最終版: 2022/3/4“日本数学会2022 年度年会

英 文

サ

マ

リ

2022 年 3 月
於

埼玉大学

集

2022 日 本 数 学 会
年会プログラム期日

2022 年 3 月 28 日（ 月 ）〜 3 月 31 日（ 木 ）

後

援

埼

会

場

埼
玉
大
学
理
学
部
埼 玉 県 さ い た ま 市 桜 区 下 大 久 保 255

連 絡 先

埼 玉 大 学 理 学 部 数 学 科〒338-8570
埼 玉 県 さ い た ま 市 桜 区 下 大 久 保 255
E-mail saitama22mar mathsoc jp

玉一般社団法人大学

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

全学講義棟
1 号館 1-205

全学講義棟
1 号館 1-206

全学講義棟
1 号館 1-207

全学講義棟
1 号館 1-301

全学講義棟
1 号館 1-304

全学講義棟
1 号館 1-401

全学講義棟
1 号館 1-402

全学講義棟
1 号館 1-403

全学講義棟
3 号館 3-101

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

数学基礎論
および歴史

10:00〜11:30

28 日
（月）

9:00〜12:00 9:00〜11:50 9:30〜11:45 10:00〜12:00 9:20〜12:00 9:30〜12:00
14:15〜16:15 14:15〜15:05 15:30〜17:40 14:15〜16:00 14:15〜16:00 14:15〜15:05

企画特別講演

9:30〜11:50

9:50〜11:20
15:45〜17:15

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
14:15〜15:15 16:30〜17:30 15:15〜16:15 14:15〜15:15 16:15〜17:15 16:15〜17:15 15:20〜16:20 14:15〜15:15 14:30〜15:30
16:30〜17:30

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

9:00〜12:00

9:00〜11:30

9:00〜12:00 10:00〜11:45
13:00〜14:00 13:15〜14:15

29 日 特 別 講 演 特 別 講 演（火） 13:00〜14:00 13:00〜14:00

9:45〜11:45

9:30〜11:50

9:30〜11:30

数学基礎論
および歴史
9:45〜11:25

特別講演 特別講演 特別講演 特別講演
13:15〜14:15 13:15〜14:15 13:15〜14:15 13:00〜14:00

日 本 数 学 会 賞 授 賞 式（全学講義棟 1 号館 1-301 講義室） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:45〜15:15)
〃
総
合
講
演（
） 日 本 数 学 会 賞 春 季 賞 受 賞 者 · · · · · · · · · · · · (15:30〜16:30)
緒 方 芳 子 (東 大 数 理) · · · · · · · · · · · · (16:45〜17:45)

函数解析学 函数方程式論 統 計 数 学 代 数 学 応 用 数 学 幾 何 学 トポロジー 実 函 数 論 無限可積分系
10:00〜11:30

30 日
（水）

9:00〜12:00
14:15〜16:15

9:50〜11:40

9:30〜10:30

9:00〜10:45
14:15〜17:00

企画特別講演

9:10〜11:45

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

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
14:15〜15:15 16:30〜17:30 14:25〜15:25 14:15〜15:15 11:00〜12:00 14:15〜15:15 15:30〜16:30 16:15〜17:15 15:00〜16:00
15:45〜16:45 15:25〜16:25
15:30〜16:30
16:35〜17:35

31 日
（木）

函数方程式論 統 計 数 学 代 数 学 応 用 数 学 幾 何 学

実 函 数 論 無限可積分系

9:00〜12:00 9:50〜11:40 9:30〜12:00
14:15〜16:15 14:20〜16:25 14:15〜16:00

9:30〜12:00 10:00〜12:00
14:15〜15:15

9:00〜10:45

企画特別講演

9:15〜12:00

13:00〜14:00

特別講演

特別講演

特別講演 特別講演

16:30〜17:30

11:00〜12:00

15:30〜16:30 14:15〜15:15

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3

目次
総合講演

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

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

2

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

5

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

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

10

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

143 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

173 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

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

24

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

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

35

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

実函数論

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

56

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

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

62

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

統計数学

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

67

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

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4

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
応用数学

76

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

81

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

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

95

3 月 28 日（月） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

3 月 29 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

100

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

104

3 月 30 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104

3 月 31 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106

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1

総合講演

総 合

講

演

3 月 29 日（火） 総合講演会場
2022 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· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:30〜16:30)
Spring Prize Winner緒 方 芳 子 ( 東 大 数 理)

量子スピン系におけるギャップ相の分類問題について · · · · · (16:45〜17:45)

Yoshiko Ogata (Univ. of Tokyo)

Classiﬁcation of gapped ground state phases in quantum spin
systems

概 要 Recently, classiﬁcation problems of gapped ground state phases attract a lot of attention in quantum

statistical mechanics. We explain about our operator algebraic approach to these problems.

最終版: 2022/3/4
企画特別講演

企

画

特

別

講

2

演

3 月 28 日（月）第 II 会場
𠮷 田 悠 一 ( 国 立 情 報 学 研)

有向グラフとハイパーグラフに対するスペクトラル理論 · · · (13:00〜14:00)

Yuichi Yoshida(Nat. Inst. of Informatics)

Spectral theory for directed graphs and hypergraphs

概 要 The usual spectral graph theory is a theory for undirected graphs that considers a matrix called

the Laplacian and uses its eigenvalues and eigenvectors to reveal the properties of the graph. In practicalapplications, however, directed graphs, which have orientated edges, and hypergraphs, which can containmore than three vertices in a single edge, are also very important objects. To ﬁll this gap, spectral theory
for directed graphs and hypergraphs has recently been developed, and various results such as clustering andsparsiﬁcation were obtained. Laplacians for directed graphs and hypergraphs are not matrices (i.e., linear
operators), but nonlinear (multivalued) operators, and key mathematical tools that help us to analyze those
Laplacians are the theories of submodular functions and monotone operators. In this talk, I will review these
progresses and discuss future outlook.
第 III 会場
特別招待講演 (日本応用数理学会)
鈴 木 大 慈 (東 大 情 報 理 工) 深層学習の数理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Taiji Suzuki(Univ. of Tokyo)

Mathematical theories of deep learning

概 要 In this talk, I present mathematical theories of deep learning, especially, I discuss how deep learn-

ing can outperform shallow learning methods such as kernel methods and show its connection to classic
statistics/machine-learning theories such as “sparseness.” First, I will introduce some examples in which
deep learning can outperform the shallow methods, in which sparsity and non-convex geometry of the targetfunction space play the essential role. Next, I present a deep learning optimization theory based on anoisy gradient descent, and show how it can achieve the global optimal solution. Theoretical tools fromthe probability theory such as stochastic diﬀerential equations and Wasserstein geometry play the key role.
Throughout the talk, I also discuss the limitation of the current theory to explain the behavior of deeplearning.

最終版: 2022/3/4

3

企画特別講演

第 IV 会場
上 野 健 爾(四日市大関孝和数学研・京大⋆)

Kenji Ueno
(Yokkaichi Univ. / Kyoto Univ.⋆)

楊輝算法と関孝和 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Yang Hui suanfa and Seki Takakzu

概 要 This talk will focus mainly on the Yang Hui suanfa and discuss how it inﬂuenced the mathematics of Seki

Takakazu, such as the summation of inﬁnite geometric series, the numerical solution of algebraic equations(Seki–Horner method), and equation theory. Yang Hui was a mathematician active in the Southern Songdynasty in the second half of the 13th century. His three books, published in the 1270s, were compiled in the
Ming dynasty and published in 1378 as the Yang Hui suanfa. In this book, counting rods was used as thebasis of calculation. However, as the abacus became popular in China, the counting rods was no longer used
and the Yang Hui suanfa was lost. The book was reprinted in Korea, and the edition published in 1433 wasbrought to Japan, where it can still be seen today. This book is considered by historians of mathematics tobe an elementary textbook, as it describes how to calculate with counting rods and how to solve equations
using counting rods. From a mathematical point of view, however, the ﬁrst chapter, in which the method of
rapid arithmetic is described, is very interesting because it describes how to calculate using various properties
of integers. In addition, the method for solving quadratic and degree 4 equations using counting rods inYang Hui suanfa contains instructions on how to move the rods, which may have helped Seki Takakazu tounderstand the Tianyuan shu.
Seki Takakazu studied and transcribed this Yang Hui snafu. This transcription is not a mere copy of theoriginal, but a kind of revised edition, in which he corrected errors in the solution, corrected textual errors in
the original, and changed the order of the chapters according to the year of publication. Although the original
manuscript by Seki Takakazu has been lost, two manuscripts have survived. There are subtle diﬀerences
between the two manuscripts, such as the diﬀerent dates of Seki’s transcriptions. By comparing the two
manuscripts, this talk will show that the two manuscripts may be copies of the same manuscript, and will
clarify the dating of Seki Takakazu’s manuscript.

3 月 30 日（水）第 II 会場
久 保 雅 弘 (和歌山大システム工)

時間依存劣微分発展方程式と準変分発展方程式 · · · · · · · · · · · (13:00〜14:00)

Masahiro Kubo (Wakayama Univ.)

Time-dependent subdiﬀerential evolution equations and quasivariational evolution equations

概 要 We review the theory of time-dependent subdiﬀerential evolution equations and its application toquasi-variational evolution equations. The key concept is the energy inequality satisﬁed by the solution of
the evolution equation. We consider evolution equations of parabolic as well as elliptic-parabolic types.

最終版: 2022/3/4
企画特別講演

4

第 IV 会場
茂 手 木 公 彦 ( 日 大 文 理)

結び目をねじる, デーン手術をねじる · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Kimihiko Motegi (Nihon Univ.)

Twisting knots and twisting Dehn surgeries

概 要 Let K be a knot in the 3-sphere S 3 . Take a trivial knot c disjoint from K. Cutting K along a disk

bounded by c, and connecting it again after n full twists, we obtain a new knot Kn in S 3 . We call Kn the
knot obtained from K by an n-twist about a twisting circle c. Twisting may be applied to a Dehn surgery(K, r) (“cut and paste” of a tubular neighborhood of K) by twisting K and the surgery slope r (describing
the “pasting”) simultaneously to obtain a new Dehn surgery (Kn , rn ).
In this talk we explain how we use twisting to construct the “Seifert Surgery Network” which gives us aperspective on the entirety of Dehn surgeries producing Seifert ﬁber spaces. This viewpoint naturally leads
us to a study of twist families of Heegaard Floer L-space knots. Then we illustrate relationships amongan asymptotic behavior of Kn as |n| → ∞, the position of twisting circles, and a pattern of occurrenceof L-space knots—and more generally, tight ﬁbered knots—in twist families. We will also discuss a novel
characterization of braid axes in this context.

3 月 31 日（木）第 III 会場
東 谷 章 弘 ( 阪 大 情 報)

組合せ論的対象に付随する様々な可換環 · · · · · · · · · · · · · · · · · (13:00〜14:00)

Akihiro Higashitani (Osaka Univ.)

Various commutative rings arising from combinatorial objects

概 要 One of the goals in the area of combinatorial commutative algebra is to construct commutative rings

from combinatorial objects (e.g., graphs, simplicial complexes, matroids, posets, and so on) and to discuss
their algebraic properties in terms of the original combinatorial objects. In this talk, we present several
typical commutative rings arising from combinatorial objects and some algebraic properties of those rings.
Moreover, we focus on a couple of them and discuss their relations.
第 IV 会場
中 島

啓 (東 大 I P M U )Hiraku Nakajima (Univ. of Tokyo)

カッツ・ムーディー・リー環の幾何学的佐武対応へ向けて · (13:00〜14:00)

Towards geometric Satake correspondence for Kac–Moody
Lie algebras

概 要 About 30 years ago, I gave a geometric construction of representations of a Kac–Moody Lie algebraby quiver varieties, motivated by earlier works by Ringel, Lusztig, Ginzburg. In a 2014 proposal ‘symplectic
duality’ by Braden–Licata–Proudfoot–Webster, this construction is regarded as ‘dual’ to geometric Satakecorrespondence. Geometric Satake correspondence is formulated by using the aﬃne Grassmannian of theLanglands dual group, hence was known only for ﬁnite dimensional Lie algebras. The symplectic dual to moregeneral quiver varieties are Coulomb branches introduced by my joint work with Braverman and Finkelberg
in 2016. Hence Braverman, Finkelberg and I hoped geometric Satake correspondence for Kac–Moody Lie
algebras using Coulomb branches as substitutes of aﬃne Grassmannian. It is still conjectural in general as
we do not have enough tools to analyze Coulomb branches. When the Kac–Moody Lie algebra is of aﬃne
type A, I have an alternative description of Coulomb branches as Cherkis bow varieties, as established byjoint work with Takayama. It enables me to check geometric Satake correspondence for type A.

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5

数学基礎論および歴史

数 学

基

礎

論

3 月 28 日（月）

お

よ

び

歴

史

第 IX 会場

9:50〜11:20
1 田 中 紀 子 (愛知県立旭丘高)
Noriko Tanaka(Aichi Prefectural Asahigaoka High School)

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

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

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

were formed in four cities of Japan in the near end of the World War II. The one of the Experimental classes
were established in the Kyoto-Prefectural Kyoto First Secondary School, one each in the 3rd, 2nd and 1st
year. The origins of the classes, entrance examinations, contents of the courses, teachers are described
together until the abolition. I will once again shed light on the Experimental Class for Science Education,and make use of a part of science and technology education in Japan in the future.
2 田 村誠(大阪産大全学教育機構)

Makoto Tamura (Osaka Sangyo Univ.)

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

On the solution of cubic equations in China

概 要 “Jigu Suanjing (Continuation of Ancient Mathematics)” written in 626 deals with cubic equations,but does not explain how to solve them. However, the book shows solutions to many cubic equations, it
seems that the method was established before the book appeared. Here we consider a numeric solution
according to the text proposed by Qian Baocong.
3 小 川

束(四日市大関孝和数学研)

Tsukane Ogawa (Yokkaichi Univ.)

岡之只 (1791–?) の数学思想 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mathemacical thought of Oka Yukitada (1791–?)

概 要 Oka Shichibei Yukitada (1791–?) of the Takuma School wrote the “Regular examples for the methodsof writing solution and clarifying the path,” whch summarized the basic techniques of the “Methods ofwriting solution and clarifying the path.” It can be said to represent Oka’s mathematical thought. He
analyzed methods for solving problems in plane geometry, extracted the techniques, and organized theminto the book. He then illustrated the application of these techniques in the form of problems and theirsolutions. In this respect, Oka’s mathematics is diﬀerent from mere problem solving.
4 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 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.

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数学基礎論および歴史

5 森 本 光 生
(四日市大関孝和数学研・上智大⋆)
Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)

6

関算四伝書について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the Sekisan Shidensho

概 要 This is a survey talk on Toita Yasusuke’s Sekiryuu Shidensho, which is a collection of more than

500 wasan materials compiled by Toita Yasusuke (1708–1784). This collection contains the Taisei Sankei
and works of Seki Takakazu and mathematicians of the school Sekiryuu. The collection is composed offour parts, each of which contain about hundred materials. As Seki Takakazu passed away in 1708, thiscollection gives us interesting information about mathematical researches after Seki Takakazu’s years.
11:30〜11:45

歴史部門懇談会

14:30〜15:30

特別講演
長 田 直 樹 (東 京 女 大⋆)

Naoki Osada(Tokyo Woman’s Christian Univ.⋆)

関孝和の著作とそれらの伝播

The works of Seki Takakazu and their propagation

概 要 In order to evaluate the mathematics of Seki Takakazu, it is necessary to determine his genuine

works. In this lecture, the lecturer ﬁrst discusses whether or not the works conventionally attributed to
Seki Takakazu are his genuine works, and if not, whose works they are, based on the previous study by
Tatsuhiko Kobayashi and my recent research. Next, the lecturer describes how Seki’s manuscripts weretranscribed at Seki Takakazu’s school and discusses which of Seki’s manuscripts were in the possession of
Araki Murahide, the ﬁrst descendant of the Seki school, and Matsunaga Yoshisuke, the second descendant.
Based on these considerations and the previous research of Ken’ichi Satō, the lecturer speculates on how
the Katsuyō Sampō (Essential Mathematics) which has been said to be ”Seki’s posthumous manuscripts
published by his disciple Araki Murahide and Araki’s disciple Ōtaka Yoshimasa,” was published, In addition,
the lecturer also speculates on how the manuscripts of Seki, especially his Kaikendai no Hō (Methods ofSolving Explicit Problems) and Kaiindai no Hō (Methods of Solving Hidden Problems), were propagated.
15:45〜17:15
6 関

隆 宏 (新潟大経営戦略本部)

Takahiro Seki

(Niigata Univ.)

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

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

概 要 It is well-known that the associative substructural logic FLcw , obtained from FL by adding bothcontraction and weakening rules, derives exchange rule. In this talk, we consider the commutativity resultin non-associative substructural logics with weakening, contraction, restricted weakening and restricted
contraction axioms.
7 倉 田 俊 彦 ( 法 政 大 経 営)
藤 田 憲 悦 ( 群 馬 大 理 工)

Toshihiko Kurata (Hosei Univ.)
Ken-etsu Fujita (Gunma Univ.)

Spectral spaces for models of intuitionistic logic · · · · · · · · · · · · · · · · · · · · 15
Spectral spaces for models of intuitionistic logic

概 要 In the ordinary framework of neighbourhood semantics, the propositions of intuitionistic logic are in-terpreted as the compact open sets of Heyting spaces. In contrast, we attempt to give another interpretation
based on the open sets of spectral spaces.

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7

数学基礎論および歴史

8 荒 武 永 史 ( 京 大 数 理 研)
Hisashi Aratake (Kyoto Univ.)

Limits, colimits, and spectra of modelled spaces · · · · · · · · · · · · · · · · · · · · 15
Limits, colimits, and spectra of modelled spaces

概 要 It is well-known that the construction of Zariski spectra of commutative rings yields an adjunction

between the category of rings and the category of locally ringed spaces. Many constructions of spectra ofalgebras can be considered as such an adjunction. Michel Coste uniﬁed them in the language of categorical
logic by showing that, for any triple (T,T’,A) such as (rings, local rings, local homomorphisms), each
T-model can be associated with a T’-modelled space (Coste spectrum) and that this construction yields
an adjunction between the category of T-models and the category of T’-modelled spaces. In this talk, we
extend Coste spectra to spectra of T-modelled spaces and then show existence of limits and colimits in
categories of modelled spaces.
9 宮 部 賢 志 ( 明 大 理 工)
Kenshi Miyabe(Meiji Univ.)

Bernoulli 測度に対する予測誤差の収束速度 · · · · · · · · · · · · · · · · · · · · · · · · 15
The rate of convergence of computable inductions

概 要 In the setting of inductive inference by Solomonoﬀ, we consider predicting the next bit when we observea ﬁnite binary sequence. For a sequence that is random with respect to a computable model measure, any
suﬃciently general conditional prediction will converge to the conditional model. Furthermore, the sum of
the errors between conditional prediction and model is a left-c.e. Martin–Löf random real when the error
is measured by Kullback–Leibler. We show that this is also true for the case that the model measure is a
Bernoulli measure.
10 只 木 孝 太 郎 (中 部 大 工)

Kohtaro Tadaki (Chubu Univ.)

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

A reﬁnement of quantum information theory by algorithmic randomnessVI

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

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

3 月 29 日（火）第 IX 会場

9:45〜11:25
11 津 久 浦 健 太 (筑波大数理物質)

Kenta Tsukuura (Univ. of Tsukuba)

The extent of saturation of induced ideals · · · · · · · · · · · · · · · · · · · · · · · · · 15
The extent of saturation of induced ideals

概 要 Kunen constructed a model in which ω1 carries a saturated ideal. We give a simpliﬁed construction

by using later improvements. Furthermore, we investigate the extent of saturation of the induced ideal interms of strong saturation, layeredness, and, centeredness.

最終版: 2022/3/4
数学基礎論および歴史

12 池 上 大 祐 (芝 浦 工 大 工)
Daisuke Ikegami(Shibaura Inst. of Tech.)8

I-regularity, determinacy, and Solovay models · · · · · · · · · · · · · · · · · · · · · 15
I-regularity, determinacy, and Solovay models

概 要 We show under ZF+DC+ADR that every set of reals is I-regular for any σ-ideal I on the Baire spaceω ω such that PI is proper. This answers the question of Khomskii in his Ph.D. thesis. We also show thatthe same conclusion holds under ZF+DC+AD+ if we additionally assume that the set of Borel codes for
I-positive sets is ∆21 .
13 依 岡 輝 幸 (静 岡 大 理)

Teruyuki Yorioka (Shizuoka Univ.)

梯子系の色付けの σ-一様化とトドロチェビッチによるマーティンの公理の部分公理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

σ-uniformizations of ladder system colorings and Todorcevic’s fragmentsof Martin’s Axiom

概 要 Uniformization of ladder system colorings has been introduced by analysis of a proof of the Shelah’ssolution of Whitehead problem. Shelah’s proof can be separated into the following two theorems: MAℵ1
implies U({ω1 ∩ Lim}), and U({ω1 ∩ Lim}) implies the existence of a non-free Whitehead group. In MSJ
Autumn Meeting 2019, it is explained that the assertion K3 , which is one of Todorcevic’s fragments ofMartin’s Axiom, implies that U(stat) holds.
σ-uniformizations of ladder system colorings are introduced, and it is proved that K2 implies that every
ladder system colorings can be σ-uniformized. This implies that K2 implies U(stat). This improves theabove results.
14 池 田 宏 一 郎 (法 政 大 経 営)
Koichiro Ikeda(Hosei Univ.)

ジェネリック構造における仮想元 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Imaginaries in generic structures

概 要 The theory of a generic structure is said to be normal, if ā ∈ acl(A) implies d(ā/A) = 0 for anyā, A ⊂ M. We show that any saturated normal generic structure has weak elimination of imaginaries but
does not have the ﬁnite set property.
15 桔 梗 宏 孝 (神戸大システム情報)
Hirotaka Kikyo(Kobe Univ.)

ある種のジェネリック構造のモデル完全性について · · · · · · · · · · · · · · · · · 15

On model completeness of certain generic structures

概 要 Let δ(A) = |A| − α · e(A) for any ﬁnite graphs A where |A| is the number of all vertices of A and e(A)the number of all edges of A. Let Kf be the class of graphs like amalgamation classes used to construct
Hrushovski’s pseudoplanes using a log-like control function f . Suppose Kf has the free amalgamation
property, and let M be the generic structure of (Kf , <) where < is deﬁned as in the Hrushovski’s case. If
α is rational then the theory of M is model complete. In the case that α is irrational, with some more mild
assumptions on f , the theory of M is also model complete.
16 坪 井 明 人 (筑波大⋆)Akito Tsuboi (Univ. of Tsukuba⋆)

Instability, CH and Keisler’s isomorphism theorem · · · · · · · · · · · · · · · · · 10
Instability, CH and Keisler’s isomorphism theorem

概 要 We give a talk on our results related to Keisler’s isomorphism theorem.

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9

数学基礎論および歴史

11:30〜11:45

数学基礎論および歴史分科会総会

13:00〜14:00

特別講演
新 屋 良 磨 ( 秋 田 大 理 工)

Ryoma Sin’ya(Akita Univ.)

正規言語族の無限内部階層における分離問題および可測性について

Separation and measurability problems on an inﬁnite hierarchy of regular languages

概 要 A regular language is a set L of words described by a regular expression, but it has the following

alternative characterisation via logic: L is regular if and only if L is “deﬁnable” by a monadic second-orderformula.
This logical characterisation gives us an inﬁnite hierarchy in the class of all regular languages, e.g., the class
SF of “star-free” languages deﬁnable by ﬁrst-order logic FO and the classes of languages corresponding toseveral fragments of ﬁrst-order logic (e.g., quantiﬁer alternation hierarchy of FO, FO with restricted numberof variables or diﬀerent predicates, etc.).
The ﬁrst part of this talk introduces the well-known connection between languages, logics, and algebras (several subclasses of ﬁnite monoids). In this part, two important theorems are introduced: (1)Schützenberger’s theorem stating that the algebraic counterpart of SF is the class of aperiodic monoids. (2)Eilenberg’s variety theorem stating that there is a natural one-to-one correspondence between the subclassesof regular languages and ﬁnite monoids equipping certain rich closure properties, so-called “varieties” and“pseudovarieties”, respectively.
The second part is an invitation to recent developments on this inﬁnite hierarchy. In this part, two decision
problems are described: (1) Separation problem for subclasses of star-free languages. (2) Measurability
problem for subclasses of regular languages.

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代数学代 数
3 月 28 日（月）10

学第 IV 会場

9:30〜11:45
1 伊 藤 歌 那 (東工大情報理工)
Kana Ito(Tokyo Tech)(2)

Aodd 型レベル 2 の標準加群と Z-作用素の関係性について · · · · · · · · · · · · 15
(2)

The relation between level 2 standard modules of type Aodd and Zoperators

概 要 In this talk, we will discuss a representation of the vacuum spaces of level 2 standard modules of type(2)

A9using Z-operators in accordance with Kanade–Russell’s conjecture of partition conditions. Rogers–

Ramanujan type identities are the identities represented in the form of (inﬁnite sum)=(inﬁnite product)with the Pochhammer symbols like Rogers–Ramanujan identities. Since the work by Lepowsky–Wilson,
there has been an expectation that by assigning a non-negative integer to each vertex of an aﬃne Dynkin
diagram, we can obtain Rogers–Ramanujan type identities and integer partition theorems. Related to this,we will propose a conjecture for the relations between the vacuum spaces of level 2 standard modules of(2)

type Aodd and Z-operators.
2 吉 井

豊 ( 茨 城 大 教 育)

Yutaka Yoshii (Ibaraki Univ.)

超代数 Dist((SL2 )r ) のある種の加群の構造について · · · · · · · · · · · · · · · · · 10

Structure of certain modules for the hyperalgebra Dist((SL2 )r )概 要 In the ﬁnite-dimensional hyperalgebra Ur = Dist((SL2 )r ), certain elements B (ε) (a, j) have been

already constructed before. We report that each Ur -module Ur B (ε) (a, j) has a certain basis determined by
ε and (a, j) and that the Ur -module has simple head and simple socle, which are isomorphic.
3 川 合 遼 太 郎 ( 早 大 基 幹 理 工)
池 田
岳 ( 早 大 理 工)

Ryotaro Kawago (Waseda Univ.)
Takeshi Ikeda (Waseda Univ.)

古典型旗多様体のシューベルト多様体の点の重複度 · · · · · · · · · · · · · · · · · 15

Multiplicities of Schubert varieties in the ﬂag varieties of classical types

概 要 We consider Schubert varieties in the ﬂag varieties of classical types. For singularities of Schubertvarieties, there is a combinatorial formula for the multiplicity in the case of Grassmannian of classical types.
We obtained results extending this formula to the case of Schubert varieties associated to vexillary signed
permutations of ﬂag varieties of classical types.
4 板 垣 智 洋 ( 高 崎 経 大 経 済)
鳥 居
猛 ( 岡 山 大 自 然)
中 本 和 典 ( 山 梨 大 医)
Tomohiro Itagaki(Takasaki City Univ. of Econ.)
Takeshi Torii (Okayama Univ.)
Kazunori Nakamoto(Univ. of Yamanashi)

Hochschild cohomology of Nm · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Hochschild cohomology of Nm

概 要 Let Nm (R) = {(aij ) ∈ Mm (R) | a11 = a22 = · · · = amm and aij = 0 for any i > j} for a commutative

ring R. We calculate the Hochschild cohomology ring HH∗ (Nm (R), Nm (R)) as R-algebras. We also calculate
HH∗ (Nm (R), Mm (R)/Nm (R)) as R-modules.

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11

代数学

5 後 藤 悠 一 朗 (阪Yuichiro Goto大理) ♭ 擬遺伝代数と direct bocs における関係の一般化 · · · · · · · · · · · · · · · · · · · · 10

(Osaka Univ.)

Generalizations of the relationship between quasi-hereditary algebras
and directed bocses

概 要 Quasi-hereditary algebras were introduced by Cline, Parshall and Scott to study the highest weightcategories in Lie theory. On the other hand, bocses were introduced in the context of Drozd’s tame and wilddichotomy theorem. Koenig, Külshammer and Ovsienko connected them by giving equivalences between
the module categories of ∆-ﬁltered modules over quasi-hereditary algebras and those over directed bocses.
In this talk, we discuss some problems occurring when we prove a similar theorem for ∆-ﬁltered algebras
and give two lemmas necessary for the proof. Here, a ∆-ﬁltered algebra is known to be one of naturalgeneralizations of a quasi-hereditary algebra.
6 行 田 康 晃 ( 名 大 多 元 数 理)

Yasuaki Gyoda (Nagoya Univ.)

ガブリエルの定理の τ 傾理論における一般化とその団代数的アプローチ· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Generalization of Gabriel’s theorem in τ -tilting theory and its cluster
algebraic approach

概 要 Gabriel’s theorem, shown in 1972, is a theorem that classiﬁes path algebras of ﬁnite representation

type using Dynkin diagrams, and is a very important theorem that suggests a connection between Lie theory
and the representation theory of algebras. In this talk, I will generalize Gabriel’s theorem by using cluster
algebra theory, which has been rapidly developed recently and is closely related to both Lie theory and therepresentation theory of algebras.
7 百 合 草 寿 哉 ( 東 北 大 理)
行 田 康 晃 ( 名 大 多 元 数 理)

Toshiya Yurikusa (Tohoku Univ.)
Yasuaki Gyoda (Nagoya Univ.)

Bongartz completion via c-vectors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Bongartz completion via c-vectors

概 要 Bongartz completion is an important subject in representation theory of ﬁnite dimensional algebras,in particular, τ -tilting theory. We characterize it using c-vectors. From this point of view, we introduce
the notion of Bongartz completion for cluster algebras using c-vectors, and we give some properties. Thisis a joint work with Peigen Cao and Yasuaki Gyoda.
8 小 塩 遼 太 郎 ( 東 京 理 大 理)
小 境 雄 太 ( 東 京 理 大 理)

Ryotaro Koshio (Tokyo Univ. of Sci.)
Yuta Kozakai (Tokyo Univ. of Sci.)

剰余群における Schur multiplier の消滅条件下でのブロック上の台 τ 傾加群と半煉瓦について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Support τ -tilting modules and semibricks over blocks under vanisingconditions of Schur multipliers of factor groups

概 要 Let G be a ﬁnite group, k an algebraically closed ﬁeld of characteristic p > 0 and B a block of groupalgebra kG. Support τ -tilting modules and semibricks over B are corresponding B-modules to two-term
tilting complexes and two-term simple minded collections over B, which are both special forms of tilting
complexes and simple minded collections over B , respectively. Let G̃ be a ﬁnite group containing G
as a normal subgroup and B̃ a block of k G̃ covering B. In this talk, we will introduce the methods ofconstructions of support τ -tilting modules and semibricks over B̃ from the ones over B under the vanisingcondition of Schur multipliers of the factor group G̃/G over k.

最終版: 2022/3/4
代数学

9 小 田 文 仁 ( 近 畿 大 理 工)
竹 ヶ 原 裕 元 ( 室 蘭 工 大 理 工)
(Kinki Univ.)
Fumihito Oda
Yugen Takegahara(Muroran Inst. of Tech.)12

斜バーンサイド環とコホモロジカルマッキー 2 モチーフ · · · · · · · · · · · · · 10

Crossed Burnside rings and cohomological Mackey 2-motives

概 要 Balmer and Dell’Ambrogio introduced the pseudo-functor P from the bicategory of k-linear Mackey

2-motives to the bicategory of k-linear cohomological Mackey 2-motives over a commutative ring k. They
showed that P maps the general Mackey 2-motives to the cohomological Mackey 2-motives by using thering homomorphism from the crossed Burnside ring of a ﬁnite group G over k to the center ZkG of groupalgebra kG. We study the behavior of motivic decomposition of cohomological Mackey 2-motives as images
by P of motivic decomposition of Mackey 2-motives.
10 栗 原 大 武 (山 口 大 創 成)
東 谷 章 弘 ( 阪 大 情 報)

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

有限群から得られる等質カンドル · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Homogeneous quandles arising from ﬁnite groups

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

our talk, we investigate a special kind of quandles, called generalized Alexander quandles Q(G, ψ), which
is deﬁned by a group G together with its group automorphism ψ. We develop the quandle invariants forgeneralized Alexander quandles.
14:15〜15:15

特別講演疋 田 辰 之 ( 京 大 数 理 研)

K 理論的標準基底とその楕円化

Tatsuyuki Hikita (Kyoto Univ.)

K-theoretic canonical bases and their elliptic analogues

概 要 Representation theory of semisimple Lie algebras are closely related to the geometry of Springer

resolutions. In particular, Lusztig deﬁned certain canonical bases in equivariant K-theory of Springer
resolutions and conjectured that they describe modular representation theory of semisimple Lie algebras.
This conjecture was proved by Bezrukavnikov–Mirkovic for large enough characteristic by beautifully relating
coherent sheaves on Springer resolutions, representations of semisimple Lie algebras in positive characteristic,
and certain perverse sheaves on aﬃne ﬂag manifolds.
In this talk, I deﬁne canonical bases in equivariant K-theory of more general conical symplectic resolutions
and explain their expected properties. If time permits, I will explain an attempt to ﬁnd their elliptic
analogues which reveal new duality under symplectic duality.
15:30〜17:40
11 柴 田 康 介 (日 大 文 理)

Kohsuke Shibata (Nihon Univ.)

2 次元有理特異点次数付き環の F -有理性について · · · · · · · · · · · · · · · · · · · 15
F -rationality of two-dimensional graded rings with a rational singularity

概 要 It is known that a two-dimensional F -rational ring has a rational singularity. However a two-

dimensional ring with a rational singularity is not F -rational in general. In this talk, we investigate
F -rationality of a two-dimensional graded ring with a rational singularity in terms of the multiplicity.
Moreover, we determine when a two-dimensional graded ring with a rational singularity and a small
multiplicity is F -rational.

最終版: 2022/3/4

13

代数学

12 伊 城 慎 之 介 (日 大 総 合 基 礎)
下 元 数 馬 ( 日 大 文 理)
M. Asgharzadeh

Shinnosuke Ishiro (Nihon Univ.)
Kazuma Shimomoto (Nihon Univ.)
Mohsen Asgharzadeh

局所コホモロジーのスカラー写像の全射性と第二消滅定理への応用 · · · · 15

Surjectivity of some scalar maps on local cohomology modules and an
application to the second vanishing thorem

概 要 The second vanishing theorem has a long history in the theory of local cohomology modules overregular local rings and the case of ramiﬁed regular local rings is unsolved. We give a partial answer to it
using the surjectivity of scalar maps of local cohomology modules. In our talk, we introduce our results andsome examples of the vanishing of local cohomology modules to exhibit the non-triviality of our results.
13 伊 城 慎 之 介 (日 大 総 合 基 礎)
下 元 数 馬 ( 日 大 文 理)
仲 里
渓 ( 名 大 多 元 数 理)

Shinnosuke Ishiro (Nihon Univ.)
Kazuma Shimomoto (Nihon Univ.)
Kei Nakazato (Nagoya Univ.)

Perfectoid towers and its small tilts · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Perfectoid towers and its small tilts

概 要 Perfectoid theory has many applications to commutative ring theory and singularity theory. For

example, the direct summand conjecture, perfectoid multiplier/test ideals are such instances. However, rings
studied in the perfectoid theory are usually non-Noetherian, which are diﬃcult to study via the standard
commutative ring theory. For this reason, we build a new framework that can also treat Noetherian rings
via perfectoids, which are called perfectoid towers and small tilts. In this talk, we plan to explain deﬁnitions
and basic properties.
14 堀 内淳 ( 日 本 工 大)
下 元 数 馬 ( 日 大 文 理)
衛 藤 和 文 ( 日 本 工 大 工)

Jun Horiuchi (Nippon Inst. of Tech.)
Kazuma Shimomoto (Nihon Univ.)
Kazufumi Eto (Nippon Inst. of Tech.)

On integrality of rings and the monoidal map · · · · · · · · · · · · · · · · · · · · · · 15

On integrality of rings and the monoidal map

概 要 We will derive some ring theoretic properties of the tilt of the ring. In this process, we make use of themonoidal structure of the tilt and so-called monoidal map. We explain the key discussion due to Fontaine,
and we will discuss further development and application.
15 宮 崎 充 弘 (京 都 教 育 大)
Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)

On the non-Gorenstein locus of the Ehrhart ring of the stable set polytope of an odd cycle graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the non-Gorenstein locus of the Ehrhart ring of the stable set polytope of an odd cycle graph概 要 Let G = (V, E) be an odd cycle graph. We describe the non-Gorenstein locus of the Ehrhart ring of

the stable set polytope of G by showing the radical of the trace of the canonical module of that ring is theintersection of prime ideals corresponding to certain faces of the stable set polytope of G.

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代数学

16 石 原 侑 樹 (東 京 理 大 理)

Yuki Ishihara (Tokyo Univ. of Sci.)

14

二重イデアル商と準素イデアル分解について · · · · · · · · · · · · · · · · · · · · · · · 15

On double ideal quotient and primary decomposition

概 要 It is known that “primary decomposition” is a basic notion in Commutative Algebra. In order toanalyze properties of primary decomposition, we introduce a special ideal “double ideal quotient”, which has
the form I : (I : J). By using double ideal quotient, we can obtain criteria for prime divisors and primary
components. Also, we can generate the particular primary component from a given ideal and its prime
divisor. We can apply these properties to compute the localization of an ideal at a prime ideal in themultivariable polynomial ring over a computable ﬁeld.
17 神 代 真 也 (小 山 工 高 専)
Shinya Kumashiro(Oyama Nat. Coll. of Tech.)

次数付フィルトレーションと節減数 2 のイデアル · · · · · · · · · · · · · · · · · · · 15

Graded ﬁltrations and ideals of reduction number two

概 要 We give a way to construct graded ﬁltrations of graded modules. We then apply the ﬁltration to the

Sally module, which describes a correction term of the Hilbert function of ideals. As a result, we obtain theinequality of the Hilbert coeﬃcients for ideals of reduction number 2.
18 大 関 一 秀 (山 口 大 創 成)Kazuho Ozeki (Yamaguchi Univ.)

