Final: 2023/8/21“日本数学会
2023 年度秋季総合分科会

英 文

サ

マ

リ

2023 年 9 月
於

東北大学

集

2023 日 本 数 学 会
秋季総合分科会プログラム期

日2023 年 9 月 20 日（ 水 ）〜 9 月 23 日（ 土 ）会場

東 北 大 学 川 内 北 キ ャ ン パ ス
宮 城 県 仙 台 市 青 葉 区 川 内 41

連 絡 先

東北大学大学院理学研究科数学専攻〒980-8578
宮 城 県 仙 台 市 青 葉 区 荒 巻 字 青 葉 6–3
E-mail tohoku23sept mathsoc jp
一般社団法人

日 本 数 学 会

第 I 会場

第 II 会場

第 III 会場

第 IV 会場

第 V 会場

第 VI 会場

第 VII 会場

第 VIII 会場

第 IX 会場

A200

B200

B201

B202

B203

B101

B102

B103

C200

幾 何 学 代 数 学 トポロジー 函数解析学 函 数 論 無限可積分系 統 計 数 学 応 用 数 学 函数方程式論
9:30〜11:45 9:30〜11:45 9:30〜12:00 10:00〜12:00 9:30〜11:30
14:15〜16:15 15:30〜18:00 15:40〜17:30
14:15〜15:15

20 日
（水）

企画特別講演

9:30〜12:00

9:30〜11:30

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

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 14:15〜15:15 14:20〜15:20 14:15〜15:15 15:35〜16:35 14:15〜15:15 14:15〜15:15 16:30〜17:30 16:45〜17:45
15:30〜16:30

幾 何 学 代 数 学 トポロジー 函数解析学 函 数 論 無限可積分系 統 計 数 学 応 用 数 学 函数方程式論
9:40〜11:30

21 日
（木）

9:15〜10:45 9:30〜11:30
13:00〜14:15 13:00〜14:00

9:30〜11:15

9:30〜11:30

9:30〜10:45

9:30〜11:30

9:30〜11:30
13:00〜14:15

9:00〜12:00

特別講演

特別講演 特別講演 特別講演

特別講演

11:00〜12:00

13:15〜14:15 13:00〜14:00 11:00〜12:00

13:00〜14:00

日本数学会賞授賞式（東北大学百周年記念会館川内萩ホール） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:45〜15:15)〃
総 合 講 演（） 日 本 数 学 会 賞 秋 季 賞 受 賞 者 · · · · · · (15:30〜16:30)
斎 藤 秀 司 (東 大 数 理) · · · · · · (16:45〜17:45)
幾 何 学 代 数 学 トポロジー 函数解析学 実 函 数 論
22 日
（金）

数学基礎論
統 計 数 学 応 用 数 学 函数方程式論および歴史

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

企画特別講演

9:30〜11:30

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

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

23 日
（土）

数学基礎論
統 計 数 学 応 用 数 学 函数方程式論
および歴史

幾 何 学 代 数 学

実函数論

9:30〜10:45

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

9:15〜10:45
14:15〜17:00

企画特別講演

13:00〜14:00

特別講演 特別講演

特別講演 特別講演

特別講演 特別講演

11:00〜12:00 11:00〜12:00

16:45〜17:45 10:45〜11:45

16:15〜17:15 16:15〜17:15

Final: 2023/8/21
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 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

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

12

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

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

26

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

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

36

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38函数方程式論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

実函数論

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

62

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

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

70

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

統計数学

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

77

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

Final: 2023/8/21
4

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
応用数学

84

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

89

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

9 月 23 日（土） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

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

107

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

110

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111

9 月 22 日（金） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112

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

115

9 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115

9 月 21 日（木） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

Final: 2023/8/21
1

総合講演

総 合

講

演

9 月 21 日（木） 総合講演会場
日本数学会賞秋季賞受賞者· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:30〜16:30)

Autumn Prize Winner斎 藤 秀 司 ( 東 大 数 理)

Shuji Saito(Univ. of Tokyo)

Recent progresses on motivic cohomology · · · · · · · · · · · · · · · (16:45〜17:45)
Recent progresses on motivic cohomology

概 要 A quest for theory of motivic cohomology dates back to work of Grothendieck and early days of algebraic

geometry. Beilinson gave a precise conjectural framework for such hoped-for theory. For any quasi-compact
and quasi-separated (qcqs for short) scheme X, it foresees the existence of a spectral sequence degenerating
after ⊗Z Q:
p−q(X, Z(−q)) ⇒ K−p−q (X)E2p,q = HM(1)

whose E2 -terms are motivic cohomology of X converging to the homotopy groups of the algebraic K-theory
spectrum K(X) of X introduced by Quillen, Waldhausen, Thomason and others. It is defined using theexact category of perfect complexes on X which may be replaced by vector bundles if X is quasi-projective
over an affine scheme. The spectral sequence (1) may be viewed as an algebraic analog of the classicalAtiyah–Hirzebruch spectral sequence relating the topological K-theory of a topological space to its singularcohomology.
When X is smooth separated of finite type over a field k, the right answer was provided by two constructions:
One is Bloch’s higher Chow groups CHr (X, n), where CHr (X, 0) is the classical Chow group of codimension
r-cycles modulo rational equivalence. Another is due to Suslin–Voevodsky and both are given in termsof algebraic cycles. The equivalence of two constructions was established by Voevodsky and it provides
the motivic complex Z(n)sm as a presheaf of complexes of abelian groups on the category Smk of smoothischemes separated of finite type over a field k. Defining the motivic cohomology HM(X, Z(n)) as the i-th

cohomology group of Z(n)sm (X), which coincides with CH2n−i (X, n) by definition, the spectral sequence (1)was established by Friedlander–Suslin and Levine.
In an attempt to extend the theory of motivic complexes from Smk to the category Schftk of separated schemesof finite type over k, Voevodsky used a Grothendieck topology called the cdh topology. It is such a topology
with respect to which every X ∈ Schftk is “locally smooth over k”. Voevodsky considered the cdh cohomology
groupsi
Hcdh(X, Z(n)cdh ) for X ∈ Schftk,where Z(n)cdh is the cdh-sheafication of the left Kan extension of Z(n)sm along the inclusion Smk → Schftk.
Unfortunately, it does not gives a right motivic cohomology since the above cohomology group is always
A1 -invariant while K(X) is not in general.
Now, about 20 years have passed since the spectacular success on motivic cohomology of smooth schemes
over a field. Recently, there have emerged two independent constructions of motivic complex Z(n)(X) for
an arbitrary qcqs scheme X over a field k. One is due to Elmanto–Morrow: A basic idea is to modify
Z(n)cdh by using Hodge-completed derived de Rham complexes (in case ch(k) = 0) and syntomic complexes(in case ch(k) > 0) constructed first by Bhatt–Morrow–Scholze using topological cycle homology and later
by Bhatt–Scholze using prismatic cohomology. Another construction is due to Shane Kelly and myself: We
introduce a new Grothendieck topology called the pro-cdh topology to define the motivic complex as the
pro-cdh sheafication of the left Kan extension of Z(n)sm . Proving its basic properties (a description ofpoints (or fiber functors) of the pro-cdh topos, the conservativity of the family of points and finiteness ofcohomological dimension), it is shown that two constructions coincide if X is noetherian.

Final: 2023/8/21
企画特別講演

企

画

特

別

講

2

演

9 月 20 日（水）第 I 会場岩 崎 克 則 (北大理)Katsunori Iwasaki (Hokkaido Univ.)

超幾何群と K3 曲面上の力学系 · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Hypergeometric groups and dynamics on K3 surfaces

概 要 This talk concerns a simple question: What happens if we put the following two topics together? One

is hypergeometric groups due to Beukers and Heckman, and the other is dynamics on K3 surfaces due toMcMullen, which are seemingly quite unrelated subjects. A hypergeometric group is a matrix group modeledon the monodromy group of a generalized hypergeometric differential equation, a natural extension to ahigher rank of the Gauss hypergeometric equation. Hypergeometric groups contain a wide variety of finitegroups as well as of infinite ones. While the original motivation of Beukers and Heckman was mainly in theclassification of finite hypergeometric groups, our primary interest here is in infinite hypergeometric groups
and their applications. K3 surfaces are an interesting class of compact complex surfaces, named by Weilafter Kummer, Kähler and Kodaira (and K2, the second-highest peak on the Earth). McMullen was able tosynthesize examples of K3 surface automorphisms with Siegel disks. Here a Siegel disk is a type of invariant
set which is of interest in complex dynamics. If a K3 surface X admits an automorphism f : X → X witha Siegel disk, then X must be non-projective, that is, transcendental, and f must have positive topologicalentropy. In the talk we explain how infinite hypergeometric groups and lattices associated with them —hypergeometric lattices — are used to produce a lot of transcendental K3 surface automorphisms of positive
entropy, especially ones with Siegel disks. This talk is based on a joint work with Yuta Takada.
第 II 会場
奥 間 智 弘 ( 山 形 大 理)

複素 2 次元特異点の解析的不変量について · · · · · · · · · · · · · · · (13:00〜14:00)

Tomohiro Okuma (Yamagata Univ.)

Analytic invariants of complex surface singularities

概 要 A normal complex surface singularity is locally homeomorphic to a cone over a closed real 3-manifold

called the link of the singularity, and the link is determined by the resolution graph. For a given topologicaltype, namely a resolution graph, there are various types of complex structures that realize the graph and evenfundamental analytic invariants vary in general. I am interested in problems to give a topological bound for
those analytic invariants and to determine them for singularities with some nice properties. I will talk aboutsome topics related to those problems.
第 IX 会場
特別招待講演 (大韓数学会)
KAIST
Jaeyoung Byeon (Jaeyoung Byeon)(KAIST)

Prescribed Lorentzian mean curvature hypersurfaces and theBorn–Infeld model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)
Prescribed Lorentzian mean curvature hypersurfaces and theBorn–Infeld model

概 要 We are interested in spacelike graphs over the domain in Minkowski space with a given Lorentzianmean curvature ρ and Dirichlet boundary condition on the boundary. The graph function also represents
the electric potential generated by a charge ρ in electrostatic Born–Infeld’s theory. Even though it has avariational formulation, it is not easy to see the existence of a solution for a corresponding Euler Lagrange
equation since the corresponding energy functional is not differentiable at functions with the supremum ofgradient norm 1.
I would like to introduce some recent studies on the solvability for general sources ρ in a measure space anda critical point theory for nonlinear sources. This presentation is based on the cowork with Norishisa Ikoma,
Andrea Malchiodi and Luciano Mari.

Final: 2023/8/21
3

企画特別講演

9 月 22 日（金）第 I 会場
桑 江 一 洋 ( 福 岡 大 理)

曲率の下限概念をもつ測度距離空間上の解析学と幾何学 · · · (13:00〜14:00)

Kazuhiro Kuwae (Fukuoka Univ.)

Analysis and geometry on metric measure spaces having curvature lower bounds

概 要 I will give a survey talk on the analysis and geometry on metric measure spaces having curvature lower

bounds. Such a space was initiated by famous statistician A. Wald (1935). After Wald’s work, in 1951, A.D.
Alexandrov formulated the notion of metric space by comparing the geodesic triangle in two dimensional
space form with constant curvature. Such a space is called Alexandrov space. By Toponogov theorem,
any complete Riemannian manifolds with sectional curvature lower bounds is an Alexandrov space. M.
Gromov (1981) invented the notion of Gromov–Hausdorff distance between isometric class of compact metricspace. Then Alexandrov space naturally appears as a limit by Gromov–Hausdorff convergence of compact
Riemannian manifolds with sectional curvature lower bounds. So it can be thought as a generalization ofcomplete Riemannian manifolds with sectional curvature lower bound. In 1994, Otsu–Shioya construct thenotion of Rimannian metric tensor for Alexandrov space, which was utilized by Kuwae–Machigashira–Shioya(2001) to construct a strongly local regular Dirichlet forms, L2 -Laplacian, Sobolev spaces, and heat kernels
on Alexandrov spaces. The following natural question is raised: What is a natural generalization of complete
Riemannian manifolds with Ricci curvature lower bounds? In 1987, Bakry formulated the notion of Ricci
curvature lower bound as a generalization of Bochner inequality in terms of symmetric diffusion processes.
His notion is now called Bakry–Émery condition. Around 2000, new notion of curvature lower bounds
was proposed by Lott–Villani–Sturm, so-called the metric measure space satisfying curvature dimension
condition (CD in short). Their spaces include not only Riemannian manifolds but also Finsler manifolds, so
the Laplacian may not be linear. After 2014, Ambrosio–Gigli–Savaré invented the infinitesimal Hilbertian
condition for metric measure space and call CD space under such a condition, RCD-space (metric measurespace having Riemannian curvature dimension condition). Very recently, RCD-space is generalized in terms ofDirichlet space, so-called the tamed Dirichlet space, which is formulated as the generalization of Bakry– Émery
curvature lower bound condition for strongly local Dirichlet forms having distributional Ricci curvature lower
bound.
第 IX 会場
日 合 文 雄 (東Fumio Hiai

北大⋆)(Tohoku Univ.

⋆)

量子情報におけるデータ処理不等式とその等号条件 · · · · · · · (13:00〜14:00)

Data-processing inequalities and their equality conditions inquantum information

概 要 Different types of quantum divergences have played many roles in quantum information theory so far.

The most used and notable one is the relative entropy introduced in 1962 by Umegaki, whose generalizations
are standard f-divergences and quasi-entropies. The alpha-z-Rényi divergence is a Rényi type divergencewith two parameters alpha, z. Its special cases are the standard Rényi divergence and the sandwichedRényi divergence, having operational interpretations in the context of quantum hypothesis testing. Anothertype of quantum quantity is the monotone metric introduced in 1996 by Petz, which plays an importantrole in study of quantum information geometry. The most significant property common to those quantum
divergences is the monotonicity under quantum channels (i.e., trace-preserving and completely positive maps),
also called the data-processing inequality (DPI). The present talk is aimed at giving a survey of DPIs forthe above mentioned quantum divergences in the finite-dimensional setting, with stress on their equality
cases characterizing sufficiency and reversibility of quantum channels for given quantum states. A recent
development of approximate recoverability of quantum channels is also touched briefly.

Final: 2023/8/21
企画特別講演4

9 月 23 日（土）第 I 会場永 野 幸 一 (筑波大数理物質)

曲率が上に有界な距離空間の幾何学的トポロジー · · · · · · · · · (13:00〜14:00)

Koichi Nagano (Univ. of Tsukuba)

Geometric topology of metric spaces with upper curvaturebounds概 要 We focus on geometry of metric spaces with upper curvature bounds. In the middle of 1980s, M.

Gromov formulated the definition of CAT(κ) spaces named in honor of E. Cartan, A. D. Alexandrov, and V.
A. Toponogov. A CAT(κ) space means a complete geodesic metric space with curvature globally bounded
above by κ. A metric space is said to be CBA (Curvature Bounded Above) if it is locally CAT(κ) forsome κ. We present an overview of recent developments on geometry of CBA spaces from viewpoints ingeometric topology. While looking back on studies in geometric topology, we discuss topological regularity
and topological singularity of CBA spaces as topics in global Riemannian geometry.
第 IX 会場
大 川 新 之 介 (阪大理)Shinnosuke Okawa (Osaka Univ.)

非可換代数幾何学 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Noncommutative algebraic geometry

概 要 Derived category of coherent sheaves on algebraic varieties, and more general (enhanced) triangulated

categories arising from other mathematical objects, have been very actively studied in recent years. The
word ‘Noncommutative Algebraic Geometry’ loosely refers to such vast and interdisciplinary research area
in mathematics. In this talk I will give a gentle introduction to the subject. If time permits, I will explain
applications to deformation quantizations of del Pezzo surfaces.

Final: 2023/8/21
5

数学基礎論および歴史

数 学

基

礎

論

9 月 22 日（金）

お

よ

び

歴

史

第 VI 会場

9:20〜10:30
束(四日市大関孝和数学研)
田 中 紀 子 (奈良学園大人間教育)

宅間流岡之只『起術解路法』における整式の処理 · · · · · · · · · · · · · · · · · · · 15

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

Treatment of polynomial in Oka Yukitada’s Kijutsu Kairohou (A method
to solve the path to create a formula) in the Takuma School

1 小 川

概 要 Japanese mathematicians in pre-modern Japan expressed the final equation as a vector of coefficients.

However, in obtaining it, there were different methods of expression depending on the school. As one
such example, we will discuss the treatment of the equations in the Oka Yukitada of the Takuma school.
He expressed equations in the following three ways depending on the purpose. (1) Display all characters(Takuma style), (2) Organize and hide them in ascending order concerning a single character (Seki style), and(3) Sweep out and hide some characters of common factors in the coefficients of the equation (abbreviatedexpression).
2 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.)

宅間流岡之只『起術解路法』平面幾何解法の工夫 · · · · · · · · · · · · · · · · · · · 15

Plane geometry solution devices in Oka Yukitada’s “Kijutsu Kairohou”(A method to solve the path to create a formula) in the Takuma School

概 要 Oka Yukitada (1791–) was a Japanese mathematician of the Takuma School in the pre-modern. This

paper investigates the devices used in solving plane geometry problems in “Kijutsu Kairohou” (A method
to solve the path to create a formula) by Oka Yukitada. There are many plane geometry problems fromthe Edo period, such as nearly 1,000 pieces of “Sangaku” in shrines and temples today. Oka’s “Kijutsu
Kairohou” is a valuable source that describes the calculation process and shows the thought process forsolving the problems. The solution methods at that time included not only auxiliary lines but also folding
figures and drawing auxiliary figures, which shows a sharp point of view and way of thinking about planegeometry.
3 堀 口 俊 二
Shunji Horiguchi

村瀬義益の一般漸化式, 一般ニュートン法, 一般マンデルブローの漸化式の関連 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Relations between Murase Yoshiyasu general recurrence formula, general Newton method, and general Mandelbrot recurrence formula

概 要 In 1673, Yoshimasu Murase derives recurrence formulas. We derive a general recurrence formula fromthese. This general recurrence formula leads to the general Newton’s method and the general Mandelbrot’srecurrence formula. These show the originality of Wasan (Japanese native mathematics developed in Japanin the Edo era (1603–1868:national isolation)).

Final: 2023/8/21
数学基礎論および歴史

4 田 村

誠
(大阪産大全学教育機構)

Makoto Tamura (Osaka Sangyo Univ.)6

王孝通による句股術の展開について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the methods by Wang Xiaotong for right triangles

概 要 Wang Xiaotong explained a more complex methods for right triangles in the problems [15]–[20] of

his book “Jigu Suanjing” (Continuation of Ancient Mathematical Classic) than Liu Hui’s methods in the“Jiuzhang Suanshu” (The Nine Chapters on the Mathematical Art). In this talk, we will show proofs ofsome methods, classify their methods, and show Wang Xiaotong attained at most in some sense.
10:45〜11:45 特別講演
( 早 大 高 等 研)
A. Karaisl

Wasan 2.0: Building an online sangaku archive

Antonia Karaisl (Waseda Univ.)

Wasan 2.0: Building an online sangaku archive

概 要 The practice of dedicating sangaku, votive tablets presenting geometric problems in word and image,flourished in Japan throughout the Edo period. Although many exponents were destroyed thereafter, close
to a thousand sangaku survive in shrines and temples to this day; additionally, many lost exponents arestill documented in print. Even though presenting a fascinating example for a mathematical discourse
developed apart from the West, the custom of sangaku is almost entirely unknown outside the country. Partof the problem may be of linguistic nature, aggravated by the geographic dispersion: although there havebeen attempts to collect sangaku online, there is not much material to date that would make the traditioncollectively accessible to non-Japanese-speaking audience. My project plans to solve for this problem bybuilding a bilingual, open-access online archive for all sangaku surviving in wood and print. In the first
instance, this sangaku archive is an attempt to preserve a cultural heritage unique to Japan. Beyond
that, the archive aspires to serve as an active research space in its own right, where images, questions andsolutions can be freely annotated and shared. Where the original authors of sangaku tablets could rely on
the footfall in temples and shrines to communicate with a larger audience, the online sangaku archive means
to carry this idea forward and further by making the material accessible to scholars worldwide. My talkwill elaborate on this idea in theory and practice to showcase how said tradition can be preserved in the
21st century in both matter and spirit.
12:00〜12:15

歴史部門懇談会

14:15〜16:45
5 鈴 木 信 行 ( 静 岡 大 理)

Nobu-Yuki Suzuki (Shizuoka Univ.)

中間述語論理に於ける弱い existence property に関する補遺 · · · · · · · · · · 15

A supplementary note on a weak version of the existence property inintermediate predicate logics

概 要 A weak variant of the existence property in intermediate predicate logics is introduced. This property

is a “double-negated” version of the existence property. Very basic results will be presented.
6 志 村 立 矢 ( 日 大 理 工)

Tatsuya Shimura (Nihon Univ.)

Disjunction property に関する Minari の定理の拡張について · · · · · · · · · 15
A generalization of Minari’s theorem on disjunction property

概 要 In 1986, Minari proved the intermediate propositional logic axiomatized by Kreisel–Putnam’s andScott’s axioms has the disjunction property. We give a series of admissible rules for the intuitionistic logic,
which yields a genaralization of Minari’s result. Our proof is based on syntactical proof by Kreise–Putnam
and Sasaki.
7 志 村 立 矢 ( 日 大 理 工)

Tatsuya Shimura (Nihon Univ.)

様相論理 K4Z+
14 のカット除去について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Cut-elimination for the modal logic K4Z+
14

概 要 We give a simple proof of the cut-elimination for the modal logic K4Z+
14 , following Sasaki’s proof forthe provability logic GL.

Final: 2023/8/21
7

数学基礎論および歴史

8 小 暮 晏 佳 ( 金 沢 大 理 工)
倉 橋 太 志 (神戸大システム情報)

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

局所反映原理に関する保存性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the conservation results for local reflection principles

概 要 For a class Γ of formulas, Γ local reflection principle RfnΓ (T ) for a theory T of arithmetic is a schema

formalizing the Γ-soundness of T . Beklemishev proved that for every Γ ∈ {Σn , Πn+1 | n ≥ 1}, the full local
reflection principle Rfn(T ) is Γ-conservative over T + RfnΓ (T ). We firstly proved that the second condition
D2 of the derivability conditions is a sufficient condition for the conservation theorem to hold. We secondly
investigated the conservation theorem in terms of Rosser provability predicates. We constructed Rosser
predicates for which the conservation theorem holds and Rosser predicates for which the theorem does nothold.
9 佐 藤 雄 太 (神戸大システム情報)
倉 橋 太 志 (神戸大システム情報)(Kobe Univ.)
Yuta Sato
Taishi Kurahashi (Kobe Univ.)

必然化の論理 N の拡張論理の有限フレーム性 · · · · · · · · · · · · · · · · · · · · · · 15

The finite frame property of some extensions of the pure logic of necessitation

概 要 We study the finite frame property of some extensions of Fitting, Marek, and Truszczyński’s pure logicof necessitation N. For any natural numbers m, n, we introduce the logic N+ Am,n by adding the axiom¬□A
scheme □n A → □m A and the rule
into N. We proved the finite frame property of N+ Am,n with¬□□A¬□A
respect to Fitting, Marek, and Truszczyński’s relational semantics. We also proved that the rule
is
¬□□A
+
necessary for the completeness of N A0,n for n ≥ 2.
10 鹿 島亮 (東工大情報理工)
倉 橋 太 志 (神戸大システム情報)
岩 田 荘 平 (愛知学院大教養)(Tokyo Tech)
Ryo Kashima
Taishi Kurahashi (Kobe Univ.)
Sohei Iwata (Aichi Gakuin Univ.)

証明可能性論理 D のカット無しシークエント計算 · · · · · · · · · · · · · · · · · · · 15

Cut-free sequent calculi for the provability logic D

概 要 The provability logic D, which was studied by Beklemishev (1999), is an intermediate logic between

the provability logics GL and S. A Hilbert-style proof system for D is known, but there has been no sequentcalculus. We establish two sequent calculi for D, and show cut-elimination theorems syntactically (for one
calculus) and semantically (for both calculi). The syntactic proof is reduced to the cut-elimination for S
by Kushida (2020). The semantical proofs are obtained by showing the completeness of cut-free sequentcalculi.
11 鈴 木 登 志 雄 (都 立 大 理)

Toshio Suzuki (Tokyo Metro. Univ.)

自由な形の AND-OR 木における均衡値 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Equilibria of AND-OR trees without assumptions on tree shapes

概 要 The goal of this research is to find and prove nontrivial equations and inequalities on equilibria

of AND-OR trees without assumptions on tree shapes. In particular, we prove that two equilibria ofrandomized directional algorithms coincide; one is “d” of Saks–Wigderson (1986) and the other is that ofprobability distributions on the deterministic depth-first directional algorithms. We also show that “a” ofSaks–Wigderson (1986) is a lower bound of the equilibrium of randomized depth-first algorithms. This work
was done in collaboration with Fuki Ito.

