛 大 理 工)
渡 部 拓 也 ( 立 命 館 大 理 工)
Kenta Higuchi (Ehime Univ.)
Takuya Watanabe (Ritsumeikan Univ.)

複数の接触交差が生成する小さな擬交差間の 2 準位断熱遷移確率 · · · · · · 15

Two-level adiabatic transition probability for small avoided crossings
generated by tangential intersections

概 要 We consider a first order ordinary differential system with two small parameters, which are an

adiabatic parameter and an interaction one. This system is a model of a time-dependent Schrödinger
equation which describes that two energy-levels with tangential intersections avoid crossings. In this talk,we give asymptotic expansion of the transition probability between avoided crossings as two parameters
tend to zero as well as their ratio determined by the tangential order does.
15 宮 西 吉 久 (信 州 大 理)

Yoshihisa Miyanishi (Shinshu Univ.)

薄型領域におけるノイマン・ポアンカレ作用素のスペクトル · · · · · · · · · · 10

Spectrum of the Neumann–Poincaré operator on thin domains

概 要 The Neumann–Poincaré operator (abbreviated by NP) is a boundary integral linear operator known

as one of the important tools associated with boundary value problems in the field of partial differential
equations. Our purpose here is to introduce the spectral structure of the NP operator. In an asymptotic
sense, the NP spectrum distributed in the interval [-1/2, 1/2) as the domains become longer in 2D. In an
asymptotic sense, we also find that the NP spectrum densely distributed in the interval [-1/2, 1/2) (resp.
[0, 1/2)), as the domains which are defined by spheroids become flatter (resp. longer) in 3D.
16 穴 原 義 弘 (横浜国大先進実践)
今 野 紀 雄 ( 横 浜 国 大 工)
森 岡
悠 ( 愛 媛 大 理 工)
瀬 川 悦 生 (横浜国大環境情報)
Yoshihiro Anahara(Yokohama Nat. Univ.)
Norio Konno (Yokohama Nat. Univ.)
Morioka Hisashi (Ehime Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

流出入を伴う 1 次元格子上量子ウォークの極限定理 · · · · · · · · · · · · · · · · · 15

Limit theorem for quantum walk on one dimensional lattice with inflows
and outflows

概 要 To obtain a stationary state of quantum walks on the finite path, we set the sink and source to theboundaries of the path so that the internal path receives the inflow and raditas the outflow at every time
step. In this talk we consider one dimensional lattice as finite graph and we show the weak convergence
theorem for the scaled limit distribution of the comfortability in the limit of the length of the path.

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函数解析学

17 樋 口 健 太 (愛 媛 大 理 工)
森 岡
悠 ( 愛 媛 大 理 工)
瀬 川 悦 生 (横浜国大環境情報)
Kenta Higuchi (Ehime Univ.)
Hisashi Morioka (Ehime Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

70

Resonance expansion for finitely perturbed free quantum walks on theline · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Resonance expansion for finitely perturbed free quantum walks on theline

概 要 We introduce resonances to a class of quantum walks on the line as poles inside the unit circle of theoutgoing resolvent. With each resonance, a resonant state which behaves like an eigenvector is associated.
We show that the time evolution with an initial state with compact incoming support exactly coincides
with the evolution of a sum of resonant states in each compact set after a finite length of time has passed.
Consequently, the exponential decay rate of the time evolution is given by the modulus of resonances. We
note that in the special case where a resonance is algebraically multiple, the decay becomes polynomiallyslower.
16:30〜17:30

特別講演
髙 江 洲 俊 光 ( 群 馬 大 理 工)

相互作用する場の量子論の系のスペクトル解析について

Toshimitsu Takaesu (Gunma Univ.)

On the spectral analysis of interacting quantum field systems

概 要 In this talk, interacting systems of quantum field models are investigated. We mainly consider thesystem of quantum electrodynamics, which is the interaction system of a Dirac field and the radiation fieldin the Coulomb gauge, but the Yukawa model and ϕ4 model are also considered. By introducing momentum
and spatial cutoffs, the Hamiltonians are self-adjoint operators on a Hilbert space. Focusing on groundstates, the spectral analysis of these systems will be explained.

3 月 16 日（木）第 VI 会場

9:30〜12:00
18 里 見 貴 志 (東 大 数 理)

Takashi Satomi (Univ. of Tokyo)

ユニモジュラー局所コンパクト群上の畳み込みと再配分に関する不等式と関連する不等式の最適定数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Inequality for the convolutions on unimodular locally compact groups
and the optimal constant of related inequalities

概 要 Let µ be the Haar measure of a unimodular locally compact group G and m(G) be the infimum of theRRvolumes of all open subgroups of G. The main result is that G f ◦ (ϕ1 ∗ ϕ2 ) (g) dg ≤ R f ◦ (ϕ∗1 ∗ ϕ∗2 ) (x) dx
holds for any measurable functions ϕ1 , ϕ2 : G → R≥0 with µ(supp ϕ1 ) + µ(supp ϕ2 ) ≤ m(G) and any convex
function f : R≥0 → R with f (0) = 0. Here ϕ∗ is the rearrangement of ϕ.

Let YO (P, G) and YR (P, G) denote the optimal constants of Young’s and the reverse Young’s inequality,
respectively, on G for the pair of the exponents P = (p1 , p2 ) under the assumption µ(supp ϕ1 )+µ(supp ϕ2 ) ≤m(G). Then we have YO (P, G) ≤ YO (P, R) and YR (P, G) ≥ YR (P, R) as a corollary of the main result.
Thus, we obtain that m(G) = ∞ holds if and only if H(p, G) ≤ H(p, R) in the case of p′ := p/(p − 1) ∈ 2Z,
where H(p, G) is the optimal constant of the Hausdorff–Young inequality on G for the exponent p.

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71

函数解析学

19 久 保 利 久 (龍 谷 大 経 済)

Toshihisa Kubo (Ryukoku Univ.)

On the standardness of homomorphisms between generalized Vermamodules for sl(3, C) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the standardness of homomorphisms between generalized Vermamodules for sl(3, C)

概 要 Let g be a finite dimensional complex simple Lie algebra and b a Borel subalgebra. Let p ⊃ b bea standard parabolic subalgebra. In 1977, Lepowsky showed that a homomorphism φ : Mb (ν) → Mb (ζ)
between Verma modules induces a map φstd : Mp (ν) → Mp (ζ) between the corresponding generalized Vermamodules, provided that ν and ζ satisfy a certain integral condition. He called such a map φstd standard.
It was also observed that the standard map φstd could be zero and even in the case there could be a
non-zero homomorphism φnonstd : Mp (ν) → Mp (ζ). Any map that is not standard is called non-standard.
The classification of standard/non-standard maps is still an open problem.
In this talk, for g = sl(3, C) with a maximal parabolic subalgebra p, we shall show that all non-zero
homomorphisms ψ : Mp (ν) → Mp (ζ), where Mp (ζ) is of scalar type, are standard.
20 織 田寛 ( 拓 殖 大 工)Hiroshi Oda (Takushoku Univ.)

BC 型 Opdam–Cherednik 変換の逆変換公式 · · · · · · · · · · · · · · · · · · · · · · · 15
Inversion formula for Opdam–Cherednik transform associated with aroot system of type BC

概 要 We give the inversion formula and the Plancherel formula for Opdam–Cherednik transform associatedwith a root system of type BC, when the multiplicity parameters are not necessarily nonnegative.
21 貝 塚 公 一 (日 本 医 大)Koichi Kaizuka(Nippon Medical School)

Some remarks on the Dirac operator on symmetric spaces · · · · · · · · · · · 15
Some remarks on the Dirac operator on symmetric spaces

概 要 We develop the spectral analysis for the Dirac operator on symmetric spaces of noncompact typebased on harmonic analysis on Lie groups. In this talk, we compute the continuous spectrum of the Dirac
operator on irreducible symmetric spaces of noncompact type. We show that the continuous spectrum hasa spectral gap if and only if the symmetric space is isomorphic to a coset space of the special pseudo-unitarygroup of odd matrix size. Furthermore, we give a uniform weighted resolvent estimate for the Dirac operator
under a certain assumption on the symmetric space.
22 中 濱 良 祐(NTT 基礎数学研究センタ)
Ryosuke Nakahama(NTT Inst. for Funda. Math.)

Computation of weighted Bergman inner products on block off-diagonal
matrices in bounded symmetric domains for Sp(2r, R) · · · · · · · · · · · · · · 15
Computation of weighted Bergman inner products on block off-diagonal
matrices in bounded symmetric domains for Sp(2r, R)

概 要 Let (G, G1 ) = (G, (Gσ )0 ) be a symmetric pair of holomorphic type, and we consider a pair of Hermitiansymmetric spaces D1 = G1 /K1 ⊂ D = G/K, realized as bounded symmetric domains in complex vector
e of G acts unitarily on thespaces p+ := (p+ )σ ⊂ p+ respectively. Then the universal covering group G
1weighted Bergman space Hλ (D) ⊂ O(D) = Oλ (D) on D for sufficiently large λ. Its restriction to thee 1 decomposes discretely and multiplicity-freely, and its branching law is given in terms of thesubgroup G
e 1 -decomposition of the space P(p+ ) of polynomials on p+ := (p+ )−σ ⊂ p+ . Our goal is to understand theK22
e 1 -typedecomposition of the restriction Hλ (D)|Ge1 by studying the weighted Bergman inner product on each K
in P(p+2 ) ⊂ Hλ (D). Today we deal with the symmetric pair (G, G1 ) = (Sp(2r, R), Sp(r, R) × Sp(r, R)).

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函数解析学

23 田 中 雄 一 郎 (東 大 数 理)

Yuichiro Tanaka (Univ. of Tokyo)

72

無重複性のユニタリトリックについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A unitary trick for the multiplicity-freeness property

概 要 With the aim of uniform treatment of multiplicity-free representations of Lie groups including infinite-

dimensional representations, T. Kobayashi introduced the notion of visible actions on complex manifolds. In
this talk I would like to show a trick for obtaining the multiplicity-freeness property of infinite-dimensional
representations of real semisimple Lie groups from that of finite-dimensional ones of compact Lie groups
through visible actions on flag varieties.
24 V. Pérez-Valdés (東 大 数 理)

Vı́ctor Pérez-Valdés (Univ. of Tokyo)

3 次元球面上のベクトル束から 2 次元球面上の直線束への共形同変な微分
対称性破れ作用素の構成と分類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Construction and classification of conformally equivariant differential
symmetry breaking operators from a vector bundle over S 3 to a line
bundle over S 2

概 要 In this talk, we explain about the construction and classification problems of all differential symmetry

breaking operators D : C ∞ (S 3 , Vλ2N +1 ) → C ∞ (S 2 , Lm,ν ) between the section spaces of Vλ2N +1 → S 3 , a rank
2N + 1 vector bundle over S 3 , and Lm,ν → S 2 , a line bundle over S 2 .
25 中 島 秀 斗 (統 計 数 理 研)

Hideto Nakashima (Inst. of Stat. Math.)

等質開凸錐に付随するゼータ関数のガンマ行列の分解定理 · · · · · · · · · · · 15

Decomposition formulas for gamma matrices of zeta functions associatedwith homogeneous cones

概 要 Associated with homogeneous cones, we are able to construct solvable prehomogeneous vector spaces.

In the previous paper, we calculate gamma matrices of the associated zeta functions explicitly. In this talk,we show that the gamma matrices can be decomposed into variable-wise matrices. Moreover, under suitablecondition, we show that the associated zeta functions admit a kind of completion forms.
13:10〜14:10 特別講演
橋 本 隆 司(鳥取大教育支援・国際交流推進機構)

Takashi Hashimoto (Tottori Univ.)

シンプレクティック・ベクトル空間上の運動量写像の量子化と極小表現

Qunatization of the moment map on symplectic vector spaces and minimal representation

概 要 Let G be Sp(n, R), U(p, q), or O∗ (2n), which acts on a symplectic vector space W in a Hamiltonian

way with moment map µ. The purpose of this talk is twofold: the first one is to show that the canonicalquantization of µ with a choice of a Lagrangian subspace of W provides the oscillator representations of G,
which have been extensively studied in relation to the Howe duality and to minimal representations. The
second one is to construct the minimal representation of O(p, q) by applying this method to O(p, q) andusing the fact that (O(p, q), SL2 (R)) is a Howe’s dual pair.

3 月 17 日（金）9:30〜12:00
26 大 井 志 穂 (新 潟 大 理)
Shiho Oi

(Niigata Univ.)

第 VI 会場

行列値リプシッツ環上の全射線形等距離写像の代数的反射性 · · · · · · · · · · 15

Algebraic reflexivity of isometry groups of Lipschitz algebras

概 要 We consider Banach algebras of Lipschitz maps taking the values in a Banach algebra of complex

matrices of degree n. The unital subjective linear isometries on the Banach algebras have been obtained.
In this talk, we study the algebraic reflexivity of the set of subjective linear isometries. The subset S of
the set of all bounded linear operators from A1 into A2 is called algebraically reflexive if a bounded linear
operator T : A1 → A2 which satisfies T a ∈ Sa for every a ∈ A1 implies T ∈ S. We show the set of unitalsubjective linear isometries is algebraic reflexivity.

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73

函数解析学

27 榎 並 優 太 (新 潟 大 自 然)
三 浦
毅 ( 新 潟 大 理)
(Niigata Univ.)
Yuta Enami(
Takeshi Miura Niigata Univ.)

Surjective isometries on the Banach algebra of analytic functions with
C n -boundary values · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Surjective isometries on the Banach algebra of analytic functions with
C n -boundary values

概 要 Let D, D and T be the open unit disk, closed unit disk and unit circle in the complex plane C. The

disk algebra A(D) is the algebra of all continuous functions on D that is holomorphic in D. We consider thesubalgebra An (D) consisting of all f ∈ A(D) whose restrictions f |T are of class C n . For each f ∈ An (D),
we denote by Dk (f ) the k-th derivative of f |T . The algebra An (D) is a Banach algebra, with the normPnkkf kΣ =
k=0 kD (f )k∞ /k!, where kgk∞ = supz∈T |g(z)|. We characterized surjective, not necessarily
linear, isometries on An (D) with respect to the norm k · kΣ .
28 三 浦毅 ( 新 潟 大 理)
廣 田 大 輔 ( 新 潟 大 自 然)
Takeshi Miura (Niigata Univ.)
Daisuke Hirota (Niigata Univ.)

