2024/08/21 作成“日本数学会2024 年度秋季総合分科会

英 文

サ

マ

リ

2024 年 9 月
於

大阪大学

集

2024 日 本 数 学 会
秋季総合分科会プログラム期

日2024 年 9 月 3 日（ 火 ）〜 9 月 6 日（ 金 ）会場

大 阪 大 学 豊 中 キ ャ ン パ ス
大 阪 府 豊 中 市 待 兼 山 町 1–1

連 絡 先

大阪大学大学院理学研究科数学専攻〒560-0043
大 阪 府 豊 中 市 待 兼 山 町 1–1
E-mail osaka24sept mathsoc jp
一般社団法人

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

日 本 数 学 会

第 VIII 会場

第 IX 会場

理学 J 棟
基礎工学研究科 B 棟 全学教育講義 B 棟 全学教育講義 B 棟 全学教育講義 A 棟 全学教育講義 A 棟 全学教育講義 B 棟 全学教育講義 B 棟 全学教育講義 B 棟
南部陽一郎ホール Sky Lecture Room B300
大講義室
共 B118
共 A201
共 A301
共 B107
共 B108
共 B218幾 何 学 函数方程式論 代 数 学 応 用 数 学 函数解析学 函 数 論 統 計 数 学 無限可積分系 トポロジー
9:30〜11:45 9:00〜12:00 9:30〜12:00 9:00〜11:40
14:15〜16:15 14:15〜16:45 15:30〜18:00 15:30〜16:25

3日（火）

9:00〜10:45

企画特別講演

9:30〜11:00

9:30〜11:50

9:30〜10:35

9:30〜12:00

13:00〜14:00

特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演 特別講演
16:30〜17:30 17:00〜18:00 14:15〜15:15 14:15〜15:15 11:00〜12:00 14:20〜15:20 14:15〜15:15 10:45〜11:45 14:30〜15:30
16:40〜17:40
15:30〜16:30

函数方程式論 代 数 学 応 用 数 学 函数解析学 函 数 論 統 計 数 学 無限可積分系
9:00〜12:00

9:15〜10:45 9:00〜11:40 10:00〜11:45
13:00〜14:00 13:00〜14:00

9:30〜11:00

9:30〜11:40

9:30〜10:30

特別講演 特別講演 特別講演

特別講演 特別講演

特別講演

4 日 10:20〜11:20 13:00〜14:00 11:00〜12:00（水） 12:50〜13:50

13:00〜14:00 13:00〜14:00

10:45〜11:45

日本数学会賞授賞式（大 阪 大 学 会 館 2 階, 3 階 講 堂） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30〜15:00)〃
総 合 講 演（） 日 本 数 学 会 賞 秋 季 賞 受 賞 者 · · · · · · (15:15〜16:15)
白 井 朋 之 (九 大 I M I) · · · · · · (16:30〜17:30)
懇親会（カ フ ェ テ リ ア か さ ね） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:00〜20:00)

5日（木）

幾 何 学 函数方程式論 代 数 学 応 用 数 学 函数解析学 実 函 数 論 統 計 数 学

数学基礎論
トポロジー
および歴史

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

9:30〜11:30 9:30〜12:00
15:30〜17:00 15:40〜18:00

企画特別講演

9:30〜11:40

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
17:00〜18:00 17:00〜18:00 16:15〜17:15 16:15〜17:15 17:00〜18:00 14:15〜15:15 14:15〜15:15 14:20〜15:20
15:30〜16:30

数学基礎論
トポロジー
および歴史

幾 何 学 函数方程式論 代 数 学 応 用 数 学

実函数論 統計数学

9:30〜11:45

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

9:15〜12:00

9:15〜10:45 10:00〜12:00

6 日 14:15〜16:45 14:15〜16:45 14:15〜17:30 14:15〜16:00（金）

企画特別講演

13:00〜14:00

特別講演 特別講演 特別講演

特別講演

特別講演

17:00〜18:00 11:00〜12:00 16:15〜17:15

15:20〜16:20

10:45〜11:45

2024/08/21 作成
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

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

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

11

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

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

29

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

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

41

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

実函数論

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

66

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

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

74

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

統計数学

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

81

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

2024/08/21 作成4

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
応用数学

88

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

93

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

106

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

111

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

9 月 5 日（木）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

114

9 月 6 日（金）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

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

122

9 月 3 日（火）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

122

9 月 4 日（水）. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123

2024/08/21 作成
1

総合講演

総 合

講

演

9 月 4 日（水） 総合講演会場
日本数学会賞秋季賞受賞者· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:15〜16:15)

Autumn Prize Winner
白 井 朋 之 (九 大 I M I )行列式点過程の諸相 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16:30〜17:30)

Tomoyuki Shirai (Kyushu Univ.)

Aspects of determinantal point processes

概 要 The importance of determinantal point processes (DPPs) has become widely recognized, within prob-

ability theory and diverse application areas, oﬀering both theoretical elegance and practical utility. Theirroots trace back to the 1970s when Macchi introduced them as a model for fermions in quantum mechanics.
In the late 1990s, driven by the surge of interest in random matrix theory, Soshnikov and Shirai–Takahashi
independently extended the framework of DPPs and established the theoretical foundation. Since then, DPPs
have seen remarkable growth both in theoretical development and in diverse applications. These applications
include studying eigenvalues of certain random matrices, the zeros of certain Gaussian analytic functions, thenon-trivial zeros of Riemann zeta function, Poissonized Young diagrams, uniform spanning trees, and evenmachine learning. In this talk, we provide the background of DPPs, and overview the related topics in DPPs
and beyond.

2024/08/21 作成
企画特別講演

企

画

特

別

講

2

演

9 月 3 日（火）第 I 会場石 川 剛 郎 (北大⋆)Goo Ishikawa (Hokkaido Univ.

⋆)

サブリーマン空間の特異曲線とその周辺 · · · · · · · · · · · · · · · · · (13:00〜14:00)

Singular curves of sub-Riemannian spaces and related topics

概 要 A sub-Riemannian structure is given by a Riemannian metric on a vector subbundle of the tangent

bundle (distribution) over a manifold. Then the notion of geodesics or length minimisers are naturally deﬁned
on sub-Riemannian spaces. Unlike Riemannian case, there appear abnormal geodesics or singular curves, as
sub-Riemannian geodesics, in addition to normal geodesics. It turns out that singular curves are deﬁned,
depending just on the distribution, as critical points of end-point mapping in the context of control theory,and they are signiﬁcant objects also in geometry and topology in their own right. In this talk, several topics
and results on singular curves of distributions will be explained for speciﬁc cases, say, (2, 3, 4)-distributions(Engel), in terms of the growth of ranks by taking Lie brackets, (2, 3, 5)-distributions (Cartan), (3, 5)distributions, (4, 5)-distributions, (3, 6)-distributions, (4, 7)-distributions, (8, 15)-distributions and so on,with some perspectives.
第 II 会場
川 平 友 規 ( 一 橋 大 経 済)

複素力学系のアナロジー, あるいはアンソロジー · · · · · · · · · · (13:00〜14:00)

Tomoki Kawahira (Hitotsubashi Univ.)

Analogies of complex dynamics, or an anthology

概 要 I will talk about some analogies between one dimensional complex dynamics (CD1) and other types ofanalytic dynamical systems. We will begin with classical “Sullivan’s dictionary” linking CD1 with Kleiniangroups (KG), which later yields the Lyubich–Minsky theory of hyperbolic 3-laminations for CD1. We cannot
miss the Bullett–Penrose theory of holomorphic correspondence, and the Hinkkanen–Martin–Sumi theoryof (random) rational semigroups which provide fascinating uniﬁcations of CD1 and KG. Anti-holomorphic
dynamics is often called an “evil twin” of CD1. Complex dynamics in several variables and non-Archimedean
dynamics initially developed as analogies to CD1, have recently achieved signiﬁcant advancements thattranscend their original analogical frameworks. With such diversity in the ﬁeld, we are now at an exciting
juncture. The question is: where do we go from here?
第 III 会場
特別招待講演 (台湾数学会)
Hsueh-Yung Lin (国 立 台 湾 大)

On the cone conjectures for Calabi–Yau pairs · · · · · · · · · · · · (13:00〜14:00)

Hsueh-Yung Lin (Nat. Taiwan Univ.)

On the cone conjectures for Calabi–Yau pairs

概 要 We will discuss the shapes of various positive cones of divisors of a Calabi–Yau pair, with a special

focus on the Kawamata–Morrison–Totaro cone conjectures, as well as the analogous conjecture formulated
for the eﬀective cone. We will illustrate some relations between these cone conjectures and some ﬁnitenessstatements in birational geometry. Along the way, we will also survey some known results related to the cone
conjectures. The content of the talk is based on the works by many birational geometers, and partly on joint
works with C. Gachet, I. Stenger, and L. Wang.

2024/08/21 作成
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企画特別講演

9 月 5 日（木）第 II 会場中 村

周 ( 学 習 院 大 理)

Shu Nakamura (Gakushuin Univ.)

散乱理論における超局所解析的方法 · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Microlocal methods in scattering theory

概 要 We discuss how the microlocal analysis methods are applied eﬀectively to the scattering theory. The

microlocal analysis was originally developed to investigate very precise singularity properties of solutions
to partial diﬀerential equations, whereas the scattering theory concerns long time behaviors of solutions to
Schrödinger equations or wave equations. Roughly speaking, if we apply the microlocal methods to theequations in the Fourier space, we expect to obtain detailed information on the scattering phenomena. Thisidea goes back at least to the works by Kitada, Yajima and Isozaki in early 1980’s. We introduce very basic
concepts of the microlocal analysis and the scattering theory, and we survey some historical developments on
the microlocal methods in the scattering theory. Then we review several recent results, including long-range
scattering for discrete Schrödinger equations and the microlocal structure of long-range scattering matrices.
第 III 会場
清 水 泰 隆 ( 早 大 理 工)

Yasutaka Shimizu (Waseda Univ.)

保険数理と Gerber–Shiu 解析: レヴィ・リスク過程に対するスケール関数の推定問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Gerber–Shiu analysis in insurance mathematics: estimationof the scale functions for Levy risk processes

概 要 In insurance mathematics, the theory of the expected discounted penalty function, known as the“Gerber–Shiu function,” introduced by Gerber and Shiu (1998, NAAJ), has evolved into a comprehensive
framework that fully embraces classical insurance risk theory. Notably, applying this theory using thespectrally negative Levy process as a model for insurance surplus proves to be an eﬀective tool for analyzing
unforeseen risks in ﬁnance and insurance, a methodology now commonly referred to as “Gerber–Shiu
Analysis.” Over two decades have passed since its inception, and the foundational aspects of the theory
appear to have been extensively studied. Nonetheless, research from a statistical point of view remains
underdeveloped.
The general theory of Gerber-Shiu analysis is discussed under an asset process that follows a spectrally
negative Levy process, and it is known that many ruin-related risk quantities can be expressed by using its
scale function. Thus, the main statistical issue is estimating the scale functions of Levy processes.
In this talk, we will review the development of Gerber–Shiu analysis and introduce a novel method forstatistical estimation of scale functions with its asymptotic theory.

9 月 6 日（金）第 II 会場
利 根 川 吉 廣 ( 東 工 大 理)

Yoshihiro Tonegawa (Tokyo Tech)

一般化された平均曲率流の存在定理について · · · · · · · · · · · · · (13:00〜14:00)

Existence theorems for generalized mean curvature ﬂow

概 要 Suppose that we have a moving n-dimensional surface Mt in Rn+1 where t is the time variable. If

the speed of motion of Mt is equal to the mean curvature of Mt at that point, Mt is said to be a mean
curvature ﬂow. Typically, Mt develops some singularity in ﬁnite time and there has been numerous attempts
to formulate the existence theorem of generalized solution of the mean curvature ﬂow past the singular time.
In my talk, I start with some basics such as the deﬁnition and the area-decreasing property, and move on to
the ﬁner points such as Huisken’s monotonicity formula, the tangent ﬂow and the local regularity theorems,
and then describe more recent existence theorems for initial value problem with a reasonable coverage of thedeﬁnition of the generalized solution. These results led us to new insights on the very notion of the mean
curvature ﬂow and, moreover made us rethink what it means for surfaces to move at a speciﬁed speed in a
generalized setting of measures.

2024/08/21 作成
企画特別講演

4

第 III 会場
桑 原 敏 郎 (筑波大数理物質)

シンプレクティック特異点解消に付随する頂点代数 · · · · · · · (13:00〜14:00)

Toshiro Kuwabara (Univ. of Tsukuba)

Vertex algebras associated with symplectic resolutions

概 要 The central quotient of the universal enveloping algebra of a simple Lie algebra coincides with the algebraof diﬀerential operators on the ﬂag manifold of the corresponding Lie group. Therefore, the enveloping algebraof a Lie algebra can be regarded as an algebra obtained by quantizing the coordinate ring of the cotangent
bundle, which is a symplectic manifold, of the ﬂag manifold. Relatively new algebras that have appearedin representation theory, such as rational Cherednik algebras and ﬁnite W-algebras, are also obtained as
quantizations of the coordinate rings of symplectic manifolds that are not cotangent bundles, such as
Nakajima quiver varieties and Slodowy varieties. Symplectic manifolds related to such noncommutative
algebras are called symplectic resolutions. These are symplectic manifolds that provide a resolution of
singularities for a Poisson manifold with singularities, where the morphism giving the resolution preserves
the Poisson structure.
Vertex algebras are algebraic structures that can handle the structure of the enveloping algebra of aﬃne Liealgebras, which are inﬁnite-dimensional analogues of simple Lie algebras, in an algebraic manner. Just as
simple Lie algebras and rational Cherednik algebras were described using algebras of diﬀerential operators
on symplectic resolutions, we consider introducing new vertex algebras by constructing sheaves of free ﬁeld
vertex algebras, which are vertex algebra analogues of algebras of diﬀerential operators, such as the betagamma system, on symplectic resolutions. The sheaves of vertex algebras considered here are partly known
as the theory of chiral diﬀerential operators (CDOs), but in general, they are a new class of objects that arevertex algebra analogues of sheaves of microlocal diﬀerential operators. It is nontrivial whether coordinatetransformations between diﬀerential operators lift to coordinate transformations of free ﬁeld vertex algebras,
and in fact, nontrivial obstructions appear for the existence of such sheaves.
However, as a result of research, it has gradually become clear that such sheaves of vertex algebras can be
explicitly constructed using BRST reduction (quantum Hamiltonian reduction) for at least some symplectic
resolutions. Furthermore, it is gradually becoming clear that some of the vertex algebras constructed in thisway coincide with vertex algebras arising from 3-4 dimensional conformal ﬁeld theories studied by theoreticalphysicists. In this talk, I will explain what is currently known about vertex algebras constructed as sheavesof free ﬁeld vertex algebras on symplectic resolutions.

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5

数学基礎論および歴史

数 学

基

礎

論

9 月 5 日（木）

お

よ

び

歴

史

第 VIII 会場

9:30〜11:30
1 脇

克 志 ( 山 形 大 理)

Katsushi Waki (Yamagata Univ.)

佐久間文庫デジタルアーカイブの構成 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Composition of the SAKUMA Collection Digital Archive

概 要 By digitizing the Sakuma Collection, we will build a digital archive of Japanese mathematics books

that can be used by researchers, educators, and the general public.
2 田 中 紀 子 (奈良学園大人間教育)
大⋆)
松 原
望 (東

Noriko Tanaka (Naragakuen Univ.)
Nozomu Matsubara (Univ. of Tokyo⋆)

現実の現象を描く確率・統計 —Pattern theory · · · · · · · · · · · · · · · · · · · · · 15

Probability and statistics for real-world —Pattern theory

概 要 For over two millennia, Aristotle’s logic has ruled over the thinking of western intellectuals. Probability

theory and statistical inference now emerge as better foundations for scientiﬁc models, especially those of
the process of thinking and as essential ingredients of theoretical mathematics, even the foundations ofmathematics itself. We look at probability and statistics from P. Levy, Ito and Mumford’s perspective.
3 田 村誠(大阪産大全学教育機構)

Makoto Tamura (Osaka Sangyo Univ.)

北京大学蔵秦簡中の『算書』甲種について · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the “Suanshu” Jiazhong of Qin dynasty bamboo slips housed at
Peking University

概 要 The “Suanshu” Jiazhong (arithmetic books, vol 1) in the unearthed bamboo slips of Qin dynasty

housed at Peking University is the oldest arithmetic book of the most number of slips ever excavated. In
this talk, we will overview this book, and comparing with Yuelu “Shu” and Zhangjiashan “Suanshu-shu”,
consider the standard of mathematics during the Qin-Han period in China.
4 真 島 秀 行 (お茶の水女大⋆)Hideyuki Majima (Ochanomizu Univ.

⋆)

吉田光由著「塵劫記」において円周率とされる数 3.16 について · · · · · · · 15

On he umber 3.16 as Pi in JINKOUKI by YOSHIDA Mitsuyoshi

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

on Pi. In this time, we discuss on the Number 3.16 as Pi in JINKOUKI.
5 田 中 紀 子 (奈良学園大人間教育)
小 川
束(四日市大関孝和数学研)

Noriko Tanaka (Naragakuen Univ.)
Tsukane Ogawa (Yokkaichi Univ.)

宅間流「起術解路法『省約術』」· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A Study on the Takuma School “Kijutsu Kairoho (Yakushiki-jyutsu)”

概 要 The authors have ﬁnished reading the ﬁve volumes of “Kijutsu Kairoho (Methods for creating andclarifying the process of answers),”which are not independent but refer to the younger book in many
parts and to the later book in others. In this article, we will introduce and discuss the characteristics
of mathematics in “Yakushiki jutsu (Methods for simplifying the expression).” We will also introduce thelicense of the Takuma school.

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数学基礎論および歴史

6

束(四日市大関孝和数学研)
田 中 紀 子 (奈良学園大人間教育)

算額文化論について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Tsukane Ogawa (Yokkaichi Univ.)
Noriko Tanaka (Naragakuen Univ.)

On the cultural theory of mathematical plates

6 小 川

概 要 The theory of mathematical plates is an attempt to understand the mathematical culture of pre-modern Japan, not by looking at individual tableaus separately but by considering multiple tableaus interms of their mathematical, geographical, and voter relationships. Since I ﬁrst proposed this idea in 2021,
employing examples, I have conducted some analyses with my collaborators. This time, I have obtained an
instance through Takashi Nakanishi’s analysis of a plate at Ohama Shrine in Siga Prefecture, and I would
like to discuss the possibility of the theory together with the example of 2021.
7 斎 藤憲(阪府大⋆・四日市大関孝和数学研)
Ken Saito(Osaka Pref. Univ.⋆ /Yokkaichi Univ.)

ヒュプシクレスの多面体論 (通称『原論』第 14 巻) · · · · · · · · · · · · · · · · · · 15

Hypsicles’ work on regular polyhedra (so-called Book 14 of the Elements)

概 要 Hypsicles (2nd century BCE) wrote a work on regular polyhedra after examining Apollonius’ workon the same topic which in turn was a development of Book 13 of Euclid’s Elements. Hypsicles’ work is
usually called “Book 14” of the Elements, and its manuscript is often attached to that of the Elements. In
this talk we will focus on its linguistic expressions rather than its mathematical content, and will compare
its style and vocabulary with that of the Elements.
11:45〜12:00

歴史部門懇談会

14:15〜15:15

特別講演
伊 達 悦 朗 (阪Etsuro Date

大⋆)

冊子「全国紙上数学談話会」をめぐって⋆)

On “Zenkoku Shijo Sugaku Danwakai”(Osaka Univ.

概 要 “Zenkoku Shijo Sugaku Danwakai” is a series of pamphlets published by Department of Mathematics

of Osaka (Imperial) University. The ﬁrst issue was published in June 1934. It lasted until February 1945.
The period of the second series is from November 1946 to July 1949. It was used as a communication tool
among mathematical community. We will comment a bit on these pamphlets. The third series (although
only 1 issue) was found recently. We will also touch upon it.
15:30〜17:00
8 池 田 宏 一 郎 ( 法 政 大 経 営)
Koichiro Ikeda(Hosei Univ.)

重み無限のタイプをもつ安定な理論について · · · · · · · · · · · · · · · · · · · · · · · 15

On stable theories having a type with inﬁnite weight概 要 In this talk, we explain how to construct stable theories having a type with inﬁnite weight in a ﬁnite

language.

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7

数学基礎論および歴史

9 荒 武 永 史 ( 小 山 工 高 専)
Hisashi Aratake(Oyama Nat. Coll. of Tech.)Axiomatizability of models represented by sheaves · · · · · · · · · · · · · · · · · 15
Axiomatizability of models represented by sheaves

概 要 In the theory of sheaf representation of rings, it is well-known that von Neumann regular rings (resp.

domain representable rings) are precisely the rings of global sections of sheaves whose stalks are ﬁelds (resp.
integral domains). More generally, the classes of models represented by some kinds of sheaves have been
considered in the context of universal algebra and model theory. However, the existing studies do notseem to answer to the question of why global section models in the above examples can be characterized
elementally. In this talk, we present a suﬃcient condition for ﬁrst-order axiomatizability of the class ofmodels represented by sheaves whose stalks are T-models for a given ﬁrst-order theory T. We exploit
Coste’s theory of categorical spectra and the previous studies on subcategories of locally ﬁnitely presentable
categories.
10 大 倉 昂 貴 (筑波大数理物質)

Koki Okura (Univ. of Tsukuba)

Avoiding cell decomposition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Avoiding cell decomposition

概 要 Cell decomposition is a central and fruitful technique in model theory for the study of the real andp-adic ﬁelds. However, its proof takes much eﬀort, maybe too much for many purposes. This talk is aimed
at proposing a substitute for cell decomposition. To be more speciﬁc, we discuss some behaviors of types ino-minimal theories and that of the p-adic numbers, and explain how those results reveal some properties of
those theories. One of them is the dp-minimality of the p-adic ﬁelds, whose known proof largely depends
on cell decomposition.
11 米 田 郁 生 (徳 山 工 高 専)

Ikuo Yoneda (Tokuyama Coll. of Tech.)

Weak one-basedness and CM-triviality in rosy theories · · · · · · · · · · · · · · 15
Weak one-basedness and CM-triviality in rosy theories

概 要 We present the following results; one-basedness is equivalent to weak one-basedness and CM-triviality,

moreover modularity is equivalent to weak one-basedness and CM-triviality in the real sort.
12 小 峰航 (筑波大数理物質)
波大⋆)坪 井 明 人 (筑Wataru Komine (Univ. of Tsukuba)
Akito Tsuboi (Univ. of Tsukuba⋆)

On prime models of locally o-minimal theories · · · · · · · · · · · · · · · · · · · · · 15
On prime models of locally o-minimal theories

概 要 It is well-known that every o-minimal theory has a prime model and they are isomorphic. We areinterested in locally o-minimal theory, and investigate existence and uniqueness of prime models in deﬁnably
complete locally o-minimal theory. We give some suﬃcient conditions for uniqueness.
13 桔 梗 宏 孝 (神戸大システム情報)
波大⋆)坪 井 明 人 (筑Hirotaka Kikyo (Kobe Univ.)
Akito Tsuboi (Univ. of Tsukuba⋆)

ランダム超グラフにおける分離と分岐について · · · · · · · · · · · · · · · · · · · · · 15

On dividing and forking in random hypergraphs

概 要 Let H(m, l, s) be the class of m-hypergraphs G whose l-element substructures have more than s m-element subsets which form non-hyperedges of G. We obtained the following: Suppose 3 ≤ m < l. H(m, l, s)
has a random structure F (m, l, s) if 0 ≤ s < l−2 Cm−2 . If l−2 Cm−2 < s then H(m, l, s) has no random
structures. If 0 ≤ s < l−3 Cm−3 then the theory of F (m, l, s) has SU -rank one. If l−3 Cl−3 ≤ s < l−2 Cm−2
then dividing and forking are diﬀerent in the theory of F (m, l, s).

2024/08/21 作成
数学基礎論および歴史

9 月 6 日（金）8第 VIII 会場

9:30〜10:30
14 津 久 浦 健 太 (法 政 大 理 工)
Kenta Tsukuura (Hosei Univ.)

Minimal walk method と Namba 強制拡大における準定常集合 · · · · · · · · 15
Minimal walk method and semistationary subsets in Namba forcing extensions

概 要 It is known that (†)-principle arises the compactness phenomenons. In particular, anti-compact objects(like square sequences and non-reﬂecting stationary subsets) give semistationary subsets in which Namba
forcings kill its semistationarity. We give new proofs of these using the minimal walk method.
15 依 岡 輝 幸 (静 岡 大 理)

Teruyuki Yorioka (Shizuoka Univ.)

モデルをサイドコンディションとして組み込んだ強制法に関する強制法的保存則 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Some preservation theorems for forcing notions with models as side conditions

概 要 The side condition method is a general framework of constructions of proper forcing notions deﬁned

by Stevo Todorčević. These forcing notions equip with models as side conditions. In this talk, somepreservation theorems for forcing notions with models as side conditions are introduced.
16 依 岡 輝 幸 (静 岡 大 理)

Teruyuki Yorioka (Shizuoka Univ.)

Y-proper forcing axiom における不可算線形順序 · · · · · · · · · · · · · · · · · · · 15
Uncountable linear orders in Y-proper forcing axiom

概 要 Y-Proper Forcing Axiom is introduced by Chodounský–Zapletal and implies many consequences from

Proper Forcing Axiom. In this talk, we present some consequences from Y-Proper Forcing Axiom which
are related to a ﬁve element basis for the uncountable linear orders.
17 薄 葉 季 路 (早 大 理 工)

Toshimichi Usuba (Waseda Univ.)

The tightness function of ultrapower embeddings · · · · · · · · · · · · · · · · · · · 15
The tightness function of ultrapower embeddings

概 要 Under a certain large cardinal assumption, it is consistent that the least measurable cardinal is tightly

C (1) -compact, in particular it is not C (2) -correct.
10:45〜11:45

特別講演
宮 元 忠 敏 ( 南 山 大 経 営)

Families of sets by side conditions

Tadatoshi Miyamoto (Nanzan Univ.)

Families of sets by side conditions

概 要 We consider two propositions, SAD and SC, with uncountable cardinals as parameters. SAD concerns

strongly almost disjoint families of uncountable sets. We review the work on SAD by Baumgartner andZapletal. SC concerns strong chains of uncountable sets. We review the work on SC by Koszmiderand Inamdar. We present various forcing techniques utilized in proving the relative consistency of these
propositions. We are particularly interested in the proper forcings with side conditions developed by Shelah,
Todorcevic, and Aspero–Mota.

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9数学基礎論および歴史

12:00〜12:15

数学基礎論および歴史分科会総会

14:15〜16:30
18 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力学の再構成 IV: 連続スペクトル· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A reﬁnement of quantum mechanics by algorithmic randomness IV:
Continuous spectrum

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. The principle of typicality
is about quantum measurements with ﬁnite outcomes. In this talk, we show that our framework can benaturally extended over quantum measurements of arbitrary self-adjoint operators on Hilbert spaces of
inﬁnite dimension.
19 熊 澤 昌 明 (あ べ の 翔 学 高) [ BCK-代数における上半束の新しい特徴づけについて · · · · · · · · · · · · · · · · 15
Masaaki Kumazawa(Abeno Shogaku High School)

On a characterization of the upper semi-lattice in BCK-algebras

概 要 Some characterizations of the class that is an upper semi-lattice in BCK-algebras are already known.

One is the positive implicative BCK-algebra with condition (S) by K. Iséki, and the other is the BCK-algebra
which satisfy Cornish’s identity and with condition (S) by W. H. Cornish. We introduced the condition(I)x,y as a generalization of the existence of the inﬁmum in a BCK-algebra, and characterized the lower
semi-lattice in BCK-algebras. Here, we will deﬁne the “condition (Sp)x,y ” as an analogy of condition (I)x,y
and characterize an upper semi-lattice in BCK-algebras by the condition (Sp) x,y .
20 間 庭 彬 仁 (東工大情報理工)
鹿 島
亮 (東工大情報理工)
Akinori Maniwa (Tokyo Tech)(Tokyo Tech)
Ryo Kashima

Syntactic cut-elimination for provability logic GL via nested sequents· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Syntactic cut-elimination for provability logic GL via nested sequents

概 要 The cut-elimination procedure for the provability logic is known to be problematic: a Löb-like

rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proofof termination. In this paper, we present a syntactic cut-elimination proof based on nested sequents, ageneralization of sequents that allows a sequent to contain other sequents as single elements. A similarcalculus was developed by Poggiolesi (2009), but there are certain ambiguities in the proof. Adopting
the idea of Kushida (2020) into nested sequents, our proof does not require an extra measure on cuts orerror-prone, intricate rewriting on derivations, but only straightforward inductions, thus leading to lessambiguity and confusion.
21 佐 藤 雄 太 (神戸大システム情報)
Yuta Sato(Kobe Univ.)

必然化の論理 N の拡張論理に対する補間定理 · · · · · · · · · · · · · · · · · · · · · · 15Interpolation properties of some extensions of the pure logic of necessitation N

概 要 We study interpolation properties of the logic N+ Am,n , which is obtained by adding a single axiom¬□ϕinto the pure logic of necessitation N. By embedding it to classical¬□□ϕ
propositional logic, we prove that for m, n ≥ 1, N+ Am,n enjoys Lyndon interpolation property (LIP) andscheme □n ϕ → □m ϕ and a rule

uniform interpolation property (UIP), in contrast to K4 = N+ A2,1 + K, which is known to lack UIP.

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数学基礎論および歴史

22 小 暮 晏 佳 (神戸大システム情報)
倉 橋 太 志 (神戸大システム情報)
Haruka Kogure (Kobe Univ.)
Taishi Kurahashi (Kobe Univ.)10

証明可能性の二重様相論理 GR に対する補間定理 · · · · · · · · · · · · · · · · · · 15Interpolation properties for the bimodal provability logic GR

概 要 We study interpolation properties for Shavrukov’s bimodal logic GR of usual and Rosser provability

predicates. For this purpose, we introduce a new relational semantics of GR. Based on our new relationalsemantics, we prove that GR enjoys Lyndon interpolation property and uniform interpolation property.
23 倉 橋 太 志 (神戸大システム情報)

Taishi Kurahashi (Kobe Univ.)

Collection 原理の特徴づけについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On some characterizations of collection principles

概 要 We study model theoretic characterizations of various collection schemes over PA− from the viewpointof coﬁnal extensions and end-extensions.
24 倉 橋 太 志 (神戸大システム情報)( Utrecht Univ. )A. Visser

Taishi Kurahashi (Kobe Univ.)
Albert Visser (Utrecht Univ.)

有限拡大に制限した本質的不完全性について · · · · · · · · · · · · · · · · · · · · · · · 15

On essential incompleteness restricted to ﬁnite extensions

概 要 We discuss the diﬀerences and similarities between the intensional and extensional versions of theeﬀectivization of essential incompleteness restricted to ﬁnite extensions.
25 志 村 立 矢 (日 大 理 工)

Tatsuya Shimura (Nihon Univ.)

強い disjunction property と ﬁnite model property を持つ中間命題論理の族について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A family of intermediate propositional logics with strong disjunction
property and ﬁnite model property

概 要 We give a class of intermediate logics with strong disjunction property. By modifying McKay’s resulton the logics axiomatized by disjunctionless formulas, we can show that this class contains inﬁnitely many
logics with ﬁnite model property.

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11

代数学

代

数

9 月 3 日（火）学第 III 会場

9:30〜12:00
1 K. Mousavand (沖縄科学技術大)Kaveh Mousavand(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Hom-orthogonal modules and bricks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hom-orthogonal modules and bricks

概 要 Let A be a ﬁnite dimensional associative algebra. A left A-module X is called a brick if theendomorphism algebra of X is a skew-ﬁeld. It is shown that bricks are in various conceptual correspondenceswith other important objects in representation theory. Consequently, study of bricks has received a lot of
attentions. In our recent work, we study bricks and their properties from a less technical viewpoint andparticularly through Hom-orthogonal modules. This leads to some non-trivial results on the algebraic andgeometric properties of bricks, which ultimately relate to our studies of some open conjectures. Based on
joint work with Charles Paquette.
大理)
2 平 前 直 也 (京小 境 雄 太 ( 東 京 理 大 理)

Naoya Hiramae (Kyoto Univ.)
Yuta Kozakai (Tokyo Univ. of Sci.)

ある半直積群の群代数の τ -傾有限性について · · · · · · · · · · · · · · · · · · · · · · · 15

On τ -tilting ﬁniteness of group algebras of some semidirect products

概 要 Demonet–Iyama–Jasso introduced a new class of ﬁnite dimensional algebras, τ -tilting ﬁnite algebras.

Recently, τ -tilting ﬁniteness has been studied for various ﬁnite dimensional algebras since it relates to certain
ﬁniteness of other objects: brick ﬁniteness, functorially ﬁniteness of all the torsion classes, completeness of
g-fans, and connectivity of silting complexes. For an algebraically closed ﬁeld k of positive characteristic
p and a ﬁnite group G, the classical result says that the representation type of a group algebra kG isdetermined by a p-Sylow subgroup of G. Hence, it is natural to ask what kinds of subgroups control
τ -tilting ﬁniteness of group algebras of ﬁnite groups. In this talk, we will explain that τ -tilting ﬁniteness ofgroup algebras of some semidirect products is determined by so-called p-hyperfocal subgroups.
3 㓛 刀 直 子 ( 東 京 理 大 理)
鈴 木 香 一 ( 東 京 理 大 理)

Naoko Kunugi (Tokyo Univ. of Sci.)
Kyoichi Suzuki (Tokyo Univ. of Sci.)

2 次一般線型群における主ブロックの森田同値 · · · · · · · · · · · · · · · · · · · · · · 15
Morita equivalences for the principal blocks of 2-dimensional generallinear groups

概 要 Let p be a prime. Donovan’s conjecture states that, for a given ﬁnite p-group P , there are only ﬁnitely

many Morita equivalence classes of blocks of ﬁnite groups with defect groups isomorphic to P . In this talk,we show that the principal 2-blocks of inﬁnite series of 2-dimensional general linear groups with wreathed
Sylow 2-subgroups are Morita equivalent.

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代数学

4 宮 本 雅 彦 (筑波大⋆)Masahiko Miyamoto(Univ. of Tsukuba⋆)

12

1-point functions on a VOA of moonshine type · · · · · · · · · · · · · · · · · · · · 15
1-point functions on a VOA of moonshine type

概 要 We proved the following theorem.

P
Theorem If V is a VOA with central charge 24 of moonshine type, that is, n∈Z dim Vn q n−1 = j(τ ) − 744,
then the space F(V ) =< TrV o(v)q L(0)−1 | v ∈ V > of 1-point functions associated to V is precisely C-linear
space spanned by the (meromorphic) modular forms of level 1 and integer weight k ≥ 0 satisfy holomorphic
on H and has Fourier expansion a0 q −1 + ....
This result for V ♮ was already proved by Dong–Mason in 2000.
5 Ching Hung Lam (Academia Sinica)
Xingjun Lin ( Wuhan Univ. )島 倉 裕 樹 ( 福 岡 大 理)

Ching Hung Lam (Academia Sinica)(Wuhan Univ.)
Xingjun Lin
Hiroki Shimakura (Fukuoka Univ.)

Automorphism groups of parafermion vertex operator algebras: generalcase · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Automorphism groups of parafermion vertex operator algebras: generalcase

概 要 In this talk, I will talk about the automorphism groups of parafermion vertex operator algebras

associated with simple Lie algebra and positive integral level. The automorphism group is isomorphic to
the automorphism group of the root system of the simple Lie algebra if (i) k is at least 3 or (ii) k is two andthe simple Lie algebra is non simply laced.
6 川 節 和 哉 (熊本大先導機構)

Kazuya Kawasetsu (Kumamoto Univ.)

Rogers–Ramanujan 完全系列と自由一般頂点代数上の自由加群 · · · · · · · 15
Rogers–Ramanujan exact sequences and free modules over free generalized vertex algebras

概 要 The notion of free modules over (generalized) vertex algebras is introduced and the Rogers–Ramanujan

recursions are realized as short exact sequences among the free modules over free generalized vertex algebras.
Some of them are equivalent to exact sequences introduced by S. Capparelli et al. Moreover, a polynomial
analogue of the Rogers–Ramanujan recursions are realized as exact sequences among free modules overb 2 spaces
certain vertex algebras. As applications, we study the following topics in the related ﬁelds: slof coinvariants LN,∞
1,0 (n) introduced by B. Feigin et al., generalized q-Fibonacci recursions and (q, z)-series
related to Urod vertex operator algebras.
7 元 良 直 輝 ( 東 大 数 理)
Naoki Genra (Univ. of Tokyo)

W 代数の段階的還元 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Reduction by stages on W-algebras

概 要 (Aﬃne) W-algebras are vertex algebras deﬁned as quantum Hamiltonian reductions of aﬃne vertex

algebras. Madsen and Ragoucy introduced secondary Hamiltonian reductions to show that some W-algebras
can be obtained as quantum Hamiltonian reductions of other W-algebras. The ﬁnite W-algebra analogs
were also conjectured by Morgan and recently proved by Thibault Juillard and the speaker. I’ll talk about
recent developments in aﬃne W-algebra cases. This is joint work with Thibault Juillard.

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13

代数学

8 若 尾 亮 太 ( 岡 山 理 大 理)

Ryota Wakao (Okayama Univ. of Sci.)

半単純スーパー・ホップ代数のある構成について · · · · · · · · · · · · · · · · · · · 10

On the construction of certain semisimple Hopf superalgebras

概 要 Up until now, constructions such as “crossed products” in low-dimensional semisimple Hopf algebras

have not been known in the context of Hopf superalgebras. In this talk, we introduce a new family ofsemisimple Hopf superalgebras and study its structure. Furthermore, we have shown that using this, themajority of semisimple Hopf superalgebras of dimension up to 10 over an algebraically closed ﬁeld of
characteristic zero can be realized. This is based on joint work with Taiki Shibata and Kenichi Shimizu.
9 ツァンシンイー (お茶の水女大理)
小 境 雄 太 ( 東 京 理 大 理)

Sin Yi Tsang (Ochanomizu Univ.)
Yuta Kozakai (Tokyo Univ. of Sci.)

Skew brace の表現について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On skew brace representations

概 要 Skew brace is an algebraic structure that was introduced in the study of the Yang–Baxter equationand it may be viewed as an extension of group. There has been a trend to try and generalize concepts andtechniques in the study of groups to that of skew braces. For example, recently factorizations, isoclinism,and Schur covers of skew braces have been studied. In this talk, we introduce the deﬁnition of skew brace
representation that is due to Letourmy–Vendramin and Zhu. We explain why the analogs of results, such as
Maschke’s theorem and Cliﬀord’s theorem, hold for skew brace representations. We also give some examples
to illustrate that irreducible representations are more diﬃcult to understand for skew braces than for groups.
10 小 川 健 翔 (広島大先進理工)

Kento Ogawa (Hiroshima Univ.)

アソシエーションスキームの代数的一般化 · · · · · · · · · · · · · · · · · · · · · · · · · 10

An algebraic generalization of association schemes

概 要 Association scheme is a generalization of ﬁnite homogeneous spaces. The structure of association

schemes induces a ﬁnite dimensional complex vector space with a matrix product, an Hadamard product,a transpose–conjugate, and a conjugate and a representation of the algebra with respect to the matrix
product. The vector space is called the Bose–Mesner algebra of the association scheme. In this talk, we
introduce a category of “algebras” that includes the Bose–Mesner algebra of association schemes as objects,
and a functor from a category of association schemes to the category of “algebras”.
14:15〜15:15

特別講演
ハイロンダオ (Univ. of Kansas)

局所特異点 : 代数的・圏論的・組合せ論的側面

Hailong Dao (Univ. of Kansas)

Local singularities: algebraic, categorical and combinatorial aspects

概 要 Commutative algebra deals with algebraic structures such as rings, ideals and modules that arise fromsystems of polynomial equations over a ﬁeld such as complex numbers or the integers. From a geometricpoint of view, one seeks to understand how far a commutative ring is from being nonsingular. There aremany approaches to doing so, and they frequently reveal fascinating connections, ever since the birth of thesubject.
In this talk, I will describe how the nature of singular rings (suitably called singularities) can be understood from diﬀerent points of views: categorical (via categories of modules and complexes), homological(via behavior of co/homological functors and projective resolutions) and combinatorial (via simplicial
co/homology). I will give examples to illustrates how such diverse view points enhance our understanding,and how many unexpected bridges between them remain to be discovered. I will also highlight the very
important contributions of Japanese mathematicians, both in the past and the present, on these topics.

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代数学

15:30〜18:00
11 堀 内淳 ( 日 本 工 大)
下 元 数 馬 ( 東 工 大 理)

Jun Horiuchi (Nippon Inst. of Tech.)
Kazuma Shimomoto (Tokyo Tech)

14

Matijevic–Roberts type theorems for certain graded rings · · · · · · · · · · · 13
Matijevic–Roberts type theorems for certain graded rings

概 要 We want to show Matijevic–Roberts type theorems for certain graded rings. As an application, we

can derive some ring theoretic properties of the assocaated graded rings.
12 石 塚仲 里

伶 ( 東 工 大 理)
渓
(プロキシマテクノロジー)(Tokyo Tech)Ryo Ishizuka(
Kei Nakazato Proxima Tech. Inc.)p 進コホモロジーを用いた Kunz の定理の混標数への一般化 · · · · · · · · · · 13

A generalization of Kunz’s theorem to mixed characteristic via p-adic
cohomology theory

概 要 The regularity of positive characteristic Noetherian rings is characterized by the faithful ﬂatness ofthe Frobenius map. This is known as Kunz’s theorem. Bhatt–Iyengar–Ma generalized the theorem tomixed characteristic by using perfectoid rings instead of Frobenius maps. In recent years, thanks to Bhatt’s
insight, the “mixed characteristic Frobenius map” has been studied via certain p-adic cohomology (prismatic
cohomology). In this talk, we will explain how the regularity of mixed characteristic rings is characterized
by the faithful ﬂatness of the Frobenius lift on prismatic cohomology.
13 東 谷 章 弘 (阪 大 情 報)
谷 光 一 郎 ( 阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)
Koichiro Tani (Osaka Univ.)

有限生成代数に対応する有限生成でないモノイドについて · · · · · · · · · · · 13

Non-ﬁnitely generated monoids corresponding to ﬁnitely generated subalgebras

概 要 The goal of this talk is to study the possible monoids appearing as the associated monoids of theinitial algebra of a ﬁnitely generated homogeneous k-subalgebra of a polynomial ring k[x1 , . . . , xn ]. Clearly,
any aﬃne monoid can be realized since the initial algebra of the aﬃne monoid k-algebra is itself. On
the other hand, the initial algebra of a ﬁnitely generated homogeneous k-algebra is not necessarily ﬁnitely
generated. In this talk, we provide a new family of non-ﬁnitely generated monoids which can be realized
as the initial algebras of ﬁnitely generated homogeneous k-algebras. Moreover, we also provide an example
of a non-ﬁnitely generated monoid which cannot be realized as the initial algebra of any ﬁnitely generated
homogeneous k-algebra.
14 土 谷 昭 善 (東 邦 大 理)
大 杉 英 史 ( 関 西 学 院 大 理)

Akiyoshi Tsuchiya (Toho Univ.)
Hidefumi Ohsugi(Kwansei Gakuin Univ.)

安定集合イデアルの 2 次生成性と Kempe 同値 · · · · · · · · · · · · · · · · · · · · · · 13

Quadratic toric rings and Kempe equivalence

概 要 In this talk, we characterize when the stable set ideal of a graph is generated by quadratic binomials byusing Kempe equivalence. Moreover, by using this characterization, we give a partial answer to a conjectureof an algebraic characterization of perfectly contractile graphs.
15 松 下 光 虹 (阪 大 情 報)
Koji Matsushita (Osaka Univ.)多項式環の Veronese 部分環と Segre 積の dual F -signature · · · · · · · · · · · 13

Dual F -signatures of Veronese subrings and Segre products of polynomial rings

概 要 We compute the dual F -signatures of certain toric rings by using combinatorial techniques. Speciﬁcally,

we calculate the dual F -signatures of Veronese subrings of polynomial rings. Moreover, we give an upperbound for the dual F -signatures of Segre products of polynomial rings and show that this upper bound is
attained in some cases.

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15

代数学

16 宮 下空 ( 阪 大 情 報)

Sora Miyashita (Osaka Univ.)

A linear variant of the nearly Gorenstein property · · · · · · · · · · · · · · · · · · 13
A linear variant of the nearly Gorenstein property

概 要 In commutative ring theory, the nearly Gorenstein property is one of several generalizations of theGorenstein property. In this talk, we introduce a new condition broader than the nearly Gorenstein property
deﬁned in (semi) standard graded rings and discuss this condition. It is a concept sharing good properties
which are similar to ones nearly Gorenstein rings satisfy.
17 張 間 忠 人 (新 潟 大 教 育)
五 十 川 読 ( 熊 本 高 専)
海大⋆)
渡 辺 純 三 (東Tadahito Harima (Niigata Univ.)
Satoru Isogawa(Nat. Inst. of Tech., Kumamoto Coll.)
Junzo Watanabe (Tokai Univ.⋆)

A binary tree of complete intersections with the strong Lefschetz property · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A binary tree of complete intersections with the strong Lefschetz property

概 要 We give a new family of complete intersections which have the strong Lefschetz property. The

family consists of (Artinian algebras deﬁned by) ideals generated by power sum symmetric polynomials ofconsecutive degrees and of certain ideals naturally derived from them. This family has a structure of abinary tree and this observation is a key to prove that all members in it have the strong Lefschetz property.
18 辻 栄 周 平 (北 教 大 旭 川)
陶 山 大 輔 ( 北 海 学 園 大)

Shuhei Tsujie (Hokkaido Univ. of Edu.)
Daisuke Suyama (Hokkai-Gakuen Univ.)

組紐多重超平面配置の対数的ベクトル場のジャクソン積分を用いた q 類似について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On a q-analogue using Jackson integrals of logarithmic vector ﬁelds ofa braid multiarrangement of hyperplanes

概 要 It is known that a basis for the logarithmic vector ﬁeld of a braid multiarrangement with constant

odd multiplicity has an integral expression by Bandlow and Musiker. It is also known that a basis for an
extended Catalan arrangement is obtained by discretizing this integral expression. In this talk, we considera q-analogue of the integral expression using Jackson integral.
19 小 島 秀 雄 (新 潟 大 理)
長 峰 孝 典 ( 日 大 理 工)
笹 川 理 湖 ( 十 日 町 高)
Hideo Kojima (Niigata Univ.)
Takanori Nagamine (Nihon Univ.)
Riko Sasagawa(Tokamachi High School)

3 変数多項式環のレトラクトについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Retracts of polynomial rings in three variables

概 要 Let A be a retract of the polynomial ring in three variables over a ﬁeld k. It is known that if

char (k) = 0 or tr.deg k A 6= 2 then A is a polynomial ring. In this talk, we give some suﬃcient conditions
for A to be the polynomial ring in two variables over k when char (k) > 0 and tr.deg k A = 2.