The ﬁrst Hilbert coeﬃcient of stretched ideals · · · · · · · · · · · · · · · · · · · · · 15
The ﬁrst Hilbert coeﬃcient of stretched ideals

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

3 月 29 日（火）第 IV 会場

9:00〜12:00
19 桜 井真 ( 開 智 学 園)

Makoto Sakurai (Kaichi Gakuen)

位相的カイラル代数と特性類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Topological chiral algebras and characteristic classes

概 要 The chiral-factorization algebra theory of Beilinson and Drinfeld is an algebraic system with ageometric nature inspired by the physics of holomorphic conformal ﬁeld theories. In this talk, I will try
to re-investigate the sigma-model interpretation of the chiral de Rham complex. This interpretation was
initiated by the works of Nekrasov and Witten, but my computation is after the toric diagrams andcomputational algebraic geometry. The assumption was the OPE preservation under the Nekrasov Ansatz
after the generalized complex structure of Hitchin school. The sigma-model interpretation was conﬁrmed
by Gorbounov, Gwilliam, and Williams in their Astérisque paper, but my work was earlier and has more
inclination toward Beilinson and Drinfeld.
20 中 川 彬 雄 (千葉大融合理工)
Akio Nakagawa (Chiba Univ.)有限体上の Appell–Lauricella 超幾何関数について · · · · · · · · · · · · · · · · · · 15

Appell–Lauricella hypergeometric functions over ﬁnite ﬁelds

概 要 We study ﬁnite ﬁelds analogues of integral representations of Appell–Lauricella hypergeometric func-

tions FA , FB , FC and FD . Furthermore, as an application, we see relations between these functions andthe numbers of rational points of some algebraic varieties over ﬁnite ﬁelds.

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15

代数学

大
21 山 形颯 (北シモーナセッテパネーラ

理)

So Yamagata (Hokkaido Univ.)
Simona Settepanella

超平面配置の non very genericy について · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the non very genericy of hyperplane arrangements.

概 要 In 1989, Manin and Schechtman introduced a family of arrangements of hyperplanes generalizingclassical braid arrangements, which they called the discriminantal arrangements. It is well known that there
exists an open Zariski set Z in the space of central generic arrangements of n hyperplanes in Ck such thatthe intersection lattice of the discriminantal arrangements B(n, k, A) are independent from the choice of thearrangement A ∈ Z. In this talk we see a suﬃcient condition for A to be non very generic in terms ofvectors.
工大)
22 中 島 規 博 (名辻 栄 周 平 ( 北 教 大 旭 川)
Norihiro Nakashima(Nagoya Inst. of Tech.)
Shuhei Tsujie (Hokkaido Univ. of Edu.)

A 型拡張 Shi 配置と A 型拡張 Catalan 配置が遺伝的自由配置であるための条件 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The conditions for the extended Shi and Catalan arrangements of type
A to be hereditarily free

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

hereditarily free, while we determine the dimension that the cone of the extended Shi arrangement of type
A is hereditarily free. For this purpose, we deﬁne a class of arrangements which contains the extended Shi
and Catalan arrangement of type A and which closed under restriction, using digraphs with vertex weights.
23 安 藤 哲 哉 (千 葉 大 理)
Tetsuya Ando

(Chiba Univ.)

3 変数 3 次斉次 extremal 不等式修正版 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Extremal positive semideﬁnite forms of cubic homogeneous polynomialsof three variables+
概 要 Let P3,3
be the set of all the cubic homogeneous polynomials f (x, y, z) which satisfy f (x, y, z) ≥ 0 for+
all x ≥ 0, y ≥ 0, z ≥ 0. We determine all the extremal elements of P3,3.

24 岩 見 智 宏 (九 工 大 工)

Tomohiro Iwami (Kyushu Inst. of Tech.)Intermediate Jacobian of an extended three-dimensional extremal neighborhood. Part I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Intermediate Jacobian of an extended three-dimensional extremal neighborhood. Part I

概 要 For an semi-stable extremal neighborhood (X, C) ⊂ C4 with C is irreducible and reduced, the bounded

terminality of 2-game between the invariants l(P ), q(P ), related to 0-dimensional supports of | − KX |, gives
the existence of 3-dimensional ﬂips ([S. Mori, 1988]). Regarding to [S. Mori, 1988], the author had studied:for (X, C) ⊂ C4 where C is not necessary irreducible nor reduced, denoted as (X, Cs ) ⊂ C4 ([I2019March]),i) to induce Miyaoka–Yau type inequality with c3 , as abbreviated (M Y )3,c3 , ii) to study (M Y )3,c3 by
the associated Higgs sheaves, and iii) to more study (M Y )3,c3 by introducing diﬀrential operators “ofcodimension 2 type” for ii), and so on. In this talk, based on these works i)–iii), the author will report: a)to construct “period space” for (X, Cs ), and b) for a), to introduce intermediate Jacobian for (X, Cs ), which
gives “2-Albanese”, or “2-Picard” varieties. Here, the preﬁx “2-” mainly comes from iii), probably relate ton(≥ 1)-motif. These varieties are expected to work to rationality of (X, Cs ) of type A. In the sequel parts,
the author will give studies regards to these points.

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代数学

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

16

Calabi–Yau 超曲面の幾何転移 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Geometric transitions for Calabi–Yau hypersurfaces

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

contraction followed by a complex smoothing. It has attracted the interest of both mathematicians andphysicists, since it may give the right notion to connect moduli spaces of Calabi–Yau 3-folds. For Calabi–
Yau hypersurfaces in toric varieties, a well-known idea of constructing geometric transitions is to use nested
reﬂexive polytopes. In this talk, I will introduce a reﬁnement of this idea and show recent progress.
26 遊 佐毅 (兵庫県立大物質)

The adjacent concurrence on inﬁnitesimally unstable Betti syzygy classes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

(Univ. of Hyogo)

The adjacent concurrence on inﬁnitesimally unstable Betti syzygy classes

Takeshi Usa

概 要 Even for an arithmetic D2 non-singular projective subvariety X ⊆ PN (C) = P , when we consider a

1-st inﬁnitesimal embedded deformation of X in P , some classes in the q-th Betti syzygy space (or Koszul
(q)

(q)

1,q
homology) Tm= (ZX /S+ · ZX )(m) of X in (polynomial) degree m may suddenly disappear. When weonce ﬁnd such an inﬁnitesimally unstable q-th Betti syzygy class, we often ﬁnd a non-zero (q + 1)-th Betti
1,q+1
1,q−1
syzygy space Tm
or a non-zero (q − 1)-th Betti syzygy space Tmwith the same polynomial degree mat the same time, which has also an inﬁnitesimally unstable Betti syzygy class. Here, in a general situation,

we give a steady explanation of this phenomena.
27 大 橋亮 (横浜国大環境情報)
工 藤 桃 成 ( 東 大 情 報 理 工)
原 下 秀 士 (横浜国大環境情報)

Ryo Ohashi (Yokohama Nat. Univ.)
Momonari Kudo (Univ. of Tokyo)
Shushi Harashita(Yokohama Nat. Univ.)

The a-numbers of non-hyperelliptic curves of genus three with large
cyclic automorphism group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The a-numbers of non-hyperelliptic curves of genus three with large
cyclic automorphism group

概 要 In the study of algebraic curves and their moduli spaces, it is important to determine the a-numbersof curves over a ﬁeld of positive characteristic. It is known that non-hyperelliptic curves of genus 3 areclassiﬁed by the structures of their automorphism groups as ﬁnite groups. In this paper, we determine thea-numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6 or 9. Moreover,
we also ﬁnd the exact number of the isomorphism classes of such curves attaining the possible maximal
a-number.
28 大 橋亮 (横浜国大環境情報)

Ryo Ohashi (Yokohama Nat. Univ.)

On the maximality or minimality of Howe curves of genus 3 · · · · · · · · · 15
On the maximality or minimality of Howe curves of genus 3

概 要 A nonsingular curve C over Fq is called maximal (resp. minimal) if the number of Fq -rational points

of C attains the Hasse–Weil upper (resp. lower) bound. It is known that maximal or minimal curves overFp2 are superspecial, while superspecial curves over Fp2 are not neccesarily maximal nor minimal.
In this lecture, we talk about the maximality or minimality of Howe curves of genus 3. A Howe curve is thedesingularization of the ﬁber product over P1 of two elliptic curves. We show that if a Howe curve of genus
3 is superspecial, then its standard form is maximal or minimal over Fp2 without taking its Fp2 -form.

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代数学

13:00〜14:00
29 佐 藤 宏 平 (小 山 工 高 専)
佐 藤 悠 介 ( 東 大 数 理)

Kohei Sato (Oyama Nat. Coll. of Tech.)
Yusuke Sato (Univ. of Tokyo)

Hilb-desingularizations for three-dimensional canonical cyclic quotient
singularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hilb-desingularizations for three-dimensional canonical cyclic quotient
singularities

概 要 M. Ishida and N. Iwashita classiﬁed three-dimensional canonical cyclic quotient singularities. By

using this classiﬁcation, we proved that there exists an iterated Fujiki–Oka resolution which is a Hilbdesingularization for any three-dimensional canonical cyclic quotient singularity.
30 水 野 雄 貴 (早 大 理 工)
Yuki Mizuno(Waseda Univ.)

An explicit construction of derived moduli stacks of Harder–Narasimhan
ﬁltrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An explicit construction of derived moduli stacks of Harder–Narasimhan
ﬁltrations概 要 Harder–Narasimhan(HN) ﬁltrations are ﬁltrations of sheaves obtained from semistable sheaves. Any

pure coherent sheaf has a unique HN ﬁltration. On the other hand, moduli spaces of HN ﬁltrations areconstructed as stacks (not as schemes) Moreover, Behrend, Ciocan–Fontanine, Hwang and Rose constructedderived moduli schemes of (semi) stable sheaves as diﬀerential graded (dg) schemes coming from bundlesof curved dg Lie algebras. Derived schemes and stacks are generalizations of schemes and stacks. Theirstructure sheaves are sheaves of dg algebras. By using their method, we construct derived moduli stacksof HN ﬁltrations as quotient dg-stacks explicitly. (So, they also become derived moduli stacks of unstablesheaves.)31 南

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

レトラクト (−i)-有理性への, 双有理モチーフの 2 つの応用 · · · · · · · · · · · 15

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

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

implications of the retract (−i)-rationality of a smooth projective variety: (1) in terms of an arbitrary
P 1 -invariant Nisnevich sheaf with transfer. (2) in terms of the Bloch-Srinivas type decomposition of the
diagonal.

3 月 30 日（水）第 IV 会場

9:30〜10:30
32 松 井 紘 樹 (徳島大社会産業理工)
O. Celikbas (West Virginia Univ.)(West Virginia Univ.)
Uyen Le

Hiroki Matsui (Tokushima Univ.)
Olgur Celikbas (West Virginia Univ.)
Uyen Le (West Virginia Univ.)

Huneke–Wiegand 予想とその言い換え · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Paraphrasing Huneke–Wiegand conjecture

概 要 Huenke–Wiegand conjecture is the long-standing conjecture in commutative algebra. It says that fora one-dimensional local domain, the tensor product of non-free and torsion-free module and its algebraic
dual has torsion. This conjecture is quite open and only the known case is for hypersurface local domains.
In this talk, I will paraphrase Huneke–Wiegand conjecture over complete intersection local domains to a
conjecture over hypersurface local domains.

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代数学

33 木 村 海 渡 (名 大 多 元 数 理)
大 竹 優 也 ( 名 大 多 元 数 理)髙 橋
亮 ( 名 大 多 元 数 理)
Kaito Kimura (Nagoya Univ.)(Nagoya Univ.)
Yuya Otake
Ryo Takahashi (Nagoya Univ.)

18

Cohen–Macaulay 環上の Auslander–Reiten 予想 · · · · · · · · · · · · · · · · · · · · 15

Auslander–Reiten conjecture over Cohen–Macaulay rings

概 要 Projectivity of modules in terms of Vanishing of Ext modules over a local ring is an actively studied

subject in commutative algebra. One of the most important problems is a celebrated long standing conjecture
called the Auslander–Reiten conjecture. In this talk, we consider the above problems over Cohen–Macaulayrings, which form one of the most important classes in commutative algebra.
34 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 Generalized Nakayama(Azumaya)’s lemma is a generalization of well known Nakayama(Azumaya)’s

Lemma, i.e., the assertion that MJ(R)=M implies M=0 for a module M which is a direct summand of adirect sum of ﬁnitely generated modules, where J(R) is the Jacobson radical of a ring R. First we show thislemma is equivalent to the non-existence of a non-zero Nakayama–Azumaya module. Next we show, in fact,that there is no non-zero (weak) Nakayama–Azumaya module. Also as applications of this lemma, we show
the existence of a maximal submodule for some kind modules.
35 松 野 仁 樹 (静岡大創造科学技術)
胡海 剛 (静岡大創造科学技術)
毛 利
出 ( 静 岡 大 理)

Masaki Matsuno (Shizuoka Univ.)
Haigang Hu (Shizuoka Univ.)(Shizuoka Univ.)
Izuru Mori

Noncommutative smooth conics in Calabi–Yau quantum projective planes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Noncommutative smooth conics in Calabi–Yau quantum projective planes

概 要 Throughout this talk, let k be an algebraically closed ﬁeld of characteristic 0.Let S be a 3-dimensional

Calabi–Yau quantum polynomial algebra, and f ∈ S2 a regular central element. We call A = S/(f ) a
noncommutative conic in a Calabi–Yau quantum P2 . Our goal is to classify the associated noncommutative
projective schemes Projnc A. In this talk, we will show that there exist at least 9 isomorphism classes ofProjnc A.
11:00〜12:00

2021 年度 (第 24 回), 2022 年度 (第 25 回) 日本数学会代数学賞授与式

14:15〜15:15

2022 年度 (第 25 回) 日本数学会代数学賞受賞特別講演大理) 小平消滅定理の一般化と双有理幾何への応用
修 (京

藤 野

Osamu Fujino(Kyoto Univ.)

Generalization of the Kodaira vanishing theorem and its application tobirational geometry

概 要 The Kodaira vanishing theorem plays a crucial role for the study of complex projective varieties.

We have already known many important generalizations. One of the most famous generalizations is the
Kawamata–Viehweg vanishing theorem. It is the main ingredient of the theory of minimal models forhigher-dimensional complex projective varieties. We generalize the Kodaira vanishing theorem from the
Hodge theoretic viewpoint. By using the theory of mixed Hodge structures on cohomolgy with compact
support, we establish a useful package of vanishing theorems. It greatly generalizes the framework of theminimal model program.

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代数学

15:25〜16:25

2022 年度 (第 25 回) 日本数学会代数学賞受賞特別講演
古 澤 昌 秋 (阪 市 大 理) On the Gross–Prasad conjecture with its reﬁnement for (SO(5), SO(2))
and the generalized Boecherer conjecture
(
)
Osaka
City
Univ.
On the Gross–Prasad conjecture with its reﬁnement for (SO(5), SO(2))
Masaaki Furusawa
and the generalized Boecherer conjecture

概 要 In this talk, I will describe a joint work with Kazuki Morimoto at Kobe University, where we prove theGross–Prasad conjecture and its reﬁnement, i.e. the Ichino–Ikeda type formula for the Bessel periods, in thecase of (SO(5), SO(2)), by combining several theta correspondences. Our Ichino–Ikeda type formula is valid
for any irreducible tempered cuspidal automorphic representations. In the 1980’s, Boecherer proclaimed aremarkable conjecture concerning the relationship betwee a certain sum of Fourier coeﬃcients of Siegel cusp
forms of degree two which are Hecek eigenforms and a central value of quadratic twists of degree four spinor
L-functions, which we proved earlier. As a corollary of our Ichino–Ikeda type formula above, we prove anatural gereralization of Boecherer’s conjecture to the not necessarily trivial troidal character case.
16:35〜17:35
毛 利Izuru Mori

2022 年度 (第 25 回) 日本数学会代数学賞受賞特別講演
出 (静 岡 大 理) 非可換射影曲面の分類 (AS 正則代数を中心に)(Shizuoka Univ.)

Classiﬁcation of noncommutative projective surfaces (focusing on ASregular algebras)

概 要 The classiﬁcation of 3-dimensional AS-regular algebras (introduced by Artin and Schelter) is a

starting point of noncommutative algebraic geometry. Noncommutative projective planes are deﬁned as thenoncommutative projective schemes (introduced by Artin and Zhang) associated to 3-dimensional quadratic
AS-regular algebras, and they are the most basic objects of study in noncommutative algebraic geometry.
On the other hand, it is interesting to study more general noncommutative projective surfaces. In fact,classiﬁcation of noncommutative projective surfaces is one of the major projects in noncommutative algebraic
geometry. In this talk, I will give some history of noncommutative algebraic geometry and classiﬁcation of
noncommutative projective surfaces, focusing on AS-regular algebras.

3 月 31 日（木）第 IV 会場

9:30〜12:00
36 飯 高茂 (学 習 院 大⋆)

Shigeru Iitaka (Gakushuin Univ.

⋆)

メルセンヌ型ウルトラ 2 完全数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ultra 2 perfect numbers of Mersenne type

概 要 Given odd prime h and an integer m, natural numbers a, A deﬁned by A = σ(a) − m, and B deﬁned

by B = hσ(A) + 2h̃m + h̃(h − 2), (h̃ = h + 1),
are said to be Ultra 2 perfect numbers of Mersenne type whenever σ(B) = σ(2h̃)(a + 1).
Associated nnmbers A and B are called partner and shadow, repectively.
37 飯 高茂 (学 習 院 大⋆)梶 田光(Crimson Global Academy)

Shigeru Iitaka (Gakushuin Univ.⋆)
Hikaru Kajita(Crimson Global Academy)

双子型メルセンヌ超完全数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ultra perfect numbers of twin primes type

概 要 Given an odd prime h and an integer m , if natural numbers a , A and B satisfy eualities a =2hφ(A) + m + 1, hA = φ(B) − m + 2and B = φ(a) − 1 then they are said to be ultra perfect numbers oftwin primes type.

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代数学

38 D. Tsai
Daniel Tsai

20

(名 大 多 元 数 理) ♭ The fundamental period of a periodic phenomenon pertaining to vpalindromes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Nagoya Univ.)

The fundamental period of a periodic phenomenon pertaining to vpalindromes

概 要 In March 2021, I introduced the concept of v-palindromes and proved a theorem pertaining to v-

palindromes and repeated concatenation of the decimal digits of a natural number, illustrating a periodic
phenomenon. In this talk, we show how to calculate the fundamental, i.e. smallest, period.
39 D. Duverney(Baggio Engineering School)
黒 沢
健 ( 東 京 理 大 理)
塩 川 宇 賢 ( 慶 大 理 工)
Daniel Duverney(Baggio Engineering School)
Takeshi Kurosawa (Tokyo Univ. of Sci.)
Iekata Shiokawa (Keio Univ.)

一般化 Hone 級数の無理測度について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Irrationality exponents of generalized Hone series

概 要 We compute the exact irrationality exponents of a generalized Hone series using a continued fraction

expansion.
40 小 山 信 也 (東 洋 大 理 工)
Shin-ya Koyama (Toyo Univ.)

チェビシェフの偏りと深リーマン予想 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Chebyshev’s bias and the deep Riemann hypothesis

概 要 We unravel the mystery of Chebyshev’s bias in terms of zeta-parametrization of the counting functionof primes. As applications we obtain newly discovered biases. For example, we ﬁnd the biased distributionsof 1) non-principal prime ideals in number ﬁelds of class number two, 2) non-splitting primes in certain
abelian extensions, 3) Ramanujan’s τ -functions in positive values.
41 竹 平 航 平 (東 北 大 理)

Kohei Takehira (Tohoku Univ.)

射影直線上の力学系に付随するゼータ関数について · · · · · · · · · · · · · · · · · 10

On the dynamical zeta function associated with a dynamical system on
the projective line

概 要 A discrete dynamical system is deﬁned by regarding a rational function ϕ over a ﬁeld as a self-map on

a projective line. In 1995, Hatjispyros and Vivaldi deﬁned the zeta function associated with this dynamicalsystem using a quantity called the multiplier of periodic points, which describes the local behavior of the
dynamical system. In this talk, we will give a cohomological interpretation of this zeta function and use it
to discuss the rationality of this zeta function, explicit computation of the zeta function, and other issues.
42 岩 田 英 人 (名 大 多 元 数 理)

Hideto Iwata(Nagoya Univ.)

The consideration using by the Volterra integral equation for the remainder term in the asymptotic formula on the associated Euler totientfunction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The consideration using by the Volterra integral equation for the remainder term in the asymptotic formula on the associated Euler totientfunction

概 要 J. Kaczorowski deﬁned the analogue of the Euler totient function associated with the generalized

L-functions including the Riemann zeta function, Dirichlet L-functions and obtained an asymptotic formula.
We consider the Volterra integral equation of second type for the remainder term in the asymptotic formulafor the associated Euler totient function. Moreover, we split the remainder term in the asymptotic formulafor the associated Euler totient function into two summands called the arithmetic and the analytic partrespectively.

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21

代数学

43 戸 澗 勇 一 郎 (名 大 多 元 数 理)
Yuichiro Toma (Nagoya Univ.)

Apostol–Vu 型二重ゼータ関数の 2 乗平均値 · · · · · · · · · · · · · · · · · · · · · · · · 10
The mean square values of the Apostol–Vu double zeta-function

概 要 The mean square formulas for various multiple zeta-functions have been studied in recent years.

We give the asymptotic formula for the mean square values of the Apostol–Vu double zeta-function
ζAV,2 (s1 , s2 , s3 ) on the assumption that s1 and s2 are ﬁxed.
44 武 田渉 ( 東 京 理 大 理)
中 筋 麻 貴 ( 上 智 大 理 工)

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

Hook 型 Schur 多重ゼータ値の Shuﬄe 積 · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Shuﬄe product formula for the Schur multiple zeta values of hook type

概 要 In the theory of the Euler–Zagier type multiple zeta functions, the product formula of two multiple

zeta values, called Shuﬄe product, is known. It is obtained by considering their integral expression. In thisstudy, we formulate the Shuﬄe product formula for the Schur multiple zeta values of hook type by using
their integral expression.
45 中 筋 麻 貴 (上 智 大 理 工)
大 野 泰 生 ( 東 北 大 理)
Maki Nakasuji (Sophia Univ.)(Tohoku Univ.)
Yasuo Ohno

Schur 多重ゼータ値の双対公式とその拡張 · · · · · · · · · · · · · · · · · · · · · · · · · 15
Duality formula and its generalization for Schur multiple zeta values

概 要 In the study on multiple zeta values, the duality formula is one of the families of basic relations andplays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta
values along with the generalized duality formula, so-called Ohno’s relation. As a generalization of them,
we obtain those for skew type Schur multiple zeta values by introducing the new standard piece of index,
called “admissible piece”.
46 馬 場 結 菜 (上 智 大 理 工)
中 筋 麻 貴 ( 上 智 大 理 工)
(Sophia Univ.)
Yuna Baba
Maki Nakasuji (Sophia Univ.)

Schur 型多重 Poly ベルヌーイ数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Schur type multi-poly-Bernoulli numbers

概 要 The poly-Bernoulli numbers and its relative are deﬁned by the generating series using the polylogarithm

series, and we call them type B and C, respectively. As a generalization of these poly-Bernoulli numbers, we
introduce Schur type multi-poly-Bernoulli numbers, which has relation with Schur multiple zeta functions.
We obtain the relation between Schur type multi-poly-Bernoulli numbers of type B and that of type C.
Furthermore, we deﬁne a generalization of Arakawa-Kaneko multiple zeta function to Schur type, and obtain
their expression using Schur type multi-poly-Bernoulli numbers.
14:15〜16:00
47 小 林 雅 人 (神 奈 川 大 工)
( Euler Circle )S. Chavan

Masato Kobayashi (Kanagawa Univ.)(Euler Circle)
Sarth Chavan

アペリ定数の積分表現と 多重値への応用 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An integral representation of Apery number and its applications to multiple values

概 要 I will talk on an integral representation of Apery number by arcsin function and its applications tomultiple values ζ(3, 2, ..., 2) and t(3, 2, ..., 2).

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代数学

48 伊 東 良 純 (千 葉 大 理)
Ryojun Ito(Chiba Univ.)

22

ある重さ 3 の Borweins テータ積の L 関数の特殊値の超幾何関数表示 · · 10Hypergeometric expressions of L-values for a Borweins theta product ofweight 3

概 要 In 2012, by an analytic method, Rogers–Zudilin gave a hypergeometric expression of the L-value

at 2 for a cusp form of weight 2, which is a product of the Borweins theta series. In this talk, by theRogers–Zudilin method, we express some special values of the L-function of a Borweins theta product ofweight 3 in terms of special values of the Kampé de Fériet hypergeometric function, which is a two-variablegeneralization of generalized hypergeometric functions.
49 根 本 裕 介 (千葉大融合理工)
Yusuke Nemoto (Chiba Univ.)

On the K2 -regulator of the Hesse cubic curve and hypergeometric functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the K2 -regulator of the Hesse cubic curve and hypergeometric functions

概 要 In this talk, we discuss the Hesse cubic curve which is deﬁned by x30 + y03 + z03 = 3tx0 y0 z0 . It is known

that its periods are written in terms of Gauss’s hypergeometric functions. We construct some elements in
K2 -group of the Hesse cubic curve by using the tangent lines at the ﬂex points. We compute their Beilinson
regulators via the dlog map and express them in terms of generalized hypergeometric functions 3 F2 .
50 島 田 了 輔 (東 大 数 理)

Ryosuke Shimada (Univ. of Tokyo)

GL3 のアファイン Deligne–Lusztig 多様体の幾何構造 · · · · · · · · · · · · · · · 15
Geometric structure of aﬃne Deligne–Lusztig varieties for GL3

概 要 The Langlands correspondence, which contains class ﬁeld theory as a special case, is one of themost important topics in number theory. Shimura varieties have been used, with great success, towards
applications in the realm of the Langlands program. In this context, geometric and homological properties
of aﬃne Deligne–Lusztig varieties have been used to examine Shimura varieties and the local Langlands
correspondence. In this talk we study the geometric structure of aﬃne Deligne–Lusztig varieties Xλ (b) forGL3 and b basic. We completely determine the irreducible components of the aﬃne Deligne–Lusztig variety.
In particular, we classify the cases where all of the irreducible components are classical Deligne–Lusztig
varieties times ﬁnite-dimensional aﬃne spaces.
51 水 澤

靖 (名

工

大)

Yasushi Mizusawa(Nagoya Inst. of Tech.)

実 2 次体の Z2 拡大上のメタアーベル 2-類体塔 · · · · · · · · · · · · · · · · · · · · · 10

Metabelian 2-class ﬁeld towers over Z2 -extensions of real quadratic ﬁelds

概 要 We give a family of real quadratic ﬁelds such that the 2-class ﬁeld towers over their cyclotomic Z2 -extensions have metabelian Galois groups of abelian invariants [2, 2, 2]. We also consider the boundednessof the Galois groups in relation to Greenberg’s conjecture with some explicit examples.
52 塩 見 大 輔 (山 形 大 理)

Daisuke Shiomi (Yamagata Univ.)

円分関数体の類数の可除性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The divisibility of class numbers of cyclotomic function ﬁelds+
概 要 Let h−
N (resp. hN ) be the minus (resp. plus) part of the class number of the N th cyclotomic function

ﬁeld. By using Goss’s criterion, Feng proved that there exist inﬁnitely many irreducible polynomials N+
with h−N ≡ 0 (mod p) (resp. hN ≡ 0 (mod p)). In this talk, we study the N -divisibility of some Cartliz

zeta values, and improve Feng’s results.

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23

代数学

53 兵 藤 史 武(川崎医療福祉大医療福祉マネジメント)
Fumitake Hyodo(Kawasaki Univ. of Med. Welfare)

Heisenberg のリー環に付随する Hecke 環について · · · · · · · · · · · · · · · · · · 15
A note on a Hecke ring associated with the Heisenberg Lie algebra

概 要 This talk focuses on the theory of the Hecke rings associated with the general linear groups originallystudied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated withthe automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show ananalog of the classical theory.

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幾何学

幾 何
3 月 28 日（月）24

学第 VI 会場

9:20〜12:00
1 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

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

On dense subsets of spaces of metrics

概 要 In spaces of metrics, we investigate topological distributions of the doubling property, the uniform

disconnectedness, and the uniform perfectness, which are quasi-symmetrically invariant properties appearing
in the David–Semmes theorem. We show that the set of all doubling metrics and the set of all uniformly
disconnected metrics are dense in spaces of metrics on ﬁnite-dimensional and zero-dimensional compact
metrizable spaces, respectively. Conversely, this denseness of the sets implies the ﬁnite-dimensionality, zerodimensionality, and the compactness of metrizable spaces. We also determine the topological distributionof the set of all uniformly perfect metrics in the space of metrics on the Cantor set.
2 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

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

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

spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces
equipped with the Gromov–Hausdorﬀ distance. We then construct branching geodesics of the Gromov–
Hausdorﬀ distance continuously parameterized by the Hilbert cube, passing through or avoiding sets of all
spaces satisfying some of the three properties shown above, and passing through the sets of all inﬁnitedimensional spaces and the set of all Cantor metric spaces.
大理)
3 数 川 大 輔 (阪横 田
巧 ( 東 北 大 理)

Daisuke Kazukawa (Osaka Univ.)
Takumi Yokota (Tohoku Univ.)

プレコンパクトな測度距離空間族の順序有界性 · · · · · · · · · · · · · · · · · · · · · 15

Boundedness of precompact sets of metric measure spaces

概 要 Gromov introduced a distance function, called the box distance, and a partial order, called the

Lipschitz order, on the set of isomorphism classes of metric measure spaces. These are fundamental tools
in his theory on the convergence of metric measure spaces. In this talk, we present and prove Gromov’s
statement comparing two boundedness with respect to the box distance and the Lipschitz order. He only
sketched the proof in his book.
4 田 代 賢 志 郎 ( 東 北 大 理)

Kenshiro Tashiro (Tohoku Univ.)

On the systolic inequality on compact quotients of Carnot groups · · · · 15
On the systolic inequality on compact quotients of Carnot groups

概 要 On a compact Riemannian manifold M n , the systole represents the ‘thickness’ of the manifold. Namely

it is deﬁned by the minimal length of closed non-null homologous curves. The systolic inequality asserts
1

that there is a constant C = C(n) such that systole ≤ C · (V ol(M )) n . It is shown for aspherical manifolds
and its technical generalization. We show a sub-Riemannian version of the systolic inequality for compact
quotient spaces of Carnot groups. There systole is deﬁned via the sub-Riemannian length structure, thetotal measure is given by the Popp’s volume, and the constant can be chosen so that it depends only on the
Hausdorﬀ dimension.

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25

幾何学

5 中 島 啓 貴 (東 北 大 I E H E )塩 谷
隆 ( 東 北 大 理)

Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)

A natural compactiﬁcation of the Gromov–Hausdorﬀ space · · · · · · · · · · 15
A natural compactiﬁcation of the Gromov–Hausdorﬀ space

概 要 We introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Using it,

we obtain a natural compactiﬁcation of the Gromov–Hausdorﬀ space, which is compatible with ultralimit.
6 只 野

誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Radial m-Bakry–Émery Ricci curvatures, Riccati inequalities, and Myerstype theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Radial m-Bakry–Émery Ricci curvatures, Riccati inequalities, and Myerstype theorems

概 要 By using some line integrals in terms of the radial m-Bakry–Émery Ricci curvature, we give various

compactness criteria for complete Riemannian manifolds when m is a positive constant, a negative constant,or inﬁnity. Our results not only guarantee the compactness of complete Riemannian manifolds allowing thepresence of negative amounts of the radial m-Bakry–Émery Ricci curvature, but also give new Myers-type
theorems via m-Bakry–Émery Ricci curvature even the line integrals are reduced to pointwise positive lower
bounds on the m-Bakry–Émery Ricci curvature. The key ingredients in proving our results are Riccati
inequalities obtained from Bochner–Weitzenböck formulas via m-Bakry–Émery Ricci curvature.
7 只 野

誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Ambrose and Calabi type theorems via m-Bakry–Émery Ricci curvature· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Ambrose and Calabi type theorems via m-Bakry–Émery Ricci curvature

概 要 We establish various new compactness criteria for complete Riemannian manifolds via m-Bakry–Émery

Ricci curvature when m is a positive constant, a negative constant, or inﬁnity, which not only generalize
classical compactness criteria for complete Riemannian manifolds via Ricci curvature by W. Ambrose andE. Calabi allowing some negative amounts of the m-Bakry–Émery Ricci curvature, but also relax previous
Myers and Cheeger–Gromov–Taylor type compactness criteria via m-Bakry–Émery Ricci curvature obtained
when m is a positive constant, a negative constant, or inﬁnity.
8 只 野

誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

New compactness criteria via m-Bakry–Émery Ricci curvature of exponential decay · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
New compactness criteria via m-Bakry–Émery Ricci curvature of exponential decay

概 要 We establish some new compactness criteria for complete Riemannian manifolds by assuming some

exponential decay conditions on the m-Bakry–Émery Ricci curvature. Our results not only generalize Myers
type theorems via m-Bakry–Émery Ricci curvature obtained by M. Fernández-López and E. Garcı́a-Rı́o,M. Limoncu, Z. Qian, G. Wei and W. Wylie, J.-Y. Wu, but also relax quadratic decay conditions on the
m-Bakry–Émery Ricci curvature of the Cheeger–Gromov–Taylor type theorems obtained by Y. Soylu and
L.F. Wang. The key ingredients in proving our results are Bochner formulas and Laplacian comparison
theorems via m-Bakry–Émery Ricci curvature.

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幾何学

9 只 野

誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

26

Integral radial m-Bakry–Émery Ricci curvatures and Myers–Ambrosetype theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Integral radial m-Bakry–Émery Ricci curvatures and Myers–Ambrosetype theorems

概 要 Stimulated by a recent work due to J.-Y. Wu, we establish several new compactness criteria forcomplete Riemannian manifolds via integral radial m-Bakry–Émery Ricci curvatures when m is a positive
constant, a negative constant, or inﬁnity. Our results not only relax a compactness criterion via integral
radial Bakry–Émery Ricci curvature due to J.-Y. Wu by allowing some growth conditions on integral
radial m-Bakry–Émery Ricci curvatures, but also give new Myers-type theorems for complete Riemannian
manifolds even integral radial m-Bakry–Émery Ricci curvatures are reduced to pointwise lower bounds on
m-Bakry–Émery Ricci curvatures. Moreover, we generalize these Myers-type theorems in the spirit of theclassical compactness criterion via Ricci curvature due to W. Ambrose.
10 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Cheeger–Gromov–Taylor type compactness theorems via integral radial
m-Bakry–Émery Ricci curvatures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Cheeger–Gromov–Taylor type compactness theorems via integral radial
m-Bakry–Émery Ricci curvatures

概 要 Inspired by a recent work due to J.-Y. Wu, we extend the classical compactness theorem for complete

Riemannian manifolds via Ricci curvature due to Cheeger–Gromov–Taylor by replacing a pointwise lower
bound on the Ricci curvature with integral radial m-Bakry–Émery Ricci curvatures when m is a positive
constant, a negative constant, or inﬁnity. Our results generalize Cheeger–Gromov–Taylor type compactness
theorems for complete Riemannian manifolds via m-Bakry–Émery Ricci curvatures obtained by Y. Soylu
and the author in integral sense.
14:15〜16:00
11 川 村 昌 也 (香 川 高 専)
Masaya Kawamura(Kagawa Nat. Coll. of Tech.)

概 Hermitian 多様体上の関数の評価とその Monge–Ampère 方程式への応用について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On estimates for a function on almost Hermitian manifolds and its application to the Monge–Ampère equation

概 要 Recently, there have been a lot of studies in almost Hermitian geometry. Especially, the Monge–

Ampère type equations have been investigated on almost Hermitian manifolds vigorously. For instance, J.
Chu, V. Tosatti and B. Weinkove have derived a priori estimates and have shown existence and uniqueness ofsolutions to the Monge–Ampère equation on compact almost Hermitian manifolds. In Hermitian geometry,¯
it is well-known that we have ∂ 2 = ∂¯2 = 0 and ∂ ∂¯ = −∂∂.
In almost Hermitian geometry, we do not have
¯ ∂∂
¯ ∂φ,
¯ ∂∂∂ ∂φ¯ and sothese appreciated relations, which leads that we have to deal with terms like ∂∂ ∂φ,on, where φ is a smooth real-valued function. In this regard, we need a new technique for dealing with
¯ ∂∂
¯ ∂φ.
¯
these terms. From this point of view, we establish a new estimate for ∂∂ ∂φ,
12 中 村聡 ( 沼 津 工 高 専)

Satoshi Nakamura(Numazu Nat. Coll. of Tech.)Calabi type functionals for coupled Kähler–Einstein metrics · · · · · · · · · 15
Calabi type functionals for coupled Kähler–Einstein metrics

概 要 The Calabi type functional, called the coupled Ricci–Calabi functional, for coupled Kähler–Einstein

metrics is introduced to obtain a moment weight inequality which relates this functional and an algebrogeometric invariant.

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27

幾何学

13 四 ッ 谷 直 仁 (香 川 大 教 育)

Naoto Yotsutani (Kagawa Univ.)