Tingley’s problem for uniformly closed function algebras · · · · · · · · · · · · 15
Tingley’s problem for uniformly closed function algebras

概 要 Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces X and Y ,respectively. We shall present a positive answer to Tingley’s problem for A and B. More explicitly, we
prove that every surjective isometry between the unit spheres, S(A) and S(B), of A and B admits anextension to a surjective real linear isometry between whole spaces A and B.
29 佐 野 隆 志 (山 形 大 理) ♭ クラウス行列の固有値分布について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
武 内 和 希 ( 山 形 大 理 工)

Takashi Sano (Yamagata Univ.)
Kazuki Takeuchi (Yamagata Univ.)

Inertia of Kraus matrices

概 要 Let r, p0 , p1 < · · · < pn be positive numbers. We consider the n × n matrix whose (i, j) entry is given

1  pri − pr0 prj − pr0 −. We call this a Kraus matrix associated with tr . We show the inertia of thispi − pj p i − p 0 pj − p 0
Kraus matrix.
as

30 渚

勝
(立命館大理工・千葉大理)

Masaru Nagisa(Ritsumeikan Univ./Chiba Univ.)

行列の p-ノルム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The p-norm of some matrices

概 要 We compute the operator p-norm of some n×n complex matrices, which can be seen as bounded linear



8 1

6

4 9

2


operators on the n-dimensional Banach space ℓp (n). In particular, a p-norm of a matrix A = 3 5




7

which corresponds to a magic square is 15 for any p ∈ [1, ∞].
31 遠 山 宏 明 (前 橋 工 科 大)亀井栄三郎
渡 邉 雅 之 ( 前 橋 工 科 大)Hiroaki Tohyama(Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)Operator inequalities related to Young’s inequality · · · · · · · · · · · · · · · · · 15

Operator inequalities related to Young’s inequality

概 要 In this talk, we show several operator inequalities concerning Young’s inequality by using relative

operator entropies and operator valued α-divergence. One of them is partially a refinement of Young’s
inequality.

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函数解析学

32 山 崎 丈 明 (東 洋 大 理 工)
大 坂 博 幸 ( 立 命 館 大 理 工)

Takeaki Yamazaki (Toyo Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)

74

Limit of iterated induced Aluthge transformations of centered operators· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Limit of iterated induced Aluthge transformations of centered operators

概 要 In this talk, we shall discuss on bounded linear operators on a complex Hilbert space. We will

introduce convergence property of an operator sequence which is generated by iteration of the induced
Aluthge transformation. In this talk, we consider the case of centered operators.
33 大 坂 博 幸 (立 命 館 大 理 工)
(Univ. of Gdanśk)T. Mlynik
M. Marciniak (Univ. of Gdanśk)

Hiroyuki Osaka (Ritsumeikan Univ.)
Tomasz Mlynik (Univ. of Gdanśk)
Marcin Marciniak (Univ. of Gdanśk)

On a class of K-entanglement witnesses · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On a class of K-entanglement witnesses

概 要 Recently, Yang et al.showed that each 2-positive map acting from M3 (C) into itself is decomposable.

It is equivalent to the statement that each PPT state on C3 ⊗ C3 has Schmidt number at most 2. It is a
generalization of Perez–Horodecki criterion which states that each PPT state on C2 ⊗ C2 or C2 ⊗ C3 has
Schmidt rank 1 i.e. is separable. Natural question arises whether the result of Yang at al. stays true for
PPT states on C3 ⊗ C4 . This question can be considered also in higher dimensions. We construct a positive
maps which is suspected for being a counterexample. More generally, we provide a class of positive maps
between matrix algebras whose k-positivity properties can be easily controlled.
34 瀬 尾 祐 貴 (大阪教育大教育)
Yuki Seo (Osaka Kyoiku Univ.)

量子 ♮α -Rényi ダイヴァージェンスのデータ処理不等式について · · · · · · · 15

On data processing inequality for quantum ♮α -Rényi divergences of positive order

概 要 In this talk, we show some fundamental properties of quantum ♮α -Rényi divergences of real order. In

particular, we show that the data processing inequality holds for all α > 0.
14:15〜15:30
35 井 上寛 ( 九 州 産 大 経 済)

Hiroshi Inoue (Kyushu Sangyo Univ.)

An unbounded generalization of Tomita’s observable algebras II · · · · · · 15
An unbounded generalization of Tomita’s observable algebras II

概 要 In a previous talk we tried to build the basic theory of unbounded Tomita’s observable algebras called

T † -algebras which are related to unbounded operator algebras, especially unbounded Tomita–Takesaki
theory, operator algebras on Krein spaces, studies of positive linear functionals on ∗-algebras and so on.
And we defined the notions of regularity, semisimplicity and singularity of T † -algebras and characterized
them. In this talk we shall proceed further studies of T † -algebras and investigate whether a T † -algebra isdecomposable into a regular part and a singular part.
36 伊 藤慧 ( 東 大 数 理)

Kei Ito(Univ. of Tokyo)

複素力学系に付随する C*-環のカルタン部分環 · · · · · · · · · · · · · · · · · · · · · 10

Cartan subalgebras of C*-algebras associated with complex dynamicalsystems概 要 Deaconu and Muhly was defined C ∗ -algebras associated with branched coverings. But their algebraslack information of branch points. Kajiwara and Watatani tried to modify Deaconu–Muhly algebras anddefined C ∗ -algebras associated with complex dynamical systems. Let R be a rational function and J be its
Julia set. It is known that the C ∗ -algebra C(J) of complex-valued continuous functions on J is a Cartan
subalgebra of the Deaconu–Muhly algebra for the dynamical system (J, R), but it was not known whether
C(J) is a Cartan subalgebra of the Kajiwara–Watatani algebra for (J, R) or not. In this talk, I explain that
C(J) may not be a Cartan subalgebra of the Kajiwara–Watatani algebra for (J, R).

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75

函数解析学

37 有 本 諒 也 (京 大 数 理 研)
Ryoya Arimoto (Kyoto Univ.)

On the type of the von Neumann algebra of an open subgroup of the
Neretin group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the type of the von Neumann algebra of an open subgroup of the
Neretin group

概 要 The Neretin group is the totally disconnected locally compact group consisting of almost automor-

phisms of the tree. In 2021, P.-E. Caprace, A. Le Boudec, and N. Matte Bon proved that the Neretin groupis not of type I. We prove that a distinguished open subgroup of the Neretin group is not of type I either.
38 後 藤 聡 史 (上 智 大 理 工)
Satoshi Goto

(Sophia Univ.)

On flat part commuting squares · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On flat part commuting squares

概 要 When a non-degenerate commuting square is given, we can construct a hyperfinite II 1 subfactor

N ⊂ M generated by the tower of the given non-degenerate commuting squares. From the originalcommuting square, we can also construct the flat part commuting squares. If the subfactor N ⊂ M is offinite depth, we will show that the composite connection of the original and the flat part ones (in the senseof N. Sato) produces a subfactor which is isomorphic to N ⊂ M . We also show an application of this result.
15:45〜16:45
渚

特別講演

勝
(立命館大理工・千葉大理)

Masaru Nagisa(Ritsumeikan Univ./Chiba Univ.)

コンパクト環上の非線型トレースとマジョリゼーション

Non-linear traces on the algebra of compact operators and majorization

概 要 We study non-linear traces of Choquet type and Sugeno type on the algebra of compact operators.

They have certain partial additivities. We show that these partial additivities charactererize non-linear
traces of both Choquet type and Sugeno type respectively. There exists a close relation between non-linear
traces of Choquet type and majorization theory. We study trace class operators for non-linear traces of
Choquet type. More generally we discuss Schatten–von Neumann p-class operators for non-linear tracesof Choquet type. We determine when they form Banach spaces. This is an attempt of non-commutative
integration theory for non-linear traces of Choquet type on the algebra of compact operators. We also
consider the triangle inequality for non-linear traces of Sugeno type.

最終版: 2023/2/17
統計数学

統

計

数

3 月 15 日（水）76

学第 VIII 会場

10:00〜11:30
1 久 保 田 直 樹 ( 日 大 理 工)
Naoki Kubota(Nihon Univ.)

フロッグモデルの時間定数におけるリプシッツ型評価 · · · · · · · · · · · · · · · 15

Lipschitz-tiype estimates for the time constant of the frog model

概 要 We consider the frog model on the multidimensional lattice, whose initial configuration is according

to a Bernoulli distribution. The main object of interest is the so-called time constant, which describes the
speed of the spread of frogs. The time constant depends on the parameter of the Bernoulli distribution.
Hence, in this talk, we discuss how the change in the parameter of the Bernoulli distribution affects thetime constant. More precisely, we provide some Lipschitz-type estimates for the time constant.
2 大 井 拓 夢 ( 京 大 数 理 研)
Takumu Ooi(Kyoto Univ.)

Convergence of time-changed α-stable processes by GMC · · · · · · · · · · · 15
Convergence of time-changed α-stable processes by GMC

概 要 We consider Gaussian fields whose covariance kernels are 1-order green functions of d-dimensional

symmetric α-stable processes, Gaussian multiplicative chaos (GMC) and time-changed α-stable processes
by GMC. In the case of both d and α are 2, these are the Gaussian free field, the Liouville measure andthe Liouville Brownian motion, respectively. In this talk, we explain weak convergence of the time-changed
α-stable processes by GMC with Skorokhod’s topology.
3 広 兼 巳 紀 雄 ( 阪 大 基 礎 工)
深 澤 正 彰 ( 阪 大 基 礎 工)
Mikio Hirokane (Osaka Univ.)
Masaaki Fukasawa (Osaka Univ.)

A limit theorem for generalized tempered stable processes and theirquadratic variations with stable index tending to two · · · · · · · · · · · · · · · 15
A limit theorem for generalized tempered stable processes and theirquadratic variations with stable index tending to two

概 要 Motivated by Yoshida’s martingale expansion theory, we study the limit of the joint distribution of amultidimensional Generalized Tempered Stable (GTS) process and its quadratic covariation process when
the stable index tends to two. Under a proper scaling, the GTS processes converges to a Brownian motionthat is a stable process with stable index two. We renormalize their quadratic covariation processes so thatthey have a nondegenerate limit distribution. We show that the limit is a stable process with stable index
one and is independent of the limit Brownian motion of the GTS processes.
4 鈴 木 由 紀 (慶高 橋
弘 (慶田 村 要 造

大

医)

大

商)

(Keio Univ.)
Yuki Suzuki
Hiroshi Takahashi (Keio Univ.)
Yozo Tamura

A diffusion process with a symmetric stable potential on the negativeside in R · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A diffusion process with a symmetric stable potential on the negativeside in R

概 要 We investigate a diffusion process with a symmetric stable potential on the negative side in R. In

the case of a Brownian potential on the negative side, this process was examined by Kawazu, Suzuki andTanaka (2001, 2006). We study a long-time behavior of our process by a different method from theirs. We
use a method based on a theory of bi-generalized diffusion processes studied by Ogura (1989).

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77

統計数学

5 鈴 木 由 紀 (慶Yuki Suzuki

大医)(Keio Univ.)

Limit theorems for a diffusion process with a non-selfsimilar random
potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Limit theorems for a diffusion process with a non-selfsimilar random
potential

概 要 We study a one-dimensional diffusion process with a non-selfsimilar random potential. The type of

the potential is different on the left and the right hand sides of the origin. We show that the long-time
behavior of the process is different from the behaviors of any other previous models.
6 小 川 重 義 ( 立 命 館 大 理 工)

Shigeyoshi Ogawa (Ritsumeikan Univ.)

Another representation of the mean value theorem for noncausal stochastic integrals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Another representation of the mean value theorem for noncausal stochastic integrals

概 要 This is the follow up to the preceding lecture “Mean value theorems for the noncausal stochastic

integral” that was presented at the 2022 annual meeting of Math Society of Japan held in Sappro, in
Octobre 2022. There we showed a basic fact about the validity of a mean value theorem for the noncausal
Rt
stochastic integral, also called ogawa integral, with respect to Brownian motion Wt of the form s f (Xr )d∗ Wr
Rtwhere Xt is an Itô process, We derived formulae of mean value theorem for Itô integral s f (Xr )d0 Wr andRt
for the noncausal integral s f (X̃r )d∗ Wr where X̃t (ø) is a noncausal variation of Xt .
The aim of the present talk is to give an elementary but important comment on the basic result and show
another formula of mean value theorem for each of three cases mentioned above.
14:15〜15:15

特別講演
中 島 秀 太 ( 明 大 理 工)

ファーストパッセージパーコレーションと関連する話題

Shuta Nakajima (Meiji Univ.)

First-passage percolation and its related topics

概 要 In this talk, we discuss recent progress on First-passage percolation (FPP). FPP was originallyintroduced by Hammersley and Welsh as a model of the spread of fluid in a random medium. The model
also can be regarded as a dynamic version of percolation. In FPP, a graph with random weights is given,
and we consider the optimization problem of the passage time between two fixed vertices. The minimum
value is called the first passage time and it represents the time when the fluid reaches from one point to theother. From the viewpoint of an optimization problem, properties of the optimal path that attains minimum
value are also of interest. Over 50 years, many mathematical techniques have been developed to study theseobjects. This talk mainly focuses on the fluctuations and the large deviations of the first passage times,
and the geometric properties of geodesics. We also discuss related models such as the chemical distance.

最終版: 2023/2/17
統計数学

15:30〜16:30
梁

特別講演
松 ( 早 大 教 育)Song Liang(Waseda Univ.)78

ブラウン運動と古典力学系

A mechanical model of Brownian motion

概 要 We provide a connection between Brownian motion and a classical Newton mechanical system.

Brownian motion is a well-known physical phenomenon concerning the erratic motion of a small particle
immersed into a fluid in equilibrium. The physical explanation of Brownian motion is often presented in
the following way: since the massive particle is interacted by a large number of very light environmental
particles, if we could assume that the interactions from each light particle at each time are independent,
then by the central limit theorem for the sums of i.i.d. random variables, this will give in a suitable limit
the Brownian motion. We notice that this assumption of independence can hardly be justified, even ina collision model, because of the possibility of re-collisions. This becomes a more evident and significant
drawback when considering the model of interactions caused by potentials.
In this talk, we consider a mechanical model consisting of a massive particle in an ideal gas, evolved
according to non-random Newton mechanical principles, via interaction potentials. We prove that undercertain conditions, the (position, velocity)-process of the massive particle converges to a diffusion process,when the mass of the environmental particles converges to 0, while the density and the velocities of them
go to infinity promptly. The precise expression of the limiting process is also given.