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代数学

20 遠 藤 直 樹 (明 大 政 治 経 済)
Naoki Endo

(Meiji Univ.)

16

Cohen–Macaulay normal Rees algebras of integrally closed ideals · · · · · 13
Cohen–Macaulay normal Rees algebras of integrally closed ideals

概 要 Let (R, m) be a regular local ring with d = dim R ≥ 2 and I an integrally closed m-primary ideal of

R. In this talk, we investigate a classical question of when the Rees algebra R(I) of I becomes a Cohen–
Macaulay normal domain. When d = 2, for every integrally closed m-primary ideal I of R, Zariski provedthat all the powers of I are integrally closed; Lipman and Teissier proved the reduction number of the ideal
I is at most one. Thus R(I) is a Cohen–Macaulay normal domain. When d ≥ 3, Goto (resp. Ciupercă)
studied the case where I is a complete intersection ideal (resp. an almost complete intersection ideal), andproved that the Rees algebras R(I) of such ideals I are Cohen–Macaulay normal domains. Inspired by theirresults, we start our investigation by going over the ideals generated by d + 2 elements.

9 月 4 日（水）第 III 会場

9:15〜10:45
21 渡 邉 英 也 (立 教 大 理)

Hideya Watanabe (Rikkyo Univ.)

量子対称対余イデアル部分代数の可積分表現 · · · · · · · · · · · · · · · · · · · · · · · 10

Integrable modules for quantum symmetric pair coideal subalgebras

概 要 One of the central objects in the representation theory of quantum groups is the integrable modules.

Although the quantum symmetric pair coideal subalgebras resemble to the quantum groups, their representation theory develops very slowly. For better understanding of the representation theory, I will introduce
the notion of integrable modules for the quantum symmetric pair coideal subalgebras. As an evidence thatour deﬁnition is the correct one, I will explain that the algebra of matrix coeﬃcients of simple integrable
modules over a quantum symmetric pair of ﬁnite type coincides with Bao–Song’s quantized coorinate ring.
(Duquesne Univ.)
22 R. Muth
T. Nicewicz(Washington and Jeﬀerson Coll.)(沖縄科学技術大)
L. Speyer(沖縄科学技術大)
L. Sutton

Robert Muth (Duquesne Univ.)
Thomas Nicewicz(Washington and Jeﬀerson Coll.)
Liron Speyer(Okinawa Inst. of Sci. and Tech. Grad. Univ.)
Louise Sutton(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

A new construction of simple modules for type A KLR algebras · · · · · · 15

A new construction of simple modules for type A KLR algebras

概 要 Cuspidal systems parameterise KLR algebra representations via root partitions π, where simple

modules L(π) arise as heads of proper standard modules. Working in aﬃne type A with an arbitrary convex
preorder, we construct explicit skew diagrams ζ(π) such that the skew Specht module S ζ(π) has simple headL(π) and a ﬁltration by proper standard modules. In this talk, I will describe this construction, and if time
permits, touch on some associated RoCK block combinatorics.

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17

代数学

23 鈴 木 武 史 (岡 山 大 理)
仲 田 研 登 ( 岡 山 大 教 育)
豊 澤 由 貴 ( 岡 山 大 自 然)

Takeshi Suzuki (Okayama Univ.)
Kento Nakada (Okayama Univ.)
Yoshitaka Toyosawa (Okayama Univ.)

Poset structure concerning cylindric diagrams · · · · · · · · · · · · · · · · · · · · · 15

Poset structure concerning cylindric diagrams

概 要 Cylindric diagrams admit structures of inﬁnite d-complete posets with natural ordering. The purposeof this talk is to provide a realization of a cylindric diagram as a subset of an aﬃne root system of type
A via colored hook lengths, and to describe its poset structure. Furthermore, the set of order ideals of acylindric diagram is described as a weak Bruhat interval of the aﬃne Weyl group.
24 狩 野 隼 輔 (東北大MathCCS)
石 橋
典 ( 東 北 大 理)

Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Tohoku Univ.)

Entropy of cluster DT transformations and the ﬁnite-tame-wild trichotomy of acyclic quivers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Entropy of cluster DT transformations and the ﬁnite-tame-wild trichotomy of acyclic quivers

概 要 The cluster algebra associated with an acyclic quiver has a special mutation loop τ , called the cluster

Donaldson–Thomas (DT) transformation, related to the Auslander–Reiten translation. In this talk, wecharacterize the ﬁnite-tame-wild trichotomy for acyclic quivers by the sign stability of τ introduced in [IK21]
and its cluster stretch factor. As an application, we compute several kinds of entropies of τ and othermutation loops. In particular, we show that the algebraic and categorical entropies of τ are commonly
given by the logarithm of the spectral radius of the Coxeter matrix associated with the quiver, and that any
mutation loop of ﬁnite or tame acyclic quivers have zero algebraic entropy.
25 内 海凌 (阪吉 永 正 彦 (阪

大

理)

大

理)

(Osaka Univ.)
Ryo Uchiumi
Masahiko Yoshinaga (Osaka Univ.)

格子への線形な有限群作用における mod q 置換表現の準多項式性について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The quasi-polynomiality of mod q permutation representations for alinear ﬁnite group action on a lattice概 要 Quasi-polynomials are periodic polynomials that appear in various problems in connection with tocounting problems. In particular, Ehrhart quasi-polynomials in Ehrhart theory and characteristic quasipolynomials in hyperplane arrangements have been studied extensively. Furthermore, in Ehrhart theory,
the equivariant Ehrhart theory, which involves counting up including group actions, has been studied. In
this talk, we show that the permutation representation associated with the mod q reduction of a lattice
acted on linearly by a ﬁnite group is a quasi-polynomial. This study is aimed at the equivariant theoryof characteristic quasi-polynomials in hyperplane arrangements. If time permits, we also discuss detailed
studies for Weyl groups.

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代数学

特別講演
淺 井 聡 太 ( 東 大 数 理)

18

11:00〜12:00
Sota Asai(Univ. of Tokyo)

傾理論の新潮流:semibrick と TF 同値

New trends in tilting theory: semibricks and TF equivalences

概 要 The representation theory of a ﬁnite-dimensional algebra A studies the module category over A. Suchalgebras natually appear in many ﬁelds of mathematics, including quiver representations, Fukaya categories,
cluster theory, quantum groups, and derived equivalences.
One of the important methods is tilting theory, which compare the module categories and their derived
categories over two non-isomorphic algebras. Tilting theory started with quiver reﬂection functors ofBernstein–Gel’fand–Ponomarev, and then Rickard introduced tilting complexes and showed that they
characterize derived equivalences. Tilting complexes were generalized to silting complexes in terms ofmutation, motivated by cluster algebras of Fomin–Zelevinsky. Since then, tilting theory has grown rapidly
by using silting complexes as a main means.
In this talk, I will survey such development of tilting theory, including newer tools semibricks and TF
equivalences introduced by me. These are now accepted by many researchers as important and fundamental
notions in tilting theory.
Semibricks are a generalization of semisimple modules in terms of Schur’s lemma. They determine abeliansubcategories of the module category closed under extensions. In my study, I deﬁned a certain ﬁnitenessconditions called left ﬁniteness for semibricks, and proved that left ﬁnite semibricks correspond bijectively
to many important notions including 2-term silting complexes.
For further study, it is important to consider the real Grothendieck group K0 (projA)R ' Rn . For each 2-term
silting complex, the g-vectors of its indecomposable direct summands give a simplicial cone in K0 (projA)R ,and these cones give a non-singular fan in K0 (projA)R called the silting fan. Since this fan is not necessarily
complete, I introduced an equivalence relation in K0 (projA)R called the TF equivalence, and showed that
the TF equivalence is indeed an extension of the silting fan.
13:00〜14:00
26 神 代 真 也 (大 阪 工 大 工)
Shinya Kumashiro(Osaka Inst. of Tech.)

When are trace ideals ﬁnite? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
When are trace ideals ﬁnite?

概 要 In this talk, we explore when a Noetherian local ring has a ﬁnite number of trace ideals. We provedthat if a ring has a ﬁnite number of trace ideals, then the Krull dimension is at most two. Furthermore, if
a given ring has positive depth and the integral closure of the ring is local, then the dimension of the ringmust be one. In that case, we explore the condition of having a ﬁnite number of trace ideals regarding thevalue.
27 木 村 海 渡 (名 大 多 元 数 理)
( SLMath )J. Lyle大 竹 優 也 ( 名 大 多 元 数 理)
( 名 大 多 元 数 理)
高橋亮
Kaito Kimura (Nagoya Univ.)(SLMath)Justin Lyle(
Nagoya Univ.)
Yuya Otake
Ryo Takahashi (Nagoya Univ.)

Ext と Tor の消滅問題の反例の存在について · · · · · · · · · · · · · · · · · · · · · · · 15

On the existence of counterexamples for vanishing problems of Ext andTor

概 要 We prove that there exist a Gorenstein equicharacteristic local unique factorization domain R having

an isolated singularity such that TorR
>0 (L, M ) = 0 does not imply that the pair (L, M ) satisﬁes Auslander’sdepth formula, and a Cohen–Macaulay local unique factorization domain S having an isolated singularity
such that Ext>0
S (N, S) = 0 does not imply the total reﬂexivity of N .

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代数学

28 齋 藤 由 宇 (静岡大創造科学技術)
松 野 仁 樹 (東京理大教養教育)
板 場 綾 子 (東京理大教養教育)(Shizuoka Univ.)
Yu Saito
Masaki Matsuno (Tokyo Univ. of Sci.)
Ayako Itaba (Tokyo Univ. of Sci.)

点スキームが可約である 3 次元 3 次 AS 正則環の分類 · · · · · · · · · · · · · · · 15

Classiﬁcation of 3-dimensional cubic AS-regular algebras whose point
schemes are reducible

概 要 It is known that a 3-dimensional cubic AS-regular algebra A is geometric, so we can write A = A(E, σ)where E is P1 × P1 or curves of bidegree (2,2) in P1 × P1 , and σ ∈ Autk E. In this talk, in terms of ageometric algebra, we determine the deﬁning relations of A in the cases that the point schemes of A are
reducible curves of bidegree (2, 2) in P1 × P1 . Also, by calculating the twisted superpotential corresponding
to A, we check the AS-regularity of A. By the results of Matsuno–Saito and our result in this talk, wegive the list of the deﬁning relations of 3-dimensional cubic AS-regular algebra whose point schemes are
reducible.
29 吉 井豊 ( 茨 城 大 教 育)

Yutaka Yoshii (Ibaraki Univ.)

単純代数群の超代数における積が定めるいくつかの線形同型写像 · · · · · · 10

Some linear isomorphisms induced by the multiplication in the hyperalgebra of a simple algebraic group

概 要 Let G be a simply connected simple algebraic group deﬁned and split over Fp and U a hyperalgebraof GFp . We report that some Fp -linear isomorphisms can be obtained from the multiplication in U , using
an Fp -linear map which splits the Frobenius endomorphism on U .

9 月 5 日（木）第 III 会場

9:30〜12:00
30 今 村 悠 希 (阪Yuki Imamura

大理)(Osaka Univ.)

A formal category theoretic approach to the homotopy theory of dg
categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A formal category theoretic approach to the homotopy theory of dg
categories

概 要 A dg category is an enriched category over the monoidal category of cochain complexes of k-vector

spaces. Dg categories possess a notion of weak equivalences called quasi-equivalences, and one can construct
the localization HodgCat of the category of dg categories with respect to quasi-equivalences. In this talk,
we introduce a 2-category (more precisely, a bicategory) that serves as a natural reﬁnement of HodgCat, andshow that it is equipped with the additional structure of a proarrow equipment. Proarrow equipments are
known as a framework for formal category theory and make it possible to talk about (co)limits in an abstract
way. Applying this theory, we explain how the pretriangulatedness of dg categories can be understood as acertain kind of completeness.
31 津 野 祐 司 (和 歌 山 工 高 専)
Yuji Tsuno(Nat. Inst. of Tech., Wakayama Coll.)

Fp 代数の上の位数 pn のある有限平坦可換群スキームに対する Grothendieck
resolution について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Grothendieck resolution for a certain ﬁnite ﬂat commutative
group scheme of order pn over an Fp -algebra

概 要 For any commutative ﬁnite ﬂat group scheme, Grothendieck constructed an embedding into somesmooth group scheme. This embedding is called the Grothendieck resolution. Let p be a prime number andn a positive integer. We consider the Grothendieck resolution for a certain ﬁnite ﬂat commutative groupscheme of order pn over an Fp -algebra.

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代数学

32 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)

20

Global properties of a Hecke ring associated with the Heisenberg Lie
algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Global properties of a Hecke ring associated with the Heisenberg Lie
algebra概 要 This study concerns (not necessarily commutative) Hecke rings associated with certain algebras anddescribes a formal Dirichlet series with coeﬃcients in the Hecke rings, which can be used to generalize
Shimura’s series. Considering the case of the Heisenberg Lie algebra, an analog of the identity for Shimura’sseries derived employing the rationality theorem, presented by Hecke and Tamagawa, is established. Moreover, this analog recovers the explicit formulae for the isomorphic zeta function and pro-isomorphic zetafunction of the Heisenberg Lie algebra shown by Grunewald, Segal and Smith.
33 星
明 考 ( 新 潟 大 理)
金 井 和 貴 ( 呉 工 高 専)
大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Kazuki Kanai (Kure Nat. Coll. of Tech.)
Aiichi Yamasaki (Kyoto Univ.)

Norm one tori and Hasse norm principle, III: Degree 16 case · · · · · · · · · 15

Norm one tori and Hasse norm principle, III: Degree 16 case

概 要 Let k be a ﬁeld, T be an algebraic k-torus, X be a smooth k-compactiﬁcation of T and Pic X be

the Picard group of X = X ×k k where k is a ﬁxed separable closure of k. Hoshi, Kanai and Yamasaki(1)[HKY22], [HKY23] determined H 1 (k, Pic X) for norm one tori T = RK/k (Gm ) and gave a necessary andsuﬃcient condition for the Hasse norm principle for extensions K/k of number ﬁelds with [K : k] ≤ 15.
Among 1954 transitive subgroups G = 16T m ≤ S16 up to conjugacy, we determine 1101 (resp. 774, 31,
37, 1, 1, 9) cases with H 1 (k, Pic X) = 0 (resp. Z/2Z, (Z/2Z)⊕2 , (Z/2Z)⊕3 , (Z/2Z)⊕4 , (Z/2Z)⊕6 , Z/4Z).
We see that H 1 (k, Pic X) = 0 implies that the Hasse norm principle holds for K/k. Moreover, we give anecessary and suﬃcient condition for the Hasse norm principle for K/k with [K : k] = 16 for 22 primitive
G = 16T m cases.
34 足 立 大 雅 (九 大 J G M I)
水 野 宏 亮 ( 名 大 多 元 数 理)舘 野 荘 平 ( 名 大 多 元 数 理)
Taiga Adachi (Kyushu Univ.)
Kosuke Mizuno (Nagoya Univ.)
Sohei Tateno (Nagoya Univ.)

Iwasawa theory for weighted graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Iwasawa theory for weighted graphs

概 要 In this talk, by generalizing Iwasawa theory for graphs initiated by Gonet and Vallières to weighted

graphs, we establish Iwasawa theory for weighted graphs. In particular, we deﬁne the Iwasawa invariants for
Zdp -covers of weighted graphs following Cuoco–Monsky and prove the analogue of Iwasawa’s class number
formula for Zdp -covers of weighted graphs, which is a generalization of results of DuBose–Vallières andKleine–Müller. These invariants also allow us to consider the analogue of Kida’s formula for Zdp -covers ofgraphs. We also provide several numerical examples.
√
35 隈 川 直 貴 (早 大 理 工) (1 + −7)/2 外不分岐 Z2 拡大について · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
水 澤
靖 ( 立 教 大 理)√
Naoki Kumakawa (Waseda Univ.) On Z2 -extensions unramiﬁed outside (1 + −7)/2
Yasushi Mizusawa (Rikkyo Univ.)
概 要 As an analogous study of Greenberg’s conjecture, we consider the vanishing of the Iwasawa invariantsof non-cyclotomic Z2 -extensions of some quartic number ﬁelds, which are unramiﬁed outside a prime√(1 + −7)/2 of the imaginary quadratic ﬁeld of discriminant −7, and give some criteria including ananalogue of a basic theorem of Ozaki and Taya.

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21代数学

36 田 島 凌 太 (九 大 J G M I)
Ryota Tajima (Kyushu Univ.)

The p-adic constant for mock modular forms and the degree of a certain
modular parameterization of CM elliptic curves. · · · · · · · · · · · · · · · · · · · 15
The p-adic constant for mock modular forms and the degree of a certain
modular parameterization of CM elliptic curves.

概 要 Let g ∈ Sk (Γ0 (N )) be a normalized newform and F be a harmonic Maass form that is good for g.

Then there exists a unique p-adic constant αg and we obtained a p-adic modular form from αg and theholomorphic part F + . When g has a complex multiplication by an imaginary quadratic ﬁeld K and p ∤ Nis split in OK , it is known that αg = 0. On the other hand, the speaker showed that αg is a p-adic unit for
an inert prime p ∤ 2N when dimC Sk (Γ0 (N )) = 1. In this talk, we consider a weight 2 normalized CM form
g with rational integer Fourier coeﬃcients and E denotes an elliptic curve corresponding to g. Then, there
exists a modular parameterization of E associated to the period lattice of g. We denote the degree of thismap by Cg . The speaker proved that Cg αg is a p-adic unit for almost all inert prime p. In this talk, I will
explain this result.
37 佐 久 川 憲 児 (信 州 大 教 育)
杉 山 真 吾 ( 金 沢 大 理 工)

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

Hilbert モジュラー形式と Siegel モジュラー形式の Hecke 固有値の代数的整数性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Integrality of Hecke eigenvalues for Hilbert and Siegel modular forms

概 要 We prove that Hecke eigenvalues for any Hilbert and Siegel modular forms are algebraic integers. Asan application, we give the growth of the ﬁelds of rationality of cuspidal automorphic representations ofGL(2d) for a prime number d with non-vanishing central L-values. We also apply the integrality of Hecke
eigenvalues for holomorphic Siegel cusp forms of general degree in order to give the growth of the Hecke
ﬁelds of those forms.
38 竹 平 航 平 (東 北 大 理)

Kohei Takehira (Tohoku Univ.)

力学系に付随した高さゼータ関数について · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the dynamical height zeta functions概 要 Height functions are fundamental tools in number theory, and their behavior itself is an intriguing

subject of study. For instance, Schanuel has demonstrated the asymptotic behavior of the number of rational
points with bounded height in N-dimensional projective space over number ﬁelds. On the other hand, ananalog of the height function in discrete dynamical systems has been deﬁned by Call and Silverman, whichis also useful for extracting arithmetic information from dynamical systems. In this talk, we will discuss thenumber of rational points with bounded dynamical height. The discussion will be conducted by constructing
a zeta function from the dynamical height function and examining it.

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代数学

12:00〜12:30

22

代数学分科会総会

14:15〜16:45
39 岩 見 智 宏 (九 工 大 工)

Tomohiro Iwami (Kyushu Inst. of Tech.)Analogous S. Bloch’s formula related to recovering conductors of (Q)conic bundles via three-dimensional Miyaoka–Yau type inequality withthird Chern classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Analogous S. Bloch’s formula related to recovering conductors of (Q)conic bundles via three-dimensional Miyaoka–Yau type inequality withthird Chern classes

概 要 For three-dimensional extremal neighborhood (X, C) ⊂ C2 with C reducible, the author had stud-

ied three-dimensional Miyaoka–Yau type inequality with (associated) third Chern classes, abbreviated as(MY)3,c3 , or its variant one driven by S 2 Ω1X , abbreviated as (MY)3,c3 ,S 2 ([I.2018Mar, I.2019Sep, I.2020Sep,f
I.2021Sep]), and also investigated related Intermediate Jacobian IJ(X,C) in order to study period spcaesfor (MY)3,c3 or (MY)3,c3 ,S 2 ([I.2022Mar]). In such serial studies,the author gave strong approximationffor integral structure of IJ(X,C) ([I.2022Sep, I.2023Mar]) and also gave alternative descriptions bothfor [Iskovskikh 1987] and [S.Mori-Yu.Prokhorov 2021] about rationality of (Q-)conic bundles ([I.2023Sep]),
by introducing conductors based on [I.2018Mar, I.2019Sep, I.2020Sep, I.2021Sep, I.2022Mar, I.2022Sep,
I.2023Mar], and moreover, as an application, gave canonical embedding of Clemens–Griﬃths–Kuznetsov
components ([I.2024Mar]). Based mainly on [I.2023Sep, I.2024Mar], the author present relations between
Chern classes in (MY)3,c3 or (MY)3,c3 ,S 2 and related Chow groups (with ﬁltrations), which is possible to beformed as analogous S. Bloch’s conductor formula for [S.Bloch 1987, K.Kato-T.Saito 2004], and also as anextended one, in this talk.
40 天 野 通 大 (明 星 大 教 育)Michio Amano (Meisei Univ.)

On the injectivity of certain homomorphisms between extensions of Gb(λ)
b m over a Z(p) -algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
by G
On the injectivity of certain homomorphisms between extensions of Gb(λ)
b m over a Z(p) -algebraby Glb a to G
b m . And let ψ (l) : Gb(λ) → Gb(λp ) beb(λ) be a formal group scheme which deforms G
概 要 Let G
the l-th Frobenius-type homomorphism determined by λ. We show that the homomorphism (ψ (l) )∗ :plb m ) → H 2 (Gb(λ) , G
b m ) induced by ψ (l) is injective over a Z(p) -algebra.
H 2 (Gb(λ ) , G
0

41 後 藤0

倫 (大 阪 工 大 R D) [ Marking-weighted tree stratiﬁcation of geometric moduli spaces of dynamical systems over P1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Rin Gotou (Osaka Inst. of Tech.)Marking-weighted tree stratiﬁcation of geometric moduli spaces of dynamical systems over P1

概 要 The moduli space of the dynamical systems ratd := Ratd /PGL2 is the quotient of the moduli space ofself-rational maps of degree d on P1 with respect to the conjugation action of Aut(P1 ) = PGL2 . We consider
compactiﬁcations of ratd respecting geometric behavior of dynamical systems. We give invariant-theoretic
constructions of compactiﬁed moduli spaces and a stratiﬁcation of the moduli space using marking-weighted
trees, analogous to the moduli space M 0,n of stable rational curves.
42 高 田 佑 太 (東 大 数 理)
Yuta Takada (Univ. of Tokyo)

Picard 数 2 の K3 曲面の自己同型の力学的次数 · · · · · · · · · · · · · · · · · · · · · 15
Dynamical degrees of automorphisms of K3 surfaces with Picard number
2

概 要 We show that there exists an automorphism of a projective K3 surface with Picard number 2 suchthat the trace of its action on the Picard lattice is 3. Together with a result of K. Hashimoto, J. Keum andK. Lee, we determine the set of dynamical degrees of automorphisms of projective K3 surfaces with Picard
number 2.

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代数学

43 髙 津 大 樹 (東京理大創域理工)

Taiki Takatsu (Tokyo Univ. of Sci.)

K3 曲面の自己同型群とその実質的コホモロジー次元について · · · · · · · · 15
On automorphism groups of K3 surfaces and their virtual cohomologicaldimension

概 要 In this talk, we discuss the virtual cohomological dimension of automorphism groups of K3 surfaces.

We apply the Bestvina–Mess type formula for relatively hyperbolic groups, which is established by Tomohiro
Fukaya, to automorphism groups of K3 surfaces, and we show that the virtual cohomological dimensionof automorphism groups of K3 surfaces determined by the covering dimension of the blown-up boundaries
associated with their ample cones.
44 碓 氷久 ( 群 馬 工 高 専)

Hisashi Usui
(Gunma Nat. Coll. of Tech.)

標数 11 の超特異楕円 K3 曲面のモーデル・ヴェイユ格子の生成元の例· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An example of the explicit generators of the Mordell–Weil lattice of asupersingular elliptic K3 surface in characteristic 11

概 要 We consider the Mordell–Weil lattice of the elliptic curve

E (12) : y 2 = x3 + t12 + 1
deﬁned over k(t), where k = F112 = F11 [s]/(s2 + 1). The associated elliptic surface is a supersingular K3
surface of Artin invariant σ0 = 1. So the discriminant of the Néron–Severi lattice is −char(k)2σ0 = −112 .
We give the explicit generators of the Mordell–Weil lattice and the Néron–Severi lattice of the associatedelliptic surface.
謙 (東 工 大 理) [ K3 曲面上の高次 Chow サイクルについて · · · · · · · · · · · · · · · · · · · · · · · · · 1545 佐 藤Ken Sato(Tokyo Tech)

On higher Chow cycles on K3 surfaces

概 要 The higher Chow group CHp (X, q) is a generalization of the classical Chow group. It satisﬁes many

interesting properties, but their structures are still mysterious for almost all varieties when p > 1. In thistalk, I will explain an explicit construction of higher Chow cycles in CH 2 (X, 1) on some K3 surfaces X
with a non-symplectic involution, or a purely non-symplectic automorphism of order 4. By computing
their images under the regulator map, I show that for very general cases, these cycles is non-torsion in
CH2 (X, 1)ind , which is the quotient of CH2 (X, 1) by the images of the intersection product maps. The key
for the proof is to ﬁnd a convenient variant of Jacobians for higher cycles. Some examples in this talk are
obtained in a joint work with Shohei Ma.
46 南

範 彦 (大和大理工・名工大⋆)Norihiko Minami(Yamato Univ./Nagoya Inst. of Tech.⋆)

整 Hodge/Tate 予想反例に反映される代数幾何的不変量 · · · · · · · · · · · · · 15

Algebro-geometric invariant reﬂected in counter-examples the integral
conjectues of Hodge and Tate

概 要 Some algebro-geometric invariant interpreration is given for the obvious invariant which measures thefailure of the integral conjectures of Hodge and Tate. In o corollary of our main theorem, some applicationsof the three dimensional minimal model program show up to impose some algebro-geomtric restriction tocounter examples of the integral Hodge conjecture for complex projective maifolds of any dimension equalor larger than three.

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代数学

特別講演
橋 詰 健 太 ( 新 潟 大 理)

偏極化された対数的対の極小モデル理論について

Kenta Hasizume (Niigata Univ.)

On minimal model theory for polarized log pairs

24

17:00〜18:00

概 要 Minimal model theory is a fundamental tool to study birational geometry. Especially, the theory

is indispensable to partial resolutions of singularities and moduli problems. In 2010, the breakthroughhas been made by Birkar–Cascini–Hacon–McKernan. They have established the minimal model theory forpolarized Kawamata log terminal pairs. After that, a remarkable progress in the log canonical case has been
made by Fujino, Birkar, and Hacon–Xu. In this talk, I will introduce a recent development of the minimalmodel theory for polarized log pairs.

9 月 6 日（金）第 III 会場

9:15〜10:45
47 鳥 居猛 ( 岡 山 大 理)
中 本 和 典 ( 山 梨 大 医)Takeshi Torii (Okayama Univ.)
Kazunori Nakamoto(Univ. of Yamanashi)

3 次行列環の部分代数のモジュライ (3) · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The moduli of subalgebras of the full matrix ring (3)概 要 We describe the moduli of 4-dimensional subalgebras of the full matrix ring of degree 3. We showthat the moduli scheme has three irreducible components, whose relative dimensions over Z are 5, 2, 2,
respectively.
大理)
48 齋 藤 琢 弥 (北セッテパネーラシモーナ( Torino Univ. )ダスプラギアTakuya Saito (Hokkaido Univ.)
Simona Settepanella (Torino Univ.)
Pragnya Das

Recent developments in the combinatorics of discriminantal arrangements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Recent developments in the combinatorics of discriminantal arrangements

概 要 A hyperplane is a linear subspace of codimension 1, and a ﬁnite set of hyperplanes is called a

hyperplane arrangement A. A discriminantal arrangement B(A) is a hyperplane arrangement induced in
the space of parallel translations of a given arrangement A. In this presentation, we will discuss recent
developments in the combinatorics of discriminantal arrangements.
49 東 谷 章 弘 (阪 大 情 報)
工大)中 島 規 博 (名Akihiro Higashitani (Osaka Univ.)
Norihiro Nakashima(Nagoya Inst. of Tech.)

B 型 Shi 配置の制限の特性準多項式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Characteristic quasi-polynomials of restrictions of Shi arrangements oftype B概 要 Kamiya, Takemura, and Terao introduced a characteristic quasi-polynomial which enumerates thenumbers of elements in the complement of hyperplane arrangements modulo positive integers. We computethe characteristic quasi-polynomials of restrictions of the Shi arrangement of type B by one given hyperplane.
As a corollary, we determine when the characteristic quasi-polynomials of deletions of the Shi arrangementof type B are polynomials. This implies the partial solution for the conjecture regarding period collapse.

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代数学

50 小 脇 修 和 (阪 大 情 報)

Nobukazu Kowaki (Osaka Univ.)

Tropical hyperplane arrangements and combinatorial mutations of thematching ﬁeld polytopes of Grassmannians · · · · · · · · · · · · · · · · · · · · · · · · 15
Tropical hyperplane arrangements and combinatorial mutations of thematching ﬁeld polytopes of Grassmannians

概 要 A sequence of combinatorial mutations of matching ﬁeld polytopes preserves the property of giving

rise to a toric degeneration of Grassmannians. In this paper, we ﬁnd a way to check that two matching ﬁeld
polytopes are combinatorial mutation equivalence using tropical hyperplane arrangements, “literally at a
glance”. Our way can prove that block diagonal matching ﬁelds are combinatorial mutations equivalent todiagonal matching ﬁelds. This is one of main results in [2]. Our result can be regarded as a generalizationof that result.
51 長 峰 実 央 (北大理)

Mao Nagamine (Hokkaido Univ.)A-hypergeometric series with parameters in the core · · · · · · · · · · · · · · · · 15
A-hypergeometric series with parameters in the core

概 要 We discuss conditions for applying Frobenius’s method to A-hypergeometric systems introduced by

Okuyama and Saito. We prove that, when the negative support of a fake exponent v with respect to a
generic weight w is included in the core, we can construct all A-hypergeometric series with exponent v in
the direction w by Frobenius’s method.
11:00〜12:00

特別講演

齋 藤 耕 太(筑波大数理物質・上智大理工)

数列の整数部分および小数部分の数論的性質

Kota Saito(Univ. of Tsukuba/Sophia Univ.)

Arithmetic properties of the integer and fractional parts of a sequence

概 要 For every real number x, we deﬁne bxc as the integer part of x, and {x} = x − bxc as the fractionalpart of x. The speaker will talk about a series of studies on the integer parts and fractional parts ofsequences. First, we will examine bnα c (n = 1, 2, . . .). This sequence is called the Piatetski-Shapiro
sequence (with exponent α). In this research, we considered the problem of whether there exists α > 3such that bpα c + bq α c = brα c has a solution (p, q, r) of positive integers. Considering Fermat’s equation, we
could expect that there is no such α. However, by collaborating with Toshiki Matsusaka, we ﬁnd inﬁnitely
many such α’s. The speaker plans to introduce other studies and results on Diophantine equations involving
integer parts.
The speaker next will discuss the randomness of the b-adic expansion of an algebraic irrational number
α. This problem is essentially equivalent to examining the distribution of {bn α} (n = 1, 2, . . .). Borel
conjectured that the b-adic expansion of an algebraic irrational number would be suﬃciently random. For
instance, if Borel’s conjecture is true, then the probability that the digit 1 appears in the binary expansion of√
2 should be 1/2 like a coin toss. However, even the positivity of this probability is unknown. Despite thesediﬃculties, by collaborating with Yuya Kanado, we revealed a strong relationship between the randomnessof {bn α} and the Riemann zeta function. In other words, we succeeded in linking two ﬁelds of research that
had been studied independently through a completely diﬀerent approach.
nLastly, we will discuss bA3 c (n = 1, 2, . . .). In 1947, Mills constructed a real number A > 1 such that
this sequence is always prime. The smallest such A > 1 is called Mills’ constant. Although there may be
diﬀerent opinions, we could say that the question of whether Mills’ constant is irrational has been unsolvedfor over 70 years. However, the speaker has successfully proved the irrationality of Mills’ constant by using
a simple idea. If time permits, the speaker will also discuss a partial result of its transcendency.

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代数学

26

14:15〜17:30
大
理)
52 任
鑫 (阪
(
小 木 曽 岳 義 城 西 大 理)
宮 本 賢 伍 ( 茨 城 大 工)
和 久 井 道 久 (関西大システム理工)
柳 川 浩 二 (関西大システム理工)(Osaka Univ.)
Xin RenTakeyoshi Kogiso (Josai Univ.)
Kengo Miyamoto (Ibaraki Univ.)
Michihisa Wakui (Kansai Univ.)
Kohji Yanagawa (Kansai Univ.)

Arithmetic on q-deformed rational numbers · · · · · · · · · · · · · · · · · · · · · · · 15

Arithmetic on q-deformed rational numbers

概 要 The q-deformed rational numbers were introduced by Morier-Genoud and Ovsienko based on continued

fractions and Euler q-integers. This work is related to many directions including Teichmüller spaces, the2-Calabi–Yau category of type A2 , the Markov–Hurwitz approximation theory, the modular group andPicard groups, the Jones polynomials of rational knots, and combinatorics on fence posets. In this talk,we give an arithmetic property on q-deformed rational numbers. For two rational numbers with the samedenominator, their q-deformed denominator polynomials may not be equal. We give a suﬃcient condition
for their denominator polynomials to be equal.
53 行 田 康 晃 (東 大 数 理)
丸 山 修 平 ( 金 沢 大 理 工)
佐 藤 悠 介 ( 大 阪 工 大 工)

Yasuaki Gyoda (Univ. of Tokyo)
Shuhei Maruyama (Kanazawa Univ.)
Yusuke Sato (Osaka Inst. of Tech.)

一般化マルコフ数の SL(2, Z) 行列化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

SL(2, Z)-matrixization of generalized Markov numbers

概 要 A k-generalized Markov number refers to an integer that appears in the positive integer solutions of

the k-generalized Markov equation x2 + y 2 + z 2 + k(yz + zx + xy) = (3 + 3k)xyz. The k-generalized Markov
equation possesses an algorithm that generates two distinct positive integer solutions from a single positive
integer solution, forming a tree structure through this algorithm. In this talk, we will introduce two typesof elements in SL(2, Z) that have a k-generalized Markov number as their (1, 2)-entry and show how theseelements preserve the tree structure of the positive integer solutions of the k-generalized Markov equation.
54 後 藤 新 裕 (九 大 数 理)
Akihiro Goto

(Kyushu Univ.)

On some values which do not belong to the image of Ramanujan’s taufunction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On some values which do not belong to the image of Ramanujan’s taufunction

概 要 In 1947, Lehmer conjectured that Ramanujan’s τ -function never vanishes, where the function τ :Z>0 −→ Z is deﬁned by
x

Y
n≥1

(1 − xn )24 =Xτ (n)xn .

n≥1This conjecture is still open.
It is natural to consider whether any given integer belongs to the image of τ -function. Recently, it is provedthat ±`, ±2`, ±2`2 are not τ -values, where ` < 100 is an odd prime by Balakrishnan, Ono, Craig andmany other people. The speaker proved that ±`, ±2`, ±4`, ±8` are not τ -values except for 14 cases, where` < 1000 is an odd prime.

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代数学

55 菅 野隼 ( 東 北 大 理)

Hayato Kanno (Tohoku Univ.)

一般レベルの多重 Eisenstein 級数の Fourier 級数展開と Goncharov の余
積公式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Fourier expansion of multiple Eisenstein series of arbitrary level
and Goncharov’s coproduct formula

概 要 Multiple Eisenstein series is a holomorphic function on the upper half plane, which is a generalizationof double Eisenstein series introduced by Gangl, Kaneko and Zagier. As a connection to multiple zeta value,
Bachmann and Tasaka showed that the Fourier expansion of multiple Eisenstein series can be obtained fromthe coproduct of formal iterated integrals corresponding to multiple zeta values. They also constructed
shuﬄe regularized multiple Eisenstein series. For general level, Yuan and Zhao studied double Eisensteinseries of level N and obtained analogous results of Gangl, Kaneko and Zagier. In this talk, we introduce
multiple Eisenstein series of level N and expand the results of Bachmann and Tasaka for arbitrary level.
56 佐 々 木 義 卓 (東 北 学 院 大 工)
Yoshitaka Sasaki(Tohoku Gakuin Univ.)

多重 Mahler 測度と多重 T 値について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On multiple Mahler measures and multiple T values

概 要 I plan to talk about relations between multiple Mahler measures of (X − 1)/(X + 1) and multiple zeta

values of level 2.
57 安 沢 拓 真 (名 大 多 元 数 理)
舩 倉 秀 貴 ( 名 大 多 元 数 理)

Takumi Anzawa (Nagoya Univ.)
Hidetaka Funakura (Nagoya Univ.)

q-Fibonacci 数列の合同式とある種の超越性について · · · · · · · · · · · · · · · · 15
Certain congruence of q-Fibonacci sequence and related ﬁnite transecendental numbers

概 要 J. Rosen(’20) proposes a notion of algebraic numbers in the algebra A related with the ﬁnite multiple

zeta values. In this talk, we focus on the q-Fibonacci sequence and prove its speciﬁc congruence, fromwhich we deduce a construction of certain ﬁnite transcendental numbers. This research is a joint work withHidetaka Funakura.
58 荻 原 芙 美 (上 智 大 理 工)
鈴 木 雄 太 ( 立 教 大 理)
(Sophia Univ.)(Rikkyo Univ.)

Fumi Ogihara
Yuta Suzuki

Hardy–Littlewood 予想の変形版に対する表現関数の短区間における和の評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the short interval average of the representation function for a variantof the Hardy–Littlewood conjecture

概 要 Let R(N ) be the number of representations of N as a sum of a prime and a square-full number

weighted with logarithmic function. We call the function such as R(N ) the representation function. In thistalk, we show that an asymptotic formula for the sum of R(N ) over the short interval X < N ≤ X + H
1holds when X 2 +ε ≤ H < X 1−ε .
59 戸 澗 勇 一 郎 (名 大 多 元 数 理)
Yuichiro Toma (Nagoya Univ.)

実指標で捻った Möbius 関数の高次平均について · · · · · · · · · · · · · · · · · · · 10

On the averages of quadratic twists of the Möbius function

概 要 We consider the moments of quadratic twists of the Möbius function. By combining the estimate ofquadratic character sums and the multivariable Tauberian Theorem, we give unconditional results for their
asymptotic behaviors.
60 吉 田 裕 哉 (名工大)Yuuya Yoshida (Nagoya Inst. of Tech.)

Piatetski-Shapiro 列に含まれる線型方程式の解の個数 · · · · · · · · · · · · · · · 15
The numbers of solutions of linear equations in Piatetski-Shapiro sequences

概 要 For α ≥ 1, denote by PS(α) the set {bnα c : n ∈ N}, which is called a Piatetski-Shapiro sequencewhen α > 1 is non-integral. In this talk, we give asymptotic formulas for the number of solutions of linear
equations in PS(α). We handle the three equations y − x = d, x + y = N , and x + y = z.

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代数学

61 金 堂 優 哉 (名 大 多 元 数 理)齋 藤 耕 太(筑波大数理物質・上智大理工)Yuya Kanado (Nagoya Univ.)
Kota Saito(Univ. of Tsukuba/Sophia Univ.)28

代数的数の正規性と Riemann ゼータ関数 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Normality of algebraic numbers and the Riemann zeta function

概 要 A real number α is called simply normal to base b if its base-b expansion has each digit appearing withaverage frequency tending to 1/b. Moreover, α is called normal to base b if α is simply normal to base bh
for all natural numbers h. In this talk, we discuss a relation in between the normality of algebraic numbers
and a mean value of the Riemann zeta function on arithmetic progresstions. As a consequence, we show
that
1
lim
N →∞ log NX
1≤|n|≤N

2πinζ −k +
log b



log α

e2πin log b=0
nk+1

holds for all non-negative integers k if and only if α is normal to base b. This is joint work with Kota Saito(University of Tsukuba).
62 山 田 智 宏 (神 戸 大・阪 大)
Tomohiro Yamada(Kobe Univ. / Osaka Univ.)

On an analogue of superperfect numbers involving both ordinary andinﬁnitary divisors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On an analogue of superperfect numbers involving both ordinary andinﬁnitary divisors

概 要 For integers k = 0, 1, . . ., k-ary divisors of an integer N are deﬁned. 0-ary divisors are ordinary

divisors of N . A divisor d of an integer N is k-ary if the greatest common (k − 1)-ary divisor of d and N/dis one and inﬁnitary if d is a k-ary divisor of N for suﬃciently large k. We write σ (k) (N ) and σ (∞) (N ) for
the sum of (positive) k-ary divisors and inﬁnitary divisors of N respectively. We determine all odd solutions
N to σ (∞) (σ(N )) = 2N .
63 北 島 雅 也 (名 大 多 元 数 理)

Masaya Kitajima (Nagoya Univ.)

円を一般化した閉曲線の格子点問題と対応する一般化 Bessel 関数 · · · · · 15

Generalized Bessel functions corresponding to lattice point problems ofgeneralized circles

概 要 The lattice point problems of the p-circles, which generalized circles for positive real numbers p, havebeen solved for approximately p more than 3, based on the series representation of the error term using thegeneralized Bessel functions by E. Krätzel and the results of G. Kuba. On the other hand, for the cases
0 < p < 2, the method via this series representation cannot make progress. Therefore, in this talk, I will
discuss the speaker’s result that certain functions closely related to the problems can be displayed as a series
by a newly generalized Bessel function based on the property p-radial, generalization of spherical symmetry,and highlight the possibility that attempts to solve the problems via this display are suitable especially forthe cases 0 < p < 2.

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29

幾何学

幾

何

9 月 3 日（火）学
第 I 会場

9:30〜11:45
1 伊 敷 喜 斗 (都 立 大 理) [ 距離関数の空間はベールである · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yoshito Ishiki (Tokyo Metro. Univ.)

Spaces of metrics are Baire

概 要 For a metrizable space, we consider the space of all metrics generating the same topology of themetrizable space, and this space of metrics is equipped with the supremum metric. In this paper, forevery metrizable space, we establish that the space of metrics on the metrizable space is Baire. We also
show that the set of all complete metrics is comeager in the space of metrics. Moreover, we investigate
non–Archimedean analogues of these results.
2 軸 丸 芳 揮 (東洋大情報連携)

Yoshiki Jikumaru (Toyo Univ.)

薄肉シェルの変形に現れる対称性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Symmetries in the linear theory of the deformation of thin shells

概 要 In this talk, we show that symmetries, which are known in the theory of integrable systems, naturally

appeared in the classical linear theory of deformations of thin shells. Our result shows that if the middle
surface of a shell becomes ‘integrable’, inﬁnitely many deformations exist that have no shear strains andtwisting of the coordinate lines.
3 佐 藤 健 治 ( 玉 川 大 工)
Kenzi Satô (Tamagawa Univ.)

球面単体と双曲単体のある重心の内在的特徴付け · · · · · · · · · · · · · · · · · · · 15

A intrinsic characterization of a centroid of a spherical or hyperbolic
simplex

概 要 The centroid of a planar triangle satisﬁes 6 properties, but the point with properties are divided into

4 points for a spherical or hyperbolic triangle. One of them, the center of gravity, was deﬁned by using
Euclidean or Minkowski space contains the sphere or the hyperbolic plane, respectively, but we have foundan intrinsic characterization of it. It can be extended to higher dimensional cases.
4 佐 藤 雄 一 郎 (早 大 G E C )露 木 孝 尚(北海道情報大経営情報)
Yuichiro Sato (Waseda Univ.)
Takanao Tsuyuki(Hokkaido Information Univ.)

一般次元における真空アインシュタイン方程式の空間的等質解 · · · · · · · · 15

Spatially homogeneous solutions of vacuum Einstein equations in general dimensions

概 要 In this talk, we give new solutions to the vacuum Einstein equations without cosmological constantusing almost abelian Lie groups. We consider globally hyperbolic spacetimes in which almost abelian Liegroups act on the Cauchy hypersurfaces isometrically and simply transitively. Previous studies and our
results show that such solutions are completely found for Lie groups with zero-dimensional moduli spaces ofleft-invariant Riemannian metrics. For the simplest solution, we show that each of the spatial dimensions
cannot expand or contract simultaneously in the late-time limit.

2024/08/21 作成
幾何学

5 藤 森 祥 一 (広島大先進理工)
川 上
裕 ( 金 沢 大 理 工)
國 分 雅 敏 ( 東 京 電 機 大 工)

Shoichi Fujimori (Hiroshima Univ.)
Yu Kawakami (Kanazawa Univ.)
Masatoshi Kokubu (Tokyo Denki Univ.)30

同心円状または平行直線状の等 K 線をもつ曲面について · · · · · · · · · · · · · 15

Surfaces with concentric or parallel K-contours

概 要 Surfaces with concentric K-contours and parallel K-contours in Euclidean 3-space are deﬁned. Crucial

examples are presented and characterization of them are given.
6 笹 原 優 大 ( 都 立 大 理)

Yuta Sasahara (Tokyo Metro. Univ.)

擬 Riemann 空間形内の指数 2 の 4 次元等径超曲面 · · · · · · · · · · · · · · · · · · 15

4-dimensional isoparametric hypersurfaces of index 2 in the pseudoRiemannian space forms

概 要 We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-

Riemannian space forms. We give a classiﬁcation of hypersurfaces of index 2 with respect to a pair ofa shape operator and a metric. Therefore, we can deﬁne types of isoparametric hypersurfaces of index
2 concerning the classiﬁcation. In this talk, we give a few examples of some types. Moreover, we showthat there exist no isoparametric hypersurfaces of index 2 whose shape operators have complex principal
curvatures in certain cases.
7 今 井

淳 ( 千 葉 大 理)

Jun O’Hara(Chiba Univ.)

多様体の留数と曲率 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Residues of manifolds and curvatures

概 要 We show that, depending on the parity of the dimension, the energy or the residue of a closed

submanifold of Euclidean space or a compact body is invariant under Mobius transformations. We also
express the scalar curvature and the squared norm of the mean curvature vector by local (weighted) residues,
and the mean curvature of the boundary of a compact body by local relative residues.
14:15〜16:15
8 長 屋 拓 暁 (広島大先進理工)

Hiroaki Nagaya (Hiroshima Univ.)