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

概 要 In our previous work (New York J. Math. 20 (2014) 1–33), we constructed Calabi–Yau threefolds by

a diﬀerential-geometric gluing method using Fano threefolds with their smooth anticanonical K3 divisors.
In this talk we further consider the diﬀeomorphic types of the resulting Calabi–Yau threefolds starting from
diﬀerent pairs of Fano threefolds of Picard number one.
14 渡 邊 祐 太 (東 大 数 理)

Yuta Watanabe (Univ. of Tokyo)

擬凸ケーラー多様体における非多重調和点集合の近傍上のコホモロジー· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Cohomology on neighborhoods of non-pluriharmonic loci in pseudoconvex Kähler manifolds

概 要 The classical result, the Lefschetz hyperplane theorem on complex projective manifolds, has recently

been extended by Prof. Tiba to an analogous result on Stein manifolds. This is a claim for cohomology
on open neighborhoods in non-pluriharmonic loci of exhaustive plurisubharmonic functions. In this talk, I
will introduce a new result, which is an extension from Stein manifolds to pseudoconvex Kähler manifolds
with some kind of q-completeness. An example that does not ﬁt into the situation of Stein manifolds isquasi-torus.
15 森 山 貴 之 (三重大教養教育院)
新 田 貴 士 ( 三 重 大 教 育)

Takayuki Moriyama (Mie Univ.)(Mie Univ.)
Takashi Nitta

Graded algebra structure on the space of quaternionic k-vector ﬁelds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Graded algebra structure on the space of quaternionic k-vector ﬁelds

概 要 We provided the correspondence of a quaternionic k-vector ﬁeld on a quaternionic Kähler manifold toa holomorphic (k, 0)-vector ﬁeld on the twistor space. The space of holomorphic multi vector ﬁelds admits
a graded algebra structure, naturally. In this talk, we introduce a graded algebra structure on the spaceof quaternionic multi vector ﬁelds and show that the correspondence induces an isomorphism of these twograded algebras.
16 古 賀勇 ( 明 大 理 工)
長 友 康 行 ( 明 大 理 工)
(Meiji Univ.)
Isami Koga
Yasuyuki Nagatomo (Meiji Univ.)

複素射影直線から複素グラスマン多様体への同変調和写像の分類 · · · · · · 15

Equivariant harmonic immersions of complex projective line into thecomplex Grassmannian manifolds of rank two

概 要 We construct and classify equivariant harmonic immersions of complex projective line into the complex

Grassmannian manifolds of rank two.
16:15〜17:15

特別講演
橋 本 義 規 (東 工 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 (Tokyo Tech) Recent progress on constant scalar curvature Kähler metrics with 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.

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幾何学

3 月 29 日（火）28

第 VI 会場

9:45〜11:45
17 池 田 憲 明 (立 命 館 大 理 工)
廣 田 祐 士 ( 麻 布 大 獣 医)

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

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

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

manifold. A homotopy momentum section is a generalization of the momentum map with a Lie group
action and the momentum section on a pre-symplectic manifold, and is also regarded as a generalizationof the homotopy momentum map on a multisymplectic manifold. We show that a gauged nonlinear sigma
model with Wess-Zumino term with Lie algebroid gauging has the homotopy momentum section structure.
18 奥 田 太 夏 (東 京 理 大 理)
佐 古 彰 史 ( 東 京 理 大 理)

Taika Okuda (Tokyo Univ. of Sci.)
Akifumi Sako (Tokyo Univ. of Sci.)

複素 2 次元局所対称 Kähler 多様体の変数分離変形量子化 · · · · · · · · · · · · 15

Deformation quantization with separation of variables for 2-complex
dimensional locally symmetric Kähler manifold

概 要 For a Kähler manifold, Karabegov found a method to construct a deformation quantization called

deformation quantization with separation of variables. Especially, the deformation quantizations for locallysymmetric Kähler manifolds have been studied by Sako–Suzuki–Umetsu, and Hara–Sako, and their constructions have been realized for any complex one-dimensional manifold, CN , CPN and CHN . In this work, we
obtained a formula that explicitly determines the deformation quantization for any complex two-dimensional
locally symmetric Kähler manifold.
19 高 橋 雄 也 (名 大 多 元 数 理)

Yuya Takahashi (Nagoya Univ.)

多角形のモジュライ空間と幾何学的量子化 · · · · · · · · · · · · · · · · · · · · · · · · · 15

The moduli space of spatial polygons and geometric quantization

概 要 The moduli space of spatial polygons is known as a symplectic manifold equipped with both Kähler

and real polarizations. In this talk, we will construct morphisms of operads fKäh and fre by using the quantum
Hilbert spaces HKäh and Hre associated to the Kähler and real polarizations respectively. Moreover, we
will relate the two morphisms fKäh and fre and prove the equality dim HKäh = dim Hre in general setting.
This operadic framework is regarded as a development of the recurrence relation method by Kamiyama(2000) for proving dim HKäh = dim Hre in a special case.
20 廣 田 祐 士 (麻 布 大 獣 医)郡
敏 昭 ( 早 大 基 幹 理 工)
Yuji Hirota
Tosiaki Kori

(Azabu Univ.)(Waseda Univ.)

On the existence of (twisted) Dirac structures over the space of connections on 3 and 4 dimensional manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the existence of (twisted) Dirac structures over the space of connections on 3 and 4 dimensional manifolds

概 要 We shall concretely construct (twisted) Dirac structures on the space of irreducible connections on atrivial SU (n)-bundle over three and four dimensional manifolds via bundle morphisms to show the existenceof (twisted) Dirac structures over those spaces of connections. It turns out that the twist term is givenby the Cartan 3-form on those spaces of connections. We ﬁnd that it vanishes over the subspace of ﬂatconnections, and give a Dirac structure on the space of ﬂat connections with degree 0 over the boundary
three-manifold.

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29

幾何学

21 浅 香猛 (東 大 数 理) ♭ Earthquake maps and cluster algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
石 橋
典 ( 京 大 数 理 研)
狩 野 隼 輔 (東北大RACMaS)
Takeru Asaka (Univ. of Tokyo)
Tsukasa Ishibashi (Kyoto Univ.)
Shunsuke Kano (Tohoku Univ.)

Earthquake maps and cluster algebras

概 要 Eathquake maps give important ﬂows on the Teichmuller spaces. We calculate earthquake maps interms of shear coordinates, which are examples of cluster X-variables in the cluster algebra. In this talk,we give a new relation between earthquake maps and the separation formula for cluster X-variables byidentifying the former one as a continuation of the latter. In addition, we deﬁne an analogue of earthquake
maps for any cluster algebras of ﬁnite type and prove a similar result to the Thurston’s earthquake theorem.
大工)22 乙 藤 隆 史 (日ゲストマーティン (早 大 理 工)

Takashi Otofuji (Nihon Univ.)
Martin Guest (Waseda Univ.)tt∗ -戸田方程式のストークス行列とアフィンリー代数の正エネルギー表現· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stokes matrices of tt∗ -Toda equations and positive energy representations of aﬃne Lie algebras

b n+1 C概 要 We give a construction which produces a positive energy representation of the aﬃne Lie algebra slfrom the Stokes data of a solution of the tt*-Toda equations.
23 二 木 昌 宏 (千 葉 大 理)
大理)
三 田 史 彦 (京Masahiro Futaki (Chiba Univ.)
Fumihiko Sanda (Kyoto Univ.)

1 次元射影空間に対する同変ホモロジー的ミラー対称性 · · · · · · · · · · · · · · 15
Equivariant homological mirror symmetry for CP1

概 要 We formulate an A-inﬁnity category consisting of equivariant Lagrangian branes for CP1 and prove

an equivariant version of the homological mirror symmetry.
13:15〜14:15

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 of a semi-simple Lie group

概 要 This talk deals with the complete integrability and the dynamical property of relative equilibrium

points for the geodesic ﬂow of a semi-simple Lie group equipped with a left-invariant metric. After a shortreview over the geometric settings for general left-invariant Hamiltonian systems on the cotangent bundle toa Lie group, a class of left-invariant metrics is considered on a semi-simple Lie group, following Mishchenko
and Fomenko. It is known that these metrics give rise to completely integrable geodesic ﬂows since late1970’s. It is however rather recent that their equilibrium points are studied mostly on the basis of techniquesin symplectic/Poisson geometry. In the talk, a brief overview is given on these recent progresses. Then,
as a main result, the classiﬁcation of Williamson types of relative equilibrium points for a large subclassof above integrable geodesic ﬂows is explained in terms of root systems. Related studies and remaining
problems are also mentioned.

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幾何学

3 月 30 日（水）30

第 VI 会場

9:10〜11:45
24 佐 々 木 優 (東 京 工 高 専)

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

例外型コンパクトリー群 E6 および関連するコンパクト対称空間の極大対
蹠集合 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Maximal antipodal sets of E6 and some compact symmetric spaces

概 要 We explicitly classify congruent classes of maximal antipodal sets of E6 and compact symmetric spacesof EI, EII, EIII, EIV type by using the complex exceptional Jordan algebra JC .Moreover, we realize thesecompact symmetric spaces as Grassmaniann of JC . We describe each antipodal set in this realization andobserve some relations between antipodal sets and totally geodesic submanifolds.
25 藤 森 祥 一 (広島大先進理工)金 田伸 (広島大先進理工)

Shoichi Fujimori (Hiroshima Univ.)
Shin Kaneda (Hiroshima Univ.)

高種数の向き付け不可能な極大曲面について · · · · · · · · · · · · · · · · · · · · · · · 15Higher genus nonorientable maximal surfaces

概 要 We construct higher genus nonorientable maximal surfaces in Lorentz–Minkowski 3-space.

26 澤 井洋 ( 沼 津 工 高 専)

Hiroshi Sawai(Numazu Nat. Coll. of Tech.)Vaisman 可解多様体の構造定理の逆について · · · · · · · · · · · · · · · · · · · · · · · 15
On the inverse of the structure theorem for Vaisman solvmanifolds

概 要 In locally conformal Kähler geometry (for short LCK), it is said to be Vaisman structure if Lee form

is parallel with respect to Levi–Civita connection. The nilradical of a Vaisman solvmanifold is given by
H(n) × Rk , where H(n) is a (2n + 1)-dimensional Heisenberg Lie group. In the case of Inoue surface S + with
non-Vaisman LCK structure, its nilradical is given by H(1). In this talk, we prove that a LCK solvmanifold
such that the nilradical of the solvable Lie group is given by H(n) × Rk (n ≥ 1) is Vaisman manifold or Inouesurface S + .
27 高 野 嘉 寿 彦 (信州大全学教育)

Kazuhiko Takano (Shinshu Univ.)

ミンコフスキー空間内の慣性運動する質点の軌跡について · · · · · · · · · · · 10

On trajectory of mass points inertially moving in the Minkowski space

概 要 Trajectory of mass points inertially moving on a surface is a geodesic. The simplest cosmic modelthat is uniform and isotropic is the Minkowski space. The Minkowski space is ﬂat because the Christoﬀel’s
symbols are all zero, and the timelike, spacelike and lightlike geodesics are all straight lines. We havedetermined a new connection to preserve the ﬂatness of the Minkowski space.
We discuss geodesics of inertially moving mass points in the Minkowski space with the new connection.

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31

幾何学

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

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

Riemann 多様体間の写像の第二基本形式から定まる積分不変量に関する
第一変分公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The ﬁrst variational formulae for integral invariants of the second fundamental form of a map between Riemannian manifolds

概 要 By using the idea of integral geometry, we deﬁne integral invariants of the second fundamental form ofa map between Riemannian manifolds and construct a family of energy functionals including the bienergyfunctional. In this talk, we focus on some energy functionals deﬁned by homogeneous polynomials ofdegree two among them and show their ﬁrst variational formulae. From these results, we obtain alternative
expression of the Euler–Lagrange equation of the bienergy functional and introduce the Chern–Federerenergy functional whose Euler–Lagrange equation is a second-order partial diﬀerential equation.
29 児 玉 悠 弥 (都 立 大 理)

Yuya Kodama (Tokyo Metro. Univ.)

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

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

Moore group is known as a nonamenable ﬁnitely presented group and is similar to the Thompson group F .
Since the Lodha–Moore group is deﬁned by using inﬁnite binary words, it can be generalized into “n-ary”.
After I give a short deﬁnition of the Lodha–Moore group, I will state the deﬁnitions of generalized one andresults of “expected” properties.
30 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 deﬁned by inner automorphism · · · · · · 15
Biharmonic Cartan embeddings deﬁned by inner automorphism

概 要 In this talk, we give the examples of proper biharmonic submanifolds in compact Lie groups which

are the image of Cartan embeddings deﬁned by inner automorphism.
31 坊 向 伸 隆 (大 分 大 理 工)

Nobutaka Boumuki (Oita Univ.)

楕円軌道上の正則ベクトル束に関する線形空間の次元について · · · · · · · · 15

On the dimensions of linear spaces concerning holomorphic vector bundles over elliptic orbits

概 要 In this talk, I deal with the complex linear space of holomorphic cross-sections of a homogeneous

holomorphic vector bundle over an elliptic adjoint orbit, and give a suﬃcient condition for the linear space
to be ﬁnite-dimensional.
32 奥 村 和 浩 (旭 川 工 高 専)
Kazuhiro Okumura(Asahikawa Nat. Coll. of Tech.)

非平坦複素空間形内の D-平行な star-Ricci テンソルをもつ実超曲面 · · · 10

Real hypersurfaces in a nonﬂat complex space form whose star-Ricci
tensor is D-parallel

概 要 In this talk, we give a classiﬁcation of real hypersurfaces in a nonﬂat complex space form whose

star-Ricci tensor is D-recurrent. By virtue of this result, we also know a classiﬁcation of real hypersurfaces
in a nonﬂat complex space form whose star-Ricci tensor is parallel.

最終版: 2022/3/4
幾何学

特別講演
近 藤 剛 史 ( 鹿 児 島 大 理)

CAT(0) 空間に対する Coxeter 群の非線形スペクトルギャップ

Takefumi Kondo (Kagoshima Univ.)

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

32

14:15〜15:15

概 要 Nonlinear spectral gap is an invariant deﬁned for a pair of a ﬁnite graph and a metric space andplays important roles in geometric group theory and metric geometry. Pansu calculated the exact values ofnonlinear spectral gaps of cycles and generalized triangles with respect to CAT(0) spaces by applying the
Wirtinger inequalities for ﬁnite cyclic groups proved by Gromov. However, no example of exact calculation
was known other than Pansu’s results.
In this talk, we discuss variants of the Wirtinger inequalities for ﬁnite irreducible Coveter groups and its
application to calculations of nonlinear spectral gaps of Coxeter groups. This contains a nonlinear analogueof computations of spectral gaps of Coxeter groups by Kassabov and Ivrissimtzis–Peyerimhoﬀ.
This is a joint work with Tetsu Toyoda and Takato Uehara.
15:30〜16:30

特別講演
國 分 雅 敏 ( 東 京 電 機 大 工)

Flat fronts in hyperbolic three-space and related topics

Masatoshi Kokubu (Tokyo Denki Univ.)

Flat fronts in hyperbolic three-space and related topics

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

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

3 月 31 日（木）第 VI 会場

9:15〜12:00
33 宮 武 夏 雄 (阪大理) ♭ 葉層構造付き多様体上の一般化 Kazdan–Warner 方程式について · · · · · · 15

Natsuo Miyatake (Osaka Univ.)

Generalized Kazdan–Warner equations on foliated manifolds

概 要 Generalized Kazdan–Warner equation is a second-order elliptic PDE which was introduced by speakeras a generalization of the classical Kazdan–Warner equation. In this talk, we show that on a compact
foliated Riemannian manifold, the unique solution of the generalized Kazdan–Warner equation is a basic
function with respect to the foliation if the Laplacian preserves the space of basic functions and if thefunctions which are given to deﬁne the equation are basic.
34 國 川 慶 太 (宇 都 宮 大 教 育)
櫻 井 陽 平 ( 埼 玉 大 理)

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

調和写像に関する増大度条件付き Liouville 型定理 · · · · · · · · · · · · · · · · · · 15

Liouville type theorem for harmonic maps of controlled growth

概 要 We show a Liouville type result for harmonic maps from manifolds with nonnegative Ricci curvature

into positively curved target spaces under the condition that the maps have controlled growth.

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33

幾何学

35 髙 橋 淳 也 (東 北 大 情 報)
(Univ. de Nantes)
C. AnnéJunya Takahashi (Tohoku Univ.)
Colette Anné (Univ. de Nantes)

体積一定下での Hodge–Laplacian と rough Laplacian の小さい固有値· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Small eigenvalues of the rough and Hodge Laplacians under ﬁxed volume

概 要 For each degree p and each natural number k ≥ 1, we construct on any closed manifold a family of

Riemannian metrics, with ﬁxed volume such that the k th positive eigenvalue of the rough or the Hodge
Laplacian acting on diﬀerential p-forms converge to zero. In particular, on the sphere, we can choose these
Riemannian metrics as those of non-negative sectional curvature. This is a generalization of the results by
Colbois and Maerten in 2010 to the case of higher degree forms.
36 中 村 友 哉(工学院大学習支援センター)
木 村 直 記 ( 早 大 理 工)

Tomoya Nakamura (Kogakuin Univ.)
Naoki Kimura (Waseda Univ.)

Jacobi 構造と擬 Riemann 余計量の整合性 · · · · · · · · · · · · · · · · · · · · · · · · · 15

The compatibility of Jacobi structures and pseudo-Riemannian cometrics

概 要 Boucetta introduced the compatibility between a Poisson structure π and a pseudo-Riemannian

cometric g ∗ on a smooth manifold M using the Levi–Civita connection of g ∗ on (T ∗ M )π . This is a
generalization of Kähler structures on M . This notion can be generalized on a Lie algebroid A over M . In
this talk, we generalize this notion more and deﬁne the compatibility between Jacobi structures and pseudoRiemannian cometrics on a Jacobi algebroid (A, ϕ0 ). The compatibility behaves well for the Poissonizationsof Jacobi structures. We show that this is a generalization of Sasakian structures on M .
37 高 津 飛 鳥 (都 立 大 理) ♭ 熱流における関数の凹性保存則 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15石 毛 和 弘 ( 東 大 数 理)
( Univ. Firenze )P. Salani

Asuka Takatsu (Tokyo Metro. Univ.)
Kazuhiro Ishige (Univ. of Tokyo)(Univ. Firenze)
Paolo Salani

Concavity preserved by heat ﬂow

概 要 We proved that the log-concavity is the only power concavity preserved by the Dirichlet heat ﬂow ina convex domain of a Riemannian manifold.
38 納 谷信 ( 名 大 多 元 数 理)

Shin Nayatani (Nagoya Univ.)

ラプラシアン第 1 固有値最大化と埋め込み最適化 · · · · · · · · · · · · · · · · · · · 15

Laplacian ﬁrst-eigenvalue maximization and embedding optimization

概 要 I will introduce an embedding optimization problem for a compact manifold equipped with a volume

form and a Riemannian metric. We also introduce a ﬁrst-eigenvalue maximization problem concerning
the Bakry–Émery Laplacian, as the dual problem of the former one. I will discuss an analogue of the
Nadirashvili minimal surface theorem.
39 五 明納 谷

工 ( 名 大 多 元 数 理)
信 ( 名 大 多 元 数 理)

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

有限グラフの第 1 固有値の最大化と埋め込み · · · · · · · · · · · · · · · · · · · · · · · 15

Maximization of the ﬁrst eigenvalue and embedding of a ﬁnite graph

概 要 A graph can be realized in a Euclidean space by using eigenfunctions of the ﬁrst nonzero eigenvalue ofthe graph Laplacian. Göring–Helmberg–Wappler considered the maximization of the ﬁrst nonzero eigenvalueof the weighted graph Laplacian over all edge weights under a certain normalization. For an optimal edge
weight of Göring–Helmberg–Wappler’s problem, we obtain a graph embedding having a good geometricalproperty. We also consider a variant of their problem and establish a similar result.

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幾何学

40 南

範 彦 (名工大)Norihiko Minami(Nagoya Inst. of Tech.)34

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

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

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

characterized its uniruledness by the non pseudoeﬀectivesness of its canocinal divisor. Furthermore,
Campana–Demailly–Peternell (London Math. Soc. Lecture Note Ser., 417, 2015) gave a cohomologicalcharacterization of rationally-connectedness. In this talk, I shall report these characterizations can beinterporated to give some chomological characterization of the hierarchical structures interpolating theuniruledness and the rationally connectedness.
41 相 野 眞 行 (理 化 学 研 A I P) ♭ 滑らかとは限らない部分多様体に対する Laplacian Eigenmaps の収束とそのレート · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Masayuki Aino

(RIKEN)

Convergence of the Laplacian Eigenmaps and its rate for submanifolds
that are not necessarily smooth

概 要 Laplacian Eigenmaps is a dimensionality reduction method using eigenvectors of the graph Laplacian

which approximates the eigenfunctions of the Laplacian on a submanifold under appropriate assumptions
when random samples are obtained on the submanifold in Euclidean space. The convergence of Laplacian
Eigenmaps has been discussed assuming lower bound for a quantity called reach, which does not allow
non-smooth submanifolds. In this talk, I will discuss the convergence of Laplacian Eigenmaps under the
weaker assumptions that non-smooth submanifolds can appear in the limit.

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35

函数論

函

数

3 月 28 日（月）9:30〜11:50
1 熊 谷

駿 ( 東 北 大 情 報)

Shun Kumagai (Tohoku Univ.)

論
第 VIII 会場

平行四辺形分解を持つ平坦曲面の族について · · · · · · · · · · · · · · · · · · · · · · · 15

Family of ﬂat surfaces with a parallelogram decomposition

概 要 In this century, a square-tiled translation surface (an origami) is intensively studied as an object withspecial properties of its translation structure and its SL(2, R)-orbit embedded in the moduli space. We
generalize this concept in the language of ﬂat surfaces appearing naturally in the Teichmüller theory. We
study the combinatorial structure of origamis and show that a certain system of linear equations realizes
the ﬂat surface in which rectangles of speciﬁed moduli replace squares of an origami. This construction
gives a parametrization of the family of ﬂat surfaces with two ﬁnite Jenkins–Strebel directions for eachcombinatorial structure of parallelogram decomposition.
2 奥 山 裕 介 (京都工繊大基盤)

Yûsuke Okuyama (Kyoto Inst. Tech.)

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

概 要 The notion of uniform perfectness of subsets in C (or P1 ) plays an important role in complex analysis,complex dynamics, and (complex) potential theory. In this talk, we will introduce a non-archimedeancounterpart to this important notion, and give a few applications of it in non-archimedan dynamics andpotential theory on the Berkovich projective line.
3 松 崎 克 彦 ( 早 大 教 育)
Huaying Wei (早 大 教 育)

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

BMO embeddings, chord-arc curves, and Riemann mapping parametrization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
BMO embeddings, chord-arc curves, and Riemann mapping parametrization

概 要 We consider the space of chord-arc curves on the plane passing through the inﬁnity with theirparametrization γ on the real line, and embed it into the product of the BMO Teichmüller spaces. The fundamental theorem we prove on this representation is that log γ ′ also gives a biholomorphic homeomorphismof it into the complex Banach space of BMO functions. Using these two equivalent complex structures, wedevelop a clear exposition on the analytic dependence on involved parameters in this space. Especially, we
examine the parametrization of a chord-arc curve by using the Riemann mapping and its dependence on the
arc-length parametrization. As a consequence, we can solve a conjecture of Katznelson, Nag, and Sullivan
by showing that this dependence is not continuous.
4 下 村 勝 孝 ( 茨 城 大 理)

Katsunori Shimomura (Ibaraki Univ.)

半 Euclid 空間上の caloric morphism の時間変換と実有理関数 · · · · · · · · 15

Real rational function and time transformation of caloric morphism on
semi-euclidean spaces

概 要 In this talk, we show that any non-constant real rational function appears as a time transformation ofa caloric morphism, mapping which preserves caloric functions, between semi-eucledean spaces.
5 深 作 亮 也 ( 九 大 数 理)潟大⋆)田 島 慎 一 (新Ryoya Fukasaku (Kyushu Univ.)
Shinichi Tajima (Niigata Univ.⋆)

効率的な一変数留数計算アルゴリズム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Eﬃcient algorithms for computing univariate residues

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

local cohomology classes and diﬀerential operators. In addition, we compare the algorithm with existingalgorithms.

最終版: 2022/3/4
函数論

6 四 之 宮 佳 彦 ( 静 岡 大 教 育)

Yoshihiko Shinomiya (Shizuoka Univ.)

36

Period matrices of some hyperelliptic Riemann surfaces · · · · · · · · · · · · · 15
Period matrices of some hyperelliptic Riemann surfaces

概 要 We give new examples of period matrices of Riemann surfaces. We construct Riemann surfaces frompolygons which are constructed from some rectangles and give their algebraic equations. The algebraic
equations are of the form w2 = z(z 2 − 1)(z 2 − a21 )(z 2 − a22 ) · · · (z 2 − a2g−1 ) (1 < a1 < a2 < · · · < ag−1 ). We
also see that all algebraic curves of these types of equations are constructed from our way. Period matrices
are calculated by ﬁnding symplectic bases.
7 濵 野 佐 知 子 ( 阪 市 大 理)島大⋆)柴雅 和 (広Sachiko Hamano (Osaka City Univ.)
Masakazu Shiba (Hiroshima Univ.⋆)

The period matrices of an open Riemann surface and its closings in the
Siegel upper half space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The period matrices of an open Riemann surface and its closings in the
Siegel upper half spacegR
概 要 Let R be an open Riemann surface of genus g (1 ≤ g < ∞), and χR = {ARj , Bj }j=1 be a canonicalhomology basis of R modulo dividing cycles. We show that (R, χR ) determines a unique point in the Siegel
upper half space Sg of degree g, which deserves to be called the period matrix of the open Riemann surface(R, χR ). We also prove that the period matrices of the closings of (R, χR ) satisfy a set of inequalities in Sg .
8 神 本

丈 ( 九 大 数 理)

Joe Kamimoto (Kyushu Univ.)

C ∞ 関数に関する特異点解消と局所ゼータ関数の有理型解析接続 · · · · · · 15
Resolution of singularities for C ∞ functions and meromorphy of local
zeta functions

概 要 We attempt to resolve the singularities of the zero variety of a C ∞ function of two variables as muchas possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zerovariety in the “almost” normal crossings form, which is close to the normal crossings form but may include
ﬂat functions. As an application, we investigate analytic continuation of local zeta functions associated with
C ∞ functions of two variables.
9 米 田 力 生 (金沢大人間社会)

Rikio Yoneda (Kanazawa Univ.)

ハーディー空間上とベルグマン空間上の重み付き合成作用素 · · · · · · · · · · 10

Weighted composition operators between H p and Lqa

概 要 We study weighted composition operators between the Hardy space and the Bergman spaces.

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37

函数論

14:15〜15:15

特別講演
藤 解 和 也 ( 金 沢 大 理 工)

値分布論からの Stothers–Mason の定理再訪

Kazuya Tohge (Kanazawa Univ.)

Revisiting the Stothers–Mason theorem with Nevanlinna

概 要 By the Stothers–Mason theorem we mean the well-known abc inequality for complex polynomials

stating: Three relatively prime and non-constant polynomial a, b and c satisfy the relation a + b = c only
if each of them is of degree at most the number of distinct roots of the product abc minus one. It is wellknown that this estimate is sharp by examples and applies polynomial or rational solutions to Fermat’s
equation as well as the so-called Davenport inequality. One can bring Picard’s Little Theorem over to theobservation of a + b = c so that some of the known generalizations of the Stothers–Mason theorem arestated in Nevanlinna’s value distribution theory of meromorphic functions on the complex plane. Then it isobvious that Wronskian plays an essential role in order to count the number of distinct roots of abc. In thistalk, we change a way of counting roots for another abc inequality and give an aﬃrmative partial answer tothe strange question: Can diﬀerence operation substitute well for diﬀerentiation in function theory? The
way of judging a root to be multiple in a diﬀerent angle actually observes the multiplicity as the numberof the stepping-roots with a ﬁxed stride. Therefore, our operation is naturally a shift or diﬀerence operator
with the stride. We see an abc inequality in this setting and apply it to deduce the corresponding Fermat
or Davenport type estimates and reproduce several function-theoretic generalizations of the Stothers–Mason
theorem by using this operator. The discussions proceed in parallel to those in the usual diﬀerential setting
where, for example, Wronskian is simply replaced by Casoratian, and examples to examine the sharpness of
the inequalities can be found in a simple translation rule. These are all for entire functions not for integers
but a tiny and naive attempt at the very end. This is based on a joint work with K. Ishizaki, R. Korhonen,and N. Li.

3 月 29 日（火）第 VIII 会場

9:30〜11:30
10 小 川 智 史 (阪 市 大 理)

Satoshi Ogawa (Osaka City Univ.)

S 1 束の構造を持つあるレビ平坦面周りの線形化 · · · · · · · · · · · · · · · · · · · · 15
Linearization of transition functions along some Levi-ﬂat hypersurfaces
with the structure of S 1 -bundle

概 要 We introduce suspension construction and we can obtain a Levi-ﬂat hypersurface which has the

structure of the unit circle bundle. By focusing on Diophantine condition, we investigate the linearizationof transition function along this Levi-ﬂat. Our linearization is based on Ueda’s result and primitive KAMtheory for one-variable dynamical systems.
11 菊 池 翔 太 (名 大 多 元 数 理)
Shota Kikuchi (Nagoya Univ.)

大沢–竹腰の L2 拡張定理の精密な評価の高次元化 · · · · · · · · · · · · · · · · · · · 15

On sharper estimates of Ohsawa–Takegoshi L2 -extension theorem inhigher dimensional case概 要 Hosono obtained sharper estimates of the Ohsawa–Takegoshi L2 -extension theorem by allowing theconstant depending on the weight function for a domain in C. In this talk, I explain the higher dimensionalcase of sharper estimates of the Ohsawa–Takegoshi L2 -extension theorem. In order to prove this, weestablish an analogue of Berndtsson–Lempert type L2 -extension theorem by using the pluricomplex Greenfunction with poles along subvarieties.

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函数論

38

大⋆) ♭ 擬凸境界を持つ複素多様体上の多項式増大度のコホモロジー消滅について

12 大 沢 健 夫 (名· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Takeo Ohsawa (Nagoya Univ.⋆)

On the cohomology vanishing with polynomial growth on complex manifolds with pseudoconvex boundaryr,s
概 要 ∂ cohomology groups with polynomial growth Hp.g.
will be studied. It will be shown that, given acomplex manifold M , a locally pseudoconvex bounded domain Ω ⋐ M satisfying certain geometric boundaryr,scondition and a holomorphic vector bundle E → M , Hp.g.
(Ω, E) = 0 holds for all s ≥ 1 if E is Nakanor,spositive and r = dim M . It will be also shown that Hp.g.
(Ω, E) = 0 for all r and s with r + s > dim M if

moreover rankE = 1.
13 綾 野 孝 則 (阪 市 大 数 学 研)
V. M. Buchstaber(Steklov Inst. of Math.)

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

種数 2 の超楕円関数の楕円関数への還元 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Reduction of hyperelliptic functions of genus 2 to elliptic functions

概 要 When solutions of diﬀerential equations in terms of hyperelliptic functions of genus 2 are given, underconditions when a reduction of these functions to elliptic functions is possible, it is important to ﬁnd an
explicit form of these solutions in terms of elliptic functions. In this talk, we consider a hyperelliptic curve
V of genus 2 which admits a morphism of degree 2 to an elliptic curve. Then there exist two elliptic curves
Ei , i = 1, 2, and morphisms of degree 2 from V to Ei . We express the hyperelliptic functions associatedwith V on C2 in terms of the Weierstrass elliptic functions associated with Ei . As a corollary, a solution of
the KdV-hierarchy in terms of the Weierstrass elliptic functions is given.
14 小 池 貴 之 (阪 市 大 理)

Takayuki Koike (Osaka City Univ.)

Holomorphic foliation associated with a semi-positive class of numericaldimension one · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Holomorphic foliation associated with a semi-positive class of numericaldimension one

概 要 Let X be a compact Kähler manifold and α be a class in the Dolbeault cohomology class of bidegree(1, 1) on X. When the numerical dimension of α is one and α admits at least two smooth semi-positive
representatives, we show the existence of a family of real analytic Levi-ﬂat hypersurfaces in X and aholomorphic foliation on a suitable domain of X along whose leaves any semi-positive representative of
α is zero. As an application, we give the aﬃrmative answer to our conjecture on the relation between
the semi-positivity of the line bundle [Y ] and the analytic structure of a neighborhood of Y for a smoothconnected hypersurface Y of X.
15 松 本 佳 彦 (阪大理)

Yoshihiko Matsumoto (Osaka Univ.)

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

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

almost CR structure J (also known as a strictly pseudoconvex partially integrable almost CR manifold) is
the linear diﬀerential operator describing trivial deformations of J. We report our recent ﬁnding that D canalso be found as the ﬁrst operator in the so-called Bernstein–Gelfand–Gelfand sequence. More precisely, D
is the ﬁrst BGG operator induced by a modiﬁed tractor connection introduced by Čap, not by the normal
tractor connection, of the adjoint tractor bundle.

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39

函数論

16 千 葉 優 作 (お茶の水女大基幹)

Yusaku Tiba (Ochanomizu Univ.)

Asymptotic estimates of holomorphic sections on Bohr–Sommerfeld Lagrangian submanifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic estimates of holomorphic sections on Bohr–Sommerfeld Lagrangian submanifolds

概 要 Let M be a projective manifold and L be an ample line bundle over M with a Hermitian metrich whose Chern form is a Kähler form ω. Let X ⊂ M be a Lagrangian submanifold of (M, ω). WhenX satisﬁes the Bohr–Sommerfeld condition, we give an asymptotic estimate of the norm |f |hk on X forf ∈ H 0 (M, Lk ).
13:15〜14:15

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

⋆)

特異点の複素解析, 代数解析とアルゴリズム

Complex analysis, algebraic analysis and algorithms in singularity thoery

概 要 In this talk, we consider singularities of varieties in the context of computational complex analysis andalgebraic analysis. Based on the concept of local cohomology and Grothendieck local duality, we introduce
a new approach for studying complex analytic properties of singularities. As applications of the proposed
approach, eﬀective methods for computing, for instance, logarithmic vector ﬁelds, limiting tangent spaces,
integral dependence relations, micro-local b-functions are shown.
We introduce a new method for computing holonomic D-modules associated to non-isolated hypersurface
singularities. Main ingredient of the approach are Poincaré-Birkhoﬀ-Witt algebra and the theory of comprehensive Gröbner systems. As applications, we present a method for computing vertical monodromyof vanishing cycles sheaves and micro-local b-functions. We discuss some relations between characteristic
varieties of relevant holonomic D-modules and Lê cycles introduced by D. Massey.

最終版: 2022/3/4函数方程式論函数

方3 月 28 日（月）

程

式

40

論

第 II 会場

9:00〜12:00
1 小 森 大 地 (北 大 M D S )Daichi Komori (Hokkaido Univ.)

無限階擬微分作用素の層とその表象の同型性 · · · · · · · · · · · · · · · · · · · · · · · 12

The equivalence of the sheaf of pseudodiﬀerential operator and its symbol class

概 要 The study of pseudodiﬀerential operators was developed by Aoki and Kataoka with symbol theory.

Locally they constructed the morphism between the stalks of two sheaves by the aid of the Radontransformation. However their method cannot be extended to the global case. In this talk we introduce theconstruction of the sheaf morphism from the sheaf of pseudodiﬀerential operators to the sheaf of its symbol
class via Čech–Dolbeault cohomology. The theory of Čech–Dolbeault cohomology was originated by Suwa,
and it allows us to manipulate the sheaf cohomology without some conditions such as Steinness of coverings.
We also show that two morphisms are compatible with each other.
2 安 達 駿 弥 ( 熊 本 大 自 然)

Shunya Adachi (Kumamoto Univ.)

4 つの特異点を持つ 2 階 Fuchs 型微分方程式のモノドロミー不変 Hermite
形式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Monodromy invariant Hermitian forms for second order Fuchsian diﬀerential equations with four singularities

概 要 Gauss hypergeometric diﬀerential equation (GHE) is the second order Fuchsian diﬀerential equation

with three singularities. Under some suitable condition, GHE has a monodromy invariant Hermitianform, which is useful for the study of geometric nature of solutions. More generally, it is known that for
the Fuchsian diﬀerential equation having an integral representation of solutions, there exists an invariant
Hermitian form. In this talk we consider second order Fuchsian diﬀerential equations with four singularities,
which seems to have no integral representation of solutions in general. As a main result, without assuming
the existence of integral representation of solutions, we give suﬃcient and necessary condition for the
existence of monodromy invariant Hermitian form.
3 渋 川 元 樹 ( 神 戸 大 理)

Genki Shibukawa (Kobe Univ.)

Artin-style characterizations for multiple gamma and sine functions · · 10
Artin-style characterizations for multiple gamma and sine functions

概 要 We give multiple analogues of Artin’s characterizations for the gamma function. As applications of

our results, we characterize the multiple gamma and (Kurokawa’s) sine functions.
4 小川原弘士(熊本大数理科学総合教育センター)

Hiroshi Ogawara (Kumamoto Univ.)

Ramanujan 関数の q 差分方程式の解の微分超越性 · · · · · · · · · · · · · · · · · · 12
Diﬀerential transcendence of solutions for q-diﬀerence equation of Ramanujan function

概 要 In this talk, we show any non-trivial solution for the second order linear q-diﬀerence equation of theRamanujan function, one of the q-analogue of the Airy function, satisﬁes no non-trivial algebraic diﬀerential
equation over the rational function ﬁeld. Our proof is based on the criterion for diﬀerential transcendenceof solutions for diﬀerence Riccati equations, which is constructed by Nishioka.

最終版: 2022/3/441函数方程式論畿
大⋆)5 青 木 貴 史 (近鈴 木 貴 雄 ( 近 畿 大 理 工)
内 田 匠 風 (近畿大総合理工)

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

Exact WKB analysis for the Pearcey system with a large parameter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Exact WKB analysis for the Pearcey system with a large parameter

概 要 The Pearcey system is an extension of the Airy equation for multi variables. In this talk, we showthat the Borel transform of WKB solutions for the Pearcey system can be written as linear combinations ofalgebraic functions.
6 石 橋 和 葵 ( 広 島 商 船 高 専)
Kazuki Ishibashi(Hiroshima Nat. Coll. of Maritime Tech.)