3 月 16 日（木）第 VIII 会場

10:20〜11:10
7 田 中 晴 喜 (和歌山県立医大)Haruyoshi Tanaka(Wakayama Med. Univ.)

On dimension estimates in nonconformal graph iterated function systems via asymptotic perturbation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On dimension estimates in nonconformal graph iterated function systems via asymptotic perturbation

概 要 We consider infinite graph-directed iterated function systems (GIFSs) whose contraction mappings

are nonconformal. As our main result, we formulate asymptotic perturbations from conformal GIFSs tononconformal GIFSs, and give the asymptotic behaviour of the Hausdorff dimension of the limit set of theperturbed system. We also investigate perturbed self-affine sets as special cases.
8 髙 野 凌 史 ( 阪 大 基 礎 工)
Ryoji Takano(Osaka Univ.)

Large deviation principle for the Lyons–Victoir extension · · · · · · · · · · · 15
Large deviation principle for the Lyons–Victoir extension

概 要 We study the large deviation principle for the Lyons–Victoir extension. The Lyons–Victoir extension

is known as a method to lift a general continuous path of finite p-variation to a geometric q-variation roughpath, where q is grater than p. We use the Lyons–Victoir extension as a method for lifting continuous
stochastic processes to geometric rough paths. The main idea of this study is that by using the Lyons–Victoir
extension, lifting the large deviation principle for continuous stochastic processes to that for geometirc roughpaths. To do so, we will prove the boundedness of the Lyons–Victoir extension map. As consequence of
this, the large deviation principle for rough differential equation driven by the Lyons–Victoir extenstion canbe obtained.

最終版: 2023/2/17

79

統計数学

9 柳 下 浩 紀 (京 都 産 大 理) ♭ 無限次元空間 R∞ 上の Gibbs 測度は, コンパクト空間 (R ∪ {∞})∞ 上の局所性をもつ正則 Dirichlet 形式を定める · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Hiroki Yagisita (Kyoto Sangyo Univ.)

Any Gibbs measure on infinite-dimensional space R∞ defines a regular
Dirichlet form with local property on compact space (R ∪ {∞})∞

概 要 For Gibbs measure µ on R∞ , we consider a classical symmetric form formally denoted ECD (f1 , f2 ) :=µPR

∂f1 ∂f2k∈N R∞ ∂xk ∂xk dµ.

Following, for example, Albeverio, Kondratiev, Rockner, etc., we adopt definition of

Gibbs measure by establishment of integration by parts formula. In our main result, “µ determines a regular
Dirichlet form with local property”, there are no constraints other than that µ is (what we say) Gibbs
measure. It seems that Gibbs measure (as we call it) also includes fairly marginal probability measure inthat it is “spatially spread out”. Note that we see R∞ as a direct product of Riemannian manifolds.
10 中 川 雄 太 (京 大 人 間 環 境)
Yuta Nakagawa (Kyoto Univ.)

ギブス点過程と非正のポテンシャルに関するシュレディンガー作用素の状態密度 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Density of states for Schrödinger operators associated with Gibbs point
processes and nonpositive potentials

概 要 In this talk, we consider the random Schrödinger operator for the potential generated by the nonpositive

single site potential and the points randomly located according to the Gibbs point process for the pairwiseinteraction. We determine the leading term of the asymptotic behavior of the integrated density of states(IDS) for the Schrödinger operator. This IDS vanishes much faster near −∞ than the IDS for the Poisson
point process, of which asymptotic behavior is known.
11:20〜11:50

統計数学分科会総会

3 月 17 日（金）第 VIII 会場

9:50〜11:35
11 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 —差の評価— · · · · · · · · · · · · · · · · · · · · · · 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.
12 藤 田 敏 治 (九 工 大 工)
Toshiharu Fujita(Kyushu Inst. of Tech.)

合流型推移をもつマルコフ決定過程 —乗法型評価— · · · · · · · · · · · · · · · · 10

Markov decision process with converging branch system —Multiplicative
reward system—

概 要 We consider multiplicative reward system on a certain finite-stage stochastic converging decision

process model. Converging decision process has converging transition, which is one of the nonserial branchsystems proposed by Nemhauser. We apply bidecision approach to our model and give a recursive methodby dynamic programming technique.

最終版: 2023/2/17
統計数学

13 高 橋 勇 人 (Random Data Lab.)

Hayato Takahashi (Random Data Lab.)80

Posterior distributions weakly converge to Martin-Löf random parameters · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Posterior distributions weakly converge to Martin-Löf random parameters

概 要 In parametric models estimators that are consistent at all parameters are concerned, while in Bayesmodels those that are consistent at almost all parameters are concerned. The identification of the points
at which the posterior distributions weakly converge constitutes the problem (Diaconis and Freedman
1986). We show that for joint probabilities on complete separable metric spaces, the posterior distributions
are consistent at almost all parameters if and only if the posterior distributions are consistent at MLrandom parameters. Reference: Hayato Takahashi, Bayesian definition of random sequences with respect
to conditional probabilities, preprint
14 高 橋 勇 人 (Random Data Lab.)

Hayato Takahashi (Random Data Lab.)

Some explicit formulae for the distributions of words · · · · · · · · · · · · · · · 15
Some explicit formulae for the distributions of words

概 要 Bassino et al. 2010 and Regnier et al. 1998 showed generating functions of the distributions of words

for all sample sizes. Robin et al. 1999 presented generating functions of the distributions for the return
time of words and demonstrated a recurrence formula for these distributions. These generating functions
are rational functions; except for simple cases, it is difficult to expand them into power series. In thispaper, we study finite-dimensional generating functions of the distributions of nonoverlapping words andsome overlapping words for each fixed sample size, respectively and demonstrate the explicit formulae forthe distributions of words for the Bernoulli models.
15 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 II · · · · · · · · · · · · · · · · · · · 15

Optimality of spanning bipartite block designs II

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 prove that the design matrix of an SBBD
is A-optimal under some conditions.
16 種 市 信 裕 (北 教 大 札 幌)
関 谷 祐 里 ( 北 教 大 釧 路)
Nobuhiro Taneichi(Hokkaido Univ. of Edu.)
Yuri Sekiya (Hokkaido Univ. of Edu.)

多項分布の適合度検定統計量選択の指針とその応用 · · · · · · · · · · · · · · · · · 15

An index for selecting the multinomial goodness-of-fit test statistics andits applications

概 要 For the goodness-of-fit test for a multinomial distribution, we consider phi-divergence family of

goodness-of-fit test statistics. Members of phi-divergence family of statistics all have an equivalent limiting
chi-square distribution under the null hypothesis. We consider a second-order correction term as an index
whether the distribution of statistic is close to the limiting chi-square distribution. We derive important
properties of the index for selecting a phi-divergence goodness-of-fit statistic. We also discuss an applicationof the index to the other kinds of tests.

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81

統計数学

17 栗 田 絵 梨 (東 京 理 大 理)
瀬 尾
隆 ( 東 京 理 大 理)

Eri Kurita (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

多変量歪度を用いた多変量正規性検定統計量の帰無分布について · · · · · · 15

On the null distribution of multivariate normality test statistics using
multivariate skewness

概 要 In this talk, we consider on the null distribution of multivariate normality test statistic using multivari-ate skewness. Although there are several definitions of multivariate skewness and kurtosis, this talk focuseson Mardia’s multivariate skewness and proposes a new chi-square approximation with adjusted degrees of
freedom for the null distribution of the normality test statistic using it. Finally, some simulation results arepresented to investigate the accuracy of the chi-square approximation of the test statistic proposed in thistalk.
14:25〜15:25

特別講演

松 田 孟 留(東大情報理工・理化学研)

行列の縮小推定

Takeru Matsuda(Univ. of Tokyo / RIKEN)

Shrinkage estimation: from vector to matrix

概 要 In the estimation of a normal mean vector under the quadratic loss, the maximum likelihood estimator(MLE) is inadmissible and dominated by shrinkage estimators (e.g. James–Stein estimator) when thedimension is greater than or equal to three (Stein’s paradox). In particular, generalized Bayes estimatorswith respect to superharmonic priors (e.g. Stein’s prior) are minimax and dominate MLE. Note that afunction is said to be superharmonic if its average value on a hypersphere is always not greater than its
value at the center.
In this talk, I will introduce recent studies on generalizations of the above results to matrices. First,
we develop a superharmonic prior for matrices that shrinks singular values, which can be viewed as anatural generalization of Stein’s prior. This prior is motivated from the Efron–Morris estimator, which
is an extension of the James–Stein estimator to matrices. The generalized Bayes estimator with respect
to this prior is minimax and dominates MLE under the Frobenius loss. In particular, since it shrinks
to the space of low-rank matrices, it attains large risk reduction when the unknown matrix is close to
low-rank (e.g. reduced-rank regression). Next, we construct a theory of shrinkage estimation under the“matrix quadratic loss”, which is a matrix-valued loss function suitable for matrix estimation. A notion of“matrix superharmonicity” for matrix-variate functions is introduced and the generalized Bayes estimatorwith respect to a matrix superharmonic prior is shown to be minimax under the matrix quadratic loss. The
matrix-variate improper t-priors are matrix superharmonic and this class includes the above generalizationof Stein’s prior. Applications include matrix completion and nonparametric estimation.
15:40〜16:40

特別講演
上 原 悠 槙 (関西大システム理工)

Information criteria for jump diffusion models(Kansai Univ.)

Information criteria for jump diffusion models

Yuma Uehara

概 要 In this talk, we consider ergodic jump diffusion models with high-frequency observations. We mainly

focus on the model selection problem for the models. More specifically, our interest is to select all drift
and diffusion coefficients, and jump distribution among candidates. For such a problem, the thresholdbased transition density approximation which corresponds to the case where at most one jump occur within
one observation interval is useful. We evaluate such an approximation, and propose explicit AIC-type
information criterion constructed by the threshold based quasi-likelihood function.

最終版: 2023/2/17
統計数学

3 月 18 日（土）82

第 VIII 会場

10:00〜11:10
18 八 木 文 香 (東 京 理 大 理)
尾 﨑 冬 弥 ( 東 京 理 大 理)
瀬 尾
隆 ( 東 京 理 大 理)

Ayaka Yagi (Tokyo Univ. of Sci.)
Toya Ozaki (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

On the test for adequacy in growth curve model with two-step monotone
missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the test for adequacy in growth curve model with two-step monotone
missing data

概 要 We consider the test for adequacy in growth curve model when the data set has a two-step monotone

missing pattern. For the complete data case, to test the adequacy hypothesis, Hotelling’s T 2 statistic
is presented in Fujikoshi, Ulyanov and Shimizu (2010). In this talk, we propose a test statistic for theadequacy hypothesis with two-step monotone missing data based on the above result. Further, we givethe approximation to the upper percentile of this statistic. Finally, we investigate the accuracy of theapproximation by Monte Carlo simulation.
19 小 池 祐 太 (東 大 数 理)
Xiao Fang(Chinese Univ. of Hong Kong)
Yuta Koike (Univ. of Tokyo)
Xiao Fang(Chinese Univ. of Hong Kong)

対数凹な独立同分布確率ベクトルの和に対する高次元中心極限定理 · · · · 15

A high-dimensional central limit theorem for sums of i. i. d log-concave
random vectors

概 要 We consider the problem of bounding the normal approximation error over rectangles for a sum of n

independent d-dimensional random vectors. Here, our aim is to establish such a bound with poly-logarithmic
dependence on the dimension d. It is known that such a bound is available with a nearly n−1/2 convergence
rate when the covariance matrix of the sum is non-degenerate. In this talk, we show that, if the random
vectors are i.i.d. and log-concave, we can derive an error bound with a nearly n−1/2 convergence rate andpoly-log dependence on d without any restriction on the covariance matrix.
20 山 形 浩 一 (国 立 情 報 学 研)
大理)
藤 原 彰 夫 (阪Koichi Yamagata(Nat. Inst. of Informatics)
Akio Fujiwara (Osaka Univ.)

局所漸近正規性を有する量子統計モデルに対する推定量の有効性 · · · · · · 15

Efficiency of estimators for locally asymptotically normal quantum statistical models

概 要 We herein establish an asymptotic representation theorem for locally asymptotically normal quantum

statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators suchas quantum regular estimators and quantum minimax estimators, leading to a universal tight lower boundbeyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in
the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105–2141], providing a solid foundationof the theory of weak quantum local asymptotic normality.

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83

統計数学

21 中 村 慶 太 (東 京 理 大 理 工)
中 川 智 之 ( 東 京 理 大 理 工)
田 畑 耕 治 ( 東 京 理 大 理 工)

Keita Nakamura (Tokyo Univ. of Sci.)
Tomoyuki Nakagawa(Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)

Aitchison 幾何を用いた正方分割表の対称性 · · · · · · · · · · · · · · · · · · · · · · · · 15

Symmetry in square contingency tables using aitchison geometry

概 要 The probability table obtained from a contingency table can be viewed as an element in the simplex.

Symmetric probability tables are identified as a linear subspace using the Aitchison geometry of thesimplex. Given a probability table, we can obtain the closest symmetric table by orthogonal projection
onto the symmetric subspace. The original probability table is decomposed into the symmetric and theskew-symmetric tables that are orthogonal to each other. A procedure to test symmetry of a contingency
table, based on a multinomial simulation, is developed and examples of tests carried out are given.

最終版: 2023/2/17
応用数学

応

用

3 月 15 日（水）9:50〜11:50
1 田 中 優 帆 ( 早 大 理 工)
三 枝 崎 剛 ( 早 大 理 工)
大 浦
学 ( 金 沢 大 理 工)
H. S. Chakraborty(Shahjalal Univ. of Sci. Tech.)Yuho Tanaka (Waseda Univ.)
Tsuyoshi Miezaki (Waseda Univ.)
Manabu Oura (Kanazawa Univ.)
Himadri Shekhar Chakraborty(Shahjalal Univ. of Sci. Tech.)

数

84

学

第 VII 会場

Jacobi 多項式とデザイン理論について · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Jacobi polynomials and design theory

概 要 There are Jacobi polynomials as an analogue to Jacobi forms as a powerful generalization of theta seriesof Lattices. It is a generalization of weight enumerators that M. Ozeki introduced for codes. A. Bonnecaze
et al. constructed various types of designs and did some studies to establish a relationship between Jacobi
polynomials and designs by focusing on weight enumerators, Jacobi polynomials, and the Molien series. In
this talk, we introduce the concept of multiple Jacobi polynomials and give the MacWilliams type duality forthem. We also give generalizations and analogies of some results in their paper. In addition, we introduce
a criterion for the existence of (generalized) designs using Jacobi polynomials.
衛
大)
2 須 田
庄 (防
A. L. Gavrilyuk (島根大総合理工)

Sho Suda (Nat. Defense Acad. of Japan)
Alexander L. Gavrilyuk(Shimane Univ.)