Bornological proper action について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A study of bornological proper actions

概 要 We study discontinuous groups in non Riemannian geometry, inspired by Toshiyuki Kobayashi’s 1980s

work. Unlike in Riemannian geometry, discrete groups of isometries acting non Rimeannian spaces do notalways become discontinuous groups. However, adding the condition of proper action, discrete groups ofisometries become discontinuous groups. Thus, it is important to give a properness criterion. There areconcepts called weakly proper and CI which are related to proper. Generally, proper, weakly proper, and CI
weaken in that order. In 2006, Yoshino show under which cases these conditions become equivalent using
the theory of topologies. We rewrite these conditions from the perspective of bornologies and we show inwhich cases those conditions are equivalent using the theory of bornologies.
9 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.)

Recent progress on twisted Fock representations of complex Grassmannians · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Recent progress on twisted Fock representations of complex Grassmannians

概 要 The Twisted Fock representation of Kähler manifold is the Fock representation deﬁned by Karabegov’s

star product with separation of variables, introduced by Sako–Suzuki–Umetsu. As an approach to theoreticalphysics, it is known that twisted Fock representations can be applied to the formulation of noncommutative
gauge theories in the context of deformation quantization. In this talk, we will present the results obtainedso far in our study of the twisted Fock representations of complex Grassmannians and their application tononcommutative ﬁeld theories.

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31

幾何学

10 小 林 和 志 (三 重 大 教 育)

Kazushi Kobayashi (Mie Univ.)

複素トーラス上における一般化された複素構造に対するある B-場変形について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On a B-ﬁeld transform of generalized complex structures over complex
tori

概 要 Let (X n , X̌ n ) be a mirror pair of an n-dimensional complex torus X n and its mirror partner X̌ n .

Then, by SYZ transform, we can construct a holomorphic line bundle with an integrable connection fromeach pair of a Lagrangian section of X̌ n → Rn /Zn and a unitary local system along it, and those holomorphic
line bundles with integrable connections forms a dg-category DGX n . In this talk, we focus on a certain
B-ﬁeld transform of the generalized complex structure induced from the complex structure on X n , andinterpret it as the deformation XGn of X n by a ﬂat gerbe G. Moreover, we construct the deformation of
DGX n associated to the deformation from X n to XGn , and also discuss the homological mirror symmetry
between XGn and its mirror partner on the object level.
11 山 本 悠 登 (理化学研iTHEMS)
Yuto Yamamoto(RIKEN)

Gross–Siebert プログラムと非アルキメデス的 SYZ ファイブレーション· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Gross–Siebert program and non-archimedean SYZ ﬁbrations

概 要 For a maximally degenerate Calabi–Yau variety, the Berkovich retraction associated with a (good)minimal dlt model is regarded as an SYZ ﬁbration in non-archimedean geometry. In general, the integral
aﬃne structure induced on the base space of the ﬁbration diﬀers from the one deﬁned for the dual
intersection complex of a toric degeneration in the Gross–Siebert program. In this talk, using tropicalgeometry, we construct non-archimedean SYZ ﬁbrations whose bases are integral aﬃne manifolds appearing
in the Gross–Siebert program for Calabi–Yau complete intersections of Batyrev–Borisov.
12 秦 泉 寺 雅 夫 (岡 山 大 自 然)
桑 田
健 ( 香 川 高 専)

Masao Jinzenji (Okayama Univ.)
Ken Kuwata(Kagawa Nat. Coll. of Tech.)

Elliptic virtual structure constants and generalizations of BCOV-Zinger
formula to projective fano hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Elliptic virtual structure constants and generalizations of BCOV-Zinger
formula to projective fano hypersurfaces

概 要 In this talk, we propose a recipe for B-model computation of genus 1 Gromov–Witten invariants ofCalabi–Yau and Fano Projective Hypersurfaces. Our formalism can be applied equally to both Calabi–Yauand Fano cases. In Calabi–Yau case, drastic cancellation of terms used in our formalism occurs and it
results in another representation of BCOV-Zinger formula for projective Calabi–Yau hypersurfaces.
13 宮 武 夏 雄 (東北大MathCCS)

Natsuo Miyatake (Tohoku Univ.)

巡回 Higgs 束上の調和計量の相互の揃わなさの度合いの定量化とその評価· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Quantiﬁcation and evaluation in the degree of mutual misalignment of
harmonic metrics on cyclic Higgs bundles

概 要 Let X be a Riemann surface and KX → X the canonical bundle. For each integer r ≥ 2, each1/2rq ∈ H 0 (KX), and each choice of the square root KXof the canonical bundle, we canonically obtain a

Higgs bundle, which is called a cyclic Higgs bundle. In this talk, I will introduce a function called entropy
that quantiﬁes the degree of mutual misalignment of harmonic metrics on cyclic Higgs bundles and provide
an estimate for the entropy.

2024/08/21 作成
幾何学

16:30〜17:30
入 谷

特別講演
大
寛 (京

Hiroshi Iritani

32理) [ 爆発の量子コホモロジー(Kyoto Univ.)

Quantum cohomology of blowups

概 要 Quantum cohomology is a deformation of the cohomology ring of a smooth projective variety deﬁned

by counting rational curves. The relationship between quantum cohomology and birational geometry has
attracted much interest. In this talk, I will explain the following decomposition theorem for quantum
e of X along a smooth subvariety Z is
cohomology of blowups: the quantum cohomology of the blowup X
a direct sum of the quantum cohomology of X and (codim(Z) − 1) copies of the quantum cohomology of
Z. The proof idea is based on a D-module version of Teleman’s conjecture, which relates the quantum
cohomology of a GIT quotient to the equivariant quantum cohomology of the original manifold via Fouriertransformation.

9 月 4 日（水）10:00〜10:15

第 I 会場2024 年度日本数学会幾何学賞授賞式

10:20〜11:20

2024 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
今 野 北 斗 (東 大 数 理) Diﬀeomorphism group and gauge theory

Hokuto Konno (Univ. of Tokyo)

Diﬀeomorphism group and gauge theory

概 要 The group of diﬀeomorphisms of a given smooth manifold is a fundamental object of study for topolo-

gists and geometers. One of the major advances in topology over the past decade concerns diﬀeomorphismgroups of higher-dimensional manifolds, led by many researchers such as Galatius and Randal-Williams.
On the other hand, it has been well-known since the last century that 4 is a special dimension in theclassiﬁcation of manifolds. Special phenomena are typically described in terms of comparisons between the
topological and smooth categories, and they are detected using gauge theory. In recent years, advances ingauge theory for families have revealed that special phenomena in dimension 4 also occur for diﬀeomorphismgroups in various ways, contrasting with recent results in higher dimensions. I will survey these new special
phenomena in dimension 4, also from the perspective of comparisons between the topological and smoothcategories.
12:50〜13:50
細 野

2024 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
忍 (学 習 院 大 理) カラビ・ヤウ多様体の族とミラー対称性

Shinobu Hosono (Gakushuin Univ.)

Families of Calabi-Yau manifolds and mirror symmetry

概 要 Mirror symmetry of Calabi–Yau manifolds is a mysterious symmetry that interchanges the complex

geometry of one Calabi–Yau manifold with the symplectic geometry of another Calabi–Yau manifold, calleda mirror manifold. 30 years after its discovery, we now have fascinating proposals, such as homologicalmirror symmetry and SYZ geometric mirror construction, to describe the symmetry mathematically. In
this talk, however, I will describe this symmetry in terms of two diﬀerent, and classical, nilpotent linear
actions associated with a Calabi–Yau manifold. One is the Lefschetz action in the hard Lefschetz theorem(which I call A-structure), and the other is a certain monodromy action that arises from a family of
Calabi–Yau manifolds (B-structure). I deﬁne mirror symmetry as the symmetry which exchanges these
two structures. The general existence of a mirror Calabi–Yau manifold for a given Calabi–Yau manifold
is still an open problem. However, mirror symmetry deﬁned by these classical actions motivates us to
study/construct families of Calabi–Yau manifolds, and to look into the boundary points where Calabi–Yau
manifolds degenerate in a speciﬁc way. Based on my collaborations with Hiromichi Takagi since 2010, I
will present interesting families of Calabi–Yau threefolds which are parametrized by two-dimensional toricvarieties.

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33

幾何学

9 月 5 日（木）第 I 会場

9:30〜11:45
14 山 口 健 太 朗 (都 立 大 理)
Kentaro Yamaguchi(Tokyo Metro. Univ.)

アフィン部分空間から定まる Delzant 多面体の境界と角付き部分多様体について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Submanifolds with boundary and corners in Delzant polytopes associated to aﬃne subspaces

概 要 We studied the closure of a complex subtorus in a symplectic toric manifold, which is referred to asa torus-equivariantly embedded toric manifold when the closure is a complex submanifold. In this talk, weconstruct submanifolds with boundary and corners in a Delzant polytope of the corresponding symplectic
toric manifold. We also demonstrate that the conditions for the submanifolds with boundary and corners
are equivalent to those for torus-equivariantly embedded toric manifolds.
15 森 本 真 弘 (都 立 大 理)
Masahiro Morimoto(Tokyo Metro. Univ.)

アフィン対称空間上の平行移動写像 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The parallel transport map over aﬃne symmetric space

概 要 The parallel transport map is a Riemannian submersion naturally deﬁned over a compact Riemanniansymmetric space and its total space is an inﬁnite dimensional separable Hilbert space. In this paper wedeﬁne the parallel transport map over an aﬃne symmetric space and show that it is an aﬃne submersion
with a horizontal distribution.
16 橋 永 貴 弘 (佐 賀 大 教 育)島大⋆)阿 賀 岡 芳 夫 (広Takahiro Hashinaga (Saga Univ.)
Yoshio Agaoka (Hiroshima Univ.⋆)

4 次元定曲率空間へ局所等長埋め込み可能な 3 次元等質空間の分類 · · · · 15
Local isometric embeddings of three-dimensional homogeneous spaces
into four-dimensional space forms

概 要 We give a classiﬁcation of three-dimensional homogeneous spaces which can be locally isometricallyembedded into four-dimensional spaces of constant sectional curvature.
17 田 中 真 紀 子 (東京理大創域理工)田 崎 博 之(都立大理・筑波大数理物質)
Makiko Sumi Tanaka(Tokyo Univ. of Sci.)
Hiroyuki Tasaki(Tokyo Metro. Univ./Univ. of Tsukuba)

極大対蹠部分群と奇数次数の被覆準同型写像 · · · · · · · · · · · · · · · · · · · · · · · 15

Maximal antipodal subgroups and covering homomorphisms with odd
degree概 要 A compact Lie group G equipped with a bi-invariant Riemannian metric is a Riemannian symmetricspace. The symmetry sx at x is given by sx (y) = xy −1 x. A subset S of G is called an antipodal set if
sx (y) = y holds for any x and y in S. When S is a maximal antipodal set containing the identity element,
S is a subgroup of G, which is called a maximal antipodal subgroup. We show that all of the maximal
antipodal subgroups in compact Lie groups, which are not necessarily connected, do not change throughcovering homomorphisms with odd degree.

2024/08/21 作成
幾何学

18 藤 岡 禎 司 (阪大理)Tadashi Fujioka (Osaka Univ.)34

正曲率ホモロジー多様体とリンクに対する球面定理 · · · · · · · · · · · · · · · · · 15

A sphere theorem for a positively curved homology manifold and its
links

概 要 We obtain a sphere theorem for a homology manifold of positive curvature in the sense of Alexandrov

and its links. More precisely, we show that if a homology manifold of curvature at least 1 contains
three/four points with pairwise distances strictly greater than π/2, then the homology manifold/every spaceof directions is homeomorphic to a sphere, respectively. This theorem is optimal in the sense that the
number of points and the strict inequality cannot be improved.
19 濱 中 翔 太 (阪大理)Shota Hamanaka (Osaka Univ.)

安定勾配リッチソリトンのスカラー曲率下限 · · · · · · · · · · · · · · · · · · · · · · · 15

Scalar curvature lower bounds of steady gradient Ricci soliton

概 要 In this talk, I will give some upper bounds of the inﬁmum of the scalar curvature of a complete

non-compact steady gradient Ricci soliton. The proofs use (warped) µ-bubble method.
20 船 野敬 ( 東 北 大 情 報)

Kei Funano(Tohoku Univ.)

ラプラシアンのノイマン固有値の普遍不等式 · · · · · · · · · · · · · · · · · · · · · · · 10

A universal inequality for Neumann eigenvalues of the Laplacian

概 要 I will explain some universal inequality for Neumann eigenvalues of the Laplacian on a bounded convex

domain in a Euclidean space.
14:15〜18:00
21 青 井 顕 宏 (和 歌 山 工 高 専)
Takahiro Aoi(Nat. Inst. of Tech., Wakayama Coll.)

Skoda–Zeriahi type integrability and entropy compactness for Poincaré
type Kähler metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Skoda–Zeriahi type integrability and entropy compactness for Poincaré
type Kähler metrics

概 要 I will talk about an integrability result of plurisubharmonic functions for some measure with L1 -density. In order to prove this, Skoda–Zeriahi’s integrability theorem and the Ohsawa–Takegoshi L2 extension theorem play a very important role. As an application, we obtain a certain compactness result of
the relative entropy. This work is motivated by the existence problem of constant scalar curvature Kähler
metrics of Poincaré type.
22 四 ッ 谷 直 仁 (香 川 大 教 育)King Leung Lee(IMAG, Univ. of Montpellier)

Naoto Yotsutani (Kagawa Univ.)
King Leung Lee(IMAG, Univ. of Montpellier)

Chow stability of λ-stable toric viarieties · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Chow stability of λ-stable toric viarieties

概 要 For a given polarized toric variety, we deﬁne the notion of λ-stability which is a natural generalizationof uniform K-stability. At the neighbourhoods of the vertices of the corresponding moment polytope ∆,we consider appropriate triangulations and give a suﬃcient criteria for a λ-stable polarized toric variety(X, L) to be asymptotically Chow polystable when the obstruction of asymptotic Chow semistability (theFutaki–Ono invariant) vanishes. As an application, we prove that any K-semistable polarized smooth toricvariety (X, L) with the vanishing Futaki–Ono invariant is asymptotically Chow polystable.

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35

幾何学

23 四 ッ 谷 直 仁 (香 川 大 教 育)

Naoto Yotsutani (Kagawa Univ.)

射影トーリック多様体の数値的半安定性について · · · · · · · · · · · · · · · · · · · 15

Numerical semistability of projective toric varieties

概 要 Let X → PN be a smooth linearly normal projective variety. It was proved by Paul that the K-energyof (X, ωFS X ) restricted to the Bergman metrics is bounded from below if and only if the pair of (rescaled)
Chow/Hurwitz forms of X is semistable. In this talk, we provide a necessary and suﬃcient condition for agiven smooth toric variety XP to be numerically semistable with respect to OXP (i) for a positive integer i.
Applying this result to a smooth polarized toric variety (XP , LP ), we prove that (XP , LP ) is asymptoticallynumerically semistable if and only if it is K-semistable in the toric sense.
24 米 原 修 平 (阪大理)Shuhei Yonehara (Osaka Univ.)

余シンプレクティック亜群の作用と簡約定理 · · · · · · · · · · · · · · · · · · · · · · · 15

Actions of cosymplectic groupoids and a reduction theorem

概 要 The Mikami–Weinstein reduction theorem is a generalization of the classical Marsden–Weinstein

reduction theorem to the case of symplectic groupoid actions. In recent years, the notion of cosymplectic
groupoids, which is an odd-dimensional counterpart of the one of symplectic groupoids, has begun to bestudied. In this talk, we introduce the notion of cosymplectic groupoid actions on cosymplectic manifolds
using the notion of Lagrangian–Legendrean submanifolds of cosymplectic manifolds. Following this, we
prove a theorem which is a natural analogue of the Mikami–Weinstein theorem.
25 廣 田 祐 士 (麻 布 大 獣 医)池 田 憲 明 ( 立 命 館 大 理 工)
(Azabu Univ.)
Yuji Hirota
Noriaki Ikeda (Ritsumeikan Univ.)

ホモトピー運動量切断を持つベクトル値シンプレクティック多様体の簡約について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On reduction of vector-valued symplectic manifolds with homotopy momentum sections

概 要 The notion of (bundle-valued) homotopy momentum sections, which was introduced by the speakers, isa conception subsuming both momentum maps and momentum sections under a single framework. Bundlevalued homotopy momentum sections are deﬁned for bundle-valued multisymplectic manifolds together with
Lie algebroid structures, while usual momentum maps are done for symplectic manifolds with Hamiltonian
actions. In this talk, we shall expand the Marsden–Weinstein theorem to the case of vector-valued symplectic
manifolds with Lie algebroids which do not necessarily admit Hamiltonian actions.
26 中 村 友 哉(工学院大学習支援センター)
木 村 直 記 ( 東 京 理 大 理)

Tomoya Nakamura (Kogakuin Univ.)
Naoki Kimura (Tokyo Univ. of Sci.)

Koszul–Vinberg 多様体の一般化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A generalization of Koszul–Vinberg manifolds

概 要 Koszul–Vinberg manifolds are a generalization of dually ﬂat manifolds. These manifolds have prop-

erties similar to Poisson and symplectic manifolds. It is known that Poisson manifolds are related to Lie
algebroids while Koszul–Vinberg manifolds are related to left-symmetric algebroids. By generalizing Lie
algebroids, we obtain the notion of Jacobi algebroids. Jacobi structures are the structures on a manifold
related to Jacobi algebroids. We deﬁned Jacobi-left-symmetric algebroids by analogy with Jacobi algebroids,
and deﬁned the structures on a manifold related to these, called Jacobi–Koszul–Vinberg structures.
27 澤 井洋 ( 沼 津 工 高 専)

Hiroshi Sawai(Numazu Nat. Coll. of Tech.)

Lee form on a non-Vaisman LCK solvmanifold associated to a onedimensional of a nilmanifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Lee form on a non-Vaisman LCK solvmanifold associated to a onedimensional of a nilmanifold

概 要 In this talk, we give a necessary condition for a solvmanifold associated to a one-dimensional extensionof a nilmanifold has a non-Vaisman locally conformal Kähler structure. Moreover, we prove that such a
6-dimensional solvmanifold has no non-Vaisman locally conformal Kähler structures.

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幾何学

28 鈴 木 良 明 (新 潟 大 自 然)

Yoshiaki Suzuki (Niigata Univ.)

36

Heisenberg Bieberbach 多様体上の Folland–Stein 作用素のスペクトル · 15
The spectrum of the Folland–Stein operator on Heisenberg Bieberbach
manifolds

概 要 We study the eigenvalues and eigenfunctions of the Folland–Stein operator Lα on some examples of

3-dimensional Heisenberg Bieberbach manifolds, that is, compact quotients Γ\H of the Heisenberg group H
by a discrete torsion-free subgroup Γ of H ⋊ U (1).
29 古 賀勇(九州国際大現代ビジネス)長 友 康 行 ( 明 大 理 工)

複素射影空間から複素射影空間へのシンプレクティック群同変調和写像の分類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Isami Koga (Kyushu Int. Univ.)
Yasuyuki Nagatomo (Meiji Univ.)

Classiﬁcation of Sp-equivariant harmonic maps from complex projective
spaces into complex projective spaces

概 要 In this talk, we will construct moduli spaces of Sp-equivariant harmonic maps from odd-dimensional

complex projective spaces into complex projective spaces.
30 橋 本 隆 司(鳥取大教育支援・国際交流推進機構)

Takashi Hashimoto (Tottori Univ.)

ある複素余随伴軌道上の超ケーラー計量 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A hyperkähler metric on a complex coadjoint orbit

概 要 We construct a hyperkähler metric on a complex semisimple coadjoint orbit of SL n+1 (C) explicitly interms of coordinates, realizing the orbit as a twisted cotangent bundle on a complex projective space CPn ,which is an aﬃne bundle associated to the cotangent bundle on CPn .
31 石 川 元 稀 (立 命 館 大 理 工)

Genki Ishikawa (Ritsumeikan Univ.)

Lagrange のコマに付随する楕円ファイバー空間とそのモノドロミーについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An elliptic ﬁbration arising from the Lagrange top and its monodromy

概 要 The Lagrange top is one of the typical examples of integrable systems, which describes the motion ofa rigid body around a ﬁxed point with the symmetric axis passing through the centre of mass and the ﬁxed
point. The complexiﬁcation of the energy-momentum map induces an elliptic ﬁbration over the complex
projective plane in Weierstraß normal form. In this talk, the description of the singular locus of this elliptic
ﬁbration is given in detail. Furthermore, the monodromy of the elliptic ﬁbration is described.

9 月 6 日（金）第 I 会場

9:30〜11:45
32 Sheng-Chen Mao ( Fudan Univ. )張頁 (沖縄科学技術大)

Sheng-Chen Mao (Fudan Univ.)
Ye Zhang(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

On gradient estimates of the heat semigroups on step-two Carnot groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On gradient estimates of the heat semigroups on step-two Carnot groups

概 要 In this work, we give a suﬃcient condition of measure contraction property type for a step-two Carnot

group to satisfy the quasi Bakry–Émery curvature condition. It turns out that the establishment of thequasi Bakry–Émery curvature condition does not require the precise upper and lower bound estimates of
the heat kernel and the computation of the Jacobian determinant of the sub-Riemannian exponential map,
which are diﬃcult to obtain by current methods.

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37

幾何学

33 周

暁 丹 (沖縄科学技術大)Xiaodan Zhou
(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Non-uniqueness of Green functions on metric spaces · · · · · · · · · · · · · · · · 15
Non-uniqueness of Green functions on metric spaces

概 要 We construct an explicit example showing that the uniqueness of energy minimizing harmonic Greenfunctions fails on a 2-Ahlfors regular space supporting a Poincare inequality. This result contrasts theuniqueness of Cheeger harmonic Green functions on such spaces obtained earlier by Bonk, Capogna andthe speaker. We also discuss some interesting implications of this example including the failure of strong
comparison principle. This is joint work with A. Bjorn, J. Bjorn and S. Eriksson-Bique.
34 梶 野 直 孝 (京 大 数 理 研)
清 水 良 輔 ( 早 大 理 工)
Naotaka Kajino (Kyoto Univ.)
Ryosuke Shimizu (Waseda Univ.)

Sharp Hölder regularity estimates of harmonic functions for p-resistanceforms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Sharp Hölder regularity estimates of harmonic functions for p-resistanceforms

概 要 Let p ∈ (1, ∞). The purpose of this talk is to present, on the basis of arXiv:2404.13668, our recent

result on sharp Hölder regularity estimates of harmonic functions for p-resistance forms, which are a class of
p-energy forms we have recently introduced to study p-energy forms on fractals systematically. Our Hölder
regularity estimates have an application to the proof of the triangle inequality for the p-resistance metricof any p-resistance form, which also seems new in the present abstract setting, and also are one of the key
ingredients of our ongoing study on the singularity of p-energy measures among distinct values of p for somep.-c.f. self-similar sets, which the speaker will speak about in his next talk.
35 梶 野 直 孝 (京 大 数 理 研)
清 水 良 輔 ( 早 大 理 工)
Naotaka Kajino (Kyoto Univ.)
Ryosuke Shimizu (Waseda Univ.)

On singularity of p-energy measures among distinct values of p for somep.-c. f. self-similar sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On singularity of p-energy measures among distinct values of p for somep.-c. f. self-similar sets

概 要 For p ∈ (1, ∞), a p-energy form (Ep , Fp ), a natural Lp -analog of the standard Dirichlet form for p = 2,

was constructed on a class of p.-c.f. self-similar sets by Herman–Peirone–Strichartz (2004), on general p.-c.f.
self-similar sets by Cao–Gu–Qiu (2022), on Sierpiński carpets by Shimizu (2024) and Murugan–Shimizu(2024+) and on a large class of inﬁnitely ramiﬁed self-similar fractals by Kigami (2023), but very little
has been understood concerning properties of important analytic objects associated with (Ep , Fp ) such as
p-harmonic functions and p-energy measures. This talk is aimed at presenting the result of our recent
ongoing study that, for a class of p.-c.f. self-similar sets with very good geometric symmetry, the p-energy
measure µp⟨u⟩ of any u ∈ Fp and the q-energy measure µq⟨v⟩ of any v ∈ Fq are mutually singular for any
p, q ∈ (1, ∞) with p 6= q.

36 中 島 直 道 (芝 浦 工 大 建 築)
Naomichi Nakajima(Shibaura Inst. of Tech.)

双対平坦空間における平面曲線論と特異点論 · · · · · · · · · · · · · · · · · · · · · · · 15

Dually ﬂat geometry of plane curves and singularity theory

概 要 In the Euclidean plane, classically, it is well-known that extrinsic diﬀerential geometric invariants ofcurves are characterized by singularities of the corresponding envelope, and the singularities are analyzed
by the distance-squared functions. In this presentation, I would like to talk about our generalization of
the results in the Euclidean space to the ones in a dually ﬂat space, introduced by Amari and Nagaoka togeometrically investigate various ﬁelds such as statistics, machine learning, and so on. Additionally, I would
like to introduce an application of our results to maximum likelihood estimation in statistics.

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幾何学

37 嘉 陽 海 渡 (北Kaito Kayo

大理)

(Hokkaido Univ.)38

計量の退化を許容する統計多様体 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Statistical manifold with degenerate metric

概 要 A statistical manifold is a pseudo-Riemannian manifold endowed with a Codazzi structure. This

structure plays an important role in Information Geometry and its related ﬁelds, e.g., a statistical model
admits this structure with the Fisher-Rao metric. In practical application, however, the metric may bedegenerate, and then this geometric structure is not fully adapted. In this study, for such cases, we introduce
the notion of quasi-Codazzi structure which consists of a possibly degenerate metric and a pair of coherent
tangent bundles with aﬃne connections. As a special case, the quasi-Codazzi structure with ﬂat connections
coincides with the quasi-Hessian structure previously studied by Nakajima–Ohmoto.
38 小
大
奥
田

林 彦 蔵 (広島大先進理工)
大
理)
野
優 (北
(
)
広島大先進理工田 隆 幸丸 博 士 ( 阪 公 大 理)

Hikozo Kobayashi (Hiroshima Univ.)(Hokkaido Univ.)
Yu OhnoTakayuki Okuda (Hiroshima Univ.)
Hiroshi Tamaru (Osaka Metro. Univ.)

左不変統計構造のモジュライ空間と双対平坦性および共役対称性 · · · · · · 15

Moduli spaces of left-invariant statistical structures, dually-ﬂatness andconjugate symmetries

概 要 In the context of information geometry, a concept known as left-invariant statistical structures on

Lie groups has been deﬁned by Furuhata–Inoguchi–Kobayashi [Inf.Geom.(2021)]. In this talk, we introduce
the classiﬁcation of important classes called “dually-ﬂat” and “conjugate symmetric” within left-invariant
statistical structures on commutative Lie groups Rn and certain two types of almost abelian Lie groups.
14:15〜16:45
39 成 田 知 将 (名 大 多 元 数 理)

Kazumasa Narita (Nagoya Univ.)

マジョリゼーションに関連する凸幾何学のグラフ実現問題への応用 · · · · 15

Geometric interpretation of majorization and its application to graphrealization problem

概 要 Majorization is an important combinatorial notion that has applications in many areas of mathematics.

In 1952, Rado gave a geometric characterization of majorization. By applying this theorem due to Rado, thespeaker characterized when a ﬁnite sequence of nonnegative real numbers is realized as the degree sequenceof some weighted uniform hypergraph. This theorem is an extension of a theorem due to Hakimi (1962).
The speaker also studied the properties of the closed convex polytope associated with the set of hypergraphswith a given degree sequence.
40 松 家 拓 稔 (都 立 大 理)
深 谷 友 宏 ( 都 立 大 理)

Takumi Matsuka (Tokyo Metro. Univ.)
Tomohiro Fukaya (Tokyo Metro. Univ.)

粗凸空間の自由積の境界について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Boundary of free products of coarsely convex spaces

概 要 We compute (co)homologies of ideal boundaries of free products of geodesic coarsely convex spaces interms of those of each of the components. The (co)homology theories we consider are, K-theory, AlexanderSpanier cohomology, K-homology, and Steenrod homology. These computations led to the computation of
K-theory of the Roe algebra of free products of geodesic coarsely convex spaces via the coarse Baum–Connes
conjecture.

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39

幾何学

41 見 村 万 佐 人 (東 北 大 理) [ 一般化混合 Bavard 双対 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
大理)
川 﨑 盛 通 (北(木 村 満 晃 大 阪 歯 大 歯)松 下 尚 弘 ( 信 州 大 理)
丸 山 修 平 ( 金 沢 大 理 工)

Masato Mimura (Tohoku Univ.)
Morimichi Kawasaki (Hokkaido Univ.)
Mitsuaki Kimura (Osaka Dent. Univ.)
Takahiro Matsushita (Shinshu Univ.)
Shuhei Maruyama (Kanazawa Univ.)

Generalized mixed Bavard duality

概 要 We prove the “generalized and mixed” version of the Bavard duality theorem.

42 豊 田哲(工学院大教育推進機構)

Tetsu Toyoda (Kogakuin Univ.)

Andoni–Naor–Neiman の不等式と CAT(0) 空間への等長埋め込み可能性· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Andoni–Naor–Neiman inequalities and isometric embeddability intoa CAT(0) space

概 要 Andoni, Naor and Neiman (2018) established a family of quadratic metric inequalities that hold truein every CAT(0) space. As stated in their paper, this family seems to include all previously used quadratic
metric inequalities that hold true in every CAT(0) space. We prove that there exists a metric space thatsatisﬁes all inequalities in this family but does not admit an isometric embedding into any CAT(0) space.
43 井 関 裕 靖 (慶 大 理 工)
カールソンアンダース( Univ. Geneva )(Keio Univ.)
Hiroyasu Izeki
Anders Karlsson (Univ. Geneva)

劣指数的増大度をもつ有限生成ねじれ群の有限次元 CAT(0) 空間に対す
る固定点性質 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A ﬁxed-point property of ﬁnitely generated torsion groups with subexponencial growth for CAT(0) spaces

概 要 We show that ﬁnitely generated torsion groups with subexponential growth cannot act on ﬁnite-

dimensional CAT(0) spaces without ﬁxed points. A similar ﬁxed-point theorem can be proved for ﬁnitely
generated simple groups with subexponential growth.
44 江 崎 翔 太 (大 分 大 理 工)
数 川 大 輔 ( 九 大 数 理)
三 石 史 人 ( 福 岡 大 理)
(Oita Univ.)
Syota Esaki
Daisuke Kazukawa (Kyushu Univ.)
Ayato Mitsuishi (Fukuoka Univ.)

ガウス空間の無限 lp 直積とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Convergence of lp -product Gaussian spaces and its applications

概 要 A Euclidean space with a Gaussian distribution is called a Gaussian space. The limit object ofGaussian spaces as the dimension diverges to inﬁnity in the pyramid sense is well-studied. This is a central
ﬁgure in the study of inﬁnite dimensional limit of Riemannian manifolds. In this talk, we study an lp -normed
space with a Gaussian distribution instead of the Euclidean norm. When p ≥ 2, it is easy to capture its
inﬁnite dimensional limit object. On the other hand, when p < 2, the situation is diﬀerent. We determine
the limit of lp -normed Gaussian spaces with suitable scaling as the dimension diverges to inﬁnity, and thenapply it to the phase transition phenomenon of convergence of lp -product spaces.

2024/08/21 作成
幾何学

45 尾 國 新 一 (愛 媛 大 理)
加 藤 本 子 ( 琉 球 大 教 育)
Shin-ichi Oguni (Ehime Univ.)
Motoko Kato (Univ. of Ryukyus)

40

完全グラフでない定義グラフに付随したアルティン群の非シリンダー的
双曲性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Acylindrical hyperbolicity of Artin groups associated with graphs thatare not cliques

概 要 We talk about Artin groups and acylindrical hyperbolicity, which are important in geometric grouptheory. Our main theorem claims that irreducible Artin groups associated with graphs that are not cliques
are acylindrically hyperbolic. As a corollary, we see that irreducible Artin groups of type FC and of inﬁnite
type are acylindrically hyperbolic.

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41

函数論

函

数

9 月 3 日（火）論第 VI 会場

9:30〜11:00
Newton–Mandelbrot set and Murase–Mandelbrot set · · · · · · · · · · · · · · · 15

1 堀 口 俊 二
Shunji Horiguchi

Newton–Mandelbrot set and Murase–Mandelbrot set

概 要 The Wasan (Japanese mathematics in the Edo period (1603–1868: national isolation)) of 1673

contains studies leading to three extended Newton methods and three extended Mandelbrot recurrence
formulas. Moreover, the extended Mandelbrot recurrence formula 1 is related to the extended Newton
methods (Theorem 3.1). Furthermore, from extended Mandelbrot recurrence formula 1 and 3, we obtain
Newton–Mandelbrot set and Murase–Mandelbrot set, respectively. These show the originality of Japanesemathematics Wasan.
2 塚 本 真 輝 (京大理)Masaki Tsukamoto (Kyoto Univ.)

ランダムなブロディ曲線のレート歪み次元 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Rate distortion dimension of random Brody curves

概 要 We develop an ergodic theory of entire holomorphic curves. Our theory is analogous to the ergodic

theory of Axiom A diﬀeomorphisms.
(Univ. of Würzburg) [ Peschl–Minda derivatives and convergent Wick star products · · · · · · · · 15
3 M. Heins(Univ. of Würzburg)
A. Moucha(Univ. of Würzburg)
O. Roth
須 川 敏 幸 ( 東 北 大 情 報)

Michael Heins (Univ. of Würzburg)
Annika Moucha (Univ. of Würzburg)
Oliver Roth (Univ. of Würzburg)
Toshiyuki Sugawa (Tohoku Univ.)

Peschl–Minda derivatives and convergent Wick star products

概 要 In this talk, we introduce a domain of complex 2 dimension which contains the real 2 dimensional

hyperbolic disk and 2 sphere in a special way. This approach enables us to unify the hyperbolic geometry andspherical geometry of real 2 dimension in a holomorphic manner. We apply this idea to show convergenceof the Wick star product.
4 松 崎 克 彦 ( 早 大 教 育)

Katsuhiko Matsuzaki (Waseda Univ.)

ジグムント連続な微分をもつ微分同相写像のタイヒミュラー空間 · · · · · · 15

The Teichmüller space of circle diﬀeomorphisms in the Zygmund smoothclass

概 要 We provide the complex Banach manifold structure for the Teichmüller space of circle diﬀeomorphisms

whose derivatives are in the Zygmund class. This is done by showing that the Schwarzian derivative map
is a holomorphic split submersion. We prove similar results for the pre-Schwarzian derivative map andinvestigate the ﬁber space over the Teichmüller space. Especially, we show that this projection is also aholomorphic split submersion and induces the structure of a disk bundle. Finally, we introduce the little
Zygmund class and consider the closed subspace given by this family of mappings in the Teichmüller space.

2024/08/21 作成
函数論

5 坂 井 健 人 (阪Kento Sakai

大理)(Osaka Univ.)

42

Degeneration of hyperbolic surfaces with boundary via harmonic maps
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Degeneration of hyperbolic surfaces with boundary via harmonic maps

概 要 Using harmonic maps from a punctured Riemann surface to hyperbolic surfaces with totally geodesic

boundaries, we obtain a parametrization of Teichmüller space. The parametrization space is the spaceof meromorphic quadratic diﬀerentials on the punctured Riemann surface. In this talk, we consider thedegeneration of hyperbolic surfaces parametrized by a ray from the origin in the space of meromorphic
quadratic diﬀerentials. In particular, taking the universal covers of the Riemann surface, we show thenormalized metric spaces of the hyperbolic surfaces converge to the R-tree which is determined by the
direction of the ray. Here, we discuss the convergence in the sense of Gromov–Hausdorﬀ.
14:20〜15:20

特別講演
大馬 場 伸 平 (阪Shinpei Baba理) [ Bers’ simultaneous uniformization theorem and complex projective struc-(Osaka Univ.)tures on Riemann surfaces
Bers’ simultaneous uniformization theorem and complex projective structures on Riemann surfaces

概 要 Bers’ simultaneous uniformization theorem is a generalization of the uniformization theorem ofRiemann surfaces. It establishes a bijective correspondence between pairs of Riemann surface structures
and typical discrete faithful representations into PSL(2, C). Bers’ original proof is based on the quasiconformal deformation theory. In this talk, we outline a new proof, using the intersection of holonomy
varieties.
The deformation space of complex projective structures on a Riemann surface is identiﬁed with thevector space of holomorphic quadratic diﬀerentials on the surface. This vector space properly embeds into
the space of representations of the surface group into PSL(2, C), so that its image is a smooth analytic
subvariety. Given two marked Riemann surface structures on the same topological surface, we show that theintersection of their corresponding subvarieties is a discrete set. From this, one can reprove the simultaneous
uniformization theorem.

9 月 4 日（水）第 VI 会場

9:30〜11:00
6 綾 野 孝 則 ( 阪 公 大 数 学 研)

Takanori Ayano (Osaka Metro. Univ.)

種数 2g の超楕円関数の種数 g の超楕円関数による表示 · · · · · · · · · · · · · · 15

Expressions of hyperelliptic functions of genus 2g in terms of hyperelliptic functions of genus g

概 要 The problem whether the Jacobian variety of a hyperelliptic curve is isogenous to the direct productof the Jacobian varieties of hyperelliptic curves of lower genera is considered in many papers. This problem
is naturally connected with the following well-known problem: Let solutions of diﬀerential equations anddynamical systems in terms of hyperelliptic functions are given. Under conditions when a reduction of thesefunctions to hyperelliptic functions of lower genera is possible, ﬁnd an explicit form of these solutions interms of hyperelliptic functions of lower genera. In our previous work, we solve this problem for a class of
hyperelliptic curves of genus 2. In this talk, we generalize our previous results to the case of genus 2g forany positive integer g.

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43

函数論

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

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

Bohr’s phenomena for pluriharmonic mappings in a separable complex
Hilbert space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bohr’s phenomena for pluriharmonic mappings in a separable complex
Hilbert space

概 要 Let H1 be the Euclidean space Cm or `2 , and let BH1 be the unit ball of H1 . In this talk, we will

discuss about Bohr’s phenomena for pluriharmonic mappings from BH1 into H1 , and generalize some results
about Bohr’s phenomena for locally univalent harmonic functions on the unit disc in C to pluriharmonic
mappings from BH1 into H1 .
8 大 沢 健 夫 (名 大 多 元 数 理) [ On Stein neighborhood basis of certain Stein domains · · · · · · · · · · · · · · 15
Takeo Ohsawa (Nagoya Univ.)

On Stein neighborhood basis of certain Stein domains

概 要 The purpose of this talk is to outline a proof of the following.

Theorem. There exists a two-dimensional compact complex manifold Y holomorphically embedded in CP5
and a Stein domain X ⊂ Y with real-analytic boundary such that X admits a Stein neighborhood systemwith Hölder continuous boundary in CP5 but does not admit a Stein neighborhood system with Lipschitz
continuous boundary.
9 渡 邊 祐 太 ( 中 大 理 工)
Yuta Watanabe (Chuo Univ.)

特異 Hermite 計量に関する ω-trace 正値性と Griﬃths 正値性 · · · · · · · · · 15

ω-trace and Griﬃths positivity for singular Hermitian metrics

概 要 In this talk, we investigate various positivity for singular Hermitian metrics such as Griﬃths, ω-

trace and RC, where ω is a Hermitian metric, and show that these quasi-positivity notions induce 0-th
cohomology vanishing, rational conected-ness, etc. Here, ω-trace positivity of smooth Hermitian metrics h
on holomorphic vector bundles E represents the positivity of trω iΘE,h .
10 丸 亀 泰 二 (電通大情報理工)
Taiji Marugame(Univ. of Electro-Comm.)

Ambient and Poincaré metrics for CR 3-manifolds corresponding to Einstein ACH metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Ambient and Poincaré metrics for CR 3-manifolds corresponding to Einstein ACH metrics

概 要 We construct a new ambient metric and a Poincaré metric for the Feﬀerman conformal manifold overCR 3-manifolds. These are constructed via the self-dual Einstein ACH metric which has the CR manifold
as the boundary at inﬁnity. These metrics enable us to construct CR GJMS operators and local scalar
invariants of CR 3-manifolds.
13:00〜14:00
辻

特別講演
智
元 (上

Hajime Tsuji

大⋆)(Sophia Univ.

⋆)

離散ケーラー・リッチ流について

Discrete Kähler–Ricci ﬂows

概 要 To study Kähler–Ricci ﬂows, we consider the dynamical systems of Bergman kernels (or similar dy-

namical systems) as a discrete version of them. This enables us to deduce the logarithmic plurisubharmonic
variation of Kähler Ricci ﬂows. This indicates the metric semipositivity of the relative canonical bundle ofa Kähler deformation of compact Kähler manifolds with pseudoeﬀective relative canonical bundle.

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函数方程式論函数

方9 月 3 日（火）

程

式

44

論

第 II 会場

9:00〜12:00
1 竹 井 優 美 子 ( 茨 城 工 高 専)
竹 井 義 次 ( 同 志 社 大 理 工)
Yumiko Takei(Ibaraki Nat. Coll. of Tech.)
Yoshitsugu Takei (Doshisha Univ.)

超幾何関数が満たす微分差分方程式系と積分表示式 · · · · · · · · · · · · · · · · · 12

A system of diﬀerential-diﬀerence equations and an integral representation of solutions for the hypergeometric functions

概 要 We consider a system of diﬀerential-diﬀerence equations satisﬁed by the Gauss hypergeometric function.

By using the Laplace transform with respect to parameters we get an integral representation of solutionsin the form of the triple complex integral. By using the gauge transformation the well-known integral
representation of solutions is also obtained. Similar results hold for conﬂuent hypergeometric functions as
well.
2 松
金
小
寺

本
子
原
杣

圭
譲
功
友

大
理)
司 (北
球
大⋆)
一 (琉
任 ( 金 沢 大 理 工)
秀 ( 法 政 大 理 工)

Keiji Matsumoto (Hokkaido Univ.)
Jyoichi Kaneko (Univ. of Ryukyus⋆)
Katsuyoshi Ohara (Kanazawa Univ.)
Tomohide Terasoma (Hosei Univ.)

A system of hypergeometric diﬀerential equations in m variables I, therank and the singular locus. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

A system of hypergeometric diﬀerential equations in m variables I, therank and the singular locus.

概 要 We deﬁne a hypergeometric series in m variables with p + (p − 1)m parameters, which reduces to thegeneralized hypergeometric series p Fp−1 when m = 1, and to Lauricella’s hypergeometric series FC in mvariables when p = 2. We give a system of hypergeometric diﬀerential equations annihilating the series.
Under some non-integral conditions on parameters, we give an Euler type integral representation of theseries, and linearly independent pm solutions to this system around a point near to the origin. We showthat this system is of rank pm , and determine its singular locus.
3 松
金
小
寺

本
子
原
杣

圭
譲
功
友

大
理)
司 (北
球
大⋆)
一 (琉
任 ( 金 沢 大 理 工)
秀 ( 法 政 大 理 工)

Keiji Matsumoto (Hokkaido Univ.)
Jyoichi Kaneko (Univ. of Ryukyus⋆)
Katsuyoshi Ohara (Kanazawa Univ.)
Tomohide Terasoma (Hosei Univ.)

A system of hypergeometric diﬀerential equations in m variables II, themonodromy representation. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

A system of hypergeometric diﬀerential equations in m variables II, themonodromy representation.

p,m

概 要 We study the monodromy representation of a hypergeometric system FCpm(a, B) in m variables of rankwith parameters a, B, which can be regarded as a multi-variable model of the generalized hypergeometricequation of rank p. We give m + 1 loops generating the fundamental group of the complement the singularlocus of the system FCp,m (a, B), and show that they satisfy some relations as elements of the fundamentalgroup. We give circuit matrices along these loops with respect to a fundamental system of solutions toFCp,m (a, B) under some non-integral conditions on parameters a, B.

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45

函数方程式論4 細 井 竜 也 ( 東 大 数 理)
坂 井 秀 隆 ( 東 大 数 理)

Tatsuya Hosoi (Univ. of Tokyo)
Hidetaka Sakai (Univ. of Tokyo)

パンルヴェ六型方程式の双線型方程式について · · · · · · · · · · · · · · · · · · · · · 12

A study on the bilinear equation of the sixth Painlevé transcendents

概 要 The sixth Painlevé equation is a basic equation among the non-linear diﬀerential equations withthree ﬁxed singularities, corresponding to Gauss’s hypergeometric diﬀerential equation among the linear
diﬀerential equations. It is known that 2nd order Fuchsian diﬀerential equations with three singular points
are reduced to the hypergeometric diﬀerential equations. Similarly, for nonlinear diﬀerential equations, wewould like to determine the equation from the local behavior around the three singularities. In this paper,
the sixth Painlevé equation is derived by imposing the condition that it is of type (H) at each three singularpoints for the homogeneous quadratic 4th-order diﬀerential equation.
5 細 井 竜 也 ( 東 大 数 理)

Tatsuya Hosoi (Univ. of Tokyo)

4 階 2 次斉次微分方程式の初期値に依存する複素冪を持つ形式級数解とその収束について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Formal series solutions of fourth-order homogeneous quadratic diﬀerential equations with complex powers depending on initial values andtheir convergence

概 要 It is known that all tau functions of the Painleve equations satisfy the fourth-order quadratic diﬀerential

equation. Among them, for the III, V, and VI equations, it is possible to express the formal series solutions
combinatrically by using conformal blocks. In this paper, we show the convergence of the formal series,
including the solutions of more general equations. The convergence of the conformal block function also
follows in the case c = 1 by the absolute convergence of tau series, since it is a partial sum of the tau series.
We also characterized the form of a homogeneous quadratic equation with a series solution similar to thetau functions of the Painleve equations.
6 西 口 純 矢 (東 北 大 A I M R )Junya Nishiguchi (Tohoku Univ.)

線型遅延微分方程式の軟解の正則性について · · · · · · · · · · · · · · · · · · · · · · · 12

On regularity of mild solutions for linear delay diﬀerential equations

概 要 The notion of mild solutions for linear delay diﬀerential equations (DDEs) has been introduced in[J. Nishiguchi, Electron. J. Qual. Theory Diﬀer. Equ. 2023, No. 32, 1–77] for the purpose of deﬁning
fundamental matrix solutions and obtaining a variation of constants formula for linear DDEs. This notion
gives a deﬁnition of solutions to linear DDEs under discontinuous history functions. For a given linear DDE,
the fundamental matrix solutions are locally absolutely continuous on the interval [0, ∞), however, it is notapparent that the same property is true for the mild solutions. Here we obtain a result which shows theregularity of mild solutions by proving the local absolute continuity of a function obtained by the history
segment of a locally absolutely continuous function.
7 曲
明 珠 ( 阪 府 大 理)
松 永 秀 章 ( 阪 公 大 理)

Mingzhu Qu (Osaka Pref. Univ.)
Hideaki Matsunaga(Osaka Metro. Univ.)