Final: 2023/8/21
数学基礎論および歴史

送大)12 隈 部 正 博 (放宮 部 賢 志 ( 明 大 理 工)
鈴 木 登 志 雄 ( 都 立 大 理)
Masahiro Kumabe(Open Univ. of Japan)
Kenshi Miyabe (Meiji Univ.)
Toshio Suzuki (Tokyo Metro. Univ.)

8

クエリー制限と符号付き桁数表現による Solovay 還元の特徴づけ · · · · · · 15

Characterizations of Solovay reducibility via query restriction for signeddigit representation

概 要 In the theory of algorithmic randomness, Solovay reducibility is a reducibility to compare the ran-domness of two real numbers. It has many good properties within the left-c.e. reals. This leads to thequestion: does a reduction similar to Solovay’s exist that well-behaves even for non-left-c.e. reals? One suchtrial is a computable Lipschitz reducibility, or cL-reducibility, defined by restricting oracle use in Turing
reduction. The cL-reducibility is named so because of adapting the concept of Lipschitz continuity for
Cantor space. The signed-digit representation is a real number representation used in computable analysis.
We characterize Solovay reducibility by replacing the usual binary representation in cL-reducibility with thesigned-digit representation. This result answers the classical question in a much better way.
13 只 木 孝 太 郎 (中 部 大 工)

Kohtaro Tadaki (Chubu Univ.)

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

A refinement of quantum information theory by algorithmic randomnessVII

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

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

9 月 23 日（土）第 VI 会場

9:20〜10:30
14 鈴 木 悠 大 (東 北 大 理)
横 山 啓 太 ( 東 北 大 理)
Yudai Suzuki (Tohoku Univ.)
Keita Yokoyama (Tohoku Univ.)

On the Π12 part of Π11 -CA0 . · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Π12 part of Π11 -CA0 .

概 要 It is known that there are some mathematical theorems which are expressed by Π 12 sentences andprovable from Π11 -CA0 , but stronger than ATR0 . In general, such theorems are strictly weaker than Π11 -CA0 .
In this study, we introduce an increasing sequence of Π12 sentences that captures the Π12 part of Π11 -CA0 .
With this sequence, for any Π12 sentence between ATR0 and Π11 -CA0 , we can measure how far it is from
Π11 -CA0 .

Final: 2023/8/21
9

数学基礎論および歴史

15 五 十 里 大 将 (東 北 大 理)
横 山 啓 太 ( 東 北 大 理)
Hiroyuki Ikari (Tohoku Univ.)
Keita Yokoyama (Tohoku Univ.)

RT2 と BΣ03 の Π11 -保存拡大性について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On Π11 -conservativeness between RT2 and BΣ03

概 要 In this talk we overview a new proof of Π11 -conservativeness between RT2 and BΣ03 . It’s well known

that COH+D2<∞ is equivalent to RT2 (over RCA0 ). Some basis theorems for RT2 are proved by thisdecomposition. Carrying out this proof within a model of WKL0 +BΣ03 , we can prove a conservation result.
Using effective coded ω-models of WKL0 , we see a proof of ≪2 -basis theorem for D2<∞ . These discussions
and results can give a new view point to conservation results, with help of a view point of some types ofbasis theorem. The contents are joint work with Keita Yokoyama.
16 荒 武 永 史 (京 大 数 理 研)
Hisashi Aratake (Kyoto Univ.)

層表現を持つモデル全体のクラスについて · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the class of models represented by sheaves

概 要 We consider the class Γ(T ) of structures represented by sheaves of T -models for a theory T . For

example, while an arbitrary commutative ring can be represented by a sheaf of local rings via its Zariski
spectrum, rings represented by sheaves of fields are characterized as von Neumann regular rings. Usingmachinery of categorical logic, we investigate the case when Γ(T ) is given by the image of an idempotent
dual adjunction between the category of T0 -models (for some Horn theory T0 ⊆ T ) and the category of
T -modelled spaces. In such a situation, we show that Γ(T ) is the closure of the class of T -models underlimits and filtered colimits in the class of T0 -models.
17 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⋆)

Cyclic automorphism について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On cyclic automorphisms

概 要 We give a new proof that the following countable random structures have continuously many cyclic

automorphisms: The random graph, the random tournament, and the random triangle-free graph. We also
discuss about random hypergraphs and those structures with no cyclic automorphisms.
10:45〜11:45 特別講演
津 久 浦 健 太 ( 法 政 大 理 工)
Kenta Tsukuura (Hosei Univ.)

Prikry 型強制法の商と飽和イデアル
The quotients of Prikry-type forcings and Saturated ideals

概 要 Large cardinals are “large” in the sense that they are inaccessible. But successor cardinals sometimes

have behavior like large cardinals, they appear as generic large cardinals. The notions of generic large
cardinal axioms are widely used and considered in set theory. There are various formulations of genericlarge cardinal axioms, just as the definitions of large cardinal axioms have various expressions. One of themis Foreman’s generalized large cardinal axioms. These axioms are frequently equivalent to the existence of
precipitous ideals on some sets. Then our interest is reduced to forcing properties of ideals. In this talk, we
introduce some problems of ideals over successors of singular cardinals and two strong tools to study them.
One is “Prikry-type forcings”, and the other is the duality theorem.
12:00〜12:15

数学基礎論および歴史分科会総会

14:15〜16:30
18 薄 葉 季 路 (早 大 理 工)

Toshimichi Usuba (Waseda Univ.)

Loś’s theorem without the axiom of choice · · · · · · · · · · · · · · · · · · · · · · · · 15
Loś’s theorem without the axiom of choice

概 要 We prove that, in ZF, Loś’s fundamental theorem of ultraproducts is equivalent to the following weak

form: For every structure M , an ultrapower of M by some ultrafilter is elementary equivalent to M .

Final: 2023/8/21
数学基礎論および歴史

19 高 瀬 理 人 (神戸大システム情報)
倉 橋 太 志 (神戸大システム情報)(Kobe Univ.)
Rihito Takase
Taishi Kurahashi (Kobe Univ.)10

証明可能性-強制様相論理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Modal logic of provability and forcing

概 要 So far, various kinds of models of set theory have been constructed, and recently many set theorists

are interested in the structure of the multiverse consisting of these models. Modal logic is very useful toanalyze this structure. Hamkins–Lowe studied the forcing accessibility relation on the multiverse. Moreprecisely, they introduced the modal logic of forcing and proved that it corresponds to the modal logic S4.2.
On the other hand, Solovay proved that the modal logic of provability corresponds to the modal logic GL.
In this talk, we discuss the bimodal logic obtained by combining these two modal logics. We introduce abimodal logic PF and prove that the modal logic of provability and forcing corresponds to PF.
20 平 田 康 史 (神 奈 川 大 工)家 本 宣 幸(大分大教育マネジメント機構)
矢 島 幸 信 (神 奈 川 大⋆)

Yasushi Hirata (Kanagawa Univ.)
Nobuyuki Kemoto (Oita Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)

順序数の積の部分空間における可算パラコンパクト性と閉離散部分集合の C ∗ -埋め込み · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Countable paracompactness and C ∗ -embeddings of closed discrete subsets in subspaces of products of ordinals

概 要 In this talk, we discuss countable paracompactness and C ∗ -embeddings of closed discrete subsets in

subspaces of products of ordinals. We show: it is consistent with and independent of ZFC that (ω + 1) × ω1
has a subspace which is not countably paracompact, and in which every closed discrete subset is C ∗ embedded.
21 後 藤 達 哉 (神戸大システム情報)
Tatsuya Goto

(Kobe Univ.)

基数不変量のゲーム理論的バリエーション · · · · · · · · · · · · · · · · · · · · · · · · · 15

Game theoretic variations of cardinal invariants

概 要 Cardinal invariants play an important role in the set theory of reals. In this study, we consider gameversions of some cardinal invariants.
For example, for a set A of sets of natural numbers, A is said to be a splitting family if for any infinite
set X of natural numbers there exists Y ∈ A such that both X ∩ Y and X \ Y are infinite sets. The
splitting number is defined as the minimum of the cardinality of the splitting family. We considered two
game-theoretic versions of the splitting number s and showed that one of them is equal to sσ , a cardinalinvariant similar to s, and the other is equal to the continuum.
We also considered the bounding game, the reaping game, and the anti-localizing game.
22 山 添 隆 志 (神戸大システム情報)

Takashi Yamazoe (Kobe Univ.)

Evasion number と Cichoń’s diagram · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Evasion number and Cichoń’s diagram

概 要 Cichoń’s diagram is a table of ten representative cardinal numbers related to the set theory of thereals. Recently it was shown that there is a model of set theory called Cichoń’s maximum where all theten cardinal numbers in the diagram are separated. The evasion number e is a cardinal number regarding
functions on natural numbers. More specifically, e is related to a prediction of a value of a function at somepoint from its values before the point and to an evasion from the prediction. Our ultimate goal is to add
e to the Cichoń’s maximum. We showed that we can construct a model where nine cardinal numbers inCichoń’s diagram and e are separated, which is highly close to our ultimate desired model.

Final: 2023/8/21
11

数学基礎論および歴史

23 林

佑 亮 (神戸大システム情報)

Yusuke Hayashi (Kobe Univ.)ℵω に一般化された dominating number · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Dominating number generalized to ℵω

概 要 “Cardinal characteristics” is a well-studied field in set theory. These characteristics are defined by

combinatorial properties of reals, and useful for analyzing what happens the set of real R, or the power setof ℵ0 .
In recent times, there are some results about generalizing cardinal characteristics to an appropriate cardinal
λ. By studying these generalizations, we can indirectly understand the structure of the power set of λ.
We focus on dℵω , which is a generalization of the dominating number d to ℵω . We introduce an usefulcondition for deriving the largeness of dℵω , and outline its applications.
24 丹 野 俊 将 (神戸大システム情報)

Toshimasa Tanno (Kobe Univ.)

定常塔強制と普遍ベール集合 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Stationary tower forcings and universally Baire sets

概 要 Woodin introduced stationary tower forcings, and showed that the existence of large cardinals imply

regularity properties of sets of reals in L(R). For this result, it is known that we can derive regularity
properties in L(R) from certain conditions on stationary tower forcings, without explicit using of large
cardinals such as Woodin cardinals. We investigate conditions on stationary tower forcings to derive theuniversally Baireness in L(R), which is a stronger property than regularity properties. In this talk, we
present such conditions and related properties of tower forcings.
25 依 岡 輝 幸 (静 岡 大 理)

Teruyuki Yorioka (Shizuoka Univ.)

トドロチェビッチによるマーティンの公理の部分公理と様々な梯子系の色付けの一様化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Todorcevic’s fragments of Martin’s Axiom and variations of uniformizations of ladder system colorings

概 要 Uniformizations of ladder system colorings has been introduced by analysis of a proof of the Shelah’ssolution of Whitehead problem. Shelah’s proof can be separated into the following two theorems: MAℵ1
implies any ladder system coloring can be uniformized, and the uniformizations of ladder system coloring
implies the existence of a non-free Whitehead group. In this talk, we give some implications from Todorčević’s
fragments of Martin’s Axiom to variations of uniformizations of ladder system colorings.

Final: 2023/8/21
代数学

代 数
9 月 20 日（水）12

学第 II 会場

9:30〜11:45
1 大 木 孝 一 ( オ ー ケ ー ラ ボ)

Kohichi Ohki (OK Lab. Co. Ltd.)

Proof of Riemann hypothesis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Proof of Riemann hypothesis

概 要 This lecture is almost the same content as that UP Loaded in No. 51 Lecture, 17 Sept. 2021,

Fall General Sectional Meeting of the Math. Society of Japan @ Chiba Univ. The main differences are
as follows. The title has been changed from the proof that the matrix is Hermitian to the proof of the
Riemann Hypothesis. In fact, they are equivalent. The theorem 1,2 and 3 were also added to clarify theproof and to make the content more concise.
2 塩 見 大 輔 ( 山 形 大 理)

Daisuke Shiomi (Yamagata Univ.)

Girstmair の公式の多項式類似 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A polynomial analogue of Girstmair’s formulas

概 要 For an odd prime p, Girstmair gave class number formulas for subfields of the pth cyclotomic field byusing the coefficients of the digit expression of 1/p. In this talk, we study an analogue of these formulas inpolynomial rings.
3 吉 田
学 ( 富 山 高 専)
横 山 俊 一 ( 都 立 大 理)
Manabu Yoshida(Toyama Nat. Coll. of Tech.)
Shun’ichi Yokoyama(Tokyo Metro. Univ.)

正標数局所体の拡大の計算アルゴリズムについて · · · · · · · · · · · · · · · · · · · 15

On the computation of all extensions of a p-adic field of characteristic p

概 要 We present an algorithm for the computation of defining polynomials for all extensions of a given

degree with restricted ramification over a p-adic function field.
4 武 田

渉 ( 東 京 理 大 理)

Wataru Takeda (Tokyo Univ. of Sci.)

Norm 形式に対する Brocard–Ramanujan 問題の解の存在性 · · · · · · · · · · 15
Existence of the solutions to the Brocard–Ramanujan problem for norm
forms

概 要 The Brocard–Ramanujan problem, which is an unsolved problem in number theory, is to find integer

solutions (x, ℓ) of x2 −1 = ℓ!. Many analogs of this problem are currently being considered. As one example,
it is known that there are at most only finitely many algebraic integer solutions (x, ℓ), up to a unit factor,
to the equations NK (x) = ℓ!, where NK are the norms of number fields K/Q. In this talk, we construct
infinitely many number fields K such that NK (x) = ℓ! has at least 22 solutions for positive integers ℓ.
5 Maozhou Huang (東 工 大 理)
Maozhou Huang (Tokyo Tech)

On the ramification of the torsion points of Drinfeld modules · · · · · · · · 15
On the ramification of the torsion points of Drinfeld modules

概 要 For a localization K of a function field, the ramification of the extensions generated by torsion points

of Drinfeld Fq [t]-module over a local function field has been studied by various people. In this talk, I will
discuss a theorem concerning the action of the ramification group on an Fq -base of the space of the torsion
points in a specific situation. I will also shed light on the generalization of the theorem.

Final: 2023/8/21
13

代数学

6 Xuanzhong Dai (京 大 数 理 研)
Bailin Song
(Univ. of Sci. Tech. of China)
Xuanzhong Dai (Kyoto Univ.)
Bailin Song
(Univ. of Sci. Tech. of China)

Chiral de Rham complex and the Rankin–Cohen brackets · · · · · · · · · · · 15

Chiral de Rham complex and the Rankin–Cohen brackets

概 要 It was speculated by W. Eholzer, Y. Manin and D. Zagier long time ago that the Rankin–Cohenbrackets are related to vertex operator algebras. We will apply the chiral de Rham complex to the upper
half plane, and show that the Rankin–Cohen brackets appear in the vertex operations of the invariant global
sections. We will then show that the invariant vertex algebra with a relaxing of cuspidal conditions is
simple, and generalize the Rankin–Cohen brackets to meromorphic modular forms according to the vertex
algebra structure.
7 小 林 雅 人 ( 神 奈 川 大 工)

Masato Kobayashi (Kanagawa Univ.)

ラマヌジャン微分方程式, 符号つきアイゼンシュタイン級数, ハンケル行
列式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Ramanujan differential equations, signed Eisenstein series, Hankel determinants

概 要 Ramanujan’s differential equations are qE2′ =E22 −E412 ,qE4′ = E2 E43−E6 , qE6′ =E2 E6 −E42
2

for theclassical Eisenstein series. The author (2023) proved certain signed analog of this and then derived Hankel
E ∗3 −E ∗2

2 ·3
∗6
∗3 ∗2
∗4
∗
4
6
determinants such as det(E2(i+j))3i,j=1 = 173 ·19·31
2 ·43 (−308481E4 + 191945E4 E6 + 116536E6 ) 1728E ∗3 .
87

4

8 井 川 祥 彰
南 出
真 ( 山 口 大 理)
谷 川 好 男Tadaaki Igawa
Makoto Minamide (Yamaguchi Univ.)
Yoshio Tanigawa

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

On averages of indexes of congruence subgroups in the modular group II

概 要 Let n ≥ 1 be any integer, Γ0 (n) the Hecke subgroup of the modular group. We consider an error

term E0 (x) in the average of the index of Γ0 (n). We deduce a formula for sum of E0 (n) and an Ω-result forE0 (n).
14:15〜15:15

特別講演
安 田 雅 哉 ( 立 教 大 理)

Masaya Yasuda (Rikkyo Univ.)

数理暗号の紹介:格子暗号と同種写像暗号

Introduction to mathematical cryptography: Lattice-based and isogenybased cryptography

概 要 Mathematical cryptography is an application of mathematics to cryptography. Recently, several

mathematical theories have received interest to develop post-quantum cryptography (also called quantumresistant cryptography) for the quantum computing era, such as lattices and isogenies over elliptic curves.
In this talk, I briefly introduce the background of mathematical cryptography including post-quantum cryptography. I also introduce lattice-based and isogeny-based cryptography and their underlying mathematics.
For lattice-based cryptography, its security is based on the computational hardness of solving lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). I introduce latticebasis reduction techniques to solve such lattice problems. For isogeny-based cryptography, its security isbased on isogeny problems. I present a method of solving the supersingular isogeny problem via the Deuringcorrespondence.

Final: 2023/8/21
代数学

14

15:30〜18:00
9 伊 吹 山 知 義 (阪大⋆)Tomoyoshi Ibukiyama (Osaka Univ.⋆)

極大でない 2 次整環の種指標の L 関数とアデール · · · · · · · · · · · · · · · · · · · 10

Genus character L functions of quadratic orders in an adelic way

概 要 Let O be an order of a quadratic field K over Q. We do not assume that O is maximal. Let Cl+ (O)be the narrow ideal class group of proper ideal classes of O. The real valued character χ of Cl+ (O) iscalled traditionally a genus character. The genus theory of such orders is well known since Gauss, Dirichlet,
Dedekind etc. But explicit formulas for the L functions associated to χ are given only recently, first by
Chinta and Offen for special cases and by Kaneko and Mizuno for the whole cases. Here we review the genus
theory by adelic language and give an alternative proof of the above formula. This proof is considerably
simpler than the original proof.
10 片 山 裕 太 (東 京 理 大 理)

Yuta Katayama (Tokyo Univ. of Sci.)

Hecke L-functions of certain subextensions in an extraspecial extension· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hecke L-functions of certain subextensions in an extraspecial extension

概 要 In 1924, Hecke observed the coincidence of L-functions of quadratic fields. The precise conditions of

the phenomena which Hecke observed were given in terms of Galois group of certain abelian extensions ofquadratic fields by Kida and Namura. Furthermore, I and Kida studied the coincidence of cyclic extensionsof prime degree and generalize the case of quadratic fields. I will talk about the coincidence of L-functions
in more general case of elementary abelian extensions.
11 井 上 翔 太 (東 工 大 理)
( Univ. Bonn )Junxian Li
Shota Inoue
Junxian Li(Tokyo Tech)(Univ. Bonn)

領域 1/2 < σ < 1 での Dirichlet L 関数の同時値分布 · · · · · · · · · · · · · · · · 15

Joint value distribution of Dirichlet L-functions in the strip 1/2 < σ < 1

概 要 The speaker will discuss the joint value distribution of Dirichlet L-functions in the strip 1/2 < σ < 1.

He will present results for dependence property and joint extreme values of Dirichlet L-functions.
12 小 林 弘 京 (名 大 多 元 数 理)

Hirotaka Kobayashi (Nagoya Univ.)

Riemann ゼータ関数の離散平均について · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On discrete mean-values of the Riemann zeta function

概 要 The mean values of the Riemann zeta function have been studied for many years. As for the continuous

mean values, big progress has been made. On the other hand, our knowledge of the discrete mean values islimited. Recently, Li and Radziwillrevealed that the twisted second moments of the Riemann zeta function
over arithmetic progressions show a notable correspondence with the analogous continuous moment. In thistalk, we will give the result of the second moments over arithmetic progressions without twists.
13 奥 村 喜 晶 (東 洋 大 理 工)

Yoshiaki Okumura (Toyo Univ.)

奇素数次 Fermat 曲線の Chebyshev の偏り · · · · · · · · · · · · · · · · · · · · · · · · · 10

Chebyshev’s bias for Fermat curves of odd prime degree

概 要 In this talk, we prove that an asymptotic formula on a prime number race for Fermat curves of odd

prime degree is given under the Deep Riemann Hypothesis (DRH), which is a conjecture on the convergenceof the partial Euler product on the critical line. We also obtain such asymptotics for some quotients ofFermat curves under DRH. As an application, we compute the order of zero at s = 1 for the second moment
L-functions of these curves under DRH.

Final: 2023/8/21
15

代数学

14 小 山 信 也 (東 洋 大 理 工)瀬高)
田 中 花 菜 (尾Shin-ya Koyama (Toyo Univ.)
Hana Tanaka(Gunma Pref. Oze High School)

代数曲線上のチェビシェフの偏り · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Chebyshev’s bias for algebraic curves

概 要 We extend Chebyshev’s bias to algebraic curves, and investigate examples for Fermat curves of genus

3.
15 戸 澗 勇 一 郎 (名 大 多 元 数 理)
Yuichiro Toma (Nagoya Univ.)

A relation between multiple L-functions and the confluent hypergeometric function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A relation between multiple L-functions and the confluent hypergeometric function

概 要 The multiple zeta functions are generalizations of the Riemann zeta function and have expressionsin terms of confluent hypergeometric functions. These yield the functional equation for the multiple zetafunctions. In this talk, we report the extension of the result to multiple L-functions.
16 角 野 裕 太 (東 北 大 理)
Yuta Kadono(Tohoku Univ.)

Schur 多重ゼータ値の積分表示と川島関数 · · · · · · · · · · · · · · · · · · · · · · · · · 15
Integral representation of Schur multiple zeta values and Kawashimafunction

概 要 It is known that there are many Q-linear relations among multiple zeta values. In particular, theKawashima relation is one of the families of relations expected to generate all Q-linear relations among
multiple zeta values. It can be described using the Taylor coefficients of the Kawashima function. In thistalk, we generalize the multiple integrals, which have been studied for a long time in transcendental number
theory, to give a multiple integral representation of the Kawashima function. Furthermore, we express the
Taylor coefficients of the Kawashima function in terms of multiple zeta values with explicit indices.
17 加 藤 正 輝 (富 山 高 専)
Masaki Kato(Toyama Nat. Coll. of Tech.)

多重ポリログ函数の反転公式の q-類似・楕円類似 · · · · · · · · · · · · · · · · · · · 15

q- and elliptic analogues of inversion formulas for multiple polylogarithms

概 要 In this talk, we consider q- and elliptic generalizations of the inversion formulas satisfied by multiple

polylogarithms. We establish inversion formulas for functions Lk (a, α; p, q), which can be considered to becommon deformations of q- and elliptic multiple polylogarithms. By taking the trigonometric and classicallimits in the main theorem, we obtain q- and elliptic analogues of the inversion formulas.
18 河 瀬 悠 人 (京Yuto Kawase

大理)(Kyoto Univ.)

Birkhoff’s variety theorem for relative algebraic theories · · · · · · · · · · · · 15
Birkhoff’s variety theorem for relative algebraic theories

概 要 An algebraic theory, sometimes called an equational theory, is a theory defined by finitary operations

and equations, such as groups and rings. It is well known that algebraic theories are equivalent to finitarymonads on Set. In this talk, we generalize this phenomenon to locally finitely presentable (LFP) categories
from the perspective of partial Horn logic. For each LFP category A, we define an “algebraic concept”
relative to A, which will be called an A-relative algebraic theory, and show that A-relative algebraic theories
are equivalent to finitary monads on A. Finally, we generalize Birkhoff’s variety theorem from classicalalgebraic theories to our relative algebraic theories.

Final: 2023/8/21
代数学

9 月 21 日（木）16

第 II 会場

9:15〜10:45
19 岩 見 智 宏 (九 工 大 工)

Recovering conductor condition of (Q-)conic bundles via three-dimensional
Miyaoka–Yau type inequality with the associated third Chern classes · 15

Tomohiro Iwami (Kyushu Inst. of Tech.)

Recovering conductor condition of (Q-)conic bundles via three-dimensional
Miyaoka–Yau type inequality with the associated third Chern classes

概 要 Based on S. Mori’s proof for an three-dimesnional extremal neighborhood (X, C) ⊂ C4 of type A,

with irreducible and reduced C, in the existence of three-dimensional flips,thu author had studied forthe case C not necessary irreducible nor reduced, denoted as (X, Cs ) ⊂ C4 , mainly as follows: 1) tofind three-dimensional Miyaoka–Yau type inequality with the associated third Chern classes, abbreviatedas (MY)3,c3 ([I2018Mar, I2019Sep, I2020Sep)]), 2) in order to study period space of (MY)3,c3 ,2a) toff
introduce an interemdiate Jacobians IJ(X,Cs ) ([I2022Mar]), 2b) to study strong approximation of IJ(X,Cs )([I2022Sep]), and to study double solid for it by introducing associated quaternion algebra data ([I2023Mar]).
As succeeding our results, the author will report, as main results: i) to show a kind of “relativization” for[S. Mori–Y. Prokhorov, 2008, 2009, 2021] which removes conductor condition of [V. A. Iskovskikh, 1987],
by recovering conductor condition via 1) amd 2), and ii) to give an alternative of [M. Artin–D. Mumford,
1972] via i), up to “relativization”.
20 澤 原 雅 知 (埼 玉 大 理 工)

Masatomo Sawahara (Saitama Univ.)