4-(11, 5, 1) デザインに関連するアソシエーション・スキームの一意性 · · 10
Uniqueness of an association scheme related to the 4-(11, 5, 1)-design

概 要 It follows from the Delsarte theory that the Witt 4-(11, 5, 1) design gives rise to a (Q-polynomial)

association scheme W defined on the set of its blocks. In this talk, we observe that W is unique, i.e., defined
up to isomorphism by its parameters.
3 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.)

準巡回符号における LCD 性と反転不変性 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

LCD property and reversiblity in quasi-cyclic codes

概 要 We show a necessary and sufficient condition for which quasi-cyclic codes represented by polynomial

matrices are to be LCD (Linear Complimentary Dual), and using this result, a connection between LCD
quasi-cyclic codes and reversible quasi-cyclic codes is investigated.
4 佐 竹 翔 平 ( 明 大 総 合 数 理)
Hyungrok Jo (横 浜 国 大 IAS)
(Meiji Univ.)
Shohei Satake
Hyungrok Jo (Yokohama Nat. Univ.)

高い内周をもつ弧推移的エクスパンダーグラフ · · · · · · · · · · · · · · · · · · · · · 15

On high-girth arc-transitive expander graphs

概 要 Expander graphs are highly-connected sparse graphs which have fruitful connections to mathematics,

computer science and cryptography. One of the fundamental problems about expander graphs is to constructexplicit high-girth expander graphs, which can be applied for designing cryptographic hash functions, forexample. In this talk we introduce new explicit constructions of high-girth expander graphs that are
arc-transitive.

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85

応用数学

5 藤 田 慎 也
(横浜市大データサイエンス)

Shinya Fujita (Yokohama City Univ.)

Connectivity keeping paths in highly connected graphs · · · · · · · · · · · · · 15
Connectivity keeping paths in highly connected graphs

概 要 Some recent results concerning connectivity keeping paths in highly connected graphs will be reviewed.

6 藤 村

丞

(福岡大情報基盤センター)
白 石 修 二 ( 福 岡 大 理)
Sho Fujimura (Fukuoka Univ.)
Shuji SHIRAISHI (Fukuoka Univ.)

On the generation of all Euler trails for an Eulerian graph with 2n edges· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the generation of all Euler trails for an Eulerian graph with 2n edges

概 要 For an Eulerian graph G with 2n edges, we give a new method of generating all Euler trails in G inparallel efficiently by using 2-chain cover of G.
7 町 出 智 也 ( 国 立 情 報 学 研)
Tomoya Machide(Nat. Inst. of Informatics)

Boolean 多項式の連立方程式の彩色問題への応用 · · · · · · · · · · · · · · · · · · · 15
An application of systems of Boolean polynomial equations to list color
problems

概 要 I will talk an application of systems of Boolean polynomial equations to list color problems, in which

not only vertex-coloring conditions but also edge-coloring conditions are imposed under Grünbaum method.
8 高 橋
正 (甲南大知能情報)
鷲 野 朋 広 (甲南大知能情報)

Tadashi Takahashi (Konan Univ.)
Tomohiro Washino (Konan Univ.)

グレブナー基底を用いた学習モデルにおける補題証明 · · · · · · · · · · · · · · · 10

On the proof of lemma in the learning model using Groebner basis

概 要 We consider the statistical model of three-layer neural network with H hidden units. By using taylor

expansion of activation function , the set of parameters that true density function is realizable by a statisticalmodel is a common zero points defined by finite polynomials. First, in this case H = 2, we calculate equations
define the algebraic set. The algebraic set is the set of parameters that true density function is realizable
by a statistical model with one or zero hidden unit. Next, we determine equations define the algebraic set.
The algebraic set is the set of parameters that true density function is realizable by a statistical model with
H0 < H hidden unit. We prove the lemma in the learning model applying Hilbert’s basis theorem using
Groebner basis.
14:15〜15:25
9 辻 栄 周 平 ( 北 教 大 旭 川)
大
理)
内 海
凌 (北

Shuhei Tsujie (Hokkaido Univ. of Edu.)
Ryo Uchiumi (Hokkaido Univ.)

グラフ埋め込みと辺に付随する互換の積 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Graph embedding and the product of transpositions associated withedges

概 要 Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing

a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the permutation
is a full cyclic permutation for any linear order if and only if the graph is a tree.
In this article, we characterize graphs having a linear order such that the associated permutation is a full
cyclic permutation in terms of graph embeddings.

最終版: 2023/2/17
応用数学

10 山 田 祐 見 (筑波大システム情報)
八 森 正 泰 (筑波大システム情報)
東 谷 章 弘 ( 阪 大 情 報)

Yumi Yamada (Univ. of Tsukuba)
Masahiro Hachimori(Univ. of Tsukuba)
Akihiro Higashitani (Osaka Univ.)86

格子凸多面体の free sum の Ehrhart 多項式の根の分布 · · · · · · · · · · · · · · 15

The root distributions of Ehrhart polynomials of free sums of lattice
polytopes

概 要 In this talk, we study the root distributions of Ehrhart polynomials of free sums of certain lattice

polytopes. We investigate cases where the roots of the Ehrhart polynomials of the free sums of A∗d ’s or
Ad ’s lie on the canonical line Re(z) = −1/2 on the complex plane C, where Ad denotes the root polytopeof type A of dimension d and A∗d denotes its polar dual. For example, it is proved that A∗m ⊕ A∗n withmin{m, n} ≤ 1 or m + n ≤ 7, A∗2 ⊕ (A∗1 )⊕n and A∗3 ⊕ (A∗1 )⊕n for any n satisfy this property.
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.)

行列のスイッチングと付随する単体的複体による歪多項式環の分類 · · · · 15

Classification of skew polynomial algebras by switching of matrices 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 a particular class of skew polynomial rings and discuss whether
the classification of such skew polynomial rings up to equivalence of their graded module categories can bedone by using the switching of matrices and the simplicial complexes associated to switching equivalenceclasses. We prove that we can do it if the sizes of the matrices are relatively small.
12 栗 原 大 武 (山 口 大 創 成)
橋 永 貴 弘 ( 佐 賀 大 教 育)

Hirotake Kurihara (Yamaguchi Univ.)
Takahiro Hashinaga (Saga Univ.)

根付き木を用いた等質ラグランジュ部分代数の構成 · · · · · · · · · · · · · · · · · 15

Construction of homogeneous Lagrangian subalgebras using rooted trees

概 要 In this talk, we consider the construction and classification problems of homogeneous Lagrangiansubmanifolds of the noncompact Hermitian symmetric space M = Sp(n, R)/U(n) of rank n. We give thatrooted trees contribute to the classification of homogeneous Lagrangian submanifolds in M = Sp(n, R)/U(n).
15:45〜16:45

特別講演
野 口 健 太 ( 東 京 理 大 理 工)

Kenta Noguchi (Tokyo Univ. of Sci.)

閉曲面上のグラフ, とくに三角形分割と四角形分割

Graphs on closed surfaces, expressly triangulations and quadrangulations

概 要 Graphs on closed surfaces are widely studied in the literature. We have been interested in and studied

the triangulations and quadrangulations, which are important classes of such graphs. Specifically, we havebeen investigated the relationship between them to reveal their several properties, such as the chromatic
number and the related topics. In this talk, we will present the basic background and some problems, andgive recent results on the extension from a quadrangulation to a triangulation and spanning quadrangulation
subgraphs of triangulations.

最終版: 2023/2/17

87

応用数学

3 月 16 日（木）第 VII 会場

10:00〜11:45
13 佐 藤巖 ( 小 山 工 高 専)
井 手 勇 介 ( 日 大 文 理)
小 松
尭
(産業数理研究所Calc・広島大先進理工)
今 野 紀 雄 ( 横 浜 国 大 工)

Iwao Sato (Oyama Nat. Coll. of Tech.)(Nihon Univ.)
Yusuke Ide
Takashi Komatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Norio Konno (Yokohama Nat. Univ.)

Metzler/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Metzler/Zeta correspondence

概 要 We present an explicit formula for the determinant on the Metzler matrix of a digraph D. Furthermore,

we introduce a walk-type zeta function with respect to this Metzler matrix of the symmetric digraph of afinite torus, and express its limit formula by using the integral expression.
14 佐 藤巖 ( 小 山 工 高 専)
小 松
尭(産業数理研究所Calc・広島大先進理工)
今 野 紀 雄 ( 横 浜 国 大 工)

Iwao Sato (Oyama Nat. Coll. of Tech.)Takashi Kmatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Norio Konno (Yokohama Nat. Univ.)

Alternating walk/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Alternating walk/Zeta correspondence

概 要 We express the alternating zeta function of a graph G by using the Ihara zeta function of G. Next, we

define a generalized alternating zeta function of a graph, and express it of a vertex-transitive regular graphby spectra of the transition probability matrix of the symmetric simple random walk on it and its Laplacian.
Furthermore, we present an integral expression for the limit of the generalized alternating zeta functionsof a series of vertex-transitive regular graphs. As an example, we treat the generalized alternating zetafunctions of a finite torus. Finally, we treat the relation between the Mahler measure and the alternating
zeta function of a graph.
15 穴 原 義 弘 (横浜国大先進実践)
瀬 川 悦 生 (横浜国大環境情報)
森 岡
悠 ( 愛 媛 大 理 工)
Yoshihiro Anahara(Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)
Morioka Hisashi (Ehime Univ.)

流出入を伴う 1 次元格子上量子ウォークの収束速度 · · · · · · · · · · · · · · · · · 15

Convergence speed for quantum walks on one dimensional lattice withinflows and outflows

概 要 For quantum walks on finite graphs whose time evolution is unitary operator, it is difficult to finda stationary state which is not equal to the initial state. We can consider a quantum walk model with astationary state on a connected finite graph by introducing infinite length tails and inserting a quantum
walker into the internal graph at every time step from the tail. In this talk focusing on the finite path as theinternal graph, and also on the spectrum of the truncated submatrix of the unitary time evolution operator
with respect to the internal graph, we estimate a convergence speed to the stationary state.

最終版: 2023/2/17
応用数学

16 成 松 明 廣(福知山公大数理・データサイエンスセンター)
井 手 勇 介 ( 日 大 文 理)
Akihiro Narimatsu(Univ. of Fukuchiyama)(Nihon Univ.)
Yusuke Ide

88

完全状態遷移, グラフの衝平分割と連続時間量子ウォークによる探索アル
ゴリズム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Perfect state transfer, equitable partition and continuous-time quantum
walk based search

概 要 We consider a continuous-time quantum walk based search algorithm. We introduce equitable partitionof the graph and perfect state transfer on it. By these two methods, we can calculate the success probability
and the finding time of the search algorithm. In addition, we gave some examples of graphs that we cancalculate the success probability and the finding time.
17 藪 奥 哲 史 (北 九 州 工 高 専)
蓮 井 太 朗 ( 九 大 数 理)
白 井 朋 之 (九 大 I M I )Satoshi Yabuoku(Kitakyushu Nat. Coll. of Tech.)(Kyushu Univ.)
Taro Hasui
Tomoyuki Shirai (Kyushu Univ.)

Enumeration of connected bipartite graphs with given Betti number · · 15

Enumeration of connected bipartite graphs with given Betti number

概 要 Let G = (V, E) be a simple connected bipartite graph with bipartition V = V1 t V2 , and f (r, s, q)

denote the number of Gs such that |V1 | = r, |V2 | = s and |E| = q. In this talk, we focus on the valuesf (r, s, r + s + k − 1) for given Betti number k. For k = 0, this is the number of spanning trees on Kr,s ,and Scoins proved f (r, s, r + s − 1) = rs−1 sr−1 . By recurrence equation, we obtain the explicit form of
exponential generating functions of f (r, s, r + s + k − 1) for general k, and we derive the asymptotic behaviorof their coefficients. We also give another expression of the generating functions as the summation ofrational functions of those for the number of bipartite rooted spanning trees.
18 山 岸 弘 幸 (都立産業技術高専)
衛大)
渡 辺 宏 太 郎 (防Hiroyuki Yamagishi(Tokyo Metro. Coll. of Ind. Tech.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)

完全グラフに対応する ℓp 離散ソボレフ不等式の最良定数 · · · · · · · · · · · · · 15

The best constant of the discrete ℓp Sobolev inequality on the completegraph

概 要 We assume a classical mechanical model of the complete graph KN with N vertices. We put the Natoms on vertices of KN . Its neighboring two atoms are connected to a linear spring. The spring constantis 1. Let p and q be real numbers satisfying 1/p + 1/q = 1 (p, q > 1). If u(i) takes a real value, then u(i)represents a deviation from the steady state. The discrete ℓp Sobolev inequality shows that the maximumof deviation |u(i)|p is estimated in a constant multiple of the potential energy on KN . Hence, the best
contants represent the rigidity of the mechanical model on KN .
13:00〜14:10
19 盧

暁 南 ( 岐 阜 大 工)

Xiao-Nan Lu(Gifu Univ.)

Covering arrays guaranteeing a passing test · · · · · · · · · · · · · · · · · · · · · · · 15
Covering arrays guaranteeing a passing test

概 要 Covering arrays (CAs) are a kind of combinatorial designs proposed for applications in combinatorial

testing (CT). For adaptive decoding algorithms in CT using CAs, it is required that a passing test should
be contained in the CA. In this talk, a few results on such binary CAs that guarantee at least one passing
test are introduced. In particular, it is shown that for no more than two faulty interactions, the known
optimal construction for binary CAs is good enough. Then, a general sufficient condition for such CAs interms of domination numbers of graphs associated to the CAs is proposed.

最終版: 2023/2/17

89

応用数学

20 斎
出
増
西

藤
明 (日
川 慎 悟 (日田 合 氣 (日田 大 輝 (日Akira Saito
Shingo Degawa
Aiki Masuda
Hiroki Nishida

大 文 理)

安全支配数に関する 2 つの上界 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

大 文 理)
大 文 理)
大 文 理)(Nihon Univ.)(Nihon Univ.)(Nihon Univ.)(Nihon Univ.)

Two upper bounds on secure domination number

概 要 A set of vertices S in a graph G is a dominating set if every v ∈ V (G) − S satisfies NG (v) ∩ S 6= ∅.