2 種類の遅延項をもつ線形微分方程式の漸近安定性 · · · · · · · · · · · · · · · · · · 12
Asymptotic stability in a linear diﬀerential equation with two kinds ofdelays

概 要 This study is devoted to the stability analysis of a scalar linear diﬀerential equation with discrete anddistributed delays. We establish necessary and suﬃcient conditions guaranteeing the asymptotic stabilityof the zero solution composed of explicit delay-dependent criteria.

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函数方程式論

8 宇 佐 美 広 介 ( 岐 阜 大 工)
Hiroyuki Usami(Gifu Univ.)

46

摂動項を持つ 3 階半分線形常微分方程式の正値解の漸近挙動 · · · · · · · · · · 12

Asymptotic behavior of positive solutions of perturbed third order halflinear ordinary diﬀerential equations

概 要 We consider perturbed third order half-linear ordinary diﬀerential equations near the inﬁnity. Asymp-

totic behavior of their positive solutions is established.
9 鬼 塚 政 一 ( 岡 山 理 大 理)
田 中
敏 ( 東 北 大 理)
Masakazu Onitsuka(Okayama Univ. of Sci.)
Satoshi Tanaka (Tohoku Univ.)

Box-counting dimension of spiral orbits for two-dimensional nonautonomous
nonlinear diﬀerential systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Box-counting dimension of spiral orbits for two-dimensional nonautonomous
nonlinear diﬀerential systems

概 要 This work focuses on the box-counting dimension of the spiral orbits for two-dimensional nonau-

tonomous nonlinear systems. The main result emphasizes that the box-counting dimension of the spiralorbits of the systems on the phase plane depends on the power of the nonlinear terms.
10 齋 藤 保 久 (島 根 大 理 工)

Yasuhisa Saito (Shimane Univ.)

重症患者割合と治療容量を考慮した感染症流行モデルと後退分岐 · · · · · · 12

Backward bifurcation of an epidemic model with treatment capacity
and the proportion of severe cases

概 要 This talk considers an ordinary diﬀerential system that assumes a ﬁxed internal ratio of severe cases

requiring treatment and mild cases not requiring treatment within the infected population. We take into
account the limited treatment capacity for severe cases to discuss the impact of treatment capacity and the
proportion of severe cases on the spread of diseases, and show the occurrence of backward bifurcation.
11 石 橋 和 葵 (広 島 工 大 工)
Kazuki Ishibashi(Hiroshima Inst. of Tech.)

PD 制御を利用した Sturm–Liouville 型微分方程式に対する Wintner 型非振動定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Wintner-type nonoscillation theorems for Sturm–Liouville diﬀerential
equations using a PD controller

概 要 In this study, we addressed the nonoscillation of the Sturm–Liouville diﬀerential equation with adiﬀerential operator, which corresponds to a proportional-derivative controller. A Wintner-type nonoscillation theorem was established to be applied to such equations. Using this theorem, we provided a sharp
nonoscillation condition that guarantees that all nontrivial solutions to Euler-type equations do not oscillate.
The main nonoscillation theorems can be proven by introducing a Riccati inequality, which corresponds to
the Sturm–Liouville type equation with proportional-derivative controller.
12 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

Asymptotics of solution curves of Kirchhoﬀ type elliptic equations withlogarithmic Kirchhoﬀ function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Asymptotics of solution curves of Kirchhoﬀ type elliptic equations withlogarithmic Kirchhoﬀ function

概 要 The one-dimensional nonlinear bifurcation problem of Kirchhoﬀ type is considered. Let λ be thebifurcation parameter We obtain the precise asymptotic formulas for the solutions uλ as λ → ∞ and λ → 0
by using time map method.
13 眞 﨑

聡 (北

大

理)

Satoshi Masaki (Hokkaido Univ.)あるクラスの常微分方程式系に対する解の表示 · · · · · · · · · · · · · · · · · · · · · 12

On representation of solutions to a class of systems of ordinary diﬀerential equations

概 要 We consider a class of systems of nonlinear ordinary diﬀerential equations, which has a backgroundin the study of the asymptotic behavior of solutions to NLS systems. We introduce an integration scheme.
The key point is to introduce an intermediate step to obtain quadratic quantities of the unknown.

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47

函数方程式論

14:15〜16:45
14 森
竜 樹 ( 武 蔵 野 大 工)
大理)
田 﨑 創 平 (北辻 川亨
(宮崎大⋆・明大客員研究員)
宮 本 安 人 ( 東 大 数 理)谷
大⋆)四 ツ 谷 晶 二 (龍Tatsuki Mori (Musashino Univ.)
Sohei Tasaki (Hokkaido Univ.)
Tohru Tsujikawa(Univ. of Miyazaki⋆ /Meiji Univ.)
Yasuhito Miyamoto (Univ. of Tokyo)
Shoji Yotsutani (Ryukoku Univ.⋆)

Stability of stationary solutions of a phase-ﬁeld model · · · · · · · · · · · · · · 12

Stability of stationary solutions of a phase-ﬁeld model

概 要 We have obtained all global bifurcation diagrams of stationary problems of a phase-ﬁeld model in

Mori–Tasaki–Tsujikawa–Yotsutani (DCDS-B, 2023). For special parameters, the ﬁrst bifurcation occurs
from a trivial constant solution, and secondary bifurcation occurs from odd-symmetry solutions. In thistalk, we investigate the stability of odd-symmetric solutions and asymmetric solutions near the secondary
bifurcation point by solving the nonlocal linearized eigenvalue problem by improving and developing methods
in Miyamoto– Mori–Tsujikawa–Yotsutani(JDE, 2021).
谷
大⋆)
15 四 ツ 谷 晶 二 (龍大理)
田 﨑 創 平 (北辻 川亨
(宮崎大⋆・明大客員研究員)
宮 本 安 人 ( 東 大 数 理)森
竜 樹 ( 武 蔵 野 大 工)

Shoji Yotsutani (Ryukoku Univ.⋆)
Sohei Tasaki (Hokkaido Univ.)
Tohru Tsujikawa(Univ. of Miyazaki⋆ /Meiji Univ.)
Yasuhito Miyamoto (Univ. of Tokyo)
Tatsuki Mori (Musashino Univ.)

All eigenvalues and eigenfunctions of a nonlocal linearized eigenvalue
problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

All eigenvalues and eigenfunctions of a nonlocal linearized eigenvalue
problem概 要 We investigate a nonlocal linearized eigenvalue problem arising from a phase-ﬁeld model, whichis related to the Allen–Cahn equation. For the Allen–Cahn equation in a 1D case, Wakasa (Funkcial
Ekvac., 2006) and Wakasa–Yotsutani (JDE, 2015, 2016) obtained representation formulas of all eigenvalues
and corresponding eigenfunctions. In this talk, we show representation formulas of all eigenvalues andcorresponding eigenfunctions of the nonlocal linearized eigenvalue problem.
16 石 井 裕 太 (茨 城 工 高 専)

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

Y 字グラフにおける移流項を持つ Gierer–Meinhardt モデルのピーク解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Existence of spiky stationary solutions for the Gierer–Meinhardt modelwith advection term on the Y -shaped metric graph概 要 In this talk, we consider the existence of one-peak stationary solutions for the Gierer–Meinhardt modelwith advection term on the Y -shaped metric graph. In particular, we focus on the two vertex conditions(the Kirchhoﬀ condition and the Robin condition) and the advection velocity having diﬀerent constants foreach segment. Moreover, it is shown that the location and amplitude of a spike is determined by the choiceof the vertex condition, and the size and sign of the advection velocity.

2024/08/21 作成
函数方程式論17 森 龍 之 介 (明 大 M I M S)俣 野
博 (明 大 M I M S )Ryunosuke Mori (Meiji Univ.)
Hiroshi Matano (Meiji Univ.)48

空間周期的な 2 次元帯状領域におけるブロッキングと伝播 · · · · · · · · · · · 12

Blocking and propagation in two-dimensional cylinders with spatial periodicity

概 要 We consider blocking and propagation phenomena of mean curvature ﬂow with a driving force in

two-dimensional cylinders with spatially undulating boundary. In this problem, Matano, Nakamura andLou in 2006 characterize the eﬀect of the shape of the boundary to blocking and propagation of the solutions
under some slop condition about the boundary that implies time global existence of the classical solutions.
In this talk, we consider the eﬀect of the shape of the boundary to blocking and propagation of this problem
under more general situation that the solutions may develop singularities near the boundary.
18 関 坂 歩 幹 (明 大 総 合 数 理)
山 本 宏 子 (理 化 学 研 A I P )Ayuki Sekisaka (Meiji Univ.)
Hiroko Yamamoto (RIKEN)

シリンダー領域における反応拡散系の固有値問題と Evans 関数 · · · · · · · 12

Eigenvalue problem and the Evans function of reaction-diﬀusion systems
in cylinder domains

概 要 To study the stability problem of solutions of reaction-diﬀusion systems in cylindrical domains, weconsider the eigenvalue problem of the linearized operator associated with a traveling wave solution ofreaction-diﬀusion systems. In this research, we construct the Evans function that vanishes at eigenvalues
and is analytic in a simply connected bounded domain in the complex plane. This research is a joint workwith Ayuki Sekisaka of Meiji University.
19 兼 子 裕 大 (関 東 学 院 大 工)
宮 本 安 人 ( 東 大 数 理)
若 狭
徹 ( 九 工 大 工)

Yuki Kaneko (Kanto Gakuin Univ.)
Yasuhito Miyamoto (Univ. of Tokyo)
Tohru Wakasa (Kyushu Inst. of Tech.)

Stability and bifurcation diagram for a shadow Gierer–Meinhardt system in one spatial dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stability and bifurcation diagram for a shadow Gierer–Meinhardt system in one spatial dimension

概 要 We are concerned with a Neumann problem of a shadow system of the Gierer–Meinhardt model in

an interval I = (0, 1). A stationary problem is studied, and we consider the diﬀusion coeﬃcient ε > 0 as abifurcation parameter. Then a complete bifurcation diagram of the stationary solutions is obtained, and astability of every stationary solution is determined. In particular, for each n ≥ 1, two branches of n-mode
solutions emanate from a trivial branch. All 1-mode solutions are stable for small τ > 0, and all n-mode
solutions, n ≥ 2, are unstable for all τ > 0, where τ > 0 is a time constant. The system is known for having
stationary spiky patterns with large amplitude for small ε > 0. Then, asymptotic expansions of maximum
and minimum values of a stationary solution as ε → 0 are also obtained.
20 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)

エントロピー法による等非局所拡散を伴う反応拡散系の進行波の安定性· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Stability of traveling waves in non-cooperative systems with nonlocal
dispersal of equal diﬀusivities

概 要 We ﬁrst introduce a stability theorem for traveling waves in a class of non-cooperative reaction-

diﬀusion systems with nonlocal dispersal of equal diﬀusivities. Our stability criterion is that the initial
perturbation is such that a suitable weighted relative entropy function is bounded and integrable. We apply
our main theorem to derive the stability of traveling waves for some examples of non-cooperative systems
arising in ecology and epidemiology.

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49

函数方程式論21 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)呉菁 菁 (Chung Hsing Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)
Chin-Chin Wu (Chung Hsing Univ.)

変動する環境における 1 被食-2 捕食型反応拡散方程式の伝播現象 · · · · · 12

Spreading dynamics for a predator-prey system with two predators andone prey in a shifting habitat

概 要 We discuss the spreading dynamics for a three-species predator-prey system with two weak competing

predators and one prey in a shifting habitat. First, we explain some extinction results for each species.
Then we provide some persistence theorems for each species with moving speeds exceeding the shifting
speed, but less than certain quantities. Finally, the convergence to a certain constant state is proven ineach persistent regime.
22 熊 谷 健 太 (東 工 大 理)
Kenta Kumagai (Tokyo Tech)

二次元における優臨界半線形楕円型方程式の分岐構造 · · · · · · · · · · · · · · · 12

Bifurcation structure of supercritical semilinear elliptic equations in two
dimensions

概 要 We consider the Gelfand problem with general supercritical nonlinearities in the two-dimensional unit

ball. In this talk, we prove the uniqueness of solutions for any small parameter. As a result, we obtain theexistence of a radial singular solution. Moreover, we prove the uniformly boundedness of ﬁnite Morse index
solutions. As a consequence, we show that the bifurcation curve has inﬁnitely many turning points. These
properties are known in N dimensions with 3 ≤ N ≤ 9 for general supercritical nonlinearities. On the other
hand, these properties are less known in two dimensions. Our results clarify that the bifurcation structure
solely depends on the supercriticality/subcriticality of the nonlinearities.
23 宮 本 安 人 (東 大 数 理)
内 藤 雄 基 (広島大先進理工)

Yasuhito Miyamoto (Univ. of Tokyo)Yūki Naito (Hiroshima Univ.)

A bifurcation diagram of solutions to semilinear elliptic equations withgeneral supercritical growth · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
A bifurcation diagram of solutions to semilinear elliptic equations withgeneral supercritical growth

概 要 We study the global bifurcation diagram of positive solutions to the semilinear elliptic equation∆u + λf (u) = 0. Under general supercritical growth conditions on f (u), we show that an unboundedbifurcation curve has no turning point, which indicates the existence of the singular extremal solution.
In particular, our theory can be applied to the super-exponential cases of f (u), and we exhibit that thebifurcation curve has the same qualitative property as a classical Gel’fand problem for N ≥ 3 except N = 10.

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函数方程式論特別講演
中 野 史 彦 ( 東 北 大 理)

ランダムシュレーディンガー作用素の準位統計とランダムウォーク

Fumihiko Nakano (Tohoku Univ.)

Statistics for random Schroedinger operators and random walk50

17:00〜18:00

概 要 Disordered quantum systems is one of the fundamental topics in mathematical physics. It is theorigin of various important phenomena, such as Anderson localization, quantum Hall eﬀect and topologicalinsulators. A typical feature in its spectral property is the appearance of dense point spectrum andexponential decay of corresponding eigenfunctions. Recently, much attention is being paid for its statisticalproperty, which is believed to reﬂect the structure of these systems.
In this talk, I will review results on the eigenvalue statistics problem for the following Hamiltonians, throughwhich one can see how the statistics is inked to spectral property and then its essential features.
(i) 1-dimensional model with decaying potentials : it has phase transition depending on the decay rate.
Many results have been obtained, including eigenfunction statistics.
(ii) d-dimensional model with decaying potentials : much less is known than (i), but it has another type ofphase transition.
(iii) 1-dimensional dimer model : it typically has critical energy where the Lyapunov exponent vanishes, on
which it has strange statistical behavior, except which we have usual Poisson statistics.
(iv) 1-dimensional model related to vertex reinforced jumped process (ongoing work) : spectral property islinked to the recurrence of this RW.

9 月 4 日（水）第 II 会場

9:00〜12:00
24 渡 邉

南 ( 津 田 塾 大 理)

Minami Watanabe (Tsuda Coll.)Long time perturbation theory for nonlinear Schrodinger equation withexponential nonlinearity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Long time perturbation theory for nonlinear Schrodinger equation withexponential nonlinearity

概 要 In this talk, we will deal with the nonlinear Schrödinger equation (NLS) in which the nonlinear

term is an exponential function. (NLS) has a solution called a scattering solution when the dispersion ismore dominant than the nonlinearity of the equation. When doing this analysis, we generally consider asmall solution and decompose it into a solitary wave component and a dispersive wave component, and astime passes, the solitary wave component converges to a ﬁxed solitary wave, and the dispersive component
converges more strongly to a linear solution. It is necessary to show that In the presentation, we will present
the perturbation theory used for the proof.
25 片 山翔 ( 東 大 数 理)

Sho Katayama (Univ. of Tokyo)

半空間上の Lane–Emden 方程式の非斉次 Dirichlet 問題の解の存在と多重性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Existence and multiplicity of solutions to non-homoegeneous Dirichletproblems for the Lane–Emden equation

概 要 This talk concerns a structure of positive solutions to the (not necessarily subcritical) Lane–Emdenequation −∆u = up in the half-space RN+ with the non-homogeneous Dirichlet boundary condition u = κµon ∂RN+ . Under suitable conditions on the exponent p and a nonnegative continuous boundary data µ, wegive a complete classiﬁcation of the existence/nonexistence of positive solutions with respect to the value ofparameter κ > 0. We also give a result on the multiple existence of solutions via bifurcation theory. The
most important aspect of this result is a new-type condition for the exponent p, which reﬂects the structureof the half-space.

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51

函数方程式論

26 田 中敏 (東 北 大 理) [ Existence of positive solutions to an eigenvalue problem with a variable
exponent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Satoshi Tanaka (Tohoku Univ.)

Existence of positive solutions to an eigenvalue problem with a variable
exponent

概 要 The problem −∆p(|x|) u − ∆q u = λ(|u|p(|x|)−2 u + |u|q−2 u) in B; u = 0 on ∂B is considered, whereB = {x ∈ RN : |x| < R}, N ≥ 1, ∆p(|x|) u = div(|∇u|p(|x|)−2 ∇u), p(r) is continuous and satisﬁes p(r) > 1 on
[0, R], ∆q u = div(|∇u|q−2 ∇u), and q > 1. The existence of positive solutions is proved for every λ > λ1 (q),where λ1 (q) is the ﬁrst eigenvalue of q-Laplacian.
27 田 中 視 英 子 (東 京 理 大 理)

Mieko Tanaka (Tokyo Univ. of Sci.)

Remarks on non-local eigenvalue problems for the p-Laplacian · · · · · · · 12
Remarks on non-local eigenvalue problems for the p-Laplacian

概 要 We consider the p-Laplace eigenvalue problem having a nonlocal term under the zero Dirichletboundary condition. In particular, we show the existence of the least eigenvalue µw
q such that the equation
has a nodal solution. We prove that this eigenvalue µw
q coincides with the second one in the p-sublinear
case q < p provided w ≥ 0 a.e. in Ω.
28 梶 木 屋 龍 治(大阪電通大共通教育機構)
田 中 視 英 子 ( 東 京 理 大 理)
田 中
敏 ( 東 北 大 理)
Ryuji Kajikiya(Osaka Electro-Comm. Univ.)
Mieko Tanaka (Tokyo Univ. of Sci.)
Satoshi Tanaka (Tohoku Univ.)

The best constant for the Sobolev–Poincaré inequality, I. Asymptotic
behavior · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

The best constant for the Sobolev–Poincaré inequality, I. Asymptotic
behavior

概 要 We study the best constant of the Sobolev–Poincaré inequality in the one dimensional case,λ(p, q, L)kukpLq ≤ ku′ kpLp for u ∈ W01,p (0, L). Then λ(p, q, L) is the ﬁrst eigenvalue for the second order diﬀerential equation. We study λ(p, q, L) and the n-th eigenvalue λn (p, q, L) also. We give the explicit
formula of λn (p, q, L) and investigate its asymptotic behavior as p and q tend to 1 + 0 or ∞.
29 梶 木 屋 龍 治(大阪電通大共通教育機構)
田 中 視 英 子 ( 東 京 理 大 理)
田 中
敏 ( 東 北 大 理)
Ryuji Kajikiya(Osaka Electro-Comm. Univ.)
Mieko Tanaka (Tokyo Univ. of Sci.)
Satoshi Tanaka (Tohoku Univ.)

The best constant for the Sobolev–Poincaré inequality, II. Monotonicity· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

The best constant for the Sobolev–Poincaré inequality, II. Monotonicity

概 要 We study the best constant of the Sobolev–Poincaré inequality in the one dimensional case,λ(p, q, L)kukpLq ≤ ku′ kpLp for u ∈ W01,p (0, L). Then λ(p, q, L) is the ﬁrst eigenvalue for the second order diﬀerential equation. We study λ(p, q, L) and the n-th eigenvalue λn (p, q, L) also. We compute its
partial derivatives and study the monotonicity and non-monotonicity of λn (p, q, L) with respect to p and q.
30 筒 井 容 平 (京大理)Youhei Tsutsui (Kyoto Univ.)

Two-weight inequality for the heat ﬂow and solvability of Hardy–Hénontype equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Two-weight inequality for the heat ﬂow and solvability of Hardy–Hénontype equation

概 要 We give two weight inequality for the heat ﬂow by using sparse domination. From the estimates, we

provide the existence results of Hardy–Hénon type equations.

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函数方程式論

3 波相互作用をもつ非線形シュレディンガー方程式系に対する local mountain pass approach によるピーク解の構成 · · · · · · · · · · · · · · · · · · · · · · · · · 1231 長 田 祐 輝 (埼 玉 大 理 工)
佐 藤 洋 平 ( 埼 玉 大 理 工)
Yuki Osada
Yohei Sato

52

(Saitama Univ.)(Saitama Univ.)

A construction of peak solutions by a local mountain pass approach fora nonlinear Schrödinger system with three wave interaction

概 要 In this talk, we consider the following nonlinear Schrödinger system with three wave interaction:−2 ∆u1 + V1 (x)u1 = µ1 |u1 |p−1 u1 + αu2 u3 ,
−2 ∆u2 + V2 (x)u2 = µ2 |u2 |p−1 u2 + αu1 u3 ,−2 ∆u + V (x)u = µ |u |p−1 u + αu u ,
3

3

3

3

3

3

1 2

in RN ,
in RN ,
in RN ,

where N ≤ 5, 1 < p < 2∗ − 1, 2∗ = ∞ (N ≤ 2), 2∗ = 2N/(N − 2) (N ≥ 3),  > 0, Vj (x) > 0,
µj > 0 (j = 1, 2, 3) and α > 0. We construct a peak solution that is concentrating at a local minimum pointof a function c(V1 (x), V2 (x), V3 (x)) determined from potentials V1 (x), V2 (x) and V3 (x).
32 木 下 智 晴 (早 大 理 工)長 田 祐 輝 ( 埼 玉 大 理 工)

Tomoharu Kinoshita (Waseda Univ.)(Saitama Univ.)
Yuki Osada

Multiplicity of solutions for a nonlinear Schrödinger system with three
wave interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Multiplicity of solutions for a nonlinear Schrödinger system with three
wave interaction

概 要 In this talk, we study the multiplicity of solutions for a nonlinear Schrödinger system with three wave

interaction under the radial setting. In addition, we consider the vectorness of critical values for suﬃciently
large coupling parameter.
33 牧 田 慎 平 (北
中 安
淳 (東

大

理)

大

工)

Shimpei Makida (Hokkaido Univ.)
Atsushi Nakayasu (Univ. of Tokyo)

Stability of metric viscosity solutions under Hausdorﬀ convergence · · · 12
Stability of metric viscosity solutions under Hausdorﬀ convergence

概 要 We establish a stability result for viscosity solutions of Hamilton–Jacobi equations for a sequence ofdomains converging in the Hausdorﬀ sense. A background of this study is domain perturbation problems for
Hamilton–Jacobi equations. In this talk we introduce the idea of proving the stability of viscosity solutions,starting with the deﬁnition of metric viscosity solutions. A key to the proof is a characterization of themetric viscosity solutions by the squared distance functions.
34 E. Zhanpeisov (沖縄科学技術大)柳青 (沖縄科学技術大)Erbol Zhanpeisov(Okinawa Inst. of Sci. and Tech. Grad. Univ.)
Qing Liu(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy

概 要 We study a general class of fully nonlinear boundary-degenerate elliptic or parabolic equations that

admit a trivial solution. Although no boundary conditions are posed together with the equations, weshow that the operator degeneracy actually generates an implicit boundary condition. Under appropriate
assumptions on the degeneracy rate and regularity of the operator, we then prove that there exist no
bounded solutions other than the trivial one. Our method is based on the arguments for uniqueness ofviscosity solutions to state constraint problems for Hamilton–Jacobi equations. Several concrete examplesof the equations that satisfy the assumptions are also given.

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53

函数方程式論35 藤 田 安 啓 (富 山 大 理)
山 口 範 和 ( 富 山 大 教 育)

Yasuhiro Fujita (Univ. of Toyama)
Norikazu Yamaguchi (Univ. of Toyama)

Hamilton–Jacobi ﬂow から見る Weierstrass 函数と高木函数の差異 · · · · 12
A diﬀerence between Weierstrass function and Takagi function from theviewpoint of Hamilton–Jacobi ﬂows

概 要 In this talk, we clarify a diﬀerence among everywhere continuous and nowhere diﬀerentiable func-

tions, especially between famous Takagi function and Weierstrass function. This diﬀerence is reﬂected on
Hamilton–Jacobi ﬂows starting from these functions. As far as the authors know, this is the ﬁrst attempt
to clarify such a diﬀerence.
36 江 藤 徳 宏 (東 大 数 理)
儀 我 美 一 ( 東 大 数 理)
Tokuhiro Eto (Univ. of Tokyo)
Yoshikazu Giga (Univ. of Tokyo)

A convergence result for a minimizing movement scheme for mean curvature ﬂow with prescribed contact angle in a curved domain · · · · · · · · 12
A convergence result for a minimizing movement scheme for mean curvature ﬂow with prescribed contact angle in a curved domain

概 要 We consider a minimizing movement scheme of Chambolle type for the mean curvature ﬂow equation

with prescribed contact angle condition in a smooth bounded domain in Rd (d ≥ 2). We prove that an
approximate solution constructed by the proposed scheme converges to the level-set mean curvature ﬂow
with prescribed contact angle provided that the domain is convex and that the contact angle is awayfrom zero under some control of derivatives of given prescribed angle. We actually prove that an auxiliary
function corresponding to the scheme uniformly converges to a unique viscosity solution to the level-set
equation with an oblique derivative boundary condition corresponding to the prescribed boundary condition.
13:00〜14:00

特別講演
田 中 視 英 子 ( 東 京 理 大 理)

Eigenvalue problems for (p, q)-Laplace equations with two parameters

Mieko Tanaka (Tokyo Univ. of Sci.)

Eigenvalue problems for (p, q)-Laplace equations with two parameters

概 要 We consider generalized eigenvalue problems for (p, q)-Laplacian with two parameters under the

Dirichlet boundary condition.The equations we are dealing with consist of two eigenvalue problems forp-Laplacian and q-Laplacian, which were introduced by myself and Bobkov. We have considered theclassiﬁcation of parameters such that the equation has positive solutions or sign change solutions in responseto the ﬁrst or second eigenvalue problem. This talk is based on the results of joint research works with
Vladimir Bobkov that have been in progress for the last nine years.

9 月 5 日（木）第 II 会場

9:00〜12:00
37 原 田 潤 一 (秋田大教育文化)
Junichi Harada (Akita Univ.)

藤田型熱方程式における非退化常微分的爆発解の安定性について · · · · · · 10

Stability of the nondegenerate ODE type blowup for the Fujita typeheat equation

概 要 We discuss the stability of nondegenerate ODE type blowup for the Fujita equation. This result isknown for the Sobolev subcritical case. We extend this result to the general power nonlinearity case.

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函数方程式論38 福 田 一 貴 (信 州 大 工)
佐 藤 槙 哉 ( 信 州 大 工)
Ikki Fukuda
Shinya Sato

(Shinshu Univ.)(Shinshu Univ.)

54

Higher-order asymptotic proﬁles of solutions to the convection-diﬀusion
equation with variable diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12Higher-order asymptotic proﬁles of solutions to the convection-diﬀusion
equation with variable diﬀusion

概 要 We consider the asymptotic behavior of solutions to the convection-diﬀusion equation with variable

diﬀusion coeﬃcient a(x) = 1 + b(x) > 0, where b(x) is smooth and decays fast enough at spatial inﬁnity.
It is known that the asymptotic proﬁle of the solution to this problem can be given by the heat kernel.
Moreover, the second asymptotic proﬁle of the solution have already been obtained. In particular, thefollowing three cases are distinguished: 1 + n1 < q < 1 + n2 ; q = 1 + n2 ; q > 1 + n2 , where q is the nonlinear
exponent and n is the dimension. In this paper, we focus on the critical case of q = 1 + n2 . By analyzing
the corresponding integral equation in details, we have succeeded to give the more higher-order asymptotic
expansion of the solution, which generalizes the previous works.
39 草 場 竜 之 介 (早 大 理 工)

Ryunosuke Kusaba (Waseda Univ.)

Asymptotic expansions for the convection-diﬀusion equation in the Fujitasubcritical case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Asymptotic expansions for the convection-diﬀusion equation in the Fujitasubcritical case

概 要 We consider the large-time asymptotic behavior of global solutions to the Cauchy problem for theconvection-diﬀusion equation in the Fujita-subcritical case. We improve the decay rate of the remainder
for the ﬁrst order asymptotic expansion established by Zuazua (1993). We also prove the optimality andnon-optimality for the decay rate of the remainder by deriving the second order asymptotic expansion.
40 田 中 悠 也 (関 西 学 院 大 理)
下 條 昌 彦 ( 都 立 大 理)

Yuya Tanaka (Kwansei Gakuin Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)

Asymptotic behavior of solutions for diﬀusive epidemic models withlogistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Asymptotic behavior of solutions for diﬀusive epidemic models withlogistic source

概 要 Our aim is to show boundedness and global asymptotic stability of constant equilibria for an epidemic

model with logistic source in bounded domains in RN under homogeneous Neumann boundary conditions
and initial conditions. Moreover, we give a result on the asymptotic stability of traveling waves of the modelin the whole space R with equal diﬀusivities under initial conditions with certain perturbations of initialdata.
41 鈴 木貴 (阪 大 M M D S )Takashi Suzuki (Osaka Univ.)

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

Mathematical analysis for Brownian particle gas models, II

概 要 We continue to study Streater’s model on Brownian particle gas on bounded domains in Rn . If n ≤ 2

and the entropy production is bounded, there is an a priori estimate global in time. Under additional
properties on entropy and entropy production this solution converges to a unique steady state strongly andweakly for the models on classical and quantum particles, respectively.

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55

函数方程式論42 荒 木 康 太 (日 大 理 工)
水 野 将 司 ( 日 大 理 工)
(Nihon Univ.)
Kouta Araki
Masashi Mizuno (Nihon Univ.)

空間不均一な拡散を持つ非線形 Fokker–Planck 方程式の自由エネルギーの長時間挙動 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Long-time behavior of free energy in nonlinear Fokker–Planck models
with inhomogeneous diﬀusion

概 要 We consider the long-time asymptotic behavior of solutions to a nonlinear Fokker–Planck model,

including the porous medium-type nonlinear diﬀusion and inhomogeneous spatial diﬀusion subjected to the
Neumann boundary condition. The model is based on the continuity equation and the energy law regardingsome free energy. By assuming the diﬀusion coeﬃcient is suﬃciently large, we show the exponential decayof the ﬁrst derivative of the free energy, which is called the dissipation in terms of the free energy. To
prove the main result, we extend the entropy dissipation method to the Fokker–Planck equation with theinhomogeneous spatial diﬀusion coeﬃcient.
43 水 野 将 司 (日 大 理 工)
Y. Epshteyn ( Univ. of Utah )(Illinois Inst. of Tech.)
Chun Liu
Masashi Mizuno (Nihon Univ.)
Yekaterina Epshteyn (Univ. of Utah)
Chun Liu (Illinois Inst. of Tech.)

不均一な拡散を持つ非線形 Fokker–Planck 方程式に対するエントロピー
消散法 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

The entropy dissipation method to non-linear Fokker–Planck equations
with inhomogeneous diﬀusion

概 要 We consider the long-time behavior of solutions to non-linear Fokker–Planck equations with inhomo-

geneous diﬀusion. Based on the energy law with variable coeﬃcients and the continuity equation, we obtaina non-linear partial diﬀerential equation related to stochastic diﬀerential equations. The entropy dissipation
method is a well-known way to study the long-time behavior of the solution to the Fokker–Planck equations.
We extend the entropy dissipation methods and show the exponential decay of the free energy’s dissipation
term concerning the non-linear Fokker–Planck equation when the diﬀusion coeﬃcient is large enough.
44 佐 久 間 正 樹 (東 大 数 理)

Masaki Sakuma (Univ. of Tokyo)

一般化された畳み込み核をもつ臨界分数階 Choquard 型方程式の解の無限列の存在 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Existence of inﬁnite sequences of solutions to some critical fractional
Choquard-type equations with generalized convolution kernels

概 要 We discuss the existence of inﬁnite sequences of solutions to Choquard-type equations involving thefractional Laplacian and generalized nonlocal nonlinearities with critical growth. We utilize a generalizedversion of the concentration compactness method that can be directly applied to nonlocal quantities involving
convolution with weak Lp -functions in order to assure the compactness of (P S)c sequences. We guarantee
the existence of a sequence of weak solutions corresponding to critical values converging to zero by a criticalpoint theorem based on the concept of Krasnoselskii genus, which is useful in variational methods.

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函数方程式論45 鈴 木 将 満 (明大研究・知財)Masamitsu Suzuki (Meiji Univ.)

56

Local existence and nonexistence for fractional in time reaction-diﬀusion
equations and systems with rapidly growing nonlinear terms · · · · · · · · · 12
Local existence and nonexistence for fractional in time reaction-diﬀusion
equations and systems with rapidly growing nonlinear terms

概 要 We study the fractional in time reaction-diﬀusion equation∂ α u = ∆u + f (u) in RN × (0, T ),tu(x, 0) = u (x)in RN ,
0where 0 < α < 1, N ≥ 1, T > 0 and u0 ≥ 0. The fractional derivative ∂tα is meant in a generalized
Caputo sense. We mainly consider the case where f has an exponential or a superexponential growth,and u0 has a singularity. We obtain integrability conditions on u0 which explicitly determine local intime existence/nonexistence of a nonnegative mild solution. Moreover, our analysis can be applied to time
fractional systems.
46 小 島 瑞 輝 (東 工 大 理)
Mizuki Kojima(Tokyo Tech)

一様局所弱 Zygmund 空間における藤田臨界冪の時間非整数階半線形熱方程式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

On Fujita critical time-fractional semilinear heat equations in uniformly
local weak Zygmund spaces

概 要 In this talk, we consider the time-fractional semilinear heat equation with the critical exponent, in

uniformly local weak Zygmund spaces. We obtain a suﬃcient condition for the local-in-time solvability,
which does not vanish when the order of the derivative with respect to time goes to one. Through ourarguments, we see that the solvability of the time-fractional problem connects to the usual one in a naturalway.
47 三 浦 達 彦 (弘 前 大 理 工)

Tatsu-Hiko Miura (Hirosaki Univ.)

Thin-ﬁlm limit of the Ginzburg–Landau heat ﬂow in a curved thin domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Thin-ﬁlm limit of the Ginzburg–Landau heat ﬂow in a curved thin domain

概 要 We consider the Ginzburg–Landau heat ﬂow in a curved thin domain under the Naumann boundary

condition. When the curved thin domain shrinks to a given closed hypersurface as the thickness of the thindomain tends to zero, we show that the weighted average of a weak solution to the thin-domain problem
converges weakly on the limit surface under the assumption that the initial data is in L∞ . Moreover, wederive a limit equation on the limit surface by characterizing the limit function as a weak solution to thelimit equation.
48 廣 井 楓 也 (東 北 大 理)
岡 部 真 也 ( 東 北 大 理)
(Tohoku Univ.)
Fuya Hiroi
Shinya Okabe (Tohoku Univ.)

交叉する 2 直線上に自由端を持つ開曲線に対する曲線拡散流 · · · · · · · · · 12

Curve diﬀusion ﬂow with the boundary on two skew lines

概 要 We consider curve diﬀusion ﬂow for planar open curves with the boundary on two skew lines crossing

at the origin with the angle θ ∈ (0, π). In 2022 Wheeler–Wheeler considered curve diﬀusion ﬂow for planar
open curves with the boundary on two parallel lines and they proved global in time solvability of the
problem and exponential convergence of the solution to the line segment. In this talk, we will give a suitable
extension of the result of Wheeler–Wheeler to the case of curves with the boundary on two skew lines.

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57

函数方程式論Stability of pinned planar p-elasticae · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

大理)
49 三 浦 達 哉 (京吉 澤 研 介 ( 長 崎 大 教 育)

Tatsuya Miura (Kyoto Univ.)
Kensuke Yoshizawa (Nagasaki Univ.)

Stability of pinned planar p-elasticae

概 要 In this talk we consider stability of critical points of the p-bending energy among open planar curves

pinned at the endpoints. By a geometric approach, we obtain optimal necessary conditions for stable criticalpoints, and it leads to uniqueness of stable pinned p-elasticae for p ∈ (1, 2]. Our proof is based on a simple
but robust ‘cut-and-paste’ trick without computing the energy nor its second variation.
12:15〜12:45

2024 年度日本数学会解析学賞授賞式

14:30〜16:45
球体上の渦無し場に対する Hardy 不等式の最良 L2 型補正項について · · 1250 濱 本 直 樹 (阪 公 大 理)

Sharp L2 remainder term in Hardy inequality for curl-free vector ﬁelds
on the ball

Naoki Hamamoto (Osaka Metro. Univ.)

概 要 In this lecture we consider Hardy inequality of the form

ZZ|∇u|2 dx ≥ CNB

|u|2
dx + γN2
B |x|Z|u|2 dx.

(1)

B

Here u : B → RN denotes curl-free vector ﬁelds on the ball B = {x ∈ RN | |x| ≤ 1} with u |∂B = 0 and
CN > (N − 2)2 /4 denotes the sharp constant in the original Hardy inequality whose explicit value is known
under the curl-free constraint. The same form was previously obtained by Brezis–Vázquez for unconstrained
vector ﬁelds, while we treat the problem what is the best value of the constant γN for curl-free ﬁelds.
51 石 関彩 (埼 玉 大 理 工) [ 多成分絡み目に対する Möbius エネルギーとその Möbius 不変分解 · · · · 10
長 澤 壯 之 ( 埼 玉 大 理 工)
Aya Ishizeki (Saitama Univ.)
Takeyuki Nagasawa (Saitama Univ.)Möbius energies for multi-component-links, and their Möbius-invariant
decomposition

概 要 Möbius-invariant energy for multi-component links was proposed by Freedman–He–Wang. A newenergy is proposed here, and demonstrated its Möbius-invariance. When the number of components is 2,
both energies are the same. If this number exceeds 2, the energy becomes independent of Freedman–He–
Wang’s energy. In the previous study, the present authors showed that the energy for 2-component links
can be decomposed into two Möbius-invariant energies. In this study, the decomposition of the new energy
is demonstrated for m-component. This is decomposed into 252 星 屋 陽 俊 (東 大 数 理)

Akitoshi Hoshiya (Univ. of Tokyo)

m(m−1)
2

Möbius-invariant energies.

Orthonormal Strichartz estimate for Schrödinger operator · · · · · · · · · · · 10
Orthonormal Strichartz estimate for Schrödinger operator

概 要 We consider the orthonormal Strichartz estimate for Schrödinger operator, which is a generalizationof the ordinary Strichartz estimate. Under some assumptions on potentials, we prove the estimate for thesame exponent as the free Hamiltonian. Our proof is based on the smooth perturbation theory by T. Kato.
We also discuss some applications to nonlinear Schrödinger equations.

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函数方程式論53 川 本 昌 紀 (岡山大異分野基礎研)
大理)
水 谷 治 哉 (阪Masaki Kawamoto (Okayama Univ.)
Haruya Mizutani (Osaka Univ.)

58

Modiﬁed scattering for nonlinear Schrödinger equations with long-range
potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Modiﬁed scattering for nonlinear Schrödinger equations with long-range
potentials

概 要 We study the ﬁnal state problem for the nonlinear Schrödinger equation with a critical long-range

nonlinearity and a long-range linear potential. Given a prescribed asymptotic proﬁle which is diﬀerent
from the free evolution, we construct a unique global solution scattering to the proﬁle. In particular, theexistence of the modiﬁed wave operators is obtained for suﬃciently localized small scattering data. The classof potential includes a repulsive long-range potential with a short-range perturbation, especially the positive
Coulomb potential in two and three space dimensions. The asymptotic proﬁle is constructed by combining
Yafaev’s type linear modiﬁer associated with the long-range part of the potential and the nonlinear modiﬁer
introduced by Ozawa (1991). This is the ﬁrst positive result on the modiﬁed scattering for the nonlinear
Schrödinger equation in the case when both of the nonlinear term and the linear potential are of long-range
type.
54 眞 﨑

聡 (北

大

理)

Satoshi Masaki (Hokkaido Univ.)

強圧的な保存量をもつ NLS 方程式系の解の漸近挙動に関する部分的な分類について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Partial classiﬁcation of the asymptotic behavior of solutions to NLS
systems with coercive conserved quantity

概 要 In this talk, we consider the large-time behavior of solutions to a class of systems of cubic nonlinear

Schrodinger equations in one space dimension. The cubic nonlinearity is critical in one space dimension andthe large-time behavior involves the nonlinear eﬀect. The behavior of systems with a coercive conserved
quantity is previously studied and an asymptotic proﬁle was given with the help of an ODE system. We
try to provide the proﬁle as explicitly as possible by introducing a scheme to integrate the ODE system.
55 橋 本 隼 也 (埼 玉 大 理 工)
浜 野
大 ( 早 大 理 工)
町 原 秀 二 ( 埼 玉 大 理 工)

Shunya Hashimoto (Saitama Univ.)
Masaru Hamano (Waseda Univ.)
Shuji Machihara (Saitama Univ.)

確率非線形シュレディンガー方程式系の初期値問題の時間大域解 · · · · · · 12

Global solutions of stochastic nonlinear Schrödinger system

概 要 We consider global existence results for the solutions of systems of stochastic Schrödinger equations

with multiplicative noise and quadratic nonlinear terms. The same system in the deterministic treatment
was studied by Hayashi, Ozawa, and Tanaka where the mass and energy are conserved. In our stochastic
situation, those are not conserved.
56 國 分 海 斗 (東 京 理 大 理)

Kaito Kokubu (Tokyo Univ. of Sci.)

Stability of travelling waves to Benjamin–Ono type equations with double power nonlinearities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Stability of travelling waves to Benjamin–Ono type equations with double power nonlinearities

概 要 We study travelling waves of Benjamin–Ono type equations with double power nonlinearilies |u|p−1 u +|u|q−1 u, where 1 < p < q < ∞. In this talk, we show that the travelling waves are stable if p is an
L2 -subcritical exponent, with the method of Grillakis–Shatah–Strauss (1987).

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59

函数方程式論

57 S. Gustafson(Univ. of British Columbia)
大理)
戍 亥 隆 恭 (阪大理)
清 水 一 慶 (阪Stephen Gustafson(Univ. of British Columbia)(Osaka Univ.)
Takahisa Inui
(Osaka Univ.)
Ikkei Shimizu

Multi-solitons for the nonlinear Schrödinger equation with repulsive
Dirac delta potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Multi-solitons for the nonlinear Schrödinger equation with repulsive
Dirac delta potential

概 要 In this talk, we consider multi-soliton solutions for the 1-dimensional focusing nonlinear Schrödinger

equation (NLS for short) with repulsive Dirac delta potential at the origin (δNLS). The main result is theexistence of multi-soliton solutions for (δNLS), where the unmoving part is the standing wave solution of(δNLS), while the moving parts are the solitary wave solutions for NLS without potential.
58 波 多 間 備 (京 大 数 理 研) [ Asymptotic stability of stationary solutions of the Hartree equations for(Univ. of Rennes) inﬁnite quantum systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
A. Borie(Univ. of Rennes)
J. Sabin
Sonae Hadama (Kyoto Univ.)
Antoine Borie (Univ. of Rennes)
Julien Sabin (Univ. of Rennes)

Asymptotic stability of stationary solutions of the Hartree equations forinﬁnite quantum systems

概 要 In this talk, we consider the Hartree equation describing inﬁnite quantum systems. It has inﬁnitely

many stationary solutions, and we are interested in their asymptotic stability. This problem is an analogyof the nonlinear Landau damping on the quantum side. In the known results, we need strong assumptions
for both interactions and stationary solutions when d ≥ 4. In this talk, we weaken the assumptions for bothof them. There are two main diﬃculties: (1) How to get estimates with fractional derivatives, and (2) We
cannot use Christ–Kiselev lemma. We will discuss these diﬃculties and how to overcome them. This talk isbased on the joint work with Antoine Borie (University of Rennes) and Julien Sabin (University of Rennes).
17:00〜18:00

特別講演
大戍 亥 隆 恭 (阪Takahisa Inui理)

Global dynamics of threshold solutions for the nonlinear Schrödinger
equation with repulsive Dirac delta potential(Osaka Univ.)

Global dynamics of threshold solutions for the nonlinear Schrödinger
equation with repulsive Dirac delta potential

概 要 We consider the L2 -supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential

in one-dimensional space. A previous work clariﬁed the global dynamics of solutions below a threshold.
For general solutions, the threshold is given by a moving one-soliton. On the other hand, roughly speaking,that for even solutions is given by the ground state of the equation. Moreover, a sequent work showed thatin the general setting the solutions at the threshold scatter or blow up. In this talk, we mainly consider the
global dynamic of the even solutions at its threshold. Precisely speaking, the threshold has two regions; oneis given by the ground state as stated above, and the other is given by a moving two-soliton. In the former
case, we have ﬁve scenarios: scattering solutions, blow-up ones, ground states, and asymptotic solutions to
the ground state (which scatter or blow up in the opposite time direction). In the latter case, there are
only two scenarios: scattering or blow-up. This talk is based on joint works with Prof. Gustafson in the
University of British Columbia.

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函数方程式論

9 月 6 日（金）60

第 II 会場

9:15〜12:00
59 春 山 優 樹 (東 北 大 理) [ 空間 1 次元準線形波動方程式の古典解の爆発 · · · · · · · · · · · · · · · · · · · · · · · 10
高 村 博 之 ( 東 北 大 理)

Yuki Haruyama (Tohoku Univ.)
Hiroyuki Takamura (Tohoku Univ.)

Blow-up of classical solutions of quasilinear wave equations in one spacedimension

概 要 In this talk, we report on the upper bound of the lifespan of classical solutions of initial value problem

for one dimensional wave equation with quasilinear terms of spatial derivative of the unknown function.
This result is same as that of semilinear case. But our method of proof is slightly diﬀerent, which is basedon the weighted functional method by Rammaha and the iteration argument. Moreover, it is meaningful toconsider the kind of this problem to ensure the optimality of the general theory for nonlinear wave equation.
60 側 島 基 宏 (東京理大創域理工)Motohiro Sobajima(Tokyo Univ. of Sci.)

Asymptotic behavior for wave equations with space-dependent damping
in a weighted energy class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Asymptotic behavior for wave equations with space-dependent damping
in a weighted energy class

概 要 We consider the initial-boundary value problem of wave equations with space-dependent damping.

In the previous works, the asymptotic behavior of solutions has been discussed with a class of regular
initial data. In this talk, we deal with the asymptotic behavior of solutions with initial data belonging to aweighted energy space.
61 西 井 良 徳 (東 京 理 大 理)

Yoshinori Nishii (Tokyo Univ. of Sci.)