Cylindrical ample divisors on Du Val del Pezzo surfaces · · · · · · · · · · · · · 13
Cylindrical ample divisors on Du Val del Pezzo surfaces

概 要 A cylinder in an algebraic variety is its open subset, which is isomorphic to the direct product of theaffine line and an algebraic variety. Letting X be a normal projective variety and H be an ample Q-divisor
on X, we can consider a special kind of cylinder in X depending on H, so-called an H-polar cylinder. Notethat polarized cylinders in smooth del Pezzo surfaces are well studied. In this talk, we will construct anH-polar cylinder in a Du Val del Pezzo surface S of degree at least 3 for every ample Q-divisor H on X.
21 佐 藤Ken Sato

謙 (東 工 大 理) ♭ Kummer 曲面上の高次 Chow サイクルについて · · · · · · · · · · · · · · · · · · · · 15

(Tokyo Tech)

On higher Chow cycles on Kummer surfaces

概 要 The higher Chow group CHp (X, q) introduced by Bloch is a generalization of the classical Chowgroups. It satisfies many interesting properties, but its structure is still mysterious for almost all varieties
when p is greater than 1. In this talk, I will explain the explicit construction of higher Chow cycles in
CH2 (X, 1) on a family of Kummer surfaces. By computing their images under the Beilinson regulator map,in very general cases, these cycles generate at least rank 18 subgroup of CH2 (X, 1)ind , which is the quotientof CH2 (X, 1) by the images of the intersection product maps. To compute the images under the regulator
map, we use automorphisms of the family and the explicit description of the action of the automorphisms
on the Picard–Fuchs differential equations of the family.
22 内 海 和 樹 (立 命 館 大 理 工)

Kazuki Utsumi (Ritsumeikan Univ.)

猪瀬曲面のモーデル・ヴェイユ格子について · · · · · · · · · · · · · · · · · · · · · · · 15

Mordell–Weil lattices of Inose surfaces

概 要 An elliptic K3 surface with two II ∗ fibers is called Inose surface. It is known that any Inose surface

can be constructed as a double cover of a Kummer surface associated two elliptic curves. We give a method
to find a section of an Inose surface corresponding to an isogeny of general degree between two elliptic
curves.

Final: 2023/8/21
17

代数学

23 齋 藤 夏 雄 (広 島 市 大 情 報)
大 津 嘉 輝 (広島県瀬戸内高)
伊 藤 浩 行 ( 東 京 理 大 理 工)

Natsuo Saito (Hiroshima City Univ.)
Yoshiki Ohtsu (Setouchi High School)
Hiroyuki Ito (Tokyo Univ. of Sci.)

ある準楕円 K3 曲面の Mordell–Weil 群について · · · · · · · · · · · · · · · · · · · · 15

On the Mordell–Weil group of some quasi-elliptic K3 surfaces

概 要 Ito classified rational quasi-elliptic surfaces in characteristic 2 and provided a detailed description of

the structure of the Mordell–Weil group. In this talk, we focus on K3 surfaces with quasi-elliptic surface
structures in characteristic 2. Specifically, we analyze the structure of the Mordell–Weil group of thequasi-elliptic surfaces which has 20 reducible fibers of the Kodaira-type III. Moreover, we demonstrate thata good code can be constructed from the surface we studied.
11:00〜12:00
谷 本

特別講演
祥 ( 名 大 多 元 数 理)

Sho Tanimoto (Nagoya Univ.)

Exceptional sets in Manin’s conjecture and their applications to algebraic geometry
Exceptional sets in Manin’s conjecture and their applications to algebraic geometry

概 要 Manin’s conjecture is a conjectural asymptotic formula for the counting function of rational points on

Fano varieties over global fields. When you count rational points, it is important to remove the contributionof rational points from exceptional sets so that the asymptotic formula reflects the global geometry of theunderlying variety. With Brian Lehmann, I have been studying exceptional sets arising in this conjecture.
In this talk I would like to discuss my joint work with Brian Lehmann and Akash Sengupta on birational
geometry of exceptional sets, then I will discuss applications of this study to understand the geometry ofmoduli spaces of sections on Fano fibrations over a curve which is joint work with Brian Lehmann and Eric
Riedl. The minimal model program and BAB conjecture (proved by Birkar) play essential roles in thesestudies.
13:00〜14:15
24 范

凌 虎 (東 大 数 理) ♭ Crepant resolution of A4 /A4 and its Euler number in characteristic 2· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Linghu Fan(Univ. of Tokyo)

Crepant resolution of A4 /A4 and its Euler number in characteristic 2

概 要 In characteristic 0, it is known that the quotient singularity C4 /A4 has a crepant resolution andby McKay correspondence, the topological Euler number of the crepant resolution is 4, which equals thenumber of conjugacy classes of the alternating group A4 . In this talk, we construct a crepant resolution of
A4 /A4 in characteristic 2. By computing its topological Euler number, we obtain a new counterexample tothe analog of McKay correspondence in positive characteristic.
25 三 浦 真 人 (阪Makoto Miura

大)(Osaka Univ.)

多面体の大域連結性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the global connectedness of polytopes

概 要 In this talk, I plan to discuss an approach to determining whether a specific class of polytopes forms

a connected category. The question is closely related to a famous unsolved question, posed by Miles Reid,
which asks whether all smooth Calabi–Yau 3-folds are connected via a sequence of geometric transitions. I
have already reported during MSJ Autumn Meeting 2022 that the category of reflexive or terminal polygons
is connected. Hence, this time, I would like to focus on introducing examples and reporting on the latest
developments aimed at generalizing this result to higher dimensions.

Final: 2023/8/21
代数学

26 佐 藤拓 ( 福 岡 大 理)

Hiroshi Sato

(Fukuoka Univ.)18

Anti-flips of the blow-ups of the projective spaces at torus invariant
points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Anti-flips of the blow-ups of the projective spaces at torus invariant
points概 要 We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the

projective space at torus invariant points in codimension one by anti-flips.
27 大 貫 紘 嵩 (東 大 数 理)

Hirotaka Onuki (Univ. of Tokyo)

混標数の藤田自由性予想について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On Fujita’s freeness conjecture in mixed characteristic

概 要 Fujita’s freeness conjecture predicts that for an ample line bundle L on an n-dimensional smoothprojective variety X over C, the adjoint bundle ωX ⊗ L n+1 is globally generated. This conjecture holds if
L is globally generated, and similar results are known in positive and mixed characteristics. Popa–Schnell
generalized this globally generated case to the relative setting in characteristic zero, and Ejiri showed ananalogous result in positive characteristic. In this talk, we discuss its analog in mixed characteristic.
28 野 間淳 (横浜国大環境情報)

Atsushi Noma (Yokohama Nat. Univ.)

射影多様体の非双有理中心点集合の既約成分の個数の上限 · · · · · · · · · · · 10

The number of the irreducible components of the locus of nonbirational
projection centers

概 要 We work over an algebraically closed field of characteristic zero. For a nondegenerate projective

variety X ⊆ PN , the locus of points from which X is projected nonbirationally onto its image, is called theSegre locus of X. The purpose here is to give an upper bound of the number of the irreducible componentsof the Segre locus of a projective variety in terms of its invariants.

9 月 22 日（金）第 II 会場

9:15〜11:30
29 ツァンシンイー (お茶の水女大理)

Sin Yi Tsang (Ochanomizu Univ.)

A generalization of Ito’s theorem to skew braces · · · · · · · · · · · · · · · · · · · 15
A generalization of Ito’s theorem to skew braces

概 要 The famous theorem of Ito in group theory states that a group which is the product of two abeliansubgroups is metabelian. We are able to generalize this to the setting of skew braces. In this talk, we shallfirst give a brief introduction of skew braces; they are algebraic objects introduced to study solutions to thequantum Yang–Baxter equation. We shall then explain the basic terminology needed in order to state ourmain theorem.
30 𠮷 野 聖 人 (広 島 工 大 情 報)
Kiyoto Yoshino(Hiroshima Inst. of Tech.)

The Lemmens–Seidel conjecture for base size 5 · · · · · · · · · · · · · · · · · · · · 15
The Lemmens–Seidel conjecture for base size 5

概 要 In 1973, Lemmens and Seidel raised the so-called Lemmens–Seidel conjecture, and proved it for basesize 6. In order to prove it, we need to show it for base sizes 3, 4 and 5. In 2020, Lin and Yu proved theconjecture for base size 3 with a computer, and claimed to prove it for base size 5. However, there is a gap.
In 2022, Cao, Koolen, Lin and Yu proved the conjecture for base sizes 3 and 4 without a computer. In thistalk, I show the conjecture for base size 5.

Final: 2023/8/21
19

代数学

31 渡 邉 英 也 (阪 公 大 数 学 研)

Hideya Watanabe (Osaka Metro. Univ.)

局所有限型の ı 標準基底の安定性について · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the stability of ıcanonical bases of locally finite type

概 要 We prove the stability conjecture of ıcanonical bases, which was raised by Huanchen Bao and Weiqiang

Wang in 2016, for all locally finite types. To this end, we characterize the trivial module over the ıquantum
groups of such type at q = ∞. This result can be seen as a very restrictive version of the ıcrystal basetheory of locally finite type.
32 渡 邉 英 也 (阪 公 大 数 学 研)

Hideya Watanabe (Osaka Metro. Univ.)

量子対称対の表現論から得られる一般線形群から斜交群への分岐則 · · · · 10

A branching rule from GL2n (C) to Sp2n (C) arising from the representation theory of quantum symmetric pairs

概 要 We provide a new branching rule from the general linear group GL2n (C) to the symplectic group

Sp2n (C) by establishing an easy algorithm which gives rise to a bijection from the set of semistandard
tableaux of a fixed shape to a disjoint union of several copies of the set of symplectic tableaux of various
shapes. It arises from the representation theory of the quantum symmetric pair of type AII2n−1 , which is aq-analogue of the classical symmetric pair (gl2n (C), sp2n (C)).
33 青 木 利 隆 (神戸大人間発達環境)
E. G. Escolar (神戸大人間発達環境)
多 田 駿 介 (神戸大人間発達環境)
Toshitaka Aoki (Kobe Univ.)
Emerson Gaw Escolar (Kobe Univ.)
Shunsuke Tada (Kobe Univ.)

On interval global dimension of posets: a characterization of case 0 · · 15

On interval global dimension of posets: a characterization of case 0

概 要 In topological data analysis, the persistence diagram captures the births and deaths of the topologicalfeatures of data in a filtration. Algebraically, this can be understood using interval decompositions ofrepresentations of a finite totally ordered set (or a Dynkin quiver of type A) as guaranteed by Gabriel’s
theorem. In general, representations of a finite poset are not necessarily interval decomposable. In this work,
we study the relative homological algebra of posets with respect to the intervals. We introduce our recent
research exploring the properties of the supports of interval approximations and interval resolution global
dimension. We also provide necessary and sufficient conditions on a poset to ensure that any representation
is interval decomposable (interval resolution global dimension 0).
34 行 田 康 晃 (東 大 数 理)

Yasuaki Gyoda (Univ. of Tokyo)

GLS 道代数の台 τ 傾加群と有限型ルート系の c クラスターの全単射対応· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bijection between support τ -tilting modules of GLS path algebra andc-clusters in finite root system

概 要 In 2006, Ingalls–Thomas discovered a bijective correspondence that preserves the graph structure

between support tilting modules in representation-finite path algebras and c-clusters in simply-laced finite
root systems. In this presentation, we extend path algebras to GLS path algebras, and report on theconstruction of a bijective correspondence that preserves the directed graph structure between support
τ -tilting modules in GLS algebras and c-clusters in finite root systems that are not necessarily simply-laced.
35 小 境 雄 太 (東 京 理 大 理)
小 塩 遼 太 郎 ( 東 京 理 大 理)

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

台 τ 傾加群の誘導・制限について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the induction/restriction of support τ -tilting modules

概 要 Let k be an algebraically closed field of characteristic p > 0, G a finite group and N a normal subgroupof G. We discuss induced kG-modules from support τ -tilting kN -modules and restricted kN -modules fromsupport τ -tilting kG-modules.

Final: 2023/8/21
代数学

20

36 谷 本 龍 二 (静 岡 大 教 育) ♭ Representations of the additive group into Heisenberg groups in positive
characteristic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Ryuji Tanimoto (Shizuoka Univ.)

Representations of the additive group into Heisenberg groups in positive
characteristic

概 要 Let k be an algebraically closed field of positive characteristic p and let Ga denote the additive groupof k. It is a natural problem to classify representations of Ga . In this talk, we describe representations of
Ga into Heisenberg groups. So, we can describe modular representations of elementary abelian p-groups
into Heisenberg groups.
11:30〜12:00

代数学分科会総会

14:15〜16:15
37 若 尾 亮 太 (岡 山 理 大 理)

Ryota Wakao (Okayama Univ. of Sci.)

低次元スーパー・ホップ代数の積分について · · · · · · · · · · · · · · · · · · · · · · · 10

On integrals in low-dimensional Hopf superalgebras

概 要 Integrals in finite-dimensional Hopf superalgebras also have an application to the theory of low-dimensional topologies. In this talk, we begin with the definition of an integral in a Hopf superalgebra andgive a concrete description of integrals in Hopf superalgebras of low dimension. Moreover, we determine its
unimodularity.
38 Wenda Fang

( 京 大 数 理 研)

Wenda Fang

(Kyoto Univ.)

A new scheme of integrability via vertex algebra · · · · · · · · · · · · · · · · · · · 15
A new scheme of integrability via vertex algebra

概 要 It is well-known that the affine Kac–Moody vertex algebra at the critical level has a large center called

the Feigin–Frenkel center. Also, Victor Kac and his collaborators showed that Poisson vertex algebra plays
an important role in studying infinite-dimensional Hamiltonian systems. In this talk, we define the classicalR-matrix of Lie conformal algebra. By using the Feigin–Frenkel center and the classical R-matrix we givea new integrability scheme.
39 荒 川 知 幸 (京 大 数 理 研)
Xuanzhong Dai (京 大 数 理 研)

Tomoyuki Arakawa (Kyoto Univ.)
Xuanzhong Dai (Kyoto Univ.)

Quasi-lisse vertex algebras and chiral differential operators · · · · · · · · · · 15
Quasi-lisse vertex algebras and chiral differential operators

概 要 It is known that the global chiral differential operators (CDO) on any smooth affine variety is quasi-

lisse as its associated scheme is canonically isomorphic to the cotangent bundle. We will consider global
CDO on the quasi-affine variety G/N , where G is a special linear group and N is its maximal unipotent
subgroup. We will state a conjecture that describes the relations between associated variety of the global
CDO and the affine closure of cotangent bundle of G/N , and verify the lower dimensional cases by free fieldrealizations.
40 降 旗駿 ( 京 大 数 理 研)

Shun Furihata(Kyoto Univ.)

On the Beem–Nair conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Beem–Nair conjecture

概 要 For a simple linear algebraic group G, the chiral universal centralizer IG,k is a vertex operator algebra,

which is the chiralization of the universal centralizer ZG of G. Beem and Nair conjectured that an open
symplectic immersion from KTG , the cover of the Kostant–Toda lattice associated with G, to ZG gives rise
to a free field realization of the chiral universal centralizer at the critical level. We construct a free fieldrealization of IG,k at any level, which coincides with the one conjectured by Beem and Nair at the criticallevel.

Final: 2023/8/21
21

代数学

41 A. Kontrec
Ana Kontrec( 京 大 数 理 研)
(Kyoto Univ.)

Zesting the minimal models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Zesting the minimal models

概 要 Zesting is a category-theoretical method for constructing new modular tensor category (MTC) struc-tures out of existing ones. It has been used to provide categorification of certain fusion rule algebras andminimal modular extensions of super-modular categories, but it has never been studied in the context ofvertex operator algebras. In a joint work with A. Mejia, J. Plavnik and A. Ros Camacho, our aim is tounderstand what VOA structure can be reconstructed after zesting the associated modular tensor categories.
We establish a certain decomposition result which we will use to find a description of the genus of associatedVOAs.
42 宮 本 雅 彦 (筑 波 大 数 学)
Masahiko Miyamoto(Univ. of Tsukuba)

Rationality of holomorphic vertex operator algebras · · · · · · · · · · · · · · · · 10
Rationality of holomorphic vertex operator algebras

概 要 In this talk, we prove the rationality of holomorphic vertex operator algebra, that is, if V is aholomorphic vertex operator algebra of CFT-type and V has a positive definite invariant bilinear form, thenall N-gradable V-modules are direct sums of copies of V.
43 宮 本 雅 彦 (筑 波 大 数 学)
Masahiko Miyamoto(Univ. of Tsukuba)

Borcherds’ Lie algebra and C2 -cofiniteness of moonshine VOAs · · · · · · 15
Borcherds’ Lie algebra and C2 -cofiniteness of moonshine VOAs

概 要 The classification of holomorphic vertex operator algebra of central charge 24 was almost done except

for vertex operator algebras of moonshine type. So the remaining problem is to prove the uniqueness ofvertex operator algebra of moonshine type. In this talk, by using Borcherds’ Lie algebra, we will show that
if V is a vertex operator algebra of central charge 24 and its character is J(z) = j(z) − 744, then V isC2 -cofinite.
16:30〜17:30

特別講演
柴 田 大 樹 ( 岡 山 理 大 理)

スーパー代数群の表現論

Taiki Shibata (Okayama Univ. of Sci.)

Representations of algebraic supergroups

概 要 The representation theory of algebraic supergroups over a field of positive characteristic has applica-

tions to non-super modular representations, making it more than just a generalization and quite interesting.
However, compared to the non-super case, the behavior of super root systems is quite special, and that’s
why the representation theory does not always proceed in parallel. In this talk, we will begin with thedefinition of algebraic supergroups, explain what is already known, and what is yet to be understood (orwhere difficulties lie).

Final: 2023/8/21
代数学

9 月 23 日（土）9:15〜10:45
44 板 場 綾 子 (東京理大教養教育)

Ayako Itaba (Tokyo Univ. of Sci.)

22

第 II 会場

非可換射影平面と Type S’ に対する 3 次元 quantum polynomial algebraの Beilinson 多元環 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Quantum projective planes and Beilinson algebras of 3-dimensional quantum polynomial algebras for Type S’

概 要 Let A = A(E, σ) be a 3-dimensional quantum polynomial algebra where E is P2 or a cubic divisorin P2 , and σ ∈ Autk E. In this talk, we prove that, for a Type S’ algebra A, the following conditions areequivalent; (1) The quantum projective plane Projnc A is finite over its center. (2) The Beilinson algebra∇A of A is 2-representation tame. (3) The isomorphism classes of simple 2-regular modules over ∇A are
parametrized by P2 . This result holds for a Type S algebra by I. Mori.
45 松 野 仁 樹 (東京理大教養教育)
斎 藤 由 宇 (静岡大総合技研)

Masaki Matsuno (Tokyo Univ. of Sci.)(Shizuoka Univ.)
Yu Saito

S 型の 3 次元 3 次 Artin–Schelter 正則環の分類について · · · · · · · · · · · · · 15
Classification of 3-dimensional cubic Artin–Schelter regular algebras ofType S

概 要 In noncommutative algebraic geometry, classification of Artin–Schelter regular (AS-regular) algebras

is one of the main interests. Artin–Tate–Van den Bergh found a nice one-to-one correspondence between
the set of 3-dimensional AS-regular algebras and the set of regular geometric pairs (E, σ) where E is ascheme and σ is an automorphism of E. From the point of view, we introduce the notion of geometricalgebra A(E, σ) which plays an important role to classify 3-dimensional AS-regular algebras. In this talk,we give all possible defining relations of 3-dimensional cubic AS-regular algebras of Type S.
46 塚 本 真 由 (山 口 大 創 成)
足 立 崇 英 (山口大国際総合)

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

混合階層化代数の構成 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A construction of mixed stratified algebras

概 要 Dlab and Ringel gave a realization of quasi-hereditary algebras as an endomorphism algebra of a

projective generator of the smallest extension-closed subcategory containing a standardizable set. Ágoston,
Dlab and Lukács introduced the notion of stratified algebras of type s (mixed stratified algebras), which is a
generalization of quasi-hereditary algebras. In this talk, we construct stratified algebras of type s following
Dlab–Ringel’s method.
47 大 竹 優 也 (名 大 多 元 数 理)
Yuya Otake(Nagoya Univ.)

剰余体のシジジーに関連する Ext 加群 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Ext modules related to syzygies of the residue field

概 要 We investigate when a given module can be embedded in a module of finite projective dimension,and as an application, we examine the behavior of Ext modules related to the residue field over local
rings. In particular, we observe that the n-torsionfreeness of syzygies of the residue field characterizes theGorensteinness of the local ring.
48 木 村 海 渡 (名 大 多 元 数 理)
Kaito Kimura (Nagoya Univ.)

正規環上の Ext 加群の消滅と Auslander–Reiten 予想 · · · · · · · · · · · · · · · · 15

Vanishing of Ext modules and Auslander–Reiten conjecture over normalrings

概 要 Characterizing the projectivity of a module in terms of vanishing of Ext modules has been actively

studied in ring theory. One of the most celebrated long-standing conjectures is the Auslander–Reiten
conjecture. In this talk, sufficient conditions for finitely generated modules over a ring satisfying Serre’s
condition (S2 ) to be projective are given in terms of vanishing of Ext modules. Applying those results, weconsider the Auslander–Reiten conjecture over normal rings.

Final: 2023/8/21
23

代数学

11:00〜12:00

特別講演
榎 本 悠 久 ( 阪 公 大 理)Haruhisa Enomoto(Osaka Metro. Univ.)

アーベル圏の部分圏のいくつかのクラスについて

On some classes of subcategories of abelian categories

概 要 In the study of abelian categories, particularly in the representation theory of algebras, one topic ofinterest is the examination of subcategories within a given abelian category that satisfy specific conditions.
For instance, Serre subcategories are subcategories closed under taking subobjects, quotients, and extensions.
In this presentation, we will explore various conditions such as closure under taking images, kernels, cokernels,
and others. We will provide a classification of these types of subcategories, and establish non-trivial
combinatorial relationships between them.
14:15〜17:00
49 小 野 舞 子(岡山理大教育推進機構)
S. Nasseh(Georgia Southern Univ.)
吉 野 雄 二 (岡山大環境生命)

Maiko Ono (Okayama Univ. of Sci.)
Saeed Nasseh (Georgia Southern Univ.)
Yuji Yoshino (Okayama Univ.)

DG 加群の素朴持ち上げの障害類について · · · · · · · · · · · · · · · · · · · · · · · · · 15

On a obstruction class to naive liftability

概 要 Let R be a commutative ring, A → B be a homomorphism of commutative DG R-algebras such thatthe underlying graded A-module B is free. Under the situation, a semi-free right DG B-module N is said
to be naively liftable to A if the DG B-module epimorphism πN : N ⊗A B → N defined by πN (n ⊗ b) = nb
splits. In my talk, we explain the existence of an obstruction to naive liftability of a semi-free right DG
B-module N as a certain homology class in Ext1B (N, N ⊗B J), where J is a diagonal ideal. In particular,
we give an explicit description of a DG B-homomorphism ∆N : N → N ⊗B J(−1) whose homology class[∆N ] is the obstruction to naive liftability. Moreover, we show that ∆ N is given by a “connection” which
was introduced by A. Connes in non-commutative differential geometry.
50 吉 田 健 一 (日 大 文 理)
奥 間 智 弘 ( 山 形 大 理)
渡 辺 敬 一(日大文理・明大研究・知財)

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

Gorenstein normal tangent cones · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Gorenstein normal tangent cones

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

The graded ring defined by all integral closures of powers of an ideal I of A is called the normal tangent
cone of I = IZ . We give a criterion for Gorensteinness of normal tangent cones in terms of the cycle Z.
51 遠 藤 直 樹 (明 大 政 治 経 済)
Naoki Endo

(Meiji Univ.)

Graded ideals whose quotient rings are Gorenstein · · · · · · · · · · · · · · · · · 15
Graded ideals whose quotient rings are Gorenstein

概 要 We investigate a naive question of how many non-principal ideals whose residue class rings are

Gorenstein exist in a given Gorenstein ring. The main result provides that the number of such graded ideals
in a symmetric numerical semigroup ring R over a field coincides with the conductor of the semigroup. We
furthermore provide a complete list of non-principal graded ideals I in R whose quotient rings R/I are
Gorenstein.

Final: 2023/8/21
代数学

52 大 関 一 秀 (日 大 文 理)
Kazuho Ozeki(Nihon Univ.)