A dominating set S is secure if for every v ∈ V (G) − S, there exists x ∈ S such that (S − {x}) ∪ {v}
is a dominating set. The order of a smallest secure dominating set of G is called the secure domination
number of G and denoted by γs (G). In this talk, we report an upper bound γs (G) ≤ 53 |G| for a graph G ofminimum degree at least 2. Then we generalize the notion of a secure dominating set. A dominating set
S = {x1 , . . . , xk } in G is weakly secure if for every v ∈ V (G) − S, there exists yi ∈ NG (xi ) ∪ {xi } for each
i with 1 ≤ i ≤ k such that {y1 , . . . , yk } is a dominating set and v ∈ {y1 , . . . , yk }. The order of a smallest
weakly secure dominating set of G is called the weakly secure domination number and denoted by γws (G).
We report γws (G) ≤ d|G|/2e for every onnected graph G of minimum degree at least 1.
21 吉 田 裕 一 (北 見 工 大 工)
松 田 一 徳 ( 北 見 工 大 工)

Yuichi Yoshida (Kitami Inst. of Tech.)
Kazunori Matsuda(Kitami Inst. of Tech.)

連結単純グラフのマッチングに付随する 3 種の不変量 · · · · · · · · · · · · · · · 15

On the three graph invariants related to matching of finite simple graphs

概 要 We determine the relationship between the matching number,the minimum matching number,theinduced matching number and the number of vertices.
22 R. E. L. Aldred (Univ. of Otago)
大
商)
藤 沢
潤 (慶

Robert E. L. Aldred (Univ. of Otago)(Keio Univ.)
Jun Fujisawa

閉曲面上の三角形分割でない 5-連結グラフにおけるマッチング拡張問題· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Distance restricted matching extension in 5-connected graphs on surfaces which are not triangulation

概 要 In this talk, we show the following result. Let G be a 5-connected graph of even order which is 2-cell

embedded in a surface F 2 with sufficiently
 and let M be a matching of G such that any large face-width,2)+25
two edges in M are at distance at least 2 20 − 12χ(F|M |in the face subdivision G. Then G has a perfectmatching containing M .

3 月 17 日（金）第 VII 会場

9:50〜11:50
23 三 好 啓 也 (埼 玉 大 理 工)

Hironari Miyoshi (Saitama Univ.)

Derivation of Brownian motion from the Goldstein–Taylor model · · · · · 15
Derivation of Brownian motion from the Goldstein–Taylor model

概 要 In this lecture, we consider a random walk associated with the initial value problem of the Goldstein–

Taylor model. First, we show the existence of the solution for a scaled Goldstein–Taylor model by using thecorresponding telegraph equation. Next, we find the probability density function pε (x, t) associated with arandom process of particles for the Goldstein–Taylor model. Finally, we prove that the scaling limit of the
cumulative distribution function for pε (x, t) converges to the Brownian motion in the sense of distributions.

最終版: 2023/2/17
応用数学

24 渡 辺樹 ( 早 大 理 工)

Itsuki Watanabe (Waseda Univ.)90

High-density limit of controlled density-dependent Markov processes · · 15
High-density limit of controlled density-dependent Markov processes

概 要 We consider the high-density type scaling limit of the controlled stochastic model. The stochastic

model can be constructed as a particle system with birth and death events whose transition rate depends
on its density and control. In this talk, we reveal that the scaling limit of this model is governed by thecontrolled stochastic differential equation by showing the relative compactness and using the continuous
mapping theorem.
25 A. Diez
Antoine Diez

(京 大 A S H B i )(Kyoto Univ.)

Scaling limits and emergent phenomena in a system of body-oriented
particles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Scaling limits and emergent phenomena in a system of body-oriented
particles

概 要 Biological phenomena such as the flock of birds or the swarm of bacteria and other active cells revealthat complex self-organized patterns can emerge from active particle systems when the number of particles
becomes very large. In this talk, I will describe a modelling framework based on classical tools developedin the mathematical kinetic theory of gas. The core idea is the derivation of PDE models from stochastic
many-particle systems. I will illustrate these ideas with a system of so-called body-oriented particles andexplain how the behavior of many-particle systems can be inferred by looking at appropriate scaling limits.
In particular, this work demonstrates the influence of stochasticity and geometry on self-organization.
26 長 瀬 准 平(芝浦工大理工・ZOZO Research)
斎 藤 侑 輝 (ZOZO Research)
石 渡 哲 哉
(芝浦工大システム理工)
Jumpei Nagase(Shibaura Inst. of Tech./ZOZO Research)
Yuki Saito (ZOZO Research)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)

階層的な集合を表現する部分置換不変な深層ニューラルネットモデル · · 15

Permutation invariant deep neural network model for representing hierarchical sets

概 要 Deep neural network models, which have been rapidly developing and expanding their range ofapplication in recent years, need to be applied to structured data. Specifically, there is a wide range ofapplications such as face recognition, set matching, and point cloud segmentation. A set data is interpreted
as structured data, and representations of a set data based on permutations equivalence / invarianceproperties are known. In particular, Renhao et al. have made a mathematical discussion of a machinelearning model that satisfies equivalence / invariance for hierarchical group actions by introducing the ideaof Wreath product. In this paper, we focus on the results of Renhao et al. especially for hierarchical set
data, and discuss the representation of hierarchical sets by specifically discussing hierarchical permutationequivalence / invariance.

最終版: 2023/2/17

91

応用数学

27 米 田剛 ( 一 橋 大 経 済)

Tsuyoshi Yoneda (Hitotsubashi Univ.)

深層ニューラルネットワークのミニバッチ勾配降下に対する各点収束定理· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Pointwise convergence theorem of mini-batch gradient descent in termsof deep neural network

概 要 The theoretical understanding of deep neural network (DNN) has not yet been fully understood.

Nevertheless, even in this recent circumstance, Imaizumi-Fukumizu (2019) and Suzuki (2019) clarified thatthe learning ability of DNN is superior to the previous theories when the target function is non-smoothfunctions. In this talk we give a convergence problem in more practical setting. More precisely, we provethat a certain prescribed function pointwisely converges to a step function provided by mini-batch gradientdescent process with ReLU DNN.
28 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 ( 日 立 製 作 所)
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 (Hitachi, Ltd.)(Chuo Univ.)
Kota Ohno

毛包形成の数理モデルの数値計算とその考察 · · · · · · · · · · · · · · · · · · · · · · · 15

Numerical simulations of a mathematical model of hair follicle formation

概 要 As an appendage of the skin, a hair follicle is the source of the hair. Moreover, the hair follicle hasa cylinder-like structure. In this study, we attempt to examine the mechanism of hair follicle formationfrom a mathematical viewpoint by applying a mathematical model of the basement membrane, whichenables us to describe plastic deformation. In this presentation, we will introduce numerical examples ofour mathematical model and discuss what assumptions play an essential role in shaping the cylinder shapeof the hair follicle. If possible, we will also present the numerical results that consider the epithelium,
while previous mathematical models have considered only the basal layer, basement membrane, and dermal
structure.
29 シュワドレンカカレル(京大

構造材料の弾塑性有限変形の変分解析 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
理)

Karel Svadlenka (Kyoto Univ.)

Variational analysis of finite strain elastoplasticity for structured materials

概 要 Structured materials, such as metallic alloys with atomic-scale layers, show peculiar deformation

patterns, which may have significant implications on material properties. In this talk, we discuss one
possible approach to modeling and understanding of this kind of pattern formation through the so-called
rate-independent evolution in the variational setting of finite-strain elastoplasticity. Besides mentioning
connections to homogenization via Gamma-convergence, we present the underlying mathematical theory
and show numerical simulations in comparison to experimental measurements.

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応用数学

14:15〜14:40

922022 年度日本数学会応用数学賞授賞式

14:45〜16:30
30 土 屋 拓 也 (八 戸 工 大)
中 村
誠 ( 阪 大 情 報)
Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Makoto Nakamura (Osaka Univ.)de Sitter 時空中における半線形 Klein–Gordon 方程式の精度と数値安定性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Numerical accuracy and stability of semilinear Klein–Gordon equationin de Sitter spacetime

概 要 The Klein–Gordon equation is known as the fundamental wave equation in relativistic phenomena

such as near light speed phenomena. We perform numerical simulations of this equation using the structurepreserving scheme in the de Sitter spacetime. The discretization equation proposed in our previous work
(J. Comput. Appl. Math. 361 pp.364–412) has good accuracy but poor numerical stability. In this talk,we propose a new discretization equation with the structure-preserving scheme and show numerical resultswith high-accuracy and high-stability.
31 土 屋 拓 也 (八 戸 工 大)
中 村
誠 ( 阪 大 情 報)
Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Makoto Nakamura (Osaka Univ.)収縮する de Sitter 時空における半線形 Klein–Gordon 方程式の解の挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On behaviors of solutions of semilinear Klein–Gordon equation in contracting de Sitter spacetime

概 要 de Sitter spacetime is a well-known model of expanding or contracting universes. In this spacetime,

we investigate numerical solutions of the semilinear Klein–Gordon equation. In particular, in the caseof contracting spacetime, it is difficult to investigate the behaviors of the solutions even by numericalcalculations because of the blow-up solutions. Therefore, we apply the structure-preserving scheme to the
Klein–Gordon equation to obtain accurate and stable numerical solutions and show the behaviors of thesolutions.
32 竹 田 航 太 (京坂 上 貴 之 (京

大

理)

大

理)

(Kyoto Univ.)
Kota Takeda
Takashi Sakajo (Kyoto Univ.)

HMC による球面上 N 点渦系不変測度の計算 · · · · · · · · · · · · · · · · · · · · · · · 15
Computing an invariant measure of the N -vortex problem on the sphereby Hamiltonian Monte Carlo概 要 Hamiltonian Monte Carlo (HMC) is a stochastic method to approximate high-dimensional integrals by

the samples from the target distribution, efficiently by utilizing the Hamiltonian dynamics. In general, theefficiency of HMC is characterized by a geometric convergence rate of the associated Markov chain, known
as a property ‘geometric ergodicity’. For a class of target distributions on the Euclidean space, geometricergodicity for HMC has been established, however, that has not yet been established on manifolds. Hence,
we prove geometric ergodicity for HMC on compact manifolds. As an application, we consider the sampling
problem from the invariant measure of the N -vortex problem on the sphere, which is relevant to twodimensional turbulence on geophysical fluid.

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93

応用数学

33 藤 原 宏 志 (京 大 情 報)
K. Sadiq(Johann Radon Inst. for Comput. Appl. Math.)
A. Tamasan(Univ. Central Florida)

Hiroshi Fujiwara (Kyoto Univ.)
Kamran Sadiq(Johann Radon Inst. for Comput. Appl. Math.)
Alexandru Tamasan(Univ. Central Florida)

On a Cauchy-type singular integral equation for x-ray computerized
tomography with partial measurement · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On a Cauchy-type singular integral equation for x-ray computerized
tomography with partial measurement

概 要 In this talk we propose a direct numerical reconstruction procedure for x-ray tomography with partial

measurement. The proposed method is based on Bukhgeim–Cauchy boundary integral formula developed
for an inverse source problem of the transport equation, and is characterized by a singular integral equation
with Cauchy kernel for the considering partial measurement case. We also show its quantitative stability interms of the condition number with a particular discretization for reliable numerical reconstruction.
34 石 毛 利 昌 (千葉大融合理工)高 安 亮 紀 (筑波大システム情報)

Toshimasa Ishige (Chiba Univ.)
Akitoshi Takayasu (Univ. of Tsukuba)

ある K3 曲面族についての Picard–Fuchs 微分方程式のモノドロミーに対する精度保証付き数値計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Rigorous numerics for finding the monodromy of Picard–Fuchs differential equations for a family of K3 toric hypersurfaces

概 要 In this talk, we introduce a method for finding monodromy matrices of linear differential equations withfinite-dimensional solution spaces using rigorous numerics. We also provide a result of computer-assisted
proof that yields monodromy matrices of Picard–Fuchs differential equations for a certain family of K3 toric
hypersurfaces.
35 木 下 武 彦 (佐 賀 大 理 工)
渡 部 善 隆(九大情報基盤研究開発センター)
中 尾 充 宏 ( 早 大 理 工)

Takehiko Kinoshita (Saga Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

2 階楕円型線形作用素に対する近似逆作用素ノルムの収束オーダー評価· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Convergence order estimations of approximate inverse operator norm
for second-order elliptic linear operators

概 要 In this talk, we consider the convergence order of the approximate inverse operator norm for second-√order elliptic linear operators. We show that the general order of convergence is O( h), and give concrete
computable error bounds for achieving the same order.
16:45〜17:45

特別講演
榊 原 航 也 (岡山理大理・理化学研)

Koya Sakakibara(Okayama Univ. of Sci. / RIKEN)

界面現象の構造保存型数値解析

Structure-preserving numerical analysis of interfacial phenomena

概 要 Soap bubbles, falling water droplets, and other phenomena that deform from moment to moment

are all around us. The problem of mathematically investigating these phenomena is known as the moving
boundary problem, which has been studied in mathematics, physics, and various other fields. Numericalanalysis of interfacial phenomena is more complicated than the usual numerical analysis of differential
equations on a fixed domain because the problem domain changes from moment to moment. In this talk,we will review what has been known about attempts to design structure-preserving numerical methods formathematical models describing interfacial phenomena. Further directions of research development will also
be discussed.

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応用数学

3 月 18 日（土）9:50〜11:50
36 國 谷 紀 良 (神戸大システム情報)

Toshikazu Kuniya (Kobe Univ.)

94

第 VII 会場

隔離と時間遅れを考慮した感染症モデルにおけるホップ分岐 · · · · · · · · · · 15

Hopf bifurcation in a delayed epidemic model with quarantine

概 要 In this study, we construct a time-delayed epidemic model with quarantine and obtain sufficientconditions for a Hopf bifurcation, which represents the recurrent epidemic waves. We show that if the basic
reproduction number R0 is less than 1, then the disease-free equilibrium is globally asymptotically stable,
whereas if R0 > 1, then the unique endemic equilibrium exists and it can be destabilized and a nontrivial
periodic solution can arise in a Hopf bifurcation. Our numerical simulation suggests that the quarantine
and time delay play important roles in the occurrence of recurrent epidemic waves.
37 竹 口 佳 輝 (京 大 情 報)
矢 ヶ 崎 一 幸 ( 京 大 情 報)

Yoshiki Takeguchi (Kyoto Univ.)
Kazuyuki Yagasaki (Kyoto Univ.)