消散構造を伴う非線形 Klein–Gordon 方程式の小振幅解の減衰評価 · · · · 12

On the decay estimate for small solutions to nonlinear Klein–Gordon
equations with dissipative structure

概 要 We consider the Cauchy problem for cubic nonlinear Klein–Gordon equations in one space dimension.

We give the Lp -decay estimate for the small data solution and show that it decays faster than the freesolution if the cubic nonlinearity has the suitable dissipative structure.
62 高 山 正 宏 (慶 大 理 工)
井 口 達 雄 ( 慶 大 理 工)

Masahiro Takayama (Keio Univ.)(Keio Univ.)
Tatsuo Iguchi

局所項をもつ退化双曲系に対する初期境界値問題の適切性 · · · · · · · · · · · 12

Well-posedness of the initial boundary value problem for degenerate
hyperbolic systems with a localized term

概 要 We consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems

with a localized term and show its well-posedness. This problem arises in the analysis on the well-posednessof the initial boundary value problem for the motion of an inextensible hanging string of ﬁnite length under
the action of the gravity. One of diﬃculties of this problem comes from the degeneracy of the coeﬃcientmatrix. This diﬃculty can be overcome by using appropriate weighted Sobolev spaces. Another diﬃcultyof this problem comes from the localized term, which cannot be regarded as a lower order term. However,by introducing an appropriate energy functional we obtain an a priori energy estimate for the solution.
63 高 山 正 宏 (慶 大 理 工)
井 口 達 雄 ( 慶 大 理 工)

Masahiro Takayama (Keio Univ.)(Keio Univ.)
Tatsuo Iguchi

吊り下げられた紐の運動に対する線形化問題の適切性 · · · · · · · · · · · · · · · 12

Well-posedness of the initial boundary value problem for the linearized
system for the motion of an inextensible hanging string

概 要 We consider the linearized system for the motion of an inextensible hanging string. Well-posedness of

its initial boundary value problem is demonstrated as an application of the result obtained in the ﬁrst talk.
To this end, we reduce the linearized system to a degenerate hyperbolic system with a localized term.

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61

函数方程式論64 鶴 見 裕 之 (徳 島 大 理 工)
Jin Tan(CY Cergy Paris Univ.)( Tongji Univ. )Xin Zhang

Hiroyuki Tsurumi (Tokushima Univ.)
Jin Tan (CY Cergy Paris Univ.)(Tongji Univ.)
Xin Zhang

Solutions to the stationary Hall-MHD equations in Besov spaces · · · · · 12

Solutions to the stationary Hall-MHD equations in Besov spaces

概 要 We consider the solutions to the incompressible stationary Hall-magnetohydrodynamic (Hall-MHD)3/p−3

system in R3 . We ﬁrst show the existence and uniqueness of solutions with given forces in Ḃp,qfor

1 ≤ p < 3 and q = 1. Moreover, this result can be extended to any 1 ≤ q ≤ ∞ whenever p = 2. On
the other hand, when p ≥ 3, we show some ill-posedness results for the Hall-MHD system by using thediscontinuity of the solution mapping.
65 近 藤 信 太 郎 (岐 阜 大 工)
中 村 辰 樹 ( ア イ シ ン)
Shintaro Kondo (Gifu Univ.)
Tatsuki Nakamura(AISIN CORPORATION)

Global strong solution for the 2D MHD equations with shearing-periodic
boundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Global strong solution for the 2D MHD equations with shearing-periodic
boundary condition

概 要 In this talk, we consider the two-dimensional, two-ﬁeld MHD equations with imposed shear ﬂow whenplasma viscosity and resistivity are positive. We established the global-in-time existence and uniqueness ofa strong solution for the 2D two-ﬁeld MHD equations with shearing-periodic boundary condition which was
proposed by Hawley et al. in 1995. The main result is obtained by using Sobolev space.
66 鈴 木 政 尋 (名 工 大 工)
W. A. Strauss ( Brown Univ. )Masahiro Suzuki (Nagoya Inst. of Tech.)
Walter A. Strauss (Brown Univ.)

環状領域における気体放電 I: 安定性解析 · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Gas discharge in an annular region I: stability analysis

概 要 We study the initial–boundary value problem of the Morrow model which describes gas discharge overan annular region. This problem has a trivial stationary solution whose electron and ion densities are zero.
We analyze the stability and instability of the trivial stationary solution according to the voltage posed asa boundary condition, and also ﬁnd the threshold of voltage (sparking voltage).
67 鈴 木 政 尋 (名 工 大 工)
W. A. Strauss ( Brown Univ. )Masahiro Suzuki (Nagoya Inst. of Tech.)
Walter A. Strauss (Brown Univ.)

環状領域における気体放電 II: 分岐解析 · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Gas discharge in an annular region II: bifurcation

概 要 We study the boundary value problem of the stationary Morrow model which describes gas dischargeover an annular region. This problem has a trivial solution whose electron and ion densities are zero. It
is known that the trivial solution becomes unstable from stable when the voltage posed as a boundary
condition increases. The threshold is called a sparking voltage. In this talk, we analyze the bifurcation of
non-trivial solutions around the sparking voltage.

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函数方程式論68 小 池開 ( 東 工 大 理)
(Univ. Bordeaux)F. Sueur
G. Vergara-Hermosilla(Univ. Paris-Saclay)(Tokyo Tech)Kai KoikeFranck Sueur (Univ. Bordeaux)Gastón Vergara-Hermosilla(Univ. Paris-Saclay)

62

Local exact Lagrangian controllability of the 1D compressible Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Local exact Lagrangian controllability of the 1D compressible Navier–Stokes equations

概 要 We consider barotropic Navier–Stokes equations in a 1D channel [0, π] with homogeneous Dirichletboundary conditions at the ends. Given suﬃciently close subintervals I = [α1 , α2 ] and J = [β1 , β2 ], we showthat there exists an external force on the momentum equation such that the associated ﬂow maps I to J in
any given time T > 0. We show this by ﬁnding two external forces that have independent stretching eﬀects
on the interval I, then applying the inverse function theorem. That there exist such external forces is proved
as a consequence of a unique continuation property which we prove using Fourier analytic techniques.
69 出 口 直 人 (東 工 大 理)
Naoto Deguchi(Tokyo Tech)

定常外力付き圧縮性 Navier–Stokes 方程式の低 Mach 数極限について · · 12

Low Mach number limit of the compressible Navier–Stokes equation
with stationary force

概 要 We are concerned with the low Mach number limit of the compressible Navier–Stokes equation withstationary external force in the 3D whole space. It is known that if the external force decays in time, thenthe compressible Navier–Stokes ﬂows converge to the corresponding incompressible Navier–Stokes ﬂow when
the Mach number goes to zero. We derive the low Mach number limit of the compressible Navier–Stokes
equation when the external force is stationary and small enough.
14:15〜16:45
大理)
70 武 内 太 貴 (京()
諏訪東京理大工渡 邊 圭 市

Taiki Takeuchi (Kyoto Univ.)
Keiichi Watanabe (Suwa Univ. of Sci.)

Maximal regularity approarch to the Keller–Segel–Navier–Stokes systemwith nonlinear boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Maximal regularity approarch to the Keller–Segel–Navier–Stokes systemwith nonlinear boundary conditions

概 要 The Keller–Segel–Navier–Stokes system in a bounded smooth domain Ω ⊂ RN (N ≥ 2) is considered,

where the cell density n satisﬁes nonlinear boundary conditions due to the tensor-valued chemotactic
sensitivity function S. The aim of this talk is to construct a unique global strong solution of the system
by applying suitable maximal regularity theorems. In particular, to this end we establish a new maximal
regularity theorem for some linear heat equation with an inhomogeneous Neumann boundary condition.
71 飯 田 祥 樹 (早 大 理 工)
Yoshiki Iida

(Waseda Univ.)

Global well-posedness of the primitive equations on non-ﬂat layers in
the framework of maximal Lq -regularity · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Global well-posedness of the primitive equations on non-ﬂat layers in
the framework of maximal Lq -regularity

概 要 In this talk, we consider the primitive equations on non-ﬂat layers. We ﬁrst deﬁne the hydrostatic

Stokes projection operator on non-ﬂat layers, and we prove the maximal Lq -regularity of the corresponding
linearized equation via H ∞ -calculus. At the next step, in order to extend the local solution to the global
one, we establish an energy estimate in the framework of L2 -space.

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63

函数方程式論72 中 里 亮 介 (信 州 大 工)

Ryosuke Nakasato (Shinshu Univ.)

臨界 Fourier–Herz 空間に於ける Navier–Stokes 方程式の解の解析性と長時間挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Analyticity and asymptotic behavior of solutions to the Navier–Stokes
equations in critical Fourier–Herz spaces

概 要 We consider the initial value problem of the incompressible Navier–Stokes equations (NS) in thewhole space Rd (d ≥ 2). Starting with the pioneering work by Fujita–Kato (1964), many researchers havestudied the well-posedness of this problem (NS) in scaling critical spaces. In this talk, we focus on the endpoint critical spaces which guarantees the global well-posedness of the problem (NS). In such an end-point
framework, we newly establish the Foias–Temam type analyticity and Fujigaki–Miyakawa type asymptotic
expansion of mild solutions to the problem (NS).
73 小 薗 英 雄 (早 大 理 工)
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.)
Yutaka Terasawa (Nagoya Univ.)
Yuta Wakasugi (Hiroshima Univ.)

Asymptotic behavior of solutions to elliptic equations in 2D exterior
domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic behavior of solutions to elliptic equations in 2D exterior
domains

概 要 The asymptotic behavior of solutions to the second order elliptic equations in exterior domains isstudied. In particular, under the assumption that the solution belongs to the Lorentz space Lp,q or the
weak Lebesgue space Lp,∞ with certain conditions on the coeﬃcients, we give natural and an almost sharp
pointwise estimate of the solution at spacial inﬁnity.
74 大 石 健 太 (香 川 高 専)齋 藤 平 和 (電通大情報理工)
Kenta Oishi(Kagawa Nat. Coll. of Tech.)
Hirokazu Saito(Univ. of Electro-Comm.)

密度が一様でない非圧縮性粘性流体の 2 相問題の時間大域的可解性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Global solvability of the two-phase problem of inhomogeneous incompressible viscous ﬂuids

概 要 We develop the global solvability for a two-phase free boundary problem describing the motion of theinhomogeneous incompressible viscous ﬂuids in RN with N ≥ 3. The ﬂuids are separated from one anotherby a sharp interface, which is close to the hyperplane xN = 0. The proof is based on the maximal regularity
for a linearized problem and the time decay estimate of Stokes semigroup established by Saito. We also
introduce a norm of solutions simpler than that employed in the study due to Oishi and Shibata on the
one-phase ﬂows of homogeneous incompressible ﬂuids in a half-space-like domain.
75 津 田 和 幸 (九 州 産 大)(TU Darmstadt)
R. Farwig
Kazuyuki Tsuda(Kyushu Sangyo Univ.)
Reinhard Farwig (TU Darmstadt)

The time periodic problem for the Navier–Stokes equations on half
spaces with moving boundary: Linear theory · · · · · · · · · · · · · · · · · · · · · · 12
The time periodic problem for the Navier–Stokes equations on half
spaces with moving boundary: Linear theory

概 要 In this talk, we study a linear theory to deal with the time periodic problem for the Navier–Stokes

equations on unbounded domains with moving boundary. Compared to the case of bounded domains
the underlying modiﬁed time-dependent Stokes operators are no longer invertible, thus leading to a moresophisticated construction of the evolution operator. Moreover, Sobolev embeddings on Lq spaces imply
restrictions on q depending on geometric properties of the domain. The theory is focusing on the half spacecase, the construction and local-in-time estimates of the evolution operator and its adjoint in view of time
periodic solutions.

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函数方程式論76 津 田 和 幸 (九 州 産 大)(TU Darmstadt)
R. Farwig
Kazuyuki Tsuda(Kyushu Sangyo Univ.)
Reinhard Farwig (TU Darmstadt)

64

The time periodic problem for the Navier–Stokes equations on half
spaces with moving boundary: Nonlinear theory · · · · · · · · · · · · · · · · · · · 12
The time periodic problem for the Navier–Stokes equations on half
spaces with moving boundary: Nonlinear theory

概 要 This talk studies the construction of mild periodic solutions to the Navier–Stokes system in a family of

domains close to the half space with boundary moving periodically in time and perturbed locally in space.
In our ﬁrst talk we dealt with basic properties of the underlying modiﬁed Stokes operators, their adjoints
and the construction of their evolution operators with estimates locally in time. This talk proves via a
decomposition into low and high frequency parts global estimates of the evolution operator with algebraic
decay rates less than -1. Then nonlinear estimates using also duality techniques show that a corresponding
Poincare map locally has a unique ﬁxed point, the mild periodic solution. Various results also hold globallyin time in the case that the compactly supported perturbation of ∂Rn+ is uniformly bounded.
77 G. P. Galdi (Univ. of Pittsburgh)
山 本 立 規 ( 早 大 理 工)
Giovanni Paolo Galdi(Univ. of Pittsburgh)
Tatsuki Yamamoto (Waseda Univ.)

多重連結領域における非斉次 slip 境界条件を課した定常 Navier–Stokes
方程式の可解性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Nonhomogeneous boundary value problem for the steady Navier–Stokes
equations with the slip boundary conditions

概 要 We consider the nonhomogeneous boundary value problem for the steady Navier–Stokes equations un-

der the slip boundary conditions in a two-dimensional bounded domain with multiple boundary components.
By the incompressibility condition of the ﬂuid, the total ﬂux of the given boundary datum through theboundary must be zero. We prove that this problem has a solution if the friction coeﬃcient is suﬃciently
large compared with the kinematic viscosity constant and the curvature of the boundary. No additional
assumption (other than the necessary requirement of zero total ﬂux through the boundary) is imposed on
the boundary data. The required a priori estimate to apply the Leray–Schauder ﬁxed point theorem isproved by a contradiction argument.
78 渡 邊 圭 市 (諏訪東京理大工)

Keiichi Watanabe (Suwa Univ. of Sci.)

The Helmholtz decomposition of vector ﬁelds for two-dimensional exterior Lipschitz domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
The Helmholtz decomposition of vector ﬁelds for two-dimensional exterior Lipschitz domains

概 要 Let Ω be an exterior Lipschitz domain in R2 . It is proved that the Helmholtz decomposition of thevector ﬁelds in Lp (Ω; R2 ) exists if p satisﬁes |1/p − 1/2| < 1/4 + ε with some constant ε = ε(Ω) ∈ (0, 1/4],
where it is allowed to take ε = 1/4 if ∂Ω ∈ C 1 .
79 高 橋 知 希 (神 奈 川 大 工)
渡 邊 圭 市 (諏訪東京理大工)

Tomoki Takahashi (Kanagawa Univ.)
Keiichi Watanabe (Suwa Univ. of Sci.)

The Navier–Stokes ﬂow in the exterior of a moving obstacle with a
Lipschitz boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
The Navier–Stokes ﬂow in the exterior of a moving obstacle with a
Lipschitz boundary

概 要 Consider the three-dimensional Navier–Stokes ﬂow past a moving rigid body O ⊂ R3 with prescribedtranslational and angular velocities, where O stands for a bounded Lipschitz domain. We prove that thesolution to the linearized problem is governed by a C0 -semigroup on solenoidal Lq -vector spaces with the
Lq -Lr estimates provided that |1/q − 1/2| < 1/6 + ε with some ε > 0. As an application, we prove theexistence and uniqueness of mild solutions to the Navier-Stokes problem when the translational and angularvelocities and the initial are suﬃciently small.

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函数方程式論17:00〜18:00

特別講演
ブレジナヤン (九 大 基 幹)

Long-time behavior of the dissipative compressible MHD(Kyushu Univ.)

Long-time behavior of the dissipative compressible MHD

Jan Brezina

概 要 Dissipative systems are thermodynamically open systems often in the out of equilibrium regime. They

are examples of the most interesting real world phenomena developing patterns, structures, or behaviours
that they did not have when ﬁrst formed. The dissipative systems exchange energy and matter with theirenvironment, while dissipating mechanical and other forms of energy in accordance with the Second law ofthermodynamics. In continuum ﬂuid mechanics, a family of ﬁeld equations accompanied with inhomogeneous
boundary conditions are often used to model dissipative systems.
Many spectacular events occurring in geophysics or astrophysics, among which the dynamics of the solar
convection zone, are attributed to the action of the magnetic ﬁeld. As direct measurements and data collecting are often hampered by obvious technical limitations, reliable mathematical models are indispensable forunderstanding the observed phenomena. As pointed out by Gough, a correct choice of boundary conditions
plays a crucial role.
In this talk we discuss the long time behavior of the complete system of equations governing the motion ofa general compressible, viscous, electrically and heat conductive ﬂuid driven by non–conservative boundary
conditions. That is, the time evolution of the solutions to a dissipative compressible magnetohydrodynamics.

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実函数論

実

函

数

9 月 5 日（木）66

論第 VI 会場

9:00〜12:00
1 加
宮
至
冨

藤
地
田
田

睦
晶
直
直

也 ( 岐 阜 大 工)
彦 (東京女大現代教養)
人 ( 名 大 多 元 数 理)
大
理)
人 (阪

(Gifu Univ.)
Tomoya Kato
Akihiko Miyachi(Tokyo Woman’s Christian Univ.)(Nagoya Univ.)
Naoto Shida
Naohito Tomita (Osaka Univ.)

Bilinear oscillatory Fourier multipliers · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Bilinear oscillatory Fourier multipliers

概 要 In this talk, we consider bilinear Fourier multipliers that contain some oscillatory factors. In particular,

we consider the boundedness of these operators between Lebesgue spaces including endpoint cases. Our
results improve Bergfeldt, Rodriguez-Lopez, Rule and Staubach’s results for the case of bilinear Fourier
multiplier operators.
2 陳

彦 含 (京Yanhan Chen

大理)

(Kyoto Univ.)

Weighted weak type bounds for fractionally sparsely dominated operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Weighted weak type bounds for fractionally sparsely dominated operators

概 要 We consider operators satisfying a fractionally sparse domination property, according to the deﬁnition

by Lerner, Lorist and Ombrosi. As a supplement to their strong type estimates, we establish two weighted
weak type estimate for those operators. Firstly, we give a quantitative bound in multiplier weak type sensewith the Muckenhoupt weight. Then we introduce the class of weights that characterizes the restricted
weak type bounds (for example, maximal operator), and establish such bounds for fractionally sparsely
dominated operators.
3 李
旭 (奈良女大人間文化)
森 藤 紳 哉 ( 奈 良 女 大 自 然)

Akira Lee (Nara Women’s Univ.)
Shinya Moritoh (Nara Women’s Univ.)

パンディ–ウパディヤイのウェーブレット変換と関数の超局所的特異性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Pandey–Upadhyay’s wavelet transform and microlocal singularities offunctions

概 要 The main objective of this talk is to deﬁne microlocal singularities of functions using the Pandey–

Upadhyay wavelet transform and provide a comparison with another microlocal singularities.
4 加 藤 睦 也 ( 岐 阜 大 工)
宮 地 晶 彦 (東京女大現代教養)
大理)
冨 田 直 人 (阪(Gifu Univ.)
Tomoya Kato
Akihiko Miyachi(Tokyo Woman’s Christian Univ.)
Naohito Tomita (Osaka Univ.)ある双線形波動作用素の評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Estimates for some bilinear wave operators

概 要 We consider some bilinear Fourier multiplier operators and give a bilinear version of Seeger, Sogge,

and Stein’s result on Fourier integral operators. Our results improve, for the case of Fourier multiplier
operators, Rodrı́guez-López, Rule, and Staubach’s result for bilinear Fourier integral operators. We also
give partial results on the sharpness of the estimates.

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実函数論

5 川 澄 亮 太 (神戸学院大経営)
米 田
剛 ( 一 橋 大 経 済)

Ryota Kawasumi (Kobe Gakuin Univ.)
Tsuyoshi Yoneda (Hitotsubashi Univ.)

定義関数の各点収束に対する深層ニューラルネットワークとフーリエ級数の違いについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Diﬀerence between the deep neural network and the Fourier series frompointwise convergence for the indicator function

概 要 For the multiple Fourier series of periodization of some radial functions on Rd , Kuratsubo (2010)

investigated the behavior of the spherical partial sum and discovered the third phenomenon other than
Gibbs–Wilbraham and Pinsky phenomena. In particular, the third one exhibits prevention of pointwise
convergence. On the other hand, in the ﬁeld of deep learning, one of the purposes is to ﬁnd an approximationof the function as a universal approximation theorem. Therefore, it is important that a function converges
pointwise. In this talk, we clarify the crucial diﬀerence between the deep neural network and the Fourier
series from pointwise convergence for the indicator function. Further, we deﬁne a speciﬁc deep neuralnetwork and prove pointwise convergence.
6 山 口 哲 志 ( 茨 城 大 理 工)
中 井 英 一 ( 茨 城 大 理)

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

Generalized fractional integral operators on subspaces of generalized
Morrey spaces with variable growth condition · · · · · · · · · · · · · · · · · · · · · 15
Generalized fractional integral operators on subspaces of generalized
Morrey spaces with variable growth condition∞
概 要 We consider the closure of Ccomp(Rd ) with respect to generalized Morrey spaces with variable growth

condition. We show the boundedness of generalized fractional integral operators on them.
7 野 ヶ 山 徹 ( 東 京 理 大 理)

Toru Nogayama (Tokyo Univ. of Sci.)

Weighted maximal inequalities for local Bourgain–Morrey spaces · · · · · 15
Weighted maximal inequalities for local Bourgain–Morrey spaces

概 要 In this talk, we consider the boundedness of the Hardy–Littlewood maximal operator on weighted

local Bourgain–Morrey spaces. In particular, we consider the case of power weights. The diﬀerence of theclassical one is only endpoint case.
8 中 村
元(松江工高専⋆・明石工高専)
橋 本 一 夫 (広島女学院大⋆)Gen Nakamura(Matsue Coll. of Tech.⋆/Akashi Coll. of Tech.)Kazuo Hashimoto(Hiroshima Jogakuin Univ.⋆)

Sobolev 空間 W n.p (Ω) の n 階-有限差分を用いた特徴付けについて · · · · 15

On the characterizaton of one-dimensional, n-order Sobolev spaces interms of higher-order ﬁnite diﬀerences

概 要 We characterize n-order Sobolev spaces deﬁned on open sets in Real numbers in terms of higher-orderﬁnite diﬀerences (i.e. center diﬀerence, forward diﬀerence and backward diﬀerence). It allows us to give adeﬁnition of one-dimensional Sobolev spaces that does not involve derivatives.
9 筒 井 容 平 (京大理)Youhei Tsutsui (Kyoto Univ.)

A proof of Alvino’s embedding BV ,→ Ln/(n−1),1 via medians · · · · · · · 15
A proof of Alvino’s embedding BV ,→ Ln/(n−1),1 via medians

概 要 We give an alternative proof of Alvino’s embedding by using medians.

10 波 多 野 修 也 (中 大 理 工)
池 田 正 弘(理化学研 AIP・慶大理工)(Chuo Univ.)
Naoya Hatano
Masahiro Ikeda (RIKEN/Keio Univ.)

Smoothing estimate for the heat semigroup with a homogeneous weighton Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Smoothing estimate for the heat semigroup with a homogeneous weighton Morrey spaces

概 要 We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the

Hardy–Hénon parabolic equation on Morrey spaces.

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実函数論

68

14:15〜16:45
11 波 多 野 修 也 (中 大 理 工)
池 田 正 弘(理化学研 AIP・慶大理工)
川 澄 亮 太 (神戸学院大経営)(Chuo Univ.)
Naoya Hatano
Masahiro Ikeda (RIKEN/Keio Univ.)
Ryota Kawasumi (Kobe Gakuin Univ.)

Boundedness of composition operators from Lorentz spaces to Orlicz
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Boundedness of composition operators from Lorentz spaces to Orlicz
spaces

概 要 The boundedness (continuity) of composition operators from some function space to another one issigniﬁcant, though there are few results about this problem. Thus, in this study, we provide necessary andsuﬃcient conditions on the boundedness of composition operators from Lorentz spaces to Orlicz spaces. We
emphasize that the measure spaces associated with the Lorentz space may be diﬀerent from those associatedwith the Orlicz spaces. Moreover we give some examples and counterexamples of the composed mappingsin the conditions.
12 宮 崎 洋 一 (日大歯)Yoichi Miyazaki (Nihon Univ.)

トリーベル・リゾルキン空間における対数型不等式 · · · · · · · · · · · · · · · · · 15

Logarithmic inequalities in Triebel–Lizorkin spaces

概 要 Let us consider the logarithmic inequalities of Brezis–Gallouet–Wainger type in Triebel–Lizorkin spaces

and Triebel–Lizorkin–Morrey spaces. We obtain the inequalities
kf kL∞ ≲n,p,r,s 1 + kf kḞ n/r log+ (kf kLp + kf kĊ s )1− r1r,∞

for 1 ≤ p < ∞, 1 < r ≤ ∞, s > 0, and0
kf kB∞,1≲n,p,q,r,r1 ,s 1 + kf kĖ n/r

r,r1 ,∞

ulog+ kf kEp,q,∞

for 0 < q ≤ p < ∞, 1 ≤ r1 ≤ r < ∞, n/p < u < ∞. These inequalities improve the results obtained by
Kozono–Wadade (2008) and Sawano–Wadade (2013) respectively.
13 北
廣 男 (鹿 児 島 大⋆)宮 本 孝 志 ( 大 阪 教 育 大)
尾 形 尚 子 (神戸大教育推進機構)

Hiro-o Kita (Kagoshima Univ.⋆)
Takashi Miyamoto(Osaka Kyoiku Univ.)(Kobe Univ.)
Naoko Ogata

ϕ-関数により構成される一般化された弱 Orlicz 空間における ∆0 -条件について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On ∆0 -condition for generalized weak Orlicz space constructed by ϕfunction

概 要 The importannce of ∆0 -condition in generalized weak Orlicz space will be given.

14 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 and meandemiclosed mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Convergence theorems for monotone nonexpansive mappings and meandemiclosed mappings

概 要 In this talk, we prove weak convergence theorems for monotone nonexpansive mappings and α-

nonexpansive mappings. Further, we prove convergence theorems for mean-demiclosed mappings.

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実函数論

15 本 田 あ お い (九 工 大 情 報 工)
福 田 亮 治 ( 大 分 大 理 工)
岡 崎 悦 明 (ファジィシステム研)

Aoi Honda (Kyushu Inst. of Tech.)(Oita Univ.)
Ryoji Fukuda
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

Choquet 積分による関数空間 L1 (Ch) の一様構造 · · · · · · · · · · · · · · · · · · · · 15

Uniform Structure of the Choquet Function Space L1 (Ch)概 要 Let µ be a non-additive measure on the measurable space (X, B). For a non-negative B-measurable

R
R∞
function f , the Choquet integral is deﬁned by X f (x) dµ = 0 µ(f > r) dr. The Choquet function spaceR∞
L1 (Ch) is deﬁned by {f | 0 µ(|f | > r) dr < ∞}. The uniform structure of L1 (Ch) is investigated.

16 河 邊

淳 ( 信 州 大 工)

Jun Kawabe(Shinshu Univ.)

連続型ショケ積分表示定理の抽象形 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The abstract forms of the continuous Choquet integral representation
theorems

概 要 The purpose of the talk is to present the abstract forms of the Choquet integral representation

theorems in such a way that the representing measures are simultaneously inner and outer continuous
on appropriate collections of tractable sets such as open, closed, compact, and measurable. This type oftheorem is referred to as the continuous Choquet integral representation theorem and will be discussed in asetting general enough for practical use.
17 川 﨑 敏 治 (玉川大工・千葉大理)
Toshiharu Kawasaki(Tamagawa Univ. / Chiba Univ.)

拡張不定積分について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the extended indeﬁnite integral

概 要 We would like to consider a case where the indeﬁnite integral takes an inﬁnite value. For that reason,

we extend the concept of integrals. In this talk, we discuss the extended indeﬁnite integral.
18 伊 東 由 文 (徳島大⋆)Yoshifumi Ito (Tokushima Univ.

⋆)

空間・時間・物質考究 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Study on space-time-matter

概 要 In this lecture, we give the fundamental facts on the concepts of space, time and matter.

We determine that the cosmic space is the 3-dimensional Euclidean space.
We give the concept of time at ﬁrst, and the condition which the material particle must satisfy.
We study what are the physical phenomena and the natural statistical phenomena.
17:00〜18:00

特別講演
齋 藤 洋 樹 ( 日 大 理 工)Fractional integrals and related phenomena in analysis(Nihon Univ.)

Fractional integrals and related phenomena in analysis

Hiroki Saito

概 要 The purpose of this talk is to investigate the behavior of the Riesz potential on several functions spaces

containing Choquet and Choquet–Morrey spaces. To clearly describe the connection between Morrey spaces
and Hausdorﬀ capacities, Riesz potentials will be placed at the center of the discussion. In the ﬁrst halfof this talk, we will review some elementary facts about Hausdorﬀ capacities and maximal theorems, andintroduce its applications to PDEs. In the latter half, several recent works by other authors, as well as theauthor’s results based on joint work with Hatano, Kawasumi, and Professor Tanaka, will be discussed.

2024/08/21 作成
実函数論

9 月 6 日（金）70

第 VI 会場

10:00〜12:00
19 垣 内花 ( 日 本 女 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)

Hana Kakiuchi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

焼成過程を記述する自由境界問題の解の存在について · · · · · · · · · · · · · · · 15

On existence of solutions to free boundary problems representing thebaking process

概 要 In this talk we establish existence of solutions to the one-dimensional free boundary problem describing

a baking process of bread. For the problem we assume that a region occupied by the breads consists of
crumb, crust and the evaporation front, and unknown functions are the position of the evaporation front,
the temperature ﬁeld and the mass distribution. By the diﬃculty of the boundary condition, we haveconsidered only the approximation problem. Now, we aim to show existence of solutions to the original
problem by applying the weak formulation.
20 鵜 飼 直 孝 (千葉大融合理工)
水 野 大 樹 (千葉大融合理工)白 川
健 ( 千 葉 大 教 育)(George Mason Univ.)
H. Antil(Chiba Univ.)
Naotaka Ukai
(Chiba Univ.)
Daiki Mizuno
Ken Shirakawa (Chiba Univ.)
Harbir Antil (George Mason Univ.)

方位調整を考慮するモノクロ画像処理過程の解の一意性 · · · · · · · · · · · · · 15

Uniqueness for gray-scale imege-denoising process with anisotropic orientation adjustment

概 要 In this talk, we consider a gradient system of a non-convex functional, based on a governing energy foranisotropic image denoising, developed in [Berkels et al., SFB 611, 2006]. A characteristic of our gradientsystem lies in the nonstandard part, which consists of the (set-valued) subdiﬀerential of an anisotropic
norm denoted by γ, and a two dimensional rotation matrix denoted by R. These play a key role in theorientation adjustment within the image denoising process. Under appropriate settings, we will provide theconstruction of an energy gradient system where the uniqueness of the solution is guaranteed in both thecontinuous system and the discrete approximation scheme.
21 水 野 大 樹 (千葉大融合理工)白 川
健 ( 千 葉 大 教 育)
(Chiba Univ.)
Daiki Mizuno
Ken Shirakawa (Chiba Univ.)

緩和項付き放物型 KWC システムにおける解の擬放物型正則性 · · · · · · · 15

Pseudo-parabolic type regularity in parabolic KWC system with relaxation

概 要 In this talk, we deal with a parabolic system to represent planar grain boundary motion, known as

KWC-type system, proposed by [Kobayashi et al., Physica D, 140, 141–150(2000)]. In this system, thediﬃculties lie in singular diﬀusion of the second equation of the system, and unknown-dependent mobilities
of grain boundary motion, which cause many challenges especially in the uniqueness. To address these,previous works have proposed speciﬁc settings on the spatial dimension, or certain adjustments on themobility. In this light, we here discuss the pseudo-parabolic type regularity for solutions to our parabolic
system. Consequently, we will obtain some positive answer for the uniqueness question, which has been oneof open problems in the studies of KWC system.

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実函数論

22 赤 川 佳 穂 (岐 阜 工 高 専)
Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)

ある線形ひずみ弾塑性モデルの閾値関数に対する連続依存性について · · 15

Continuous dependence of a hardening plasticity model on the threshold
function

概 要 This paper discusses the continuous dependence of a hardening plasticity model. This model is

described as an evolution inclusion with a constraint that is depend on unknown. The constraint set isdeﬁned by a threshold function and a parallel shift. In previous work, we obtained a continuous dependencewith respect to outer force and initial value. In particular, this talk will discuss the continuous dependence
respected to the threshold function and the parallel shift. To obtain continuous dependence, we take care
to choose the test function.
23 池 田 正 弘(理化学研 AIP・慶大理工)内 田俊 ( 大 分 大 理 工)
深 尾 武 史 (龍谷大先端理工)

Masahiro Ikeda (RIKEN/Keio Univ.)(Oita Univ.)
Shun Uchida
Takeshi Fukao (Ryukoku Univ.)

Optimal control problem of ODE governed by hypergraph Laplacian· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Optimal control problem of ODE governed by hypergraph Laplacian

概 要 In this talk, we consider some optimal control problem of an ODE governed by the hypaergraphLaplacian. Since the hypaergraph Laplacian is a set-valued operator, it seems to be diﬃcult to derive thenecessary optimality condition for this problem. To cope with this diﬃculity, we introduce an approximation
problem and assure the optimality condition for this. We also discuss the convergence of the condition tothat for the original problem.
24 熊 崎 耕 太 (京 都 教 育 大)

Kota Kumazaki (Kyoto Univ. of Edu.)

ある 1 次元自由境界問題の解の正則性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Regularity of a solution to a one-dimensional free boundary problem

概 要 In this talk, we consider a one-dimensional free boundary problem. This problem is a model describing

micro-swelling in pores of porous materials. Here, let the porous materials and each pore be the macro
domain and the micro domain, respectively, and we assume that each pore exists at the point of thematerials. Under this assumption, we deﬁne a model describing micro-swelling at each pore. For thisproblem, we have already proved the existence and uniqueness of a solution to the model. In this talk, as aregularity of the solution in the micro domain, we discuss the diﬀerentiabilty of the solution with respect tomacro variables and its applications.
25 加 納 理 成 (高 知 大 教 育)方高)
山 中 貴 博 (大(Kochi Univ.)
Risei Kano
Takahiro Yamanaka(Ogata High School)

静電状態における圧電効果を持つ Bernoulli–Euler 梁モデルの可解性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the solvability of the Bernoulli–Euler beam model with piezoelectriceﬀects

概 要 This talk presents a discussion of the solvability of the beam model problem for piezoelectric materials

proposed by Tiersten and discussed by Morris–Ozer and Alaoui–Ozer–Ouzahra.

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実函数論

72

14:15〜15:05
26 深 尾 武 史 (龍谷大先端理工)( Univ. di Pavia )P. Colli
L. Scarpa(Politecnico di Milano)

Takeshi Fukao (Ryukoku Univ.)
Pierluigi Colli (Univ. di Pavia)
Luca Scarpa (Politecnico di Milano)

境界拡散粘性消滅に対する誤差評価について · · · · · · · · · · · · · · · · · · · · · · · 15

An error estimate of some vanishing surface diﬀusion

概 要 In this talk, some Cahn–Hilliard equation with forward-backward dynamic boundary condition istreated. This problem can be discussed as the limit of the vanishing diﬀusion on the surface from theequation and the dynamic boundary condition of Cahn–Hilliard type, called the GMS model. Especially,
we discuss the error estimate coupled with the regularity theory. We can treat very general monotone terms
in the GMS model, such as the maximal monotone graphs. In the previous study, we assumed the growth
condition between the bulk and surface. When we add a stronger assumption we can recover the higher
regularity and then we deduce the error estimate.
27 山 崎 教 昭 (神 奈 川 大 情 報)
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.)

Solvability result of second order nonlinear quasi-variational evolution
inclusions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Solvability result of second order nonlinear quasi-variational evolution
inclusions

概 要 In this talk we consider a second order doubly nonlinear evolution inclusion, including a feedback

system, in a uniformly convex Banach space. Under appropriate assumptions, we establish the abstract
result on the existence of solutions to our problem by applying the abstract theory of the time-derivative
operators and the ﬁxed-point theorem of Schauder type.
28 吉 住 拓 真 (阪 大 情 報)
中 村
誠 ( 阪 大 情 報)

Takuma Yoshizumi (Osaka Univ.)
Makoto Nakamura (Osaka Univ.)

Global solutions for semi-linear Klein–Gordon equations in FLRW spacetimes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Global solutions for semi-linear Klein–Gordon equations in FLRW spacetimes

概 要 We consider the Cauchy problem of semi-linear Klein–Gordon equations in Friedmann–Lemaı́tre–

Robertson–Walker spacetimes. In this talk, we consider a concrete scale-function a(·), which describes
various types of spaces as the expanding space, the blowing-up space (the “Big-Rip” in cosmology), thecontracting space and the vanishing space (the “Big-Crunch” in cosmology). We proved global solutions
for any initial data under some conditions on semi-linear terms, and global solutions for small initial data.
The proofs are based on the contraction argument.
29 吉 住 拓 真 (阪 大 情 報)
中 村
誠 ( 阪 大 情 報)

Takuma Yoshizumi (Osaka Univ.)
Makoto Nakamura (Osaka Univ.)

Blowing-up solutions for semi-linear Klein–Gordon equations in FLRW
spacetimes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Blowing-up solutions for semi-linear Klein–Gordon equations in FLRW
spacetimes

概 要 We consider the Cauchy problem of semi-linear Klein–Gordon equations in Friedmann–Lemaı́tre–

Robertson–Walker spacetimes. In this talk, we consider a concrete scale-function a(·), which describes
various types of spaces as the expanding space, the blowing-up space (the “Big-Rip” in cosmology), thecontracting space and the vanishing space (the “Big-Crunch” in cosmology). For these equations, we have
proved the blowing-up solutions for the gauge invariant semi-linear term and the gauge variant one.

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73

実函数論

15:20〜16:20

特別講演
喜 多 航 佑 ( 東 北 大 理)

Kosuke Kita

(Tohoku Univ.)

On nonlinear heat equations with nonlinear boundary conditions in abounded domain
On nonlinear heat equations with nonlinear boundary conditions in abounded domain

概 要 In this talk, we are mainly concerned with the existence and nonexistence of global solutions tononlinear heat equations with nonlinear boundary conditions in a bounded domain. In the case of the whole
space, it is well known that the Fujita critical exponent is the threshold of the existence of nonnegative global
solutions to nonlinear heat equations with a power-type nonlinearity. On the other hand, in the case of abounded domain, we show that the existence and nonexistence of global nonnegative solutions to nonlinear
heat equations of the Fujita type are characterized by not exponents but boundary conditions. Moreover,
we also discuss a new comparison theorem for parabolic equations with nonlinear boundary conditions,which is the key to its proof.

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函数解析学

函

数

解

9 月 3 日（火）

析

74

学

第 V 会場

9:00〜10:45(沖縄科学技術大)
1 N. Evseev
M. Kampschulte ( Charles Univ. )A. Menovschikov(Ben-Gurion Univ. of the Negev)
Nikita Evseev(Okinawa Inst. of Sci. and Tech. Grad. Univ.)
Malte Kampschulte (Charles Univ.)
Alexander Menovschikov(Ben-Gurion Univ. of the Negev)

Zero-extension convergence and Sobolev spaces on changing domains· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Zero-extension convergence and Sobolev spaces on changing domains

概 要 We extend the deﬁnition of weak and strong convergence of a sequence of Sobolev functions whose

underlying domains themselves are converging. In contrast to previous works, we do so without assuming any
reference conﬁguration. We then develop the respective theory and counterparts to all classical compactness
theorems from the ﬁxed domain case.
2 岩 田 順 敬 (大阪経法大経営)
Yoritaka Iwata(Osaka Univ. of Economics Law)

非有界作用素に対する分数冪表現の一般化と Heinz–Kato の不等式 · · · · 15

Fractional power representation of general unbounded operators and theHeinz–Kato inequalities

概 要 The logarithmic representation theory of inﬁnitesimal generators is generalized to any unboundedinﬁnitesimal generators in abstract Banach spaces. In this paper, the generalized logarithmic representation
is applied to improve the theory of fractional power of operators.
3 大 森 祥 輔 (群馬工高専・早大理工)
Shosuke Omori(Gunma Nat. Coll. of Tech./Waseda Univ.)

多粒子系における quasi-Hermitian 作用素の rigged Hilbert 空間に基づく定式化について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the rigged Hilbert space formulation for a quasi-Hermitian operator
in composite system

概 要 The present talk delves into Dirac’s bra-ket formalism for a quasi-Hermitian quantum composite

system based on the rigged Hilbert space (RHS). Using the RHS for a composite system, the bra and ket
vectors and the spectral decomposition of the quasi-Hermitian operator are built. We also show that all
descriptions obtained using the bra-ket formalism are completely developed in the dual spaces.
4 渡 辺 秀 司 ( 群 馬 大 理 工)

Shuji Watanabe (Gunma Univ.)

外部磁場のあるときの超伝導の BCS 理論における Bogoliubov 変換とギャップ方程式 II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Bogoliubov transformation and the gap equation in the BCS modelof superconductivity with external magnetic ﬁeld II

概 要 We deal with a type I superconductor in a constant external magnetic ﬁeld and the BCS-Bogoliubov

gap equation with external magnetic ﬁeld. We show that there is a unique magnetic ﬁeld (the criticalmagnetic ﬁeld) given by a smooth function of the temperature and that there is also a unique nonnegative
solution (the gap function) given by a smooth function of both the temperature and the external magnetic
ﬁeld. We then show that the transition from the normal state to the superconducting state in a type I
superconductor is a ﬁrst-order phase transition. Moreover, we obtain the explicit expression for the gap inthe entropy.

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函数解析学

5 佐
松
泉
井

々
澤
真
村

木
泰
之
航

格 ( 信 州 大 理)
道 ( 信 州 大 教 育)介 ( 信 州 大 理)
太 (長野県富士見高)

Itaru Sasaki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Shinnnosuke Izumi (Shinshu Univ.)
Kouta Imura(Nagano Pref. Fujimi High School)

対相互作用模型の基底状態の正則性について · · · · · · · · · · · · · · · · · · · · · · · 15

Holomorphy of the ground states of the pair interaction models

概 要 We show the analyticity of the ground state of the pair interaction model. Previously, we directly

estimated the radius of convergence, but constructing the analytic continuation in the abstract setting
improves the prospect of the proof.
6 廣 島 文 生 ( 九 大 数 理)

Fumio Hiroshima (Kyushu Univ.)

Exponential decay of the ground state of the renormalized Nelson Hamiltonian by Agmon type metric · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Exponential decay of the ground state of the renormalized Nelson Hamiltonian by Agmon type metric

概 要 Lower bound of the spatial decay of the ground state of the renormalized Nelson Hamiltonian

with a continuous and conﬁning potential V is considered. The ground state of the renormalized Nelson
Hamiltonian is a boson Fock space -valued L2 function. The boson Fock space norm of the ground state isestimated from below by Agmon type distance.
7 廣 島 文 生 ( 九 大 数 理)

Fumio Hiroshima (Kyushu Univ.)

On the ergodicity of renormalized translation-invariant Nelson-type semigroups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the ergodicity of renormalized translation-invariant Nelson-type semigroups

概 要 We present a simple functional integration based proof that the semigroups generated by theultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians is positivity improving (and hence ergodic) with respect to the Froehlich cone for arbitrary values of the total
momentum. Our argument signiﬁcantly simpliﬁes known proofs for ergodicity. In the semi-relativistic casethe result is new for non-zero total momentum.
11:00〜12:00

特別講演

熊ノ郷直人
(工学院大教育推進機構)

トーラス上の相空間 Feynman 経路積分 —経路空間上の解析として

Naoto Kumanogo (Kogakuin Univ.)

Phase space Feynman path integrals on the torus —An analysis on pathspace

概 要 We present two general sets of functionals for which phase space Feynman path integrals on the torus

have a mathematically rigorous meaning. For each functional in each set, the time slicing approximationof the phase space path integral converges uniformly on compact subsets with respect to the ending pointof position paths and to the starting point of momentum paths. Each set of functionals is closed under
addition, multiplication, translation of paths, linear transformation of paths by invertible integer matrices,and functional diﬀerentiation. Therefore, we can construct a large number of path-integrable functionals.
While caution must be exercised when using phase space path integrals, several properties analogous tothose of conventional integrals are valid in the phase space path integral.

2024/08/21 作成
函数解析学

9 月 4 日（水）76

第 V 会場

10:00〜11:45
8 井 上 公 人 ( 西 日 本 工 大 工)
Hiroto Inoue(Nishinippon Inst. of Tech.)F -t joint distributions associated to quadratic maps of homogeneouscones · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
F -t joint distributions associated to quadratic maps of homogeneouscones

概 要 The Wishart distribution on a homogeneous cone Ω is deﬁned as the image of normal distribution

by an Ω-positive quadratic map, and it is a general case of the classical Wishart distribution on thecone of positive-deﬁnite symmetric matrices. In this talk, we deﬁne probability variables valued in a real
Siegel domain associated with the quadratic map, so that we obtain analogies of the multivariate F andt-distributions.
9 田 内 大 渡 ( 青 学 大 理 工)
西 山
享 ( 青 学 大 理 工)

Taito Tauchi (Aoyama Gakuin Univ.)
Kyo Nishiyama (Aoyama Gakuin Univ.)

Real double ﬂag variety for indeﬁnite unitary group U (p, p) · · · · · · · · · 15
Real double ﬂag variety for indeﬁnite unitary group U (p, p)

概 要 Let G be a real reductive Lie group and H its symmetric subgroup. Then, the product X :=H/PH × G/PG of two ﬂag manifolds H/PH and G/PG is called a real double ﬂag variety, where PH
and PG are parabolic subgroups of H and G, respectively. Although there are many studies of thetheory of double ﬂag varieties over the complex number ﬁeld, there are few studies in the case over thereal number ﬁeld. In this talk, we give a combinatrial classiﬁcation of the orbit space H\X in the case
(G, H, PG , PH ) = (U (p, p), GLp (C), PS , BH ), where PS is the Siegel parabolic subgroup of G, and BH is a
Borel subgroup of H.
10 有 本 諒 也 (京 大 数 理 研)
Ryoya Arimoto (Kyoto Univ.)