24

第 1 オイラー標数と随伴次数環の深さについて · · · · · · · · · · · · · · · · · · · · · 15

The first Euler characteristic and the depth of associated graded rings

概 要 The homological property of the associated graded ring of an ideal is an important problem incommutative algebra. In this talk, we explore the structure of the associated graded ring of m-primary
ideals in a Cohen–Macaulay local ring (A, m), in the case where the first Euler characteristic attains almost
minimal value.
53 松 下 光 虹 (阪 大 情 報)
Koji Matsushita (Osaka Univ.)

Ehrhart 環の nearly Gorenstein 性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nearly Gorensteinness of Ehrhart rings

概 要 In this talk, we discuss nearly Gorensteinness of Ehrhart rings arising from lattice polytopes. We

give necessary conditions and sufficient conditions on lattice polytopes for their Ehrhart rings to be nearly
Gorenstein. Moreover, we determine the structure of (0, 1)-polytopes whose Ehrhart rings are standard
graded and nearly Gorenstein.
54 宮 下空 ( 阪 大 情 報)

Sora Miyashita (Osaka Univ.)

余次元の低い射影的単項曲線の nearly Gorenstein 性について · · · · · · · · 15

Nearly Gorenstein projective monomial curves of small codimension

概 要 We characterize nearly Gorenstein projective monomial curves of codimension 1, 2 or 3.

55 宮 崎 充 弘 (京 都 教 育 大)
Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)

The flaw of the h-vector of a standard graded Cohen–Macaulay domain
may be arbitrarily deep · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The flaw of the h-vector of a standard graded Cohen–Macaulay domain
may be arbitrarily deep概 要 In 1989, Hibi conjectured that the h-vectors of Cohen–Macaulay standard graded domains over a field

are flawless. The h-vector (h0 , h1 , . . . , hs ), hs ̸= 0 of a Cohen–Macaulay standard graded algebra is flawless
if hi ≤ hs−i for 0 ≤ i ≤ ⌊s/2⌋ and hi−1 ≤ hi for 1 ≤ i ≤ ⌊s/2⌋. Niesi and Robbiano disproved this conjecture
by constructing a Cohen–Macaulay standard graded domain whose h-vector is (1, 3, 5, 4, 4, 1). Further, Hibi
and Tsuchiya showed that the Ehrhart rings of the stable set polytopes of cycle graphs of length 9 and 11
have non-flawless h-vectors by computation. Moreover, we showed that the Ehrhart ring of the stable set
polytope of any odd cycle graph with length at least 9 has non-flawless h-vector by proving the conjectureof Hibi and Tsuchiya.
However, these examples have slightest flaws, i.e., there exists i with 0 ≤ i ≤ ⌊s/2⌋ and hi = hs−i + 1. In
this talk, we show that for a given number, there is a standard graded Cohen–Macaulay domain which havethe h-vector with a flaw deeper than the given number.
56 柳 川 浩 二 (関西大システム理工)任鑫 (関西大システム理工)

Kohji Yanagawa (Kansai Univ.)(Kansai Univ.)
Xin RenGröbner bases of radical Li–Li type ideals associated with partitions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Gröbner bases of radical Li–Li type ideals associated with partitions

概 要 For a partition λ of n, the Specht ideal Iλ ⊂ K[x1 , . . . , xn ] is the ideal generated by all Specht

polynomials of shape λ. In their unpublished manuscript, Haiman and Woo showed that Iλ is a radical
ideal, and gave its universal Gröbner basis (Murai et al. published a quick proof of this result). On theother hand, an old paper of Li and Li studied analogous ideals. In this talk, we introduce a class of ideals
generalizing both Specht ideals and Li–Li ideals (of special type), and show their radicalness and give theirGröbner bases. However the universality of our Gröbner bases is an open problem.

Final: 2023/8/21
25

代数学

57 神 戸 祐 太 (三 菱 電 機)

Yuta Kambe (Mitsubishi Electric Corp.)

Signature 理論を通じた Gröbner 基底計算と Gröbner 退化の解析 · · · · · 15
Analysis of the computation of Gröbner bases and Gröbner degenerations via theory of signatures

概 要 The Buchberger algorithm, which is the basis of Gröbner basis calculations, repeatedly divides the

S-polynomial obtained by canceling the leading terms. One problem with this operation is that the result orprocess of the division has unpredictable behavior. To solve this problem, it is essential to construct a theory
that accurately represents the mathematical structure of each computation instance. In this presentation, I
will describe the relationship between syzygies and Gröbner basis calculus using the signature theory, which
has been formulated in recent years, and explain the results obtained from this relationship.

Final: 2023/8/21
幾何学

幾 何
9 月 20 日（水）26

学第 I 会場

9:30〜11:45
1 青 木 侑 省 (名足 立 俊 明 (名

工

大)

工

大)

Yusei Aoki (Nagoya Inst. of Tech.)Toshiaki Adachi (Nagoya Inst. of Tech.)

複素空間形上の軌道と A 型実超曲面上の軌道 · · · · · · · · · · · · · · · · · · · · · · 15

Trajectories on nonflat complex space forms and those on their real
hypersurfaces of type (A)概 要 We study the condition that trajectories for Sasakian magnetic fields on real hypersurfaces of type (A)are seen as those for Kähler magnetic fields. We show that how many congruency classes of non-geodesic
trajectories on a real hypersurface correspond to a given congruency classes of trajectories for a Kählermagnetic field.
2 藤 原 尚 俊 ( 東 京 理 大 理)

Naotoshi Fujihara (Tokyo Univ. of Sci.)

Warped product 多様体上の平均曲率流のグラフ保存性及び時間大域的存在 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Graph-preserving property and long-time existence of mean curvature
flows on warped product manifolds

概 要 We investigate mean curvature flows on warped product manifolds defined by open intervals and closed

Riemannian manifolds. We consider the geodesic graphs on the warped product manifolds and assume thatthe warping functions on the intervals are monotonic and convex. In this talk, we prove the preservation ofgraphs under the mean curvature flow and the long-time existence of the flow.
3 清 原 悠 貴 (北大理)Hirotaka Kiyohara (Hokkaido Univ.)

3 次元ハイゼンベルグ群の極小 null scroll の構成 · · · · · · · · · · · · · · · · · · · · 15
Construction of minimal null scrolls in the three-dimensional Heisenberg
group

概 要 Non-vertical timelike minimal surfaces in the three-dimensional Heisenberg group equipped with someleft invariant Lorentzian metric can be represented by a quadratic form which is an analogy of the Hopf
differential and the support function which denotes the angle between a certain normal vector field and theReeb vector field of Heisenberg group. In this presentation, we show that a timelike minimal surface witha special quadratic form can be represented as one which is a generalization of ruled surfaces, and such
surfaces can be constructed by an elementary method.
4 笹 原 優 大 ( 都 立 大 理)

Yuta Sasahara (Tokyo Metro. Univ.)

擬球面内の非等質な OT-FKM 型等径超曲面 · · · · · · · · · · · · · · · · · · · · · · · 15

Inhomogeneous isoparametric hypersurfaces of OT-FKM-type in thepseudo-sphere

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

Riemannian space forms, especially in the pseudo-sphere Ss2l−1 . A connected submanifold L of Ss2l−1 ishomogeneous if a Lie subgroup of the isometry group of Ss2l−1 acts on L transitively. In this talk, we showthat (connected) isoparametric hypersurfaces of OT-FKM-type and each connected component of its focal
variety in Ss2l−1 are inhomogeneous if the signature (m, r) of its Clifford system satisfies m ≡ 0 (mod 4) andr ≡ 0 (mod 2).

Final: 2023/8/21
27

幾何学

5 松 本

洵 ( 東 工 大 理)

Jun Matsumoto (Tokyo Tech)

3 次元アファイン空間内の全曲率の小さい完備非固有アファイン波面の分類と新しい例 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The classification of complete improper affine fronts of low total curvature in affine three space R3 and new examples

概 要 We describe a classification of complete improper affine fronts in unimodular affine three-space whose

total curvature is greater than or equal to −8π. We also describe the asymptotic behavior of complete
embedded ends of improper affine fronts and give new examples with embedded ends.
6 森 本 真 弘 ( 都 立 大 理)
Masahiro Morimoto(Tokyo Metro. Univ.)

ヒルベルト空間への極作用における例外軌道の非存在 · · · · · · · · · · · · · · · 15

Non-existence of exceptional orbits under polar actions on Hilbert spaces

概 要 In this talk, we show that any polar action on a separable Hilbert space by a connected Hilbert Liegroup does not have exceptional orbits. This generalizes a result of Berndt, Console and Olmos in the caseof finite dimensional Euclidean spaces. Using this result, we give an alternative proof of the fact that any
hyperpolar action on a simply connected compact Riemannian symmetric space by a connected Lie groupdoes not have exceptional orbits.
7 米 原 修 平 (阪大理)Shuhei Yonehara (Osaka Univ.)

一般化された接触多様体の部分多様体について · · · · · · · · · · · · · · · · · · · · · 15

On submanifolds of generalized contact manifolds

概 要 The notion of generalized complex structures, which was introduced by Hitchin and Gualtieri, isa geometric framework on even-dimensional manifolds which encompass both complex and symplectic
structures. Then it is natural to study an odd-dimensional analogue of generalized complex structures.
There are several approaches to this problem. In this talk, we adopt the definition and notation ofgeneralized contact structures by Sekiya. This concept has two typical cases: almost contact structures andcontact structures. Ben-Bassat and Boyarchenko defined a notion of suitable submanifolds of generalized
complex manifolds, which is called generalized complex submanifolds. In this talk, we introduce an odddimensional analogue of this concept, namely, generalized contact submanifolds of generalized contact
manifolds, and investigate its nature.
14:15〜16:15
8 溝 口 史 華 ( 阪 公 大 理)
田 丸 博 士 ( 阪 公 大 理)

Fumika Mizoguchi (Osaka Metro. Univ.)
Hiroshi Tamaru (Osaka Metro. Univ.)

Nilpotent Lie algebras obtained by quivers and Ricci solitons · · · · · · · · 15
Nilpotent Lie algebras obtained by quivers and Ricci solitons

概 要 Nilpotent Lie groups with left-invariant metrics provide non-trivial examples of Ricci solitons. A

quiver is a directed graph where loops and multiple arrows between two vertices are allowed. In this talk,
we introduce a new method for obtaining nilpotent Lie algebras from finite quivers without cycles. For
all of these Lie algebras, we prove that the corresponding simply connected nilpotent Lie groups admit
left-invariant Ricci solitons. This constructs a large family of examples of Ricci soliton nilmanifolds with
arbitrarily high nilpotency steps.

Final: 2023/8/21
幾何学

9 張

頁 (沖縄科学技術大)

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

28

The h-logconcavity breaking by the Dirichlet heat flow on the Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The h-logconcavity breaking by the Dirichlet heat flow on the Heisenberg group

概 要 Considering the nonnegative and bounded solution of the heat equation ∂t u − ∆u = 0 on Ω × (0, +∞)with Dirichlet boundary condition u|∂Ω = 0 and initial data u(·, 0) = ϕ, it is well-known that logconcavity
is preserved by the Dirichlet heat flow on Euclidean spaces. That is, if ϕ is logconcave, then so does u(·, t)
for every t > 0. We will show in this talk that due to the non-triviality of the cut-locus, the heat kernel on
the Heisenberg group fails to be h-quasiconcave. As a result, we can show that for every t > 0, we can finda h-logconcave function ϕ such that u(·, t) fails to be h-quasiconcave.
10 田 崎 博 之(都立大理・筑波大数理物質)
田 中 真 紀 子 (東京理大創域理工)
Hiroyuki Tasaki(Tokyo Metro. Univ./Univ. of Tsukuba)
Makiko Sumi Tanaka(Tokyo Univ. of Sci.)

古典型コンパクト対称空間の極大対蹠集合 III · · · · · · · · · · · · · · · · · · · · · · 15

Maximal antipodal sets of classical compact symmetric spaces III

概 要 In previous MSJ meetings we gave the classification of maximal antipodal sets of some classicalcompact symmetric spaces. This talk is a continuation of the previous talk. We give the classification of
maximal antipodal sets of U II(n) = U (2n)/Sp(n), AI(n) = SU (n)/SO(n), AII(n) = SU (2n)/Sp(n) andtheir quotient spaces.
11 大 仁 田 義 裕(早大理工・阪公大数学研)
Jong Taek Cho (Chonnam Nat. Univ.)
橋 本
要(大和大理工・阪公大数学研)
Yoshihiro Ohnita(Waseda Univ./Osaka Metro. Univ.)
Jong Taek Cho (Chonnam Nat. Univ.)
Kaname Hashimoto(Yamato Univ./Osaka Metro. Univ.)

全複素部分多様体と R-空間 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Totally complex submanifolds and R-spaces

概 要 We study totally complex submanifolds immersed in a quaternionic projective space and related

minimal submanifolds in its quaternionic Kaehler geometry. In this talk our main result is the constructionof a (non Levi–Civita) canonical connection on the inverse image of a totally complex submanifold underthe Hopf fibration over a quaternionic projective space such that the parallelism of the second fundamental
form of the inverse image with relative to our canonical connection is equivalent to the parallelism of thesecond fundamental form of a totally complex submanifold. From this result we obtain that the inverse
image of a totally complex submanifold with parallel second fundamental form is obtained as a certain
R-space associated with a quaternionic Kaehler symmetric pair.

Final: 2023/8/21
29

幾何学

12 古 賀勇(産業数理研 Calc・広島大理)
長 友 康 行 ( 明 大 理 工)
Isami Koga
(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Yasuyuki Nagatomo (Meiji Univ.)

複素射影空間から四元数射影空間への同変調和写像 · · · · · · · · · · · · · · · · · 15

Equivariant harmonic maps of the complex projective spaces into thequaternion projective space

概 要 In this talk we would like to introduce the classification result of Equivariant harmonic maps of thecomplex projective space into the quaternion projective space. To classify them, we use the gauge theoretic
approach.
13 篠 田 裕 佑 (岡 山 大 自 然)
近 藤
慶 ( 岡 山 大 理)

Yusuke Shinoda (Okayama Univ.)
Kei Kondo (Okayama Univ.)

フィンスラー多様体上の等長変換群がリー群であることの測地線論的別証明 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Another proof of the Myers–Steenrod theorem for Finsler manifolds
from geodesic theory

概 要 In 1939 S. B. Myers and N. E. Steenrod proved that the group of isometries of a Riemannian manifold

is a Lie transformation group. In this talk we will give another proof of the Myers–Steenrod theorem for
Finsler manifolds from geodesic theory inspired by Myers–Steenrod.
16:30〜17:30

特別講演

B. Doubrov(Belarusian State Univ.)

Extrinsic nilpotent differential geometry and linear PDEs of finite type

Boris Doubrov (Belarusian State Univ.)

Extrinsic nilpotent differential geometry and linear PDEs of finite type

概 要 The goal of this talk is to extend the principles of nilpotent differential geometry developed by

N. Tanaka and T. Morimoto to the geometry of submanifolds in filtered homogeneous spaces. Namely, we
study filtration preserving embeddings of filtered manifolds into flag varieties, Flag(V, ϕ) or, more generally,
into filtered homogeneous spaces L/L0 ⊂ Flag(V, ϕ). It turns out that the category of such embeddings isequivalent to the category of special linear finite type PDEs modelled by the L-module V . This generalizes
a well-known correspondence between non-degenerate curves in P n and linear scalar ODEs of order n + 1.
Formalizing the notion of normalization conditions, we prove the existence of a normal “moving frame” forosculating embeddings with constant symbol. This solves the local equivalence problem of filtration preserving embeddings and allows to describe their fundamental invariants in terms of Lie algebra cohomology.
Finally, we apply these results to study symbol preserving deformations of rational homogeneous varieties,
where these cohomology spaces can be effectively computed.

9 月 21 日（木）第 I 会場

9:40〜11:30
14 泉

宏 明 (広島

大)Hiroaki Izumi (Hiroshima Univ.)

ミクロ・マクロの新しい力学系 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

New micro-macro dynamical systems

概 要 If macroscopic phenomena were derived from microscopic laws, it would be a dream come true for

economists, physicists, biologists, and others. In this talk, I will present “New Micro-Macro Dynamical
Systems” and “Fundamental Theorem of Micro-Macro”. Through this, the mathematical structures of“phase transition”, “synchronization”, and “circadian rhythm” proposed by Hiroaki Izumi can be understoodin a unified manner. We can say that we are one step closer to realizing our dreams.

Final: 2023/8/21
幾何学

15 前 田 陽 一 (東 海 大 理)
岡 田 浩 一
大⋆)
一 松
信 (京
(Tokai Univ.)
Yoichi Maeda
Koichi Okada
Sin Hitotumatu (Kyoto Univ.⋆)30

重心を中心とする円と, 垂心を中心とする円 ―外接円, 九点円, 重垂円と根軸の, 球面上での統一的把握― · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Circles centered at centroid and orthocenter

概 要 For an acute triangle, we consider a circle CG centered at the centroid G. Then, the inversion of thecircumscribed circle CO with respect to CG is the nine-point circle CN . In addition, let CGH be the circle
with segment GH (H is the orthocenter) as a diameter, and lA be the radical axis of CO and CN . Then,the inversion of CGH with respect to CG is lA . Further, we consider a circle CH centered at the orthocenter
H. If we take the stereographic projection from the plane containing the triangle to a sphere with CH as
an equator, then, the five images of CGH , CN , CG , CO , and lA are symmetrical and parallel small circles on
the sphere.
16 前 田 陽 一 (東 海 大 理)
岸 根
誠 ( 洛 星 中 高)(Tokai Univ.)
Yoichi Maeda
Makoto Kishine(St.Viator Rakusei Junior and Senior High School)

観るものと観られるものの双対性 ―楕円が円に見える視点の軌跡― · · · 10

Locus of viewpoints from which a conic appears circular

概 要 We know that circular shapes we encounter in daily life may appear to be elliptical from some viewing

points. It is reasonable to expect that an ellipse may appear to be circular from certain viewpoints. We
investigate the locus of viewpoints from which an ellipse appears circular. The locus of viewpoints is a
hyperbola passing through the two foci of the ellipse. Conversely, the locus of viewpoints from which a
hyperbola looks circular is an ellipse passing through the two foci of the hyperbola. Further, the locus ofviewpoints from which a parabola looks circular is itself a parabola, passing through the focus of the original
parabola. There is a simple duality between the object to be observed and the observer.
17 鹿 俣 尚 志 (東 京 理 大 理)
佐 古 彰 史 ( 東 京 理 大 理)
Naoyuki Kanomata(Tokyo Univ. of Sci.)
Akifumi Sako (Tokyo Univ. of Sci.)

有限 Φ3 -Φ4 ハイブリッド行列模型の厳密解と摂動計算 · · · · · · · · · · · · · · · 15

Exact solutions and perturbative calculations of finite Φ3 -Φ4 hybridmatrix-model

概 要 We construct a one-matrix model (Φ3 -Φ4 Hybrid-Matrix-Model) with multiple potentials, which is

a combination of a 3-point interaction and a 4-point interaction, where the 3-point interaction of Φ 3 ismultiplied by some positive definite diagonal matrix M . This model is solvable due to the effect of this M .
First, we construct Feynman rules for Φ3 -Φ4 Hybrid-Matrix-Model and calculate perturbative expansionsof some multipoint functions in ordinary methods. Second, we calculate the path integral of the partition
function Z[J] and use the result to compute exact solutions for 1-point function G|a| with 1-boundary,
2-point function G|ab| with 1-boundary, 2-point function G|a|b| with 2-boundaries, and n-point function
G|a1 |a2 |···|an | with n-boundaries. They include contributions from Feynman diagrams corresponding to
nonplanar Feynman diagrams or higher genus surfaces.

Final: 2023/8/21
31

幾何学

18 佐 々 木 東 容 (学 習 院 大 理)

Dounnu Sasaki (Gakushuin Univ.)

Counting subgroups and subset currents · · · · · · · · · · · · · · · · · · · · · · · · · · 15Counting subgroups and subset currents

概 要 Given a closed hyperbolic surface S of genus g, Mirzakhani proved that the number of closed geodesics

of length at most L and of a given type is asymptotic to cL6g−6 for some c > 0. Since a closed geodesic
is corresponding to a conjugacy class of the fundamental group G of S, as a generalization, we consider
the counting problem of conjugacy classes of finitely generated subgroups of G. In this context, insteadof measuring the length of a closed geodesic, we use “half the sum of the lengths of the boundaries of theconvex cores of a subgroup”. We find that the number of conjugacy classes is also asymptotic to cL6g−6
for some c > 0. Moreover, we observe that this particular length associated with a subgroup has a natural
significance from the perspective of subset currents.
19 佐 藤 健 治 (玉 川 大 工)
Kenzi Satô (Tamagawa Univ.)

双曲単体の重心と Minkowski 空間の Minkowski の定理 · · · · · · · · · · · · · · 15

Centroids of hyperbolic simplices and Minkowski theorem on Minkowski
spaces

概 要 The equation defining a kind of centroids of hyperbolic simplices is derived by Minkowski theorem on

Minkowski spaces.
11:40〜12:00

2023 年度日本数学会幾何学賞受賞者発表

9 月 22 日（金）第 I 会場

9:30〜11:45
20 秦 泉 寺 雅 夫 (岡 山 大 自 然)

Masao Jinzenji (Okayama Univ.)

Geometrical proof of generalized mirror transformation of projective
hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Geometrical proof of generalized mirror transformation of projective
hypersurfaces

概 要 In this talk, we outline a geometrical proof of the generalized mirror transformation of genus 0

Gromov–Witten invariants of degree k hypersurface in CP N −1 .
21 澤 井洋 ( 沼 津 工 高 専)

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

Non-Vaisman LCK structures on a solvmanifold constructed by a 2-stepnilpotent Lie group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Non-Vaisman LCK structures on a solvmanifold constructed by a 2-stepnilpotent Lie group

概 要 Inoue surface S + is a solvmanifold, and it has a non-Vaisman locally conformal Kähler structure. In

this talk, we consider a non-Vaisman locally conformal Kähler structure on a solvmanifold constructed bya one-dimensional extension of a nilmanifold. Concretely, we prove that, if a solvmanifold constructed bya one-dimensional extension of a 2-step nilmanifold has a non-Vaisman locally conformal Kähler structure,then it is 4-dimensional and Inoue surface S + .
22 中 村聡 ( 東 工 大 理)

Satoshi Nakamura (Tokyo Tech)Calabi type functionals for coupled Kähler–Einstein metrics · · · · · · · · · 15
Calabi type functionals for coupled Kähler–Einstein metrics

概 要 We introduce the coupled Ricci–Calabi functional and the coupled H-functional which measure how far

from a coupled Kähler–Einstein metric in the sense of Hultgren–Witt Nyström. We first give corresponding
moment weight type inequalities which estimate each functional in terms of algebraic invariants. Secondly,
we give corresponding Hessian formulas for these functionals at each critical point, which have an application
to a Matsushima type obstruction theorem for the existence of a coupled Kähler–Einstein metric.

Final: 2023/8/21
幾何学

23 長 谷 川 和 志 (金沢大人間社会)(Univ. of Hamburg)
V. Cortés

Kazuyuki Hasegawa (Kanazawa Univ.)
Vicente Cortés (Univ. of Hamburg)

32

The H/Q-correspondence and a generalization of the supergravity c-map· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The H/Q-correspondence and a generalization of the supergravity c-map

概 要 Given a hypercomplex manifold M with a rotating vector field and additional data, we constructa conical hypercomplex manifold M̂ of dim M̂ = dim M + 4 with H∗ (:= H\{0})-action and show thatM̄ := M̂ /H∗ possesses a quaternionic structure. As a consequence, we associate the quaternionic manifold
M̄ to the hypercomplex manifold M of the same dimension. This is a generalization of the HK/QKcorrespondence. We call this construction M̄ from M the H/Q-correspondence. We can apply the H/Qcorrespondence to a hypercomplex Hopf manifold which does not admit any hyperKähler structure. A
compact Lie group SU(3) with the left invariant hypercomplex structure can be also applied to the H/Qcorrespondence.
24 村 上怜 ( 東 北 大 理)

Rei Murakami (Tohoku Univ.)

ファイバー空間上の J-方程式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

J-equations on fiber spaces

概 要 Finding a canonical metric is a central topic in complex differential geometry. The constant scalar

curvature Kaehler metric (cscK metric, for short) is one class of canonical metrics. Dervan–Sektnan
proved that a total space of a holomorphic submersion admits a cscK metric if its fibers and base space
admit (twisted) cscK metrics. On the other hand, the J-equation was discovered by X. X. Chen and
S. K. Donaldson and has appeared in various contexts. One such context is that the solvability of the
J-equation implies the existence of a cscK metric under some conditions. In this talk, we prove that theresult of Dervan–Sektnan’s type also holds for the J-equation.
25 宮 武 夏 雄 (東北大MathCCS)

Natsuo Miyatake (Tohoku Univ.)

巡回 Higgs 束の Hermitian-Einstein 方程式の劣調和関数を用いた拡張とその解のアプリオリ評価について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Generalization of the Hermitian-Einstein equation for cyclic Higgs bundles using subharmonic functions and a priori estimates of the solutions
to the equation

概 要 We derive a priori estimates for the solution to the generalization of the Hermitian-Einstein equation

for cyclic Higgs bundles which is defined by using subharmonic functions.
26 青 井 顕 宏 (和 歌 山 工 高 専)
Takahiro Aoi(Nat. Inst. of Tech., Wakayama Coll.)