力学系理論の手法による感染症数理モデル SEIR 系の最適制御 · · · · · · · · 15

Optimal control of the SEIR epidemic model using a dynamical systems
approach

概 要 We consider the susceptible-exposed-infected-removed (SEIR) epidemic model and apply optimal

control to it. Our approach is to reduce the computation of the optimal control input to that of thestable manifold of an invariant manifold in a Hamiltonian system. Some numerical examples in which thecomputer software AUTO is used to numerically compute the stable manifold are given to demonstrate theusefulness of our approach for the optimal control in the SEIR model. Our study suggests how we candecrease the number of infected individuals quickly before a critical situation occurs while keeping socialand economic burdens small.
大理)
38 田 﨑 創 平 (北長 井 広 樹(東大薬・東北大学際フロンティア研)
ルイスアウグストエイジナガイ(東大薬)中 戸 隆 一 郎 (東大定量生命研)
大薬)
三 浦 正 幸 (東中嶋悠一朗
(東大薬・東北大学際フロンティア研)

Sohei Tasaki (Hokkaido Univ.)
Hiroki Nagai(Univ. of Tokyo / Tohoku Univ.)
Luis Augusto Eijy Nagai(Univ. of Tokyo)
Ryuichiro Nakato (Univ. of Tokyo)
Masayuki Miura (Univ. of Tokyo)
Yu-ichiro Nakajima(Univ. of Tokyo / Tohoku Univ.)

腸管上皮細胞社会における脱分化現象の数理解析 · · · · · · · · · · · · · · · · · · · 15

Mathematical analysis of dedifferentiation in the intestinal epithelial cellcommunity

概 要 The intestinal epithelium is a highly flexible and adaptive cell community that is formed and regulatedby the proliferation and differentiation of intestinal stem cells (ISCs). We have quantitatively analyzed
the nutrient-dependent tissue expansion of the adult Drosophila intestinal epithelium just after eclosion.
We have shown that stem cell division alone cannot explain the increase in stem cell number, and haveproposed a novel dedifferentiation phenomenon as a possible compensatory mechanism. We have developed
a mathematical model of intestinal epithelial cell society and established a simulation system that enables
quantitative prediction of cell population dynamics. The analysis is revealing that enteroendocrine cell
dedifferentiation is a good way to efficiently achieve intestinal enlargement while maintaining cell diversity.

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95

応用数学

39 松 江要(九大 IMI・九大 I2CNER)
落 合 啓 之 (九 大 I M I )小 谷 久 寿 (九 大 I M I )高 安 亮 紀 (筑波大システム情報)
Kaname Matsue(Kyushu Univ. / Kyushu Univ.)
Hiroyuki Ochiai (Kyushu Univ.)
Hisatoshi Kodani (Kyushu Univ.)
Akitoshi Takayasu (Univ. of Tsukuba)

常微分方程式の爆発解の漸近展開と無限遠ダイナミクス · · · · · · · · · · · · · 15

Correspondence between asymptotic expansions of blow-up solutions for
ODEs and dynamics at infinity

概 要 We provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria

for appropriately transformed two systems (describing asymptotic expansions and dynamics at infinity)
describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As a corollary,
we see that asymptotic expansions of blow-ups themselves provide a criterion of the existence of blow-ups
with an intrinsic gap structure of stability information among two systems.
40 劉

逸 侃 ( 北 大 電 子 研)

Yikan Liu

(Hokkaido Univ.)

非整数階拡散方程式系の初期値境界値問題について · · · · · · · · · · · · · · · · · 15

Initial-boundary value problems for coupled systems of time-fractional
diffusion equations

概 要 This talk is concerned with the initial-boundary value problem for a moderately coupled systemof time-fractional diffusion equations with Caputo derivatives of orders in (0, 1). Regarding the coupledpart of components as a source term, we define the mild solution by an integral equation. Then we
establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior of
the solution, which mostly inherit those of a single equation.
41 宮 路 智 行 (京R. Sinclair

大理)

Tomoyuki Miyaji (Kyoto Univ.)
Robert Sinclair

A conjecture on the asymptotic reflection rule of a self-propelled particle· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A conjecture on the asymptotic reflection rule of a self-propelled particle

概 要 We consider a four-dimensional ODE model of a self-propelled particle that interacts repulsively withthe domain boundary. It is derived from certain planar reaction-diffusion systems. A previous study provesthat the particle governed by this model moves almost in a straight line and reflects from the boundary
without collision. In addition, numerical simulations suggest that the angle of reflection is greater thanthat of incidence, which is proved under certain conditions. Recently, we have proposed a conjecture on thefunctional relationship between the angles. We will discuss how we arrived at the conjecture and became
convinced.
42 石 井 宙 志 (京 大 A S H B i)
Hiroshi Ishii(Kyoto Univ.)

十分弱い非局所効果を持つ反応拡散方程式における積分核形状に依存したパターンダイナミクス · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Pattern dynamics depending on integral kernel shape in reaction-diffusion
equations with sufficiently weak nonlocal effect

概 要 In this talk, we consider reaction-diffusion equations with nonlocal effects described by the convolution

with an appropriate integral kernel. Such a nonlocal effect is used to describe the diffusion process of
substances and cell-cell interactions, for example. This work is particularly concerned with the behaviorof the widths of phase-separated patterns. The equation of motion of the width is derived and applied toseveral integral kernels as examples to explain how the pattern dynamics of the solution depend on the
shape of the integral kernel.

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応用数学

96

14:15〜15:05
43 大 野 航 太 (中 大 理 工)
小 川 知 之 ( 明 大 先 端 数 理)
(Chuo Univ.)
Kota Ohno
Toshiyuki Ogawa (Meiji Univ.)

Stability of traveling wave in nonlocally coupled oscillator system · · · · 15
Stability of traveling wave in nonlocally coupled oscillator system

概 要 Coupled oscillator systems have been studied in various fields of physical and biological phenomena.

Among them, systems of nonlocally coupled oscillators can exhibit chimera states, which consist of spatiallycoherent and incoherent states. However, the stability and bifurcation origin of chimera states have not been
understood. Stuart–Landau type nonlinearity enables us to formulate the stability problem of travelingwaves precisely through Floquet theory. We analyzed Floquet multiplier and confirmed the transition ofstability of traveling wave by changing the parameters of nonlocal coupling. In this study, we will state therelationship between the stability of traveling waves and chimera states.
44 関 坂 歩 幹 (明大研究・知財)
小 川 知 之 ( 明 大 先 端 数 理)
Ayuki Sekisaka (Meiji Univ.)
Toshiyuki Ogawa (Meiji Univ.)

振動場反応拡散系に現れるセグメントパターンの安定性について · · · · · · 15

Stability problem of segmented pattern for oscillatory reaction-diffusion
systems

概 要 In reaction-diffusion systems of oscillatory fields, especially those in which wave bifurcations occur, it

is known that traveling waves with periodic profiles appear. Even if the traveling waves are asymptoticallystable, starting from a random initial value, several segments are formed, each consisting of different periodic
traveling waves. Pattern dynamics is then observed in which the segments change from one to another.
The transition between different segments is considered to be the so-called defect solution. In this lecture,
we will discuss whether the defect solution can be regarded as a steady-state observation of the segment
pattern.
45 小 川 知 之 (明 大 先 端 数 理)
小 林 俊 介 ( 宮 崎 大 工)
Toshiyuki Ogawa (Meiji Univ.)
Shunsuke Kobayashi(Univ. of Miyazaki)

Compact metric graph 上の Turing 不安定性 · · · · · · · · · · · · · · · · · · · · · · · 15
Turing instability on compact metric graph

概 要 Studies on the behavior of reaction-diffusion systems on a one-dimensional domain with junctions(metric graph) have been increasing recently. It is expected that joint research with cell physiology andecology will progress more and more in the future. So, we would like to clarify from the basics what kindof pattern formation occurs in compact metric graphs. First, by preparing 2 or 3 bounded intervals, let usclassify the metric graph that is created by connecting them, and consider the eigenvalue problem there.
Then, we describe the conditions under which Turing instability occurs for each modes, and discuss thedifferences in pattern formation by metric graphs.

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97

応用数学

15:20〜16:20
西特別講演
慧 ( 京 都 産 大 理)

Kei Nishi (Kyoto Sangyo Univ.)

3 種反応拡散方程式のパルスダイナミクスについて
Pulse dynamics in a three-component reaction-diffusion system

概 要 The pulse dynamics in a three-component FitzHugh–Nagumo system is considered both numericallyand analytically. The system admits a pulse solution of bistable type, which exhibits a variety of interface
dynamics, not observed for the two-component FitzHugh–Nagumo systems. In this talk, we focus on theparameter regime α > 0, β < 0, where there appear not only two types of pulse solutions, whose profiles
are mutually inverted, but also multiple-pulse solutions which show collective motions such as clustered
traveling pulses and an array of oscillating pulses. In order to analytically investigate these pulse behaviors,
we apply the multiple scales method to the original reaction-diffusion system, and derive finite-dimensional
ordinary differential equations which describe the motions of the pulse interfaces. The reduced ODEs enable
us to reveal the global bifurcation structures of the pulse solutions, as well as the clustered multiple-pulse
solutions, and to elucidate the mechanism for the rich variety of pulse dynamics in a clear, unified manner.

最終版: 2023/2/17
トポロジー

ト

ポ

ロ

3 月 15 日（水）

ジ

98

ー

第 III 会場

9:30〜12:00
1 黒 木 慎 太 郎 ( 岡 山 理 大 理)
Shintaro Kuroki(Okayama Univ. of Sci.)

Orlik–Raymond type classification of simply connected 6-dimensional
torus manifolds with vanishing odd degree cohomology · · · · · · · · · · · · · 15
Orlik–Raymond type classification of simply connected 6-dimensional
torus manifolds with vanishing odd degree cohomology

概 要 A torus manifold is defined as an even-dimensional compact manifold with a half-dimensional torus

action which has fixed points. This notion was introduced by Hattori–Masuda in 2003 as the generalizationof the toric and the quasitoric manifolds. The aim of this talk is to classify simply connected 6-dimensional
torus manifolds with vanishing odd-degree cohomology. It is shown that there is a one-to-one correspondence
between equivariant diffeomorphism types of such manifolds and 3-valent torus graphs introduced by Maeda–
Masuda–Panov. Using this correspondence and combinatorial arguments, we prove that such a manifold
is equivariantly diffeomorphic to the 6-dimensional sphere or an equivariant connected sum of copies of
6-dimensional quasitoric manifolds or 4-dimensional sphere bundles over the 2-dimensional sphere.
2 那 須 正 和
Masakazu Nasu

The limits of resolving directions of automorphisms of sofic systems · · 15
The limits of resolving directions of automorphisms of sofic systems

概 要 We present the results that an automorphism of a sofic system has the same limits of resolving

directions as those of its canonical support by way of the Krieger cover and that a similar result to thisholds for an automorphism of a transitive sofic system and its canonical support by way of the Fischer cover.
One of the corollaries to these proves that no automorphism of a transitive sofic system has an irrational
unique non-expansive direction.
3 白 根 竹 人 ( 徳 島 大 理 工)
M. Amram(Shamoon Coll. of Eng.)
坂 内 真 三 ( 岡 山 理 大 理)
U. Sinichkin (Tel Aviv Univ.)
徳 永 浩 雄 ( 都 立 大 理)

Taketo Shirane (Tokushima Univ.)
Meirav Amram (Shamoon Coll. of Eng.)
Shinzo Bannai (Okayama Univ. of Sci.)
Uriel Sinichkin (Tel Aviv Univ.)
Hiro-o Tokunaga (Tokyo Metro. Univ.)

Splitting invariants and a π1 -equivalent Zariski pair of conic-line arrangements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Splitting invariants and a π1 -equivalent Zariski pair of conic-line arrangements

概 要 In this talk, we consider the embedded topology of plane curves on the complex projective plane P2 .

It is known that there are π1 -equivalent Zariski pairs (C1 , C2 ) of plane curves C1 , C2 ⊂ P2 , i.e., C1 and C2
have the same embedded topology in their tubular neighborhoods but different embedded topology in P2 ,∼ π1 (P2 \ C2 ). Known examples of π1 -equivalent Zariski pairs consist of curves containingand π1 (P2 \ C1 ) =a component with either singularities or genus g ≥ 1. The aim of this talk is to give a π1 -equivalent Zariski
pair of conic-line arrangements, i.e., a pair of curves consisting of smooth rational curves.

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99

トポロジー

4 山 﨑 薫 里 ( 高 崎 経 大 経 済)
Kaori Yamazaki(Takasaki City Univ. of Econ.)

Extensions of continuous increasing functions · · · · · · · · · · · · · · · · · · · · · · 10
Extensions of continuous increasing functions

概 要 In this talk, we study extensions of continuous increasing functions, and provide an increasing versionof Gillman–Jerison theorem.
5 深 沢 尚 希 ( 都 立 大 理)

Naoki Fukasawa (Tokyo Metro. Univ.)

Persistent cohomology と cup length function の計算 · · · · · · · · · · · · · · · 15
Persistent cohomology and computation of cup length function

概 要 We introduce the structure theorem of the persistent cohomology to describe the representative

cocycles in detail. Then, taking cup products of representative cocycles, we can compute the cup length
function of a finite metric space.
6 田 嶌
優 (北
吉 永 正 彦 (阪

大

理)

大

理)

Yu Tajima (Hokkaido Univ.)
Masahiko Yoshinaga (Osaka Univ.)

グラフのマグニチュードホモトピー型と Mayer–Vietoris 型定理 · · · · · · · 15

Magnitude homotopy type of graphs and Mayer–Vietoris type theorem

概 要 Magnitude homology is defined by Hepworth and Willerton as a categorification of the magnitude(an invariant for metric spaces). They proved the Kunneth formula and Mayer–Vietoris type theorem for
magnitude homology of graphs. Recently, Asao–Izumihara introduced the pair of simplicial complexes (K,K’) whose homology groups are isomorphic to direct summands of graph magnitude homology groups. We
call the CW complex K/K’ magnitude homotopy type. In this talk, we give a new proof of Mayer–Vietoris
type theorem using Discrete Morse theory on magnitude homotopy types. If time permits, we also talkabout generalizatios to metric spaces.
7 原 子 秀 一 ( 東 大 数 理)

Shuichi Harako (Univ. of Tokyo)

The modular class of an orientable ρ-Q-manifold · · · · · · · · · · · · · · · · · · · 15
The modular class of an orientable ρ-Q-manifold

概 要 As one generalization of Lie algebras and commutative algebras, we have ρ-Lie algebras and ρ-commutative algebras, respectively. We will introduce a concept of a ρ-manifold, whose functional algebra
is locally isomorphic to a ρ-commutative algebra, and discuss its modular class where the ρ-manifold isorientable and equipped with a Q-structure.
8 若 月
駿 (名 大 多 元 数 理) ♭ Independence complexes of grid graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
松 下 尚 弘 ( 琉 球 大 理)

Shun Wakatsuki (Nagoya Univ.)
Takahiro Matsushita(Univ. of Ryukyus)

Independence complexes of grid graphs

概 要 We determine the homotopy types of the independence complexes of (n × 4), (n × 5) and (n × 6)-squaregrid graphs. In fact, they are homotopy equivalent to wedges of spheres.