Simplicity of crossed products of the actions of totally disconnected
locally compact groups on their boundaries · · · · · · · · · · · · · · · · · · · · · · · · 15
Simplicity of crossed products of the actions of totally disconnected
locally compact groups on their boundaries

概 要 We prove that if a totally disconnected locally compact group admits a topologically free boundary,then the reduced crossed product of continuous functions on its Furstenberg boundary by the group issimple. We also prove a partial converse of this result.
11 中 田 彬 文 (広島大先進理工)小 川 健 翔 (広島大先進理工)奥 田 隆 幸 (広島大先進理工)

Akifumi Nakada (Hiroshima Univ.)
Kento Ogawa (Hiroshima Univ.)
Takayuki Okuda (Hiroshima Univ.)

Harmonic analysis on compact association schemes · · · · · · · · · · · · · · · · · 15

Harmonic analysis on compact association schemes

概 要 In ﬁnite homogeneous spaces and their generalizations, compact homogeneous spaces, analyticallyimportant propositions such as the Peter–Weyl theorem and the Plancherel theorem hold. It is also known
that these theorems hold for the class of ﬁnite association schemes, which is another generalization of
the class of ﬁnite homogeneous spaces. In this talk, we deﬁne a compact association scheme as a common
generalization of compact homogeneous spaces and ﬁnite association schemes, and show that the Peter–Weyltheorem and the Plancherel theorem hold in the commutative case.

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77

函数解析学

12 嵐

晃 一 ( 東 京 学 大 教 育)

Koichi Arashi (Tokyo Gakugei Univ.)

擬対称領域上の冪零リー群の無重複表現 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Multiplicitiy-free representations of nilpotent Lie groups over a quasisymmetric domain

概 要 We investigate the multiplicity-freeness property of a representation of an aﬃne transformation groupon a Siegel domain of the second kind. A necessary and suﬃcient condition for the representation to be
multiplicity-free is given. We relate the multiplicity-freeness property to the coisotropicity and the visibilityof the group action.
13 伊 藤 久 優 雅 (名 大 多 元 数 理)
Hyuga Ito

(Nagoya Univ.)

On free divergence-free vector ﬁelds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On free divergence-free vector ﬁelds

概 要 In 1990’s, Dan Voiculescu introduced the notion of entropy and Fisher’s information measure in

free probability theory. Related to this study, he studied a certain non-commutative diﬀerential operator,
which is called the cyclic derivative (associated with the free diﬀerence quotient). In 2020, Voiculescu
studied the Euler equation in free probabilistic setting (the free Euler equation). In the free Euler equation,
the cyclic derivative and its orthogonal complement play roles of gradient and divergence-free vector ﬁeld
(free divergence-free vector ﬁeld), respectively. In this talk, I would like to introduce the structure of free
divergence-free vector ﬁelds with respect to a free semi-circular system. This talk is based on the joint workwith Akihiro Miyagawa (UCSD).
13:00〜14:00

特別講演

田 森 宥 好(芝浦工大システム理工)

Strichartz estimates for the (k, a)-generalized Laguerre operator

Hiroyoshi Tamori(Shibaura Inst. of Tech.)

Strichartz estimates for the (k, a)-generalized Laguerre operator

概 要 The (k, a)-generalized Laguerre semigroup was introduced by Ben Said–Kobayashi–Orsted as aninterpolation of the Hermite semigroup (the k = 0, a = 2 case) and the Laguerre semigroup (the k = 0, a = 1case) from the viewpoint of unitary representations of the universal cover of SL(2, R). Based on a joint
work with Kouichi Taira (Kyushu University), I will explain an integral expression of the semigroup and an
upper estimate of the integral kernel. As applications, under some conditions on the deformation parameter(k, a), an explicit formula of the integral kernel and Strichartz estimates for the (k, a)-generalized Laguerre
operator (−|x|2−a ∆k + |x|a )/a (∆k denotes the Dunkl Laplacian) are obtained.

9 月 5 日（木）第 V 会場

10:00〜12:00
14 廣 田 大 輔 (鶴 岡 工 高 専)
Daisuke Hirota(Nat. Inst. of Tech., Tsuruoka Coll.)

Surjective isometries on the Banach algebra of continuously diﬀerentiable maps values in Lipschitz algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Surjective isometries on the Banach algebra of continuously diﬀerentiable maps values in Lipschitz algebra

概 要 Let Lip(I) be the Banach algebra of all Lipschitz functions on the closed unit interval I with the norm

kf kL = kf k∞ + L(f ) for f ∈ Lip(I), where L(f ) is the Lipschitz constant of f . We denote by C 1 (I, Lip(I))
the Banach algebra of all continuously diﬀerentiable functions F from I into Lip(I) equipped with the norm
kF kΣ = sups∈I kF (s)kL + supt∈I kD(F )(t)kL for F ∈ C 1 (I, Lip(I)). In this presentation, I will discuss theresults obtained by determining the form of surjective, not necessarily linear, isometries on C 1 (I, Lip(I)).

2024/08/21 作成
函数解析学

15 伊 佐 浩 史 (前 橋 工 科 大)
亀井栄三郎
遠 山 宏 明 ( 前 橋 工 科 大)
渡 邉 雅 之 (前 橋 工 科 大⋆)Hiroshi Isa (Maebashi Inst. of Tech.)
Eizaburo Kamei
Hiroaki Tohyama(Maebashi Inst. of Tech.)
Masayuki Watanabe(Maebashi Inst. of Tech.⋆)78

Inequalities among the n-th residual relative operator entropies · · · · · · 15

Inequalities among the n-th residual relative operator entropies

概 要 We show several operator inequalities among the n + 1-th residual relative operator entropies and thediﬀerence of the n-th residual relative operator entropies. It is an extension of operator valued inequalities
which start from a reﬁnement of Young’s inequality.
16 瀬 尾 祐 貴 (大 阪 教 育 大)
Yuki Seo (Osaka Kyoiku Univ.)実次数の Tsallis 相対エントロピーに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 two Tsallis relative entropies of all real

order: For density matrices ρ and σ, and each α ∈ R\{0}, the Tsallis relative entropy Dα (ρ|σ) is deﬁned byσ α −ρ
) and N Tα (ρ|σ) is deﬁned by N Tα (ρ|σ) = −Tr[ ρ ♮αασ−ρ ], where \α is deﬁned byα−1/2−1/2 α 1/2

Dα (ρ|σ) = −Tr( ρρ \α σ = ρ1/2 (ρ

1−α

σρ

) ρ

. Then we show the order relation between two Tsallis relative entropies

Dα and N Tα of all real order α ∈ R and a 1-parameter extension of the path connecting them of all real
order.
17 伊 藤 公 智 (前 橋 工 科 大)Masatoshi Ito (Maebashi Inst. of Tech.)

The weighted power diﬀerence mean and its generalization · · · · · · · · · · 15
The weighted power diﬀerence mean and its generalization

概 要 In this talk, based on the result by Pal, Singh, Moslehian and Aujla (2016), we newly introduce

the weighted power diﬀerence mean and get relations among the weighted power, power diﬀerence andarithmetic means. Moreover, we also obtain its generalization by considering the notion of a transpose
symmetric path of weighted means.
18 内 山充 (島根大⋆・立命館大)

Mitsuru Uchiyama(Shimane Univ.⋆ /Ritsumeikan Univ.)

Symmetric operator means · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Symmetric operator means

概 要 The aim of this talk is to construct symmetric means of a ﬁnite number of operators on an inﬁnite

dimensional Hilbert space.
19 渚
勝 ( 千 葉 大 理)
大⋆)綿 谷 安 男 (九Masaru Nagisa (Chiba Univ.)
Yasuo Watatani (Kyushu Univ.⋆)

II 型因子環上の Chouquet 型の非線型トレース · · · · · · · · · · · · · · · · · · · · · 15
Non-linear traces of the Choquet type on factors of type II

概 要 We introduce non-linear traces of the Choquet type on a semiﬁnite factor M as a non-commutative

analog of the Choquet integral for non-additive measures. We need weighted dimension function p 7→ α(τ (p))
for projections p ∈ M, which is an analog of a monotone measure. They have certain partial additivities.
We show that these partial additivities characterize non-linear traces of the Choquet type. For the algebras
of compact operators and factors of type II, we completely determine the condition that the associatedweighted Lp -spaces for the non-linear traces become quasi-normed spaces in terms of the weight functions
α for any 0 < p < ∞.

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79

函数解析学

20 綿 谷 安 男 (九 大 数 理)
渚勝
(千葉大理・立命館大理工)

Yasuo Watatani (Kyushu Univ.)
Masaru Nagisa(Chiba Univ./Ritsumeikan Univ.)

II 型因子環上の菅野型の非線形トレース · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Non-linear traces of the Sugeno type on factors of type II

概 要 We introduce non-linear traces of the Sugeno type on a semiﬁnite factor M as a non-commutative

analog of the Sugeno integral for non-additive measures. We need weighted dimension function p 7→ α(τ (p))
for projections p ∈ M, which is an analog of a monotone measure. They have certain partial F-additivities.
We show that these partial F-additivities characterize non-linear traces of the Sugeno type. We show thatany non-linear trace of the Sugeno type gives a certain metric on the factor.
14:15〜16:00
21 守 屋創 ( 金 沢 大 理 工)

Hajime Moriya (Kanazawa Univ.)

C*-ﬂow extension of discrete shift-translations on one-dimensional lattice systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
C*-ﬂow extension of discrete shift-translations on one-dimensional lattice systems

概 要 Kuiper examined the topological structure of unitary operators on inﬁnite-dimensional Hilbert spaces.

This is known as Kuiper’s problem, and it has been generalized to general von Neumann algebras and to some
C*-algebraic settings. In this talk, we address Kuiper’s problem for the discrete group of shift-translations
on one-dimensional quantum lattice systems and explore whether its C*-ﬂow extension exists.
22 佐 藤 僚 亮 (中 大 理 工)
Ryosuke Sato

(Chuo Univ.)

CAR algebras and stochastic dynamics on random point processes · · · 15
CAR algebras and stochastic dynamics on random point processes

概 要 CAR algebras are one of the fundamental operator algebras and are intimately related to random

point processes, which are models of random interacting particles. In this talk, we discuss the constructionof stochastic dynamics on random point processes within an operator algebraic framework.
23 松 本 健 吾 (上 越 教 育 大)大理)
曽 我 部 太 郎 (京Kengo Matsumoto(Joetsu Univ. of Edu.)(Kyoto Univ.)
Taro Sogabe

Cuntz–Krieger 環の Ext 群と自己同型群のホモトピー群について · · · · · · 15
The Ext-groups and the homotopy groups of the automorphisms groupsof Cuntz–Krieger algebras

概 要 We present the homotopy groups of the automorphism groups of Cuntz–Krieger algebras in termsof the underlying matrices of the Cuntz–Krieger algebras. We also show that the homotopy groups arecomplete invariants of the isomorphism classes of the Cuntz–Krieger algebras. As a result, the isomorphism
type of Cuntz–Krieger algebras are completely characterized by the group structure of the weak extension
groups and the strong extension groups.
24 後 藤 聡 史 (上 智 大 理 工)
鈴 木 翔 龍 ( 上 智 大 理 工)
(Sophia Univ.)
Satoshi Goto
Shôryû Suzuki (Sophia Univ.)

Haagerup fusion category から生じる connection system について · · · · 15
On the connection system arising from the Haagerup fusion categories

概 要 The ﬁrst named speaker generalized Ocneanu’s ADE inter-Dynkin connection systems to the case ofan arbitrary ﬁnite depth subfactor with its maximal atlas. In this talk, we show the computation of theconnection system arising from the Haagerup fusion categories, and also show some applications of thecomputation.

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函数解析学

25 窪 田 陽 介 (京大理・理化学研)

Yosuke Kubota (Kyoto Univ./RIKEN)80

C*-環の K 理論におけるスペクトル系列の計算例 · · · · · · · · · · · · · · · · · · · 15
Examples of spectral sequence computations in C*-algebra K-theory

概 要 The K-group of a crossed product C*-algebra by a free abelian group is considered computable using

Kasparov’s spectral sequence, which is a schematic reﬁnement of the iterated use of the Pimsner–Voiculescu
exact sequence. However, this method does not guarantee that any such K-group is exactly computable.
In this talk, we introduce two examples of such crossed products, both originating from a dynamical systemassociated with an ax+b semigroup with number-theoretic origin, where the K-group can be computed bycomparing the spectral sequence with that of groupoid homology via Raven’s equivariant bivariant Chern
character.
26 森
迪 也(東大数理・理化学研 iTHEMS)

Michiya Mori (Univ. of Tokyo/RIKEN)

On the shape of correlation matrices for unitaries · · · · · · · · · · · · · · · · · · 15
On the shape of correlation matrices for unitaries

概 要 For a positive integer n, we study the collection Fﬁn (n) formed of all n × n matrices whose entries

aij , 1 ≤ i, j ≤ n, can be written as aij = τ (Uj∗ Ui ) for some n-tuple U1 , U2 , . . . , Un of unitaries in a ﬁnitedimensional von Neumann algebra M with tracial state τ . We show that Fﬁn (n) is not closed for everyn ≥ 8.
16:15〜17:15
古 市

特別講演
茂 ( 日 大 文 理)

Shigeru Furuichi (Nihon Univ.)

一般化エントロピーとトレース不等式

Generalized entropies and trace inequalities

概 要 Relative entropies and skew information were given by the trace. In this talk, we consider the trace

inequalities on their bounds. Previously obtained results and recent results on the Tsallis relative entropy
and the Tsallis relative operator entropy will be reported. Although, partially, skew information anduncertainty relation which is also given by the trace inequality, will be reviewed, almost results are related
to the trace inequalities in relation to entropies.

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81

統計数学

統 計
9 月 3 日（火）数学

第 VII 会場

9:30〜11:50
1 稲 吉

凌 ( 名 城 大 理 工)

Ryo Inayoshi(Meijo Univ.)

A characterization of the operator entropy in terms of an isometry property related to trace norms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A characterization of the operator entropy in terms of an isometry property related to trace norms

概 要 We introduce two new mean operators acting on trace class operators, and using the mean operators,

we provide a new characterization theorem of operator entropy in terms of an isometry property between
two trace norms. It is a very important point that we can characterize the operator entropy only using theisometry property for a continuous operator on some class of density operators.
2 赤 堀 次 郎 ( 立 命 館 大 理 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)
岡 本 陸 希 ( 立 命 館 大 理 工)佐 藤
巖 ( 小 山 工 高 専)

Jiro Akahori (Ritsumeikan Univ.)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Rikuki Okamoto (Ritsumeikan Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)

相互作用粒子系の量子化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A quantization of interacting particle systems

概 要 Interacting particle systems studied in this presentation are probabilistic cellular automata withnearest-neighbor interaction including the Domany–Kinzel model. A special case of the Domany–Kinzel
model is directed percolation. We regard the interacting particle system as a Markov chain on a graph.
Then we present a new quantization of the interacting particle system. After that, we introduce a zetafunction of the quantized model and give its determinant expression.
3 Hoang-Long Ngo(Hanoi Nat. Univ. of Edu.)
Minh Thang Do(Hanoi Nat. Univ. of Edu.)
田 口
大 (関西大システム理工)
Hoang-Long Ngo(Hanoi Nat. Univ. of Edu.)
Minh Thang Do(Hanoi Nat. Univ. of Edu.)(Kansai Univ.)
Dai Taguchi

Strong solutions and numerical schemes for non-colliding particle systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Strong solutions and numerical schemes for non-colliding particle systems

概 要 In this talk, we ﬁrst prove the existence of strong solution for (time inhomogeneous) non-colliding

particle systems. The idea of the proof is to use some Lyapunov function. We also consider numerical
schemes for these stochastic processes and provide their rate of convergence.

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統計数学

4 笹 谷 晃 平 ( 東 大 数 理)
Kôhei Sasaya (Univ. of Tokyo)

82

強局所な p-エネルギーに付随する p-エネルギー測度の構成 · · · · · · · · · · · 15

Construction of p-energy measures associated with strongly local penergies

概 要 A p-energy (E, F) on a metric space with a measure is an analog of a Dirichlet form in the Lp space.

Recently, this energy has been studied in order to considering “(1, p)-Sobolev space” on fractals.
In this talk, we construct the p-energy measures associated with strongly local, regular p-energies (theequivalent of the energy measures associated with Dirichlet forms) without any assumptions of symmetry or
self-similarity of the metric space. Moreover, with assuming separability of a quotient space of the domain
F induced by the seminorm E 1/p , we prove that the non-symmetric form of the p-energy measures satisfy
the chain rule and the Leibniz rule.
5 清 水 良 輔 ( 早 大 理 工)
梶 野 直 孝 ( 京 大 数 理 研)

Ryosuke Shimizu (Waseda Univ.)
Naotaka Kajino (Kyoto Univ.)

Construction of Korevaar–Schoen p-energy forms and associated p-energy
measures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Construction of Korevaar–Schoen p-energy forms and associated p-energy
measures

概 要 In this talk, I will present our recent result on constructions of good p-energy forms on metric measurespaces as pointwise subsequential limits of Besov-type p-energy functionals. Such forms are often called
Korevaar–Schoen p-energy forms in the literature. As an advantage of our approach, the resulting p-energy
forms satisfy the strongly local property and a good contraction property called the generalized p-contraction
property. In addition, similar to energy measures associated with a regular symmetric Dirichlet form, we
obtain the associated p-energy measures through the Riesz–Markov–Kakutani representation theorem.
6 Khanh Duy Trinh (早 大 理 工)
中 野 史 彦 ( 東 北 大 理)
Hoang Dung Trinh(VNU Univ. of Science)

Khanh Duy Trinh (Waseda Univ.)
Fumihiko Nakano (Tohoku Univ.)
Hoang Dung Trinh(VNU Univ. of Science)

Classical beta ensembles at high temperature and the Markov–Krein
relation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classical beta ensembles at high temperature and the Markov–Krein
relation

概 要 Three classical beta ensembles (Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi

ensembles) are now realized as the eigenvalues of tridiagonal random matrices. In a high temperature regime,
the regime where the parameter beta is proportional to the reciprocal of the system size, the empirical
distribution of the eigenvalues converges weakly to a limiting measure which is related to associated Hermite/ Laguerre / Jacobi polynomials. Moreover, the Gaussian (resp. gamma and beta) distribution and thelimiting distribution in the Gaussian (resp. Laguerre and Jacobi) case satisfy the Markov–Krein relation.
This talk will explain such relation by investigating the spectral measure of the tridiagonal random matrix
model.
7 千 野 由 喜 (Yuki Chino

NYCU

)

(NYCU)

A characterization of symmetric environment for RWRE · · · · · · · · · · · · 15
A characterization of symmetric environment for RWRE

概 要 Random walk in cooling random environment (RWCRE) is one of random walk in dynamical random

environment models. RWCRE interpolates the modiﬁcation from the classical random walk in random
environment (RWRE). To characterize recurrence for RWCRE, we need to understand the balance between
speed of dynamics and environment, especially for the case that environment is not symmetric. In this talk,we consider one characterization of symmetric environment for classical model. The talk is based on a joint
work with Conrado da Costa (Durham University).

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83

統計数学

8 徐
梓 健 ( 福 岡 大 理)
桑 江 一 洋 ( 福 岡 大 理)
江 崎 翔 太 ( 大 分 大 理 工)
(Fukuoka Univ.)
Zijian Xu
Kazuhiro Kuwae (Fukuoka Univ.)(Oita Univ.)
Syota Esaki

The Littlewood–Paley–Stein inequality for tamed Dirichlet spaces · · · · 15

The Littlewood–Paley–Stein inequality for tamed Dirichlet spaces

概 要 In recent years, Erbar–Rigoni–Sturm–Tamanini established the theory of tamed spaces, which are

Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature. More precisely, tamed spaces
are quasi-regular strongly local Dirichlet forms satisfying a Bakry–Émery curvature lower bound in thesense of distribution. Using the equivalence between these lower bounds and gradient estimates for the heat
semigroup in terms of the Feynman–Kac semigroup, we establish the Littlewood–Paley–Stein inequality for
Lp -functions for p > 1.
9 上 村 稔 大 (関西大システム理工)

Toshihiro Uemura (Kansai Univ.)

ソボレフ空間 W01,2 (D) を定義域とするジャンプ拡散過程に対応する半
ディリクレ形式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On semi-Dirichlet forms of jump-diﬀusion processes based on the Sobolev
space W01,2 (D)概 要 We construct the lower bounded, regular semi-Dirichlet forms on L2 (D) associated with jump-diﬀusion

processes on an open convex set D of Rd having the Sobolev space W01,2 (D) as their domains under someconditions on the diﬀusion coeﬃcients, drifts and the Lévy densities. In the talk, we introduce a stable-type
jump diﬀusion process as an example.
14:15〜15:15

特別講演
村 山 拓 也 ( 九 大 数 理)

Takuya Murayama (Kyushu Univ.)

レヴナー微分方程式の跡と駆動函数に関するいくつかの問題

Some problems on the traces and driving functions of the Loewner differential equation

概 要 The Loewner diﬀerential equation produces a family of conformal mappings on a planar domain,

whose images are expanding or shrinking in time. In probability theory, the most famous case is that thedriving term of the equation is a one-dimensional Brownian motion, which turns the complements of theseimages (let us call them the trace here) into a random path, that is, the Schramm-Loewner evolution (SLE).
In this talk, I shall present a brief (and possibly very personal) survey on some problems on the relation of
the traces and driving functions, from both function-theoretic and probabilistic points of view.
15:30〜16:30
畑特別講演
宏 明 ( 一 橋 大 商)

Hiroaki Hata (Hitotsubashi Univ.)

一般的な非線形確率ファクターモデルを用いた最適消費投資問題とその方策改善アルゴリズム

An optimal consumption and investment problem with a general nonlinear stochastic factor model and its policy improvement algorithm

概 要 In this talk, we employ a general nonlinear stochastic factor model where the returns and volatilities

of assets are random and aﬀected by some economic factors, modeled as diﬀusion processes. Additionally,
we address an optimal consumption and investment problem on a ﬁnite time horizon to optimize thediscounted expected power utility of consumption and terminal wealth. Furthermore, we propose a policy
improvement algorithm, which establishes an iteration procedure converging to the value function and the
optimal strategy.

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統計数学

9 月 4 日（水）84

第 VII 会場

9:30〜11:40
10 アリババイ仁真 (京大理)Nima Alibabaei (Kyoto Univ.)

重み付き位相エントロピーとハウスドルフ次元 · · · · · · · · · · · · · · · · · · · · · 15

Weighted topological entropy and Hausdorﬀ dimension

概 要 Motivated by the geometry of self-aﬃne fractals, an invariant called weighted topological entropy wasrecently introduced. We have discovered a new formulation, and the coincidence of the two deﬁnitions seems
highly non-trivial. This provides us with a novel way to calculate the Hausdorﬀ dimension of some fractals
such as soﬁc aﬃne-invariant sets.
11 中 島 和 基 (総合研究大複合)
Kazuki Nakajima(Grad. Univ. for Adv. Stud.)

Zd 上の定常確率場に対する極値理論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Extreme value theory for stationary ramdom ﬁelds on Zd

概 要 Stehr and Rønn–Nielsen (2021) studies a stationary random ﬁeld on Zd and obtain that under someconditions the normalized version of the distribution of the maximum of the ﬁeld over an increasing sequenceof index sets converges to an extreme value distribution. We consider the increase rate of index sets, which
they make conditions on in the paper. We relax the conditions, and, in addition, investigate the cases offaster increase rates.
12 髙 野 凌 史 (阪 大 基 礎 工)
Ryoji Takano(Osaka Univ.)

確率積分が駆動する確率微分方程式に対する大偏差原理 · · · · · · · · · · · · · 15

Large deviation principle for stochastic diﬀerential equations driven bystochastic integrals

概 要 The large deviation principle for stochastic diﬀerential equations is important from the viewpoint ofapplications in mathematical ﬁnance. In this talk, I will present results on the large deviation principle for
one-dimensional stochastic diﬀerential equations driven by stochastic integrals. Our results can be provedby combining the large deviation principle of stochastic integrals and rough path theory. First of all, we
will show that the large deviation principle for stochastic integrals can be proved. Then, we will show thatrough path theory can be applicable to prove the large deviation principle for one-dimensional stochastic
diﬀerential equations driven by stochastic integrals.
大理)
13 濵 口 雄 史 (京(田 口
大 関西大システム理工)

Yushi Hamaguchi (Kyoto Univ.)(Kansai Univ.)
Dai Taguchi

一般化カップリング法による経路依存型確率微分方程式の弱近似 · · · · · · 15

A generalized coupling approach for the weak approximation of stochastic functional diﬀerential equations

概 要 We are concerned with the weak approximation of the weak solutions of stochastic functional diﬀerential

equations (SFDEs) by means of the Euler–Maruyama schemes. Under quite general assumptions on thecoeﬃcients, we provide an estimate for the Lévy–Prokhorov metric between the paths of the weak solutionof the original SFDE and the corresponding scheme. The weak convergence rate in terms of the Lévy–
Prokhorov metric is characterized by the probability of a “rare event” where the weak solution of the
SFDE exits a large sub-domain, which can be easily estimated in many examples. The proof is based on
the generalized coupling approach which has been studied in the ﬁeld of ergodicity of inﬁnite dimensional
stochastic systems.

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85

統計数学

14 中 野張 (東工大情報理工)

Yumiharu Nakano (Tokyo Tech)

拡散生成モデルの収束について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On convergence of the diﬀusion generative models

概 要 We theoretically analyze the original version of the denoising diﬀusion probabilistic models (DDPMs)

presented in Ho, J., Jain, A., and Abbeel, P., Advances in Neural Information Processing Systems, 33 (2020),
pp. 6840–6851. Our main theorem states that the sequence constructed by the original DDPM samplingalgorithm weakly converges to a given data distribution as the number of time steps goes to inﬁnity, undersome asymptotic conditions on the parameters for the variance schedule, the L2 -based score estimation
error, and the noise estimating function with respect to the number of time steps. In proving the theorem,
we reveal that the sampling sequence can be seen as an exponential integrator type approximation of areverse time stochastic diﬀerential equation.
15 上 島 芳 倫 (東洋大情報連携)

Yoshinori Kamijima (Toyo Univ.)

長距離相互作用を持つ自己回避歩行に対する局所極限定理 · · · · · · · · · · · 15

A local limit theorem for the long-range self-avoiding walk

概 要 The self-avoiding walk (SAW) is a model added self-avoidance interaction to the random walk. In

other words, each path does not visit the same vertex on a graph more than once. It is known that the
spread-out ﬁnite-range SAW enjoys the central limit theorem [van der Hofstad and Slade (2003) AAM].
Taking an average on a ball, they also proved a certain type of a local limit theorem. For the spread-out
long-range SAW, the power-law decay of the two-point function was shown in [Chen and Sakai (2019) CMP].
In this talk, I will explain an attempt to prove a local limit theorem for the spread-out long-range SAW
in the original sense. Our motivations come from combining the results of the previous researches. Thisis joint work with Lung-Chi Chen (National Chengchi University) and Yuki Chino (National Yang-Ming
Chiao-Tung University).
16 山 上 智 輝 (東 大 情 報 理 工)
成 松 明 廣(福知山公大数理・データサイエンスセンター)

Tomoki Yamagami (Univ. of Tokyo)
Akihiro Narimatsu(Univ. of Fukuchiyama)

Antlion ランダムウォークの解析 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Analyses of Antlion random walks

概 要 In this study, we analyze the random walk on R, so called antlion random walk. This model is related

to the one concerning decision-making on multi-armed bandit problems via chaotic laser.
17 田
赤
今
佐

村 勇 真 ( 立 命 館 大 理 工)
堀 次 郎 ( 立 命 館 大 理 工)
野 紀 雄 ( 立 命 館 大 理 工)
藤巌 ( 小 山 工 高 専)

Yuma Tamura (Ritsumeikan Univ.)
Jirô Akahori (Ritsumeikan Univ.)
Norio Konno (Ritsumeikan Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)

サイクルグラフ上の多状態量子ウォークの周期と絶対ゼータ関数 · · · · · · 15

Periodicity and absolute zeta function of multistate quantum walk on
cycle graph

概 要 The quantum walk is a quantum counterpart of the classical random walk and the absolute zetafunction can be considered as a zeta function over F1 . We showed a connection between the quantum walkand the absolute zeta function. Then we focused Grover walks on cycle graphs, which are typical models ofquantum walks, and using cyclotomic polynomials, we calculated the periods and absolute zeta functions ofsuch quantum walk with 3 states previously. In this talk, we report on the development of the method for3 states and its application to 5 states or a general odd number of states.

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統計数学

11:40〜12:10

86

統計数学分科会総会

9 月 5 日（木）第 VII 会場

9:30〜11:40
18 高 橋 勇 人 (Random Data Lab.)

Hayato Takahashi (Random Data Lab.)

Exact Kolmogorov–Smirnov tests of random numbers with distributionsof runs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Exact Kolmogorov–Smirnov tests of random numbers with distributionsof runs

概 要 We demonstrate tests of random number generators by exact Kolmogorov–Smirnov tests for discrete

probabilities with the exact distributions of runs in H. Takahashi arXiv:2302.14356.
19 城 野 悠 志 (山 梨 大 医)
駒 場
敦 ( 山 梨 大 医)中 本 和 典 ( 山 梨 大 医)Hisashi Johno (Univ. of Yamanashi)
Atsushi Komaba (Univ. of Yamanashi)
Kazunori Nakamoto(Univ. of Yamanashi)

1 標本 Kolmogorov–Smirnov 検定の拡張 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Extension of the one-sample Kolmogorov–Smirnov test

概 要 We propose here a new goodness-of-ﬁt test, named the one-sample OVL-q test (q = 1, 2, . . .), which canbe considered an extension of the one-sample Kolmogorov–Smirnov test (equivalent to the one-sample OVL-1
test). We have analyzed the asymptotic properties of the one-sample OVL-2 test statistic and enabled thecalculation of asymptotic p-values for the test statistic. We further conducted numerical experiments anddemonstrated that the one-sample OVL-2 test can sometimes exceed the detection power of conventional
goodness-of-ﬁt tests.
20 前 園 宜 彦 (中 大 理 工)
秋 葉 翔 太 ( 中 大 理 工)

Yoshihiko Maesono (Chuo Univ.)(Chuo Univ.)
Shota Akiba

ノンパラメトリックな分位点回帰の平均二乗誤差 · · · · · · · · · · · · · · · · · · · 15

Asymptotic mean squared error of nonparametric quantile regression

概 要 In this talk, we discuss mean squared error of nonparametric quantile regression. The quantile

regression is based on kernel type estimator of conditional distribution function.
21 佃康 司 ( 九 大 数 理)
松 浦
峻 ( 慶 大 理 工)
Koji Tsukuda (Kyushu Univ.)
Shun Matsuura (Keio Univ.)

Allometric 回帰モデルにおける推定量 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Estimator for allometric regression model

概 要 The allometric regression model is a multivariate multiple regression model imposing that the diﬀerence

between expectation vectors of two observations with diﬀerent values of explanatory variables is parallelto the ﬁrst principal eigenvector. In this presentation, estimation of the ﬁrst principal eigenvector in the
allometric regression model is discussed. Considering a class of estimators based on a weighted matrix ofthe regression sum of square matrix and the residual sum of squares matrix, we propose a new estimatorthat purposes to decrement an upper bound of the mean squared error of an estimator contained in thisclass. The proposed estimator and some conventional estimators are numerically compared.

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87

統計数学

22 河 本 亘 平 (九 大 J G M I)
後 藤 佑 一 ( 九 大 数 理)佃康 司 ( 九 大 数 理)

Kohei Kawamoto (Kyushu Univ.)(Kyushu Univ.)
Yuichi Goto
Koji Tsukuda (Kyushu Univ.)

Spectral clustering algorithm for the allometric extension model · · · · · 15

Spectral clustering algorithm for the allometric extension model

概 要 The spectral clustering algorithm is used as a binary clustering method by applying the principal

component analysis. Homoscedasticity of two clusters is commonly supposed in existing studies, but thisrestrictive assumption is often unrealistic in practice. Therefore, we consider the allometric extension model,that is, the directions of the ﬁrst eigenvectors of two covariance matrices and the direction of the diﬀerenceof two mean vectors coincide. A non-asymptotic bound of the error probability is provided for the spectralclustering.
23 小 池 祐 太 (東 大 数 理)
Yuta Koike(Univ. of Tokyo)

高次元ブートストラップ法における被覆確率の漸近展開 · · · · · · · · · · · · · 15

Asymptotic expansion of coverage probability for the high-dimensionalbootstrap

概 要 The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approx-

imation for the maximum of a sum of independent random vectors is justiﬁed even when the dimension ismuch larger than the sample size. In this context, numerical experiments suggest that third-moment matchbootstrap approximations would outperform normal approximation even without studentization, but theexisting theoretical results cannot explain this phenomenon. In this talk, we derive an asymptotic expansion formula of the bootstrap coverage probability and show that the third-moment match wild bootstrap
is second-order accurate in high-dimensions even without studentization when the covariance matrix has
identical diagonal entries and bounded eigenvalues.
24 渡 名 喜 庸 蔵 (阪 大 基 礎 工)
貝 野 友 祐 ( 神 戸 大 海 事)
内 田 雅 之 ( 阪 大 基 礎 工)
(Osaka Univ.)
Yozo Tonaki(Kobe Univ.)
Yusuke Kaino
Masayuki Uchida (Osaka Univ.)

空間 2 次元線形放物型 SPDE モデルのパラメータ推定 · · · · · · · · · · · · · · · 15

Parameter estimation for a linear parabolic SPDE in two space dimensions

概 要 We consider parameter estimation for a linear parabolic second-order stochastic partial diﬀerential

equation (SPDE) in two space dimensions driven by a Q-Wiener process based on high-frequency data withrespect to time and space. Applying the methodology of Hildebrandt and Trabs (2021,EJS) to the SPDEin two space dimensions, we obtain minimum contrast estimators (MCEs) of the coeﬃcient parameters of
the SPDE in two space dimensions based on temporal and spatial increments. Furthermore, we develop
adaptive estimators of the coeﬃcient parameters based on an approximate coordinate process. It is shownthat the adaptive estimators have asymptotic normality under certain regularity conditions.
25 増 田 弘 毅 (東 大 数 理)
江 口 翔 一 ( 大 阪 工 大 工)

Hiroki Masuda (Univ. of Tokyo)
Shoichi Eguchi (Osaka Inst. of Tech.)

Robustiﬁed asymptotics for estimating volatility · · · · · · · · · · · · · · · · · · · 15
Robustiﬁed asymptotics for estimating volatility

概 要 We propose an M-estimator through the density-power weighting of the conventional Gaussian quasi-

score function, and prove its asymptotic mixed normality at the usual rate. It is theoretically shown thatthe estimator is robust against contamination by jumps and spike-type noise. The estimation procedure
involves one user-input tuning parameter.

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統計数学

特別講演
上 原 悠 槙 (関西大システム理工)Predictive model selection for jump diﬀusion models(Kansai Univ.)

Predictive model selection for jump diﬀusion models

88

14:15〜15:15

Yuma Uehara

概 要 A model selection problem is considered for jump-diﬀusion models based on high-frequency samples.

The terminal time is supposed to diverge (ergodic setting), and the interest is to select drift and diﬀusion
coeﬃcients and jump distribution among candidates. An explicit AIC-type information criterion is proposed
based on the threshold quasi-likelihood. Unlike the diﬀusion case, when the jump term is parametrized
in some way, the stochastic ﬂow approach cannot be directly used to get the transition density estimates,
which is essential to evaluate the bias. To validate such an approximation, new transition density estimates
are presented.
15:30〜16:30

特別講演
仲 北 祥 悟 ( 東 大 総 合 文 化)

非スパース高次元統計理論における最近の展開

Shogo Nakakita (Univ. of Tokyo)

Recent development in theories of non-sparse high-dimensional statistics

概 要 We introduce two topics and our studies on them: (1) non-sparse high-dimensional linear regression

problems and (2) non-sparse high-dimensional logistic regression problems. We ﬁrst show a study on benign
overﬁtting of linear regression under time series dependence. Benign overﬁtting is a phenomenon where
over-parameterized statistical models can achieve small prediction errors even if they overﬁt training data.
Whilst previous studies on this phenomenon are based on i.i.d. settings, we examine this phenomenon under
temporal dependence. We observe that the coherence of autocorrelation matrices serves small prediction
errors; such a phenomenon is not seen in under-parameterized regression under dependence. In the second
place, we show a novel uniform concentration bound and a uniform law of large numbers of constrained
logistic regression. Logistic models are fundamental in the binary classiﬁcation problem in statistics andmachine learning. Under high-dimensional settings, it is known that the maximum likelihood estimation(MLE) for logistic regression can be biased. We investigate when the MLE can perform well even underhigh-dimensional settings and see that an eﬀective rank of the covariance matrix of inputs plays an importantrole.

9 月 6 日（金）第 VII 会場

10:00〜11:45
26 江 頭 健 斗 (東京理大創域理工)矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)

Kento Egashira (Tokyo Univ. of Sci.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

高次元データにおける k-means 法の補正について · · · · · · · · · · · · · · · · · · · 15

Modiﬁcation to k-means for high-dimensional data

概 要 k-means has been approved as a useful methodology for analysing high-dimensional, low-sample-size

data. There remains scope for research on the asymptotic properties of the k-means about high-dimensional
data. In the k-means, an appropriate increase in the number of initial data can be expected to enhance
performance. In this talk, we derive the asymptotic properties of this approach and conduct a comparison
with the conventional k-means. Additionally, based on the asymptotic properties of the conventional kmeans, a modiﬁed method is proposed and evaluated in comparison to the conventional k-means. At last,
we present numerical simulation studies that demonstrate the performance of k-means for high dimensionaldata, discussing the achieved results.

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統計数学

27 今 野 良 彦 (阪 公 大 理)

Yoshihiko Konno (Osaka Metro. Univ.)

An adaptive singular value shrinkage for estimation problem of low-rankmatrix mean with unknown covariance matrix · · · · · · · · · · · · · · · · · · · · · 10
An adaptive singular value shrinkage for estimation problem of low-rankmatrix mean with unknown covariance matrix

概 要 Matrix models which are constructed from a deterministic signal plus noise are used in variety of ﬁelds.

In particular it commonly happens that a signal matrix is of low-rank, however the rank itself is unknown.
In this paper it is assumed that the noises are distributed as real normal or complex normal distributions,
across columns are independently and identically distributed, and across rows of noise matrix are correlated.
But the covariance matrix is unknown. For the problem of estimating a low-rank matrix, estimators with
soft-thresholding singular values are considered and a formula to choose a threshold is proposed based on
the SURE method.
28 若 木 宏 文 (広 島 大 理)
栁 原 宏 和 ( 広 島 大 理)

Hirofumi Wakaki (Hiroshima Univ.)
Hirokazu Yanagihara (Hiroshima Univ.)

Complete bias modiﬁcation of the risk of the model based on KL divergence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Complete bias modiﬁcation of the risk of the model based on KL divergence

概 要 Consider the estimation of a risk function based on the KL divergence for a variable selection problem ina linear regression model. Fujikoshi and Satoh (1997) proposed Modiﬁed AIC (MAIC) as an asymptoticallyunbiased estimator of this risk function. MAIC corrects for bias for the underspeciﬁed model that does
not include the true model, but leaves bias in the overspeciﬁed model, which was completely corrected by
Corrected AIC by Sugiura (1978). Therefore, this study proposes an unbiased estimator that can fully
correct the bias for both overspeciﬁed and underspeciﬁed models. Numerical experiments are conducted to
conﬁrm its performance as an information criterion.
29 佐 川 凜 華 (早 大 理 工)劉言 ( 早 大 理 工)
Rinka Sagawa (Waseda Univ.)(Waseda Univ.)
Yan Liu

An information criterion for detecting periodicities in functional timeseries · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An information criterion for detecting periodicities in functional timeseries概 要 Let us consider a trigonometric model in functional time series. In practice, functional data often

exhibit periodic behaviors. Detecting these periodic behaviors helps us understand the functional features
better. In this research, we propose a BIC-type information criterion for detecting the unknown number of
periodicities. Additionally, we suggest an iterative algorithm that utilizes the residual processes obtainedby the least squares method. We establish the consistency of this estimator minimizing the proposed
information criterion. The resulting procedure automatically determines the number of periodicities in both
multivariate and functional time series, thereby avoiding the issue of multiple testing.
30 曾
小 強
柿 沢 佳 秀 ( 北 大 経 済)
Xiaoqiang Zeng
Yoshihide Kakizawa (Hokkaido Univ.)

INAR(p) 過程における Whittle 推定量 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Whittle likelihood estimation in INAR(p) process

概 要 The frequency domain analysis is considered in the stationary INAR(p) process under a generalinnovation. Here, we say that the innovation is general, if we do not assume its distributional form. In
that case, the ML method is thus unavailable. Strong consistency and asymptotic normality of the Whittle
estimator are established. It should be stressed that Silva and Oliveira (2004) gave some simulation studies
about the Whittle estimation in the INAR(1) process with the Poisson marginals (Zhang and Wang (2015)
for random coeﬃcient INAR(1) process), without no theoretical results.

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統計数学

90

31 後 藤 佑 一 (九 大 数 理) [ A test for counting sequences of integer-valued autoregressive models
藤 森洸 ( 信 州 大 経 法)
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Kyushu Univ.)
Yuichi Goto(
Kou Fujimori Shinshu Univ.)

A test for counting sequences of integer-valued autoregressive models

概 要 The integer autoregressive (INAR) model is one of the most commonly used models in nonnegative

integer-valued time series analysis and is a counterpart to the traditional autoregressive model for continuousvalued time series. To guarantee the integer-valued nature, the binomial thinning operator or more generally
the generalized Steutel and van Harn operator is used to deﬁne the INAR model. However, the distributionsof the counting sequences used in the operators have been determined by the preference of analyst without
statistical veriﬁcation so far. In this talk, we propose a test based on the mean and variance relationships
for distributions of counting sequences and a disturbance process to check if the operator is reasonable. We
show that our proposed test has asymptotically correct size and is consistent.
( 統 計 数 理 研)
32 Yujie Xue
谷 口 正 信 ( 早 大 理 工)

Yujie Xue (Inst. of Stat. Math.)
Taniguchi Masanobu (Waseda Univ.)

Introduction of general distributions on sphere and torus in view of timeseries spectra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Introduction of general distributions on sphere and torus in view of timeseries spectra

概 要 There are various ﬁelds where observations are taken on directions in three dimensions, e.g., sphereand torus. Here we introduce a very general family of distributions on sphere and torus by use of time series
spectra, which includes a lot of proposed classical one as special cases. Because time series spectra can be
described by a lot of famous parametric models, e.g., AR, ARMA etc., we can develop the systematic model
selection in this ﬁeld by use of AIC, BIC, etc. Applications are very wide.
14:15〜15:45
33 川 崎 英 文 (九 大 数 理)

Hidefumi Kawasaki (Kyushu Univ.)

Borsuk の対心定理に基づく集合の評価付け定理 · · · · · · · · · · · · · · · · · · · · 15
A grading theorem of sets based on Borsuk’s antipodal theorem

概 要 Borsuk’s antipodal theorem states that for any continuous mapping f from the n-sphere S n to Rn ,there exists a point x ∈ S n such that f (x) = f (−x). Recently, by applying it to an n-tuple of parametric
optimization problems with parameter u ∈ S n , we presented an antipodal theorem for them. Further, we
showed that given n convex sets in Rn , it is possible to divide each width in half with a hyperplane. In thistalk, we take another approach, and present a result beyond the scope of the previous research. We call it
a grading theorem of sets.
34 田 中 輝 雄 (広 島 市 大 情 報)

Teruo Tanaka (Hiroshima City Univ.)

多次元離散時間変数をもつマルコフ過程に対する最適停止問題 · · · · · · · · 10

Optimal stopping problems for discrete time multiparameter Markov
processes

概 要 We consider optimal stopping problems for discrete time N-parameter Markov processes, and give themultiexcessive characterization of optimal value functions.

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91

統計数学

35 地 嵜 頌 子 (大 阪 工 大 情 報)
波
大⋆)
藤 原
良 (筑
宮 本 暢 子 (東京理大創域理工)

Shoko Chisaki (Osaka Inst. of Tech.)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

A construction of GDD-type spanning bipartite block designs · · · · · · · · 10

A construction of GDD-type 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
have a structure. There is a one-to-one correspondence between the point set of a group divisible design(GDD) with v1 groups of v2 points and the edge set of a complete bipartite graph Kv1 ,v2 . A block of
GDD corresponds to a subgraph of Kv1 ,v2 . Then the set of subgraphs also satisﬁes the spanning bipartite
block design (SBBD) conditions. It’s called GDD-type. In this talk, we introduce a method to construct a
GDD-type SBBD directly from an (r, λ)-design and a diﬀerence matrix over a group.
36 岡 原 久 也 (東京理大創域理工)
田 畑 耕 治 (東京理大創域理工)

Hisaya Okahara (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)

多元分割表における一般化順序準対称モデルと対称性の必要十分条件 · · 15

Generalized ordinal quasi-symmetry model in multi-way tables and necessary and suﬃcient conditions for symmetry

概 要 We propose a generalized ordinal quasi-symmetry model based on f -divergence for multi-way con-tingency tables. This model builds upon the work of Saigusa et al. (2015), extending their model tomulti-way tables. Additionally, we revisit and modify the properties discussed by Kateri and Agresti(2007), introducing a necessary and suﬃcient condition for the complete symmetry model.
37 佐 藤 哲 也 (東 京 理 大 理)
八 木 文 香 ( 東 京 理 大 理)
瀬 尾
隆 ( 東 京 理 大 理)

Tetsuya Sato (Tokyo Univ. of Sci.)
Ayaka Yagi (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

Sphericity test on variance-covariance matrices with monotone missing
data for a multi-sample problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Sphericity test on variance-covariance matrices with monotone missing
data for a multi-sample problem

概 要 In the case of complete data for a one-sample problem, the likelihood ratio (LR) and an asymptotic

expansion of the modiﬁed likelihood ratio test statistic for the null distribution were given by Muirhead(1982). As an extension, Sato et al. (2024) has discussed the same problem for the two-step and general
step monotone missing data. In this talk, we consider sphericity test under general step monotone missing
data for a multi-sample problem, and using Box’s method, we also give the LR and derive asymptotic
expansions of the test statistics for the LR and modiﬁed LR. Furthermore, we numerically evaluate theactual type I error rates for approximate upper percentiles using Monte Carlo simulation.

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統計数学

38 細 沼 璃 玖 (東 京 理 大 理)
川 崎 玉 恵 ( 青 学 大 経 済)
瀬 尾
隆 ( 東 京 理 大 理)

Riku Hosonuma (Tokyo Univ. of Sci.)
Tamae Kawasaki(Aoyama Gakuin Univ.)
Takashi Seo (Tokyo Univ. of Sci.)