A conical approximation of constant scalar curvature Kähler metrics ofPoincaré type and log K-semistability · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A conical approximation of constant scalar curvature Kähler metrics ofPoincaré type and log K-semistability

概 要 The existence of constant scalar curvature Kähler (cscK) metrics is a fundamental problem in complex

geometry. In this talk, we consider cscK metrics with some singularities along a smooth divisor. Guenancia
shows that a Kähler–Einstein metric of Poincaré type can be approximated by the sequence of Kähler–
Einstein metrics with cone singuarities. If there is no nontrivial holomorphic vector field, we can show ananalogue of this Guenancia’s result for cscK metrics. As a corollary, we can show log K-semistability with
angle 0. This corollary is related to two conjectures of J. Sun–S. Sun and Székelyhidi.

Final: 2023/8/21
33

幾何学

14:15〜16:15
27 濱 中 翔 太(三菱電機先端技術総合研)
Shota Hamanaka(Mitsubishi Electric Corp. Adv. Tech. R&D Center)

共形類内での全スカラー曲率の上からのバウンドの保存性について · · · · 15

Upper bound preservation of the total scalar curvature in a conformalclass

概 要 We show that in a conformal class on a closed manifold, if its Yamabe constant is nonpositive, thetotal scalar curvature upper bound is preserved under the C 0 -convergence of metric tensors. Moreover, we
also show that in a conformal class on a closed manifold whose Yamabe constant is positive, the total scalar
curvature upper bound is preserved under the C 0 -convergence of metric tensors providing that those scalar
curvatures are uniformly bounded from below.
28 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Myers-type theorems via m-Bakry–Émery Ricci curvatures of quadratic
decays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Myers-type theorems via m-Bakry–Émery Ricci curvatures of quadratic
decays概 要 Inspired by a recent work due to B.Y. Wu (Internat. J. Math. 32 (2021), 2150048), we establish

several Myers-type theorems by assuming some quadratic decays of the m-Bakry–Émery Ricci curvaturewhen m is a positive constant, a negative constant, or infinity. Moreover, in a spirit of V. Boju and L.
Funar (Z. Anal. Anwendungen 15 (1996), 275–278), we generalize them by assuming some weaker decaysof the m-Bakry–Émery Ricci curvature when m is a positive constant, a negative constant, or infinity. Our
results not only generalize the Myers-type theorem by B.Y. Wu (Internat. J. Math. 32 (2021), 2150048)
and L.F. Wang (Kodai Math. J. 37 (2014), 187–195), but also are new even the m-Bakry–Émery Ricci
curvature is reduced to the Ricci curvature.
29 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Myers-type theorems via m-Bakry–Émery Ricci curvatures of quartic
decays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Myers-type theorems via m-Bakry–Émery Ricci curvatures of quartic
decays概 要 We establish several Myers-type theorems for n-dimensional complete Riemannian manifolds assumingsome quartic decays of the m-Bakry–Émery and m-modified Bakry–Émery Ricci curvatures with m ∈(−∞, 1] ∪ [n, +∞] in terms of the distance function from a fixed point.
30 髙 橋 淳 也 (東 北 大 情 報)
(Univ. de Nantes)
C. Anné

断面曲率が下に有界な場合の Hodge–Laplacian の小さい固有値 · · · · · · · 15

Junya Takahashi (Tohoku Univ.)
Colette Anné (Univ. de Nantes)

Small eigenvalues of the Hodge–Laplacian with sectional curvature bounded
below

概 要 For each degree p and each natural number k ≥ 1, we construct a one parameter family of Riemannian

metrics on any connected oriented closed manifold with volume one and sectional curvature bounded below
such that the k-th positive eigenvalue of the Hodge–Laplacian acting on differential p-forms converge tozero. This is a generalization of our previous results in 2022.

Final: 2023/8/21
幾何学

31 山 口 夏 穂 里 (立 命 館 大 理 工)
野 澤
啓 ( 立 命 館 大 理 工)

Kaori Yamaguchi (Ritsumeikan Univ.)
Hiraku Nozawa (Ritsumeikan Univ.)

34

On statistics which are almost sufficient from the viewpoint of the Fisher
metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On statistics which are almost sufficient from the viewpoint of the Fisher
metrics

概 要 We introduce a quantitatively weak version of sufficient statistics such that the Fisher metric of

the induced parametrized measure model is bi-Lipschitz equivalent to the Fisher metric of the originalmodel. We characterize such statistics in terms of the conditional probability or by the existence of acertain decomposition of the density function in a way similar to characterizations of due to Ay–Jost–Lê–
Schwachhöfer and Fisher–Neyman for sufficient statistics.
32 藤 谷 恭 明 (阪大理)Yasuaki Fujitani (Osaka Univ.)

Aronson–Bénilan gradient estimates for porous medium equations underlower bounds of N -weighted Ricci curvature with N < 0 · · · · · · · · · · · · 15
Aronson–Bénilan gradient estimates for porous medium equations underlower bounds of N -weighted Ricci curvature with N < 0

概 要 As a counterpart to the Li–Yau gradient estimate for the heat equation, the Aronson–Bénilan gradientestimate for the porous medium equation has been studied. In this talk, we show the Aronson–Bénilan
gradient estimate for the porous medium equation on weighted Riemannian manifolds under lower bounds of
N -weighted Ricci curvature with ε-range for some N < 0. This generalizes those estimates under constantlower bounds of N -weighted Ricci curvature with N ∈ [n, ∞).
16:30〜17:30

特別講演
河 井 公 大 朗 (BIMSA・阪市大理)

Kotaro Kawai(BIMSA / Osaka City Univ.)

例外型ホロノミー群をもつ多様体およびその部分多様体のミラー

Manifolds with exceptional holonomy and mirrors of their submanifolds

概 要 The existence of manifolds with exceptional holonomy was implied by the Berger’s classification of

Riemannian holonomy groups, and it was later confirmed that they actually existed. In addition, there is a
special parallel differential form on them, which is a calibration, and we can define calibrated submanifolds.
Manifolds with exceptional holonomy are considered to be analogous to the Calabi–Yau manifolds, and
it is also considered that a higher-dimensional analogue of gauge theory might be established. Fromthese viewpoints, the introduction of enumerative invariants and mirror symmetry for these manifolds are
expected. In fact, what is considered as a mirror of a calibrated submanifold is defined.
In this talk, after introducing these outlines, I would like to explain the properties of the mirror of acalibrated submanifold, such as the similarities to calibrated submanifolds and gauge-theoretic objects.

9 月 23 日（土）第 I 会場

9:30〜10:45
33 高 津 飛 鳥 (都 立 大 理) ♭ 星状集合と capacitary 問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15石 毛 和 弘 ( 東 大 数 理)
(Univ. di Firenze)
P. Salani

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

Riemannian starshape and capacitary problems

概 要 I first define the notion of starshaped set in Riemanian manifold. Then I consider capacitary problems

in Riemannian manifolds. I show that every level set of the capacitary potential of a starshaped ring in arotationally symmetric domain is starshaped. This talk is based on joint work with Kazuhiro Ishige andPaolo Salani.

Final: 2023/8/21
35

幾何学

34 高 津 飛 鳥 (都 立 大 理) ♭ Sliced Monge–Kantorovich 距離の幾何学的性質 · · · · · · · · · · · · · · · · · · · · 15北 川
潤(Michigan State Univ.)

Asuka Takatsu (Tokyo Metro. Univ.)
Jun Kitagawa (Michigan State Univ.)

On geometric properties of sliced Monge–Kantorovich metrics

概 要 A sliced Monge–Kantorovich metric is a metric on the space of probability measures over the Euclidean

space.This is a variant of the Monge–Kantorovich metric and two special case are originally proposed as away to use 1D transport to speed up computation of the usual Monge–Kantorovich metrics. In this talk, I
explain some geometric properties of sliced Monge–Kantorovich metrics. This talk is based on joint workwith Jun Kitagawa.
大理)
35 藤 岡 禎 司 (阪
(
福
岡
大
理)
三 石 史 人波大⋆)山 口 孝 男 (筑Tadashi Fujioka (Osaka Univ.)
Ayato Mitsuishi (Fukuoka Univ.)
Takao Yamaguchi (Univ. of Tsukuba⋆)

Alexandrov 空間の定量的 Lipschitz ホモトピー収束 · · · · · · · · · · · · · · · · · 15

Quantitative Lipschitz homotopy convergence of Alexandrov spaces

概 要 We obtain a quantitative version of the Lipschitz homotopy convergence of Alexandrov spaces in-troduced by Mitsuishi–Yamaguchi (2019). They proved that if two compact Alexandrov spaces of thesame dimension are close enough in the Gromov–Hausdorff distance, then they are Lipschitz homotopy
equivalent. We improve this result by showing that the Lipschitz constant can be chosen to depend only on
the dimension, lower bounds on curvature and volume, and an upper bound on diameter, and the time ofhomotopy can be chosen to be the Gromov–Hausdorff distance.
36 藤 岡 禎 司 (阪大理)Tadashi Fujioka (Osaka Univ.)崩壊する Alexandrov 空間の Euler 標数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Euler characteristics of collapsing Alexandrov spaces

概 要 We give an explicit formula for the Euler characteristic of a collapsing Alexandrov space in terms of

those of the strata of the limit Alexandrov space and of the fibers over the strata. This was conjectured by
Alesker (2018).
11:00〜12:00

特別講演
数 川 大 輔 ( 九 大 数 理)

Daisuke Kazukawa (Kyushu Univ.)

測度の集中現象に基づいた測度距離空間の収束理論

Convergence theory of metric measure spaces based on the concentrationof measure phenomenon

概 要 In recent years, convergence theory of Riemannian manifolds and metric measure spaces has been

actively studied. Gromov introduced a distance function, called the observable distance, on the set of
isomorphism classes of metric measure spaces and developed his distinctive theory. The observable distanceinduces a very characteristic topology, called the concentration topology, based on the concentration of
measure phenomenon due to Lévy and Milman. The concentration topology is effective to capture thehigh-dimensional aspects of spaces. In this talk, I would like to present recent developments in convergence
theory with respect to the concentration topology. This talk will focus on three topics: Examples ofsequences that converge as the dimension diverges to infinity, Continuity of invariants of metric measurespaces, Geometry of the space of metric measure spaces.

Final: 2023/8/21
函数論

函 数
9 月 20 日（水）36

論
第 V 会場

9:30〜11:30
1 米 田 力 生 (金沢大人間社会)

Rikio Yoneda (Kanazawa Univ.)

ハーディー空間とベルグマン空間の間の合成作用素 · · · · · · · · · · · · · · · · · 15

Composition operators between the Hardy space H p and the Bergman
spaces Lqa

概 要 We study Cφ between H p and Lqa , between the Besov type space Bp,p−1 and Lqa . Using the main

results, we can prove the following : If 0 < q ≤ p, then Cφ : H p → Lqa is bounded, while there is no symbol
φ such that it is bounded below.
2 下
菱
西
山

村
川
尾
田

勝
洋
昌
雅

孝 ( 茨 城 大 理)
介 ( 岐 阜 大 教 育)
治 ( 中 部 大 理 工)
博 ( 岐 阜 大 教 育)

Katsunori Shimomura (Ibaraki Univ.)Yôsuke Hishikawa (Gifu Univ.)
Masaharu Nishio (Chubu Univ.)
Masahiro Yamada (Gifu Univ.)

A remark on the dual spaces of bi-parabolic Bergman spaces · · · · · · · · 15

A remark on the dual spaces of bi-parabolic Bergman spaces

概 要 In this note, we give a remark on the dual spaces of bi-parabolic Bergman spaces, where the bi-

parabolic Bergman spaces are spaces of all integrable solutions of bi-parabolic equation (∂t + (−∆)α )2 u = 0
for 0 < α ≤ 1 on the upper half space.
3 四 之 宮 佳 彦 ( 静 岡 大 教 育)

Yoshihiko Shinomiya (Shizuoka Univ.)

Period matrices of L-shapes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Period matrices of L-shapes

概 要 A period matrix Π of a curve X of genus g is a g × g matrix defined by the pairing of a symplectic

basis of H1 (X, Z) and a basis of Ω(X). L-shape is a curve of genus 2 constructed from a polygon whose
form is L. We give a formula for period matrices of L-shapes with some symmetry. The period matrices aredescribed by a Euclidean length parameter of the polygon.
4 中 村

豪 ( 愛 知 工 大 工)

Gou Nakamura (Aichi Inst. of Tech.)

種数 3 の向き付け不可能な極値的曲面に対する複素ダブルのワイエルシュ
トラス点について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weierstrass points of the complex double for non-orientable extremal
surfaces of genus 3

概 要 In this talk we give the Weierstrass points of the complex doubles for non-orientable extremal surfacesof genus 3. As an application, we construct a canonical polygon for the complex double and consider it as
an element of Teichüller space. We also calculate the distance between the marked complex double and amarked extremal Riemann surface of genus 2.
5 松 田

凌 (京

Ryo Matsuda

大理)(Kyoto Univ.)

Maximal cusps are not dense · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Maximal cusps are not dense

概 要 It is known that the Bers boundary of a finite-dimensional Teichmüller space has only a cusp andtotally degenerate. McMullen has also shown that the set of all maximal cusps is dense in the Bers boundary.
In this talk, we first show that a new type of degenerate called the David-quasiconformal b group, exists
when Riemann surfaces satisfy the lower condition. Using this result, I will prove that the maximal cusps
are not dense if the Riemann surface has at least two non-planar ends and satisfies the Shiga condition.

Final: 2023/8/2137

函数論

6 志 賀 啓 成 ( 京 都 産 大 理)

Hiroshige Shiga (Kyoto Sangyo Univ.)

Quasicircles and Dirichlet finite harmonic functions on Riemann surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Quasicircles and Dirichlet finite harmonic functions on Riemann surfaces

概 要 A Jordan curve in C is called a quasicircle if it is the image of the unit circle by a quasiconformal self-

mapping of the complex plane. While a lot of characterizations of quasicircles are known, we are interested
in the characterization by an extendability condition on Dirichlet finite harmonic functions. Recently,
Schippers and Staubach (2020) consider quasicircles on compact Riemann surfaces and characterize thecircles by the extendability condition. In this talk, we present a generalization of their result.
7 志 賀 啓 成 ( 京 都 産 大 理)

Hiroshige Shiga (Kyoto Sangyo Univ.)

Uniform domains and generalized Cantor sets · · · · · · · · · · · · · · · · · · · · · · 15
Uniform domains and generalized Cantor sets

概 要 We consider a generalized Cantor set E(ω) for an infinite sequence ω = (qn )∞n=1 of positive numberswith 0 < qn < 1, and examine the quasiconformal geometry of the Cantor set E(ω). We may give anecessary and sufficient condition for the complement of E(ω) to be a uniform domain in terms of ω.
14:15〜15:15
Generalized Mandelbrot sets by zk+1 = (zkm + c)n · · · · · · · · · · · · · · · · · · 15

8 堀 口 俊 二

Generalized Mandelbrot sets by zk+1 = (zkm + c)n

Shunji Horiguchi

概 要 We find how to make a general recurrence formula from the recurrence formulas of Wasan (Japanesenative mathematics developed in Japan in the Edo era (1603–1868:national isolation)). Using this method,
we derive a general Mandelbrot recurrence formula. This shows originality of Wasan. We lead four types ofgeneral Mandelbrot recurrence formulas. Next, we show that these become the same generalized Mandelbrot
set and connected and closed set.
9 八 木 拓 己 ( 京 大 人 間 環 境)

Connectedness and hyperbolicity of perturbations of semi-parabolic Hénonmaps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

(Kyoto Univ.)

Connectedness and hyperbolicity of perturbations of semi-parabolic Hénonmaps

Takumi Yagi

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

where δ > 0 is a small number. Suppose that Ha,t has a fixed point qa,t ∈ C2 , depending continuously ona and t, with one eigenvalue λt such that λt → λ0 = exp(2πip/r), (p, r) ∈ Z × N as t → 0. Let λt /λ0 be
expressed by exp(Lt + iθt ) and suppose θt → 0 as t → 0. We see that Ha,t is hyperbolic if θt = O(Lt ) andLt ̸= 0. By hyperbolicity of Ha,t for t ̸= 0, we obtain that the Julia set Ja,t of Ha,t is connected for t ̸= 0.
Without using hyperbolicity, we prove that Ja,t is connected if θt2 = o(Lt ). Moreover, we prove that there
is a family {λt } of one eigenvalues with θt2 ≍ |Lt | such that Ja,t is disconnected for t ̸= 0 and r = 1.
10 奥 山 裕 介 (京都工繊大基盤)

Yûsuke Okuyama (Kyoto Inst. Tech.)

A local a priori bound for endomorphisms of the projective spaces · · · · 15
A local a priori bound for endomorphisms of the projective spaces

概 要 We will discuss about a local a priori bound of a rational function or a holomorphic endomorphismof (algebraic) degree more than 1 on the complex projective space and the (Berkoivch) projective line
under some assumption on the mass of the equilibrium measure on the boundary of Fatou components. In
complex setting, this assumption would be conjecturely always the case and, in one complex variable case, isrelated to the non-existence problem on a lake of Wada Fatou components and to the Abikoff theorem-type
problem.

Final: 2023/8/21
函数論

11 綾 野 孝 則 (阪 公 大 数 学 研)

Takanori Ayano (Osaka Metro. Univ.)38

種数 2 の超楕円積分の逆問題の解の間の差 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Difference between the solutions for the inversion problem of the hyperelliptic integrals of genus 2

概 要 Let V be a curve of genus 2 defined by y 2 = f (x), where f (x) is a polynomial with degree 5, and σ bethe sigma function of V . We consider the inversion problem of the integral of the holomorphic one forms
on V . Grant expressed the x-coordinate of V in terms of a function F which is defined by the ratio of thederivatives of σ. Matsutani expressed the x-coordinate of V in terms of a function G which is defined by
the logarithmic derivatives of σ. Since F and G coincide on the zero set of σ, it is expected that F − G canbe divided by σ. We decompose F − G into the product of σ and a meromorphic function explicitly.
15:35〜16:35

特別講演
瀬 戸 道 生 (防衛大総合教育)

Michio Seto
(Nat. Defense Acad. of Japan)

正則性 vs 正定値性

Holomorphic functions vs positive definite matrices

概 要 In complex analysis, the Schwarz–Pick inequality is elementary, and it is often mentioned as an

exercise topic that the inequality is equivalent to the solvability of some two point interpolation problem inthe open unit disk. Generally, for n points, such problem is called Pick interpolation problem. It might
be unexpected for complex analysts that Pick interpolation problem is fundamental in functional analysis.
In fact, functional analysis brought by Pick interpolation problem has been very developed by a number ofpeople. In this talk, I would like to give an introductory survey on the progress in this research field.

9 月 21 日（木）第 V 会場

9:30〜11:30
12 杉 山俊 ( 北 九 州 工 高 専)

Shun Sugiyama(Nat. Inst. of Tech., Kitakyushu Coll.)

局所的に中間的 Cousin-I 条件を満たす領域 · · · · · · · · · · · · · · · · · · · · · · · · 15

An open set satisfying a local intermediate Cousin-I condition in a complex space

概 要 Let D be an open set in a pure n-dimensional complex space X, q an integer such that 1 ≤ q ≤ n andS(X) the set of singular points in X. In this talk, we prove the following two theorems: If D is exhausted
by open sets {Dν } such that H q (Dν ∩ U, O) → H q (Dν ∩ U, M) is injective for every ν ∈ N and for every
relatively compact Stein open set U , then D is locally q-complete with corners at every point x ∈ ∂D \ S(X).
If D has a continuous boundary and H q (D ∩ U, O) → H q (D ∩ U, M) is injective for every relatively compact
Stein open set U , then D is locally q-complete with corners at every point x ∈ ∂D \ S(X).
13 鍋 島 克 輔 (東 京 理 大 理)潟
大⋆)田 島 慎 一 (新Katsusuke Nabeshima(Tokyo Univ. of Sci.)
Shinichi Tajima (Niigata Univ.⋆)

A new look at Yano–Kato method for computing s-parametric annihilators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A new look at Yano–Kato method for computing s-parametric annihilators

概 要 Local b-functions and s-parametric annihilators associated to hypersurfaces with an isolated singularity

are considered. A new computational methods of s-parametric annihilators are introduced. The underlying
ideas of the proposed methods are adopting T. Yano method and modern computer algebra techniques.
The resulting methods do not require non-commutative Groebner bases computation. It is shown that,for the case of semi-weighted homogeneous hypersurface singularities, Yano–Kato method for computing
s-parametric annihilators can also be realized as an algorithm. As an application, a new effective method is
obtained for computing local b-functions associated to semi-weighted homogeneous hypersurface singularities.
The results of benchmark test are also given.

Final: 2023/8/21
39

函数論

潟
大⋆)
14 田 島 慎 一 (新鍋 島 克 輔 ( 東 京 理 大 理)

多項式函数の tame 性の判定 —包括的グレブナー基底系の利用— · · · · · 15

Shinichi Tajima (Niigata Univ.⋆)
Katsusuke Nabeshima(Tokyo Univ. of Sci.)

Testing tameness of a complex polynomial map via comprehensive Gröbner
systems

概 要 The tameness of a complex polynomial function is considered in the context of symbolic computation.

The method due to S. A. Broughton for testing tameness is realized as an algorithm via comprehensiveGröbner systems.
15 田 中 仁 一 朗 (阪 公 大 理)

Jinichiro Tanaka (Osaka Metro. Univ.)

Bochner–Martinelli 核の複素可換 Lie 群への一般化について · · · · · · · · · · 15
Generalizations of the Bochner–Martinelli kernel to complex abelian Liegroups

概 要 This talk is on constructions of solutions of ∂-equations for given differential forms with compact

support. In previous research, a solution of such a ∂-equation on Cn was given by using the Bochner–
Martinelli kernel. We generalize the argument on Cn to complex abelian Lie groups. In the last half,
we construct the integral kernel on some complex abelian Lie groups and confirm the vanishing of thecohomology of some toroidal group under some condition which comes from Dynamics.
16 小 川 智 史 (阪 公 大 理)

Satoshi Ogawa (Osaka Metro. Univ.)

コンパクト複素曲線近傍の完全線形化とユニタリ平坦束のブルーノ的条件· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Full linearization along a compact complex curve and Brjuno like condition of unitary flat line bundles

概 要 Linearization of horizontal and transverse transitions on a neighborhood of a compact complex

manifold is full linearization. X. Gong and L. Stolovitch gave a sufficient condition for full linearization byfocusing on estimates of operator norms of a Čech coboundary map with L2 norm. In this research, wegive an explicit criterion for full linearization along a compact complex curve embedded holomorphically in
a complex surface. We obtain Brjuno-like condition of unitary flat line bundles as a result.
17 足 立 真 訓 (静 岡 大 理)
S. Biard(Univ. Polytechnique Hauts-de-France)
J. Brinkschulte ( Univ. Leipzig )Masanori Adachi (Shizuoka Univ.)Séverine Biard(Univ. Polytechnique Hauts-de-France)
Judith Brinkschulte (Univ. Leipzig)

有理型接続の留数定理と葉層の安定集合への応用 · · · · · · · · · · · · · · · · · · · 15

A residue formula for meromorphic connections and applications to stable sets of foliations

概 要 We discuss residue formulae that localize the first Chern class of a line bundle to the singular locus

of a given holomorphic connection. As an application, we explain a proof for Brunella’s conjecture about
exceptional minimal sets of codimension one holomorphic foliations with ample normal bundle and for anonexistence theorem of Levi flat hypersurfaces with transversely affine Levi foliation in compact Kähler
surfaces.

Final: 2023/8/21
函数論

18 大 沢 健 夫 (名40大⋆) ♭ On the Levi problem under the negativity of canonical bundles on theboundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Takeo Ohsawa (Nagoya Univ.⋆)

On the Levi problem under the negativity of canonical bundles on theboundary

概 要 A theorem asserting the existence of nonconstant holomorphic functions on certain bounded domains

in Kähler manifolds will be improved by removing the Kählerness assumption. Related results of Takayama
on the holomorphic embeddability and holomorphic convexity of pseudoconvex manifolds will be extended
by weakening the curvature conditions.
13:00〜14:00

特別講演
丸 亀 泰 二 (電通大情報理工)

Taiji Marugame(Univ. of Electro-Comm.)