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トポロジー

14:20〜15:20
小 川

特別講演
竜 ( 東 海 大 理)

Noboru Ogawa(Tokai Univ.)100

凸シンプレクティック多様体の Liouville 構造と Weinstein 構造

Liouville and Weinstein structures on convex symplectic manifolds

概 要 In symplectic geometry, there are two important classes on convexity: Liouville structures andWeinstein structures. The former is a symplectic manifold equipped with a conformally expanding symplectic
vector field which is pointing outward. The latter is imposed so that the vector field is gradient-like. Suchstructures have played a significant role in the study of symplectic and contact topology. For example, theconvexity provides a constraint on the behavior of pseudo-holomorphic curves by the maximum principle.
By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff
gave the first example which is a Liouville manifold without any Weinstein structures. The purpose ofthis talk is to present recent advances on the difference between the two structures, up to homotopy. In
particular, I will show that the stabilization of McDuff’s example admits a flexible Weinstein structure.
The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu(Kyoto University of Education). If time permits, I would like to discuss some open questions, progress andperspective.
15:40〜17:30
9 知 念 直 紹 (防衛大)Naotsugu Chinen(Nat. Defense Acad. of Japan)

Isometry groups of symmetric products of (Rk )qp · · · · · · · · · · · · · · · · · · · 15
Isometry groups of symmetric products of (Rk )qp

概 要 By Fn (X), n ≥ 1, we denote the n-th symmetric product of a metric space (X, d) as the space ofthe nonempty finite subsets of X with at most n elements endowed with the Hausdorff metric dH . By
Iso(X) we denote the topological group of all isometries from X onto itself with the topology of pointwise
convergence. We are interested in what topological group Iso(Fn (X)) is.The aim is to decide a topologicalgroup structure of Iso(Fn ((Rk )qp )) for any (n, k, p, q) ∈ N × N × (N ∪ {∞}) × (N ∪ {∞}).
10 森

淳 秀 ( 大 阪 歯 大 歯)Atsuhide Mori (Osaka Dent. Univ.)多様体の相互 Bayes 学習 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mutual Bayesian learning for manifolds

概 要 In previous work, the author described the geometry of Bayesian learning on a manifold. In this talk,we take the square of any manifold and a positive function which takes the maximum 1 on the diagonal set.
Then we define the mutual Bayesian learning between the factors of the square. Particularly, we consider
mutual learning between two copies of the parameter space of a statiscal model, and associate the above
function with the relative entropy. Although the mutual learning forgets all about the model except therelative entropy, it still substitutes for the usual Bayesian estimation of the parameter in a certain case.
11 狩 野 隼 輔 (東北大RACMaS)
石 橋
典 ( 東 北 大 理)

Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Tohoku Univ.)

Unbounded sl3 -laminations and their shear coordinates · · · · · · · · · · · · · 15
Unbounded sl3 -laminations and their shear coordinates

概 要 Generalizing the work of Fock–Goncharov on rational unbounded laminations, we give a geometricmodel of the tropical points of the moduli space XP GL3 ,Σ of framed P GL3 -local systems on a marked surface
Σ based on the Kuperberg’s sl3 -webs. We introduce their tropical cluster coordinates as an sl3 -analogue of
the Thurston’s shear coordinates associated with any ideal triangulation. We also describe tropical points
of Goncharov–Shen’s moduli space PP GL3 ,Σ . Then we give a tropical anologue of gluing morphisms among
the moduli spaces as a geometric gluing procedure of sl3 -laminations with “shearings”. We also investigate
a relation to the graphical basis of the sl3 -skein algebra by Ishibashi–Yuasa, which conjecturally leads to aquantum duality map.

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12 越 野 克 久 (神 奈 川 大 工)

Katsuhisa Koshino (Kanagawa Univ.)

A characterization of compact sets in Lp -spaces and its application · · · 15
A characterization of compact sets in Lp -spaces and its application

概 要 In this talk, we give a characterization of compact sets in Lp -spaces on metric measure spaces. As

its application, we investigate the topological types of the subspace consisting of lipschitz functions withbounded supports.
13 足 立 真 訓 (静 岡 大 理)
松 田 能 文 ( 青 学 大 理 工)
野 沢
啓 ( 立 命 館 大 理 工)

Masanori Adachi (Shizuoka Univ.)
Yoshifumi Matsuda(Aoyama Gakuin Univ.)
Hiraku Nozawa (Ritsumeikan Univ.)

Harmonic measures and rigidity for surface group actions on the circle· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Harmonic measures and rigidity for surface group actions on the circle

概 要 We study rigidity properties of surface group actions on the circle via foliated harmonic measures on

the suspension bundles. We show a curvature estimate and a Gauss–Bonnet formula for an S 1 -connection
obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonicmeasure. As consequences, we give a precise description of the harmonic measure on suspension foliations
with maximal Euler number and an alternative proof of rigidity theorems of Matsumoto and Burger–Iozzi–
Wienhard.

3 月 16 日（木）第 III 会場

9:30〜12:00
14 山 本 卓 宏 (東 京 学 大 教 育)
Takahiro Yamamoto(Tokyo Gakugei Univ.)

連続写像のファイバー特異点 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Fiber singularities of continuous maps

概 要 The notion of fiber-singularities of continuous maps between topological manifolds are introduced.

Then, we investigate some examples of fiber-singularities and, study fiber-singularities of simplicial maps of
PL maps of surfaces.
15 濱 田 直 希 ( KLab(株) )早 野 健 太 ( 慶 大 理 工)
寺 本
央 (関西大システム理工)(KLab Inc.)
Naoki Hamada(
Keio Univ.)
Kenta Hayano
Hiroshi Teramoto (Kansai Univ.)

多目的最適化問題における制約関数芽および実行可能領域芽の分類と認識· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classification and recognition of constraint function-germs and feasible
set-germs in multiobjective optimization

概 要 For functions g1 , . . . , gq and h1 , . . . , hr on the Euclidian space, we consider the minimizing problemsof some given functions on the set M (g, h) = {x | ∀i, gi (x) ≤ 0, ∀j, hj (x) = 0}. The functions gi ’s, hj ’s andthe set M (g, h) are respectively called the constraint functions and the feasible set for the problem. In thistalk, we will explain the results on classification and recognition of constraint function-germs under suitableequivalence for them (called K[G]-equivalence). If time permits, we will also discuss how the results are
related with classification of feasible set-germs.

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16 久 野 恵 理 香 (阪Erika Kuno

大理)

(Osaka Univ.)102

向き付け不可能曲面の非分離曲線グラフの一様双曲性 · · · · · · · · · · · · · · · 10

Uniform hyperbolicity of nonseparating curve graphs of nonorientablesurface概 要 Let N be a connected nonorientable surface with or without boundary components and punctures.

We prove that the graph consists of the isotopy classes of nonseparating curves of N is connected andGromov hyperbolic with a constant which does not depend on the topological type of the surface by using
the bicorn curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on
the uniform hyperbolicity for the graphs consists of the isotopy classes of nonseparating curves for orientablesurfaces.
17 久 野 恵 理 香 (阪木 村 満 晃 (京

大

理)

大

理)

(Osaka Univ.)
Erika Kuno
Mitsuaki Kimura (Kyoto Univ.)

向き付け不可能曲面のファイン曲線グラフの一様双曲性 · · · · · · · · · · · · · 10

Uniform hyperbolicity of fine curve graphs of nonorientable surfaces

概 要 A fine curve graph defined by Bowden, Hensel, and Webb (J. Amer. Math. Soc. (2021)) is a new curve

graph consists of all essential simple closed curves on a surface. They proved that the fine curve graph ofany closed orientable surface of genus g ≥ 1 is uniformly hyperbolic in the sense of Gromov. We provedthat the fine curve graph of any closed nonorientable surface of genus g ≥ 2 is also uniformly hyperbolic.
18 小 林 竜 馬 (石 川 工 高 専)
井 本 奈 緒Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)
Nao Imoto

向き付け不可能閉曲面のレベル 2 写像類群による非分離単純閉曲線への作用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Action on non-separating simple closed curves by the level 2 mappingclass group of a non-orientable closed surface

概 要 The level 2 mapping class group M2 (N ) of a non-orientable closed surface N is the subgroup of the

mapping class group of N consisting of elements acting trivially on H1 (N ; Z/2Z). In our work, we provedthat for any non-separating simple closed curves α and β of N , there is φ ∈ M2 (N ) such that φ(α) = β if
and only if α and β are equal as elements in H1 (N ; Z/2Z).
19 小 林 竜 馬 (石 川 工 高 専)
井 本 奈 緒Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)
Nao Imoto

向き付け不可能閉曲面の非分離単純閉曲線に沿った Dehn ツイストの 2 乗が生成する群 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The group generated by squares of Dehn twists about non-separating
simple closed curves of a non-orientable closed surface

概 要 The level 2 mapping class group of an orientable closed surface is equal to the group generated bysquares of Dehn twists about non-separating simple closed curves. In our work, we proved that the twist
subgroup of the level 2 mapping class group of a non-orientable closed surface is not equal to the group
generated by squares of Dehn twists about non-separating simple closed curves and Dehn twists about
separating simple closed curves. As an application, we gave a finite generating set for this group.
20 大 森 源 城 (東 京 理 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)

A finite presentation for the balanced superelliptic handlebody group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A finite presentation for the balanced superelliptic handlebody group

概 要 The balanced superelliptic handlebody group is the normalizer of the transformation group of thebalanced superelliptic covering space in the handlebody group of the total space. We give a finite presentation
for the balanced superelliptic handlebody group. To give this presentation, we construct a finite presentation
for the liftable Hilden group.

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21 大 森 源 城 (東 京 理 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)

A small generating set for the balanced superelliptic handlebogy group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A small generating set for the balanced superelliptic handlebogy group

概 要 The balanced superelliptic handlebody group is the normalizer of the transformation group of thebalanced superelliptic covering space in the handlebody group of the total space. We prove that the balanced
superelliptic mapping class group is generated by four elements. To prove this, we also proved that theliftable Hilden group is generated by three elements. This generating set for the liftable Hilden group is
minimal except for some hyperelliptic cases and the generating set for the balanced superelliptic mappingclass group above is also minimal for several cases.
13:00〜14:00
22 北 野 晃 朗 (創 価 大 理 工)
清 水 達 郎
(東京電機大システムデザイン工)
Teruaki Kitano (Soka Univ.)
Tatsuro Shimizu (Tokyo Denki Univ.)

Morse–Smale flow を用いた Reidemeister torsion のトーラス和公式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the torus sum formula of Reidemeister torsion defined by Morse–
Smale flows

概 要 We consider Reidemeister torsion for a 3-manifold. It can defined by several ways. For a 3-manifoldwith a torus decomposition, the torus sum formula of Reidemeister torsion is well known. In this talk wegive a proof of the torus sum formula by using Morse–Smale flows.
23 寺 垣 内 政 一 (広 島 大 教 育)

Masakazu Teragaito (Hiroshima Univ.)

双曲的 L 空間結び目の Upsilon 不変量について · · · · · · · · · · · · · · · · · · · · · 10Hyperbolic L-space knots and their Upsilon invariants

概 要 For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval[0, 2]. It is known that for an L-space knot, the Upsilon invariant is determined only by the Alexanderpolynomial. We exhibit infinitely many pairs of hyperbolic L-space knots such that two knots of each pair
have distinct Alexander polynomials, so they are not concordant, but share the same non-zero Upsilon
invariant. Conversely, we examine the restorability of the Alexander polynomial of an L-space knot fromthe Upsilon invariant through the Legendre–Fenchel transformation.
24 門 上 晃 久 (金 沢 大 理 工)

Teruhisa Kadokami (Kanazawa Univ.)

The Ma–Qiu index and the Nakanishi index for a fibered knot are equal,and ω-solvability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Ma–Qiu index and the Nakanishi index for a fibered knot are equal,and ω-solvability

概 要 For a knot K, let G(K) be the knot group of K, a(K) the Ma–Qiu index, which is the minimal

number of normal generators of the commutator subgroup of G(K), and m(K) the Nakanishi index of K,
which is the minimal number of generators of the Alexander module of K. We generalize the notions fora pair of a group G and its normal sugroup N , and we denote them by a(G, N ) and m(G, N ) respectively.
Then it is easy to see m(G, N ) ≤ a(G, N ) in general. We also introduce a notion “ω-solvability” for a group.
Our main theorem is that if N is ω-solvable, then we have m(G, N ) = a(G, N ). As corollaries, for a fiberedknot K, we have m(K) = a(K), and we could determine the MQ indices of prime knots up to 9 crossingscompletely.

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3 月 17 日（金）104

第 III 会場

9:30〜12:00
25 松 土 恵 理 (日大文理自然研)
大 城 佳 奈 子 ( 上 智 大 理 工)
山 岸 凱 司 ( 上 智 大 理 工)
(Nihon Univ.)
Eri Matsudo
Kanako Oshiro (Sophia Univ.)
Gaishi Yamagishi (Sophia Univ.)