92

Bartlett-type correction of the test statistics for sub-mean vector with
two-step monotone missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bartlett-type correction of the test statistics for sub-mean vector with
two-step monotone missing data

概 要 We consider the one-sample problem of testing for a sub-mean vector. In the case where the data

set consists of complete data with p(= p1 + p2 + p3 + p4 ) dimensions and incomplete data with p1 + p2
dimensions, we consider the one-sample problem of testing the p2 + p3 + p4 mean vector, p3 + p4 mean vector,
and p4 mean vector under the given mean vector of remaining dimensions. In considering these hypotheses,
we construct test statistics based on Rao’s U -statistic structure. Furthermore, we perform a probability
expansion to obtain the distribution function of the test statistics and derive the upper 100α percentiles.
We also propose a Bartlett-type corrected statistic. Moreover, we perform Monte Carlo simulations to verify
approximation accuracy of the proposed approximate upper 100α percentiles and Bartlett-type correction.

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93

応用数学

応 用
9 月 3 日（火）数学第 IV 会場

9:00〜11:40
大⋆)1 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 (日大理工一般数学)
山 岸 弘 幸 ( 産 業 技 術 高 専)
關 戸 啓 人(大阪成蹊大データサイエンス)

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.)
Hiroto Sekido (Osaka Seikei Univ.)

C60 の異性体 1812 個に対応する離散ソボレフ不等式の最良定数 · · · · · · 15

The best constant of discrete Sobolev inequality on 1812 C60 fullerene
isomers

概 要 The best constants of discrete Sobolev inequalities corresponding to 1812 isomers of C60 fullerene arefound. Classical mechanical models of these isomers with a linear spring on each edge are investigated. The
best constants stand for rigidities of these models. We show the best constants of 1812 isomers are distinct
rational numbers and among these, Buckyball (or equivalently truncated icosahedron) takes the least. In
other words, one can say that the Buckyball is the most rigid among 1812 C60 fullerene isomers.
2 浅 芝 秀 人 ( 静 岡 大 理)
E. Gauthier (École Polytechnique)大理)劉恩 豪 (京Hideto Asashiba (Shizuoka Univ.)
Etienne Gauthier (École Polytechnique)(Kyoto Univ.)
Enhao Liu

Interval replacements of persistence modules · · · · · · · · · · · · · · · · · · · · · · 15Interval replacements of persistence modules

概 要 Persistent homology is a powerful technique in topological data analysis employed to explore topologicalfeatures of complex datasets. Multi-parameter persistent homology is less understood than one-parameter
persistent homology because of its more intricate algebraic structure. This presentation will ﬁrst introduce
the interval rank invariant (under the compression system) of persistence modules. This allows us to deﬁne
the interval replacement of persistence modules. Then, we will show the main contribution: providing an
explicit and general formula to compute the interval rank invariant directly under any compression system,
utilizing the Auslander–Reiten theory.

2024/08/21 作成
応用数学

3 中 田 彬 文 (広島大先進理工)小 川 健 翔 (広島大先進理工)奥 田 隆 幸 (広島大先進理工)

Akifumi Nakada (Hiroshima Univ.)
Kento Ogawa (Hiroshima Univ.)
Takayuki Okuda (Hiroshima Univ.)

94

Compact association schemes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Compact association schemes

概 要 In code theory and design theory, we often consider ﬁnite association schemes and compact homoge-

neous spaces. In these spaces, analytically important propositions such as the Peter–Weyl theorem and the
Plancherel theorem hold. In this talk, we deﬁne a compact association scheme as a generalization of ﬁnite
association schemes and compact homogeneous spaces.
4 小 川 健 翔 (広島大先進理工)

Kento Ogawa (Hiroshima Univ.)

アソシエーションスキームの代数化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

An algebraization of association schemes

概 要 Association scheme is a most important object in algebraic combinatorics. The structure of association

schemes induces a ﬁnite dimensional complex vector space with a matrix product, an Hadamard product,a transpose–conjugate, and a conjugate and a representation of the algebra with respect to the matrix
product. The vector space is called the Bose–Mesner algebra of the association scheme. In this talk, we
introduce a category of “algebras” that includes the Bose–Mesner algebra of association schemes as objects,
and a functor from a category of association schemes to the category of “algebras”.
5 野 﨑
寛 (愛知教育大教育)
澤正 憲 (神戸大システム情報)

Hiroshi Nozaki (Aichi Univ. of Edu.)
Masanori Sawa (Kobe Univ.)

Polynomial space を用いた求積公式の点数削減法 · · · · · · · · · · · · · · · · · · · 15
Reducing the number of points of cubature formulas using polynomial
space

概 要 Victoir (2004) provided a method for reducing the number of points in a cubature formula with a

speciﬁc substructure using combinatorial designs and orthogonal arrays. On the other hand, the concept ofpolynomial space, given by Godsil (1988), refers to a space where certain designs, including combinatorial
designs and orthogonal arrays, can be deﬁned. In this talk, we generalize Victoir’s point reduction method
using polynomial space.
6 松 村 英 樹 (都立大理・慶大理工)澤
正 憲 (神戸大システム情報)
Hideki Matsumura(Tokyo Metro. Univ./Keio Univ.)
Masanori Sawa (Kobe Univ.)

Galois 共役な点配置を持つ重み付きデザインについて · · · · · · · · · · · · · · · 15
On Galois conjugate weighted designs for Bessel polynomials

概 要 A quadrature formula is a formula computing a deﬁnite integration by evaluation at a set of ﬁnitely

many points (design). Examining the existence of certain rational quadrature formulas leads to applications
to interesting problems such as Waring’s problem in number theory and spherical design in combinatorics.
A centrally symmetric quadrature is a central research object in the real case. What is a complex analogueof central symmetry? In many interesting quadratures for Bessel polynomials, the points appear with their
Galois conjugates. Therefore, it seems natural to consider such quadratures (Galois conjugate quadratures)
as a complex analogue of central symmetry. In this talk, we discuss such quadratures with examples. We
also describe the relationship with a Diophantine problem called Prouhet–Tarry–Escott problem.

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95

応用数学

7 三 島 輝 之 (アクセンチュア)澤正 憲 (神戸大システム情報)
内 田 幸 寛 ( 都 立 大 理)盧
暁 南 ( 岐 阜 大 工)
Teruyuki Mishima(Accenture Japan Ltd)
Masanori Sawa (Kobe Univ.)
Yukihiro Uchida (Tokyo Metro. Univ.)(Gifu Univ.)
Xiao-Nan Lu

有理的区間デザインの明示的構成法について · · · · · · · · · · · · · · · · · · · · · · · 15

On explicit construction of rational interval designs

概 要 If the integral of a polynomial with respect to a measure on an interval is represented as a linear

combination of the values of the polynomial at ﬁnitely many points, this representation is called a quadratureformula. If all the coeﬃcients of the linear combination are equal, the quadrature formula is called a
Chebyshev-type quadrature formula, and the set of the points is called an interval design. In this talk,we give explicit construction of interval designs whose points are rational for a certain measure. We also
investigate when this construction is applicable by classifying certain algebraic curves.
8 谷 口 浩 朗
(大和大教育・香川高専⋆)
Hiroaki Taniguchi(Yamato Univ./Kagawa Nat. Coll. of Tech.⋆)

APN 関数の隣接グラフと Dillon’s property · · · · · · · · · · · · · · · · · · · · · · · · 15
On Incidence graphs of APN functions and Dillon’s propertym
概 要 Firstly, we give a condition that Gf is a covering graph of Gf1 for APN functions f : Fn
2 → F2 and1
f1 : Fn2 → Fmwith m ≥ m1 , where Gf and Gf1 are incidence graphs (Cayley graphs) of f and f1 . Using
2

this condition, we see that, for APN functions, Dillon’s property is preserved under CCZ-equivalence. Also,
some results on Dillon’s property are given.
9 江 川 嘉 美 (東 京 理 大⋆)
松 田 晴 英 ( 芝 浦 工 大 工)

Yoshimi Egawa (Tokyo Univ. of Sci.⋆)Haruhide Matsuda(Shibaura Inst. of Tech.)

グラフをいくつかの閉路で被覆できるための次数和条件について · · · · · · 15

Degree sum conditions for covering cycles in graphs

概 要 This talk gives the degree sum condition for covering a graph with some cycles. In fact, we showedthat a 2-connected graph G is covered with k cycles if G satisﬁes the following two conditions for a vertex
subset S of G; (i) the minimum degree sum of any independent k + 1 vertices in S is greater than or equal
to |G| or the number of independent vertices in S is less than or equal to k and (ii) the vertex subset otherthan S is a clique.
10 藤 田 慎 也(横浜市大データサイエンス)

Shinya Fujita (Yokohama City Univ.)

辺着色グラフにおける虹色閉路の存在について · · · · · · · · · · · · · · · · · · · · · 10

On the existence of rainbow cycles in edge-colored graphs

概 要 In this talk, we consider the existence of rainbow cycles in edge-colored graphs. In particular, we

discuss color degree conditions for the existence of rainbow 4-cycles in edge-colored graphs. Some recent
results will be reviewed.
14:15〜15:15 特別講演
三 枝 崎 剛 ( 早 大 理 工)

Universal graph series, chromatic functions, and their index theory

Tsuyoshi Miezaki (Waseda Univ.)

Universal graph series, chromatic functions, and their index theory

概 要 In this talk, we introduce the concept of universal graph series. We then present four invariants ofgraphs and discuss some of their properties. In particular, one of these invariants is a generalization of thechromatic symmetric function and a complete invariant for graphs.

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96

15:30〜16:25
11 横 村 国 治(東海大理系教育センター)

Kuniharu Yokomura (Tokai Univ.)

Balanced k 部グラフの Hamiltonian-connected 性について · · · · · · · · · · · 15
On degree conditions of balanced k-partite Hamiltonian-connected graphs

概 要 For a graph G and u, v ∈ V (G), a path in G from u to v is called a (u, v)-path, and if (u, v)-path is a

Hamiltonian path from u to v, then (u, v)-path is called a (u, v)-Hamiltonian path. A graph G is said to be
Hamiltonian-connected if there exists a (u, v)-Hamiltonian path between any two vertices u, v. A k-partite
graph is said to be a balanced k-partite graph if each partite set has the same number of vertices. We givesome conditions for balanced k-partite graphs to be Hamiltonian-connected.
12 弘 畑 和 秀 (茨 城 工 高 専)
( Lehigh Univ. )M. Cream
R. J. Gould ( Emory Univ. )Kazuhide Hirohata(Ibaraki Nat. Coll. of Tech.)
Megan Cream (Lehigh Univ.)
Ronald J. Gould (Emory Univ.)

Chorded pancyclicity with distance two degree condition · · · · · · · · · · · · 15

Chorded pancyclicity with distance two degree condition

概 要 A graph G of order n ≥ 3 is said to be pancyclic if G contains a cycle of each length from 3 to n.

A chord of a cycle is an edge between two nonadjacent vertices of the cycle, and a chorded cycle is a cycle
containing at least one chord. We deﬁne a graph G of order n ≥ 4 to be chorded pancyclic if G contains
a chorded cycle of each length from 4 to n. We improve some known results on pancyclic and chorded
pancyclic graphs.
13 鹿 島柾 ( 慶 大 理 工)
R. Škrekovski (Univ. of Ljubljana)Rongxing Xu (浙 江 師 範 大)
Masaki Kashima (Keio Univ.)
Riste Škrekovski (Univ. of Ljubljana)Rongxing Xu (Zhejiang Normal Univ.)

Proper conﬂict-free 彩色における次数彩色の類似 · · · · · · · · · · · · · · · · · · · 15

Analogies of degree coloring in proper conﬂict-free colorings

概 要 A proper coloring of a graph is a map from the vertex set of the graph to positive integers suchthat every pair of adjacent vertices receive distinct colors. For a graph and its proper coloring, if there isa color that appears exactly once in the neighborhood of a vertex, then we say that the vertex satisﬁes
the conﬂict-free condition. A proper conﬂict-free coloring of a graph is a proper coloring such that every
vertex satisﬁes the conﬂict-free condition. We investigate analogies of degree coloring in proper conﬂict-freecolorings and improve the known upper bound of the proper conﬂict-free chromatic number of graphs withbounded maximum degree.
14 中 村 伊 南 沙 (佐 賀 大 理 工)
Inasa Nakamura (Saga Univ.)

Partial matchings の変形と dotted graphs · · · · · · · · · · · · · · · · · · · · · · · · · 10
Transformations of partial matchings and dotted graphs

概 要 We present partial matchings by lattice presentations, and we consider transformations of partial

matchings. Transformations of partial matchings are associated with transformations of lattice polytopes.
We give the notion of the area of a transformation and we consider transformations of partial matchings withminimal area. Further, we consider dotted graphs that are planar graphs associated with lattice polytopes,
and we consider deformations of dotted graphs.

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応用数学

16:40〜17:40

2023 年度日本数学会応用数学賞受賞特別講演
城
大⋆) Two degree factors of graphs and related topics
加 納 幹 雄 (茨Mikio Kano

(Ibaraki Univ.⋆)

Two degree factors of graphs and related topics

概 要 We ﬁrst present some results on (1, f )-odd factors of graphs, which is a generalization of a 1-factor, andthen show some results on degree factors with red-blue vertex coloring of graphs, which is a new type of degree
factors. We also present some results together with some problems related to these factors. For a function
f : V (G) → {1, 3, 5, ..}, a spanning subgraph F of G is called a (1, f )-odd factor if degF (v) ∈ {1, 3, . . . , f (v)}for all vertices v of G. If f (v) = 1 for every v ∈ V (G), then a (1, f )-odd factor becomes a 1-factor. For
two sets SR , SB ⊆ Z of integers, a spanning subgraph F of G is called a two-tone (SR , SB )-factor of G if
degF (x) ∈ SR for every red vertex x and degF (y) ∈ SB for every blue vertex y. For example, we showthat for every red-blue vertex coloring of an r-regular graph G, in which the distance between any two
red vertices is at least 3, G has a two-tone ({a}, {k, k + 1})-factor, where r, a and k be integers such that1 ≤ a ≤ r and 0 ≤ k < r.

9 月 4 日（水）第 IV 会場

9:00〜11:40
15 小 関 健 太 (横浜国大環境情報)
城大⋆)
加 納 幹 雄 (茨江 川 嘉 美 (東 京 理 大⋆)

Kenta Ozeki (Yokohama Nat. Univ.)(Ibaraki Univ.⋆)
Mikio Kano
Yoshimi Egawa (Tokyo Univ. of Sci.⋆)

正則グラフにおける, 道-閉路システム · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Path-cycle systems in regular graphs

概 要 A spanning subgraph F in G is said to be a path-cycle system with respect to W if each componentof F is either a path or a cycle, and the set of end-vertices of the paths in F is equal to W . For an integerr ≥ 4, we prove that for an r-edge-connected K1,r -free r-regular graph G and a set of even number ofvertices of G such that the distance between any two vertices of W in G is at least 3, G contains a path-cycle
system with respect to W . We also showed that the conditions in the theorem are best possible in several
meanings.
16 毛 利 健 太 (関 西 学 院 大 理)
森
亜 貴 (摂南大全学教育機構)
大 杉 英 史 ( 関 西 学 院 大 理)

Kenta Mori (Kwansei Gakuin Univ.)(Setsunan Univ.)
Aki Mori
Hidefumi Ohsugi(Kwansei Gakuin Univ.)

ジョイングラフに付随する symmetric edge polytope のファセット数の上限及び下限 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The number of facets of symmetric edge polytopes arising from joingraphs概 要 In this talk, we study the upper and lower bounds for the number of facets of symmetric edge polytopesof connected graphs conjectured by Braun and Bruegge. In particular, we show that their conjecture is true
for any graph that is the join of two graphs (equivalently, for any connected graph whose complement graphis not connected). It is known that any symmetric edge polytope is a centrally symmetric reﬂexive polytope.
Hence our results give a partial answer to Nill’s conjecture: the number of facets of a d-dimensional reﬂexive
polytope is at most 6d/2 .

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17 佐 藤 洋 輔 (早 大 理 工)
Yosuke Sato

(Waseda Univ.)98

頂点重み付き彩色対称関数の一般化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Generalization of the vertex-weighted version of the chromatic symmetric function

概 要 One of the invariants of graphs is the chromatic symmetric function invented by R.P. Stanley. The

result of this study is a synthesis of two generalizations of this function. The ﬁrst is a generalization
using Kneser graphs, which is a complete invariant of simple graphs. The second is a generalization tovertex-weighted graphs. In this study, we newly generalize the vertex-weighted version using Kneser graphs.
In conclusion, this new function was found to be a complete invariant of the vertex-weighted graph. In
addition, this result allows us to construct a complete invariant for directed acyclic graphs and partiallyordered sets.
18 坂 本齋 藤

光 ( 神 奈 川 大 工)
渓 ( 日 大 文 理)

Hikari Sakamoto (Kanagawa Univ.)(Nihon Univ.)
Kei Saito

モーメント母数推定法による時系列データの古典性・量子性の判別 · · · · 15

A method of discrimination of time series whether classical or quantum
type via moment parameter estimation

概 要 It is typical for analysing time series models to take noise as white noise with the Gaussian distribution.

This time series is aﬀected by classical noise following a random walk, but we would like to consider thecase where it is aﬀected by quantum noise following a quantum walk.
19 齋 藤渓 ( 日 大 文 理)
船 川 大 樹 ( 北 海 学 園 大 工)
(Nihon Univ.)
Kei Saito(
Daiju Funakawa Hokkai-Gakuen Univ.)

グラフ上の量子ウォークにおける一般化されたスペクトル写像定理 · · · · 15

A generalized spectral mapping theorem for quantum walks on graphs

概 要 Quantum walk is a mathematical model which is a quantum version of the random walk, and many

applications are known in various research ﬁelds, e.g., quantum information. It is important to clarify its
eigenvalues and eigenvectors, and the spectral mapping theorem for quantum walk is a very useful tool. In
this talk, we present a generalized spectral mapping theorem for quantum walk that can be applied to moregeneral models.
大理) [ Transport distance between Grover walks on graphs and coarse Ricci
20 藤 谷 恭 明 (阪黄 海 仲 星 (阪 大 基 礎 工) curvature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yasuaki Fujitani (Osaka Univ.)(Osaka Univ.)
Chusei Kiumi

Transport distance between Grover walks on graphs and coarse Ricci
curvature

概 要 The main purpose of this talk is contributing to the study of the relationships between the quantum

walks and their underlying graphs. The coarse Ricci curvature on graphs is usually deﬁned using random
walks. In this talk, we introduce a new deﬁnition of the coarse Ricci curvature induced from the Groverwalk, which is one of the quantum walks. We refer to this curvature as Grover Ricci curvature. Notably,
quantum walks can also be deﬁned on hypergraphs, and we deﬁne the Grover Ricci curvature on hypergraphs
aiming for further applications. This talk is based on Y. Fujitani and C. Kiumi, Quantum Inf Process 23,
180 (2024).

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応用数学

21 𠮷 野 聖 人 (広 島 工 大 情 報)
久 保 田 匠 (愛知教育大教育)
Kiyoto Yoshino(Hiroshima Inst. of Tech.)
Sho Kubota (Aichi Univ. of Edu.)

グローヴァーウォーク上の perfect state transfer と対称性について · · · · 15

Symmetry of graphs and perfect state transfer in Grover walks

概 要 We provide a necessary and suﬃcient condition for perfect state transfer between two vertices in theGrover walk on a graph to occur. Additionally, we prove that automorphisms preserve the occurrence ofperfect state transfer. In 2019, Zhan provided an inﬁnite family of circulant graphs of valency 4 that admit
perfect state transfer. As an application of our results, we characterize circulant graphs of valency at most
4 that admit perfect state transfer.
22 遠藤 (渡邊) 隆子 (東 北 大 工)
小 松
尭 ( 山 梨 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)
三 橋 秀 生 ( 法 政 大 理 工)
佐 藤
巌 ( 小 山 工 高 専)
Takako Endo(Watanabe)(Tohoku Univ.)
Takashi Komatsu (Univ. of Yamanashi)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Hideo Mitsuhashi (Hosei Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)

The second matrix-weighted zeta function of a graph · · · · · · · · · · · · · · · 10

The second matrix-weighted zeta function of a graph概 要 We introduce a new matrix-weighted zeta function, i.e., the second matrix-weighted zeta function of agraph, and give its determinant expression. Furthermore, we deﬁne the second matrix-weighted L-functionof G, and give a determinant expression of it. As an application, we express the second matrix-weighted
zeta function of a regular covering of G by a product of second matrix-weighted L-functions of G.
23 佐 藤巖 ( 小 山 工 高 専)
遠藤 (渡邊) 隆子 (東 北 大 工)
小 松
尭 ( 山 梨 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)
松 本 洋 平 ( 信 州 大 理)

Iwao Sato (Oyama Nat. Coll. of Tech.)
Takako Endo (Tohoku Univ.)
Takashi Komatsu (Univ. of Yamanashi)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Yohei Matsumoto (Shinshu Univ.)

The second matrix-weighted alternating zeta function of a digraph · · · 15

The second matrix-weighted alternating zeta function of a digraph概 要 We deﬁne the second weighted alternating zeta function of a digraph D, and give its determinant

expression. We present a decomposition formula for the second weighted alternating zeta function of a group
covering of D. Furthermore, we introduce the second weighted alternating L-function of D, and present a
determinant expression of it. As a corollary, we express the second weighted alternating zeta function of agroup covering of D by its second weighted alternating L-functions.

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応用数学

24 佐 藤巖 ( 小 山 工 高 専)
赤 堀 次 郎 ( 立 命 館 大 理 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)鈴 木 良 一 ( 立 命 館 大 理 工)

Iwao Sato (Oyama Nat. Coll. of Tech.)Akahori Jiro (Ritsumeikan Univ.)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Suzuki Ryoichi (Ritsumeikan Univ.)100

A zeta function of a pseudo quantization of a Markov chain on a graph· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A zeta function of a pseudo quantization of a Markov chain on a graph概 要 We consider a Markov chain on a simple graph, and introduce a pseudo quantization for it. Further-more, we deﬁne a zeta function for the pseudo quantization, and present the Euler product, the exponential
generating function and the determinant expression of Ihara type for the zeta function. Moreover, we treat
this zeta function for a regular covering of a graph. Finally, we deﬁne an L-function of a graph, and present
the Euler product, the exponential generating function and the determinant expression of Ihara type of it.
13:00〜14:00
25 加 藤 寛 大 (日 大 総 合 基 礎)
井 手 勇 介 ( 日 大 文 理)
成 松 明 廣(福知山公大数理・データサイエンスセンター)
今 野 紀 雄(立命館大理工・横浜国大⋆)(Nihon Univ.)
Tomoki Kato
(Nihon Univ.)
Yusuke Ide
Akihiro Narimatsu(Univ. of Fukuchiyama)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)

出生死滅連鎖に付随する多変数直交多項式の構成 · · · · · · · · · · · · · · · · · · · 15

Construction of multivariate orthogonal polynomials related to birthand death chains概 要 In this talk, we consider multivariate orthogonal polynomials related to birth and death chains. In ourconstruction, we consider d types of birth and death chains. Then we combine these d types of chains by using
tensor product. Each of birth and death chains has reversible distribution then the probability transition
matrix can be transformed to real symmetric matrix. Thus we can consider orthogonal polynomials related
to the chains. By using tensor product construction, we obtain multivariate orthogonal polynomials. We
also propose a concrete method for reduction from multivariate polynomial to univariate polynomial.

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応用数学

26 成 松 明 廣(福知山公大数理・データサイエンスセンター)
井 手 勇 介 ( 日 大 文 理)
今 野 紀 雄(立命館大理工・横浜国大⋆)Akihiro Narimatsu(Univ. of Fukuchiyama)(Nihon Univ.)
Yusuke Ide
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)

多次元エーレンフェストモデルに対応する連続時間量子ウォークの解析· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Continuous time quantum walk related to the multi- dimensional Ehrenfest model

概 要 In this study, we consider and analyze Continuous time quantum walk related to the multi- dimensional

Ehrenfest model. We obtain that there exists a form of independence among the random variables in eachdimension, which is achieved by scaling time according to the ratio of the number of balls in the multidimensional Ehrenfest model. By using the independence, we can analyze the continuous time quantum
walk on the path graph easier than the previous study did.
27 関 藤 寛 人 (横浜国大環境情報)
瀬 川 悦 生 (横浜国大環境情報)

Hiroto Sekido (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

量子グラフウォークの周期性と律動性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Periodicity and rhythmicity of quantum graph walks

概 要 Quantum graph walks are a quantum walk induced by the stationary Schrödinger equation oneach vertex of a metric graph satisfying certain boundary conditions. Quantum graph walks are also a
generalization of Grover walks. In this study, we obtain the parameters for a quantum graph walk deﬁned
from a strongly regular graph to be periodic and its period. In addition, we newly deﬁne a strike-in quantum
walk, its rhythmicity, and its beat, and clarify the parameters that satisfy the conditions. The strike-inquantum walk is a model that includes quantum search, and rhythmicity is expected to play a role incontrolling the length of a period. Periodicity is also a special case of rhythmicity.
28 穂 坂 大 将 (横浜国大環境情報)
瀬 川 悦 生 (横浜国大環境情報)

Taisuke Hosaka (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)ジョンソングラフ上の量子ウォークにおける拍動現象 · · · · · · · · · · · · · · · 15

Pulsation of the quantum walk on the Johnson graph概 要 In this talk, we introduce a phenomenon called “pulsation” in quantum walk. This phenomenon is asfollows: For two connected graphs G1 , G2 , we consider the composite graph formed by a disjoint union ofG1 and G2 . In addition, we assume that the initial state exists only on G1 . Then almost all states transfer
to G2 on a suitable step. Moreover, almost all states return to G1 on a suitable step. These phenomena
occur periodically. We analyzed the existence of this phenomenon when G1 is the Johnson graph and G2 isa star graph by using perturbation theory.

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応用数学

9 月 5 日（木）102

第 IV 会場

9:45〜12:00
29 シュワドレンカカレル( 都 立 大 理)

Karel Svadlenka (Tokyo Metro. Univ.)

障害物上の非等方的な界面運動に対する近似スキームについて · · · · · · · · 15

On an approximation method for anisotropic interfacial motions on obstacle

概 要 While isotropic interfacial network motion is already well studied, theoretical understanding ofcurvature-driven motion of interfacial networks with anisotropic energies and global constraints is stilllacking. In this talk, I will present theoretical analysis of an intermediate-level problem with three phases,
where one phase plays the role of a ﬁxed obstacle and one phase represents a volume-preserving anisotropic
particle. A generalization of the so-called heat-content approximation leads to an approximation scheme,
which is suitable for both theoretical existence analysis and numerical approximation. Both theoreticalconvergence results and numerical simulations will be shown.
30 市 田優 ( 関 西 学 院 大 理)
中 田 行 彦 ( 青 学 大 理 工)

Yu Ichida (Kwansei Gakuin Univ.)
Yukihiko Nakata(Aoyama Gakuin Univ.)

Global dynamics of a simple model for wild and sterile mosquitoes · · · 15
Global dynamics of a simple model for wild and sterile mosquitoes

概 要 There are known methods to manage the population dynamics of wild and sterile mosquitoes by

releasing genetically engineered sterile mosquitoes. Even if a two-dimensional system of ordinary diﬀerential
equations is considered as a simple mathematical model for developing release strategies, fully understanding
the global behavior of the solutions is challenging, due to that the probability of mating is ratio-dependent.
In this talk, we combine a geometric approach called the time-scale transformation and blow-up techniqueto provide a complete understanding of dynamical systems near the origin. Then, the global behavior of
the solution of the system is classiﬁed in a two-parameter plane represented by the natural death rate ofmosquitoes and the sterile mosquito release rate.
31 Bendong Lou(Shanghai Normal Univ.)谷大⋆)
森 田 善 久 (龍Bendong Lou (Shanghai Normal Univ.)
Yoshihisa Morita (Ryukoku Univ.⋆)

Asymptotic behavior for solutions to reaction-diﬀusion equations on aroot-like metric graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic behavior for solutions to reaction-diﬀusion equations on aroot-like metric graph概 要 We deal with symmetric solutions of the bistable reaction-diﬀusion equation on an unbounded root-like

metric graph. Our goal is to provide a spreading-transition-vanishing trichotomy result on the asymptotic
behavior for symmetric solutions with compact supported initial data on the graph. To this end, we needa convergence result for bounded and symmetric solutions to the equation. The convergence result can beproved using a version of zero number diminishing properties on the graph.
32 奥 村 真 善 美 (甲南大知能情報)

Makoto Okumura (Konan Univ.)

ある保存系に対する平方差分に基づく構造保存数値解法について · · · · · · 15

Structure-preserving numerical methods based on square diﬀerences forconservative PDEs

概 要 Recently, Furihata has proposed various types of nonlinear diﬀerence operators, such as logarithmic

diﬀerence, aiming to bring out other superior features instead of relaxing linearity. In this study, a certain
summation formula is derived for the square diﬀerence operator among the above nonlinear diﬀerence
operators. Using the summation formula, we construct a structure-preserving scheme based on the discretevariational derivative method (DVDM). In this talk, we report the results.

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応用数学

33 Junyong Eom (北 大 電 子 研)
(北大理)
Shuli Chen(
中 村
玄 北 大 電 子 研)
西 村 吾 朗 ( 北 大 電 子 研)

Junyong Eom (Hokkaido Univ.)
Shuli Chen (Hokkaido Univ.)
Gen Nakamura (Hokkaido Univ.)
Goro Nishimura (Hokkaido Univ.)

Approximation peak time to time-domain ﬂuorescence diﬀuse optical
tomography for ﬁnite ﬂuorescence lifetime · · · · · · · · · · · · · · · · · · · · · · · · · 15

Approximation peak time to time-domain ﬂuorescence diﬀuse optical
tomography for ﬁnite ﬂuorescence lifetime

概 要 In this talk, we concerns an inverse problem for ﬂuorescence diﬀuse optical tomography (FDOT)

reconstructing locations of multiple point targets from the measured temporal response functions. Peaktime, the time when the temporal response function of the ﬂuorescence reaches its maximum, is an importantmeasurement in FDOT because it is most less suﬀered by noise. We derive an approximation peak time
formula in an explicit way based on asymptotic analysis and the formula is veriﬁed numerically in a practicalrange of physical parameters including ﬂuorescence lifetime.
大⋆)34 西 田 孝 明 (京隠 居 良 行 ( 東 工 大 理)
藤 原 宏 志 ( 京 大 情 報)

Takaaki Nishida (Kyoto Univ.⋆)
Yoshiyuki Kagei (Tokyo Tech)
Hiroshi Fujiwara (Kyoto Univ.)

A thermal convection in the horizontal layer with non-uniform heat
supply · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A thermal convection in the horizontal layer with non-uniform heat
supply概 要 We consider a model problem of thermal convection in a long liquid layer under gravity with

non-uniform heat supply. The system is described by the Oberbeck–Boussinesq equations in the two spacedimension. An existence theorem of stationary solutions is proved under some assumptions. Several ﬂow
patterns are obtained by the numerical computations which include the cases out of the assumptions of theexistence theorem.
35 武 村 一 雄 (日大理工一般数学)
永 井
敦 ( 津 田 塾 大 学 芸)
關 戸 啓 人(大阪成蹊大データサイエンス)

Kazuo Takemura (Nihon Univ.)(Tsuda Coll.)
Atsushi Nagai
Hiroto Sekido (Osaka Seikei Univ.)(−1)M (d/dx)2M に対する両端固定条件の境界値問題におけるグリーン関数の正値性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Positivity of the Green’s function corresponding to clamped boundary
value problem for (−1)M (d/dx)2M

概 要 We found two types of expressions for the Green’s function G(x, y) in the boundary value problem

with clamped conditions at both ends for the diﬀerential operator (−1)M (d/dx)2M on the interval (−s, s)
presented in the paper [1] published in 2011. By determining the maximum value of the diagonal valueG(y, y) for |y| ≤ s, the best constant for the corresponding Sobolev inequality was calculated. In thispresentation, in addition to the matrix representation of the Green’s function in the boundary value problem
with clamped conditions at both ends for the diﬀerential operator (−1)M (d/dx)2M on the interval (0, 1), a
newly obtained integral representation is reported. Furthermore, the positivity of the Green’s function is
deduced from this integral representation.

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応用数学

36 土 屋 拓 也 (明治学院大経済)中 村
誠 ( 阪 大 情 報)

Takuya Tsuchiya (Meiji Gakuin Univ.)
Makoto Nakamura (Osaka Univ.)104

半線型 Klein–Gordon 方程式の解の収束性と挙動について · · · · · · · · · · · · 15

On convergence and behavior of solutions for semi-linear Klein–Gordon
equation

概 要 We talk about the convergence, the stability, and the accuracy of the numerical solutions for thesemi-linear Klein–Gordon equation. In this talk, we report the changes of the convergence and the behaviorof the solutions when the amplitude of the initial condition, the magnitude of the mass, the existence of thenonlinear term, and the numbers of the grid are changed.
14:15〜16:00
37 大 澤 知 己(Univ. of Texas at Dallas)
矢 ヶ 崎 一 幸 ( 京 大 情 報)
Tomoki Ohsawa(Univ. of Texas at Dallas)
Kazuyuki Yagasaki (Kyoto Univ.)

Semiclassical perturbations of single-degree-of-freedom Hamiltonian systems: Separatrix splitting and nonintegrability · · · · · · · · · · · · · · · · · · · · 15
Semiclassical perturbations of single-degree-of-freedom Hamiltonian systems: Separatrix splitting and nonintegrability

概 要 We study semiclassical perturbations of single-degree-of-freedom Hamiltonian systems and provide

suﬃcient conditions for the separatrices to split and for their meromorphic nonintegrability such that theﬁrst integrals depend on the small parameter meromorphically. To obtain the former and latter results, weuse a Melnikov-type approach and a generalization due to Ayoul and Zung of the Morales–Ramis theory,
respectively. We illustrate the theoretical results for bounded potentials including a simple pendulum.
38 三
小
関
杉

大
医)
浦
岳 (九
(
川 知 之 明 大 総 合 数 理)
坂 歩 幹 ( 明 大 総 合 数 理)
大
医)
原
圭 (九

Takashi Miura (Kyushu Univ.)
Toshiyuki Ogawa (Meiji Univ.)
Ayuki Sekisaka (Meiji Univ.)
Kei Sugihara (Kyushu Univ.)

精細管に現れるセグメントパターンと defect 解の諸性質 · · · · · · · · · · · · · 15

Segmented patterns appearing in seminiferous tubules and various properties of defects

概 要 We discuss the properties of segmented patterns and defect solutions that appear in seminiferous

tubules. defects are a type of modulated traveling waves in reaction-diﬀusion systems, and the transition
phenomena between wave trains. In this talk, we will also discuss some mathematically necessary properties
that can be derived from observations when defects appear as segmented patterns in seminiferous tubules.
39 穴 田 浩 一 (早 大 高 等 学 院)
石 渡 哲 哉
(芝浦工大システム理工)
牛 島 健 夫 (東京理大創域理工)
Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Takeo Ushijima (Tokyo Univ. of Sci.)

ある自己交差する閉曲線の曲線短縮問題における曲線の漸近挙動に関する一考察 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Remark on the asymptotic behavior of curves in a curve shortening
problem for convex immersed curves with self-crossing points

概 要 We consider a curve-shortening problem for convex immersed curves with self-crossing points. We

deal with curve contractions by the power of their curvatures with a positive exponent α. The motion canbe described by a quasilinear parabolic partial diﬀerential equation and some of the solutions blow up withType 1 or Type 2 singularities, depending on the exponent α. Our purpose in this talk is to investigate theasymptotic behavior of curves contracting in the case that solutions have Type 1 singularity.

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105

応用数学

40 上 田 祐 暉 (北 大 電 子 研)
Junyong Eom (北 大 電 子 研)
内 海 晋 弥 ( 北 大 電 子 研)
Yueyuan Gao(島根大材料エネルギー)
中 岡 慎 治 ( 北 大 先 端 生 命)
水 藤
寛 (東 北 大 A I M R )久 米 真 司 ( 滋 賀 医 科 大)
片 桐 秀 樹 ( 東 北 大 医)長 山 雅 晴 ( 北 大 電 子 研)
Yuuki Ueda (Hokkaido Univ.)
Junyong Eom (Hokkaido Univ.)
Shinya Uchiumi (Hokkaido Univ.)
Yueyuan Gao (Shimane Univ.)
Shinji Nakaoka (Hokkaido Univ.)
Hiroshi Suito (Tohoku Univ.)
Shinji Kume
(Shiga Univ. of Medical Sci.)
Hideki Katagiri (Tohoku Univ.)
Masaharu Nagayama (Hokkaido Univ.)

グルコース-インスリン代謝動態モデルの構築とパラメータ推定 · · · · · · · 15

Mathematical modeling of glucose-insulin metabolism dynamics and parameter estimation

概 要 We propose a mathematical model of the dynamics of glucose-insulin metabolism. The model describes

detailed dynamics in pancreas, hepatocyte and skeleton muscle. We connect each organ by blood circulationand provide the ODE system. We estimate model parameters by ﬁtting the numerical results of glucose andinsulin (and C-peptide) concentrations to clinical data. The estimation is based on the Metropolis–Hastings
algorithm, which is widely used for sampling in statistics. We can verify that the computational result
which ﬁts the clinical data provides valid quantities and properties in terms of medical knowledge.
41 荻 原 俊 子 (城 西 大 理)
中 村 健 一 (明大研究・知財)Toshiko Ogiwara (Josai Univ.)
Ken-Ichi Nakamura (Meiji Univ.)

Lotka–Volterra 競争拡散系の双安定フロント波の進行方向 · · · · · · · · · · · 15
Propagating direction of bistable traveling fronts in the Lotka–Volterracompetition-diﬀusion system

概 要 We consider front propagation in the classical 2-species Lotka–Volterra competition-diﬀusion system

under strong competition conditions. The system has a unique traveling front solution (up to translation)connecting two stable states. The sign of the front speed gives us signiﬁcant information about which
species prevails over the other, and identifying the sign is still a challenging problem. In this talk, wegive some new results on the sign of the speed of bistable traveling fronts based on comparison arguments.
The results determine the propagation direction of the front for a much broader range of parameters thanprevious results.
42 星 野 秀 朋 (早 大 理 工)
土 屋 拓 也 (明治学院大経済)米 田
元 ( 早 大 理 工)

Hidetomo Hoshino (Waseda Univ.)
Takuya Tsuchiya (Meiji Gakuin Univ.)(Waseda Univ.)
Gen Yoneda

一様等方時空を背景とした場合の Einstein 方程式の数値安定性の解析および改善 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Analysis and improvement of numerical stability of the Einstein equations against homogeneous and isotropic spacetime background概 要 In this study, we investigate the numerical stability of the covariant Baumgarte–Shapiro–Shibata–

Nakamura (cBSSN) formulation against homogeneous and isotropic spacetime. To evaluate the numericalstability, we calculate the constraint ampliﬁcation factor (CAF), which is obtained from an eigenvalue
analysis of the evolution of the constraint. We propose a modiﬁcation to the time evolution equations of
the cBSSN formulation that achieves higher numerical stability.

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106

16:15〜17:15

特別講演
物 部 治 徳 (阪 公 大 理) [ 反応拡散方程式系の特異極限に現れるスポット型の進行波について

Harunori Monobe (Osaka Metro. Univ.)

On compact traveling waves in the singular limit problem of some reaction diﬀusion systems

概 要 The singular limit method is sometimes used for some mathematical models, written by partial

diﬀerential equations (PDEs), to describe complex phenomena. The idea is to contract original PDEs andcreate simple equations which maintains its essential property. As a typical example, it is well known thatthe singular limit of the Allen–Cahn–Nagumo equation, describing phase transition phenomena, becomes
Mean-curvature ﬂow. In this talk, we focus on the Allen–Cahn–Nagumo equation and its singular limit(Mean-curvature ﬂow with driving force), and introduce some results, e.g., spot patterns.

9 月 6 日（金）第 IV 会場

10:00〜12:00
43 市 田優 ( 関 西 学 院 大 理)
坂 元 孝 志 ( 明 大 理 工)

Yu Ichida (Kwansei Gakuin Univ.)
Takashi Sakamoto (Meiji Univ.)

無限遠分岐の幾何学的様相: ケーススタディ · · · · · · · · · · · · · · · · · · · · · · · 15

Geometric approach to the bifurcation at inﬁnity: A case study

概 要 In this talk, the reaction-diﬀusion equation in space 1D with negative power nonlinearity is presented

as an example the stationary solutions of which are characterized by the bifurcation at inﬁnity. The all
dynamics, including to inﬁnity, of the ordinary diﬀerential equation concerning with the stationary problemof the reaction-diﬀusion equation are obtained by the Poincaré-type compactiﬁcation. The results of thistalk give relationship between the bifurcation at inﬁnity of the stationary solutions for the reaction-diﬀusion
equation and the connecting orbits of the ordinary diﬀerential equations, especially, that connect theequilibria at inﬁnity. Moreover, this result also answers the question of what kind of solutions appear (ordisappear) associated with the bifurcation.
44 近 藤 真 純 (岡 山 理 大 理 工)
鬼 塚 政 一 ( 岡 山 理 大 理)

Masumi Kondo (Okayama Univ. of Sci.)
Masakazu Onitsuka(Okayama Univ. of Sci.)

Ulam stability for von Bertalanﬀy growth model with Allee eﬀect · · · · 15
Ulam stability for von Bertalanﬀy growth model with Allee eﬀect

概 要 In this study, we consider conditional Ulam stability for von Bertalanﬀy growth model with Alleeeﬀect. Ulam stability means that for any approximate solution, there exists a true solution such that theerror between them always remains within a certain width. This study gives a better Ulam constant thana previous result.

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107

応用数学

45 竹 田 航 太 (京坂 上 貴 之 (京

大

理)

大

理)

(Kyoto Univ.)
Kota Takeda
Takashi Sakajo (Kyoto Univ.)

Uniform error bounds of the ensemble transform Kalman ﬁlter for chaotic
dynamics with multiplicative covariance inﬂation · · · · · · · · · · · · · · · · · · · 15
Uniform error bounds of the ensemble transform Kalman ﬁlter for chaotic
dynamics with multiplicative covariance inﬂation

概 要 Data assimilation is a method of uncertainty quantiﬁcation to estimate the hidden true state by

updating the prediction owing to model dynamics with observation data. As a prediction model, we considera class of nonlinear dynamical systems on Hilbert spaces. For nonlinear model dynamics, the ensemble
Kalman ﬁlter (EnKF) is often used to approximate the probability distribution with a set of particles called
an ensemble. Especially, a deterministic version of the EnKF known as the ensemble transform Kalmanﬁlter (ETKF) performs well even with limited ensemble sizes compared to other stochastic implementationsof the EnKF. Despite the practical eﬀectiveness of the ETKF, little is theoretically known. The present
study aims to establish the theoretical analysis of the ETKF.
46 石 井 宙 志 (北 大 電 子 研)
Hiroshi Ishii (Hokkaido Univ.)

非整数階時間微分を持つ Fisher-KPP 型方程式の解の伝播について · · · · 15

On the propagation of solutions to Fisher-KPP type equation with timefractional derivative

概 要 This talk deals with the Fisher-KPP equation with the Caputo derivative as time derivative. The

propagation of the solution is considered and the concept of travelling wave solution, which is diﬀerent
from the usual meaning, is introduced as a characterization of the solution. Assuming that the solution
asymptotically approximates the travelling wave solution, asymptotic travelling wave solution is deﬁned,
and its existence and usefulness are explained in this talk.
47 渡 部 善 隆(九大情報基盤研究開発センター)特異項を持つ無限次元線形作用素に対する Bünger–Rump 理論による精度保証付き逆作用素ノルム計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yoshitaka Watanabe (Kyushu Univ.)

A veriﬁed operator norm estimation for the inverse of an inﬁnite-dimensional
linear operator with singular term by Bünger–Rump’s theory

概 要 In this talk, we present a veriﬁed operator norm estimation for the inverse of an inﬁnite-dimensional

linear operator which has a singular term. Our approach is based on a veriﬁed computation method byBünger and Rump, and the operator norm estimation gives important information in the computation ofrigorous error bounds for the solution of ordinary diﬀerential equations involved with a nonlinear wave
equation.
48 坂 口 文 則 (福 井 大 工)Fuminori Sakaguchi (Univ. of Fukui)

固有関数の特異性の自動相殺を利用した微分作用素の固有値の 2 次/3 次収束する新しい整数型計算法 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A new integer-type algorithm with 2nd/3rd-order convergence for calculating eigenvalues of diﬀerential operators by using auto-cancellationsof the singularities of their eigenfunctions

概 要 In this study, a new integer-type algorithm is proposed for calculationg eigenvalues of linear diﬀerential

operators with a high accuracy, by using a kind of auto-cancellation of the singularities caused by thedeviations of eigenvalues from exact ones. This algorithm is baed on non-linear eigenvalue problems interms of the powers of the left hand sides of the characteristic equations of the linear diﬀerential operators.
Theoretically the numerical performance of this algorithm has p-th order convergence, with p aritrary
chosen, Some succesfull numerical results are given in this presentation.

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応用数学

49 飯 田 渓 太 (阪 大 蛋 白 質 研)
Keita Iida

(Osaka Univ.)

108

Semiology-based clustering method for single-cell data · · · · · · · · · · · · · · 15
Semiology-based clustering method for single-cell data

概 要 Various cells in living tissues produce numerous molecules to sustain life. However, the molecularbasis of life is complex, making theoretical elucidation of its control mechanisms diﬃcult. Here, we
present ASURAT, a computational tool for unsupervised clustering and functional annotation of cell type,biological process, and signaling pathway activity for single-cell data (Iida, Bioconductor, 2022). We apply
ASURAT to human pancreatic cancer data and identify previously overlooked subpopulations (Iida et al.,Bioinformatics, 2022). ASURAT is a powerful tool for dissecting cell subpopulations and improving thebiological interpretability of complex and noisy transcriptomic data.
14:15〜16:00
50 井倉 (参納) 弓彦 (明 大 総 合 数 理)
二 宮 広 和 ( 明 大 総 合 数 理)

Greenberg–Hastings セルオートマトンがつくるパターンダイナミクスに対する数理的考察 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yumihiko S. Ikura (Meiji Univ.)
Hirokazu Ninomiya (Meiji Univ.)

A mathematical study on the pattern dynamics of the Greenberg–Hastings
cellular automaton.

概 要 Periodic solutions appearing in the 3-valued Greenberg Hastings cellular automaton on rectangularlattice points are studied. Here, a von Neumann neighborhood type was used for the interaction between
lattice points. Vorticity was used as an index and was shown to be an invariant quantity. Using this index,
it was shown that there are restrictions on spontaneously occurring periodic solutions. The results suggestthat the 3-period solution is the strongest and the 4-period solution is the weakest. It was also shown that
there is no 5-period solution.
51 金
平
宮
角

澤
秀 ( 京 大 高 等 研)
岡 裕 章 ( 京 大 高 等 研)
永潤 ( 東 北 大 工)
田 謙 吉 ( 九 大 数 理)

Shu Kanazawa (Kyoto Univ.)
Yasuaki Hiraoka (Kyoto Univ.)
Jun Miyanaga (Tohoku Univ.)
Kenkichi Tsunoda (Kyushu Univ.)