Hyperkähler ambient metrics associated with twistor CR manifolds
Hyperkähler ambient metrics associated with twistor CR manifolds

概 要 The ambient metric, introduced by Fefferman, is a Ricci-flat Kähler metric associated with CR

manifolds embedded in a complex manifold. It is defined on (a fractional power of) the canonical bundleof the complex manifold with the zero section removed, and gives a powerful tool to construct invariantsof CR manifolds. In this talk, we consider the ambient metric for a special class of CR manifolds, namely
the twistor CR manifolds, introduced by LeBrun. A twistor CR manifold is a Lorentzian (neutral) CR
5-manifold defined as a sphere bundle over a 3-dimensional conformal manifold. In the flat case, it appears
in Penrose’s twistor theory as the set of light rays (null twistors) in the Minkowski spacetime. Anotherconstruction of LeBrun shows that in the real analytic case the base conformal 3-manifold can be realized
as the conformal infinity of an anti self-dual Einstein metric. We prove that the twistor CR manifold canbe embedded to the twistor space of this metric and construct the ambient metric as a neutral hyperkähler
metric defined on the total space of the spinor bundle with the zero section removed.

Final: 2023/8/2141

函数方程式論函 数

方9 月 20 日（水）

程

式

論

第 IX 会場

9:00〜12:00
1 根 上

春 (千葉大融合理工)

Haru Negami(Chiba Univ.)

組紐群の表現の構成法の拡張と KZ 方程式のミドルコンボリューション
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Katz–Long–Moody construction of braid group representations and multiplicative middle convolution of KZ equation

概 要 The Long–Moody construction is a technique to obtain representations of braid groups, introduced

by Long and Moody. Through this method, various braid group representations can be constructed. In
this talk, we will introduce the Katz–Long–Moody construction, which is an extension of the Long–Moody
construction. Additionally, we will show that the representation of pure braid group obtained through KLMconstruction is isomorphic to Haraoka’s middle convolution, a method to gain a monodromy representationof KZ-type equations, which is a Pfaffian system of differential equations. Lastly, we will show that theKLM construction preserves unitarity, and so is Haraoka’s middle convolution. This talk includes joint workwith Kazuki Hiroe.
2 廣 惠 一 希 ( 千 葉 大 理)
岡 田 靖 則 ( 千 葉 大 理)澁 澤健 (千葉大融合理工)(Chiba Univ.)
Kazuki Hiroe
Yasunori Okada (Chiba Univ.)
Ken Shibusawa (Chiba Univ.)

クンマー型一般超幾何微分方程式の解空間が満たす隣接関係のある種の拡張について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On an extension of contiguity relations for the solution spaces of theconfluent hypergeometric system of Kummer type

概 要 Kimura, Haraoka, and Takano gave confluent hypergeometric systems and contiguity relations forthe solution spaces. To make differential operators giving those relations, they used eigenvectors in an
eigenspace corresponding to the system. In the talk, we use generalized eigenvectors to give extended
relations.
畿
大⋆)3 青 木 貴 史 (近高 橋 甫 宗 (関西学院大理工)
反 田 美 香 ( 関 西 学 院 大 理)

Takashi Aoki (Kindai Univ.⋆)
Toshinori Takahashi(Kwansei Gakuin Univ.)
Mika Tanda (Kwansei Gakuin Univ.)

超幾何関数と WKB 解の関係 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The relation between the hypergeometric function and WKB solutions

概 要 The Gauss hypergeometric equation with a large parameter is considered from the view point of

the exact WKB analysis. In this talk,we give the linear relation between the solution basis to the Gauss
equation in the neighborhood of the origin, one of which is the Gauss hypergeometric function, and the
Borel sums of the WKB solutions.

Final: 2023/8/21
函数方程式論4 高 橋 甫 宗 (関西学院大理工)
反 田 美 香 ( 関 西 学 院 大 理)
Toshinori Takahashi(Kwansei Gakuin Univ.)
Mika Tanda (Kwansei Gakuin Univ.)

42

Simple pole 型変わり点をもつ超幾何微分方程式の標準的解と WKB 解の関係 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Relation between the standard solutions of the hypergeometric differential equation and WKB solutions with a simple-pole-type turning point

概 要 The Gauss hypergeometric differential equation with a large parameter deformed to a differential

equation with a simple-pole-type turning point at the origin is considered. In this talk, the relations
between the standard solutions of the hypergeometric differential equation in the neighborhood of the origin
and Borel sums of WKB solutions are given.
5 大 内

忠 (上

Sunao Ōuchi

智大⋆)(Sophia Univ.⋆)

Remarks on Cauchy problem in function spaces with asymptotic expansions with respect to time variable t · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Remarks on Cauchy problem in function spaces with asymptotic expansions with respect to time variable t

概 要 We study an initial value problem of a system of nonlinear partial differential equations in (t, x) ∈ Cn+1 .

∂t ui = fi t, x, U, ∇x U

ui (0, x) = ui (x) 1 ≤ i ≤ m

Suppose {fi (t, x, u, p)}mi=1 have asymptotic expansion with respect to t at t = 0. Then there exists formalP∞ee (t, x) at t = 0 by
power series solution U (t, x) =Un (x)tn . We study the asymptotic behavior of U
n=0

using summability theory of asymptotic analysis. A generalization of Cauchy–Kowalevskaja theorem isgiven...
6 石 橋 和 葵 ( 広 島 工 大 工)
Kazuki Ishibashi(Hiroshima Inst. of Tech.)

Nonoscillation of the Mathieu-type half-linear differential equation · · · 10
Nonoscillation of the Mathieu-type half-linear differential equation

概 要 The nonoscillation of Mathieu-type half-linear differential equations was investigated. The particularequation under consideration is an extension of the Mathieu equation, which has been widely applied inmechanical and electrical engineering. The investigation led to the main finding that all nontrivial solutionsof the Mathieu-type half-linear differential equations are nonoscillatory under simple parametric conditions.
Proving the finding requires a simple nonoscillation theorem to compare the two equations.
7 宇 佐 美 広 介 ( 岐 阜 大 工)
媛
大⋆)
内 藤
学 (愛
Hiroyuki Usami (Gifu Univ.)
Manabu Naito (Ehime Univ.⋆)

半分線形常微分方程式の解の漸近挙動について · · · · · · · · · · · · · · · · · · · · · 10

On asymptotic behavior of solutions of half-linear ordinary differential
equations

概 要 We consider the Poincaré–Perron problem for second order half-linear ordinary differential equations.

The classical results concerning Poincaré–Perron problem for linear equations by Hartman–Wintner andmost of recent results for half-linear equations are unified and generalized to our results.
8 吉 野 正 史 ( 広 島 大 理)

Masafumi Yoshino (Hiroshima Univ.)

Summability of transseries solution of Hamiltonian system · · · · · · · · · · 10
Summability of transseries solution of Hamiltonian system

概 要 We construct the transseries solution of a nonintegrable Hamiltonian system via the summability

theory for the partial differential equation. We solve the Hamiltonian system by using the formal transseries
solution and the Borel summability.

Final: 2023/8/2143函数方程式論9 鬼 塚 政 一 ( 岡 山 理 大 理)
Masakazu Onitsuka(Okayama Univ. of Sci.)

Stability regions for discrete diamond-alpha operator · · · · · · · · · · · · · · · 10
Stability regions for discrete diamond-alpha operator

概 要 In this talk, we introduce the imaginary diamond-alpha ellipse and use it to establish the stability

regions for the Lyapunov and Ulam stabilities of a diamond-alpha difference equation.
10 畑
裕 貴
松 永 秀 章 ( 阪 公 大 理)
Yuki Hata
Hideaki Matsunaga(Osaka Metro. Univ.)

2 次元線形微分方程式における時間遅れに依存した漸近安定条件 · · · · · · 10
Delay-dependent stability switches in a delay differential system

概 要 In this study, stability properties of a linear delay differential system x′ (t) = −ax(t − τ ) − by(t),y ′ (t) = −cx(t) − dy(t − τ ) are considered, where a, b, c, and d are real numbers and τ > 0. Some explicit
conditions are presented for the zero solution of the system to be asymptotically stable. The results
demonstrate that delay-dependent stability switches in the system can occur not only when bc < 0 but also
when a > 0, b > 0, c > 0, and d > 0.
11 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

Asymptotic behavior of solution curves of nonlocal one-dimensional elliptic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic behavior of solution curves of nonlocal one-dimensional elliptic equations

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

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

Naoki Hamamoto (Osaka Metro. Univ.)

球体上のソレノイダル場に対するポアンカレ定数 · · · · · · · · · · · · · · · · · · · 10

The Poincaré constant for solenoidal fields on the ball

概 要 We consider the N -dimensional Poincaré inequality with 0-Dirichlet condition:Z

Z|∇u|2 dx ≥ CN
BN

|u|2 dx,BNu|∂BN = 0for vector fields u on the ball BN = x ∈ RN ; |x| ≤ 1 with N ≥ 2. The best value of the constant CN on
the right-hand side is known to be z N −2 when u is unconstrained, where zν denotes the first zero of Bessel
2function of degree ν with zν > 0. The problem is what is the new best value of CN when the solenoidal
condition divu = 0 is assumed. Our result is that CN = zN/2 and it is attained by a class of solenoidal
fields satisfying x · u = 0.
13 安 藤広 ( 茨 城 大 理 工)
城大⋆)
堀 内 利 郎 (茨城大⋆)中 井 英 一 (茨Hiroshi Ando (Ibaraki Univ.)
Toshio Horiuchi (Ibaraki Univ.⋆)
Eiichi Nakai (Ibaraki Univ.⋆)

On the critical Caffarelli–Kohn–Nirenberg type inequalities involving
super-logarithms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the critical Caffarelli–Kohn–Nirenberg type inequalities involving
super-logarithms

概 要 We establish the Caffarelli–Kohn–Nirenberg type inequalities involving super-logarithms (infinitely

iterated logarithms). As a result the critical Caffarelli–Kohn–Nirenberg type inequalities will be improved,
and in certain cases the best constants will be discovered.

Final: 2023/8/21
函数方程式論14 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.)

44

Radial eigenvalues for the p-Laplacian, I. Asymptotic behavior · · · · · · · 10

Radial eigenvalues for the p-Laplacian, I. Asymptotic behavior

概 要 We study the radial eigenvalues of the p-Laplacian in a domain Ω with the Dirichlet boundary

condition, where Ω is a ball or an annulus. For the k-th eigenvalue λk (p, Ω), we study the asymptotic
behavior of λk (p, Ω) as p → 1 + 0 or p → ∞.
15 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.)

Radial eigenvalues for the p-Laplacian, II. Monotonicity · · · · · · · · · · · · · 10

Radial eigenvalues for the p-Laplacian, II. Monotonicity

概 要 We study the radial eigenvalues of the p-Laplacian in a domain Ω with the Dirichlet boundary

condition, where Ω is a ball or an annulus. For the k-th eigenvalue λk (p, Ω), we study the monotonicity ofλk (p, Ω) with respect to p.
14:15〜16:30
16 北 野 修 平 (早 大 理 工)
Shuhei Kitano (Waseda Univ.)

弱いスケール条件下での完全非線形積分方程式に対する Harnack 不等式
及び Hölder 評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Harnack inequalities and Hölder estimates for fully nonlinear integral
equations with weak scaling conditions

概 要 In this talk, we present Harnack inequalities and Hölder estimates for fully nonlinear integral equations

with general scaling condition. Our relaxed condition allows to treat integral kernels of variable order andcritically close to 2. We also demonstrate that the Harnack inequality fails for harmonic functions of thevariable order fractional Laplacian, by constructing a counterexample.
17 田 中 視 英 子 (東 京 理 大 理)
V. Bobkov(Ufa Federal Research Cente)

Mieko Tanaka (Tokyo Univ. of Sci.)
Vladimir Bobkov(Ufa Federal Research Cente)

Multiplicity of solutions for (p, q)-Laplace equations with two parameters · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Multiplicity of solutions for (p, q)-Laplace equations with two parameters

概 要 We consider the (p, q)-Laplace equations with two parameters under the Dirichlet boundary condition,and provide the results on the multiplicity of solutions via Lusternik–Schnirelman method.

Final: 2023/8/2145函数方程式論18 熊 谷 健 太 (東 工 大 理)
Kenta Kumagai (Tokyo Tech)

重み付き半線形楕円型方程式の極解の有界性の分類 · · · · · · · · · · · · · · · · · 10Classification of boundedness of extremal solutions to semilinear elliptic
equations with weighted terms

概 要 We consider the Gelfand problem with the exponential nonlinearity and a radially-symmetric weighted

term 0 < a(|x|) ∈ C 2 (B1 ) in the unit ball. We are interested in the boundedness of extremal solutions.
It is known that the extremal solution is bounded if the dimension N ≤ 9 and is singular if a = 1 andN ≥ 10. We consider the following: when N ≥ 10, does the perturbation of a change the boundedness of
extremal solutions? For any h > 0, we find singular solutions Uh with specific weighted terms ah and study
the stability of the solutions. As a result, we verify that the boundedness of extremal solutions changes
depending only on h. Moreover, we give an optimal classification of the boundedness of extremal solutions
for general a.
19 足 達 慎 二 (静 岡 大 工)
渡 辺 達 也 ( 京 都 産 大 理)
Shinji Adachi (Shizuoka Univ.)
Tatsuya Watanabe(Kyoto Sangyo Univ.)

Sobolev 臨界型の半線形楕円型方程式に対する基底状態解の存在ついて· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Existence of ground state solutions for a class of semilinear elliptic equations involving Sobolev critical term

概 要 In this talk, we are interested in the existence of ground state solutions for a class of semilinear elliptic

equations of Berestycki–Lions’ type with Sobolev critical term. By introducing a new cut-off technique andperforming a detailed asymptotic estimate, we show the existence of a ground state solution for a wideclass of nonlinearities. Our existence result for the case N = 3 covers many important cases such as the
cubic-quintic problem and the doubly critical problem.
20 滝 本 和 広 (広島大先進理工)張彧瀟 (広島大先進理工)

Kazuhiro Takimoto (Hiroshima Univ.)
Yuxiao Zhang (Hiroshima Univ.)

二重冪乗型非線形項をもつ半線形ポアソン方程式の large solution の境界付近における高次漸近展開 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Higher order estimate near the boundary of a large solution to semilinear
Poisson equation with double-power like nonlinearity

概 要 We consider a large solution for the semilinear Poisson equation ∆u = up + φ (u) in a bounded smoothdomain D ⊂ Rn where p > 1 and φ (u) behaves like αuq with q < p. We obtain the precise asymptotic
behavior of a solution u near the boundary ∂D up to the third term.
21 A. Dall’Acqua ( Ulm Univ. )( Leipzig Univ. )M. Müller
岡 部 真 也 ( 東 北 大 理)
吉 澤 研 介 (九 大 I M I )Anna Dall’Acqua (Ulm Univ.)
Marius Müller (Leipzig Univ.)
Shinya Okabe (Tohoku Univ.)
Kensuke Yoshizawa (Kyushu Univ.)

An obstacle problem for the p-elastic energy · · · · · · · · · · · · · · · · · · · · · · · 10

An obstacle problem for the p-elastic energy

概 要 This talk is devoted to an obstacle problem for the p-elastic energy among graph curves with fixed

ends. There are two causes of the loss of regularity of solutions to the obstacle problem: one is ‘degeneracy’of the Euler–Lagrange equation; the other is the presence of the ‘obstacle’. In this talk we address thequestion which is the main cause of the loss of regularity.

Final: 2023/8/21
函数方程式論22 三 浦 達 哉 (東 工 大 理)
( Univ. Leipzig )M. Müller(
Univ. Vienna )F. Rupp
Tatsuya Miura (Tokyo Tech)
Marius Müller (Univ. Leipzig)
Fabian Rupp (Univ. Vienna)

46

Optimal thresholds for preserving embeddedness of elastic flows · · · · · · 10

Optimal thresholds for preserving embeddedness of elastic flows

概 要 We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds

below which elastic flows preserve embeddedness of initial curves for all time.
23 三 浦 達 哉 (東 工 大 理)
大工)
剱 持 智 哉 (名Tatsuya Miura (Tokyo Tech)
Tomoya Kemmochi (Nagoya Univ.)

Migrating elastic flows · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Migrating elastic flows

概 要 Huisken’s problem asks whether there is an elastic flow of closed planar curves that is initiallycontained in the upper half-plane but ‘migrates’ to the lower half-plane at a positive time. Here we consider
variants of Huisken’s problem for open curves under the natural boundary condition, and construct various
migrating elastic flows both analytically and numerically.
24 利 根 川 吉 廣 (東 工 大 理)
スチュバードサルバトーレ( Univ. Milan )Yoshihiro Tonegawa (Tokyo Tech)
Salvatore Stuvard (Univ. Milan)

End-time regularity theorem for Brakke flows · · · · · · · · · · · · · · · · · · · · · · 10

End-time regularity theorem for Brakke flows

概 要 For a general k-dimensional Brakke flow in the n-dimensional Euclidean space locally close to ak-dimensional plane in the sense of measure, it is proved that the flow is represented locally as a smoothgraph over the plane with estimates on all the derivatives up to the end-time.
25 坪 内 俊 太 郎 (東 大 数 理)

Shuntaro Tsubouchi (Univ. of Tokyo)

Gradient continuity for anisotropic singular equations · · · · · · · · · · · · · · 10
Gradient continuity for anisotropic singular equations

概 要 We consider weak solutions to anisotropic singular elliptic or parabolic equations, which involve one-

Laplacian. The aim of this talk is to briefly report recent regularity results, related to continuity of a spatial
gradient.
16:45〜17:45

特別講演
宮 西 吉 久 ( 信 州 大 理)

Layer potential type operator のスペクトル理論とその応用に向けて

Yoshihisa Miyanishi (Shinshu Univ.)

Spectral theory of layer potential type operators and its applications

概 要 Spectral theory of boundary integral operators is discussed. Especially, we consider operators of layer

potential type on boundaries of bounded domains. Then we find some relationships between geometricstructures of boundaries and spectra of canonically defined layer potential type operators. These facts
are applicable to many PDEs. As more concrete examples, the Neumann–Poncaré operators (abbreviatedby NP) are considered as boundary integral operators. We then introduce the details of the NP spectral
properties. We also apply the results for Transmission problems, Dirichlet–Neumann map, partition problem,
etc. as long as time permits.

Final: 2023/8/2147

函数方程式論

9 月 21 日（木）第 IX 会場

9:00〜12:00
26 田 代 紀 一 (東 工 大 理)
Kiichi Tashiro(Tokyo Tech)

フェーズフィールド法による移流項付き平均曲率流の面積変化公式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the area formula for the mean curvature flow with transport term
via phase-field method

概 要 We investigate a mean curvature flow obtained by the Allen–Cahn equation with transport term, andprove that the change in volume of the evolving phase can be expressed in terms of the generalized mean
curvature of the Brakke flow and the transport term. Under suitable assumptions on the initial datum, thisproperty resolves the non-uniqueness of the Brakke flows obtained from this method.
27 南
香 名 (奈良女大人間文化) ♭ n 次元熱方程式の長時間漸近形 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
柳 沢
卓 ( 奈 良 女 大 理)

Kana Minami (Nara Women’s Univ.)
Taku Yanagisawa(Nara Women’s Univ.)

Long-time asymptotic profile of the n-dimensional heat equation

概 要 We construct a long-time asymptotic profile to the initial value problem of the n-dimensional heat

equation. Specifically, we present a modified heat kernel as a long-time asymptotic profile which changes
the mass, the center of mass and the variance of the n-dimensional heat kernel in accordance with themoments of the initial data.
28 草 場 竜 之 介 (早 大 理 工)
小 澤
徹 ( 早 大 理 工)Commutator estimates between the heat semigroup and monomial weights
and its application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ryunosuke Kusaba (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

Commutator estimates between the heat semigroup and monomial weights
and its application

概 要 In this talk, we present a new approach to obtain weighted estimates of global solutions to the semilinear

heat equation with a single power of supercritical Fujita-exponent. Our method is based on direct andexplicit calculations of commutation relations between the heat semigroup and monomial weights, while it isindependent of standard parabolic arguments which rely on the comparison principle or some compactness
arguments.
29 武 内 太 貴 (早 大 理 工)
Taiki Takeuchi (Waseda Univ.)

Breakdown of C ∞ -smoothing effects for the Fujita type equation · · · · · 10
Breakdown of C ∞ -smoothing effects for the Fujita type equation

概 要 The Fujita type equation in the whole space Rn is considered, where the nonlinear terms are given as

the forms ±|u|κ or ±|u|κ−1 u. In particular, we focus on the global mild solutions for small initial data inL(κ−1)n/2 (Rn ) under the conditions 1 + 2/n < κ < ∞ and κ ∈/ N. We show that the global mild solutions
become classical solutions. In addition, by taking special initial data, we also show that the solutions do
not belong to C ∞ -class in space.
30 小 島 瑞 輝 (東 工 大 理)
比 佐 幸 太 郎 ( 東 北 大 理)
Mizuki Kojima (Tokyo Tech)(Tohoku Univ.)
Kotaro Hisa

時間分数階微分をふくむ熱方程式の可解性とその対応方程式への関連について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On solvability of a time-fractional semilinear heat equation, and its
quantitative approach to the classical counterpart

概 要 The global or local-in-time solvability of the typical semilinear heat equation, the Fujita equation fails

under certain critical conditions. However, the problem in which the derivative with respect to time isreplaced by the fractional one is solvable even under such conditions. We study how the solvability of thetime-fractional model quantitatively approaches the unsolvability of the corresponding problem.

Final: 2023/8/21
函数方程式論31 原 田 潤 一 (秋田大教育文化)
Junichi Harada (Akita Univ.)

48

複素数熱方程式における爆発解の漸近挙動について · · · · · · · · · · · · · · · · · 10

Asymptotic behavior of blowup solutions to complex valued semilinear
heat equations for complex time

概 要 We investigate solutions of complex valued semilinear heat equations for complex time. We provide

the asymptotic behavior of blowup solutions from the viewpoint of their blowup rates. Our result agrees
with numerical computations in A. Takayasu–J. p. Lessard–J. Jaquett–H. Okamoto (2022).
32 鈴 木貴 (阪 大 M M D S )石 井 克 幸 ( 神 戸 大 海 事)
Takashi Suzuki (Osaka Univ.)
Katsuyuki Ishii (Kobe Univ.)

放物型方程式の爆発・消滅形状の形成について · · · · · · · · · · · · · · · · · · · · · 5

Formation of blowup and quenching patterns in parabolic equations

概 要 We formulate a quasi-linear parabolic equation to describe blowup and quenching patterns of semilinear

parabolic equations. Methods of functional analysis and viscosity solutions are applied for this equation,
which results in the convergence of the approximate solution and a comparison principle.
33 川 合 聡 志 ( SOLIZE(株) )大 沼 正 樹 ( 徳 島 大 理 工)

Kawai Satoshi (SOLIZE Corp.)
Masaki Ohnuma (Tokushima Univ.)

ある非線形放物型方程式の半連続粘性解に対する強比較原理のための補題· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A lemma for a strong comparison principle of a nonlinear parabolic
equation

概 要 We prove a lemma for a strong copmarison principle of a nonlinear parabolic equation. We show thata subsolution minus a supersolution of an equation becomes a subsolution of another equation that may notcoincide with the original equation.
34 M. Fuest(Leibniz Univ. Hannover)J. Lankeit(Leibniz Univ. Hannover)
水 上 雅 昭 ( 京 都 教 育 大)

Mario Fuest (Leibniz Univ. Hannover)
Johannes Lankeit(Leibniz Univ. Hannover)
Masaaki Mizukami(Kyoto Univ. of Edu.)

Possible points of blow-up in a fully parabolic chemotaxis system withenvironmental dependent logistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Possible points of blow-up in a fully parabolic chemotaxis system withenvironmental dependent logistic source

概 要 This talk discusses the influence of possible spatial inhomogeneities in the coefficients of logistic source

terms in fully parabolic chemotaxis-growth systems in two-dimensional smoothly bounded domains, andshows that finite-time blow-up of the classical solution can only occur in points where the coefficient functionis zero.

Final: 2023/8/2149

函数方程式論35 M. Fuest(Leibniz Univ. Hannover)J. Lankeit(Leibniz Univ. Hannover)
田 中 悠 也 ( 東 京 理 大 理)

Mario Fuest (Leibniz Univ. Hannover)
Johannes Lankeit(Leibniz Univ. Hannover)Yuya Tanaka (Tokyo Univ. of Sci.)

Occurrence of a critical mass phenomenon in a higher dimensional quasilinear Keller–Segel system with indirect signal production · · · · · · · · · · · 10

Occurrence of a critical mass phenomenon in a higher dimensional quasilinear Keller–Segel system with indirect signal production

概 要 This talk deals with a quasilinear Keller–Segel system with indirect signal production. In the two-

dimensional case, a critical mass phenomenon was shown by Tao–Winkler (2017). The purpose of this talkis to obtain a critical mass phenomenon in the higher dimensional cases.
36 勝 呂 剛 志 (阪 公 大 数 学 研) ♭ 移流拡散方程式の初期値問題のアマルガム空間における適切性について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Takeshi Suguro (Osaka Metro. Univ.)