タイムスケール上における 2 種類の導関数をもつ半分線形ダイナミック
方程式の解の非振動性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Nonoscillation theorems for half-linear dynamic equations with mixed
derivatives on a time scale

概 要 This talk deals with half-linear dynamic equations on a time scale that have two types of derivatives,and obtains suﬃcient conditions to be nonoscillatory. Note that if the time scale is selected from the setof all real numbers or the set of all natural numbers, then these equations will be half-linear diﬀerential
equations and half-linear diﬀerence equations.
7 宇 佐 美 広 介 ( 岐 阜 大 工)
媛
大⋆)
内 藤
学 (愛
Hiroyuki Usami (Gifu Univ.)
Manabu Naito (Ehime Univ.⋆)

摂動された半分線形常微分方程式の解の存在と漸近挙動について · · · · · · 12

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

概 要 The existence and asymptotic behavior of solutions of half-linear ordinary diﬀerential equations with

perturbed terms are investigated. The proofs of the results are based on the analysis of generalized Riccati
equations associated with this half-linear equation.
8 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

Asymptotic behavior of solution to semilinear eigenvalue problem · · · · 12
Asymptotic behavior of solution to semilinear eigenvalue problem

概 要 We consider the asymptotic behavior of the solution curve of nonlinear ODEs with logarithmic

nonlinear term. It is known that the bifurcation curve λ is a continuous function of the maximum norm
α = ∥uλ ∥∞ of the solution uλ associated with λ, and is written as λ = λ(α). We establish the asymptotic
formulas for uα (t) and ∥uα ∥1 as α → ∞.
(Univ. College Dublin)
9 M. Ghergu
宮 本 安 人 ( 東 大 数 理)
( Swansea Univ. )V. Moroz

Marius Ghergu (Univ. College Dublin)
Yasuhito Miyamoto (Univ. of Tokyo)
Vitaly Moroz (Swansea Univ.)

Polyharmonic inequalities with nonlocal terms · · · · · · · · · · · · · · · · · · · · · 10

Polyharmonic inequalities with nonlocal terms

概 要 We study the existence and non-existence of classical solutions for inequalities of type±∆m u ≥ Ψ(|x|) ∗ up uq

in RN (N ≥ 1).

Here, ∆m (m ≥ 1) is the polyharmonic operator, p, q > 0 and ∗ denotes the convolution operator, whereΨ > 0 is a continuous non-increasing function. We devise new methods to deduce that solutions of the above
inequalities satisfy the poly-superharmonic property. This further allows us to obtain various Liouville type
results. Our study is also extended to the case of systems of simultaneous inequalities.

最終版: 2022/3/4函数方程式論10 長 澤 壯 之 (埼 玉 大 理 工)
石 関
彩 ( 埼 玉 大 理 工)

Takeyuki Nagasawa (Saitama Univ.)
Aya Ishizeki (Saitama Univ.)

42

結び目と絡み目 Möbius エネルギー: 分解定理, 余弦公式と Möbius 不変性· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The Möbius energies of knots and links: Decomposition, the cosine
formula, and their Möbius invariance

概 要 The Möbius energy of knots is one of O’Hara’s energies, named after the invariance under Möbiustransformations. A similar energy is deﬁned for links. In this talk, we unify the treatment of these energies,
and give a Möbius invariant decomposition in a way simpler than before. For this, we use a map which iscalled the Gauss map in the case of links. Using it, we ﬁnd that the decomposition of energy density isderived from the parallelogram theorem. Also, the cosine formula holds for the decomposed energies, which
is known as an alternative expression for the original energy.
11 長 澤 壯 之 (埼 玉 大 理 工)
石 関
彩 ( 埼 玉 大 理 工)

Takeyuki Nagasawa (Saitama Univ.)
Aya Ishizeki (Saitama Univ.)

絡み目の Möbius エネルギーの極限としての結び目の Möbius エネルギー· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The Möbius energy of knots as a limit of the Möbius energy of links

概 要 Analyzing the Möbius energy of knots, we always encounter diﬃculties of singularity of integrand at

the diagonal part. As a simple way to avoid them, we regularize the denominator in the integrand. The
regularized energy, however, loses the Möbius invariant property. Introducing the Möbius energy of links,
we attempt a way to avoid singularity preserving this geometrically interesting property. Precisely saying,
we show that the energy of links with a compensated term convergences to the Möbius energy of a knot as
two components of links approaches to one closed curve which represents the knot. The link energy diverges
without a compensated term. Our compensated term, which is constructed from the Gauss map, vanishes
for any knots.
14:15〜16:15
12 堀 内 利 郎 (茨 城 大 理)

Toshio Horiuchi (Ibaraki Univ.)

The CKN type inequalities involving non-doubling weights · · · · · · · · · · 12
The CKN type inequalities involving non-doubling weights

概 要 We discuss validity of CKN type inequalities involving non-doubling weights, after a quick review of

the classical CKN type inequalities. In one-dimensional case, a function w(t) on (0, ∞) is said to be adoubling weight if there exists a positive number C such that we haveC −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 bea non-doubling weight in the present talk. In one-dimensional case we typically treat e−1/t and e1/t . In
such cases the limit of ratio w(t)/w(2t) as t → +0 may become 0 or +∞, and hence they are regarded as
non-doubling weights according to our notion.
13 安 藤広 ( 茨 城 大 理 工)
城大⋆)
堀 内 利 郎 (茨Hiroshi Ando (Ibaraki Univ.)
Toshio Horiuchi (Ibaraki Univ.⋆)

Variational problems relating the generalized weighted Hardy’s inequalities with compact perturbations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Variational problems relating the generalized weighted Hardy’s inequalities with compact perturbations

概 要 Let Ω be a bounded domain of RN with boundary of class C 2 . We consider the variational problems

relating the generalized weighted Hardy’s inequalities with compact perturbations. As weights we treat
the functions of distance to the boundary of Ω. We study the inﬁmum of the variational problem and it’sachievability. Then we use the generalized weighted Hardy’s inequalities with remainder terms on a tubularneighborhood of the boundary of Ω.

最終版: 2022/3/443函数方程式論14 濱 本 直 樹 (阪 府 大 理)

Naoki Hamamoto (Osaka Pref. Univ.)

制約条件付きベクトル場に対する Rellich–Hardy 不等式の最良定数について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Sharp Rellich–Hardy inequality for constrained vector ﬁelds

概 要 We report on sharp constant in the Rellich–Hardy inequality for constrained vector ﬁelds, especiallyfor solenoidal ﬁelds. This inequality serves as an intermediate between the weighted Hardy and Rellich
inequalities for solenoidal ﬁelds, which we established in our previous work as a development of Costin–
Maz’ya’s work on sharp Hardy inequality for axisymmetric solenoidal ﬁelds.
大⋆)15 亀 高 惟 倫 (阪衛大)渡 辺 宏 太 郎 (防永 井
敦 ( 津 田 塾 大 学 芸)
武 村 一 雄 ( 日 大 理 工)
山 岸 弘 幸 ( 産 業 技 術 高 専)

Yoshinori Kametaka (Osaka Univ.⋆)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)(Tsuda Coll.)
Atsushi Nagai
Kazuo Takemura (Nihon Univ.)
Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)

弾性基盤上の張力をかけた半無限長の棒のたわみのグリーン関数の階層
構造とソボレフ不等式の最良定数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Positivity and hierarchical structure of Green functions and the best
constant of Sobolev inequality corresponding to a bending problem of abeam on a half line

概 要 We consider the boundary value problem for 4-th order linear ordinary diﬀerential equation in a

half line (0, ∞), which represents bending of a beam on an elastic foundation under a tension. A tension
is relatively stronger than a spring constant of elastic foundation. We here treat 4 self-adjoint boundary
conditions, clamped, Dirichlet, Neumann and free edges, at x = 0. We show the positivity and thehierarchical structure of 4 Green functions and the best constants of the corresponding Sobolev inequalities.
16 森
竜 樹 ( 武 蔵 野 大 工)
大理)
田 﨑 創 平 (北
(
崎
大⋆)
辻 川
亨 宮
谷
大⋆)
四 ツ 谷 晶 二 (龍Tatsuki Mori (Musashino Univ.)
Sohei Tasaki (Hokkaido Univ.)
Tohru Tsujikawa (Univ. of Miyazaki⋆)
Shoji Yotsutani (Ryukoku Univ.⋆)

Global structure of stationary solutions for the 1-dimension Fix–Caginalp
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Global structure of stationary solutions for the 1-dimension Fix–Caginalp
equation

概 要 We are interested in stationary solutions of the Fix–Caginalp equation, which is proposed by Fix(1983) and Caginalp (1986) to understand phenomena of the non-isothermal solid-liquid phase transition.
Elliott–Zheng (1990) and Suzuki–Tasaki (2009) obtained some partial results concerning the existence andnon-existence of stationary solutions under restricted conditions. In this talk, we show the global structureof all stationary solutions of the 1-dimensional Fix–Caginalp equation with Neumann boundary conditions.
17 寺 井 健 悟 (東 大 数 理)
三 竹 大 寿 ( 東 大 数 理)
Kengo Terai (Univ. of Tokyo)
Hiroyoshi Mitake (Univ. of Tokyo)

On weak solutions to ﬁrst-order discount mean ﬁeld games · · · · · · · · · · 10
On weak solutions to ﬁrst-order discount mean ﬁeld games

概 要 In this talk, we establish the existence and uniqueness of weak solutions to ﬁrst-order discount meanﬁeld games and a stability result to give the existence for the ergodic problem. We show an example toillustrate the multiplicity of weak solutions to the ergodic problem. With this motivation, we address aselection condition, which is a necessary condition that any limit of solutions under subsequence satisﬁes.
As an application, we show a nontrivial example to get the convergence of weak solutions.

最終版: 2022/3/4函数方程式論18 森 龍 之 介 (明 大 M I M S)
富 松 瑛 太 ( 東 工 大 理)
利 根 川 吉 廣 ( 東 工 大 理)
Ryunosuke Mori (Meiji Univ.)
Eita Tomimatsu (Tokyo Tech)
Yoshihiro Tonegawa (Tokyo Tech)44

移流項付き一般化平均曲率流に対する強解について · · · · · · · · · · · · · · · · · 12

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

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

with a given transport vector in the sense of Brakke’s formulation of velocity. When the ﬂow is locallyclose to a time-dependent k-dimensional plane in a weak sense of measure in space-time, it is represented
as a graph of a C 1,α function over the plane. On the other hand, it is not known if the graph satisﬁes thecorresponding PDE pointwise in general. For this problem, when k = n − 1 and the distributional time
derivative of the graph is a signed Radon measure, it is proved that the graph satisﬁes the PDE pointwise.
An application to a short-time existence theorem for a surface evolution problem is given.
16:30〜17:30
高 橋

2021 年度 (第 20 回) 日本数学会解析学賞受賞特別講演
太 (阪 市 大 理) ♭ Hardy 不等式に関連する数学解析

Futoshi Takahashi (Osaka City Univ.)

Mathematical analysis related with Hardy inequalities

概 要 In this talk, I will concern several topics on Hardy inequalities in subcritical or critical regime, Hardy–

Leray inequalities for vector ﬁelds, and related functional inequalities. This talk is based on several works
with Megumi Sano, and Naoki Hamamoto.

3 月 29 日（火）第 II 会場

9:00〜12:00
19 岡
大 将 ( 東 北 大 理)
赤 木 剛 朗 ( 東 北 大 理)
Tomoyuki Oka (Tohoku Univ.)(Tohoku Univ.)
Goro Akagi

Space-time periodic homogenization for the porous medium equation
with nonnegative initial data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12Space-time periodic homogenization for the porous medium equation
with nonnegative initial data

概 要 In this talk, we shall discuss a space-time periodic homogenization problem for the porous medium

equation with periodically oscillating (in space and time) coeﬃcients and nonnegative initial data.
20 佐 藤 龍 一 (福 岡 大 理)
小 杉 卓 裕(鳥取環境大人間形成教育センター)
Ryuichi Sato (Fukuoka Univ.)
Takahiro Kosugi(Tottori Univ. of Environ. Stud.)On existence of solutions to a system of fully nonlinear parabolic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On existence of solutions to a system of fully nonlinear parabolic equations

概 要 We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this talkwe shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global
existence is speciﬁc to the fully nonlinear parabolic system.

最終版: 2022/3/445函数方程式論21 吉 見優 ( 京 大 人 間 環 境)
小 川 卓 克 ( 東 北 大 理)
清 水 扇 丈 ( 京 大 人 間 環 境)
(Kyoto Univ.)
Yu Yoshimi
Takayoshi Ogawa (Tohoku Univ.)
Senjo Shimizu (Kyoto Univ.)

熱方程式の斜め境界条件下での最大 L1 -正則性 · · · · · · · · · · · · · · · · · · · · · 10

Maximal L1 -regularity of the heat equation under the oblique boundary
condition

概 要 For the inhomogeneous oblique boundary data, maximal L1 -regularity of the heat equation is obtainedsin time end-point case upon the homogeneous Besov space Ḃp,1(Rn+ ) with 1 < p < ∞. We use the methodof Ogawa–Shimizu (arXiv:2110.10442 to be published in JEE) in which they utilized the almost orthogonal
properties between the boundary potential and the Littlewood–Paley dyadic decomposition of unity in theBesov and the Lizorkin–Triebel spaces.
22 和 久 井 洋 司 (東 京 理 大 理)
(Univ. of Wroclaw)
S. Cygan(Univ. of Wroclaw)
G. Karch
K. Krawczyk (Univ. of Wroclaw)

Hiroshi Wakui (Tokyo Univ. of Sci.)
Szymon Cygan (Univ. of Wroclaw)
Grzegorz Karch (Univ. of Wroclaw)
Krzysztof Krawczyk (Univ. of Wroclaw)

移流拡散方程式の定数定常解の安定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Stability of constant steady states of a drift-diﬀusion equation

概 要 We study stability of constant steady states of a drift-diﬀusion equation on n-dimensional Euclidean

spaces. Our problem has its constant steady states which can be chosen as arbitrary real number. We have
proved that stability of each constant steady states depend on the value of itself.
23 Y. Epshteyn ( Univ. of Utah )(Illinois Inst. of Tech.)
Chun Liu
水 野 将 司 ( 日 大 理 工)

Yekaterina Epshteyn (Univ. of Utah)
Chun Liu (Illinois Inst. of Tech.)
Masashi Mizuno (Nihon Univ.)

結晶粒界の運動モデルに由来する Fokker–Planck 方程式の解の長時間挙動· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Long-time asymptotic behavior for solutions to the Fokker–Planck equation related to the evolution of grain boundaries

概 要 We consider long-time asymptotic behavior for solutions to the Fokker–Planck equation, which isrelated to the mathematical model of the evolution of grain boundaries with two state variables, the latticemisorientation and the triple junction. Since the Fokker–Planck equation satisﬁes the energy law, thelong-time asymptotics of the solutions seems the Boltzmann distribution of the state variables. We show
the exponential stability of the Boltzmann distribution in a weighted L2 space. Furthermore, we explain
the relationship between the Boltzmann distribution and the marginal distribution.
24 塚 本 悠 暉 (明大研究・知財)

有界領域上の移流項付きアレン・カーン方程式の収束性 · · · · · · · · · · · · · 10

Yuki Tsukamoto (Meiji Univ.)

Convergence of the Allen–Cahn equation with transport term in a boundeddomain

概 要 In this talk, we explane the Allen–Cahn equation with transport term in a bounded domain. We provethat the limit interface is mean curvature ﬂow with transport term under the condition that the energy isuniformly bounded with respect to time. Using this result, we can show the existence of mean curvature
ﬂow with a gradient vector ﬁeld as transport term.

最終版: 2022/3/4函数方程式論25 岩 渕

司 ( 東 北 大 理)

Tsukasa Iwabuchi (Tohoku Univ.)

46

A spectral localization applied to the critical surface quasi-geostrophic
equation on a ball · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
A spectral localization applied to the critical surface quasi-geostrophic
equation on a ball

概 要 We study the Cauchy problem for the quasi-geostrophic equations in a ball of the two dimensional

space under the homogeneous Dirichlet boundary condition. We show the existence, the uniqueness of thestrong solution in the framework of Besov spaces. In the proof, we establish a spectral localization techniqueand commutator estimates.
26 オーヘーダヒ (東 北 大 理)
岩 渕
司 ( 東 北 大 理)

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

表面準地衡方程式の解の最適な減衰評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

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

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

two-dimensional Euclidean space, and obtain a convergence rate, in the Lebesgue norm, between the solution
and this approximation with respect to time. We also demonstrate that the nonlinear term of the solution
is bounded sharply by the same function of time.
27 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)

反応拡散方程式の伝播現象と Liouville 型定理 · · · · · · · · · · · · · · · · · · · · · · 12

A Liouville type theorem of reaction diﬀusion system and its application
to spreading problem

概 要 We establish a Liouville type theorem for entire solutions of these reaction-diﬀusion systems. Basedon this theorem, we derive the stabilization of the solutions of the reaction-diﬀusion system to the uniquepositive constant state, under the condition that this positive constant state is globally stable in thecorresponding kinetic systems. An example about spreading phenomena from epidemiology are given toillustrate the applications of this theory.
28 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)
Yu-Shuo Chen (Tamkang Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)
Yu-Shuo Chen (Tamkang Univ.)

特異被食捕食系の伝播現象と進行波 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Spreading problem and traveling wave of a singular predator-prey system

概 要 We concern the dynamical behaviors of a singular predator-prey model. We compute the spreading

speed of the predator and asymptotic behavior of the spreading solution beyond and behind the front. Someexistence theorems of traveling wave on a line is also discussed.
29 久 藤 衡 介 (早 大 理 工)
Kousuke Kuto (Waseda Univ.)

重定・川崎・寺本モデルにおける交差拡散極限系の棲み分け定常解の大域分岐構造 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Global bifurcation structure of segregated steady-states for a crossdiﬀusion limit in the Shigesada–Kawasaki–Teramoto model

概 要 Recently, the author obtained a limiting (shadow) system of the stationary Shigesada–Kawasaki–

Teramoto model as both cross-diﬀusion terms tend to inﬁnity with the same order. This talk is concernedwith the bifurcation structure of nonconstant solutions of the limiting system. In the one-dimensional case,this result gives inﬁnitely many branches that connect the positive constant solution with a singular limit.

最終版: 2022/3/447函数方程式論13:00〜14:00
松 澤

特別講演
寛 ( 神 奈 川 大 理)

Hiroshi Matsuzawa (Kanagawa Univ.)

高次元空間における多安定型非線形項をもつ反応拡散方程式の自由境界問題についてA free boundary problem of reaction-diﬀusion equation with a multistable type nonlinearity in high space dimensions

概 要 In this talk, I will treat propagation phenomena in a free boundary problem of reaction diﬀusion

equation of the form : ut = ∆u + f (u) (t > 0, x ∈ Ω(t)) with free boundary Γ(t) = ∂Ω(t) which isdetermined by the Stefan condition of the form ut = µ|∇u|2 on Γ(t). In the work of Du and Lin (2010),
this type of problem was introduced when N = 1 as a model which describes the spreading of new orinvasive species. From this work, propagating phenomena in the free boundary problems attract more andmore attention of mathematicians. In this talk, I will present some recent study on propagation proﬁlesof solutions for the free boundary problem of reaction-diﬀusion equation with some class of multi-stablenonlinearity in high space dimensions. I will give ﬁrst the result about radially symmetric case. I will alsopresent the general (non-symmetric) case. This talk is based on some joint works with Dr. Yuki Kaneko(Japan Women’s University) and Professor Yoshio Yamada (Waseda University).

3 月 30 日（水）第 II 会場

9:00〜12:00
30 勝 呂 剛 志 (東 北 大 理) ♭ 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 (Tohoku Univ.)

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

概 要 We consider the Cauchy problem of the parabolic-elliptic Keller–Segel system. This system is one ofthe diﬀusion equations involving a nonlocal term. It is interesting whether this problem is well-posed infunction spaces containing non-decaying functions. We show that the Cauchy problem of the Keller–Segelsystem is well-posed in uniformly local Lebesgue spaces.
31 細 野 竜 也 (東 北 大 理) ♭ Finite time blow-up of solutions to an attraction–repulsion chemotaxis
system in four dimensional case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Tatsuya Hosono (Tohoku Univ.)

Finite time blow-up of solutions to an attraction–repulsion chemotaxis
system in four dimensional case

概 要 This talk deals with the solution of the Cauchy problem for an attraction-repulsion chemotaxis system

in Rn with the positive parameters β1 , β2 , λ1 , λ2 . According to previous results in R2 , it has shown that for
the initial mass ∥u0 ∥L1 , the value 8π/(β1 − β2 ) is the threshold whether the solution exists globally in timeor not under the attractive dominant case β1 > β2 . In this talk, for the 4-dimensional case, we show thatthe solution with ∥u0 ∥L1 > (8π)2 /χ may blow up in ﬁnite time, where χ is a positive constant explicitly
determined by β1 , β2 , λ1 , λ2 . The constant (8π)2 can be regarded as the 4-dimensional threshold value forthe global existence corresponding to the system which has 8π-dichotomy in R2 .
32 田 中 悠 也 (東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

Yuya Tanaka (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Blow-up in a degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Blow-up in a degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production

概 要 This talk deals with a degenerate parabolic-elliptic chemotaxis system with logistic source andnonlinear production. In a nondegenerate case, a condition such that solutions blow up in ﬁnite time wasobtained in our previous work (J. Math. Anal. Appl.; 2022; 506; 29). The purpose of this talk is to showthat solutions blow up in ﬁnite time in a degenerate case.

最終版: 2022/3/4函数方程式論33 上 村48

豊 (東京海洋大海洋) ♭ Boussinesq system のソリトン解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.)

Soliton solutions of the Boussinesq system

概 要 Based upon a reﬂectionless inverse scattering theory we establish an inverse scattering method bywhich N-soliton solutions of a nonlinear evolution system (the Boussinesq system) are constructed.
34 米 田 昌 史 (千葉大融合理工)

Masafumi Yoneda (Chiba Univ.)

Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice概 要 Discrete nonlinear Schrödinger equation (DNLS) is a partial diﬀerential equation which appear invarious region of physics. We will explain the behavior of the solution of DNLS. In particular, we focus on
the stability of soliton. The stability is that the solution of DNLS converge to standing wave solutions insome sense for a long time. The standing wave solution is a special solution of DNLS.We will explain proofof the stability which consists of spectrum theory, linear estimates and boot strap argument.
35 吉 野 正 史 (広 島 大 理)

Masafumi Yoshino (Hiroshima Univ.)

Movable singular point of non autonomous Hamiltonian system of degree of freedom one · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Movable singular point of non autonomous Hamiltonian system of degree of freedom one

概 要 In this talk we study the movable singular point of a Hamiltonian system with Hamiltonian H :=H0 + H1 . Here H0 is integrable and has a singular solution v while H1 is a perturbation. A singular solutionfor H has the form F (v) for some transformation F deﬁned on a domain of the phase space which contains
the orbit of v tending to inﬁnity.
36 深 谷 法 良 (東 京 理 大 理)
V. Georgiev ( Pisa Univ. )池 田 正 弘 (理化学研・慶大理工)

Noriyoshi Fukaya (Tokyo Univ. of Sci.)
Vladimir Georgiev (Pisa Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

点相互作用を持つ 2 次元非線形シュレディンガー方程式の定在波解の安定性と不安定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

On stability and instability of standing waves for 2d-nonlinear Schrödinger
equations with point interaction

概 要 We study existence and stability properties of ground-state standing waves for two-dimensional

nonlinear Schrödinger equation with a point interaction and a focusing power nonlinearity. The Schrödinger
operator with a point interaction (−∆α )α∈R describes a one-parameter family of self-adjoint realizationsof the Laplacian with delta-like perturbation. The operator −∆α always has a unique simple negative
eigenvalue eα . We prove that if the frequency of the standing wave is close to −eα , it is stable. Moreover,
if the frequency is suﬃciently large, we have the stability in the L2 -subcritical or critical case, while theinstability in the L2 -supercritical case.
37 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.

最終版: 2022/3/449

函数方程式論38 浜 野大 ( 埼 玉 大 理 工)
池 田 正 弘(理化学研 AIP・慶大理工)
町 原 秀 二 ( 埼 玉 大 理 工)

Masaru Hamano (Saitama Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Shuji Machihara (Saitama Univ.)

逆冪乗型ポテンシャルをもつ非線形シュレディンガー方程式の爆発解について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Blow-up solutions to nonlinear Schrödinger equation with an inverse
power potential

概 要 In this talk, we treat nonlinear Schrödinger equation with a mass-critical nonlinear term and an

inverse power potential in one dimension. We note that the equation is not scale invariant. We consider thetime behavior of solutions for initial data with negative energy. In particular, we prove that the solutions
blow up. Ogawa–Tsutsumi proved the similar result for an equation without a potential. They used scale
invariance of the equation without the potential. Since our equation has not scale invariance, we cannot
apply directly Ogawa–Tsutsumi’s argument. Therefore, we change scale of weighted function in a localized
virial identity and prove our result.
39 佐 藤 拓 也 (東 北 大 理) ♭ Lower bound estimates of solutions to the dissipative nonlinear Schrödinger
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Takuya Sato

(Tohoku Univ.)

Lower bound estimates of solutions to the dissipative nonlinear Schrödinger
equation

概 要 We consider the Cauchy problem for the nonlinear Schrödinger equation with a power type nonlinearity

λ|u|p−1 u. The condition Im λ < 0 yields a dissipative property for the solution to the nonlinear Schrödinger
equation. We show that p = 1 + 2/n is the critical exponent to exhibit the L2 -decay of dissipative solutions,
namely we show the L2 -lower bound of the solution when p > 1 + 2/n.
40 波 多 間 備 (京 大 数 理 研)
Sonae Hadama (Kyoto Univ.)

リースポテンシャルを持つ無限粒子系に対する Hartree 方程式の初期値問題の適切性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Well-posedness of the Hartree equation for inﬁnitely many particles with
the Riesz potential

概 要 We study the Hartree equation describing the time evolution of the wave functions of N fermionsinteracting with each other. From a physics perspective, the case where N is inﬁnite is also important. In
this case, the well-posedness and scattering was ﬁrst studied by Lewin–Sabin. It has been advanced recently
by Chen–Hong–Pavlović and Collot–de Suzzoni. However, these studies only deal with the cases where theinteraction is weak, and therefore, there were no results for the cases with strong interaction, for example,
the Riesz potential. In this talk, we report the results on the local and global well-posedness of the Hartree
equation with the Riesz potential, which is important from a physics perspective.
14:15〜16:15
41 橋 本 隼 也 (埼 玉 大 理 工)
玉
大⋆)
道 工
勇 (埼
町 原 秀 二 ( 埼 玉 大 理 工)

Shunya Hashimoto (Saitama Univ.)
Isamu Dôku (Saitama Univ.⋆)
Shuji Machihara (Saitama Univ.)

確率非線形シュレディンガー方程式の H 2 -時間局所適切性 · · · · · · · · · · · 10

The local well-posedness of the stochastic nonlinear Schrödinger equations in H 2

概 要 The Cauchy problem for the stochastic nonlinear Schrödinger equation with a multiplicable noise

is considered where the nonlinear term is of a power type and its coeﬃcients are complex numbers. In
particular, it is important to consider the complex coeﬃcients in the noise which cover non-conservative
cases, because they include measurement eﬀects in quantum physics. The main purpose of this work is toconstruct classical solutions in H 2 (Rd ) for the problem in question.

最終版: 2022/3/4函数方程式論42 加 藤Isao Kato

勲 (京

大

理)

(Kyoto Univ.)

50

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

概 要 We study ill-posedness for the half wave Schrödinger equation introduced by Xu (2017). Ill-posedness

is obtained in the super-critical or at the critical space. The proof for the super-critical space is based on
the argument established by Christ, Colliander and Tao (2003). For the critical space, we use the standing
wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi (2021).
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 a classiﬁcation result of systems with two unknowns and cubic polynomial

nonlinearities. We deﬁne an equivalence relation between two systems by the linear transformation of
unknowns. The goal is to understand a quotient set with respect to the equivalence relation. To this end,
we introduce a matrix representation of a system. The representation not only gives us an explicit formulaof the equivalence relation and but also describes characteristic properties of the system such as conservation
laws. The classiﬁcation result is based on the study of nonlinear dispersive equations but it is applicable toa wide class of systems of PDEs and ODEs.
44 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.)

ある非線形クラインゴルドン方程式系の解の漸近挙動について · · · · · · · · 10

On asymptotic behavior of solutions to a nonlinear Klein–Gordon system

概 要 In this talk, we study the asymptotic behavior of solutions to a speciﬁc system of the cubic Klein–

Gordon equations in one dimension. The cubic nonlinearity is critical in one dimension with respect to thelarge-time behavior of (small) solutions. It turns out that the system, which is obtained systematically by
our classiﬁcation result, admits a solution with a new type of asymptotic behavior.
45 北 村 駿 介 (東 北 大 理) ♭ 特性方向の重みを持つ一次元半線形波動方程式の古典解の lifespan 評価
高 村 博 之 ( 東 北 大 理)
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
若 狭 恭 平 ( 釧 路 工 高 専)

Shunsuke Kitamura (Tohoku Univ.)
Hiroyuki Takamura (Tohoku Univ.)
Kyouhei Wakasa(Kushiro Nat. Coll. of Tech.)

The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights

概 要 In this talk, we report on the lifespan estimates of classical solutions of semilinear wave equations

with characteristic weights and compactly supported data in one space dimension. The results includes
those for weights by time-variable, but excludes those for weights by space-variable in some cases. We haveinteractions of two characteristic directions.

最終版: 2022/3/451函数方程式論46 高 村 博 之 (東 北 大 理) ♭ 空間 1 次元における空間変数による重み付き微分型半線形波動方程式の北 村 駿 介 (東 北 大 理) 古典解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
森 澤 功 暁 ( 東 北 大 理)

Hiroyuki Takamura (Tohoku Univ.)
Shunsuke Kitamura (Tohoku Univ.)
Katsuaki Morisawa (Tohoku Univ.)

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

概 要 In this talk, we discuss about the initial value problems for semilinear wave equations of derivative typewith spatial weights in one space dimension. The lifespan estimates of classical solutions are quite diﬀerent
from those for nonlinearity of unknown functions itself as the global-in-time existence can be established byspatial decay.
47 高 村 博 之 (東 北 大 理) ♭ 非線形波動方程式の一般論を超える空間 1 次元の combined eﬀect · · · · · 12
佐々木多希子 (武蔵野大工・東北大理)
森 澤 功 暁 ( 東 北 大 理)

Hiroyuki Takamura (Tohoku Univ.)
Takiko Sasaki(Musashino Univ./Tohoku Univ.)
Katsuaki Morisawa (Tohoku Univ.)

The combined eﬀect in one space dimension beyond the general theory
for nonlinear wave equations

概 要 In this talk, we introduce lifespan estimates for a special class of semi-linear wave equations in one

space dimension for which the so-called combined eﬀect is observed. It is remarkable that we have better
results than those in the general theory which was established in 1992.
16:30〜17:30

特別講演側 島 基 宏 ( 東 京 理 大 理 工)Motohiro Sobajima(Tokyo Univ. of Sci.)

Weighted energy estimates for wave equations with space-dependent
damping
Weighted energy estimates for wave equations with space-dependent
damping

概 要 In this talk we summarize recent progress on weighted energy estimates of polynomial type for thewave equation with space-dependent damping ∂t2 u − ∆u + a(x)∂t u = 0, where the damping coeﬃcient a
decays like a polynomial |x|−α (α ∈ [0, 1)) at spatial inﬁnity. When we consider weighted energy estimatesto such problems, usually the exponential function of the form eψ(x,t) appears as a weight function in theenergy functional. However, this choice excludes a class of initial data with polynomial decay. In contrast,
we introduce another class of weight functions involving the conﬂuent hypergeometic functions to provide
corresponding weighted energy estimates which have weight functions with polynomial order. Next, we deal
with global existence for the semilinear problem with a power type nonlinearity as an application of such
estimates.

最終版: 2022/3/4函数方程式論3 月 31 日（木）52

第 II 会場

9:00〜12:00
48 柏 原 崇 人 (東 大 数 理)
伊 藤 弘 道 ( 東 京 理 大 理)

Takahito Kashiwabara (Univ. of Tokyo)
Hiromichi Itou (Tokyo Univ. of Sci.)

速度を含む Signorini 型接触条件と Tresca 摩擦条件下での線形動弾性体
方程式の一意可解性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Unique solvability of a crack problem with Signorini-type and Tresca
friction conditions in a linearized elastodynamic body

概 要 We consider a time-dependent linear elasticity equation including a crack, which is a thin surface

embedded in a bulk domain. On the crack we impose a non-penetrating (a.k.a. Signorini) condition anda given friction (a.k.a. Tresca) condition for the normal and tangential directions, respectively. Sincean original Signorini condition involving only displacement leads to a severe mathematical diﬃculty, we
modiﬁed it in such a way that it includes velocity. For this problem we are able to prove existence anduniqueness of a strong solution, which is our main result.
49 福 田 一 貴 (信 州 大 工)
板 坂 健 太Ikki Fukuda (Shinshu Univ.)
Kenta Itasaka

粘性 Fornberg–Whitham 方程式の解の高次漸近形 · · · · · · · · · · · · · · · · · · 10Higher-order asymptotic proﬁles of the solutions to the viscous Fornberg–
Whitham equation

概 要 We consider the Cauchy problem for the viscous Fornberg–Whitham equation which is one of thenonlinear and nonlocal dispersive-dissipative equations. In this talk, we establish the global existence ofthe solutions and study its asymptotic behavior. We show that the solution to this problem converges tothe self-similar solution to the Burgers equation called the nonlinear diﬀusion wave, due to the dissipationeﬀect by the viscosity term. Moreover, we analyze the optimal asymptotic rate to the nonlinear diﬀusion
wave and the detailed structure of the solution by constructing higher-order asymptotic proﬁles. Also, weinvestigate how the nonlocal dispersion term aﬀects the asymptotic behavior of the solutions and compare
the results with the ones of the KdV–Burgers equation.
50 杉 崎 聡 平 (東工大情報理工)
西 畑 伸 也 (東工大情報理工)
橋 本 伊 都 子 ( 金 沢 大 理 工)
Souhei Sugizaki (Tokyo Tech)
Shinya Nishibata (Tokyo Tech)
Itsuko Hashimoto (Kanazawa Univ.)

流入境界条件下での流体の方程式の球対称な定常解の漸近安定性について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Asymptotic stability of a radially symmetric stationary solution for thecompressible Navier–Stokes equation with an inﬂow boundary condition

概 要 We study a radially symmetric stationary solution for the compressible Navier–Stokes equation withan inﬂow boundary condition. Precisely, we obtain the decay rates of the solution and its ﬁrst derivatives.
Moreover, we show an asympotic stability of the stationary solution.
51 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 energy conservation law for the full system of compressible
Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
On the energy conservation law for the full system of compressible
Navier–Stokes equations

概 要 We study a suﬃcient condition such that a weak solution of the full system of compressible Navier–Stokes equations satisﬁes the energy conservation law. We focus on two and three space dimensions andespecially consider the case that the pressure is written by the ideal gas law.

最終版: 2022/3/453函数方程式論52 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.)

砕波を伴う山越え気流の漸近安定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Asymptotic stability of air ﬂow over mountains with wave breaking

概 要 We consider stationary shock waves appearing in air ﬂow over mountains modeled by one-dimensional

shallow water equation. The shock wave connects an upstream supercritical state to a downstream subcriticalstate discontinuously. If the discontinuity is located in a lee side of the mountain, we claim the asymptotic
stability of the stationary shock wave whatever large the strength of the shock or the gradient of themountain height may be.
53 池 田 幸 太 (明 大 総 合 数 理)
Kota Ikeda(Meiji Univ.)

樟脳粒の集団運動における一様流の安定性解析 · · · · · · · · · · · · · · · · · · · · · 12

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

概 要 Various collective motions of camphor boats, called jamming, clustering, and swarming state observedin a one-dimensional circuit, have been studied. It is expected that the center manifold theories proposed inprevious works are useful for the analysis of the collective motion of camphor boats. In my previous work,
we have developed a new theory for a system with Dirac’s delta functions in L2 -framework. In this talk, wewill examine the stability analysis in the reduced system and numerically show that the uniform ﬂow canbe destabilized even if the length of the circuit is large.
54 古 川賢 ( 理 化 学 研)
柏 原 崇 人 ( 東 大 数 理)
(RIKEN)Ken Furukawa
Takahito Kashiwabara (Univ. of Tokyo)

異方 Lebesgue 空間におけるプリミティブ方程式と Navier–Stokes 方程式に関連する特異極限問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Singular limit problems on the primitive equations and Navier–Stokes
equations in anisotropic spaces

概 要 In this talk, we introduce the mathematical relationship between the Navier–Stokes equations and theprimitive equations. Then we show that the solution of the scaled Navier–Stokes equations converges to thesolution of the primitive equations in anisotropic Lebesgue spaces under less regularity assumptions.
55 後 藤 田 剛 (東工大情報理工)
Takeshi Gotoda (Tokyo Tech)

Energy conservation in 2D incompressible inviscid ﬂows · · · · · · · · · · · · · 10
Energy conservation in 2D incompressible inviscid ﬂows

概 要 We consider energy conservation in 2D incompressible inviscid ﬂows through weak solutions of theﬁltered-Euler equations, which describe a regularized Euler equations. We show that the energy dissipation
rate for the ﬁltered weak solution with vorticity in Lp , p > 3/2 converges to zero in the limit of the ﬁlter
parameter. Although the energy deﬁned in the whole space is not ﬁnite in general, we formally extract atime-dependent part from the energy and deﬁne the energy dissipation rate as its time-derivative. Moreover,the limit of the ﬁltered weak solution is a weak solution of the Euler equations and it satisﬁes a local energybalance in the sense of distributions.
56 鶴 見 裕 之 (京前 川 泰 則 (京

大

理)

大

理)

Hiroyuki Tsurumi (Kyoto Univ.)
Yasunori Maekawa (Kyoto Univ.)

Existence of the 2D stationary Navier–Stokes ﬂow on the whole planearound a radial ﬂow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Existence of the 2D stationary Navier–Stokes ﬂow on the whole planearound a radial ﬂow

概 要 We consider the stationary Navier–Stokes equations on the whole plane R2 . We show that for a given

small and smooth external force around a radial ﬂow, there exists a classical solution decaying like |x|−1 .
In our result, it is not necessary to impose any symmetric conditions on external forces.