Large deviation principle for persistence diagrams of random cubicalﬁltrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Large deviation principle for persistence diagrams of random cubicalﬁltrations

概 要 The objective of this work is to investigate the asymptotic behavior of the persistence diagrams ofa random cubical ﬁltration as the window size tends to inﬁnity. Here, a random cubical ﬁltration is anincreasing family of random cubical sets, which are the union of randomly generated higher dimensional
unit cubes with integer coordinates in a Euclidean space. In this talk, we discuss the exponential decayrate of the probability that the persistence diagram is far from the typical behavior. This is the ﬁrst resulton the large deviation behavior of persistence diagrams. (Joint work with Yasuaki Hiraoka, Jun Miyanaga,
and Kenkichi Tsunoda)

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109

52 田 中 一 成 (早 大 理 工)
柏 木 雅 英 ( 早 大 理 工)
内 藤 雄 基 (広島大先進理工)田 中
敏 ( 東 北 大 理)衛
大)渡 辺 宏 太 郎 (防Kazuaki Tanaka (Waseda Univ.)
Masahide Kashiwagi (Waseda Univ.)
Yuki Naito (Hiroshima Univ.)
Satoshi Tanaka (Tohoku Univ.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)

計算機援用による scalar ﬁeld 方程式の符号変化球対称解の一意性証明· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Computer-assisted uniqueness proof for sign-changing radially symmetric solutions of scalar ﬁeld equations

概 要 In this talk, we report on the results of proving the uniqueness of sign-changing radially symmetricsolutions of scalar ﬁeld equations on Euclidean space via computer assistance. The proof employs anapproach that combines analytical methods with rigorous numerical computations.
53 行
田
岸
梶
松
池
津

木
所
本
川
橋
田
田

大
孝 夫 (北
大
智 (北
(
北
大
勇 太
大
駿 介 (京大眞 生 (京(大昭 夫 京一 郎 (札 幌 市

理)

順列エントロピーによるてんかん焦点ネットワーク抽出 · · · · · · · · · · · · · 10

理)
理)
医)
医)
医)
大)

Takao Namiki (Hokkaido Univ.)
Satoru Tadokoro (Hokkaido Univ.)
Yuta Kishimoto (Hokkaido Univ.)
Shunsuke Kajikawa (Kyoto Univ.)
Masao Matsuhashi (Kyoto Univ.)(Kyoto Univ.)
Akio Ikeda
Ichiro Tsuda (Sapporo City Univ.)

Permutation entropy and epileptgenetic zone

概 要 Epilepsy is a disease that aﬀects about 1/80th of the population. Surgical resection is necessary totreat refractory epilepsy, and the area to be resected should be limited. For this purpose, we apply amathematical method. First, we show that permutation entropy can be used to identify the epileptic focus.
Second, the correlation of permutation entropy allows us to extract the epileptogenic zone. We report theseresults.
54 渡 辺樹 ( 大 分 大 理 工)
熊 谷 大 雅 ( 舞 鶴 工 高 専)
Itsuki Watanabe (Oita Univ.)
Taiga Kumagai(Nat. Inst. of Tech., Maizuru Coll.)

Markov chain approximation for Hamilton–Jacobi–Bellman equation
with reﬂecting boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Markov chain approximation for Hamilton–Jacobi–Bellman equation
with reﬂecting boundary

概 要 We consider the inﬁnite horizon optimal control problems of the controlled Markov process in which

the state 0 is reﬂecting state. We verify the relationship between the controlled Markov process and its ﬂuid
limit by the viscosity solution approach. More precisely, we show that the value function of the controlled
Markov process converges to one of its limit process which is the viscosity solution of the corresponding
Hamilton–Jacobi–Bellman equation with Neumann boundary condition.

2024/08/21 作成
応用数学

55 石 渡 哲 哉(芝浦工大システム理工)
河 西 航 也 ( 日 本 総 合 研)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)
Kouya Kawanishi(Japan Res. Inst., Ltd)110

強化学習における SARSA・Q 学習の学習挙動に関する考察とハイブリッ
ドアルゴリズムについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the learning behavior of SARSA and Q-learning in reinforcement
learning and a hybrid algorithm

概 要 SARSA and Q-learning are two typical methods of reinforcement learning. We ﬁrst describe thelearning behavior of these two algorithms. Then, we propose a hybrid algorithm that combines these
two methods. Finally, we show a convergence result for the proposed hybrid algorithm and demonstratenumerical experiments on the learning behaviors.
16:15〜17:15

特別講演
中 井 拳 吾 (岡山大環境生命)

Kengo Nakai (Okayama Univ.)

Evaluation of a data-driven model using reservoir computing from dynamical system point of view
Evaluation of a data-driven model using reservoir computing from dynamical system point of view

概 要 It has been reported that reservoir computing is eﬀective in the inference of time-series and somecharacteristics. A reservoir is a recurrent neural network whose internal parameters are not adjusted to ﬁt
the data in the training process. What is done is to train the reservoir by feeding it an input time-series
and ﬁtting a linear function of the reservoir state variables to a desired output time-series. We havesucceeded in modeling a macroscopic behavior of a three-dimensional chaotic ﬂuid ﬂow, which requires only
past time-series data as training data. A single model can infer short time behaviors from various initialconditions. The model also generates statistical properties which mimic the original ones. However, it is
not clear to what extent a model constructed by reservoir computing can capture dynamical structures. We
conﬁrm that dynamical properties such as ﬁxed points, periodic orbits, and non-hyperbolic structures canbe reconstructed by reservoir computing. We will discuss these results and some ongoing works. This talkis based on [1,2].
[1] M.Kobayashi, K.Nakai, Y.Saiki, and N.Tsutsumi, Dynamical system analysis of a data-driven model
constructed by reservoir computing, Phys.Rev.E 104, 044215:1-7 (2021) [2] M.Kobayashi, K.Nakai, andY.Saiki, Reconstruction of hetero-chaos by a data-driven model using reservoir computing, Journal of
Physics: Complexity, in press, DOI 10.1088/2632-072X/ad5264.

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111

ト ポ

ロ

9 月 3 日（火）ジー

第 IX 会場

9:30〜12:00
1 東
鎌
小
栗

谷 章 弘 ( 阪 大 情 報)大理)
田 聖 一 (阪坂迅
原 大 武 ( 山 口 大 創 成)

Akihiro Higashitani (Osaka Univ.)
Seiichi Kamada (Osaka Univ.)
Jin Kosaka
Hirotake Kurihara (Yamaguchi Univ.)

一般化 Alexander カンドルの分類 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classiﬁcation of generalized Alexander quandles

概 要 In thik talk, we provide a new characterization of isomorphism classes of generalized Alexander

quandles in terms of the underlying groups and their automorphisms. This extends the previous result
Higashitani–Kurihara (2024). Additionally, we give the computational results of the number of generalizedAlexander quandles up to quandle isomorphism arising from groups up to order 127 and their group
automorphisms.
大理)
2 久 野 恵 理 香 (阪木 村 満 晃 ( 大 阪 歯 大 歯)(Osaka Univ.)
Erika Kuno(
Mitsuaki Kimura Osaka Dent. Univ.)

The automorphism groups of the ﬁne curve graphs for nonorientale surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
The automorphism groups of the ﬁne curve graphs for nonorientale surfaces

概 要 The ﬁne curve graph of a surface was introduced by Bowden, Hensel, and Webb as a graph consistingof the actual essential simple closed curves on the surface. Long, Margalit, Pham, Verberne, and Yao provedthat the automorphism group of the ﬁne curve graph of a closed orientable surface Sg of genus g ≥ 2 isisomorphic to the homeomorphism group of the surface. Based on their argument, we generalized theirresult to closed nonorientable surfaces Ng of genus g ≥ 4.
3 廣 瀬
進 ( 東 京 理 大 理 工)
門 田 直 之 ( 岡 山 大 理)

Susumu Hirose (Tokyo Univ. of Sci.)
Naoyuki Monden (Okayama Univ.)

On generating mapping class groups by pseudo-Anosov elements · · · · · 15
On generating mapping class groups by pseudo-Anosov elements

概 要 Wajnryb proved that the mapping class group of a closed oriented surface is generated by two elements.

We prove that the mapping class group is generated by two pseudo-Anosov elements. In particular, if thegenus is greater than or equal to nine, we can take the generators to two conjugate pseudo-Anosov elementswith arbitrarily large dilatations. Another result we prove is that the mapping class group is generated by
two conjugate reducible but not periodic elements if the genus is greater than or equal to eight. We also
give similar results to the ﬁrst and third results for the hyperelliptic mapping class group when the genus isgreater than or equal to one.

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4 笠 原

泰 ( 高 知 工 科 大)Yasushi Kasahara(Kochi Univ. of Tech.)112

Low dimensional MCG-invariant representations of surface groups in
the naive deformation spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Low dimensional MCG-invariant representations of surface groups in
the naive deformation spaces

概 要 We report that the Franks–Handel and the Korkmaz theorems on low dimensional linear represen-tations of pure mapping class group of orientable surface (MCG) of suﬃciently large genus implies thetriviality of the linear representations of the corresponding surface group into GL(r,C) with the property ofthe title, provided r be less than or equal to the square root of twice the genus of the surface. To derive
the result, we apply our construction of linear representation of the MCG starting with a representation of
the corresponding surface group MCG-invariant in the naive deformation space we once used to derive the“visualization of the linearity problem” for the MCG.
5 谷 口 東 曜 ( 東 大 数 理)

Toyo Taniguchi (Univ. of Tokyo)

Topology of loops via non-commutative diﬀerential geometry · · · · · · · · 15
Topology of loops via non-commutative diﬀerential geometry

概 要 The Turaev cobracket is a topologically deﬁned operation on the space of free loops on an oriented

surface. When the surface is further bordered and compact, it is factored into two maps in a paper byAlekseev–Kawazumi–Kuno–Naef, one of which is called the divergence map. We reconstruct it in termsof non-commutative diﬀerential geometry featuring a non-commutative analog of a ﬂat connection andgeneralize it to the case of closed surfaces.
6 和 久 田 葵 ( 東 大 数 理)

Thurston–Wolpert–Goldman Lie 代数の中心定理の一般化 · · · · · · · · · · · 15

Aoi Wakuda (Univ. of Tokyo)

A generalization of the Center Theorem of the Thurston–Wolpert–Goldman
Lie algebra

概 要 The Goldman Lie algebra of an oriented surface was deﬁned by Goldman. By the natural involutionthat opposes the orientation of curves, the Goldman Lie algebra becomes a Z2 -graded Lie algebra. Its evenpart is isomorphic to the Thurston–Wolpert–Goldman Lie algebra or, brieﬂy, the TWG Lie algebra. Chasand Kabiraj proved the center of the TWG Lie algebra is generated by the class of the unoriented trivial
loop and the classes of unoriented loops parallel to boundary components or punctures. The center of theeven part can be rephrased as the set of elements of the even part annihilated by all the elements of theeven part.
7 桑 垣

樹 (京

大

理)

Tatsuki Kuwagaki (Kyoto Univ.)

WKB スペクトルネットワークの構成について · · · · · · · · · · · · · · · · · · · · · 15
On the construction of WKB spectral network

概 要 The trajectory of quadratic diﬀerentials on Riemann surfaces is an important object in mathemat-

ics and mathematical physics. Similar theories for higher-order diﬀerentials (spectral networks, Stokes
diagrams) have also attracted attention in WKB analysis, Teichmuller theory, and related mathematicalphysics, but little is known about them. In this talk, we will outline the existence of spectral networks inthe case of general higher-order diﬀerentials.

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トポロジー

14:30〜15:30
片 田

特別講演
大
舞 (九

Mai Katada理)

The stable Albanese homology of the IA-automorphism groups of freegroups(Kyushu Univ.)

The stable Albanese homology of the IA-automorphism groups of freegroups

概 要 The IA-automorphism group IAn of the free group Fn of rank n is the kernel of the map between theautomorphism groups induced by the abelianization map of Fn . The structure of the rational (co)homology
of IAn is mysterious for small n, but we have made progress for suﬃciently large n with respect to the(co)homological degree. In this talk, we will determine the quotient of the rational homology of IA n that iscalled the Albanese homology of IAn , which plays an important role of the whole rational homology of IAn .

9 月 4 日（水）10:00〜10:15

第 I 会場2024 年度日本数学会幾何学賞授賞式

10:20〜11:20

2024 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
今 野 北 斗 (東 大 数 理) Diﬀeomorphism group and gauge theory

Hokuto Konno (Univ. of Tokyo)

Diﬀeomorphism group and gauge theory

概 要 The group of diﬀeomorphisms of a given smooth manifold is a fundamental object of study for topolo-

gists and geometers. One of the major advances in topology over the past decade concerns diﬀeomorphismgroups of higher-dimensional manifolds, led by many researchers such as Galatius and Randal-Williams.
On the other hand, it has been well-known since the last century that 4 is a special dimension in theclassiﬁcation of manifolds. Special phenomena are typically described in terms of comparisons between the
topological and smooth categories, and they are detected using gauge theory. In recent years, advances ingauge theory for families have revealed that special phenomena in dimension 4 also occur for diﬀeomorphismgroups in various ways, contrasting with recent results in higher dimensions. I will survey these new special
phenomena in dimension 4, also from the perspective of comparisons between the topological and smoothcategories.
12:50〜13:50
細 野

2024 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
忍 (学 習 院 大 理) カラビ・ヤウ多様体の族とミラー対称性

Shinobu Hosono (Gakushuin Univ.)

Families of Calabi-Yau manifolds and mirror symmetry

概 要 Mirror symmetry of Calabi–Yau manifolds is a mysterious symmetry that interchanges the complex

geometry of one Calabi–Yau manifold with the symplectic geometry of another Calabi–Yau manifold, calleda mirror manifold. 30 years after its discovery, we now have fascinating proposals, such as homologicalmirror symmetry and SYZ geometric mirror construction, to describe the symmetry mathematically. In
this talk, however, I will describe this symmetry in terms of two diﬀerent, and classical, nilpotent linear
actions associated with a Calabi–Yau manifold. One is the Lefschetz action in the hard Lefschetz theorem(which I call A-structure), and the other is a certain monodromy action that arises from a family of
Calabi–Yau manifolds (B-structure). I deﬁne mirror symmetry as the symmetry which exchanges these
two structures. The general existence of a mirror Calabi–Yau manifold for a given Calabi–Yau manifold
is still an open problem. However, mirror symmetry deﬁned by these classical actions motivates us to
study/construct families of Calabi–Yau manifolds, and to look into the boundary points where Calabi–Yau
manifolds degenerate in a speciﬁc way. Based on my collaborations with Hiromichi Takagi since 2010, I
will present interesting families of Calabi–Yau threefolds which are parametrized by two-dimensional toricvarieties.

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9 月 5 日（木）114

第 IX 会場

9:30〜12:00
8 田 中 康 平 ( 信 州 大 経 法)
Kohei Tanaka (Shinshu Univ.)

Cone complexes and group actions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Cone complexes and group actions

概 要 Cone complexes are a generalization of simplicial complexes compatible with the quotients by group

actions. In this talk, we focus on group actions on cone complexes, and compare them with the case ofsmall categories.
9 加 藤
諒 ( 高 知 工 科 大)
下 村 克 己 ( 高 知 大 理)
下 村 磨 生 将 (高知大総合人間自然)

Ryo Kato (Kochi Univ. of Tech.)
Katsumi Shimomura (Kochi Univ.)
Mao-no-suke Shimomura (Kochi Univ.)

On the Greek letter elements of the homotopy groups of the E(n)localized sphere spectrum · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the Greek letter elements of the homotopy groups of the E(n)localized sphere spectrum

概 要 Miller, Ravenel and Wilson introduced the n-th Greek letter elements in the E2 -term of the Adams–

Novikov spectral sequence. We then have a problem asking whether or not the n-th Greek letter elements(n)αtsurvive in the homotopy groups of the sphere spectrum in the spectral sequence. So far, we haveanswers only when n ≤ 3. In this talk, we report the condition under which an n-th Greek letter element(n)αt for n ≥ 1 exists in the homotopy groups of the E(n)-localized sphere spectrum.
10 内 藤 貴 仁 (日 本 工 大)

Takahito Naito (Nippon Inst. of Tech.)

Cartan calculus in string topology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Cartan calculus in string topology

概 要 In this talk, we investigate a Cartan calculus on the homology of free loop spaces due to Kuribayashi,

Wakatsuki, Yamaguchi and the speaker. In particular, it is proved that the Cartan calculus can be describedby the loop product and the loop bracket in string topology. As an application, we also show that the Liederivative on the homology is a derivation with respect to the loop product.
11 加 藤 裕 基 (宇 部 工 高 専)

Yuki Kato (Ube Nat. Coll. of Tech.)

Application of Smith ideal theory to almost ring theory of pointed symmetric monoidal model categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Application of Smith ideal theory to almost ring theory of pointed symmetric monoidal model categories

概 要 This talk generalizes a result in Quillen’s note, “Module theory over non-unital rings,” which gives a

one-to-one correspondence between bilocalizations of abelian categories of module categories and idempotent
ideals of the base rings. Faltings, Gabber, and Ramero established almost ring theory which is the same as
Quillen’s bilocalization of a category of modules by nil-modules. By using the theory of Smith ideals theory
mentioned by Hovey, we consider the almost ring theory of symmetric monoidal pointed model categories
and prove a weak analogue of the one-to-one correspondence.
12 越 野 克 久 (神 奈 川 大 工)

Katsuhisa Koshino (Kanagawa Univ.)

The Borel complexity and the complete metrizability of spaces of metrics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Borel complexity and the complete metrizability of spaces of metrics

概 要 For a metrizable space X, let AM (X) be the space of continuous bounded admissible metrics on X

with the sup-metric. In this talk, we shall investigate the Borel complexity of AM (X) and show that aseparable metrizable space X is σ-compact if and only if AM (X) is completely metrizable.

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115

13 平 田 康 史 (神 奈 川 大 工)
矢 島 幸 信 (神 奈 川 大⋆)

Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)

一般順序空間・単調正規空間上の irreducibility の基数関数による特徴づけ· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Characterizations of irreducibility on GO-spaces and monotonically normal spaces by cardinal functions

概 要 We characterize irreducibility on GO-spaces and monotonically normal spaces by cardinal functions.

As an application, an irreducible subspace without Property D is found in an ordinal.
14 石 黒 賢 士 (福 岡 大 理)
西 原 夢 斗 ( 福 岡 大 理)

Kenshi Ishiguro (Fukuoka Univ.)
Naito Nishihara (Fukuoka Univ.)

Modular invariant rings and the Weyl groups of special unitary groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Modular invariant rings and the Weyl groups of special unitary groups

概 要 We consider certain invariant rings under the actions of reﬂection groups. The mod p representations

come from the Weyl groups of special unitary groups, which are isomorphic to symmetric groups. We
will ask, particularly, if such invariant rings are polynomial algebras. In the projective case, the answer isnegative.
15 今 井淳 ( 千 葉 大 理)

Jun O’Hara(Chiba Univ.)

有限距離空間のマグニチュードによる同定 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Characterization of generic ﬁnite metric spaces by magnitude

概 要 We show that a ﬁnite metric space can be identiﬁed by the magnitude function if the edge lengths arerationally independent.
14:20〜15:20

特別講演
大吉 永 正 彦 (阪理) [ 実超平面配置のトポロジー

Masahiko Yoshinaga (Osaka Univ.)

Topology of real hyperplane arrangements

概 要 We discuss topology of hyperplane arrangements via real structures.

15:40〜18:00
16 岡

睦 雄
(東工大⋆・東京理大創域理工)Mutsuo Oka(Tokyo Tech⋆ /Tokyo Univ. of Sci.)

Comment on Briançon–Speder polynomial · · · · · · · · · · · · · · · · · · · · · · · · 15
Comment on Briançon–Speder polynomial

概 要 Briançon and Speder gave an example of a µ-constant family of weighted homogeneous polynomials

for which µ∗ is not constant. In this talk, we analyze this example. Briançon–Speder family is given byft (x, y, z) = x15 + z 5 + tz 6 y + z 7 x and it has weight t (1, 2, 3) and degree 15. Its Milnor number is 364
but its plane section give respective Milnor number 26 and 28 for f1 and f0 . They missed two more classwhich have diﬀerent topology for plane sections. We generalize this observation for other similar weighted
homogeneous polynomials.
17 菅 原 朔 見 (北大理)Sakumi Sugawara (Hokkaido Univ.)

First homology groups of the Milnor ﬁber boundary for generic hyperplane arrangements in C3 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
First homology groups of the Milnor ﬁber boundary for generic hyperplane arrangements in C3

概 要 A ﬁnite set of linear hyperplanes in a complex vector space is called a hyperplane arrangement. A

hyperplane arrangement deﬁnes a variety with a non-isolated singularity at the origin. In this talk, we
study the ﬁrst homology group of the Milnor ﬁber boundary of a generic hyperplane arrangement in C3 andprove it is combinatorially determined. This gives the aﬃrmative answer to the conjecture of Suciu.

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18 田 邊 真 郷 (北大理)Masato Tanabe (Hokkaido Univ.)116

曲面特異点リンクのはめ込みとそのトポロジー · · · · · · · · · · · · · · · · · · · · · 10

Immersions of surface singularity links and their topology

概 要 A surface singularity in complex 3-space deﬁnes a closed orientable 3-manifold, known as the linkor the Milnor ﬁber boundary, in a small 5-sphere centered at the singularity itself. The inclusion mapof this 3-manifold into the 5-sphere can be considered as an immersion. In this talk, we determine theregular homotopy class of the inclusion map by computing a complete invariant which was introduced by
Wu and Saeki–Szűcs–Takase. Furthermore, for each singularity of type ADE, we demonstrate the regularhomotopicity between the inclusion map and Kinjo’s immersion.
19 小 川吉 安

竜 ( 東 海 大 理)
徹 ( 京 都 教 育 大)Noboru Ogawa (Tokai Univ.)
Toru Yoshiyasu (Kyoto Univ. of Edu.)

Liouville 領域の懸垂構成と接触構造の圧縮性 · · · · · · · · · · · · · · · · · · · · · · · 15
Suspension conﬁguration of Liouville domains and compressibility ofcontact manifolds

概 要 Inspired by Huang’s work, we studied the compressibility of contact manifolds and the suspension

conﬁguration of Liouville domains. We show that compressible contact manifolds are tight. If time permits,
we will also discuss some new concrete examples and applications.
20 多 寳 雅 樹 (東 大 数 理)
Masaki Taho (Univ. of Tokyo)

Tangent spaces of diﬀeological spaces and their variants · · · · · · · · · · · · · 15
Tangent spaces of diﬀeological spaces and their variants

概 要 Several methods have been proposed to deﬁne tangent spaces for diﬀeological spaces. Among them, theinternal tangent functor is obtained as the left Kan extension of the tangent functor for manifolds. However,
the right Kan extension of the same functor has not been well-studied. In this paper, we investigate therelationship between this right Kan extension and the external tangent space, another type of tangent spacefor diﬀeological spaces. We prove that by slightly modifying the inclusion functor used in the right Kan
extension, we obtain a right tangent space functor, which is almost isomorphic to the external tangent space.
Furthermore, we show that when a diﬀeological space satisﬁes a favorable property called smoothly regular,
this right tangent space coincides with the right Kan extension mentioned earlier.
21 林

弘 幸 ( 神 戸 大 理)

Hiroyuki Hayashi (Kobe Univ.)

ホイットニーの傘を通る曲線の幾何学 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Geometry on curves passing through Whitney umbrella

概 要 Whitney umbrella is a singularity which appears most frequently on surfaces. To study diﬀerential

geometry on a surface, a unit normal vector plays a central role. However, a unit normal vector on Whitneyumbrella is not extended. We show that we can extend a unit normal vector beyond a Whitney umbrella
if we consider a curve passing through Whitney umbrella. We then study geometry by using invariants
deﬁned by a Darboux frame consisting of smoothly deﬁned unit normal and tangent vectors along a curve
passing through Whitney umbrella. We also give geometric meanings of the invariants.
22 藤 岡 禎 司 (阪大理)Tadashi Fujioka (Osaka Univ.)

曲率の下界をもつ空間の stratiﬁcation について · · · · · · · · · · · · · · · · · · · · · 15

On the stratiﬁcation of spaces with curvature bounded below

概 要 We prove that the extremal stratiﬁcation of an Alexandrov space deﬁnes a CS structure in thesense of Siebenmann. An Alexandrov space is a metric space with sectional curvature bounded below
in the generalized sense. The extremal stratiﬁcation is a decomposition of an Alexandrov space into its
geometrically singular sets. The CS structure is a type of topological stratiﬁcation, i.e., a decompositionof a topological space into topological manifolds of diﬀerent dimensions. The main theorem improves an
earlier result of Perelman–Petrunin, who introduced the extremal stratiﬁcation.

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23 テ イ チ ュ ウ (早 大 理 工)
Chong Zheng(Waseda Univ.)

On the connectedness homomorphism between discrete Morse complexes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the connectedness homomorphism between discrete Morse complexes

概 要 Given two discrete Morse functions on a simplicial complex, we introduce the connectedness homo-morphism between the corresponding discrete Morse complexes. This concept leads to a novel frameworkfor studying the connectedness in discrete Morse theory at the chain complex level. In particular, we apply
it to describe a discrete analogy to ‘cusp-degeneration’ of Morse complexes. A precise comparison between
smooth case and our discrete cases is also given.

9 月 6 日（金）第 IX 会場

9:30〜12:00
24 村 上順 ( 早 大 理 工)

Jun Murakami (Waseda Univ.)

ダブルツイスト結び目の体積予想について · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the volume conjecture for double twist knots

概 要 A proof of the volume conjecture for double twist knots are proposed by using the relation between

the SL(2, C) representation of the fundamental group of the complement and the complexiﬁed tetrahedron
which is newly introduced. The relation between the colored Jones polynomial and the ADO invariant arealso used.
25 合 田洋 ( 東 京 農 工 大 工)
森 藤 孝 之 ( 慶 大 経 済)
Hiroshi Goda
(Tokyo Univ. of Agri. and Tech.)Takayuki Morifuji (Keio Univ.)

双曲ファイバー結び目の体積表示 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A volume presentation of a hyperbolic ﬁbered knot

概 要 In this talk, we provide a volume presentation of a hyperbolic ﬁbered knot using the Bell polynomials.

More precisely, we show that the hyperbolic volume of a ﬁbered knot can be expressed in terms of the tracesof powers of a monodromy matrix. We also explain that the hyperbolic volume of the ﬁgure-eight knot is
obtained by the asymptotics of a positive integer sequence consisting of the special values of the twisted
Alexander invariants.
26 中 江 康 晴 (秋 田 大 理 工)
北 野 晃 朗 ( 創 価 大 理 工)
Yasuharu Nakae (Akita Univ.)
Teruaki Kitano (Soka Univ.)

Symmetric Union の拡張となるモンテシノス結び目とその Alexander 多項式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Montesinos knots as an extension of symmetric unions and its Alexanderpolynomial

概 要 We construct a family of Montesinos knots as an extension of symmetric unions. Each Montesinos

knot consists of three rational tangles with slopes p/q, -b/a, and b/a where q is even. The Alexanderpolynomial of each of these knots becomes the product of the Alexander polynomial of the numerator of
the rational tangle with the slope p/q and the square of the Alexander polynomial of the denominator of
the rational tangle with b/a. Moreover, there is an epimorphism from the knot group of these Montesinos
knots to the knot group of the denominator of the rational tangle with b/a whose image of the longitude ofthese Montesinos knots is trivial.

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27 中
中
佐
和

村 拓 司 ( 山 梨 大 教 育)
西 康 剛 ( 神 戸 大 理)
藤進 ( 神 戸 大 理)
田 康 載 ( 神 戸 大 理)

Takuji Nakamura (Univ. of Yamanashi)
Yasutaka Nakanishi (Kobe Univ.)(Kobe Univ.)
Shin Satoh(Kobe Univ.)
Kodai Wada118

Fox の Z-彩色と Zm 上の 12 種類の同値関係 · · · · · · · · · · · · · · · · · · · · · · · · 10

Fox Z-colorings and 12 equivalence relations on Zm

概 要 Using the notion of Fox Z-colorings, we deﬁne 12 equivalence relations on Zm for an integer m ≥ 2.

In this talk, we completely characterize these 12 equivalence relations by introducing several invariants of
Fox Z-colorings.
28 小 鳥 居 祐 香(広島大先進理工・理化学研)
Sonia Mahmoudi(東北大 AIMR・理化学研)
Elisabetta Matsumoto( Georgia Tech. )吉 田 建 一 (広島大 SKCM2)
Yuka Kotorii(Hiroshima Univ. / RIKEN)
Sonia Mahmoudi(Tohoku Univ. / RIKEN)
Elisabetta Matsumoto (Georgia Tech.)
Ken’ichi Yoshida (Hiroshima Univ.)

厚みつきトーラス内の絡み目の被覆とイソトピー · · · · · · · · · · · · · · · · · · · 15

Coverings and isotopies of links in the thickened torus

概 要 A doubly periodic tangle is the lift of a link in the thickened torus by the universal covering. Then thislink is called a motif of a doubly periodic tangle. To investigate doubly periodic tangles, it is necessary toconsider relations between ﬁnite coverings and isotopies of links in the thickened torus. In this presentation,
we show two results. If two links in the thickened torus have isotopic lifts in a common ﬁnite covering, thenthey are isotopic. A non-split doubly periodic tangle has a unique minimal motif. To prove these, we use
the standard decomposition of the complement of a link.
29 吉 田 建 一 (広島大 SKCM2)

Ken’ichi Yoshida (Hiroshima Univ.)

四元数群からえられる多様体内の絡み目とそのリフト · · · · · · · · · · · · · · · 10

Links in the spherical 3-manifold obtained from the quaternion groupand their lifts

概 要 The free action of the quaternion group Q8 on the 3-sphere S 3 induces the spherical 3-manifold S 3 /Q8 .

The manifold S 3 /Q8 is covered by the lens space L(4, 1) in three ways. A link in S 3 /Q8 has three diﬀerent
lifts in L(4, 1) in general. However, their lifts in S 3 coincide. In fact, we obtain inﬁnitely many triples ofhyperbolic links in L(4, 1) such that the three lifts of each triple in S 3 are isotopic.
30 柳 田 幸 輝 (東 工 大 理)
Koki Yanagida(Tokyo Tech)

Dijkgraaf–Witten 不変量の K 理論的研究 · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Dijkgraaf–Witten invariant in topological K-theory

概 要 Given a ﬁnite group G, we deﬁne a new invariant of odd-dimensional oriented closed manifolds andcall it the KDW invariant. This invariant is the Dijkgraaf–Witten invariant in terms of K-homology. In thispaper, we compute the KDW invariants of some Brieskorn homology spheres with G = PSL(Fp ) without
2-torsion. We should remark that, in these computational results, both the fundamental groups of theBrieskorn homology spheres and PSL(Fp ) are not nilpotent. In the previous studies, there have been nocomputational results of the Dijkgraaf–Witten invariants in cases where both the fundamental groups ofmanifolds and ﬁnite groups are not nilpotent.

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31 地 引 知 栄 (東 工 大 理)
丸 山 修 平 ( 金 沢 大 理 工)
Chihaya Jibiki (Tokyo Tech)
Shuhei Maruyama (Kanazawa Univ.)

Isom+ (H2 ) の性質を用いた孤立順序の構成 · · · · · · · · · · · · · · · · · · · · · · · · · 15
Construction of isolated orders using properties of Isom+ (H2 )概 要 This talk is about circular orders on groups. It follows from a dynamical realization that every circularorder can be realized as an orientation preserving homeomorphism action on S 1 . On certain subgroups of
Isom+ (H2 ), the action can be extended on H2 . By using this action, we constructed isolated orders on thegroups. The talk is mainly based on a joint work with Shuhei Maruyama.
14:20〜16:50
32 石 橋典 ( 東 北 大 理)
狩 野 隼 輔 (東北大MathCCS)
大
理)
湯 淺
亘 (京

Tsukasa Ishibashi (Tohoku Univ.)
Shunsuke Kano (Tohoku Univ.)
Wataru Yuasa (Kyoto Univ.)

Skein and cluster algebras with coeﬃcients for unpunctured surfaces · · 10

Skein and cluster algebras with coeﬃcients for unpunctured surfaces

概 要 We propose a skein model for the quantum cluster algebras of surface type with coeﬃcients. We
Aintroduce a skein algebra SΣ,Wof a walled surface (Σ, W), and prove that it has a quantum cluster structure.

The walled surfaces naturally generalize the marked surfaces with multi-laminations, which have been used
to describe the quantum cluster algebras of geometric type for marked surfaces by Fomin–Thurston.
33 逆 井 卓 也 (東 大 数 理)
田 所 勇 樹 ( 木 更 津 工 高 専)
田 中
心 ( 東 京 学 大 教 育)

Takuya Sakasai (Univ. of Tokyo)
Yuuki Tadokoro(Kisarazu Nat. Coll. of Tech.)
Kokoro Tanaka (Tokyo Gakugei Univ.)

Matrix representations for groups of Kim–Manturov · · · · · · · · · · · · · · · · 10

Matrix representations for groups of Kim–Manturov

概 要 We construct matrix representations for groups of Kim–Mantorov Γ 4n . As a corollary, we show thatthe group Γ4n is non-commutative for n ≥ 6.
34 久 保 田 肇 (京大理)Hajime Kubota (Kyoto Univ.)

On the knot concordance invariant Upsilon using grid homology · · · · · 15
On the knot concordance invariant Upsilon using grid homology

概 要 The Upsilon invariant is a knot concordance invariant in knot Floer homology. Földvári deﬁned thegrid Upsilon invariant using grid homology and proved some properties known in knot Floer homology. I
gave another formulation of the grid Upsilon invariant and proved that it is a concordance invariant. In thistalk, I will show that the grid Upsilon invariant coincides with the Upsilon invariant in knot Floer homology
and that the grid Upsilon invariant behaves additively under connected sums.
35 山 田 裕 一 (電通大情報理工)
Yuichi Yamada(Univ. of Electro-Comm.)

Exceptional Dehn surgeries along a certain family of two component
links · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Exceptional Dehn surgeries along a certain family of two componentlinks

概 要 A hyperbolic 3-manifold that has a torus boundary component can change to a non-hyperbolic 3-

manifold by ﬁlling the boundary by a solid torus. Such surgeries are called exceptional Dehn surgeries. We
study the distribution of integral exceptional Dehn surgeries along a certain family of two component links,
related 4-dimensional rational blow-down.

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トポロジー

36 丹 下 基 生 (筑波大数理物質)
田 内 光 一 (筑波大数理物質)

Motoo Tange (Univ. of Tsukuba)
Koichi Tauchi (Univ. of Tsukuba)120

λ = −2, −3 のホモロジー球面上のレンズ空間手術 · · · · · · · · · · · · · · · · · · 15
Lens space surgeries over homology spheres with λ = −2, −3

概 要 Berge discovered ten families of lens space surgeries over the 3-sphere, in the 1990s. In 2006, thesecond speaker found twenty families of lens space surgeries over the Poincare homology sphere. These
results from the fact that many well-known lens space surgeries are yielded by surgeries of simple (1,1)-simple
knots in lens spaces. Indeed, in 2009, and 2023, these families were characterized as lens spaces constructedby Dehn surgery over the 3-sphere or the Poincare homology sphere by Greene and Caudell respectively.
This talk will reveal candidates of lens space surgeries over homology spheres with Casson invariant -2 or -3
by using surgeries over (1,1)-simple knots in lens spaces.
37 高 橋 夏 野 (阪 大 情 報)

Natsuya Takahashi (Osaka Univ.)

境界付き 4 次元多様体の非微分同相な最小種数相対トライセクション · · 15

Non-diﬀeomorphic minimal genus relative trisections of the same 4manifold with boundary

概 要 It is known that every compact smooth 4-manifold X admits a (relative) trisection, which is adecomposition of X into three 4-dimensional 1-handlebodies intersecting along a compact surface. In thistalk, we show that there exists a 4-manifold with a boundary that admits two non-diﬀeomorphic minimal
genus relative trisections. To prove this, we use a simple operation that produces a trisection diagram of aclosed 4-manifold from a relative trisection diagram.
38 磯 島司 ( 東 工 大 理)
小 川 将 輝 (東北大MathCCS)

Tsukasa Isoshima (Tokyo Tech)
Masaki Ogawa (Tohoku Univ.)

Nielsen equivalence and multisections of 4-manifolds · · · · · · · · · · · · · · · · 15
Nielsen equivalence and multisections of 4-manifolds

概 要 A trisection is roughly a decomposition of a closed, oriented, smooth 4-manifold into three 4-

dimensional 1-handlebodies. As an extension of a trisection, Islambouli and Naylor introduced a multisection
or n-section which is a decomposition of a closed, oriented, smooth 4-manifold into n 4-dimensional 1handlebodies for n ≥ 3. when n = 2, it is called a bisection. Islambouli proved, using a Nielsen equivalent,that for any integer n ≥ 2, there exist 4-manifolds with non-isotopic (3n, n)-trisections of minimal genus. In
this talk, we report that for any integer n ≥ 2, there exist 4-manifolds with non-isotopic (2n, n)-bisectionsof minimal genus. We also introduce a similar result for 4-sections.
39 二 村 弥 彦 (東 海 大 理)
Yahiko Nimura(Tokai Univ.)Type 2 の lens を持つ (2, 4, 2) 型の chart · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Charts of type (2, 4, 2) with a lens of type 2

概 要 Charts are oriented labeled graphs in a disk. A chart represents an oriented closed surface embedded

in 4-space. For each label m, we denote by Γm the subset of a chart Γ consisting of edges of label m.
For any subset X of Γ, we denote by w(X) the number of white vertices in X. In this talk, we show thefollowing.
Let Γ be a chart. If Γ is a chart of type (m; 2, 4, 2) (In other words, there exists label m such thatw(Γm ∩ Γm+1 ) = 2, w(Γm+1 ∩ Γm+2 ) = 4, w(Γm+2 ∩ Γm+3 ) = 2, w(Γ) = 8), and if Γ is a minimal chart, thenthere does not exist any lens of Γ of type 2. Here, a lens is a disk D such that ∂D contains exactly two
white vertices and ∂D ⊂ Γm ∪ Γm+1 for some label m and D satisﬁes some conditions.

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121

トポロジー

大
理)
40 安 田 順 平 (阪中 村 伊 南 沙 ( 佐 賀 大 理 工)

Jumpei Yasuda (Osaka Univ.)
Inasa Nakamura (Saga Univ.)

ニット状曲面を用いた 4 次元球体内の曲面の表示 · · · · · · · · · · · · · · · · · · · 15

Knitted surfaces and presentations of knotted surfaces in a four ball

概 要 In 1983, Rudolph introduced braided surfaces as a generalization of braids. He showed that every

properly embedded orientable surface with boundaries in a 4-ball is ambiently isotopic to a braided surface
if and only if it is ribbon. In this talk, we generalize this concept and introduce knitted surfaces, usingknits. Here, knits are a generalization of braids by J. Murakami. We show that every properly embedded
surface with boundaries in a 4-ball is ambiently isotopic to a knitted surface.

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無限可積分系

無限

可9 月 3 日（火）

積

分

122

系

第 VIII 会場

9:30〜10:35
1 土 見 怜 史 ( 神 戸 大 理)
渋 川 元 樹 ( 神 戸 大 理)

Satoshi Tsuchimi (Kobe Univ.)
Genki Shibukawa (Kobe Univ.)

Zwegers µ 函数の多変数類似 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A multivariate analogue of the Zwegers’ µ-function

概 要 In this talk, we introduce a multivariable µ-function from the view of q-diﬀerence equations, andpresent some properties satisﬁed by the multivariable µ-function such as symmetries and mock modularity
relations.
2 渋 川 元 樹 ( 神 戸 大 理)

Genki Shibukawa (Kobe Univ.)

ある “特異級数” の一般化と一般化 µ 函数の特殊化 · · · · · · · · · · · · · · · · · · 15

A generalization of “summatio quarumdam serierum singularium” andspecialization of the generalized µ-function

概 要 We give a generalization of certain Gauss’ summation (special values of q-Bessel function) formulas,

and as an application, derive explicit formulas for some specializations of the generalized µ-function.
3 新 井 由 美
(お茶の水女大人間文化)
竹 村 剛 一 (お茶の水女大基幹)
Yumi Arai (Ochanomizu Univ.)
Kouichi Takemura (Ochanomizu Univ.)

On q-middle convolution and q-hypergeometric equations, I · · · · · · · · · 15

On q-middle convolution and q-hypergeometric equations, I

概 要 Sakai and Yamaguchi introduced a q-deformation of the middle convolution some time ago. Motivatedby applications to special functions, we reformulate the q-middle convolution and the associated q-integral
transformations. We obtain a better description of additivity on composition of the q-middle convolution
by our reformulation.
4 新 井 由 美
(お茶の水女大人間文化)
竹 村 剛 一 (お茶の水女大基幹)
Yumi Arai (Ochanomizu Univ.)
Kouichi Takemura (Ochanomizu Univ.)

On q-middle convolution and q-hypergeometric equations, II · · · · · · · · · 15

On q-middle convolution and q-hypergeometric equations, II

概 要 We show some examples of the composition of q-middle convolution by using the reformulated q-middle

convolution.
10:45〜11:45

特別講演
信 川 喬 彦 ( 神 戸 大 理)

点平等な q 超幾何方程式としての 10 W9 ・8 W7 ・変異版 2 ϕ1

Takahiko Nobukawa (Kobe Univ.)

10 W9 , 8 W7 and variant of 2 ϕ1 as democratic q-hypergeometric equations

概 要 In this talk, we ﬁrst study the variant of q-hypergeometric equation for 2 ϕ1 deﬁned by Hatano–Matsunawa–Sato–Takemura (Funkcial. Ekvac., 2022). We give Euler type integral solutions, series solutionsin terms of very-well-poised q-hypergeometric series 8 W7 for the equation, and connection formulas for thesesolutions. Second, we introduce a similar extension of the q-hypergeometric equation for 3 ϕ2 . We construct
Euler type integral solutions and series solutions in terms of 10 W9 for the equation. These results are
obtained using the democratic viewpoint. Here the word “democratic” means that every point can betreated equally.

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123

無限可積分系

9 月 4 日（水）第 VIII 会場

9:30〜10:30
5 山 口 航 平 ( 名 大 多 元 数 理)

Kohei Yamaguchi (Nagoya Univ.)

アフィン・グラスマン多様体の同変 K ホモロジー · · · · · · · · · · · · · · · · · · 15

Equivariant K-homology of aﬃne Grassmannian

概 要 Let G be the special linear group SLn (C), and let T be its maximal torus. This study focuses on the

T -equivariant K-homology ring K∗T (GrG ) of the aﬃne Grassmannian GrG of G. In this talk, I would likeR(T )to outline two realizations of K∗T (GrG ). One is the realization through the algebra Λ̂G, which is spannedby the ”double K-k-Schur functions” representing Schubert classes. The other is the realization throughthe coordinate ring O(ZG∨ ) of the aﬃne variety ZG∨ over T determined by G∨ = PGLn (C). This talk isbased on joint work with Takeshi Ikeda, Shinsuke Iwao, Satoshi Naito, and Mark Shimozono.
6 河 本 陽 介 (岡山大環境生命)
A. Bufetov(Steklov Math. Inst. of RAS 他)

Yosuke Kawamoto (Okayama Univ.)
Alexander Bufetov(Steklov Math. Inst. of RAS, etc.)

The intertwining property for Laguerre processes with a ﬁxed parameter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The intertwining property for Laguerre processes with a ﬁxed parameter

概 要 We investigate the intertwining of Laguerre processes of parameter α in diﬀerent dimensions. We

introduce a Feller kernel so that intertwines the α-Laguerre process in N + 1 dimension and that in
N dimension. When α is a non-negative integer, this kernel is interpreted in terms of the conditional
distribution of the squared singular values: if the singular values of a unitary invariant random matrix is
ﬁxed, then the those of its truncation matrix are given by the new kernel.
7 舘 川 暁 斗 ( 明 大 先 端 数 理)
Akito Tatekawa (Meiji Univ.)

Kitaev モデルの拡張による一般次元ダイアモンド格子のエネルギー関数の計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Calculating the energy functions of diamond lattices of general dimensions as a generalization of the Kitaev model

概 要 The Kitaev model is an exactly solvable model of a spin 1/2 system on a honeycomb lattice.

The purpose of this talk is to describe energy functions of diamond lattices of general dimensions as a
generalization of the Kitaev model. The diamond lattices of general dimensions are deﬁned by the Ad crystal. We describe the Hamiltonian by means of Majorana operators based on the Cliﬀord algebra. Thenwe express the energy function as eigenvalues of the Hamiltonian by using the discrete Fourier transform.
For this calculation we make use of a method of a base graph developed by Sunada in the framework of
topological crystallography. We show that the energy function is identiﬁed with the one appearing in thetight biding model of diamond lattices of general dimensions.
8 増 田

哲 ( 青 学 大 理 工)

Tetsu Masuda (Aoyama Gakuin Univ.)

Painlevé V 方程式の梅村多項式の根が満たす Stieltjes 型関係式 · · · · · · 15
Stieltjes type relations for the Umemura polynomials of the ﬁfth PainlevéV equation

概 要 We present some relations of Stieltjes type satisﬁed by the zeros of the Umemura polynomials whicharise associated with the rational solutions to the ﬁfth Painlevé V equation.

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無限可積分系

特別講演
中 屋 敷 厚 ( 津 田 塾 大 学 芸)

KP 階層の準周期解と頂点作用素

Atsushi Nakayashiki (Tsuda Coll.)

Quasi-periodic solutions of the KP-hierarchy and vertex operator

124

10:45〜11:45

概 要 The KP-hierarchy is the inﬁnite system of diﬀerential equations containing the Kadomtsev-Petviashvili(KP) equation as a part. The vertex operator of the KP-hierarchy transforms one solution to another one.
Quasi-periodic solutions of the KP-hierarchy are those described by theta functions of non-singular algebraic
curves. We apply the vertex operators to quasi-periodic solutions and study their properties. Such solutions
had appeared in the study of limits of quasi-periodic solutions. We show, in general, that solutions thus
obtained correspond to singular algebraic curves and rank one torsion free sheaves on them. We use the Sato
Grassmannian for this purpose. We also show that the solutions obtained here are considered as solitonson quasi-periodic backgrounds.