Well-posedness of the Cauchy problem of a drift-diffusion equation in
amalgam spaces

概 要 We consider the Cauchy problem of a drift-diffusion equation on Euclidean space. This equation is

one of the diffusion equations involving a nonlocal drift term given by the Poisson equation. A nonlocal
effect of the Green’s function influences the solution to the problem, and it is interesting how much decaying
we need to impose on the function for the problem to be well-posed. We show that the Cauchy problem of
the drift-diffusion equation is well-posed in amalgam spaces.
37 小 波 津 晶 平 (東 京 理 大 理)
J. Lankeit(Leibniz Univ. Hannover)

Shohei Kohatsu (Tokyo Univ. of Sci.)
Johannes Lankeit(Leibniz Univ. Hannover)Transient growth phenomena in a two-species chemotaxis-competition
model on domains without radial symmetry · · · · · · · · · · · · · · · · · · · · · · · 10
Transient growth phenomena in a two-species chemotaxis-competition
model on domains without radial symmetry

概 要 We deal with a two-species chemotaxis system with Lotka–Volterra type competitive kinetics. For the

one-species chemotaxis-growth system under the radially symmetric setting, it is known that if death rateis small enough, then under some conditions on initial data, there is some time up to which any thresholdof the population density is surpassed, provided that diffusion rate is sufficiently small. The purpose is toshow this transient growth phenomena for the two-species model on domains without radial symmetry.
38 石 井 裕 太 (茨 城 工 高 専)

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

メトリックグラフにおける移流項を持つ Schnakenberg モデルのピーク解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the existence of spiky stationary solutions for the Schnakenberg
model with advection term on the Y -shaped metric graph概 要 In this talk, we consider the existence of one-peak solutions for the Schnakenberg model with advection

term on the Y -shaped compact metric graph. In particular, we show that the location and the amplitudeof a spike is determined by the interaction of the advection term with the geometry of the Y -shaped graph,
represented by the associated Green’s function. Moreover, by considering the Neumann boundary condition
and the Robin boundary condition, it is shown that the location of a spike moves to the junction point or
the boundary point depending on boundary conditions.

Final: 2023/8/21
函数方程式論特別講演
髙 坂 良 史 ( 神 戸 大 海 事)

Willmore 流に対する閾値型近似アルゴリズムについて

Yoshihito Kohsaka (Kobe Univ.)

A threshold-type approximation algorithm for the Willmore flow50

13:00〜14:00

概 要 The motion of evolving surfaces by the Willmore flow is studied in this talk. Let Γ t be an evolving

surface in R3 . Then the Willmore functional is defined asZ
H 2 dS,W[Γt ] =Γtwhere H denotes the mean curvature of Γt and dS is the area measure. The Willmore flow is the L2 -gradient
flow of W[Γt ] and is given by
V = −∆Γt H − 2H(H 2 − K),
where ∆Γt is the Laplace–Beltrami operator on Γt and K is the Gaussian curvature of Γt . We will propose
a threshold-type approximation algorithm for the Willmore flow. This algorithm is constructed based on
an asymptotic expansion of the convolution of the fundamental solution to the 4th order diffusion equation
and an indicator function. A threshold-type approximation algorithm for the gradient flow of the modified
Willmore functional W[Γt ] + λ A[Γt ], where λ ∈ R is a Lagrange multiplier and A[Γt ] is the area of Γt , willbe also discussed.

9 月 22 日（金）第 IX 会場

9:15〜12:00
39 塚 本 悠 暉 (明大研究・知財)Yuki Tsukamoto (Meiji Univ.)

指数型反応拡散近似の極限について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Convergence of the fast reaction limit

概 要 Singular limit problems called the fast reaction limit have been studied extensively when the reaction

terms of each component are the same function in a two-component system. However, fast reaction limits
with different fast reaction terms are still far from being well understood. In this talk, we will consider
the problem where the reaction term is represented by a power term that is different from each other. We
proved that the initial interface does not move and the function converges to a function satisfying the heat
equation for Dirichlet boundary conditions.
40 関坂 (山本) 宏子 (理 化 学 研 A I P)
関 坂 歩 幹 ( 明 大 総 合 数 理)

Hiroko Sekisaka(Yamamoto) (RIKEN)
Ayuki Sekisaka (Meiji Univ.)

非局所反応拡散方程式に対する反応拡散近似 · · · · · · · · · · · · · · · · · · · · · · · 10

Reaction-diffusion approximation of nonlocal reaction-diffusion equation

概 要 Mathematical models involving nonlocal interactions have been proposed in ecology, biology, neuro-science, and so on. In this talk, we will introduce a reaction-diffusion approximation of nonlocal reactiondiffusion equations. By this result, we can see nonlocal interactions as a phenomenon resulting from anumber of reactions and diffusion.
41 藤 原瑠 ( 明 大 先 端 数 理)

Ryu Fujiwara(Meiji Univ.)

非有界な積分核を有する非局所 Allen–Cahn 方程式の定常解 · · · · · · · · · · 10

Steady state to the nonlocal Allen–Cahn equation with unbounded kernel

概 要 We consider steady states of the nonlocal Allen–Cahn equation whose nonlocality is composedof unbounded kernel. The goal of this talk is to prove the existence of the steady states which havediscontinuities. The key idea of proving the existence is to define the functional in weighted L1 space whose
fixed point is the Volterra integral of the first kind.

Final: 2023/8/2151函数方程式論42 谷 口 雅 治 (岡山大異分野基礎研)

Masaharu Taniguchi (Okayama Univ.)

等エネルギー型反応拡散方程式における与えられた長軸と短軸をもつ凸図形を切断面とする進行波 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

A traveling front solution whose cross section has any given major axis
and any given minor axis in balanced reaction-diffusion equations

概 要 or a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been studied.

We prove that an axially asymmetric traveling front with any positive speed does exist in a balanced
bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an
imbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving
the major axis and the minor axis to be given constants and taking the balanced limit, we obtain anaxially asymmetric traveling front in a balanced bistable reaction-diffusion equation. This traveling front
is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with any
given major axis and any given minor axis.
43 下 條 昌 彦 (都 立 大 理)
Jong-Shenq Guo (Tamkang Univ.)(Providence Univ.)
Karen Guo
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)
Karen Guo (Providence Univ.)

Forced waves for diffusive competition systems in shifting environments· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Forced waves for diffusive competition systems in shifting environments

概 要 We discuss the existence of forced waves for a 3-species diffusive competition system in shifting

environments. We derive two different classes of forced waves connecting two unstable constant equilibria.
The minimal environmental shifting speeds are determined under the equal diffusivities condition.
44 森
竜 樹 ( 武 蔵 野 大 工)
久 藤 衡 介 ( 早 大 理 工)
辻 川亨
(宮崎大⋆・明大研究・知財)谷
大⋆)四 ツ 谷 晶 二 (龍Tatsuki Mori (Musashino Univ.)
Kousuke Kuto (Waseda Univ.)
Tohru Tsujikawa(Univ. of Miyazaki⋆ /Meiji Univ.)
Shoji Yotsutani (Ryukoku Univ.⋆)

Exact solutions of full stationary problems for a cell polarization model· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Exact solutions of full stationary problems for a cell polarization model

概 要 We are interested in all exact solutions of full stationary problem for a cell polarization model proposed

by Y. Mori, A. Jilkine and L. Edelstein-Keshet (SIAM J. Appl. Math., 2011). We reported some exact
solutions of this problem under special conditions in MSJ autumn meeting 2016. In this talk, we reportthat we have obtained all exact solution. This is a joint work with Professors K. Kuto (Waseda Univ.),
T. Tsujikawa (Univ. of Miyazaki, Meiji Univ.) and S. Yotsutani (Ryukoku Univ.).
45 佐 藤 洋 平 (埼 玉 大 理 工)
Yohei Sato

(Saitama Univ.)

引力的・斥力的相互作用項を同時に含む連立シュレディンガー方程式の偶対称基底状態 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Even ground state for nonlinear Schrödinger systems with mixed couplings on RN

概 要 For a coupled nonlinear elliptic system having both attractive and repulsive couplings involved, weconstruct a non-radial bound state solution characterized as the ground state in the subspace of evensymmetric functions while it is known that the ground state in the full space of Sobolev functions does notexist.

Final: 2023/8/21
函数方程式論(Univ. of Bordeaux)46 M. Colin
渡 辺 達 也 ( 京 都 産 大 理)

Mathieu Colin (Univ. of Bordeaux)Tatsuya Watanabe(Kyoto Sangyo Univ.)

52

Stable standing waves for a Schrödinger system with nonlinear χ3 response · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Stable standing waves for a Schrödinger system with nonlinear χ3 response

概 要 In this talk, we consider standing wave solutions for a certain nonlinear Schrodinger system whichappears in nonlinear optics. This two-component system contains a cubic nonlinear term which is calledχ3 -interaction, and has a strong coupling on one side only.
Oliveira–Pastor (2021) showed the existence of ground state solutions for the corresponding stationary
problems, and investigated their stability and instability. In our study, by considering the solvability ofa constraint minimization problem, we show the existence of stable standing wave solutions. We also
investigate the correspondence between minimizers and ground state solutions.
47 眞 﨑

聡 (北

大

理)

Satoshi Masaki (Hokkaido Univ.)あるクラスの非線型シュレディンガー方程式系の定在波解の存在および解の形状について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the existence and the shape of the standing wave solutions to a classof systems of nonlinear Schrödinger equations

概 要 We consider scalar-type standing wave solutions to a class of nonlinear elliptic systems in an abstract

setting. The setting is made to handle the standard forms of a class of nonlinear cubic systems introduced
in my talk at the previous MSJ meeting. We also consider the stability problem as a standing-wave solution
to the corresponding NLS system.
48 山 下 龍 生 (都 立 大 理)

Ryusei Yamashita (Tokyo Metro. Univ.)

A remark on the local uniqueness by the monotonicity based method
for the magnetic Schrödinger equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
A remark on the local uniqueness by the monotonicity based method
for the magnetic Schrödinger equation

概 要 We prove a local uniqueness by the monotonicity based method for a potential q of the magnetic2
u + qu = 0 in a bounded domain Ω from partial boundary data. Moreover, we
Schrödinger operator −DA

give monotonicity tests to detect an unknown obstacle for the magnetic Schrödinger equation.
49 加 藤 圭 一 (東 京 理 大 理) ♭ 空間減衰磁場中のシュレーディンガー方程式の解のモジュレーション空村 松
亮 (東 北 大 理) 間上での評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Keiichi Kato (Tokyo Univ. of Sci.)
Ryo Muramatsu (Tohoku Univ.)

Estimates on modulation spaces for solutions to Schrödinger equations
with spatially decaying magnetic fields

概 要 In this talk, we study the estimate of the solutions of the Schrödinger equation in a magnetic field byinitial data in the modulation space. Comparing with the Schrödinger equation in the cases of free or scalarpotentials, it is difficult to estimate the solutions using conventional methods for the case of magnetic fields
due to the increase in frequency components caused by first-order derivative term. In this presentation, we
discuss the estimate of the M p,p norm of the solutions by the M p,p norm of the initial data in the cases ofspatially decaying magnetic fields and its proof. This talk is based on the joint work with Professor Keiichi
Kato (Tokyo University of Science).

Final: 2023/8/2153函数方程式論50 川 上 隼 平 (京大理)Jumpei Kawakami (Kyoto Univ.)

Global approximation for the cubic NLS with strong magnetic confinement · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Global approximation for the cubic NLS with strong magnetic confinement

概 要 We consider nonlinear Schrödinger equation with strong magnetic fields in 3D. This model was derived

by R L. Frank, F. Méhats, C. Sparber in 2017. We prove modified scattering for small initial data and theexistence of modified wave operator for small final data. To describe asymptotic behavior of the NLS we
use the time-averaged model which was derived by the same authors as “the strong magnetic confinement
limit” of the NLS. We construct asymptotic solutions which satisfy both asymptotic in time evolution andconvergence in the strong magnetic confinement limit. We also analyze the error between the solution to
the NLS and the time-averaged model for the same initial data.
51 津 原駿 (東 北 大 理) ♭ 非線型 Neumann 境界条件下での 2 次元半空間非線型 Schrödinger 方程小 川 卓 克 (東 北 大 理) 式の時間局所適切性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
佐 藤 拓 也 ( 熊 本 大 先 端)
Shun Tsuhara (Tohoku Univ.)
Takayoshi Ogawa (Tohoku Univ.)
Takuya Sato (Kumamoto Univ.)

Well-posedness of nonlinear Schrödinger equation on the two dimensional half-plane with a nonlinear Neumann boundary condition

概 要 We consider the initial-boundary value problem of the nonlinear Schrödinger equation on the halfplane with a nonlinear Neumann boundary condition. After establishing the boundary Strichartz estimate
in L2 (R2+ ), we consider the time local well-posedness of the problem in L2 (R2+ ).
14:15〜16:30
52 富 岡 健 太 (早 大 理 工) ♭ 非線型分散型方程式系に対する初期値境界値問題の大域適切性について
小 澤
徹 ( 早 大 理 工)
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Kenta Tomioka (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

The global well-posedness of the initial boundary value problem for
nonlinear dispersive systems

概 要 We consider the initial boundary value problem for Zakharov system (Z) and Schrödinger-improved

Boussinesq system (S-iB) in two space dimensions. We show the global well-posedness for these systems.
Moreover, we prove the vanishing improvement limit problem for (S-iB). We focus on a general domain withthe smooth boundary. There are many results for these problems in the whole space. However, there arefew papers for these problems in a general domain since it is difficult to use the Fourier analysis in a generaldomain. We use the method of the modified energy for these problems without the Fourier analysis. These
results are based on joint works with Professor Tohru Ozawa (Waseda University).
53 佐 藤 拓 也 (熊 本 大 先 端) ♭ Asymptotic behavior of large solutions to dissipative nonlinear Schrödinger
equations in the analytic class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Takuya Sato (Kumamoto Univ.)

Asymptotic behavior of large solutions to dissipative nonlinear Schrödinger
equations in the analytic class

概 要 We consider the Cauchy problem for the dissipative nonlinear Schrödinger equation with a critical

cubic nonlinearity in one space dimension. We show the a priori bound of dissipative solutions in theanalytic class and its L2 -decay order without any restriction of the size of smooth initial data.

Final: 2023/8/21
函数方程式論54 浜 野大 ( 早 大 理 工)
池 田 正 弘(理化学研 AIP・慶大理工)

Masaru Hamano (Waseda Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

54

Scattering and blow-up solutions to energy critical NLS with an inverse
square potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Scattering and blow-up solutions to energy critical NLS with an inverse
square potential

概 要 In this talk, we deal with energy critical nonlinear Schrödinger (NLS) equation with an inverse squarepotential. Prof. Kai Yang (in his thesis) investigated time behavior of solutions to the NLS equation under
the following two situations : The first case is that the potential is attractive and the energy of initial datais less than or equal to the energy of the static solution to the NLS equation. The second case is that thepotential is repulsive and the energy of initial data is less than the energy of the static solution to the NLS
equation without a potential. In this talk, we consider time behavior of solutions with initial data having
the equal energy for the second case.
55 駒 田 洸 一 (中 京 大 工)
大
理)
眞 崎
聡 (北

Koichi Komada (Chukyo Univ.)
Satoshi Masaki (Hokkaido Univ.)

空間 1 次元における 4 階非線形シュレディンガー方程式に対する散乱問題· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Scattering problem for fourth-order nonlinear Schrödinger equations in
one dimension

概 要 We consider fourth-order nonlinear Schrödinger equations with focusing, L2 -supercritical nonlinearity

in one dimension. In this talk, we prove global existence and scattering of solutions below the ground state
threshold under the evenness assumption.
56 福 田 一 貴 (信 州 大 工)
平 山 浩 之 ( 宮 崎 大 教 育)
Ikki Fukuda (Shinshu Univ.)
Hiroyuki Hirayama (Univ. of Miyazaki)

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

Large time behavior and optimal decay estimate for solutions to thegeneralized Zakharov–Kuznetsov–Burgers equation

概 要 In this talk, we consider the Cauchy problem for the generalized Zakharov–Kuznetsov– Burgers

equation in 2D. This is one of the nonlinear dispersive-dissipative type equations, which has a spatial
anisotropic dissipative term. In this study, we consider the large time behavior of the solution to thisproblem. In particular, we give the time decay estimates for the solution, in L2 and L∞ . In addition, we
also derive an asymptotic formula for the solution in the L∞ -sense. Moreover, in view of the asymptotic
profile of the solution, we show that the optimal decay rate for the L∞ -norm of the solution is given by t− 4 .
357 平 良 晃 一 (立 命 館 大 理 工)
田 森 宥 好(芝浦工大システム理工)

Kouichi Taira (Ritsumeikan Univ.)
Hiroyoshi Tamori(Shibaura Inst. of Tech.)

Strichartz estimates for (k, a)-generalized Laguerre operators · · · · · · · · 10

Strichartz estimates for (k, a)-generalized Laguerre operators

概 要 In this talk, we introduce results on Strichartz estimates for the (k, a)-generalized Laguerre operators.

The cases a = 1, 2 were studied previously. Here we consider more general cases. These proof depends on
symbol-type estimates of special functions and a discrete analog of the stationary phase theorem inspiredby the work of Ionescu–Jerison.

Final: 2023/8/2155

函数方程式論58 生 駒真 ( 名 大 多 元 数 理)
鈴 木 聡 一 郎 ( 中 大 理 工)
Makoto Ikoma (Nagoya Univ.)
Soichiro Suzuki (Chuo Univ.)

2 次元 Dirac 方程式の平滑化評価式の最良定数 · · · · · · · · · · · · · · · · · · · · · 10
Optimal constants of smoothing estimates for the 2-dimensional Diracequation

概 要 Kato–Yajima smoothing estimates are one of the fundamental results in study of dispersive equations

such as Schrödinger equations and Dirac equations. For d(≥ 2)-dimensional free Schrödinger equations,
optimal constants of smoothing estimates were given by Bez–Saito–Sugimoto (2015). In contrast, optimal
constants for free Dirac equations are known only in the 2-dimensional case (Ikoma, 2022). In this talk, wegive another proof of optimal constants for the 2-dimensional free Dirac equation. We also give the optimal
constants for 1-dimensional free Schrödinger and Dirac equations.
59 井 波 虎 太 郎 (名 大 多 元 数 理)
鈴 木 聡 一 郎 ( 中 大 理 工)
Kotaro Inami (Nagoya Univ.)
Soichiro Suzuki (Chuo Univ.)

摩擦項を持つ Klein–Gordon 型方程式のエネルギー減衰と摩擦係数の幾何学的条件との同値性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

The equivalence of an energy decay for damped Klein–Gordon typeequations and the geometric condition for damping coefficients概 要 We will discuss an equivalence between energy decay estimates for damped Klein–Gordon equations

and geometric conditions for the damping coefficient. To show this equivalence, we use the Paneah–
Logvinenko–Sereda type uncertainty principle. We will briefly introduce these uncertainty principles andshow how energy decay estimates and uncertainty principles are connected.
大理)
60 岡 本葵 (阪Tadahiro Oh (Univ. of Edinburgh)
N. Tzvetkov(École Normale Supérieure de Lyon)

Mamoru Okamoto (Osaka Univ.)
Tadahiro Oh (Univ. of Edinburgh)
Nikolay Tzvetkov(École Normale Supérieure de Lyon)

Gauss 型の初期値をもつ非線形 Klein–Gordon 方程式のほとんど確実な解について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the solution of the cubic nonlinear Klein–Gordon equation with
Gaussian random initial data

概 要 We consider the solution of the cubic nonlinear Klein–Gordon equation with Gaussian random initial

data. We prove that the solution is the limit of solutions with smoothed Gaussian initial data obtainedby mollification. We also show that there is a regularization of the Gaussian initial data so that thecorresponding smooth solutions almost surely have no limit.
61 西 井 良 徳 (東 京 理 大 理)
佐 川 侑 司(熊本大数理科学総合教育センター)
佐 藤 拓 也 ( 熊 本 大 先 端)

Yoshinori Nishii (Tokyo Univ. of Sci.)
Yuji Sagawa (Kumamoto Univ.)
Takuya Sato (Kumamoto Univ.)

弱消散構造を伴う半線形波動方程式の小振幅解のエネルギーに対する上下からの評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Upper and lower bounds for energy of small solutions to semilinear wave
equations with weakly dissipative structure

概 要 We consider the Cauchy problem for the semilinear wave equations with weakly dissipative nonlin-

earities in two space dimension. We show the energy of small solutions decays like (log t)−1/(4ν) for ν ≥ 2.
This part is an improvement of the previous work by Nishii–Sunagawa–Terashita (2021). Furthermore, wefind that this decay rate is optimal by giving a lower estimate of the same order.

Final: 2023/8/21
函数方程式論特別講演
赤 堀 公 史 ( 静 岡 大 工)

56

16:45〜17:45

Takafumi Akahori (Shizuoka Univ.)

Global dynamics above the ground state threshold for nonlinear Schrödinger
equationsGlobal dynamics above the ground state threshold for nonlinear Schrödinger
equations

概 要 We consider the dynamics above the ground state threshold for the following nonlinear Schrödinger

equations in Rd × R: (1) i∂t ψ + ∆ψ + |ψ|p−1 ψ = 0,

4(2) i∂t ψ + ∆ψ + |ψ|p−1 ψ + |ψ| d−2 ψ = 0.

The first half of my talk deals with (1) under the assumption that d ≥ 1 and p is mass-supercritical and
4
if d ≥ 3, and 1 + d4 < p < ∞ if d = 1, 2). When d = 3 andenergy-subcritical (namely, 1 + d4 < p < 1 + d−2

p = 3, Nakanishi and Schlag (Calc. Var. PDE, 2012) proved that the behavior of radial solutions whoseenergies are slightly larger than the energy of the ground state is classified into 9 scenarios described by thescattering, blowup and trapping; employing their idea, we can generalize the range of d and p. However, it
is still open whether the same conclusion holds for nonradial solutions. I would like to give a partial answer
to this problem.
4
The second half deals with (2) under the assumption that d ≥ 3 and 1 + d4 < p < 1 + d−2. Since (2) is

not scale invariant and the limiting profiles of ground states differ for low and high frequencies, we needto pay attention to the frequencies of ground states; in particular, for d = 3 and 1 < p ≤ 3, there exists afrequency threshold above which there is no ground state. For low frequencies, we see that the behaviorof radial solutions whose energies are slightly larger than the energy of the ground state is classified into 9
scenarios as well as (1). For high frequencies, a similar result can be proved except for the case d = 3 and1 < p ≤ 3. The study for the intermediate frequencies is still developing.

9 月 23 日（土）第 IX 会場

9:30〜12:00
62 北 村 駿 介 (東 北 大 理) ♭ 増大する空間変数重みを持つ一次元半線形波動方程式の解の瞬間爆発 · · 10

Shunsuke Kitamura (Tohoku Univ.)

Instant blow-up of solutions of one-dimensional semilinear wave equations with increasing spatial weights

概 要 In this talk, I will report on the “instant blow-up” of solutions of semilinear wave equations withspatial weights and non-compactly supported data in one space dimension. This technical term means that
there is no local-in-time solution. I found a sufficient condition to occur the instant blow-up by means ofspatial weights and the decay of initial data.
63 髙 松脩 (東 北 大 理) ♭ 空間微分からなる非線型項を持つ一次元波動方程式の古典解の lifespan 評
佐々木多希子 (武蔵野大工・東北大理) 価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
高 村 博 之 ( 東 北 大 理)

Shu Takamatsu (Tohoku Univ.)
Takiko Sasaki(Musashino Univ./Tohoku Univ.)
Hiroyuki Takamura (Tohoku Univ.)

The lifespan of classical solutions of one dimensional wave equation withsemilinear terms of the spatial derivative概 要 In this talk, we report on the lifespan estimates of classical solutions of solutions of one dimensional

wave equation with semilinear terms of the spatial derivative. The result is same as one of semilinear termsof the time derivative. But there are so many differences among their proofs. Moreover, it is meaningful tostudy this problem in the sense that it may help us to investigate its blow-up boundary in the near future.

Final: 2023/8/2157

函数方程式論64 川 下 美 潮 (広島大先進理工)
川 下 和 日 子 (広島大先進理工)

Mishio Kawashita (Hiroshima Univ.)
Wakako Kawashita (Hiroshima Univ.)

複数種の穴を持つ媒質についての波動方程式による逆問題における指示関数の漸近挙動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Asymptotic behavior of the indicator function in the inverse problem of
the wave equation for media with multiple types of cavities

概 要 In this presentation, we consider the inverse problem of the wave equation by the enclosure method

for a medium with multiple types of cavities. In the case considered here, the sign of the indicator functionof the enclosure method is not determined and sign cancellation may occur, resulting in loss of information.
By using the asymptotic solution and examining in detail the main terms of the asymptotic expansion of
the indicator function, we show that the shortest distance to the cavities can be obtained even in such a
case.
65 岡

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

消散型波動方程式に対する準周期的時空均質化問題 · · · · · · · · · · · · · · · · · 10Space-time quasi-periodic homogenization for damped wave equations

概 要 In this talk, we shall discuss a space-time quasi-periodic homogenization problem for damped wave

equations with periodically oscillating in space and quasi-periodically oscillating in time coefficients. The
main purpose of this talk is to present a homogenization theorem, i.e., convergence of solutions andcharacterization of the homogenized equation. The proof is based on the space-time two-scale convergence
theory.
66 側 島 基 宏 (東京理大創域理工)
池 田 正 弘 ( 理 化 学 研)
谷 口 晃 一 (東 北 大 A I M R )若 杉 勇 太 (広島大先進理工)
Motohiro Sobajima(Tokyo Univ. of Sci.)(RIKEN)
Masahiro Ikeda(
TohokuUniv.)
Koichi Taniguchi
Yuta Wakasugi (Hiroshima Univ.)