最終版: 2022/3/4函数方程式論54

14:15〜16:15
57 小 薗 英 雄(早大理工・東北大 RACMaS)寺 澤 祐 高 ( 名 大 多 元 数 理)
若 杉 勇 太 (広島大先進理工)
Hideo Kozono(Waseda Univ. / Tohoku Univ.)
Yutaka Terasawa (Nagoya Univ.)
Yuta Wakasugi (Hiroshima Univ.)

Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier–Stokes equations outside of an inﬁnite cylinder with aperiodic boundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier–Stokes equations outside of an inﬁnite cylinder with aperiodic boundary condition

概 要 We study the asymptotic behavior of solutions to the steady Navier–Stokes equations outside of an

inﬁnite cylinder in R3 . We assume that the ﬂow is periodic in x3 -direction and has no swirl. This problem isclosely related with two-dimensional exterior problem. Under a condition on the generalized ﬁnite Dirichlet
integral, we give a pointwise decay estimate of the vorticity at the spatial inﬁnity. Moreover, we prove a
Liouville-type theorem only from the condition of the generalized ﬁnite Dirichlet integral.
58 L. Brandolese ( Univ. Lyon 1 )岡 部 考 宏 ( 阪 大 基 礎 工)

Lorenzo Brandolese (Univ. Lyon 1)
Takahiro Okabe (Osaka Univ.)

Control of weak solutions of the Navier–Stokes equation by external
forcing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Control of weak solutions of the Navier–Stokes equation by external
forcing

概 要 We consider the incompressible Navier–Stokes equations in the whole space Rn , n = 2, 3, 4. The aimof this talk is to control of the energy decay of weak solutions by external force. For this purpose, we givea reﬁnement of the method in our previous result and derive weighted L1 -estimate of weak solutions of theNavier–Stokes equations which satisﬁes the strong energy inequality.
59 渡 邊 圭 市 (早 大 理 工)

Keiichi Watanabe (Waseda Univ.)

Stability of stationary solutions to a free boundary problem of theNavier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Stability of stationary solutions to a free boundary problem of theNavier–Stokes equations

概 要 We consider the stability of equilibrium ﬁgures of uniformly rotating viscous incompressible ﬂuid in

R3 with surface tension, where the equilibrium ﬁgures are rotationally symmetric about a certain axis. It
is proved that this stability result can be obtained by the positivity of the second variation of the energyfunctional associated with the equation that determines equilibrium ﬁgures, provided that initial data areclose to an equilibria state. The solution converges exponentially to an equilibrium. The proof is inspiredby a series of papers due to Shibata, but a new orthogonal condition is introduced in order to show the
exponential stability of an associated analytic C0 -semigroup. If a value of initial angular momentum issmall, the steady-state is determined uniquely.
60 村 田 美 帆 (静 岡 大 工)
柴 田 良 弘 ( 早 大 理 工)
Miho Murata (Shizuoka Univ.)
Yoshihiro Shibata (Waseda Univ.)

Global well posedness for a Q-tensor model of nematic liquid crystals· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Global well posedness for a Q-tensor model of nematic liquid crystals

概 要 We consider the global well posedness and the decay estimates for a Q-tensor model of nematic liquid

crystals in RN , N ≥ 3. This system is coupled system by the Navier–Stokes equations with a parabolictype equation describing the evolution of the director ﬁelds Q. The proof is based on the maximal Lp -Lq
regularity and the Lp -Lq decay estimates to the linearized problem.

最終版: 2022/3/455

函数方程式論61 藤 井 幹 大 (九 大 数 理)
Mikihiro Fujii (Kyushu Univ.)

Large time behavior of solutions to the 3D anisotropic Navier–Stokes
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Large time behavior of solutions to the 3D anisotropic Navier–Stokes
equation

概 要 We consider the large time behavior of the solution to the 3D Navier–Stokes equation with horizontal

viscosity and show that the Lp decay rate of the horizontal components of the velocity ﬁeld coincides to thatof the 2D heat kernel, while the vertical component decays like the 3D heat kernel. Moreover, we consider
the asymptotic expansion of the solution and ﬁnd that a portion of the nonlinear term aﬀect the leading
term of the horizontal components of the velocity ﬁeld, whereas the leading term of the vertical component
is given by only the linear solution.
62 柴 田 良 弘 (早 大 理 工)

Yoshihiro Shibata (Waseda Univ.)

Global solution of the 3D compressible Navier–Stokes equations withfree surface in the maximal regularity class · · · · · · · · · · · · · · · · · · · · · · · · 10
Global solution of the 3D compressible Navier–Stokes equations withfree surface in the maximal regularity class

概 要 In this paper concerns the global wellposedness issue of the barotropic compressible Navier–Stokes

equations (CNS) with free surface in the smooth exterior domain in 3D Euclidean space. By using the decay
estimate in the semigroup theory, we construct the global-in-time solution in the time weighted maximal
Lp -Lq regularity class for some p > 2 and q > 3. Namely, the solution is bounded as Lp in time and Lq
in space. Compared with the previous results of the free boundary value problem of (CNS) in unboundeddomains, we relax the regularity assumption on the initial states, which is the advantage by using the
maximal Lp -Lq regularity framework.
63 柴 田 良 弘 (早 大 理 工)

Yoshihiro Shibata (Waseda Univ.)

The Lp -Lq decay estimate for the multidimensional compressible ﬂow
with free surface in the exterior domain · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
The Lp -Lq decay estimate for the multidimensional compressible ﬂow
with free surface in the exterior domain

概 要 The aim of this talk is to develop the general Lp theory for the barotropic compressible Navier–Stokes

equations with the free boundary condition in the exterior domain in the N dimensional Euclidean space(N ≥ 3). By the spectral analysis, we obtain the classical Lp -Lq decay estimate for the linearized model
problem in view of the partial Lagrangian transformation.
16:30〜17:30

特別講演

上 田 好 寛 ( 神 戸 大 海 事)

Yoshihiro Ueda

(Kobe Univ.)

緩和項を持つ対称双曲型方程式系における消散構造の数学解析

Mathematical analysis of the dissipative structure for the symmetric
hyperbolic system with relaxation

概 要 In this talk, we consider the dissipative structure for the linear symmetric hyperbolic system with

non-symmetric relaxation. If the relaxation matrix of the system has symmetric property, Shizuta andKawashima in 1985 introduced the suitable stability condition, and Umeda, Kawashima and Shizuta in
1984 analyzed the dissipative structure. On the other hand, Ueda, Duan and Kawashima in 2012 and 2018
focused on the system with non-symmetric relaxation, and got the partial results. Furthermore, they argued
the new dissipative structure called the regularity-loss type. In this situation, our purpose of this talk is
to extend the stability theory introduced by Shizuta and Kawashima in 1985 and Umeda, Kawashima and
Shizuta in 1984 for our general system.

最終版: 2022/3/4
実函数論

実

函

数

3 月 30 日（水）56

論第 VIII 会場

9:30〜11:45
1 冨 澤 佑 季 乃 ( 新 潟 工 大 工)
Yukino Tomizawa(Niigata Inst. of Tech.)

測地距離空間の幾何学的性質 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Geometric properties of complete geodesic space

概 要 In general, geodesic spaces is not linear, but they have generalization of properties in linear spaces.

The purpose of this study is to elucidate the geometrical characteristics of geodesic spaces. We report somegeometric properties such as uniform convexity in complete Busemann spaces.
2 松 下 慎 也
(秋田県立大システム科学技術)

Shin-ya Matsushita (Akita Pref. Univ.)

Douglas–Rachford 法について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Douglas–Rachford algorithm

概 要 The Douglas–Rachford algorithm is an important and powerful algorithm that can be applied tosolving problems, such as minimizing the sum of two proper closed convex functions, or, more generally,ﬁnding a zero point of the sum of two monotone operators. In this talk, we study a modiﬁed version of the
Douglas–Rachford algorithm for convex minimization problem in a real Hilbert space.
3 厚 芝 幸 子 (東京女大現代教養)
Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Convergence theorems for monotone nonexpansive mappings · · · · · · · · 15
Convergence theorems for monotone nonexpansive mappings

概 要 In this talk, we prove nonlinear ergodic theorems for a family of monotone nonexpansive mappings inordered uniformly convex Banach spaces. We also weak and strong convergence theorems for the mappings.
4 青 山 耕 治 ( 千 葉 大 社 会)
Koji Aoyama(Chiba Univ.)

吸引点と擬非拡大拡張 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A quasinonexpansive extension of a mapping with an attractive point

概 要 We show that, under appropriate conditions, there exists a quasinonexpansive extension of a mappingwith an attractive point in the sense of Takahashi and Takeuchi (2011) such that the ﬁxed point set of theextension equals the attractive point set of the given mapping. Then using the quasinonexpansive extension,
we establish some convergence theorems for approximating attractive points of a generalized hybrid mappingin the sense of Kocourek, Takahashi, and Yao (2010).
5 田 中 亮 太 朗 ( 東 京 理 大 教 養)

Ryotaro Tanaka (Tokyo Univ. of Sci.)

Birkhoﬀ–James 直交性に基づくバナッハ空間の非線形分類について · · · 15
Nonlinear classiﬁcation of Banach spaces based on Birkhoﬀ–James orthogonality

概 要 For Banach spaces X, Y , we say that X is isomorphic to Y with respect to the structure of Birkhoﬀ–

James orthogonality, denoted by X ∼BJ Y , if there exists a bijection T : X → Y that preserves Birkhoﬀ–
James orthogonality in both directions. It is shown that the ﬁnite dimension of a Banach space is preserved
under “∼BJ ”, reﬂexive smooth Banach spaces are isomorphically classiﬁed from the viewpoint of Birkhoﬀ–
James orthogonality, and three or more dimensional Hilbert spaces are characterized by their structure of
Birkhoﬀ–James orthogonality.

最終版: 2022/3/4

57

実函数論

6 三 谷 健 一 (岡山県立大情報工)潟
大⋆)斎 藤 吉 助 (新Kenichi Mitani (Okayama Pref. Univ.)
Kichi-Suke Saito (Niigata Univ.⋆)

バナッハ空間の skewness に関する最近の進展について · · · · · · · · · · · · · · 15

Some recent results on skewness of Banach spaces

概 要 In this talk, we present some recent results on the skewness of Banach spaces, especially in connection

with James constant and characteristic of convexity.
7 川 﨑 敏 治 ( 玉 川 大 工)

Toshiharu Kawasaki (Tamagawa Univ.)

拡張不定積分に関する注意点 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Notes on the extended indeﬁnite integral

概 要 In this talk, we will describe the points to note regarding the family of indeﬁnite integral with respect

to the extended integral.
14:30〜16:00
8 河 邊

淳 ( 信 州 大 工)

Jun Kawabe(Shinshu Univ.)

非加法的測度空間上の可測関数空間の位相構造 · · · · · · · · · · · · · · · · · · · · · 15

A topology on the space of measurable functions on a nonadditive measure space

概 要 In this talk, given a nonadditive measure µ, a topology, which is compatible with convergence inµ-measure, is deﬁned on the real linear space of all measurable functions by using the distance introduced by
Dunford and Schwartz. Some properties of the topology, such as the open sphere condition, completeness,
the Hausdorﬀ separation axiom, separability, linearlization, and pseudo-metrizability, are related to thecharacteristics of nonadditive measures.
9 福 田 亮 治 ( 大 分 大 理 工)
本 田 あ お い ( 九 工 大 情 報 工)
岡 崎 悦 明 (ファジィシステム研)(Oita Univ.)
Ryoji Fukuda(
KyushuInst.
of Tech.)Aoi Honda
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

単調測度空間の完備化と測度代数・L0 完備性 · · · · · · · · · · · · · · · · · · · · · · 15

Completion of a monotone measure space and completeness of a measure
algebra and L0 space

概 要 Let (X, B, µ) be a monotone measure space. We discuss the µ-completion of the σ-algebra B andcompleteness of the measure algebra and the L0 topology. We consider these problems under the conditionof weak zero additivity, quasi subadditivity, and some other assumptions for the monotone measure µ. To
prove the completeness, we deﬁne power transform of a monotone measure or a pseudo metric. This concept
is very useful for our proof. Using this concept, we also prove the metrizability of these topologies.
10 山 口 哲 志 (茨 城 大 理 工)
中 井 英 一 ( 茨 城 大 理 工)

Satoshi Yamaguchi (Ibaraki Univ.)(Ibaraki Univ.)
Eiichi Nakai

Generalized fractional integral operators on Campanato spaces and theirbi-preduals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Generalized fractional integral operators on Campanato spaces and theirbi-preduals

概 要 In this talk we prove the boundedness of the generalized fractional integral operator Iρ on generalizedCampanato spaces with variable growth condition, which is a generalization and improvement of previous
results, and then, we establish the boundedness of Iρ on their bi-preduals. We also prove the boundednessof Iρ on their preduals by the duality.

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実函数論

58

Pointwise multipliers on weak Orlicz–Morrey spaces · · · · · · · · · · · · · · · · 1511 川 澄 亮 太
Ryota Kawasumi

Pointwise multipliers on weak Orlicz–Morrey spaces

概 要 In this talk we give the characterization of pointwise multipliers on weak Orlicz–Morrey spaces. To dothis we ﬁrst prove a generalized Hölder’s inequality for the weak Orlicz–Morrey spaces. Next, to characterize
the pointwise multipliers, we use the fact that all pointwise multipliers from a weak Orlicz–Morrey space
to another weak Orlicz–Morrey space are bounded operators. Weak Orlicz–Morrey spaces contain weak
Lp , weak Orlicz and generalized weak Morrey spaces. Then our results contain several previous results as
corollaries.
12 波 多 野 修 也 (中 大 理 工)
Naoya Hatano(Chuo Univ.)

Weak-type boundedness of commutators with respect to singular integral operators on Orlicz–Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Weak-type boundedness of commutators with respect to singular integral operators on Orlicz–Morrey spaces

概 要 In this paper, we give the weak-type boundedness of its commutators on Orlicz–Morrey spaces.

16:15〜17:15

特別講演
木 村 泰 紀 ( 東 邦 大 理)

完備測地距離空間上のリゾルベント作用素

Yasunori Kimura (Toho Univ.)

Resolvent operators on complete geodesic spaces

概 要 The convex minimization problem is one of the central topics in convex analysis, and many researchers

have investigated this problem in various ways. The notion of resolvent operators is an essential and powerfultool for studying this topic because it connects convex analysis to ﬁxed point theory for nonexpansive andother nonlinear mappings.
This talk focuses on the convex functions deﬁned on complete geodesic spaces with their curvature bounded
above. According to the geometric structures of the underlying space, we need to change the deﬁnition of
the resolvent operator. We ﬁrst survey the variety of known deﬁnitions and their fundamental properties.
Then, we consider minimization problems for such functions. To generate an approximating sequence
converging to a solution to this problem, we use a resolvent operator. Finally, we obtain some convergence
theorems of the generated iterative sequence.
We can extend the notion of resolvent operators for convex functions to that for bifunctions for equilibrium
problems. We will also discuss this topic and recent developments.

3 月 31 日（木）第 VIII 会場

9:30〜12:00
13 久 保 田 翔 大 (千葉大融合理工)白 川
健 ( 千 葉 大 教 育)
Shodai Kubota (Chiba Univ.)
Ken Shirakawa (Chiba Univ.)

Optimal controls in 1D-time-discrete Warren–Kobayashi–Lobkovsky–
Carter system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Optimal controls in 1D-time-discrete Warren–Kobayashi–Lobkovsky–
Carter system

概 要 We consider optimal control problems for time-discrete state problems of one-dimensional systems.

Each state problem is denoted by (S)ε , with ε ≥ 0, and is based on the non-isothermal model of grainboundary motion.In this regard, each optimal control problem is denoted by (OP) ε , with ε ≥ 0, and it isprescribed as a minimization problem of a cost function. Additionally, the problems (S) ε and (OP)ε aresupposed to admit limiting proﬁles as ε ↓ 0, and then, the limiting problems are supposed to contain no little
singularities. The main mathematical results concerned with: (A) the solvability to the problems (S) ε ; (B)the existence of the optimal control; (C) the necessary condition for the optimal control when ε > 0; (D)limiting observation as ε ↓ 0; will be reported as the main theorems of this talk.

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実函数論

14 千 代 祐 太 朗 (東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

Yutaro Chiyo (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

A simpliﬁed quasilinear attraction-repulsion chemotaxis system: boundedness · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A simpliﬁed quasilinear attraction-repulsion chemotaxis system: boundedness

概 要 This talk deals with a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system.

When there is no repulsion term, global existence and boundedness were obtained by the eﬀect of thediﬀusion term by Tao–Winkler (J. Diﬀerential Equations; 2012; 252; 692–715). The purpose of this talk is
to establish global existence and boundedness in a quasilinear attraction-repulsion chemotaxis system byusing the repulsion term instead of the diﬀusion term.
15 千 代 祐 太 朗 (東 京 理 大 理)

Yutaro Chiyo (Tokyo Univ. of Sci.)

A simpliﬁed quasilinear attraction-repulsion chemotaxis system: stabilization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A simpliﬁed quasilinear attraction-repulsion chemotaxis system: stabilization

概 要 This talk deals with stabilization in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemo-

taxis system. As to a quasilinear parabolic-parabolic Keller–Segel system, it was shown by Cieślak–Winkler(Nonlinear Anal.; 2017; 159; 129–144) that solutions converge to the mean value of the initial data. The
purpose of this talk is to conﬁrm that their method is also eﬀective for a quasilinear parabolic-elliptic-elliptic
attraction-repulsion chemotaxis system.
16 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.)

平面上の圧縮性弾性体の伸縮運動に対する初期値境界値問題の強解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence of strong solutions for the model representing motions of compressible elastic materials on the plane

概 要 We talk about existence of strong solutions to the initial and boundary value problem for beam

equations with the viscosity term. For this model, we have already shown the existence and uniqueness of
weak solutions. On our problem we suppose that the stress function has a singularity such that the value
tends to inﬁnity as the strain goes to −1. By applying this singularity, we obtain an estimate for the strain
from below, and from the estimate and the time discretization method, we can prove existence of a strong
solution. The uniqueness is guaranteed by the uniqueness of the weak solution. We would like to consider
the large time behavior of solutions as future work.
17 熊 崎 耕 太 (長 崎 大 教 育)
愛 木 豊 彦 ( 日 本 女 大 理)
A. Muntean (Karlstad Univ.)

Kota Kumazaki (Nagasaki Univ.)
Toyohiko Aiki (Japan Women’s Univ.)
Adrian Muntean (Karlstad Univ.)

非単調な境界条件を持つ気泡ゴム内の拡散物質の浸透を表すある 1 次元
自由境界問題について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A one-dimensional free boundary problem describing migration into rubber with a non-monotone boundary condition

概 要 In this talk, we consider a one-dimensional free boundary problem describing the migration of diﬀusants

into rubber. In this problem, the free boundary represents the front of the diﬀusant region and its growthrate is given by an ordinary diﬀerential equation including the eﬀect of breaking the growth of the diﬀusant
region. Due to the breaking eﬀect, it is diﬃcult to prove the existence of a solution because the boundary
condition imposed on the moving boundary becomes non-monotone. In this talk, we establish the existence
and uniqueness of a solution to the problem and give the maximum value of the free boundary.

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実函数論

18 深 尾 武 史 (京都教育大教育)

Takeshi Fukao (Kyoto Univ. of Edu.)60

境界上での擬不良設定問題について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A quasi ill-posed problem on the boundary

概 要 In this talk, we consider a quasi ill-posed problem on the boundary on some two or three dimensionalbounded domain. In order to discuss the solvability of the quasi ill-posed problem on the boundary, we
consider a transmission problem with the Cahn–Hilliard equations as an auxiliary condition in the bulk. In
a previous study, we characterize the second-order nonlinear diﬀusion equation as an asymptotic limit fromthe fourth-order Cahn–Hilliard equations. Following this idea, we apply the vanishing viscosity method to
LW model, that is, the equation and dynamic boundary condition of Cahn–Hilliard type.
19 山 崎 教 昭 (神 奈 川 大 工)葉大⋆)剣 持 信 幸 (千白 川
健 ( 千 葉 大 教 育)

Noriaki Yamazaki (Kanagawa Univ.)
Nobuyuki Kenmochi (Chiba Univ.⋆)
Ken Shirakawa (Chiba Univ.)

Singular optimal control problems for doubly nonlinear evolution inclusions with quasi-variational structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Singular optimal control problems for doubly nonlinear evolution inclusions with quasi-variational structure

概 要 In this talk we consider singular optimal control problems for abstract doubly quasi-variational

evolution inclusions governed by time-dependent subdiﬀerentials with the unknown-dependent constraints.
Then, we show the existence of optimal control for our problems. Also, we apply our abstract results toquasi-variational inequalities with time-dependent gradient constraints.
14:15〜15:15
20 来 間 俊 介 (東 京 理 大 理)

Shunsuke Kurima (Tokyo Univ. of Sci.)

A nonlocal Penrose–Fife type phase ﬁeld system with inertial term · · · 15
A nonlocal Penrose–Fife type phase ﬁeld system with inertial term

概 要 This talk deals with a nonlocal Penrose–Fife type phase ﬁeld system with inertial term. Colli–

Grasselli–Ito (2002) have proved existence of solutions to a parabolic-hyperbolic Penrose–Fife phase ﬁeld
system. However, nonlocal Penrose–Fife type phase ﬁeld systems with inertial term seem to be not studied
yet. The present work asserts that we can establish existence of solutions to a nonlocal Penrose–Fife typephase ﬁeld system with inertial term.
21 渡 邉紘 ( 大 分 大 理 工)

Hiroshi Watanabe (Oita Univ.)

放物型・双曲型単独保存則のエントロピー解に対する Oleinik 型評価とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Oleinik type estimates for entropy solutions to scalar parabolic-hyperbolic
conservation laws and their applications

概 要 We consider one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation laws.

The equation has both properties of hyperbolic equations and those of parabolic equations. Accordingly, it
is diﬃcult to investigate the regularity and the behavior of solutions to (CP). In this talk, we prove Oleinik
type estimates for entropy solutions to (CP). Moreover, we also discuss their applications.
22 赤 木 剛 朗 (東 北 大 理)
田 中 直 樹 ( 静 岡 大 理)
(Tohoku Univ.)
Goro Akagi
Naoki Tanaka (Shizuoka Univ.)

Gradient ﬂow theory for time-dependent energies and applications tononlinear PDEs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Gradient ﬂow theory for time-dependent energies and applications tononlinear PDEs

概 要 In this talk, we shall present an abstract theory for (generalized) gradient ﬂows and applications tononlinear PDEs.

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実函数論

15:30〜16:30

特別講演
吉 川 周 二 ( 大 分 大 理 工)

Shuji Yoshikawa(Oita Univ.)

炭素繊維複合材料の動的変形に関連する問題の数学解析

Mathematical analysis for the problems related to dynamic deformationof CRFP概 要 CFRP (Carbon-Fiber-Reinforced Plastics) are well-known materials that are layered plastic plates

strengthened by ﬁbered carbons like plywoods. My interest is directed to consider the dynamical behavior
of CFRP. To give a mathematical analysis for CFRP, we ﬁrst decompose the problem into four components:
thermo-elastic, plastic, anisotropic, and composite materials. Each problem has interesting open problems
from the mathematical viewpoint. I will ﬁrst introduce some results related to these problems, especiallythrough the perspective of the energy method and structure-preserving discretization technique.

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函数解析学

函

数

解

3 月 28 日（月）

析

62

学

第 I 会場

10:00〜11:30
1 佐 々 木 俊 二 ( 上 青 木 中)
Shunji Sasaki(Kamiaoki Junior High School)

リーマンゼータ関数のオマージュ —「ゼータワン関数」から「zeta-denominatorα 関数」· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Homage of Riemann zeta function “Zeta one function”

概 要 In researching the “Riemann zeta function”, we created a new function “zeta-one function” which is

obtained by adding 1 to the denominator of the function and derives the relation equation between this new
function and the “Riemann zeta function” It was also found to be represented by the “digamma function.”
It would be greatly appreciated if it could help research future zeta functions.
衛大)2 瀬 戸 道 生 (防(桑 原 修 平 札 幌 静 修 高)Michio Seto
(Nat. Defense Acad. of Japan)
Shuhei Kuwahara(Sapporoseishu High School)

狭義正定値核の構成法について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On construction of strictly positive deﬁnite kernels

概 要 In this talk, we give new examples of strictly positive deﬁnite kernels with the theory of the Hardy

space over the unit disk.
3 甘 中 一 輝 (理化学研iTHEMS) ♭ 3 次元コンパクト反ド・ジッター多様体の安定固有値の重複度 · · · · · · · · 15
Kazuki Kannaka(RIKEN)

Multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds

概 要 A pseudo-Riemannian locally symmetric space is the quotient manifold Γ\G/H of a semisimple

symmetric space G/H by a discontinuous group Γ. Toshiyuki Kobayashi initiated the study of spectral
analysis of intrinsic diﬀerential operators (such as the Laplacian) of a pseudo-Riemannian locally symmetricspace. For instance, Kassel–Kobayashi studied the behavior of eigenvalues of intrinsic diﬀerential operatorsof Γ\G/H when deforming a discontinuous group Γ. As a special case, they found inﬁnitely many stableeigenvalues of the (hyperbolic) Laplacian of a compact anti-de Sitter 3-manifold Γ\SO(2, 2)/SO(2, 1) ([Adv.
Math. 2016]). In this talk, I would like to explain recent results about multiplicities of stable eigenvalues in
the anti-de Sitter setting.
4 髙 江 洲 俊 光 ( 群 馬 大 理 工)

Toshimitsu Takaesu (Gunma Univ.)

空間・運動量切断が加わった ϕ4 モデルの 基底状態エネルギーの 1 次の摂動展開について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the ﬁrst order expansion of a ground state energy of the ϕ4 modelwith cutoﬀs

概 要 We consider the ϕ4 model with a spatial cutoﬀ and momentum cutoﬀ. The total Hamiltonian is aself-adjoint operator on a boson Fock space. Suppose regularity conditions of the momentum cutoﬀ. Then
we obtain the ﬁrst order expansion of a non-degenerate ground state energy of the total Hamiltonian.

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函数解析学

5 岩 田 順 敬 (関西大化学生命工)
Yoritaka Iwata (Kansai Univ.)作用素の対数表現を用いた非線形半群の生成 · · · · · · · · · · · · · · · · · · · · · · · 15

Generation of nolinear semigroup by the logarithm of operators

概 要 Logarithmic representation of inﬁnitesimal generators are directly associated with the higher order

evolution equations, as well as some nonlinear evolution equations. In particular nonlinear transforms
such as the Cole–Hopf transform and the Miura transform are the transform to the nonlinear diﬀerential
equations. Meanwhile the recurrence formula generalizing the Cole–Hopf transform and the Miura transform
clariﬁes the unknown relation between the 1st order and higher order evolution equations. In this talk,nonlinear abstract evolution equation in a Banach space is studied by the logarithmic representation ofoperators. In conclusion a representation for the nonlinear semigroup is obtained.
14:15〜15:15 特別講演
佐 野 め ぐ み (広島大先進理工)

Megumi Sano (Hiroshima Univ.)

調和移植とその関数不等式への応用

Harmonic transplantation and its application to functional inequalities

概 要 First, we will introduce harmonic transplantation proposed by Hersch in 1969. Also, we will explain

the diﬀerence between harmonic transplantation and Mobius transformation. We will point out that varioustransformations can be understood as a special case or a general case of harmonic transplantation. As anapplication, we will derive several improvements and several limiting forms of the Hardy and the Sobolev
inequalities via harmonic transplantation. In the half-space, we cannot apply harmonic transplantation tothese inequalities directly due to the lack of the explicit form of the p-Green function. Therefore, we willconsider a modiﬁcation of the original harmonic transplantation. By using that, we derive the improved
Hardy inequality in the half-space and the critical Hardy inequality as the limiting form.

3 月 29 日（火）10:00〜12:00
6 示 野 信 一 (関西学院大理工)
谷 口 大 和 (関西学院大理工)
中 村 麦 穂 (関西学院大理工)Nobukazu Shimeno(Kwansei Gakuin Univ.)
Yamato Taniguchi(Kwansei Gakuin Univ.)
Mugiho Nakamura(Kwansei Gakuin Univ.)

第 I 会場

実斜交群上の帯球関数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Zonal spherical function on a real symplectic group

概 要 We give explicit expressions of the zonal spherical functions on some weakly symmetric spaces that areclose to a rank one symmetric space for a real symplectic group by using the Jacobi function and elementaryfunctions.
7 井 上 順 子
(鳥取大教育支援・国際交流推進機構)
A. Baklouti ( Univ. of Sfax )Junko Inoue
Ali Baklouti(Tottori Univ.)(Univ. of Sfax)

局所コンパクト群のコンパクト拡大における Lp -Fourier 変換のノルムについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The norm of the Lp -Fourier transform on compact extensions of locallycompact groups

概 要 We study the norm of the Lp -Fourier transform on locally compact groups. Let G be a separable

unimodular locally compact group of type I, and let N be a unimodular closed normal subgroup oftype I such that G/N is compact. For all exponents p such that 1 < p ≤ 2, we show the inequality∥F p (G)∥ ≤ ∥F p (N )∥, where ∥F p (G)∥ and ∥F p (N )∥ are the norms of Lp -Fourier transforms on G and N
respectively.

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函数解析学

8 V. Pérez Valdés (東 大 数 理)

Vı́ctor Pérez Valdés (Univ. of Tokyo)

64

Construction of vector-valued diﬀerential symmetry breaking operators
for the group SO(4, 1) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Construction of vector-valued diﬀerential symmetry breaking operators
for the group SO(4, 1)

概 要 In this talk, we construct and give a complete classiﬁcation of all the symmetry breaking operators

D : C ∞ (S 3 , Vλ3 ) → C ∞ (S 2 , Lν,m ) that can be written as diﬀerential operators, between the spaces of smoothsections of a 3-rank vector bundle Vλ3 → S 3 over the 3-sphere, and a line bundle Lν,m → S 2 over the
2-sphere. In particular, we give the necessary and suﬃcient condition on the tuple of parameters (λ, ν, m)
for which these diﬀerential symmetry breaking operators exist.
9 中 濱 良 祐 (九 大 I M I )Ryosuke Nakahama (Kyushu Univ.)

Computation of weighted Bergman norms on block diagonal matrices
in bounded symmetric domains for Sp(r, R) · · · · · · · · · · · · · · · · · · · · · · · 15
Computation of weighted Bergman norms on block diagonal matrices
in bounded symmetric domains for Sp(r, R)

概 要 Let G/K ≃ D ⊂ p+ be a Hermitian symmetric space realized as a bounded symmetric domain, and we

consider the weighted Bergman space Hλ (D) on D. Then the norm on each K-type in Hλ (D) is explicitly
computed by Faraut–Korányi (1990). In this talk, we consider the case G = Sp(r, R), p+ = Sym(r, C), ﬁxr = r′ + r′′ , and decompose p+ into 2 × 2 block matrices. Then the speaker presents the results on explicit
computation of the norm of Hλ (D) on each K ′ -type in the space of polynomials on the block diagonal+
matrices p+
11 ⊕ p22 . Also, as an application, the speaker presents the results on Plancherel-type formulas on

the branching laws for the symmetric pair (Sp(r, R), U (r′ , r′′ )).
10 伊 師 英 之 (阪 市 大 理)
大 城 和 秀 ( HOSEI(株) )Hideyuki Ishi (Osaka City Univ.)
Kazuhide Oshiro (HOSEI Inc.)

ベクトル値函数の連続ウェーブレット変換 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Continuous wavelet transforms for vector-valued functions

概 要 We give a suﬃcient condition for the existence of admissible vectors for a unitary representation of

the semidirect product group of a linear Lie group with the vector group, where the unitary representation
is naturally deﬁned on the space of square-integrable vector-valued functions. Moreover, we give a concrete
admissible vector explicitly for the unitary representation of the 3-dimensional similitude group realized on
the space of square-integrable complex vector ﬁelds.
11 笹 木 集 夢 (東 海 大 理)
Atsumu Sasaki(Tokai Univ.)

A realization of the restriction of quasi-regular representations of the
Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A realization of the restriction of quasi-regular representations of the
Heisenberg group

概 要 This talk gives a realization of the restriction of quasi-regular representations of the Heisenberg group

to a certain closed subgroup in the continuous representation on the space of holomorphic functions on thecomplex Heisenberg homogeneous space. Our realization is based on the heat kernels and the heat kernel
transforms on Rk and the Heisenberg group.
12 嵐

晃 一 ( 名 大 多 元 数 理)

Koichi Arashi (Nagoya Univ.)

一般化 Heisenberg 群のコヒーレント状態表現と無重複表現 · · · · · · · · · · · 15

Coherent state representation and multiplicity-free representation of ageneralized Heisenberg group

概 要 We classify holomorphic multipliers of a generalized Heisenberg group over a (not necessarily homo-

geneous) Siegel domain of the second kind, and show that the natural representations of the group deﬁned
by the multipliers are multiplicity-free.

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65

函数解析学

13:00〜14:00
池 田

特別講演
岳 (早 大 基 幹 理 工) ♭ K 理論的シューベルト・カルキュラス

Takeshi Ikeda (Waseda Univ.)

K-theoretic Schubert calculus

概 要 During the last decade, there were signiﬁcant progress in K-theoretic (quantum) Schubert calculus.

First of all, I will try to give an overview on these works. The spaces we consider are the generalized
ﬂag varieties of semisimple linear algebraic group G. We are interested in the basis of the cohomology ringof these varieties associated to Schubert subvarieties. Main question is to determine the coeﬃcients when
we multiply two elements from the Schubert basis. Similar questions exist for a reasonable cohomology
theory. In this talk, we consider the ordinary cohomology and the algebraic K-theory, and their quantum(equivariant) versions. Even in type A, i.e. G is the special linear group, and for the ordinary cohomology,
we do not know an explicit formula for the Schubert structure constants of the full ﬂag variety. On theother hand, the structure constants for the Grassmannian variety is also (well) known as the Littlewood–
Richardson rule. I will explain the corresponding results for some typical Grassmannians in other classicaltypes.
In the second part, we will discuss a remarkable new aspects in Schubert calculus stemming from the study
on the aﬃne Grassmannian variety. The cohomology groups of the aﬃne Grassmannian has a natural ring
structure. D. Peterson discovered a connection between the quantum cohomology ring of ﬂag variety andthe homology ring of the aﬃne Grassmannian. The topics were further studied by many authors including
Lam, Shimozono, Lapointe, Morse, Schilling. I will report on recent progress on the topics mainly fromcombinatorial point of view.

3 月 30 日（水）第 I 会場

10:00〜11:30
13 瀬 尾 祐 貴 (大阪教育大教育)
Yuki Seo (Osaka Kyoiku Univ.)

一般化 Tsallis 相対エントロピー関する行列トレース不等式について · · · 15

Matrix trace inequalities related to the Tsallis relative entropies of realorder

概 要 In this talk, we show matrix trace inequalities related to Tsallis relative entropies. Hiai and Petzshow the Hiai–Petz inequality related to Umegaki relative entropy and Fujii–Kamei relative entropy and a
1-parameter extension of it. We extend it by virtue of the Tsallis relative entropies.
14 内 山充(島根大⋆・立命館大総合科学技術研究機構)
Mitsuru Uchiyama(Shimane Univ.⋆ /Ritsumeikan Univ.)

Operator means and matrix quadratic equations · · · · · · · · · · · · · · · · · · · 15
Operator means and matrix quadratic equations

概 要 Let A, B be Hermitian matrices satisfying A ≥ B ≥ 0. Then we determine X ≥ 0 and Y ≥ 0 suchthat the arithmetic mean and the geometric mean of X and Y are respectively A and B. Further, we referto a quadratic equation which these X and Y are solutions of.

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函数解析学

66

勝
(千葉大理・立命館大理工)
綿 谷 安 男 ( 九 大 数 理)

C*-環の間の非線型正写像 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Masaru Nagisa(Chiba Univ./Ritsumeikan Univ.)
Yasuo Watatani (Kyushu Univ.)

Non-linear positive maps on C*-algebras

15 渚

概 要 We study non-linear positive maps on C*-algebras, which are not necessary completely positive.

We give several examples of such non-linear positive maps. We characterize the class of compositions of*-multiplicative maps and positive linear maps as the class of non-linear maps of boundedly positive typeabstractly.
16 大 坂 博 幸 (立 命 館 大 理 工)
葉
大⋆)
渚
勝 (千
冨 田 来 成 ( 厚 木 商 高)

Hiroyuki Osaka (Ritsumeikan Univ.)
Masaru Nagisa (Chiba Univ.⋆)
Raisei Tomita(Atsugi-Commercial Senior High School)

Stable rank for inclusions of Banach algebras · · · · · · · · · · · · · · · · · · · · · · 15

Stable rank for inclusions of Banach algebras

概 要 We present a formula for the stable rank of inclusions of unital Banach algebras in the sense of ﬁnite

Watatani index. As an application we show that the stable rank of ℓ1 -algebras of Disk algebras by any
action of ﬁnite groups is 2.
17 細 川 卓 也 (茨 城 大 工)

Takuya Hosokawa (Ibaraki Univ.)

Weighted composition operators from the Lipschitz space to the spaceof bounded functions on a tree · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Weighted composition operators from the Lipschitz space to the spaceof bounded functions on a tree

概 要 We study the weighted composition operators between the Lipschitz space and the space of bounded

functions on the set of vertices of an inﬁnite tree. We characterized the boundedness, the compactness, andthe boundedness from below, the isometricity of weighted composition operators.
14:15〜15:15

特別講演

大 野 修 一Weighted composition operators and their diﬀerences

Shûichi Ohno

Weighted composition operators and their diﬀerences

概 要 (Weighted)composition operators have been extensively investigated on various analytic function

spaces, especially the Hardy and Bergman spaces, during recent decades. Then the main theme is tocharacterize the operator-theoretic behavior of weighted composition operators in terms of the functiontheoretic properties of their weight and analytic self-map. We here list problems on weighted composition
operators and their diﬀerences on the Hardy and Bergman spaces.