Minimum numbers of Dehn colors and R-palette graphs · · · · · · · · · · · · 10

Minimum numbers of Dehn colors and R-palette graphs

概 要 We consider the number of colors for Dehn-colorings, and we define a R-palette graphs. In this talk,for any Dehn p-colorable knot, we give a lower bound of the minimum number of colors on diagrams.
26 市
石
鈴
松

原
川
木
土

一
勝
正
恵

裕 ( 日 大 文 理)
巳 ( 京 大 数 理 研)
明 ( 明 大 総 合 数 理)
理 (日大文理自然研)

Kazuhiro Ichihara (Nihon Univ.)
Katsumi Ishikawa (Kyoto Univ.)
Masaaki Suzuki (Meiji Univ.)(Nihon Univ.)
Eri Matsudo

絡み目群の全射二面体群表現と二相彩色について · · · · · · · · · · · · · · · · · · · 10

Two-tone colorings and surjective dihedral representations for links

概 要 It is well-known that a knot group admits a surjective homomorphism to the dihedral group of degree

n if and only if the knot is Fox n-colorable. However, it is not true for links with two or more components.
In this talk, I will introduce a two-tone coloring on a link diagram, and give a condition for links that thelink groups admit surjective representations to dihedral groups.
27 野 坂 武 史 (東 工 大 理)

Takefumi Nosaka (Tokyo Tech)

閉 3 次元多様体の対称ラックコサイクル不変量 · · · · · · · · · · · · · · · · · · · · · 10

Symmetric rack cocycle invariants of closed 3-manifolds

概 要 We establish a new approach to obtain 3-manifold invariants via Dehn surgery. For this, we introduce

racks with good involution and Property FR, and define cocycle invariants as 3-manifold invariants.
28 松 崎 尚 作(足利大共通教育センター)
村 尾
智 (早 大 G E C )Shosaku Matsuzaki(Int. Aﬀairs Ashikaga Univ.)
Tomo Murao (Waseda Univ.)

空間曲面と多重群ラックコサイクル不変量 · · · · · · · · · · · · · · · · · · · · · · · · · 10

Spatial surfaces and multiple group rack cocycle invariants

概 要 A spatial surface is a compact surface embedded in the 3-sphere. A multiple group rack is an algebraic

structure motivated from Reidemeister moves of oriented spatial surfaces. In this talk, we introduce a
multiple group rack cocycle invariant for oriented spatial surfaces and give some calculation examples.
大理)
29 谷 口 雄 大 (阪
(
)
東
京
学
大
教
育
田 中
心

Yuta Taniguchi (Osaka Univ.)
Kokoro Tanaka (Tokyo Gakugei Univ.)

結び目の n-カンドルの中心拡大 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A central extension of the n-quandle of a knot

概 要 The fundamental quandle is a powerful invariant for knots. However, it is difficult to compare them.

Then, we often use a certain quotient of the fundamental quandle of a knot, which is called an n-quandle
of a knot. In this talk, we show that the fundamental quandle of the n-twist spun knot, which is a 2-knot
introduced by Zeeman, is a central extension of the n-quandle. As a corollary, we determine the second
quandle homology group of n-quandles.

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30 田 中心 ( 東 京 学 大 教 育)大理)
谷 口 雄 大 (阪Kokoro Tanaka (Tokyo Gakugei Univ.)
Yuta Taniguchi (Osaka Univ.)

二次元結び目の結び目カンドルと結び目群について · · · · · · · · · · · · · · · · · 10

Knot quandles and knot groups for 2-knots

概 要 We give examples of 2-knots with the same knot group but different knot quandles by analyzing theknot quandles of twist-spun knots. As a byproduct of our method, we give a classification of all twist-spunknots with finite knot quandles.
31 和 田 康 載 (神 戸 大 理)
Kodai Wada

(Kobe Univ.)

ブルンの性質をもつリボン 2 次元ストリング絡み目の有限型不変量 · · · · 10

Finite type invariants of ribbon 2-dimensional string links with generalized Brunnian properties

概 要 Gusarov and Habiro independently gave a topological interpretation of finite type invariants for

1-dimensional knots in terms of Ck -equivalence. As a 4-dimensional analogue, Watanabe introduced thenotion of RCk -equivalence on ribbon knotted surfaces and proved that two ribbon 2-dimensional knots are
RCk -equivalent if and only if they cannot be distinguished by any finite type invariant of degree less than k.
In this talk, we provide an extension of the above result of Watanabe to ribbon 2-dimensional string links
with generalized Brunnian properties.
14:20〜15:20

特別講演
敦 (筑波大数理物質)

Alexander type invariants of groups, quandles and MCQs

Atsushi Ishii (Univ. of Tsukuba)

Alexander type invariants of groups, quandles and MCQs

石 井

概 要 Groups, quandles and MCQs are algebraic objects appeared in low-dimensional topology. In partic-

ular, the notions of quandles and multiple conjugation quandles (MCQs) were introduced via the axioms
corresponding to the Reidemeister moves for oriented knots and handlebody-knots, respectively. In thistalk, we discuss Alexander type invariants of groups, quandles and MCQs, which include the Alexander
ideal and the (twisted) Alexander polynomial.
15:40〜17:00
32 若 槇 洋 平 (阪 大 情 報)

Yohei Wakamaki (Osaka Univ.)

いくつかの有理曲面のコルク · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Corks of some rational surfaces

概 要 Corks of 4-manifolds are one of the most important objects in the study of exotic 4-manifolds.

Nevertheless, we only have a few explicit examples of corks of standard simply-connected closed 4-manifolds
with small second Betti numbers b2 . In this talk, we give the first example of a cork of CP2 #8CP2 . This
achieves the smallest b2 where a cork of standard simply-connected closed 4-manifold has been found. We
also talk about new examples of corks of CP2 #9CP2 .

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33 浅 野 喜 敬 (津 山 工 高 専)
直 江 央 寛 ( 中 大 理 工)
小 川 将 輝 ( 埼 玉 大 理 工)
Nobutaka Asano(Tsuyama Nat. Coll. of Tech.)
Hironobu Naoe (Chuo Univ.)
Masaki Ogawa (Saitama Univ.)

106

Some lower bounds for the Kirby–Thompson invariant of 4-manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Some lower bounds for the Kirby–Thompson invariant of 4-manifolds

概 要 A trisection is a decomposition of a 4-manifold into three 1-handlebodies. This decomposition ischaracterized by a diagram called a trisection diagram. A trisection diagram is a 4-tuple consisting of aclosed surface and three cut systems. Kirby and Thompson introduced an invariant of a 4-manifold thatis a kind of complexity defined by its trisection diagrams. This invariant is called the Kirby–Thompson
invariant. In this talk, we give some lower bounds for the Kirby–Thompson invariant of certain 4-manifolds.
As an application, we find the first example of a 4-manifold with non-trivial Kirby–Thompson invariant.
34 磯 島司 ( 東 工 大 理)
小 川 将 輝 ( 埼 玉 大 理 工)

Tsukasa Isoshima (Tokyo Tech)
Masaki Ogawa (Saitama Univ.)

Gluck twist により得られる 4 次元球面の trisection · · · · · · · · · · · · · · · · · 15
Trisections of the 4-sphere obtained by Gluck twisting概 要 A trisection of a 4-manifold, introduced by Gay and Kirby in 2012, is a decomposition of the 4-

manifold into three 4-dimensional 1-handlebodies. A trisection can be described by a trisection diagramthat is similar to a Heegaard diagram. In this talk, we construct infinitely many trisection diagrams of the
4-sphere obtained by Gluck twisting along some spun torus knots. We also study the standardness of thetrisection diagrams.
35 大 場 貴 裕 (阪Takahiro Oba

大理)(Osaka Univ.)

Symplectic submanifolds in dimension 6 from Lefschetz fibrations · · · · 15
Symplectic submanifolds in dimension 6 from Lefschetz fibrations

概 要 Thanks to the affirmative answer to the symplectic Thom conjecture, all connected symplectic

surfaces representing the same homology class in a closed symplectic 4-manifold are diffeomorphic. In
higher dimension, for example, take CP3 with the Fubini–Study form. Then, it is known that its connected
symplectic submanifolds representing the class d[CP2 ] are mutually diffeomorphic as long as 1 ≤ d ≤ 3. In
this talk, I will present arbitrarily (finitely) many codimension 2 connected symplectic submanifolds in aclosed symplectic 6-manifold which are mutually homotopy inequivalent but homologous. A key ingredientof the construction is hyperelliptic Lefschetz fibrations.

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無限可積分系無 限

可3 月 17 日（金）

積

分

系

第 IX 会場

9:45〜10:45
1 上 野 祐 一
(皇學館大教育・神戸大理)

Polynomial Hamiltonians for quantum Garnier system in two variables· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Polynomial Hamiltonians for quantum Garnier system in two variables

Yuichi Ueno
(Kogakkan Univ. / Kobe Univ.)

概 要 Garnier system is the extension of Painlevé equations and is given as Frobenius integrable multi-time

Hamiltonian systems. In this talk, we construct and characterize the quantum Gariner system by certain
holomorphic properties. The characterization of the classical Garnier system by holomorphic properties has
been given by Sasano, and our result is a quantization of that work. In other words, we introduce quantum
canonical transformations such that the Hamiltonian system of the Garnier system is again transformed
into a polynomial Hamiltonian system, and show that the Hamiltonian can be uniquely characterized bythis holomorphic properties.
離散 KdV 方程式の立方体周りの整合性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

2 中 園 信 孝 ( 東 京 農 工 大 工)Nobutaka Nakazono(Tokyo Univ. of Agri. and Tech.)Consistency around a cube property of Hirota’s discrete KdV equation

概 要 It has been unknown whether Hirota’s discrete analogue of the Korteweg-de Vries (KdV) equation

have the consistency around a cube (CAC) property, which is known as an integrability of 2-dimensional
difference equation. In this talk, we show that Hirota’s discrete KdV equation has the CAC property.
q-ガルニエ系に由来する q-超幾何級数へのアフィン・ワイル群作用 · · · · 15

3 鈴 木 貴 雄 ( 近 畿 大 理 工)
Takao Suzuki(Kindai Univ.)

An affine Weyl group action on the basic hypergeometric series arisingfrom the q-Garnier system

概 要 Recently, we formulated the q-Garnier system and its variations as translations of an extended affine
(1)

(1)

(1)

Weyl group of type A2n+1 × A1 × A1 . On the other hand, those systems admit particular solutions interms of the basic hypergeometric series n+1 ϕn . In this talk, we investigate an action of the extended affine
Weyl group on n+1 ϕn . This talk is based on a joint work with Taiki Idomoto of Kindai University.
4 大 山 陽 介 ( 徳 島 大 理 工)

Yousuke Ohyama (Tokushima Univ.)(1)

Boundary behavior of q-Painlevé equation of type A4 · · · · · · · · · · · · · · 15
(1)

Boundary behavior of q-Painlevé equation of type A4

概 要 We study asymptotic analysis on the q-Painleve V equation around the origin. We solve the q-

Riemann–Hilbert problem for any asymptotic series of q-Painleve V functions. We show the Mano-type
decomposition for q-Painleve V.

最終版: 2023/2/17
無限可積分系

11:00〜12:00
井 上

特別講演
玲 ( 千 葉 大 理)

Rei Inoue(Chiba Univ.)108

ワイル群のクラスター実現と表現論への応用

Cluster realization of Weyl groups and its applications to representation
theory概 要 The cluster algebra is a commutative algebra introduced by Fomin and Zelevinsky around 2000. The

characteristic operation in the algebra called ‘mutation’ is related to various notions in mathematics andmathematical physics.
In this talk we introduce a realization of Weyl groups in terms of cluster mutations, for finite dimensional
semisimple Lie algebras. We discuss its applications to (1) the geometric R-matrix of symmetric power
representations for the affine quantum algebra of A-type, and to (2) the q-characters of quantum non-twisted
affine algebras introduced by Frenkel and Reshetikhin, when q is a root of unity. If time permits we alsomention the application to higher Teichmüller theory.
This talk is based on joint works with Thomas Lam, Pavlo Pylyavskyy, Tsukasa Ishibashi, Hironori Oya,and Takao Yamazaki.

3 月 18 日（土）第 IX 会場

10:00〜10:45
5 小 見 山 尚 ( 名 大 多 元 数 理)

Nao Komiyama (Nagoya Univ.)

Associators and the Grothendieck–Teichmüller group in mould theory· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Associators and the Grothendieck–Teichmüller group in mould theory

概 要 In this talk, we explain the mould theory introduced by Jean Ecalle, and we introduce mould theoretic

formulations of Drinfeld’s notion of the associator set and that of the Grothendieck–Teichmüller group.
This talk is based on the joint work with Hidekazu Furusho and Minoru Hirose.
6 国 場 敦 夫 ( 東 大 総 合 文 化)
松 生 周 一 郎 ( 東 大 総 合 文 化)
米 山 瑛 仁 ( 東 大 総 合 文 化)

Atsuo Kuniba (Univ. of Tokyo)
Shuichiro Matsuike (Univ. of Tokyo)
Akihito Yoneyama (Univ. of Tokyo)

New solutions to the tetrahedron equation associated with quantizedsix-vertex models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
New solutions to the tetrahedron equation associated with quantizedsix-vertex models

概 要 In this talk, we present a family of new solutions to the tetrahedron equation of the form RLLL =LLLR, where L operator may be regarded as a quantized six-vertex model whose Boltzmann weights are
specific representations of the q-oscillator or q-Weyl algebras. When the three L’s are associated with theq-oscillator algebra, R coincides with the known intertwiner of the quantized coordinate ring Aq (sl3 ). On
the other hand, L’s based on the q-Weyl algebra lead to new R’s whose elements are either factorized or
expressed as a terminating q-hypergeometric type series.
7 中 島 俊 樹 ( 上 智 大 理 工)

Toshiki Nakashima (Sophia Univ.)

Geometric crystal on unipotent variety and crystal of modified quantum
algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Geometric crystal on unipotent variety and crystal of modified quantum
algebra概 要 We shall define a geometric crystal structure on the unipotent variety of a simple, simply connectedcomplex algebraic group. In SL(2)-case, certain relation to crystal base of a modified quantum algebra will
be presented.

最終版: 2023/2/17

109

無限可積分系

11:00〜12:00

特別講演
T. Scrimshaw (北大教育推進機構) ♭ Krystal theory

Travis Scrimshaw (Hokkaido Univ.)

Krystal theory

概 要 Kashiwara’s theory of crystal bases has been applied to many different problems in representation

theory, physics, and geometry. In this talk, we will focus on their appearance in the K-theoretic Schubert
calculus of the Grassmannian. Specifically, we look at the symmetric function representatives of K-theory
classes that arise from Schubert varieties called (symmetric) Grothendieck polynomials {Gλ }λ and three otherrelated bases: the dual basis and their “weak” analogs. We construct a gln -crystal using the combinatorialdescriptions of Buch and Lam–Pylyavskyy to describe the decomposition of these bases into Schur functions
and describe their multiplicties. We will then discuss extensions to the (refined) canonical Grothendieckpolynomials introduced by Hwang et al. and Yeliussizov. This suggest an extension of Kashiwara’s theory
which we call K-crystals, or Krystals for short. We conclude with some open problems. This is based on
joint works with Graham Hawkes, Cara Monical, Oliver Pechenik.