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67

統計数学

統 計
3 月 28 日（月）数学
第 III 会場

9:00〜11:50
1 豊 嶋 隆 晃 (東工大情報理工)

Takaaki Toyoshima (Tokyo Tech)

時空ホワイトノイズに駆動される分数階確率 Navier–Stokes 方程式 · · · · 15

Fractional stochastic Navier–Stokes equation driven by space-time whitenoise

概 要 We consider the stochastic Navier–Stokes equation driven by space-time white noise, where theLaplacian is replaced by a fractional one. In this equation, the nonlinearity has no meaning as a product ofthe distributions due to the poor regularity of the space-time white noise. To handle this type of singularstochastic partial diﬀerential equations, we use the renormalization method. In addition, the lower fractional
index reduces the order of regularity expected in the Schauder estimate, and as a result, the number of
elements to be renormalized increases. To deal with this situation, we use the theory of regularity structure
for the construction. In particular, we will solve the equation without changing the form although we need
the renormalization procedure.
2 伊 藤悠 ( 京 都 産 大 理)

Yu Ito(Kyoto Sangyo Univ.)

Backward representation of rough integral: an approach via fractional
calculus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Backward representation of rough integral: an approach via fractional
calculus

概 要 Using fractional calculus, M. Zähle (1998) introduced an approach to the Stieltjes integrals. As an

extension of the (forward) integral by Zähle (1998), Y. Hu and D. Nualart (2009) and the speaker (2019)
introduced an approach to the rough integral of controlled paths along Hölder rough paths of orderβ ∈ (1/3, 1/2]. In this talk, we extend the backward integral by Zähle (1998) to the rough integral, anddescribe a backward representation of the rough integral. Our deﬁnitions of the rough integral are given
explicitly in terms of Lebesgue integrals for fractional derivatives, without using any arguments from discrete
approximation.
3 高 野 凌 史 ( 阪 大 基 礎 工)
深 澤 正 彰 ( 阪 大 基 礎 工)
(Osaka Univ.)
Ryoji Takano
Masaaki Fukasawa (Osaka Univ.)

A partial rough path space for rough volatility · · · · · · · · · · · · · · · · · · · · · 15
A partial rough path space for rough volatility

概 要 A rough volatility model is a stochastic volatility model for an asset price process with volatility being

rough, meaning that the Holder regularity of the volatility path is less than half. Unfortunately, this model
does not fall into the framework of the existing rough path theory because the integrand is not a controlled
path of the integrator. In this talk, we will discuss about a new variant of rough path theory to analyze
such a rough volatility model. Our ﬁrst step is to construct an integration of an uncontrolled path and toprove its continuity. Second step is then to show the continuity of the solution of RDE which is driven bysuch an integral.

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統計数学

4 鵜 飼 拓 人 ( 阪 大 基 礎 工)
深 澤 正 彰 ( 阪 大 基 礎 工)
(Osaka Univ.)
Takuto Ugai
Masaaki Fukasawa (Osaka Univ.)

68

Limit distributions for the discretization error of stochastic Volterra
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Limit distributions for the discretization error of stochastic Volterra
equations概 要 Our study aims to specify the asymptotic error distribution in the discretization of a stochastic Volterra

equation with a fractional kernel. It is well-known that for a standard stochastic diﬀerential equation, the√discretization error, normalized with its rate of convergence 1/ n, converges in law to the solution of acertain linear equation. Similarly to this, we ﬁrst consider the rate of convergence to normalize the error.
Then we show that the normalized discretization error of the Volterra equation converges in law to thesolution of a certain linear Volterra equation.
5 濵 口 雄 史 ( 阪 大 基 礎 工)

Yushi Hamaguchi (Osaka Univ.)

線形な確率 Volterra 積分方程式の一般解法 · · · · · · · · · · · · · · · · · · · · · · · · · 15

On general solutions of linear stochastic Volterra integral equations

概 要 We provide a general solution to a linear stochastic Volterra integral equation, which includes a classof fractional stochastic diﬀerential equations. By means of the chaos expansion technique, we introduce a
notion of the product generalizing the stochastic convolutions and show that the class of stochastic Volterra
kernels becomes a Banach algebra. Then, we give a variation of constant formula for a general class of
linear stochastic Volterra integral equations.
6 篠 崎 裕 司 (日本銀行・東工大理)
二 宮 祥 一 ( 東 工 大 理)
Yuji Shinozaki(Bank of Japan / Tokyo Tech)
Syoiti Ninomiya (Tokyo Tech)

再結合測度法による確率微分方程式の弱近似の効率化 · · · · · · · · · · · · · · · 15

Application of high-order recombination to weak approximations of stochastic diﬀerential equations

概 要 In this presentation, the error evaluation formula for the high-order recombination method given by

Litterer–Lyons is improved and some partitioning algorithms based on this improved estimation are alsopresented. Speciﬁcally, it is proved that the error depends not only on the radiuses of the partitioned
patches but also the weights of them. The algorithms are applied to some known higher-order discretization
methods. Some numerical examples of practical ﬁnancial problems are also discussed.
7 道 工

勇 ( 埼 玉 大 教 育)

Isamu Dôku(Saitama Univ.)

レヴィ雑音を伴う確率方程式の解について · · · · · · · · · · · · · · · · · · · · · · · · · 10

On a solution for random equations with Lévy noise

概 要 We consider the random equations driven by a Lévy noise. Actually we treat the Cauchy problem

for random equations with compensated Poisson random measure. The principal operator part is describedin an abstract manner in the sense of functional analysis. Other coeﬃcient parts are given by somemeasurability and slight regularity assumptions. With an appropriate additional assumption we show thatthe random equation in question possesses a unique local mild solution.
8 小 川 重 義 ( 立 命 館 大 理 工)

Shigeyoshi Ogawa (Ritsumeikan Univ.)

Noncausal integrals and mean value theorems · · · · · · · · · · · · · · · · · · · · · · 10
Noncausal integrals and mean value theorems

概 要 The mean value theorem for the integral is well known. But we are now concerned with the validityof a statement like the mean value theorem for the stochastic integral. The aim of the talk is to showthat we can establish mean value theorems as exact formula when limitted to the noncausal stochastic
Rb
integral(also called ogawa integral) of the form a f (Xt )d∗ Wt , where Wt is Brownain motion and Xt an
RbItô process, causal or not. We also discsuss the case of Itô integral a f (Xt )d0 Wt , moreover such a genuin
noncausal case where the process Xt is noncausal. Whole discussions are developed in the framework of
the noncausal stochastic calculus. hence for the related materials and basic facts we would refer to themonograph “Noncausal Stochastic Calculus” by Ogawa,S.,(2017, Springer).

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69

統計数学

9 石 谷 謙 介 ( 都 立 大 理)

Kensuke Ishitani (Tokyo Metro. Univ.)

Brown 引越過程の構成と諸性質 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the construction of Brownian house-moving and its properties

概 要 The purpose of this presentation is to construct a new stochastic process “Brownian house-moving,”

which is a Brownian bridge that stays between its starting point and its terminal point. To construct thisprocess, statements are prepared on the weak convergence of conditioned Brownian bridge and conditioned
three-dimensional Bessel bridge. Also studied are the sample path properties of Brownian house-moving
and the decomposition formula for its distribution.
10 簗 島瞬 ( 都 立 大 理)
石 谷 謙 介 ( 都 立 大 理)

Shun Yanashima (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

Bessel 引越過程の構成と諸性質 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the construction of Bessel house-moving and its properties

概 要 The purpose of this presentation is to introduce the construction of a new stochastic process “δ-dimensional Bessel house-moving” and its properties. δ-dimensional Bessel house-moving is a δ-dimensional
Bessel process hitting a ﬁxed point at t = 1 ﬁrstly. We have two methods of the construction of this process,which are to characterize it using the ﬁrst hitting time of a Bessel process, and to obtain it as the weaklimit of conditioned Bessel bridges. We also study sample path properties of this process, and give thedecomposition formula for its distribution.
14:15〜15:05
11 黒 澤 哲 生 (都 立 大 理)
西 島 駿 介 ( 都 立 大 理)
服 部 久 美 子 ( 都 立 大 理)

Tetsuo Kurosawa (Tokyo Metro. Univ.)
Shunsuke Nishijima(Tokyo Metro. Univ.)
Kumiko Hattori (Tokyo Metro. Univ.)

ランダム枝分かれコッホ曲線上での Loop 消しランダムウォーク · · · · · · 15

Loop erased random walk on a random branched Koch curve

概 要 A loop erased random walk is a random walk obtained by removing the loop from a simple random

walk. It is a non-Markovian process that has been studied on Zd and on fractals. In this talk, we deal witha loop erased random walk under random environments. I will discuss the existence of a continuous limit
on a random branching Koch curve and the asymptotic properties of the sample function around time 0.
12 笹 谷 晃 平 (京 大 数 理 研)
Koĥei Sasaya(Kyoto Univ.)

Some relation between spectral dimension and Ahlfors regular conformal
dimension of resistance metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Some relation between spectral dimension and Ahlfors regular conformal
dimension of resistance metrics

概 要 The spectral dimension dS of a metric space is an exponent associated with the asymptotic behaviorof the heat kernel of the standard Dirichlet form and Brownian motion on the space. The Ahlfors regularconformal dimension dimAR of the metric space is a quasisymmetric invariant, where quasisymmetry is awell-studied property of homeomorphisms between metric spaces. For (generalized) Sierpiński carpets or
Sierpiński gaskets, Kigami showed that dimAR ≤ dS < 2 or dimAR ≥ dS ≥ 2 holds, in 2020. In this lecture,
we give an appropriate extension of these results to the framework of resistance forms. We also show that
another simple extension, which is to be expected, does not hold in the framework in general.

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統計数学

13 梶 野 直 孝 (京 大 数 理 研)
Naotaka Kajino (Kyoto Univ.)70

On singularity of energy measures for symmetric diﬀusions with fulloﬀ-diagonal heat kernel estimates II: Some borderline examples · · · · · · 15
On singularity of energy measures for symmetric diﬀusions with fulloﬀ-diagonal heat kernel estimates II: Some borderline examples

概 要 We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular

Sierpiński gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichletform. We prove that any fractal K in this family satisﬁes the full oﬀ-diagonal heat kernel estimates withsome space-time scale function ΨK and the singularity of the associated energy measures with respect tothe canonical volume measure (uniform distribution) on K, and also that the decay rate of r−2 ΨK (r) to 0
as r ↓ 0 can be made arbitrarily slow by suitable choices of K. These results together support [Ann. Probab.
48 (2020), no. 6, 2920–2951, Conjecture 2.15] stating that the full oﬀ-diagonal heat kernel estimates withspace-time scale function Ψ satisfying limr↓0 r−2 Ψ(r) = 0 imply the singularity of the energy measures.
15:15〜16:15

2021 年度 (第 20 回) 日本数学会解析学賞受賞特別講演
香 取 眞 理 (中 大 理 工) 多重シュラム・レヴナー発展とダイソンのブラウン運動模型

Makoto Katori(Chuo Univ.)

Multiple Schramm–Loewner evolution and Dyson’s Brownian motion
model

概 要 Schramm–Loewner evolution (SLE) is a stochastic extension of the classical Loewner theory in complex

analysis on a simply connected proper domain of C such that the driving function of the Loewner chain ofconformal maps is given by a one-dimensional stochastic process. Here we assume that the domain is theupper-half complex-plane H and the driving process runs on R. It was proved that the SLE driven by atime changed Brownian motion on R, (Bκt )t≥0 , κ > 0, determines a one-parameter family of probability
laws of a random continuous curve in H connecting 0 and ∞, and that this family, denoted by SLEκ ,κ > 0, covers all probability laws of such curves having the conformal invariance and the domain Markov
property. In probability theory and statistical physics, the SLE κ has been playing a central role in studying
critical phenomena associated with continuous phase transitions and fractal geometries in two dimensions.
Therefore, it is natural to generalize the SLE theory to describe random multiple curves in H driven by aninteracting particle system on R. The problem is that the requirement of the conformal invariance and thedomain Markov property is not suﬃcient to determine a ‘canonical’ family of multiple SLEs. Motivated by
the recent work by Sheﬃeld on the quantum gravity zipper and a series of papers by Miller and Sheﬃeld
on the imaginary geometry, we employ the coupling of Gaussian free ﬁelds (GFFs) and multiple SLEs. We
show that a multiple SLE is correctly coupled with a certain GFF if and only if the driving particle system
is given by Dyson’s Brownian motion model studied in random matrix theory. Dyson’s Brownian motion
model is also a one-parameter (β > 0) family of one-dimensional log-gases. The coupling is achieved if
and only if β = 8/κ. The present study on the GFF/multiple SLE coupling enables us to clarify the basic
properties of the constructed multiple SLE (e.g., continuity of multiple SLE curves, ‘phase transitions’ atκ = 4 and 8). Moreover, we expect that a notion of conformal invariance of SLE will enrich the study ofrandom matrix theory via the present results on the trinity of the GFF, the multiple SLE, and Dyson’s
Brownian motion model. The present talk is based on a joint work with Shinji Koshida (Aalto University).

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71

統計数学

16:30〜17:30 特別講演
大長 谷 部 高 広 (北理)Takahiro Hasebe (Hokkaido Univ.)

Loewner chains, Markov processes and non-commutative stochastic processes
Loewner chains, Markov processes and non-commutative stochastic processes

概 要 Loewner chains had been a key tool for proving the Bieberbach conjecture, which was ﬁnally settled

by de Branges in 1985. The second main application of Loewner chains was discovered in the ﬁeld of SLE
around 2000, where a randomized Loewner chain is used to describe certain scaling limits of probabilistic
models. It was realized more recently that Loewner chains also appear in connection with a certain class of
non-commutative stochastic processes, which are further in correspondent with Markov processes. In thistalk I will summarize the work on the interplay between those objects (Loewner chains, Markov processes
and non-commutative stochastic processes). The talk is based on joint works with Uwe Franz, Sebastian
Schleissinger and Ikkei Hotta.

3 月 29 日（火）9:00〜11:30
14 藤 江 克 徳 (北長 谷 部 高 広 (北

大

理)

大

理)

Katsunori Fujie (Hokkaido Univ.)
Takahiro Hasebe (Hokkaido Univ.)

第 III 会場

ユニタリ共役不変なランダム行列とその主小行列の固有値分布 · · · · · · · · 15

The spectra of principal submatrices in unitarily invariant random matrices

概 要 In this talk, we observe a concentration phenomenon on the empirical eigenvalue distribution (EED)of the principal submatrix in a random hermitian matrix whose distribution is invariant under unitaryconjugacy; for example, this class includes GUE (Gaussian Unitary Ensemble) and Wishart matrices. Moreprecisely, if the EED of the whole matrix converges to some deterministic probability measure m, then thediﬀerence of rescaled EEDs of the whole matrix and of its principal submatrix concentrates at the Rayleighmeasure (in general, a Schwartz distribution) associated with m by the Markov–Krein correspondence. For
the proof, we use the moment method with Weingarten calculus and free probability. This talk is based on
joint works with Takahiro Hasebe in Hokkaido university.
大⋆)
15 前 島信 (慶佐 久 間 紀 佳 ( 名 古 屋 市 大 理)

Makoto Maejima (Keio Univ.⋆)
Noriyoshi Sakuma (Nagoya City Univ.)

自由加法・自由自己相似過程と自由自己分解可能分布について · · · · · · · · 10

On free selfsimilar additive processes and free selfdecomposable distributions

概 要 In this talk, we shall introduce new deﬁnition of selfsimilarity in free probability theory and construct

free analogue of the theorem by Sato, which connects H-selfsimilar free additive processes and selfdecomposable distributions. In addition, we give stochastic integration with respect to free additive processes andgive a stochastic integral representation to construct back driving Lévy process for free selfdecomposable
distributions.
16 野 場啓 ( 統 計 数 理 研)
佐 久 間 紀 佳 ( 名 古 屋 市 大 理)
植 田 優 基 ( 北 教 大 旭 川)
Kei Noba (Inst. of Stat. Math.)
Noriyoshi Sakuma (Nagoya City Univ.)
Yuki Ueda (Hokkaido Univ. of Edu.)

ブール自己分解可能分布について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On Boolean selfdecomposability

概 要 In this talk, we will introduce Boolean selfdecomposable distributions. In the case of classical and freecase, there are distributional similarities. In Boolean case, they are broken. We will show it with explicit
examples.

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統計数学

17 鈴 木 良 一 (慶 大 理 工)
佐 久 間 紀 佳 ( 名 古 屋 市 大 理)
(Keio Univ.)
Ryoichi Suzuki(
Noriyoshi Sakuma Nagoya City Univ.)

72

カノニカルレヴィ過程に対する修正 Φ-ソボレフ不等式とその応用 · · · · · 10

A modiﬁed Φ-Sobolev inequality for canonical Lévy processes and its
applications

概 要 In this talk, we derive a new modiﬁed Φ-Sobolev inequality for canonical L2 -Lévy processes. This isa generalization of Φ-Sobolev inequality for the Poisson space and it for the Wiener space. Moreover, as anapplication of main theorem, we also get a concentration inequality for canonical Lévy processes and derive
several examples.
18 野 場啓 ( 統 計 数 理 研)

Kei Noba (Inst. of Stat. Math.)Lévy 過程に対する屈折–反射戦略の最適性について · · · · · · · · · · · · · · · · · 10
On the optimality of the refraction–reﬂection strategies for Lévy processes

概 要 In this talk, we think about de Finetti’s optimal dividend problem with capital injection under theassumption that the dividend strategies are absolutely continuous. In many previous studies, the process
before being controlled was assumed to be a spectrally one-sided Lévy process, however in this paper weuse a Lévy process that may have both positive and negative jumps. In the main theorem, we show that a
refraction–reﬂection strategy is an optimal strategy.
19 上 村 稔 大 (関西大システム理工)
竹 田 雅 好 (関西大システム理工)

Toshihiro Uemura (Kansai Univ.)
Masayoshi Takeda (Kansai Univ.)

特異な Lévy 密度を持つ対称 Lévy 型過程について · · · · · · · · · · · · · · · · · · 15

On symmetric stable-type processes with singular Lévy densities

概 要 We are concerned with symmetric stable-type processes with singular Lévy densities. We ﬁrst intro-

duce a class of test functions of the inﬁnitesimal generators of the symmetric Dirichlet forms associated withthe processes as a “core” and then show some estimates of the processes in the talk.
20 永 沼 伸 顕 (熊 本 大 先 端)

Nobuaki Naganuma (Kumamoto Univ.)

4 次モーメント定理の一般化について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On generalization of the fourth moment theorem

概 要 In this talk, we consider generalization of the fourth moment theorem shown by Nualart and Peccati(2005) and provide new criterion on central convergence of Wiener functionals belonging to a ﬁxed Wiener
chaos. We show the assertion by borrowing idea developed by Azmoodeh et al. (2016).
21 林
正 史 ( 琉 球 大 理)
大 城
壮 ( 琉 球 大 理 工)
竹 居 正 登 ( 横 浜 国 大 工)

Masafumi Hayashi (Univ. of Ryukyus)
So Oshiro (Univ. of Ryukyus)
Masato Takei (Yokohama Nat. Univ.)

Elephant random walk に対する中心極限定理におけるモーメント収束の速さについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Rate of moment convergence in the central limit theorem for elephantrandom walks

概 要 The one-dimensional elephant random walk is a typical model of discrete-time random walk withstep-reinforcement, and is introduced by Schütz and Trimper (2004). The walk admits a phase transition
from the diﬀusive behavior to the superdiﬀusive behavior. We study the rate of the moment convergencein the central limit theorem for the position of the walker in the diﬀusive regime.

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73

統計数学

22 高 橋 博 樹 (慶 大 理 工)
鈴 木 新 太 郎 ( 慶 大 理 工)
Hiroki Takahashi (Keio Univ.)
Shintaro Suzuki (Keio Univ.)

Almost-sure weighted equidistibution of cycles for the random Gauss
map · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Almost-sure weighted equidistibution of cycles for the random Gaussmap

概 要 We consider an i.i.d. random dynamical system generated by the Gauss map and an alternating

Gauss map with a neutral ﬁxed point. We show that cycles of this random system weighted with theirrandom Lyapunov exponents equidistribute with respect to the unique stationary measure that is absolutely
continuous with respect to the Lebesgue measure. Our main tool is a level-2 large deviations for topological
Markov shifts over countably inﬁnite alphabet.
23 イェーリッシュヨハネス
( 名 大 多 元 数 理)(
高 橋 博 樹 慶 大 理 工)

Johannes Jaerisch (Nagoya Univ.)
Hiroki Takahasi (Keio Univ.)

Multifractal analysis of homological growth rates for hyperbolic surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Multifractal analysis of homological growth rates for hyperbolic surfaces

概 要 We perform a multifractal analysis of homological growth rates of oriented geodesics on a hyperbolic

surface. Our main result provides a formula for the Hausdorﬀ dimension of level sets of prescribed growthrate in terms of a generalized Poincare exponent of the Fuchsian group. Using methods of ergodic theory
and thermodynamic formalism we prove the analyticity of the dimension spectrum.
11:30〜12:00

統計数学分科会総会

3 月 30 日（水）第 III 会場

9:50〜11:40
24 田 中 輝 雄 (広 島 市 大 情 報)

Teruo Tanaka (Hiroshima City Univ.)

分数型評価基準のマルコフ決定過程 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Markov decision processes with fractional rewards

概 要 We consider a Markov decision process with Borel state and action spaces under a discounted fractional

criterion. At ﬁrst, the fractional discounted Markov decision process is transformed to a discounted Markov
decision process by using the parametric method. Next, assuming suitable conditions on the componentsof the corresponding Markov decision process, a standard approach is used. Applying these procedures andthe dynamic programming approach, we obtain the optimal value function and policy for our problem.
25 藤 田 敏 治 (九 工 大 工)
Toshiharu Fujita(Kyushu Inst. of Tech.)

分岐・合流型推移をもつ決定過程 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Decision process model with feedforward loop system

概 要 In this study, we consider a deterministic decision process model with a feedforward loop system which

is one of the nonserial transition systems. We introduce recursive equations by using dynamic programming
technique.

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統計数学

26 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.)

74

Optimality of spanning bipartite block designs · · · · · · · · · · · · · · · · · · · · · 10

Optimality of spanning bipartite block designs

概 要 It is usually to design an experiment using treatments and its blocks in the design of experiments.

Consider a set of edges of a complete bipartite graph as a treatments set and suppose the treatments havea structure. Then, we proposed a spanning bipartite block design (SBBD) to achieve better estimation
accuracy. In this talk, using an SBBD as a statistical model, we discuss the optimality of how small
the variance of the estimator was. And we prove that the variances of all estimators are equal (variancebalanced). We also show the goodness of SBBD by the simulation.
27 門 脇聖 ( 松 江 工 高 専)島大⋆)
景 山 三 平 (広Satoru Kadowaki(Matsue Coll. of Tech.)
Sanpei Kageyama (Hiroshima Univ.⋆)

Two existence results between an aﬃne resolvable SRGD design and adiﬀerence scheme · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Two existence results between an aﬃne resolvable SRGD design and adiﬀerence scheme

概 要 The existence of aﬃne resolvable block designs has been discussed since 1942 in the literature (cf.

Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2010, 2012) obtained anumber of results on combinatorics for the existence of an aﬃne resolvable SRGD design. In this paper,a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama(2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and alsoa generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2010).
28 平 尾 将 剛 (愛知県立大情報)

Masatake Hirao (Aichi Pref. Univ.)

On p-frame potential of the Beltrán and Etayo point processes on thesphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On p-frame potential of the Beltrán and Etayo point processes on thesphere概 要 We address the expectation of the p-frame potential of two types of point processes on the sphere

introduced by Beltrán and Etayo (2018, 2019). In particular, we show that the expectation of the p-frame
potential of the process on the odd dimensional sphere has low potential among those of other well-studied
random conﬁgurations on the sphere. As a by-product, we show that the random conﬁgurations of points
coming from the process converge more rapidly towards ﬁnite unit norm tight frames than those comingfrom i.i.d. random points according to uniform measure on the sphere.
29 高 橋 勇 人 (Random Data Lab.)

Hayato Takahashi (Random Data Lab.)

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.

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75

統計数学

30 藤 澤 健 吾 (東 京 理 大 理 工)
田 畑 耕 治 ( 東 京 理 大 理 工)

Kengo Fujisawa (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)

順序カテゴリをもつ正方分割表における非対称かつ連関モデル · · · · · · · · 15

Asymmetry plus association model for square contingency tables withordinal categories

概 要 For the analysis of contingency tables, we are interested in considering a statistical model instead ofindependence when the independence between row and column variable does not hold. Many association
models which indicate the structure of odds ratios have been proposed. Also, symmetry and asymmetry
models which indicate the symmetric or asymmetric structure for cell probabilities have been proposed forthe analysis of square contingency tables. We propose an asymmetry plus association model for squarecontingency tables with ordinal categories and provide its characteristics.
12:15〜12:45

2021 年度 (第 20 回) 日本数学会解析学賞授賞式

14:25〜15:25

特別講演
廣 瀬 雅 代 (九 大 I M I )エリアレベルモデルに基づく小地域推定とその応用

Masayo Hirose (Kyushu Univ.)

Small area inference under area level model and its application

概 要 An empirical best linear unbiased predictor (EBLUP) can contribute in terms of the eﬃciency especiallywhen the sample size within each area is not large enough to make reliable direct estimates. Moreover, it isof importance to assess its mean squared prediction error in small area inference. In this conference, I will
brieﬂy introduce to small area inference under area level model and then explain some of our recent resultsfor EBLUP having further desired properties. Some data analysis results will be shown in conclusion.
15:45〜16:45

特別講演

江 村 剛 志(久留米大バイオ統計センター)

2 群間の生存時間の差の推定 —コピュラに基づく従属打ち切り問題への対処—

Takeshi Emura (Kurume Univ.)

Estimating the diﬀerence of survival distributions; a copula-based approach to dependent censoring

概 要 Traditional estimators for survival distributions can handle censored data under the independent

censoring assumption. When the assumption of independent censoring fails to hold, the traditional Kaplan–
Meier estimator is biased. Accordingly, any two-sample comparison based on two Kaplan–Meier estimators
leads to biased results, in particular, the Mann–Whitney eﬀect estimator derived from two Kaplan–Meierestimators. We derive the asymptotic bias of this naive estimator of the Mann–Whitney eﬀect under
dependent censoring. We also propose a copula-based estimator of the Mann–Whitney eﬀect, which canadjust for the bias due to dependent censoring. We derive the consistency and asymptotic normality of the
proposed estimator under a misspeciﬁed copula. Simulations are conducted to check the performance of the
proposed method. We apply our proposed method to a real dataset.

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統計数学

3 月 31 日（木）76

第 III 会場

9:50〜11:40
31 藤 森洸 ( 信 州 大 経 法)
後 藤 佑 一 ( 早 大 理 工)劉言 ( 早 大 理 工)
谷 口 正 信 ( 早 大 理 工)
Kou Fujimori (Shinshu Univ.)(Waseda Univ.)
Yuichi Goto
(Waseda Univ.)
Yan Liu
Masanobu Taniguchi (Waseda Univ.)Sparse principal component analysis for high-dimensional stationary
time series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Sparse principal component analysis for high-dimensional stationary
time series

概 要 In this talk, we discuss the sparse principal component analysis for high-dimensional stationary

processes. The standard principal component analysis performs poorly when the dimension of the process
is large. We establish the oracle inequalities for penalized principal component estimators for the processes
including heavy-tailed time series. The rate of convergence of the estimators is established. We also
elucidate the theoretical rate for choosing the tuning parameter in penalized estimators. The performanceof the sparse principal component analysis is demonstrated by numerical simulations.
( 早 大 理 工)
32 Yujie Xue
谷 口 正 信 ( 早 大 理 工)
(Waseda Univ.)
Yujie Xue
Masanobu Taniguchi (Waseda Univ.)

Hellinger distance estimation for non-regular spectra · · · · · · · · · · · · · · · 15
Hellinger distance estimation for non-regular spectra

概 要 For a Gaussian stationary process, in this talk, we will derive a time series Hellinger distance for spectra

f and g: T (f, g) =Rlog{ 21p

f (λ)/g(λ)+ 12

pg(λ)/f (λ)}dλ. By evaluating T (fθ , fθ+h ) of the form O(hα ), we

elucidate the 1/α-consistent asymptotics of the maximum likelihood estimator of θ for non-regular spectra.
For regular spectra, we introduce the minimum Hellinger distance estimator θT (ĝn ) = arg minθ T (fθ , ĝn ),where ĝn is a nonparametric spectral density estimator, and as a benchmark, we introduce the Whittle
divergence estimator θW (ĝn ). It can be shown that both θT (ĝn ) and θW (ĝn ) are asymptotically eﬃcient,and that the former is more robust than the latter. Small numerical studies will be provided.
33 シュシャオフェイ (早 大 理 工) ♭ Comparison between the exact likelihood and Whittle likelihood for(早 大 理 工) moving average processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Zhengze Li
谷 口 正 信 ( 早 大 理 工)
(Waseda Univ.)
Xiaofei Xu(Waseda Univ.)
Zhengze Li
Masanobu Taniguchi (Waseda Univ.)

Comparison between the exact likelihood and Whittle likelihood formoving average processes

概 要 In this talk, we investigate the diﬀerence between the exact likelihood and Whittle likelihood withﬁnite sample size for moving average processes of order one. We elucidate the theoretical expressions of
two likelihood functions and their expectations and evaluate the performance between exact likelihood andWhittle likelihood numerically. We ﬁnd that the exact likelihood and Whittle likelihood perform similarly
when the true value of parameter is close to zero, while the diﬀerence becomes large and Whittle estimator
performs poorly when parameter is close to one. This is an important warning when we use the Whittle
likelihood and estimator if the moving average process has near unit root.

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77

統計数学

34 劉
Yan Liu

言 ( 早 大 理 工)

(Waseda Univ.)

On the model selection of symmetric α-stable processes · · · · · · · · · · · · · 15
On the model selection of symmetric α-stable processes

概 要 In this talk, we consider the model selection problem of symmetric α-stable processes. The symmetricα-stable processes are known as a model with inﬁnite variance. This is a distinct feature from the model withﬁnite variance considered in the usual time series analysis. We consider the GAIC, an extended information
criterion of AIC, to choose the correct model. It is shown that the selected order of the model is consistent
with the true order of the model. This is a remarkable diﬀerence from the original property of AIC for aregular model with ﬁnite variance. The proof and numerical results will be shown in the presentation.
35 後 藤 佑 一 (早鈴 木 琴 音 (早(早Xiaofei Xu
谷 口 正 信 (早大 理 工)
大 理 工)

Tests for the existence of group eﬀects and interactions for two-way
models with dependent error · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

大 理 工)
大 理 工)(Waseda Univ.)
Yuichi Goto(
Kotone Suzuki Waseda Univ.)(Waseda Univ.)
Xiaofei Xu
Masanobu Taniguchi (Waseda Univ.)

Tests for the existence of group eﬀects and interactions for two-way
models with dependent error

概 要 In this talk, we propose tests for the existence of group eﬀects and interactions for two-way models

with dependent errors. Our framework allows us to deal with correlated groups, although many existing
papers assume the independence of groups. Our test statistics are in the form of the natural extension of
the classical F-statistic. We show the asymptotic null distribution of the proposed test statistic and theconsistency of the test. Moreover, the nontrivial power of our test under the alternative is derived. A
simulation study illustrates the ﬁnite-sample performance of the test. In the empirical study, we apply our
test to the daily log-returns of 24 stock prices from six countries and four sectors.
36 波 止 元 仁 (東 京 工 高 専)
Jin Hatomoto(Tokyo Nat. Coll. of Tech.)

Poisson limit distributions for diﬀeomorphisms with weak hyperbolic
product structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Poisson limit distributions for diﬀeomorphisms with weak hyperbolic
product structure

概 要 We consider a diﬀeomorphism which admits a weak hyperbolic product structure region, which is

the intersection of two transversal families of weak stable and weak unstable disks, with countably manybranches and integrable return times. We introduce that for such maps the distribution of the number ofvisits to balls converges to the Poisson distribution as the radius decays to 0.

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統計数学

大
理)
37 行 木 孝 夫 (北
大
理)
田 所
智 (北
大
医)
梶 川 駿 介 (京大医)松 橋 眞 生 (京大医)池 田 昭 夫 (京津 田 一 郎(中部大創発学術院・中部大AI数理データサイエンスセンター)

Takao Namiki (Hokkaido Univ.)
Satoru Tadokoro (Hokkaido Univ.)
Shunsuke Kajikawa (Kyoto Univ.)
Masao Matsuhashi (Kyoto Univ.)(Kyoto Univ.)
Akio Ikeda
Ichiro Tsuda(Chubu Univ. / Chubu Univ.)

78

時系列遷移グラフ解析による順列エントロピーの評価とてんかん脳波に対する応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Evaluation of permutation entropy by time-series transition graph analysis and its application to epilepsy

概 要 We proposed a method called time series transition graph for nonlinear time series analysis, which

improves the evaluation of permutation entropy. We also applied this method to ECoG recorded brain wave
data of epilepsy patients to characterize seizures in the epileptic focus.
14:20〜16:25
38 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.)

A sample measure of Mardia’s multivariate kurtosis with three-stepmonotone missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A sample measure of Mardia’s multivariate kurtosis with three-stepmonotone missing data

概 要 In this talk, we consider a sample measure of Mardia’s multivariate kurtosis with three-step monotone

missing data. In the case of complete data, Mardia (1970) has deﬁned the sample measure of multivariate
kurtosis and given its exact mean and exact variance under multivariate normal population. In this talk, wedeﬁne a new sample measure of multivariate kurtosis for three-step monotone missing data. Furthermore, we
derive its expectation and variance using perturbation method. From this result, we obtain a multivariate
normality test statistic in the case of three-step monotone missing data. Finally, some simulation results forthree-step monotone missing data are presented to investigate the accuracy of the normal approximation of
the test statistic proposed in this talk.
39 種 市 信 裕 (北 教 大 札 幌)
関 谷 祐 里 ( 北 教 大 釧 路)
外 山
淳 ( 数 学 利 用 研)
Nobuhiro Taneichi(Hokkaido Univ. of Edu.)
Yuri Sekiya (Hokkaido Univ. of Edu.)
Jun Toyama(Inst. for Pract. Appl. of Math.)

3 次元分割表における条件付き独立性検定統計量の分布の近似について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On an approximation of the distribution of test statistics for conditional
independence of 3-way contingency tables.

概 要 Tests of the hypothesis of conditional independence in J x K x L contingency tables are considered.

Class of statistics based on fai-divergence for testing the hypothesis are also considered. All members of thestatistics have the same chi-square limiting distribution under the hypothesis. We show derivation of an
expression of approximation for the distributions of the class of statistics based on an asymptotic expansion.
Using the expression, transformed statistics are obtained which converge to a chi-square limiting distribution
faster than the original ones.

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79

統計数学

40 坂 東 拓 馬 (東 大 情 報 理 工)清智 也 ( 東 大 情 報 理 工)
矢 田 和 善 (筑波大数理物質)

Takuma Bando (Univ. of Tokyo)
Tomonari Sei (Univ. of Tokyo)
Kazuyoshi Yata (Univ. of Tsukuba)

高次元における客観的総合指標の一致性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Consistency of the objective general index in high-dimensional settings

概 要 The objective general index is a scale-invariant weighting method for ranking of multivariate data.

We show that the sample objective general index is a consistent estimator of the population counterpart in
high-dimensional settings together with a set of conditions, where the ratio of the dimension to the sample
size is assumed to tend to zero. The proof is based on a recent result on random matrix theory. Numericalexperiments are conducted to support the theoretical result. An example of real data analysis suggests anapplication of the weight to variable selection.
41 前 園 宜 彦 (中 大 理 工)
S. Penev(Univ. of New South Wales)

Yoshihiko Maesono (Chuo Univ.)
Spiridon Penev(Univ. of New South Wales)

Improved conﬁdence intervals for expectiles in risk management · · · · · 15

Improved conﬁdence intervals for expectiles in risk management

概 要 In this presentation, we will study asymptotic properties of the expectile estimator. We obtain

asymptotic representations of the estimator and Edgeworth expansion of the estimator.
42 増 田 弘 毅 (九 大 数 理)
江 口 翔 一 ( 大 阪 工 大 情 報)
Hiroki Masuda (Kyushu Univ.)
Shoichi Eguchi (Osaka Inst. of Tech.)

レヴィ確率微分方程式のモデル選択規準について · · · · · · · · · · · · · · · · · · · 15

On model selection of Lévy driven SDE models

概 要 We develop information criteria for the parametric coeﬃcients of a semiparametric ergodic Lévy driven

model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasilikelihood function of the Euler-approximation type. For model selections of the scale and drift coeﬃcients,
we propose explicit Gaussian quasi-information criteria through the stepwise inference procedure.
43 小 池 祐 太 (東 大 数 理)
Yuta Koike(Univ. of Tokyo)

実現共分散行列の高次元漸近混合正規性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Asymptotic mixed normality of realized covariance in high-dimensions

概 要 The asymptotic mixed normality of the realized covariance matrix of a multi-dimensional continuous

semimartingale observed at a high-frequency is established, where the dimension may be much larger than
the sample size. More precisely, a mixed-normal approximation of the error distribution in terms of theKolmogorov distance is shown in such a setting. The proof is based on a variant of the Chernozhukov–
Chetverikov–Kato theory on high-dimensional central limit theorems for sums of independent random
vectors, where the theory is accommodated to random asymptotic covariance matrices with the help of
Malliavin calculus.

最終版: 2022/3/4
統計数学

44 中 山 優 吾 (京 大 情 報)
矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)
Yugo Nakayama (Kyoto Univ.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

80

高次元主成分スコアに基づく異常値の検出法 · · · · · · · · · · · · · · · · · · · · · · · 15

Outlier detection based on high-dimensional principal component scores

概 要 In this talk, we consider outlier detection based on the principal component analysis (PCA) for high-dimensional low-sample-size data. The classical method of outlier detection uses the Mahalanobis distance.
However, if the dimension is large, inverting the sample covariance matrix used in the Mahalanobis distance
may result in substantial numerical instability, so that the alternative is needed. On the other hand, one
example of the methods for the univariate data is the Smirnov–Grubbs test. We propose a test procedureby applying the ﬁrst PC scores to the Smirnov–Grubbs test. By using asymptotic properties of the PCA,
we evaluate its size and power. Finally, we check the performance of the test procedure both theoreticallyand numerically.

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81

応用数学

応 用
3 月 28 日（月）数学
第 V 会場

10:00〜12:00
1 盧
暁 南 ( 山 梨 大 工)
川 口 翔 大 (日本エンヂニヤ)
三 嶋 美 和 子 ( 岐 阜 大 工)

Xiao-Nan Lu (Univ. of Yamanashi)
Shota Kawaguchi(Nippon-Engineer Co. Ltd.)
Miwako Mishima (Gifu Univ.)

Almost external diﬀerence families via cyclotomy · · · · · · · · · · · · · · · · · · 15

Almost external diﬀerence families via cyclotomy

概 要 In this talk, we will introduce a new type of combinatorial designs, called almost external diﬀerence

families (AEDFs). The notion of AEDFs is a generalization of external diﬀerence families, and AEDFs also
have natural relationship with well-studied combinatorial designs such as almost diﬀerence sets, disjoint
diﬀerence families, and diﬀerence systems of sets. AEDFs can be used as a combinatorial characterization
for special types of optimal weak algebraic manipulation detection codes, which are employed as coding
schemes for linear secret sharing. Furthermore, a construction of AEDFs via cyclotomy in ﬁnite ﬁelds will
be proposed.
2 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.)

有理整数剰余環上の反転不変な誤り訂正符号 · · · · · · · · · · · · · · · · · · · · · · · 15

Reversible error-correcting codes over rational integer residue rings

概 要 Codes over the ring of rational integers modulo ideal are called integer codes. We formulate a theorem

on reversibility of the prime factorization for generator matrices of integer codes. To show that this theorem
brings an eﬀective construction of reversible integer codes of large modulus, we exhibit searching results forreversible and self-dual integer codes of various modulus at code lengths 3 and 4.
3 神 吉 知 博 ( 松 江 工 高 専)
名 倉
誠 (大阪電通大基礎理工)大 谷 信 一 (関東学院大理工)
Tomohiro Kamiyoshi(Matsue Coll. of Tech.)
Makoto Nagura(Osaka Electro-Comm. Univ.)
Shinichi Otani (Kanto Gakuin Univ.)

指数型 extended Riordan array と統一スターリング数について · · · · · · · 10

On exponential extended Riordan array and uniﬁed Stirling numbers

概 要 We propose the notion of extended Riordan array, permitted negative indices, of exponential type byusing the Roman factorial. In this context, we will establish a fundamental theory of the uniﬁed Stirlingnumbers that were introduced by Hsu and Shiue. As a consequence, we give a luminous explanation for thereciprocity law among those numbers that was discovered by Choi, et al. and Maltenfort. Moreover, ourmethods reveal that some interesting numbers appear in a certain part of the exponential extended array,
although the numbers in the area had been regarded as zero until now.

最終版: 2022/3/4
応用数学

4 弘 畑 和 秀 ( 茨 城 工 高 専)
(Univ. of Kentucky)
B. Elliott
R. J. Gould ( Emory Univ. )Kazuhide Hirohata(Ibaraki Nat. Coll. of Tech.)
Bradley Elliott (Univ. of Kentucky)
Ronald J. Gould (Emory Univ.)

82

Degree sum conditions for the existence of vertex-disjoint chorded cycles
in a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Degree sum conditions for the existence of vertex-disjoint chorded cycles
in a graph概 要 Let k be a positive integer. In 2008, Finkel proved that if G is a graph of order at least 4k and theminimum degree of G is at least 3k, then G contains k vertex-disjoint chorded cycles. Chiba et al. and
Gould et al. improved Finkel’s result. In this talk, we consider a generalization of these results.
5 安 藤

清 ( 国 立 情 報 学 研)

Kiyoshi Ando (Nat. Inst. of Informatics)

Properly 3-contractible edges in a minimally 3-connected graph · · · · · · 15
Properly 3-contractible edges in a minimally 3-connected graph

概 要 A 3-contractible edge is said to be “properly 3-contractible” if it is contained in no triangle. Let

E ∗ (G) denote the set of edges of G which are contained in no triangle and let Ec∗ (G) denote the set ofproperly 3-contractible edges of G. Let U (i) (G) denote the set of degree 3 vertices x of G such that the
subgraph of G induced by the neighborhood of x has i edges.
We prove that, “For a minimally 3-connected graph G, the following (1), (2) and (3) are equivalent. (1) G
is a wheel, (2) E ∗ (G) = ∅ and (3) U (0) (G) = U (1) (G) = ∅.” and (I) |Ec∗ (G)| ≥ 21 |U (1) (G)| + |U (0) (G)| and(II) |Ec∗ (G)| > 21 |E ∗ (G)|.” We also show the sharpness of the inequalities.
6 藤 田 慎 也
(横浜市大データサイエンス)

Shinya Fujita (Yokohama City Univ.)

辺着色グラフの rainbow connectivity に関する極値問題 · · · · · · · · · · · · · 10

Extremal problems on rainbow connectivity in edge-colored graphs

概 要 Some recent results on rainbow connectivity in edge-colored graphs will be reviewed.

7 松 本 直 己 (慶 大 D M C )Naoki Matsumoto (Keio Univ.)

Chromatic number of triangle-free and broom-free graphs in terms of
their order · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Chromatic number of triangle-free and broom-free graphs in terms of
their order

概 要 The Gyárfás–Sumner conjecture asks whether for every tree T , the class of (induced) T -free graphs isχ-bounded. The conjecture is solved for several special trees, but it is still open in general. Motivated by
the conjecture, the chromatic number of triangle-free and broom-free graphs is well studied, since a broomis one of the generalizations of a star, where a broom B(m, n) is the graph obtained from a star K1,n andan m-vertex path Pm by identifying the center of K1,n and a leaf of Pm . Gyárfás, Szemeredi and Tuza
proved that for every triangle-free and B(m, n)-free graph G, χ(G) ≤ m + n − 1. This upper bound has
been improved by Wang and Wu to m + n − 2 for m ≥ 2, n ≥ 1. In this talk, we introduce the result thatany triangle-free and B(4, 2)-free graph G is 3-colorable if the number of vertices of G is at least 17. The
sharpness of the bound of the order is attained by the Clebsch graph.

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83

応用数学

14:15〜16:00
8 松 原 和 樹 ( 埼 玉 大 教 育)奈 良 知 惠 (明 大 M I M S )Kazuki Matsubara (Saitama Univ.)(Meiji Univ.)
Chie Nara

Continuous ﬂattening of multi-layered pyramids with rigid radial edges· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Continuous ﬂattening of multi-layered pyramids with rigid radial edges

概 要 There are many ways to continuously ﬂatten polyhedra. In this talk, under the assumption that every

radial edge is rigid, we prove that a continuous ﬂattening motion exists for any multi-layered pyramid having
a common convex base, with each apex having a common perpendicular foot. Furthermore, we illustrate
an example of a multi-layered pyramid with a non-convex base that cannot be continuously ﬂattened while
maintaining the rigidity of the radial edges.
9 篠 原 雅 史 ( 滋 賀 大 教 育)
衛
大)
須 田
庄 (防
野 崎
寛 (愛知教育大教育)

Masashi Shinohara (Shiga Univ.)
Sho Suda (Nat. Defense Acad. of Japan)
Hiroshi Nozaki (Aichi Univ. of Edu.)

R8 上の最良な 2-距離集合の一意性について · · · · · · · · · · · · · · · · · · · · · · · 15

Uniqueness of optimal two-distance sets in R8

概 要 A ﬁnite subsets X in the d-dimensional Euclidean space Rd is called a two-distance set if there are

only two diﬀerent values of distances between two distinct points in X. A two-distance set X in Rd is said
to be optimal if |X ′ | ≤ |X| for any two-distance set X ′ in Rd . It is known that |X| ≤ (d + 1)(d + 2)/2 for
two-distance set X in Rd . Lisoněk construct a two-distance set L in R8 with 45 points. By the inequality,
L is optimal two-distance set in R8 . In this talk, we prove a uniqueness of optimal two-distance sets in R8
up to isomorphism.
10 久 保 田 匠 (横 浜 国 大 工)
瀬 川 悦 生 (横浜国大環境情報)

Sho Kubota (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

Perfect state transfer in Grover walks between states associated to vertices of a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Perfect state transfer in Grover walks between states associated to vertices of a graph概 要 We study perfect state transfer in Grover walks, which are typical discrete-time quantum walk models.

In particular, we focus on states associated to vertices of a graph. We call such states vertex type states.
Perfect state transfer between vertex type states can be studied via Chebyshev polynomials. We derive anecessary condition on eigenvalues of a graph for perfect state transfer between vertex type states to occur.
In addition, we perfectly determine the complete multipartite graphs whose partite sets are the same sizeon which perfect state transfer occurs between vertex type states, together with the time.

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応用数学

11 大 野 博 道 (信 州 大 工)
成 松 明 廣 ( 横 浜 国 大 工)
M. S. A. Nirjhor(東工大環境・社会理工)和 田 和 幸 ( 八 戸 工 高 専)

Hiromichi Ohno (Shinshu Univ.)
Akihiro Narimatsu(Yokohama Nat. Univ.)
Md Sams Aﬁf Nirjhor (Tokyo Tech)
Kazuyuki Wada(Nat. Inst. of Tech., Hachinohe Coll.)

84

円上の量子ウォークとスプリットステップ量子ウォークのユニタリ同値類· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Unitary equivalence classes of quantum walks on cycles and split-step
quantum walks

概 要 We investigate unitary equivalence classes of quantum walks on cycles and split-step quantum walks(SSQWs). Unitary equivalence classes of quantum walks on a cycle with N vertices are parameterized by
2N real parameters. Moreover, the ranges of two of the parameters are restricted depending on the parity
of N. SSQWs are introduced by Kitagawa and generalized by Suzuki. We deﬁne a new class of quantum
walks which includes the above SSQWs, and clarify their unitary equivalence classes.
12 黄 海 仲 星 (横 浜 国 大 理 工)

Chusei Kiumi (Yokohama Nat. Univ.)

多状態量子ウォークの固有値解析 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Eigenvalues of multi-state quantum walks

概 要 Localization is a characteristic property of multi-state quantum walks. It is well known that theexistence of eigenvalues of time evolution operator is a necessary and suﬃcient condition of the occurrence of
localization. The localization of space-homogeneous (i.e., the time evolution is consistent for every position.)
multi-state quantum walks is studied by various previous research. However, the mathematical analysisof the space-inhomogeneous case is not studied yet. Therefore, in this paper, we focus on the eigenvalue
problem on two-phase three and four-state quantum walks with one defect, which is very important forvarious applications. We use the transfer matrix to construct a generalized eigenfunction, then we derive
the necessary and suﬃcient condition for the existence of eigenvalue and its concrete solution for someexamples.
13 吉 田 建 一 (埼 玉 大 理 工)児 玉 大 樹 (東 北 大 A I M R )Ken’ichi Yoshida (Saitama Univ.)
Hiroki Kodama (Tohoku Univ.)

ネットワークによる弾塑性のモデル化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A mathematical model of network elastoplasticity

概 要 A thermoplastic elastomer (TPE) is a polymeric material with rubber elasticity and is removable athigh temperatures. In this talk, we present results of modeling the elastoplastic deformation of a TPE byusing a network represented as a periodic graph. A TPE consists of a soft domain, which exhibits rubber
elasticity, and hard domains, which act as cross-links. This structure can be represented as a graph. We
introduce the tension tensor for a periodically realized graph, which induces the stress and the elasticity.
The hard domains of a TPE are less robust than the cross-links of vulcanized rubber. We express this as
local moves of a graph, which induce the plasticity in elongation.

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85

応用数学

16:15〜17:15

特別講演
谷 口 哲 至 ( 広 島 工 大 工)

Tetsuji Taniguchi(Hiroshima Inst. of Tech.)

グラフの固有値とライングラフの一般化

A smallest eigenvalues of graphs and a generalization of line graphs

概 要 There is a previous study that uses the root system to classify graphs with smallest eigenvalue≥ −2. It

follows that such graphs are classiﬁed by the A, D, E-root systems. The A, D-integral lattice is a sublatticeof the standard lattice, but the E-integral lattice is not a sublattice of the standard lattice. However,E-integral lattice is 2-integrable. The integrability of integral lattices constructed from graphs with smallest
eigenvalue≥ λ is a subject of interest.
It is also well known that the smallest eigenvalue of a line graph is greater than or equal to −2. Thisnaturally raises the question of knowing the hierarchical structure of graphs with smallest eigenvalues, but
the (well-known) method of constructing line graphs cannot construct graphs with smallest eigenvalues< −2.
Therefore, R. Woo and A. Neumaier formulated a method for constructing graphs with smallest eigenvalue<−2 by highly generalizing the method of constructing line graphs, which is a simple task of replacing ”edges”√
by ” vertices”. They studied graphs with smallest eigenvalue≥ −1 − 2 (1995). They introduce a graphcalled a Hoﬀman graph, and give a generalization of line graphs by the sum of Hoﬀman graphs. Then comesa relation between graphs and root systems, along with an irreducibility of Hoﬀman graphs.

3 月 29 日（火）第 V 会場

10:00〜11:45
14 今 野 紀 雄 (横 浜 国 大 工)
大 島 優 季 ( 横 浜 国 大 理 工)

Norio Konno (Yokohama Nat. Univ.)
Yuki Oshima (Yokohama Nat. Univ.)

Domany–Kinzel モデルに対する IPS/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · 10
IPS/Zeta Correspondence for the Domany–Kinzel model

概 要 Our previous works presented zeta functions by the Konno–Sato theorem or the Fourier analysis for

one-particle models including random walks, correlated random walks, quantum walks, and open quantum
random walks. Moreover, we gave zeta functions for multi-particle models with probabilistic or quantum
interactions, called the interacting particle system (IPS). In this talk, we consider the zeta function for the
Domany–Kinzel model, as a special case of the IPS.
15 今 野 紀 雄 (横 浜 国 大 工)
田 村 駿 也 ( 横 浜 国 大 理 工)

Norio Konno (Yokohama Nat. Univ.)
Shunya Tamura (Yokohama Nat. Univ.)

量子ウォークと相関付ランダムウォークに対する Walk/Zeta 対応 · · · · · 10

Walk/Zeta Correspondence for quantum and correlated random walks

概 要 We compute the zeta function for the three- and four-state quantum walk, correlated random walk,and multi-state random walk on the one-dimensional torus using the Fourier analysis. We deal with also
the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we
introduce a new class of models determined by the generalized Grover matrix bridging the gap between theGrover matrix and the positive support of the Grover matrix. Finally, we give a generalized version of theKonno–Sato theorem for the new class. We calculate the zeta function for the generalized Grover matrix
on the d-dimensional torus as a result.

最終版: 2022/3/4
応用数学

16 佐 藤巖 ( 小 山 工 高 専)
今 野 紀 雄 ( 横 浜 国 大 工)
小 松
尭(産業数理研究所Calc・広島大先進理工)

Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Takashi Komatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)

86

Vertex-face/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Vertex-face/Zeta correspondence

概 要 We present the characteristic polynomial for the transition matrix of a vertex-face walk on a graph,and obtain its spectra. Furthermore, we express the characteristic polynomial for the transition matrix ofa vertex-face walk on the 2-dimensional torus by using its adjacency matrix, and obtain its spectra. As anapplication, we deﬁne a new walk-type zeta function with respect to the transition matrix of a vertex-facewalk on the 2-dimensional torus, and present its explicit formula.
17 石 川 彩 香 (横 浜 国 大 理 工)

Ayaka Ishikawa (Yokohama Nat. Univ.)

グラフゼータから定まる量子ウォークモデルの族 · · · · · · · · · · · · · · · · · · · 15

A family of quantum walks on a ﬁnite graph corresponding to the generalized weighted zeta function

概 要 We obtain a condition that associates the generalized weighted zeta function with a quantum walks

on a ﬁnite graph. The spectrum of the transition matrix of the quantum walk is given by the zeta function.
This result gives a family of quantum walks that follow from the generalized weighted zeta function.
18 森 田 英 章 (室 蘭 工 大 工)

Hideaki Morita (Muroran Inst. of Tech.)

交代経路上のグラフゼータについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On an alternating graph zeta function

概 要 We consider a zeta function deﬁned for alternating paths on a ﬁnite digraph, and provide thethree expressions; the exponential expression, the Euler expression, and the Hashimoto expression, in theframework of the combinatorial zeta function.
19 加 田修 ( 法 政 大 理 工)

Osamu Kada

(Hosei Univ.)

Characteristic polynomials and zeta functions of equitably partitioned
graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Characteristic polynomials and zeta functions of equitably partitioned
graphs概 要 It is well known that for an equitable partition of the vertex set of a directed graph (digraph) X,

the characteristic polynomial of a quotient graph divides that of X, but the remainder part is not wellinvestigated. In this paper, we deﬁne a deletion graph which is a signed directed graph deﬁned for a ﬁxed
set of deleting vertices, and give a similarity transformation exchanging the adjacency matrix A(X) whichis compatible with the equitable partition for a block triangular matrix whose diagonal blocks are theadjacency matrix of the quotient graph and the deletion graph. In fact, we show the result for more generalmatrices, and as a corollary, we show a decomposition formula of the reciprocal of the Ihara–Bartholdi zetafunction over an equitably partitioned undirected graph into the quotient graph part and the deletion graphpart.

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87

応用数学

20 齋 藤 正 顕(工学院大教育推進機構)
Seiken Saito (Kogakuin Univ.)

正則グラフにおける non-backtracking cycle の個数の誤差項の分布 · · · · 15

The distribution of the error terms of the number of non-backtracking
cycles for a regular graph

概 要 For the number Nm of non-backtracking cycles of length m in a (q + 1)-regular graph, we consider

the error term tm of Nm . The sequence tm can be expressed by the adjacency eigenvalues whose absolute√values are less than 2 q. In this study, we investigate the distribution of the data tm (m = 1, 2, ...) and give√its moment generating function. We also applied this to show that the limit distribution of tm / n (where√
n is the number of eigenvalues whose absolute value is less than 2 q) becomes a normal distribution whena sequence of growing regular graphs satisﬁes certain conditions.
11:50〜12:10

2021 年度日本数学会応用数学研究奨励賞授賞式

13:15〜14:15
21 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 · · · · · · · · · · · · · · · · · · · 10
An application of systems of Boolean polynomial equations to list color
problems

概 要 We give an application of systems of Boolean polynomial equations to list color problems to obtaina computational complexity result having the bandwidth parameter. To symmetrize the result, we also
discuss a generalization of list color problem.
22 大 野 由 美 子(横浜国大研究推進機構)
松 本 直 己 (慶 大 D M C )Yumiko Ohno (Yokohama Nat. Univ.)
Naoki Matsumoto (Keio Univ.)

キャタピラの achromatic number と pseudoachromatic number について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The achromatic number and the pseudoachromatic number of caterpillars

概 要 A pseudocomplete k-coloring of a graph is a (not necessarily proper) k-coloring such that each pairof colors appears on at least one edge. A complete k-coloring is a pseudocomplete k-coloring which is also
a proper k-coloring. The pseudoachromatic number of a graph G is the largest number k such that G has
a pseudocomplete k-coloring and the achromatic number of G is the largest number k such that G has acomplete k-coloring.
In this talk, we deal with caterpillars, where a caterpillar is a tree such that the set of vertices of degree atleast two induces a path, and we shall show that pseudoachromatic number and achromatic number are thesame for a caterpillar satisfying certain conditions.
23 永 並 健 吾 (成 蹊 大 理 工)
小 関 健 太 (横浜国大環境情報)
山 口 知 記(Seikei Univ.)
Kengo Enami(
Kenta Ozeki Yokohama Nat. Univ.)
Tomoki Yamaguchi

虹色面の現れないような平面四角形分割の頂点彩色 · · · · · · · · · · · · · · · · · 15

Proper colorings of plane quadrangulations without rainbow faces

概 要 We consider a proper coloring of a plane graph such that no face is rainbow, where a face is rainbow

if any two vertices on its boundary have distinct colors. Such a coloring is said to be proper anti-rainbow.
A plane quadrangulation G is a plane graph in which all faces are bounded by a cycle of length 4. In thispaper, we show that the number of colors in a proper anti-rainbow coloring of a plane quadrangulation G
does not exceed 3α(G)/2, where α(G) is the independence number of G. Moreover, if the minimum degreeof G is 3 or if G is 3-connected, then this bound can be improved to 5α(G)/4 or 7α(G)/6 + 1/3, respectively.
All of these bounds are tight.

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応用数学

24 中 本 敦 浩 (横浜国大環境情報)
小 関 健 太 (横浜国大環境情報)
Atsuhiro Nakamoto(Yokohama Nat. Univ.)
Kenta Ozeki (Yokohama Nat. Univ.)88

射影空間の四角形分割の染色数について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Chromatic number of quadrangulations of the projective space

概 要 Youngs proved that every quadrangulation on the 2-dimensional projective plane is 4-chromatic, if it

is non bipartite. In our talk, we deﬁne a quadrangulation of a 3-dimensional space, and consider chromatic
number of quadrangulations of the 3-dimensional projective space. We can ﬁnd a similar result on the topic,
but we can ﬁnd an essential diﬀerence between this and ours.

3 月 30 日（水）第 V 会場

9:00〜10:45
25 軸 丸 芳 揮 (九 大 I M I)
横 須 賀 洋 平 ( 鹿 児 島 大 理)

Yoshiki Jikumaru (Kyushu Univ.)
Yohei Yokosuka (Kagoshima Univ.)

吊り下げ曲面の微分幾何学的定式化について · · · · · · · · · · · · · · · · · · · · · · · 15

On the diﬀerential geometric formulation of hanging membranes

概 要 Antoni Gaudi, famous for his design of the Sagrada Familia, proposed a mechanically eﬃcient structure

obtained by a hanging chain to be upside-down. A hanging chain, often referred as catenary, is in equilibrium
only with the tension for its own weight, therefore the upside-down object is in equilibrium only with thecompression. Due to the complexity of the treatment of membranes compared to curves, previous researchof hanging membranes in the architectural ﬁeld are based on many experiments or numerical analysis.
In this talk, we give a mathematically rigorous formulation of hanging membranes from the equilibrium
equations of membranes and variational principles and show that our formulation is also eﬃcient for thenumerical analysis.
26 須 田 智 晴 (慶 大 理 工)
Tomoharu Suda

(Keio Univ.)

Equivalence of topological dynamics without well-posedness · · · · · · · · · 15
Equivalence of topological dynamics without well-posedness

概 要 The problem of topological classiﬁcation is fundamental in the study of dynamical systems. However,when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence.
In this study, we formulate a notion of “topological equivalence” using the axiomatic theory of topologicaldynamics proposed by Yorke, which we also generalize here to the action of topological groups.
27 渡 辺樹 ( 早 大 理 工)

Itsuki Watanabe (Waseda Univ.)

Deterministic limit of the stochastic model of nonlocal cross-diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Deterministic limit of the stochastic model of nonlocal cross-diﬀusion

概 要 The deterministic limit of the stochastic model of nonlocal cross-diﬀusion is considered. The stochastic

model is given by system with types of particle which the diﬀusion rate depends on the density of anotherparticle system. In this talk, we consider the deterministic limit of this model, and show the existence ofsolution to some nonlocal cross-diﬀusion equation by Markov chain approximation method.

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応用数学

28 岩 崎悟 ( 阪 大 情 報)大理)
神 保 秀 一 (北(森 田 善 久 龍谷大先端理工)
Satoru Iwasaki (Osaka Univ.)
Shuichi Jimbo (Hokkaido Univ.)
Yoshihisa Morita (Ryukoku Univ.)

2 頂点をもつ非有界なメトリックグラフ上の反応拡散方程式の単峰定常解· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Standing unimodal waves of reaction-diﬀusion equations on an unboundedgraph with two vertices

概 要 We study standing unimodal waves of reaction-diﬀusion equations on an unbounded metric graphwith two vertices. In particular, we reveal a relation between a number of standing unimodal waves anda length of the bridge. Furthermore, stability of one of the standing unimodal waves is also studied byspectral analysis of linearized operators.
29 岩 崎悟 ( 阪 大 情 報)
山 口 勇 太 郎 ( 阪 大 情 報)
Satoru Iwasaki (Osaka Univ.)
Yutaro Yamaguchi (Osaka Univ.)

メトリックグラフ上の Allen–Cahn 方程式の定常解の個数について · · · · 15

Number of stationary solutions of the Allen–Cahn equation in compact
metric graphs

概 要 In this study, we deal with the Allen–Cahn equation in compact metric graphs. Particularly, thisstudy aims to reveal numbers of all stable stationary solutions of the problem. In this talk, we explain an
idea of an algorithm counting up numbers of stable stationary solutions based on analysis about the stargraph cases.
30 國 谷 紀 良 (神戸大システム情報)
T. M. Touaoula(Univ. Aboubekr Belkaı̈d)

Toshikazu Kuniya (Kobe Univ.)
Tarik Mohammed Touaoula(Univ. Aboubekr Belkaı̈d)

ある時間遅れをもつ双安定な反応拡散方程式の大域挙動 · · · · · · · · · · · · · 15

Global dynamics of a class of bistable reaction-diﬀusion equations withtime delay

概 要 In this study, we are concerned with a class of bistable reaction-diﬀusion equations with distributed

time delay. We investigate the global attractivity of each steady state and show that there can exist thebasins of attraction of the trivial steady state and a positive steady state, which is larger than anotherunstable positive steady state. We apply our analytical results to a delayed diﬀusive blowﬂies model with
Allee eﬀect.
11:00〜12:00

特別講演
井 元 佑 介 (京 大 A S H B i )Yusuke Imoto(Kyoto Univ.)

シングルセルデータ科学への招待

Invitation to single-cell data science

概 要 Single-cell data science is a new research ﬁeld of applied mathematics in this century. Recent devel-

opments of experimental techniques like next-generation sequencing (NGS) enable us to acquire molecular
data such as RNA, protein, and epigenome in single-cell resolutions. However, the single-cell data have thefollowing characteristics: high-dimensional, low-sample size, sparsity (low detection rate), non-time series,
and lack of 3D connectivity; these properties arose new data science challenges. In this talk, we would liketo introduce the mathematical problems in single-cell data science in detail. Moreover, the latest researchof the speaker and collaborators, which is a study of noise reduction based on high-dimensional statistics,
will be explained.

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14:15〜17:00
31 長 瀬 准 平 (芝 浦 工 大 理 工)
本 田 あ お い ( 九 工 大 情 報 工)
石 渡 哲 哉
(芝浦工大システム理工)

Jumpei Nagase (Shibaura Inst. of Tech.)Aoi Honda (Kyushu Inst. of Tech.)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)

深層ニューラルネットによるショケ積分の表現 · · · · · · · · · · · · · · · · · · · · · 15

Representation of the Choquet integral by deep neural networks

概 要 The inclusion-exclusion integral is a generalized integral on non-additive measures, and the application

to neural network models has been proposed as a data analysis method because it deals with the interactionof each input. The Choquet integral, a fuzzy integral, is known as an example of inclusion-exclusion
integral. In this research, we consider the relationship between deep neural network models, which havebeen developing in wide range of ﬁelds in recent years, and Möbius-type Choquet integrals. In other words,
the calculation of Choquet integrals can be explained as one of the functions that the perceptron model canrepresent.
32 中 井 拳 吾 (東京海洋大学術)
小 林
幹 ( 立 正 大 経 済)
齊 木 吉 隆 (一橋大経営管理)堤
夏 輝 ( 一 橋 大 商)
Kengo Nakai(Tokyo Univ. of Marine Sci. and Tech.)
Miki U. Kobayashi (Rissho Univ.)
Yoshitaka Saiki (Hitotsubashi Univ.)
Natsuki Tsutsumi (Hitotsubashi Univ.)

力学系不変集合の機械学習モデルによる再現性 · · · · · · · · · · · · · · · · · · · · · 15

Reconstruction of invariant sets of dynamical systems by machine learning models

概 要 This study evaluates data-driven models obtained by machine-learning approach from a dynamicalsystem perspective, such as unstable ﬁxed points, periodic orbits and chaotic attractors. In addition, we ﬁndthat hetero-chaotic dynamics with diﬀerent unstable dimensions can be modeled by a data-driven model.
A part of this talk is based on Kobayashi, Nakai, Saiki, Tsutsumi, Phys. Rev. E 104, 044215 (2021).
33 Qiwen Sun(名大多元数理・理化学研)
三 好 建 正 ( 理 化 学 研)
S. Richard(名大多元数理・理化学研)

Qiwen Sun (Nagoya Univ./RIKEN)
Takemasa Miyoshi (RIKEN)
Serge Richard (Nagoya Univ./RIKEN)

Control simulation experiments of extreme events with the Lorenz-96
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Control simulation experiments of extreme events with the Lorenz-96
model

概 要 In this study, we investigate the controllability of a chaotic dynamical system by adding small

perturbations to generate ampliﬁed eﬀects and to prevent extreme events. The high sensitivity to initialconditions would ultimately lead to modiﬁcations of extreme events with inﬁnitesimal perturbations. Basedon this idea, we design the control simulation experiment (CSE) for the Lorenz-96 model, a widely-used toy
system in data assimilation studies. We also study the sensitivity of the control to the amplitude of theperturbation, the forecast length, and the localized perturbation. The CSE would be applicable to otherchaotic dynamical systems including realistic numerical weather prediction models.

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91

応用数学

34 山 岡 直 人 (阪 府 大 理)

Naoto Yamaoka (Osaka Pref. Univ.)

核-周辺モデルにおける離散型レプリケータ方程式の解の漸近挙動 · · · · · 15

Asymptotic behavior of solutions of discrete replicator equations withthe core-periphery model

概 要 In this talk, we consider the asymptotic behavior of solutions of the diﬀerence equation corresponding

to a replicator equation with the core-periphery model ∆h λi (tn ) = {ωi (tn ) − ω̄(tn )}λi (tn ) (i = 1, 2). We
obtain a suﬃcient condition for solutions (λ1 (tn ), λ2 (tn )) of the diﬀerence equation to tend to the equilibrium(0, 1) as n → ∞.
35 松 江常微分方程式の爆発解の複数項漸近展開 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

要

(九大 IMI・九大 I2CNER)
落 合 啓 之 (九 大 I M I )小 谷 久 寿 (東 北 大 A I M R )佐々木多希子 (武蔵野大工・東北大理)
浅 井 大 晴 ( 早 大 基 幹 理 工)
Kaname Matsue(Kyushu Univ. / Kyushu Univ.)
Hiroyuki Ochiai (Kyushu Univ.)
Hisatoshi Kodani (Tohoku Univ.)
Takiko Sasaki(Musashino Univ./Tohoku Univ.)(Waseda Univ.)
Taisei Asai

Multiple-order asymptotic expansion of blow-up solutions for ODEs

概 要 Multiple-order asymptotic expansions of blow-up solutions near blow-up for ordinary diﬀerential

equations are considered. Under a mild assumption of vector ﬁelds involving the scale invariance, wedevelop a general strategy for obtaining asymptotic expansion of blow-up solutions under the knowledge ofblow-up rates, which can be obtained through dynamics at inﬁnity. We show that, if the blow-up is type-I,
all possible terms appearing the expansion of a blow-up solution are determined by “eigenvalues” of thematrix associated with vector ﬁelds near the principal term of the blow-up and lower order terms of vectorﬁelds. The “eigenvalues” provide some algebraic aspects of blow-ups.
36 西 田 孝 明 (京大⋆)Takaaki Nishida (Kyoto Univ.⋆)

An example of heat convection in the horizontal layer with non-uniform
heat source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An example of heat convection in the horizontal layer with non-uniform
heat source

概 要 Stommel (1950) considered a model of thermal convection in horizontally long liquid layer with gravity.

He obtained approximate solutions by asymptotic expansion of the equations with respect to a dimensionless parameter and showed its picture of contour line of the stream function and isothermal line. It may beconsidered as a simplest model of thermal eﬀect to the ocean current. (cf. Sverdrup 1942). Here we show
the existence of stationary solutions under some assumptions including h << 1/l and under stress freeboundary conditions on the velocity. Also we show a picture of the isothermal line and the contour lines ofthe solution.

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応用数学

37 榊 原 航 也 (岡 山 理 大 理)
長 山 雅 晴 ( 北 大 電 子 研)
物 部 治 徳 (岡山大異分野基礎研)
Koya Sakakibara(Okayama Univ. of Sci.)
Masaharu Nagayama (Hokkaido Univ.)
Harunori Monobe (Okayama Univ.)92

変形する自己駆動系に対する界面モデルの数値計算 · · · · · · · · · · · · · · · · · 15

Numerical computation of an interface model for deformable self-propelled
systems

概 要 In this talk, we deal with an interface model for deformable self-propelled systems in which the surface

tension diﬀerence is the driving force. Numerical results will be presented as a ﬁrst step to elucidate themathematical mechanism.
38 西
慧 ( 京 都 産 大 理)
西 浦 廉 政 ( 北 大 電 子 研)

Kei Nishi (Kyoto Sangyo Univ.)
Yasumasa Nishiura (Hokkaido Univ.)

3 種反応拡散方程式でみられる進行連結パルス解の相互作用と遷移ダイナ
ミクスについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Transient behaviors of traveling multiple-pulse solutions in a threecomponent FitzHugh–Nagumo system

概 要 The dynamics of traveling multiple-pulse solutions arising in a three-component FitzHugh–Nagumo

system is considered. It is numerically found that two traveling multiple-pulses weakly attract with eachother to become one larger multiple-pulse solution, and that, by parameter variations, such multiple-pulse
solutions are destabilized via a Hopf bifurcation and split up into smaller multiple-pulse solutions. In
order to elucidate the dynamics in more detail, we derive ordinary diﬀerential equations for the interface
motions of the multiple-pulses. The reduced ODEs allow us to reveal the global bifurcation structures ofmultiple-pulse solutions, especially traveling 2-pulse and 3-pulse solutions, and clarify the mechanism forthe numerically observed behaviors from a view point of the bifurcation theory.
39 長 山 雅 晴 (北 大 電 子 研) ♭ 2 つの自己駆動体運動を記述する反応拡散-粒子モデルに対する数値分岐大理) 解析について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
安 ヶ 平 裕 介 (北Masaharu Nagayama (Hokkaido Univ.)
Yusuke Yasugahira (Hokkaido Univ.)

On a numerical bifurcation analysis of a particle reaction-diﬀusion model
for a motion of two self-propelled disks

概 要 Theoretical analysis using mathematical models is often used to understand a mechanism of collective

motion in a self-propelled system. In the experimental system using camphor disks, several kinds ofcharacteristic motions have been observed due to the interaction of two camphor disks. In this paper, weunderstand the emergence mechanism of the motions caused by the interaction of two self-propelled material
by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematicalmodel. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, ischaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due totorus bifurcation.

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応用数学

3 月 31 日（木）第 V 会場

9:00〜10:45
40 坂 口 文 則 (福 井 大 工)Fuminori Sakaguchi (Univ. of Fukui)「不良設定」の逆利用 —微分方程式の整数型解法における多倍長の恵み—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A reverse application of ‘ill-posedness’ —an advantage of multiple precision in a integer-type algorithm for solving ODEs—

概 要 Usually, in numerical analysis, ‘ill-posedness’ and ‘ill-conditionedness’ are unwelcome. However, theyaﬀect nothing, in the algorithms based only on four arithmetical operation among integers without round-oﬀ
errors. There, their ‘reverse applications’ for simplifying algorithms and reducing computational quantities
may be possible. An integer-type algorithm for solving higher-order linear ODEs, proposed by the authorand M. Hayashi about ten years ago, turned out to have been a kind of such a ‘reverse application of
ill-posedness’, in the sense that it utilizes simple integer operations among integer basis vectors which are
numerically almost linearly dependent (almost parallel). In this study, we investigate to what extent theadvantage of its ‘reverse application’ is enlarged by the use of multiple-precision integer operations. The
results are successful in reducing computational quantities considerably.
41 土 屋 拓 也 (八 戸 工 大)
浦 川 遼 介米 田
元 ( 早 大 理 工)
Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Ryosuke Urakawa(Waseda Univ.)
Gen Yoneda

質量保存を考慮した重力崩壊する時空における Einstein 方程式の数値計算· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Numerical integration of Einstein equations in gravitational collapse
spacetime considering mass conservation

概 要 We perform numerical simulations of the Einstein equations in the gravitational collapse spacetime.

We set the mass density in spherical symmetry as the initial condition, and integrate the Einstein equations
and the conservation equations of energy momentum tensor. We reported the simulations with the Crank–
Nicolson scheme and the centered space discretization at the MSJ Spring Meeting 2021. Then, the resultsof the mass density were the partially negative. Therefore, we improve the discretization by using theforth-order Runge–Kutta scheme and the upwind scheme. In addition, we will present some hi-precision
numerical simulations by the dynamical equations with the constraint terms.
42 本 多 泰 理 (東洋大情報連携)
Hirotada Honda (Toyo Univ.)

Revisiting the stability of GAN · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Revisiting the stability of GAN

概 要 In this article, we discuss the stability of min-max GAN originally proposed by Goodfellow et al. We

will make use of the theory of iterated function system.
43 内 海 晋 弥 (学 習 院 大 理)

Shinya Uchiumi (Gakushuin Univ.)

Guermond–Minev 型射影 Lagrange–Galerkin スキームの Oseen 問題に対する圧力誤差評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A pressure error estimate for a projection Lagrange–Galerkin scheme of
Guermond–Minev type for the Oseen problem

概 要 We consider a ﬁnite element scheme for the transient Oseen problem, which is a linearization of theNavier–Stokes (NS) problem. We focus on two numerical methods. One is the Lagrange–Galerkin (LG)method, which combines the method of the characteristics and Galerkin method. We also focus on the
projection method. The main advantage is the computational eﬃciency that decouples the velocity andpressure. Guermond and Minev have developed an LG/projection scheme for the NS problem, and derived
an error estimate for the velocity. The estimate for the pressure, however, is not known to the best of theauthor’s knowledge. Here, we derive an error estimate for the pressure in the Oseen problem.

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94

44 渡 部 善 隆(九大情報基盤研究開発センター)
長藤かおり(Karlsruhe Inst. of Tech.)
M. Plum(Karlsruhe Inst. of Tech.)
木 下 武 彦 ( 佐 賀 大 理 工)
中 尾 充 宏 ( 早 大 理 工)

Orr–Sommerfeld 方程式の臨界 Reynolds 数に対する計算機援用証明 · · · 15

Yoshitaka Watanabe (Kyushu Univ.)
Kaori Nagatou(Karlsruhe Inst. of Tech.)Michael Plum (Karlsruhe Inst. of Tech.)
Takehiko Kinoshita (Saga Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

A computer-assisted proof of critical Reynolds number for Orr–Sommerfeld
equation

概 要 This talk presents a computer-assisted proofs of the critical Reynolds number for the Orr–Sommerfeld

equation describing the hydrodynamic stability of Poiseuille ﬂow. Using spectral Galerkin approximate
solutions bounding its small defect and a ﬁxed-point theorem, an enclosure of a strong candidate of thecritical Reynolds number is shown.
45 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)
大理)
安 ヶ 平 祐 介 (北Makoto Okumura (Hokkaido Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Masaharu Nagayama (Hokkaido Univ.)
Hironobu Fujiwara (RIKEN)
Yasugahira Yusuke (Hokkaido Univ.)

基底膜大変形モデルによる毛包形成メカニズムの数理的考察 · · · · · · · · · · 15

A mathematical study of the mechanism of hair follicle formation using
a mathematical model for large deformation of basement membrane

概 要 The skin is the boundary between the body and the outside world. All living things, including

humans, interact with the outside world through the skin. The skin is composed of epidermis, dermis, andsubcutaneous tissue. Besides, as an appendage of the skin, a hair follicle is the source of the hair. The hairfollicle is crucial for maintaining the epidermis and hair tissue homeostasis and for repairing damaged tissue.
In this study, we have attempted to examine the mechanism of hair follicle formation from a mathematicalpoint of view by applying a mathematical model, which enables the description of the concave deformationof the basement membrane. In this talk, we show the results obtained from this attempt.
11:00〜12:00

特別講演
飯 田 渓 太 ( 阪 大 蛋 白 質 研)

Keita Iida

(Osaka Univ.)

遺伝子発現の 1 細胞データ解析

Single-cell gene expression data analysis

概 要 Gene expression is a biochemical process producing RNA and proteins that can regulates cellular

processes such as homeostasis, adaptation, and diﬀerentiation, however its dysregulation can induce cell
death or cancer formation. In recent years, experimental technologies to quantify gene expression such as
ﬂuorescence in situ hybridization and single-cell RNA sequencing have been developed and some of thesedata are available publicly. Furthermore, mathematical and bioinformatics studies oﬀer techniques to model
stochastic gene expressions, quantify biochemical parameters, and infer cell states. Here, we introduce ourmodel- and data-driven approaches to analyze such single-cell data to understand gene expression regulations
leading to cellular diﬀerentiation and dysregulation.

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95

トポロジー

ト ポ

ロ

3 月 28 日（月）ジー

第 VII 会場

9:30〜12:00
1 狩 野 隼 輔 (東北大RACMaS)
石 橋
典 ( 京 大 数 理 研)

Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Kyoto Univ.)

A characterization of pseudo-Anosov mapping classes by tropical clustertransformations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A characterization of pseudo-Anosov mapping classes by tropical clustertransformations

概 要 For a mapping class on a punctured surface, we prove that the kind of pseudo-Anosov property isequivalent to the combinatorial property of mutation loops. In particular, we conclude that the algebraic
entropies of the cluster A- and X-transformations induced by the mutation loop given by a pseudo-Anosov
mapping class both coincide with its topological entropy.
2 バラルリホラモン(立命館大総合科学技術研究機構)
J. A. Álvarez López(Univ. of Santiago de Compostela)Ramón Barral Lijó (Ritsumeikan Univ.)
Jesús Antonio Álvarez López(Univ. of Santiago de Compostela)

Realization of manifolds as leaves of foliated spaces · · · · · · · · · · · · · · · · · 15

Realization of manifolds as leaves of foliated spaces

概 要 We will present our results about the geometric realization of Riemannian manifolds as leaves ofcompact foliated spaces with a leafwise Riemannian metric.
3 児 玉 大 樹
(東北大AIMR・理化学研iTHEMS)大理)粕 谷 直 彦 (北
(
中
大
理
工)
三 松 佳 彦森淳 秀 ( 大 阪 歯 大 歯)
Hiroki Kodama(Tohoku Univ. / RIKEN)
Naohiko Kasuya (Hokkaido Univ.)
Yoshihiko Mitsumatsu (Chuo Univ.)
Atsuhide Mori (Osaka Dent. Univ.)

ある複素曲面特異点の Milnor 束から見出された S 5 から S 3 へのトーラ
スファイブレーション · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Torus ﬁbrations from S 5 to S 3 found from Milnor ﬁbrations of certain
complex surface singularities

概 要 We explain Tpqr cusp singularities and Milnor ﬁbers Fθ of them. We construct a complex map g on a

Milnor ﬁber Fθ so that it has p + q + r critical points and the inverse images of regular values are tori T 2 .
We also construct a deformation of the Milnor ﬁber so that all critical points become Lefschetz type.

最終版: 2022/3/4
トポロジー

4 三 松 佳 彦 ( 中 大 理 工)大理)粕 谷 直 彦 (北児 玉 大 樹(東北大AIMR・理化学研iTHEMS)森淳 秀 ( 大 阪 歯 大 歯)

Yoshihiko Mitsumatsu (Chuo Univ.)
Naohiko Kasuya (Hokkaido Univ.)
Hiroki Kodama(Tohoku Univ. / RIKEN)
Atsuhide Mori (Osaka Dent. Univ.)

96

カスプ特異点のミルナーファイバーのレフシェッツファイブレーションと K3 曲面の位相分解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Lefschetz ﬁbration on Milnor ﬁbers of cusp singularities and topologicaldecomposition of K3 surfaces

概 要 We explain that the K3 surface admits a smooth topological decomposition into the two Milnor ﬁbers

of Tpqr cusp singularities which are dual in the sense of the extended strange duality. Among such 10
decompositions, the pair T237 -T237 gives a particularly good decomposition.
5 平 田 康 史 ( 神 奈 川 大 工)
矢 島 幸 信(神奈川大⋆・数学アートラボ)

Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima(Kanagawa Univ.⋆ /Math Art Laboratory)

Undecidability for the extent of products of monotonically normal spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Undecidability for the extent of products of monotonically normal spaces

概 要 We say that a space is almost discrete if it has at most one non-isolated point. In this talk, we

discuss the extent of product spaces. We show: it is consistent with and independent of ZFC that there
are a monotonically normal space X and an almost discrete space Y such that X × Y is normal ande(X × Y ) > ω = e(X) · e(Y ).
6 西 信 洋 和 ( 長 野 工 高 専)
山 口 俊 博 ( 高 知 大 教 育)

有理 H(2)-構造を持つ coformal でない分類空間の例 · · · · · · · · · · · · · · · · · 10

Hirokazu Nishinobu(Nagano Nat. Coll. of Tech.)Toshihiro Yamaguchi (Kochi Univ.)

An example of non-coformal classifying space with rational H(2)-structure

概 要 Let Baut1 X be the Dold–Lashof classifying spaces of a space X. In this talk, we give an example

that there exists a space X such that Baut1 X are not coformal and are rational H(2)-spaces.
7 山 﨑 薫 里 ( 高 崎 経 大 経 済)
Kaori Yamazaki(Takasaki City Univ. of Econ.)

Exchange economy from viewpoints of general topology · · · · · · · · · · · · · 15
Exchange economy from viewpoints of general topology

概 要 In this talk, we study exchange economy from viewpoints of general topology.

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トポロジー

8 齋 藤 幸 子 ( 北 教 大 旭 川)
高 清 水 公 星 (釧路市立青陵中)

Sachiko Saito (Hokkaido Univ. of Edu.)
Kosei Takashimizu(Seiryo Junior High School)

混合擬斉次多項式の Newton 非退化性および強義 Newton 非退化性 · · · · 10

Newton non-degeneracy and strongly Newton non-degeneracy of mixed
weighted homogeneous polynomials

概 要 A mixed polynomial f is called a mixed weighted homogeneous polynomial if it is both radially andpolar weighted homogeneous. Let f be a mixed weighted homogeneous polynomial with respect to a strictly
positive radial weight vector P and a polar weight vector Q. If f is Newton non-degenerate over the face∆(P ) and f is polar weighted homogeneous of non-zero polar degree with respect to Q, then f : C∗ n → C
has no mixed critical points. Moreover, if f −1 (0) ∩ C∗ n ̸= ∅, then f : C∗ n → C is surjective. In this talk,we give such an example of a mixed weighted homogeneous polynomial f which is Newton non-degenerateover the face ∆(P ) and for which f −1 (0) ∩ C∗ n = ∅.
9 溝 田 裕 介 ( 九 州 産 大 理 工)
一 木 俊 助 (東工大情報理工)
濱 田 直 希 ( KLab(株) )Yusuke Mizota (Kyushu Sangyo Univ.)
Shunsuke Ichiki (Tokyo Tech)(KLab Inc.)
Naoki Hamada

制約なし強凸問題は全て弱単体的である · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

All unconstrained strongly convex problems are weakly simplicial

概 要 A multi-objective optimization problem is C 0 weakly simplicial if there exists a continuous surjection

from a simplex onto the Pareto set such that the image of each subsimplex is the Pareto set of a subproblem.
In this talk, we show that all unconstrained strongly convex problems are C 0 weakly simplicial. (Joint workwith Naoki Hamada and Shunsuke Ichiki)
14:15〜15:05
10 市 原 一 裕 (日 大 文 理)鄭
仁 大 ( 近 畿 大 理 工)

Kazuhiro Ichihara (Nihon Univ.)(Kinki Univ.)
In Dae Jong

交代モンテシノス結び目に沿った純矯飾的手術 · · · · · · · · · · · · · · · · · · · · · 10

Purely cosmetic surgeries on alternating Montesinos knots

概 要 We show that alternating Montesinos knots admit no purely cosmetic surgeries. Precisely, it isshown that no pair of distinct Dehn surgeries on alternating Montesinos knots yield 3-manifolds that are
homeomorphic as oriented manifolds.
11 小 川 将 輝 (埼 玉 大 理 工)

Masaki Ogawa (Saitama Univ.)

多重分岐ハンドル体分解を持つ 3 次元多様体の特徴づけについて · · · · · · 15

A characterization of a 3-manifold with a multibranched handlebody
decompsition

概 要 A decomposition of a 3-manifold by some handlebodies is called a handlebody decomposition. Theintersection of handlebodies in handlebody decomposition is called a partition of it. We say handlebody
decomposition is multibranched if the partition of a handlebody decomposition is a multibrahced surface.
Recently we showed that multibranched handlebody decomposition is stable equivalent if the number ofhandlebodies is four. In this talk, we consider the 3-manifolds which have a multibranched handlebody
decomposition with four handlebodies with genera at most one.

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トポロジー

12 北 野 晃 朗 (創 価 大 理 工)
野 崎 雄 太 (広島大先進理工)
Teruaki Kitano (Soka Univ.)
Yuta Nozaki (Hiroshima Univ.)

98

Reidemeister torsion の代数的整数性について · · · · · · · · · · · · · · · · · · · · · · 10
Algebraic integrality of Reidemeister torsion

概 要 For a 3-manifold M and an acyclic SL(2, C)-representation ρ of its fundamental group, the Reidemeister

torsion τρ (M ) ∈ C is deﬁned. If there are ﬁnitely many conjugacy classes of irreducible representations,then the Reidemeister torsions are known to be algebraic numbers. In this talk we report that any value ofthem is an algebraic integer for a Seifert ﬁbered space under mild conditions, even though there are iniﬁnite
conjugacy classes.
15:20〜16:20

特別講演
古 宇 田 悠 哉 (広島大先進理工)

Heegaard 分解の写像類群

Yuya Koda (Hiroshima Univ.)

Mapping class groups of Heegaard splittings

概 要 The mapping class group, or the Goeritz group, of a Heegaard splitting for a closed orientable 3-

manifold is deﬁned to be the subgroup of the mapping class group of the Heegaard surface consisting ofmapping classes that extend to both of the handlebodies of the splitting. Simple problems on the structureof this group such as ﬁniteness, ﬁnite generation, ﬁnite presentability of the group are already highly
non-trivial and still open in general. In this talk, we give a short historical overview of these problems andintroduce its recent progress together with some applications.

3 月 29 日（火）第 VII 会場

9:30〜11:50
13 森
祥 仁 ( 東 北 大 理)
村 上 友 哉 ( 東 北 大 理)
Akihito Mori (Tohoku Univ.)
Yuya Murakami (Tohoku Univ.)

Plumbed 多様体に対する Witten–Reshetikhin–Turaev 不変量 · · · · · · · · 15
The Witten–Reshetikhin–Turaev invariant for plumbed manifolds

概 要 Gukov–Pei–Putrov–Vafa constructed q-series invariants called homological blocks in a physical way

in order to categorify Witten–Reshetikhin–Turaev (WRT) invariants and conjectured that radial limits ofhomological blocks are WRT invariants. In this talk, we prove their conjecture for unimodular H-graphs.
As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth
two and of weight one with the quantum set Q. In the course of the proof of our main theorem, we ﬁrst
wrie the invariants as ﬁnite sums of rational functions. We second carry out a systematic study of weighted
Gauss sums in order to give new vanishing results for them. Combining these results, we ﬁnally prove thatthe above conjecture holds for H-graphs.
14 谷 口 雄 大 (阪大理)Yuta Taniguchi (Osaka Univ.)

f -ねじれアレキサンダー行列から得られる結び目の不変量について · · · · 15
A knot invariant obtained from an f -twisted Alexander matrix

概 要 Recently, A. Ishii and K. Oshiro introduced a new notion, which is called an f -twisted Alexander

matrix. An f -twisted Alexander matrix is a quandle version of an Alexander matrix of knot groups. In
this talk, we show that a certain knot invariant obtained from a f -twisted Alexander matrix is a stronger
knot invariant than the Alexander invariant.

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99

トポロジー

15 高 野 暁 弘 (東 大 数 理)

Akihiro Takano (Univ. of Tokyo)

The Long–Moody construction and twisted Alexander invariants · · · · · 15
The Long–Moody construction and twisted Alexander invariants

概 要 The Long–Moody construction is a method of constructing a new representation of the braid groupfrom a representation of the semidirect product of the braid group and the free group. In this talk, we showthat its matrix presentation is described by the Fox derivation, and also a relation with twisted Alexander
invariants.
16 原 子 秀 一 (東 大 数 理)

Shuichi Harako (Univ. of Tokyo)

Computational results for the symplectic derivation Lie algebras · · · · · 15
Computational results for the symplectic derivation Lie algebras

概 要 The Lie algebras consisting of symplectic derivations on certain algebras are called the symplectic

derivation Lie algebras. We determined the second homology group of the certain Lie ideal of “thecommutative world” of the symplectic Lie algebras in terms of symplectic modules.
17 水 澤 篤 彦 (早 大 非 常 勤)
小 鳥 居 祐 香 (広島大理・理化学研)

Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii(Hiroshima Univ. / RIKEN)Clasper を用いた 5 成分 link-homotopy 類の分類 · · · · · · · · · · · · · · · · · · · 15
A classiﬁcation of 5-component link-homotopy classes through the clasper
theory概 要 The link-homotopy classes of links are obtained from the link-homotopy classes of string links modulo

the partial conjugations. Yasuhara and Meilhan gave a standard form of the link-homotopy classes ofstring links by using the claspers. In this talk, we calculate the actions of the partial conjugations for the
5-component link-homotopy classes of string links by using the clasper theory and give a new presentationof the link-homotopy classes of 5-component links.
18 野 坂 武 史 (東 工 大 理)

Takefumi Nosaka (Tokyo Tech)

ポアンカレ双対群の Fox ペアリング · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Fox pairings of Poincaré duality groups

概 要 We develop the study of Fox pairings of a group G from viewpoints of group cohomology. We compute

some cohomology groups of Fox pairings of G, where G admits a Poincaré duality group pair. We alsosuggest fundamental Fox pairings and higher Fox pairings.
19 米 村 拳 太 郎 (九 大 数 理)

Kentaro Yonemura (Kyushu Univ.)

一葉双曲面上のカンドルと longitudinal map · · · · · · · · · · · · · · · · · · · · · · · 15

Quandles over a one-sheet hyperboloid and longitudinal map

概 要 We deﬁne quandles over a one-sheet hyperboloid and compute longitudinal map, which is a knot

invariant deﬁned by Clark–Saito in 2019.
20 石 橋湯 淺

典 ( 京 大 数 理 研)
亘 ( 京 大 数 理 研)

Tsukasa Ishibashi (Kyoto Univ.)
Wataru Yuasa (Kyoto Univ.)Stated and marked skein algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stated and marked skein algebras

概 要 For a marked surface Σ and a Lie algebra g = sl2 , sl3 or sp4 , we construct an explicit isomorphism

between the reduced stated g-skein algebra and the boundary-localization of the (“Muller type”) marked
g-skein algebra.

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トポロジー

12:15〜12:25

1002021 年度日本数学会幾何学賞授賞式

13:15〜14:15

特別講演
野 坂 武 史 ( 東 工 大 理)

Takefumi Nosaka (Tokyo Tech)

べき零的結び目不変量と写像類群のジョンソン準同型

Nilpotent knot-invariants and Johnson homomorphisms of the mappingclass group

概 要 While there are many studies of knots in the 3-sphere, this study suggests a knot theory from theviewpoints of (nilpotently) rational homotopy theory or Johnson homomorphisms. More precisely, I deﬁned
a nilpotent monodoromy from a knot, which should be regarded as an element of an outer automorphismgroup. Fortunately, the outer automorphism group has been studied in terms from Johnson homomorphisms
and the mapping class groups, with a relation to Goldman Lie algebras. In this talk, I explain the deﬁnitionof the monodoromy, and an interaction between knot theory and studies of the mapping class group; I also
take about some approaches to the outer automorphism group in order to give some computations of themonodoromies.

3 月 30 日（水）第 VII 会場

9:30〜12:00
21 久 野 恵 理 香 (阪Erika Kuno

大理)

(Osaka Univ.)

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 nonorientablesurfaces

概 要 Let N be a connected nonorientable surface with or without boundary components and punctures.

We prove that the graph of nonseparating curves of N is connected and Gromov hyperbolic with a constantwhich does not depend on the topological type of surface by using the bicorn curves introduced by Przytycki
and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs ofnonseparating curves for orientable ﬁnite type surfaces.
22 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 ≥ 3 is also uniformly hyperbolic.
23 秋 吉 宏 尚 (阪 市 大 理)

Hirotaka Akiyoshi (Osaka City Univ.)

錐特異点つきトーラス束のディリクレ領域について · · · · · · · · · · · · · · · · · 10

Dirichlet domains for some one-cone torus bundles

概 要 Two families of one-cone torus bundles parametrized by cone angles are studied. When the cone angles

are suﬃciently small, the combinatorial structures of the Dirichlet domains with respect to the basepoints
in the singular locus are characterized.

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101

トポロジー

24 木 村 直 記 (早 大 理 工)
Naoki Kimura (Waseda Univ.)

ルジャンドル結び目の双ルジャンドルラック彩色数 · · · · · · · · · · · · · · · · · 10

Bi-Legendrian rack coloring numbers of Legendrian knots

概 要 Kulkarni and Prathamesh introduced an invariant of Legendrian knots by using rack colorings.

Ceniceros, Elhamdadi and Nelson deﬁned a Legendrian rack and generalized the invariant. In this talk,we deﬁne a bi-Legendrian rack and consider a further generalization of the invariant. We show that biLegendrian rack coloring numbers can distinguish all Legendrian unknots with the same Thurston–Bennequinnumber. We also consider pairs of Legendrian knots which cannot be distinguished by bi-Legendrian rackcoloring numbers.
25 安 田 順 平 (阪大理)Jumpei Yasuda (Osaka Univ.)

A plat form presentation for surface-links · · · · · · · · · · · · · · · · · · · · · · · · · 15
A plat form presentation for surface-links

概 要 It is known that every orientable surface-link can be described as a closed 2-dimensional braid. In

this talk, we introduce a new method of describing a surface-link using a braided surface, which we call aplat form. We prove that every surface-link, which is not necessarily orientable, can be described in a platform. We show how to obtain the surface-link group from the braided surface group by adding some simple
relations.
26 大 場 貴 裕 (阪Takahiro Oba

大理)(Osaka Univ.)

4 次元 Dehn ツイストの間の関係式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A four-dimensional mapping class relation

概 要 Relations between Dehn twists on mapping class groups of surfaces play an important role in the studyof symplectic manifolds via Lefschetz ﬁbrations. In higher dimensions, as little is known about symplectic
mapping class groups, ﬁbration-like structures are not so powerful yet. In this talk, I will give a relation
between 4-dimensional Dehn twists on a Weinstein domain. One of the key ingredients in the construction
2

is a solution to the symplectic isotopy problem for symplectic surfaces in CP2 #3CP .
27 鈴 木 龍 正 (東 工 大 理)
丹 下 基 生 (筑波大数理物質)

Tatsumasa Suzuki (Tokyo Tech)
Motoo Tange (Univ. of Tsukuba)

Pochette surgery on S 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Pochette surgery on S 4

概 要 The boundary sum of the product of a circle with a 3-ball and the product of a disk with a 2-sphere iscalled a pochette. For a pochette P embedded in a 4-manifold M , a pochette surgery on M is the operationof removing the interior of P and gluing in P by a diﬀeomorphism of the boundary of P . In this talk, wegive a necessary condition for the operation of surgery on the 4-sphere to generate a homotopy 4-sphere ina more precise manner. Furthermore, we show that any pochette surgery using the trivial 2-knot, whichbecomes a homotopy 4-sphere, is diﬀeomorphic to the 4-sphere.
28 菅 原 朔 見 (北大理)Sakumi Sugawara (Hokkaido Univ.)

Link diagrams of divides with cusps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Link diagrams of divides with cusps

概 要 A divide with cusps is the image of a generic, relative immersion allowing ﬁnite cusps of intervals andcurves into the unit disk. A divide with cusps is the generalization of the notion of the divide which is
introduced by A’Campo. We can associate the link L(P )in S 3 to a divide P . There are several ways todraw the diagram of the link L(P ) from a divide P . In this talk we introduce the algorithm to draw thediagram of the link L(P ) of a divide with cusps P , which is the application of Couture–Perron’s method.

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トポロジー

29 田 嶌優 (北吉 永 正 彦 (北

大

理)

大

理)

Yu Tajima (Hokkaido Univ.)
Masahiko Yoshinaga (Hokkaido Univ.)

102

グラフのマグニチュードホモロジーと Asao–Izumihara 複体における離散モース理論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Magnitude homology of graphs and discrete Morse theory on Asao–
Izumihara complexes

概 要 Magnitude is an invariant for metric spaces introduced by Leinster, which measures the number

of eﬃcient points. As a categoriﬁcation of the magnitude, Hepworth and Willerton deﬁned magnitude
homology for graphs. Recently, Asao and Izumihara introduced CW-complexes whose homology groups are
isomorphic to direct summands of the graph magnitude homology group. We prove that the Asao–Izumihara
complex is homotopy equivalent to a wedge of spheres for pawful graphs introduced by Y. Gu.
14:15〜15:15
30 山 﨑 晃 司 (東 工 大 理)
Koji Yamazaki(Tokyo Tech)

Sheaf theoretic characterization of étale groupoids · · · · · · · · · · · · · · · · · · 15
Sheaf theoretic characterization of étale groupoids

概 要 The study of Haeﬂier suggests that it is natural to regard a pseudogroup as an étale groupoid. We

show that any étale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup.
This correspondence is an analog of the equivalence of the two deﬁnitions of a sheaf: as an étale space andas a contravariant functor.
31 丸 山 修 平 (名 大 多 元 数 理)

Shuhei Maruyama (Nagoya Univ.)

The Dixmier–Douady class, the action homomorphism, and cocycles on
the group of symplectomorphisms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Dixmier–Douady class, the action homomorphism, and cocycles on
the group of symplectomorphisms

概 要 For a closed, one-connected, and integral symplectic manifold, there exist three kinds of cohomology

classes; the Dixmier–Douady class of symplectic ﬁbrations, Weinstein’s action homomorphism, and acohomology class of Ismagilov–Losik–Michor type. In this talk, we explain a relation between thesecohomology classes in terms of the Hochschild–Serre spectral sequence.
32 森 吉 仁 志 (名 大 多 元 数 理)
夏 目 利 一 ( 名 工 大 工)

Hitoshi Moriyoshi (Nagoya Univ.)
Toshikazu Natsume(Nagoya Inst. of Tech.)

整数格子上の量子ウォークと Nöther 指数定理 · · · · · · · · · · · · · · · · · · · · · · 15

Quantum walk on the integer lattice and the Nöther index theorem

概 要 A formulation of the index theorem for Quantum walk will be discussed. The framework of K-theory

provides a novel viewpoint that connects the classical index theorem by Fritz Noether in 1920 with the newindex theorem discovered by Suzuki–Tanaka and Matsuzawa.

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トポロジー

15:30〜16:30

特別講演
松 下 尚 弘 ( 琉 球 大 理)

Takahiro Matsushita(Univ. of Ryukyus)

不変擬準同型と混合交換子長について

Invariant quasimorphisms and mixed commutator lengths

概 要 A quasimorphism on a group G is a real-valued function f on G such that the function f (xy) − f (x) −f (y) on G × G is uniformly bounded. A quasimorphism f on G is said to be homogeneous if f (xn ) = n · f (x)for every element x in G and for every integer n. Homogeneous quasimorphisms are closely related to thesecond bounded cohomology and the stable commutator length, and they have been extensively studied ingeometric group theory, symplectic geometry, and theory of diﬀeomorphism groups.
Let N be a normal subgroup of a group G. A homogeneous quasimorphism f on N is said to be G-invariant
if f (gxg −1 ) = f (x) for every element g in G and for every element x in N . In this talk, we discuss several
relations among invariant quasimorphisms, the stabilizations of mixed commutator lengths, and the second(bounded) cohomology groups.
This talk is based on joint work with Morimichi Kawasaki (Aoyama Gakuin University), Mitsuaki Kimura(Kyoto University), Shuhei Maruyama (Nagoya University), and Masato Mimura (Tohoku University).

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無限可積分系

無限

可3 月 30 日（水）

積

分

104

系

第 IX 会場

10:00〜12:00
1 茂 木 康 平 (東京海洋大海洋工)
Kohei Motegi(Tokyo Univ. of Marine Sci. and Tech.)Yang–Baxter 代数を用いた, Grothendieck 多項式に関する恒等式の歪版への拡張 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An extension of an identity for Grothendieck polynomials to skew version using Yang–Baxter algebra

概 要 Recently, Guo and Sun derived an identity for factorial Grothendieck polynomials which generalizes

the one for Schur polynomials by Fehér–Némethi–Rimányi. We give an extension of the identity using skew
Grothendieck polynomials by using integrable model and associated Yang–Baxter algebra.
2 大 久 保 勇 輔 ( 第 一 薬 大)
星 野
歩 ( 広 島 工 大 工)
白 石 潤 一 ( 東 大 数 理)
Yusuke Ohkubo(Daiichi Univ. of Pharm.)
Ayumu Hoshino(Hiroshima Inst. of Tech.)
Jun’ichi Shiraishi (Univ. of Tokyo)

変形 Koornwinder 作用素と C 型 Macdonald 多項式 I · · · · · · · · · · · · · · · · 15

Deformed Koornwinder operators and Macdonald polynomials of typeCI

概 要 A certain deformation of the Calogero–Moser–Sutherland operator and the Macdonald operator was

given by Sergeev and Veselov, which is related to the Lie superalgebras. In this talk, we present a Fockrepresentation of the Sergeev–Veselov type deformation of the Koornwinder operator. This representation
gives another proof of the kernel function identity for the deformed Koornwinder operator which was
originally proved by Atai.
3 星 野歩 ( 広 島 工 大 工)
大 久 保 勇 輔 ( 第 一 薬 大)白 石 潤 一 ( 東 大 数 理)
Ayumu Hoshino(Hiroshima Inst. of Tech.)
Yusuke Ohkubo(Daiichi Univ. of Pharm.)
Jun’ichi Shiraishi (Univ. of Tokyo)

変形 Koornwinder 作用素と C 型 Macdonald 多項式 II · · · · · · · · · · · · · · · 15

Deformed Koornwinder operators and Macdonald polynomials of type
C II

概 要 We give explicit forms for the Macdonald polynomials of type C with hook diagrams. Moreover, wegive the Pieri formulas for the Macdonald polynomials of type C with hook diagrams and give a conjectureof the Pieri formulas for the type C degenerations of the Koornwinder polynomials with hook diagrams.
4 中 島 俊 樹 ( 上 智 大 理 工)
M. I. Alshuqayr (上 智 大 理 工)

Toshiki Nakashima (Sophia Univ.)
Manal I. Alshuqayr (Sophia Univ.)

単項式表示による Cn 型基本結晶の積の分解定理 · · · · · · · · · · · · · · · · · · · · 15

Decomposition theorem for product of fundamental crystals in monomial realization of type Cn

概 要 We shall describe the monomial realizations of the fundamental crystals of type Cn and show that

their product holds a crystal structure. Finally, we shall give the decomposition theorem of their products
explicitly and compare with the decomposition of their tensor product.

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105

無限可積分系

5 金 久 保 有 輝 (筑波大数理物質)
G. Koshevoy ( IITP RAS )中 島 俊 樹 ( 上 智 大 理 工)

Yuki Kanakubo (Univ. of Tsukuba)(IITP RAS)
Gleb Koshevoy
Toshiki Nakashima (Sophia Univ.)

An algorithm for Berenstein–Kazhdan decoration functions for minuscule representations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An algorithm for Berenstein–Kazhdan decoration functions for minuscule representations

概 要 We can deﬁne a geometric crystal structure on a variety related to a simply connected connected

simple algebraic group, which is a geometric analog of Kashiwara crystals. Deﬁning a rational function‘Berenstein–Kazhdan decoration’, one can obtain a crystal in a polyhedral cone isomorphic to the crystal
base of negative part of quantum group. In this talk, we give an algorithm to partially compute the BK
decoration. In particular, if the algebraic group is special linear group, we can completely calculate BK
decoration, which induces an explicit form of the polyhedral cone.
6 T. Scrimshaw (阪 市 大 数 学 研)

Travis Scrimshaw (Osaka City Univ.)

Quasi-solvable colored lattice models for types B and C · · · · · · · · · · · · · 15
Quasi-solvable colored lattice models for types B and C

概 要 We describe a colored vertex model whose partition function computes the Demazure atoms andcharacters for types B and C. A novel feature of this model is that it is not fully solvable (in the sensethat the exists a solution to each possible Yang–Baxter equation), but it still retains enough solutions of
the Yang–Baxter equations to compute the partition function. This is based on joint work with Valentin
Buciumas (arXiv:2101.08907)
14:15〜14:50
7 武 中
亮 ( 阪 市 大 理)
尾 角 正 人 ( 阪 市 大 理)

Ryo Takenaka (Osaka City Univ.)
Masato Okado (Osaka City Univ.)頂点作用素代数とアフィンリー環のフェルミ型指標公式 · · · · · · · · · · · · · 15

Vertex operator algebras and fermionic character formulas of aﬃne Liealgebras概 要 Using a vertex algebraic construction, we construct bases of principal subspaces, highest weight

modules of highest weight kΛ0 and parafermionic spaces for twisted aﬃne Lie algebras. As a consequence,
we obtain the fermionic character formula conjectured by Hatayama, Kuniba, Okado, Takagi and Tsuboi.
8 中 野 弘 夢 ( 東 北 大 理)

Hiromu Nakano (Tohoku Univ.)

N = 1 トリプレット頂点作用素超代数の対数的加群について · · · · · · · · · 15
On logarithmic modules of the N = 1 triplet vertex operator superalgebras

概 要 The N = 1 triplet vertex operator superalgebra SW (m) was introduced by Adamović and Milas in2009. We construct logarithmic SW (m)-modules and prove that the projective covers of every irreducible
SW (m)-modules are given by these logarithmic modules.
15:00〜16:00

特別講演
小 島 武 夫 ( 山 形 大 理 工)

変形 W 代数 Wq,t (g) の 2 次関係式

Takeo Kojima (Yamagata Univ.)

Quadratic relations of the deformed W -algebra Wq,t (g)

概 要 Deformed W -algebra Wq,t (g) associated with Lie algebra g is a two parameter deformation of theclassical W -algebra W(g), including the W -algebra Wβ (g) and the q-Poisson W -algebra as special cases.
Using the free ﬁeld construction of the basic W -current T1 (z) of Wq,t (g), we introduce the higher W -currents
Ti (z) (i = 2, 3, 4, . . .) and obtain a closed set of quadratic relations among them. This allows us to deﬁne(1)

Wq,t (g) by generators and relations. In this talk, we ﬁrst review the case of the aﬃne Lie algebra g = AN ,(2)and then study the extensions to the cases of the twisted Lie algebra A2N and the super Lie algebraA(M, N )(1) .

最終版: 2022/3/4
無限可積分系

3 月 31 日（木）106

第 IX 会場

10:00〜12:00
9 青 本 和 彦 ( 名 大 多 元 数 理)
伊 藤 雅 彦 ( 琉 球 大 理)

Kazuhiko Aomoto (Nagoya Univ.)
Masahiko Ito (Univ. of Ryukyus)

球面配置に付随する超幾何積分の準位関数 F から定まる臨界点におけるF のヘッセ行列式の積について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Product of Hessians on critical points of level function F attached to
hypergeometric integral associated with sphere arrangement

概 要 We will talk about product formulae of values of a level function at critical points involved in asymptotic

behaviors of hypergeometric integrals associated with a symmetric arrangement of three dimensional spheres.
We show in an explicit way how the product of Hessians of the level function at all critical points is related
to the behavior of its critical points. We also state two conjectures concerning the same problem associatedwith general hypersphere arrangements.
10 高 木 太 一 郎 (防衛大)Taichiro Takagi(Nat. Defense Acad. of Japan)

ループ基本対称関数を用いたラックス方程式 · · · · · · · · · · · · · · · · · · · · · · · 15

Lax equations using the loop elementary symmetric functions

概 要 We consider a set of ordinary diﬀerential equations that is a sort of Bogoyavlensky lattices with Ln

dependent variables, where L and n are any pair of coprime natural numbers. We show a Lax representation
for the system where the elements of the Lax matrix are given by the so-called loop elementary symmetricfunctions of the dependent variables. The Lax equation is viewed as a continuous limit of the discrete
time analog of the Lax equation for the geometric lifting of the integrable cellular automata studied by theauthor.
11 重 富 尚 太 (九 大 数 理)
梶 原 健 司 (九 大 I M I )Shota Shigetomi (Kyushu Univ.)
Kenji Kajiwara (Kyushu Univ.)

捩率角一定の空間離散曲線の等周変形の楕円テータ函数による明示公式· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Explicit formula of isoperimetric deformation of discrete space curvewith constant torsion angle in terms of elliptic theta function

概 要 We construct an explicit formula of isoperimetric deformation of discrete space curve with constanttorsion angle in terms of elliptic theta function. This formula represents a deformation of Kaleidocycle.
12 中 西 知 樹 (名 大 多 元 数 理)

Tomoki Nakanishi (Nagoya Univ.)

Cluster scattering diagrams, dilogarithm elements, and pentagon relation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Cluster scattering diagrams, dilogarithm elements, and pentagon relation

概 要 The cluster scattering diagrams (CSDs) was introduced by Gross, Hacking, Keel, and Kontsevich toprove several important conjectures on cluster algebras. In this talk we show that every consistency relationin any CSD can be reduced to a trivial one by the pentagon relation among dilogarithm elements in its
structure group (possibly applying inﬁnitely many times). The proof is based on a modiﬁcation of theconstruction of CSDs by Gross et al.
13 松 下 浩 大 (名 大 多 元 数 理)

Kodai Matsushita (Nagoya Univ.)

ランク 2 のアフィン型団散乱図式の整合関係式と五角関係式 · · · · · · · · · · 15

Consistency relation of rank 2 cluster scattering diagrams of aﬃne type
and pentagon relation

概 要 Cluster scattering diagrams are important tools for studying cluster algebra. In rank 2 case, thediagrams are characterized by the consistency relation. In this talk, we prove that the consistency relationof rank 2 cluster scattering diagram of aﬃne type is reduced to the trivial relation by using pentagon
relations inﬁnite times.

最終版: 2022/3/4

107

無限可積分系

14 水 野 勇 磨 (千 葉 大 理)
Yuma Mizuno(Chiba Univ.)

Mutations of blowups of toric surfaces and q-Painlevé systems · · · · · · · 15
Mutations of blowups of toric surfaces and q-Painlevé systems

概 要 We provide a relation between the geometric framework for q-Painlevé equations and cluster Poisson

varieties by using toric models of rational surfaces associated with q-Painlevé equations. We introduce thenotion of seeds of q-Painlevé type by the negative semi-deﬁniteness of symmetric bilinear forms associatedwith seeds, and classify the mutation equivalence classes of these seeds. This classiﬁcation coincides withthe classiﬁcation of q-Painlevé equations given by Sakai.
14:15〜15:15

特別講演

笹 本 智 弘 ( 東 工 大 理)

Skew RSK, aﬃne crystal and KPZ

Tomohiro Sasamoto (Tokyo Tech)

Skew RSK, aﬃne crystal and KPZ

概 要 We explain various properties and applications of the skew RSK dynamics, which we introduced

recently as a time evolution for a pair of skew Young tableaux (P,Q). The dynamics exhibits solitonic
behaviors similar to box ball systems (BBS). Associated aﬃne crystal structure allows to give a bijective
proof of the Cauchy identity for the q-Whittaker polynomials. Its reﬁnement provides a connection between
Kardar–Parisi–Zhang (KPZ) models and free fermions at ﬁnite temperature.