2 次元外部領域における臨界型半線形消散型波動方程式について · · · · · · 10

On the lifespan of solutions to the critical semilinear damped wave equation in an 2d-exterior domain

概 要 The semilinear damped wave equation ∂t2 u − ∆u + ∂t u = u2 in the exterior of the two-dimensional

closed unit ball with the Dirichlet boundary condition are dealt with. The main result is the sharp lifespanestimate of the double exponential type from below under the radially symmetric setting.
67 隠 居 良 行 (東 工 大 理)
竹 田 寛 志 ( 福 岡 工 大)
Kagei Yoshiyuki (Tokyo Tech)
Hiroshi Takeda (Fukuoka Inst. of Tech.)

準線形消散型弾性波方程式に対する時間周期解の安定性について · · · · · · 10

Stability of time periodic solution of nonlinear elastic wave equations
with viscoelastic terms

概 要 In this talk we consider time periodic problem of quasi-linear elastic wave equations with the viscoelastic

term. We prove the existence of time solution for small time periodic external force. We also show thestability of the time periodic solution for small perturbations. Our proof of the stability is based on theregularity estimates of the time periodic solution.

Final: 2023/8/21
函数方程式論68 隠 居 良 行 (東 工 大 理)
Yoshiyuki Kagei (Tokyo Tech)58

圧縮性 Taylor 渦の Eckhaus 不安定性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Eckhaus instability of compressible Taylor vortices

概 要 This talk is concerned with the stability of the bifurcating compressible Taylor vortex. Consider thecompressible Navier–Stokes equations in a domain between two concentric infinite cylinders. If the outercylinder is at rest and the inner one rotates with sufficiently small angular velocity, a laminar flow, called
the Couette flow, is stable. When the angular velocity of the inner cylinder increases, beyond a certain
value of the angular velocity, the Couette flow becomes unstable and a vortex pattern, called the Taylor
vortex, bifurcates. In this talk, the compressible Taylor vortices are shown to satisfy the Eckhaus criterion
for the stability under axisymmetric perturbations.
69 小 薗 英 雄 (早大理工・東北大理)
寺 澤 祐 高 ( 名 大 多 元 数 理)
若 杉 勇 太 (広島大先進理工)
Hideo Kozono(Waseda Univ. / Tohoku Univ.)
Yutaka Terasawa (Nagoya Univ.)
Yuta Wakasugi (Hiroshima Univ.)

Liouville-type theorems for the Taylor–Couette flow of the stationary
Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Liouville-type theorems for the Taylor–Couette flow of the stationary
Navier–Stokes equations

概 要 We study the stationary Navier–Stokes equations in the region between two rotating concentric

cylinders. We first prove that, under the small Reynolds number, if the fluid is axisymmetric and if its
velocity is sufficiently small in the L∞ -norm, then it is necessarily a generalized Taylor–Couette flow. Next,
we give a certain bound of the Reynolds number and the L∞ -norm of the velocity such as the fluid is indeed,necessarily axisymmetric.
70 小 池Kai Koike

開 (東

工

大)

(Tokyo Tech)

1 次元圧縮性 Navier–Stokes 方程式の解の時空間各点評価付き漸近展開· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Asymptotic expansion of solutions to 1D compressible Navier–Stokes
equations with space-time pointwise estimates

概 要 We consider a 1D viscous compressible flow and construct an asymptotic expansion of the flow inthe long-time regime t ≫ 1. It is well-known that the leading order asymptotic profile in the Lp (R)-norm(1 ≤ p ≤ ∞) is described by the diffusion wave (see e.g., Y. Zeng, Comm. Pure Appl. Math., 1994). In awork by van Baalen, Popović, and Wayne (SIAM J. Math. Anal., 2008), they investigated an asymptotic
expansion of the solution beyond the leading-order term. However, they studied in the L2 -framework andthe case p < 2 is excluded. In our work, we extend this result to all p by proving a sharp space-time
pointwise estimates.
71 橋 本 伊 都 子 (金 沢 大 理 工)大⋆)
松 村 昭 孝 (阪Itsuko Hashimoto (Kanazawa Univ.)
Akitaka Matsumura (Osaka Univ.⋆)

圧縮性 Navier–Stokes 方程式の球対称定常解に関する粘性零極限の考察· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Inviscid limit problem of radially symmetric stationary solutions forcompressible Navier–Stokes equation

概 要 We study an inviscid limit problem of radially symmetric stationary solutions for an exterior problem

to compressible Navier–Stokes equation, describing the motion of viscous barotropic gas without external
forces, where boundary and far field data are prescribed. For both inflow and outflow problems, the inviscid
limit is considered in a suitably small neighborhood of the far field state. The estimates of algebraic rate
toward the inviscid limit are also obtained.

Final: 2023/8/2159

函数方程式論72 藤 井 幹 大 (九 大 数 理)
Mikihiro Fujii (Kyushu Univ.)

2 次元全平面における定常 Navier–Stokes 方程式の非適切性 · · · · · · · · · · 10
Ill-posedness of the two-dimensional stationary Navier–Stokes equations
on the whole plane

概 要 We consider the two-dimensional stationary Navier–Stokes equations on the whole plane R2 . In thehigher-dimensional cases Rn with n ⩾ 3, the well-posedness and ill-posedness in scaling critical spaces are
well-investigated by numerous papers. However, despite the attention of many researchers, the corresponding
problem in the two-dimensional whole plane case was a long-standing open problem due to inherent difficulties
of two-dimensional analysis. The aim of this talk is to address this issue and prove the ill-posedness inthe scaling critical Besov spaces based on Lp (R2 ) for all 1 ⩽ p ⩽ 2 in the sense of the discontinuity of thesolution map and the non-existence of small solutions.
73 大 石 健 太 (早 大 理 工)
Kenta Oishi(Waseda Univ.)

2 次元半空間上の Navier–Stokes 方程式の自由境界問題の時間大域適切性と解の減衰について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the global well-posedness and decay of a free boundary problem of
the Navier–Stokes equation in the two-dimensional half space

概 要 We establish the global well-posedness and some decay properties for a free boundary problem of theincompressible Navier–Stokes equations in RN+ with N ≥ 2. For N = 2, the decay of the solution to the freeboundary problem is too slow to control the nonlinear term on the boundary and that is why we could nothandle the case N = 2 in our preceding work. We overcome this difficulty owing to the trace estimate in
the half space ∥f (x′ , 0)∥Lq (RN −1 ) ≤ ∥f ∥Lq (RN ) ∥∇f ∥Lq (RN ) , where x′ = (x1 , · · · , xN −1 ).
1−1/q

+

14:15〜16:00
74 出 口 直 人 (東 工 大 理)
Naoto Deguchi(Tokyo Tech)

1/q+

圧縮性 Navier–Stokes 方程式の定常解の安定性解析 · · · · · · · · · · · · · · · · · 10

Stability analysis for stationary solutions of the compressible Navier–Stokes equation

概 要 We consider the stability of the stationary solution of the compressible Navier–Stokes equation in the

3D whole space with an external force which decays at spatial infinity. We obtain the global existence resultof the non-stationary problem under the smallness assumptions on the initial value and the external force.
We also derive the time decay rates of the perturbations around the stationary solution under the smallness
assumption on the initial perturbations.
75 中 里 亮 介 (信 州 大 工) ♭ 臨界空間に於ける圧縮性 Navier–Stokes–Korteweg 方程式の解の長時間挙
小 林 孝 行 (阪 大 基 礎 工) 動について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Ryosuke Nakasato (Shinshu Univ.)
Takayuki Kobayashi (Osaka Univ.)

Long time behavior of solutions to the compressible Navier–Stokes–
Korteweg equations in critical spaces

概 要 We consider the initial value problem of the compressible Navier–Stokes–Korteweg equations in thewhole space Rd (d ≥ 2). The aim of this talk are to obtain the global-in-time solution around the constantequilibrium states (ρ∗ , 0) and investigate the Lp -L1 type time-decay estimates. In addition, we consider the
diffusion wave property came from the wave equation with strong damping for the solution with the initial
data belonging to the critical spaces. The key idea is the derivation of the time-decay for the Fourier–Besov
norm with higher derivatives by using L1 -maximal regularity for the linearized system.
76 山 本 征 法 (新 潟 大 自 然)

Masakazu Yamamoto (Niigata Univ.)

非圧縮性 Navier–Stokes 流の空間遠方での時間発展について · · · · · · · · · · 10

Time evolution of the incompressible Navier–Stokes flow in far-field

概 要 In this talk, the incompressible Navier–Stokes flow in two-dimensional whole space is treated. Asymp-

totic expansion of the velocity in far-field are established. Especially time evolution of them are clarified.
In this study the related vorticity and the technique of renormalization are applied through Biot–Savartlaw.

Final: 2023/8/21
函数方程式論

77 沖 田 匡 聡 (久 留 米 工 高 専)
Masatoshi Okita(Kurume Nat. Coll. of Tech.)60

On the blow-up criterion for the Navier–Stokes equations with criticaltime order · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the blow-up criterion for the Navier–Stokes equations with criticaltime order概 要 We prove that every smooth solution u(t, x) on (0, T ) of incompressible Navier–Stokes equations onwhole space is extensible beyond t > T if u(t, x) ∈ Lrw (0, T ; Lpσ ) for 2r + np = 1 and p > n satisfies blow-up
p−ncritical time order estimate: ∥u(t)∥Lp ≤ ϵ(T − t)− 2p for T − δ < t < T with sufficiently small positive
constants ϵ and δ. Here Lrw denote the weak Lr space. It is well-known that if the solution u satisfiesu ∈ Lr (0, T ; Lpσ ) with n < p ≤ ∞ and 2 ≤ r < ∞ such that 2r + np = 1 then u is extensible continued beyond
the time T . In this talk, we consider the blow-up criterion when u ∈/ Lr (0, T ; Lpσ ).
78 郭柔 均 ( 早 大 理 工)

Jou-chun Kuo (Waseda Univ.)

Maximal L1 regularity for the compressible Stokes equations · · · · · · · · 10
Maximal L1 regularity for the compressible Stokes equations

概 要 This talk is devoted to proving the maximal L1 regularity of the linearized system of the compressible

Navier–Stokes equations with homogeneous boundary conditions in the half-space. Here, we build thesspace, where q and s are taken such that 1 < q < ∞ andcontinuous C0 analytic semigroup in Bq,1

−1 + 1/q < s < q/1. Moreover, we prove the L1 integrability of this semigroup. The approach is by meansof the analytic semigroup theory and we use real interpolation and duality argument in order to obtain theestimates for the semigroup. The restrictions of q and s above implies that C0∞ (RN+ ) is dense.
79 柴 田 良 弘
渡 邊 圭 市 (諏訪東京理大工)
Yoshihiro Shibata
Keiichi Watanabe (Suwa Univ. of Sci.)

Maximal L1 -regularity of the Navier–Stokes equations with free boundary conditions: Local well-posedness · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Maximal L1 -regularity of the Navier–Stokes equations with free boundary conditions: Local well-posedness

概 要 We show the maximal regularity theorem of the Stokes equations with free boundary conditions in thes-in-space framework, where q and s satisfy 1 < q < ∞half-space Rd+ , d ≥ 2, within the L1 -in-time and Bq,1and −1 + 1/q < s < 1/q, respectively. The theorem is applied to show the unique existence of a local strong
solution to the Navier–Stokes equations with free boundary conditions provided that the initial velocity v0sbelongs to Bq,1
(Rd+ )d without any restriction on the size of initial data, where q and s satisfy d − 1 < q ≤ dand −1 + d/q < s < 1/q. This improves the previous result established in the maximal Lp -Lq -framework
due to a long series of papers by Y. Shibata.
80 柴 田 良 弘
渡 邊 圭 市 (諏訪東京理大工)
Yoshihiro Shibata
Keiichi Watanabe (Suwa Univ. of Sci.)

Maximal L1 -regularity of the Navier–Stokes equations with free boundary conditions: Global well-posedness · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Maximal L1 -regularity of the Navier–Stokes equations with free boundary conditions: Global well-posedness

概 要 We show the maximal regularity theorem of the Stokes equations with free boundary conditions in theshalf-space Rd+ , d ≥ 2, within the L1 -in-time and Ḃq,1-in-space framework, where q and s satisfy 1 < q < ∞and −1+1/q < s < 1/q, respectively. The theorem is applied to show the unique existence of a global strong
solution to the Navier–Stokes equations with free boundary conditions provided that the initial velocity v0−1+d/qis small in Ḃq,1(Rd+ )d , where q satisfies d − 1 < q < 2d. This improves the previous result establishedby Danchin et al. (preprint, arXiv:2011.07918).

Final: 2023/8/2161函数方程式論81 渡 邊 圭 市 (諏訪東京理大工)

Keiichi Watanabe (Suwa Univ. of Sci.)

Large time behavior of the Stokes semigroup in exterior Lipschitz domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Large time behavior of the Stokes semigroup in exterior Lipschitz domains

概 要 We prove the local energy estimate of the Stokes semigroup in exterior Lipschitz domains Ω ⊂ Rd ,d ≥ 3. As an application, we show Lp -Lq decay estimates of the gradient of the Stokes semigroup (T (t))t≥0generated by the negative of the Stokes operator in Ω, provided that p and q satisfy |1/p − 1/2| < 1/(2d) + ε,
|1/q − 1/2| < 1/(2d) + ε, and p ≤ q ≤ d with some ε > 0. We also obtain the existence theoremof global-in-time strong solutions to the three-dimensional Navier–Stokes equations in the critical space
L∞ ((0, ∞); L3σ (Ω)) provided that the initial velocity is small in the L3 -norm. It should be emphasized thatthe large time behavior of the Navier–Stokes flow is completely recovered in exterior Lipschitz domains Ω
along exactly the same argument as usual, even though the boundary ∂Ω is not smooth.
16:15〜17:15

特別講演
齋 藤 平 和 (電通大情報理工)

Hirokazu Saito(Univ. of Electro-Comm.)

Asymptotic stability of the trivial steady state for the two-phase Navier–Stokes equations
Asymptotic stability of the trivial steady state for the two-phase Navier–Stokes equations

概 要 In this talk, we consider a two-phase problem for two immiscible, viscous, incompressible fluids inthe presence of a uniform gravitational filed acting vertically downward in the N -dimensional Euclidean
space for N ≥ 3. The two fluids are separated from one another by the sharp interface xN = η(x′ , t),where x′ ∈ RN −1 is the tangential variable and t ≥ 0 is the time variable. The fluid occupying the region
xN > η(x′ , t) is called the upper fluid, while the other fluid occupying the region xN < η(x′ , t) is called thelower fluid. It is well-know that the trivial steady state, i.e., the motionless state with the flat interface
xN = 0, is unstable if the upper fluid is heavier than the lower one due to the effect of gravity. On theother hand, we prove the asymptotic stability of the trivial steady state in the case where the lower fluid isheavier than the upper one in this talk.

Final: 2023/8/21
実函数論

実

函

数

9 月 22 日（金）62

論第 V 会場

9:00〜12:00
1 冨 澤 佑 季 乃 ( 新 潟 工 大 工)
Yukino Tomizawa(Niigata Inst. of Tech.)

完備 Busemann 空間の弱一様凸性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weak uniform convexity of complete Busemann spaces

概 要 I report weak uniform convexity of complete Busemann spaces. As a main result, I prove a char-acterization of weak uniform convexity of complete Busemann spaces. This is a generalization of thecharacterization of uniform convexity of Banach spaces.
2 木 村 泰 紀 ( 東 邦 大 理)
Yasunori Kimura (Toho Univ.)

完備測地距離空間上の凸最小化問題とその解近似法 · · · · · · · · · · · · · · · · · 15

Convex minimization problems and approximation to their solutions oncomplete geodesic spaces

概 要 The convex minimization problem is a central topic of convex analysis, and it has been investigated invarious settings of underlying spaces such as Euclidean spaces, Hilbert spaces, Banach spaces, and others.
This work considers a convex function defined on a Hadamard space and proposes a new approximation
technique to solve the problem. We use a notion of resolvent operators to generate an iterative sequence
converging to a solution to our problem.
3 眞 中 裕 子 ( 日 大 短 大)
Hiroko Manaka (Nihon Univ.)

Convergence theorems with some projections in Banach spaces · · · · · · · 15
Convergence theorems with some projections in Banach spaces

概 要 A lot of studies have done with respect to the approximation methods of solutions for nonlinear

problems in a Hilbert space and Banach spaces. In this talk, we introduce our results of approximation forthe split feasibility problem and strong convergence theorems for common fixed points of nonlinear mappings
with some projection methods in Banach spaces. It is well-known that there are many convergence theorems
with the metric projection methods. We treat with not only the metric projection methods, but also thegeneralized projection methods as a special case of Bregman projection methods.
4 厚 芝 幸 子 (東京女大現代教養)
Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Attractive points, fixed points and convergence theorems for monotone
Lipschitzian mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Attractive points, fixed points and convergence theorems for monotone
Lipschitzian mappings

概 要 In this talk, we study the set of fixed points and the set of attractive points of nonlinear mappings.

We prove convergence theorems for monotone Lipschitzian mappings in Banach spaces endowed with apartial order. We also prove convergence theorems for families of monotone nonexpansive mappings.
5 松 下 慎 也
(秋田県立大システム科学技術)

Shin-ya Matsushita (Akita Pref. Univ.)

主双対分割法とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Primal-dual splitting algorithm and its applications

概 要 In this talk, we propose and analyze primal-dual splitting algorithms for finding a minimizer ofthe convex optimization problem. We show the convergence of the proposed algorithm and confirm theeffectiveness by numerical experiments.

Final: 2023/8/21
63

実函数論

6 山 口 哲 志 ( 茨 城 大 理 工)
中 井 英 一 ( 茨 城 大 理)
下 村 勝 孝 ( 茨 城 大 理)

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

Bi-preduals of generalized Campanato spaces with variable growth condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bi-preduals of generalized Campanato spaces with variable growth condition

概 要 It is known that(H 1 (Rd ))∗ = BMO(Rd ) and∞ (Rd )Ccomp


BMO(Rd ) ∗= H 1 (Rd ).

The function space BMO(Rd ) is a special case of generalized Campanato spaces Lp,ϕ (Rd ) with variable
growth condition. The first duality is extended to Lp,ϕ (Rd ). In this talk we extend the second duality to
Lp,ϕ (Rd ).
7 M. Murugan(Univ. of British Columbia)
清 水 良 輔 ( 早 大 理 工)
Mathav Murugan(Univ. of British Columbia)
Ryosuke Shimizu (Waseda Univ.)

Construction and regularity of first-order Sobolev spaces on the planar
Sierpiński carpet · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Construction and regularity of first-order Sobolev spaces on the planar
Sierpiński carpet

概 要 In this talk, we will provide a tuple of p-energy and associated (1, p)-Sobolev space on the Sierpiński

carpet for all p > 1 via discrete approximations. The main difficulty is to show its regularity in the following
sense: the intersection of the continuous functions and our (1, p)-Sobolev space is dense in the continuousfunctions. As observed by the classical Sobolev embedding theorems, it is hard to get the regularity when p
is less than or equal to the “dimension” of the underlying space. We establish the regularity for p between
1 and the dimension so-called Ahlfors regular conformal dimension of the Sierpiński carpet. This is joint
work with Mathav Murugan (University of British Columbia).
8 波 多 野 修 也 ( 中 大 理 工)
川 澄 亮 太齋 藤 洋 樹 ( 日 大 理 工)
田 中
仁 ( 筑 波 技 術 大)(Chuo Univ.)
Naoya Hatano
Ryota Kawasumi(Nihon Univ.)
Hiroki Saito
Hitoshi Tanaka(Tsukuba Univ. of Tech.)

弱 Choquet 空間上の分数冪極大作用素の有界性 · · · · · · · · · · · · · · · · · · · · 15

Fractional operators on weak Choquet spaces with Hausdorff capacities

概 要 The purpose of this paper is to prove that fractional integral and maximal operators are bounded

on weak Choquet spaces with Hausdorff capacity. These results generalize the previous works of Adams,
Orobitg and Verdera.
9 野 ヶ 山 徹 ( 中 大 理 工)
Toru Nogayama (Chuo Univ.)

Littlewood–Paley characterization for mixed Morrey spaces · · · · · · · · · · 15
Littlewood–Paley characterization for mixed Morrey spaces

概 要 In this talk, we consider the Littlewood–Paley characterization for mixed Morrey spaces. The topology

to converge the Littlewood–Paley decomposition for the element of mixed Morrey spaces is the weak-*
topology. If we consider the topology of mixed Morrey spaces, we must give other characterization by using
the heat semigroup.

Final: 2023/8/21
実函数論

12:15〜12:45

642023 年度日本数学会解析学賞授賞式

14:15〜15:25
10 川 澄 亮 太
池 田 正 弘 (理 化 学 研 A I P )石 川勲(愛媛大データサイエンスセンター)
Ryota Kawasumi(RIKEN)
Masahiro Ikeda(Ehime Univ.)
Isao Ishikawa

Boundedness of composition operators on Orlicz–Morrey spaces · · · · · · 15

Boundedness of composition operators on Orlicz–Morrey spaces

概 要 In this talk, motivated the result about boundedness of composition operators on Morrey space byHatano, Ikeda, Ishikawa and Sawano in 2021, we extend the result to Orlicz–Morrey spaces. To do this, wefirst prove the boundedness of composition operators from Orlicz–Morrey spaces to themselves. Next, tofind a bi-Lipschitz map, using singular value decomposition, we prove that the first singular value is greaterthan a positive constant. Orlicz–Morrey spaces contain Lebesgue and generalized Morrey spaces. Thus
our results contain previous results on their spaces as corollaries. Composition operators are often called
Koopman operators and have been applied to data science and dynamical system.
11 齋 藤 洋 樹 (日 大 理 工)
Hiroki Saito(Nihon Univ.)

Some embedding inequalities for fractional Sobolev spaces · · · · · · · · · · · 15
Some embedding inequalities for fractional Sobolev spaces

概 要 In this talk, we investigate a classical embedding Ẇ 1,1 ⊂ Lq (µ) and a sufficient condition for µ sothat one guarantees this embedding. We extend this embedding inequality to the fractional Sobolev spaces.
Note that these inequalitis are related to the classical isoperimetric inequalities and Sobolev’s inequality.
12 飯 田 毅 士 (福 島 工 高 専)
Takeshi Iida
(Fukushima Nat. Coll. of Tech.)Remarks on the fractional operators on Orlicz–Morrey spaces · · · · · · · · 15
Remarks on the fractional operators on Orlicz–Morrey spaces

概 要 Fractional integral operators Iα and Orlicz fractional maximal operators are essential for studying

partial differential equations and harmonic analysis. In this talk, we focus on the boundedness of these
operators in the framework of Orlicz–Morrey spaces. We examine specific examples of triplets of Youngfunctions where the boundedness of these operators can be established. By these examples, we aim toreinforce the boundedness property for the fractional integrals and Orlicz fractional maximal operators in
Orlicz–Morrey spaces.
13 河 邊

淳 ( 信 州 大 工)

Jun Kawabe(Shinshu Univ.)

Sugeno–Lorentz 空間の位相及び線形位相的性質 · · · · · · · · · · · · · · · · · · · · 15
Topological and linear topological properties of the Sugeno–Lorentz
spaces

概 要 The properties of the spaces of Sugeno integrable functions are quite different from those of ordinary

spaces of Lebesgue integrable functions. In this talk, the Sugeno–Lorentz spaces and Sugeno–Lorentz
topologies are defined by the Sugeno integral and their topological and linear topological properties are
discussed. Of particular interest is that the Sugeno–Lorentz spaces and their topologies are unique regardlessof indices p and q.

Final: 2023/8/21
65

実函数論

15:40〜16:40 2022 年度 (第 21 回) 日本数学会解析学賞受賞特別講演
中 井 英 一 (茨 城 大 理) 平均振動量が一様でないカンパナト空間とそれに関連する話題
Eiichi Nakai(Ibaraki Univ.)

Generalized Campanato spaces with variable growth condition and related topics

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

in 1985 to characterize the space of pointwise multipliers on BMO(Rn ). This characterization was extended
from Rn to spaces of homogeneous type in 1997, to probability spaces with filtration in 2014, and, to Rn
with non-doubling measures in 2018. On the other hand, this characterization was used by Lerner in 2005
to study the class P(Rn ) of functions p(·) for which the Hardy-Littlewood maximal operator is bounded on
the Lebesgue spaces Lp(·) (Rn ) with variable exponent, and positively solve a conjecture of Deining in 2005
saying that there are discontinuous functions belonging to P(Rn ). Moreover, in 2012 it was discovered by
Nakai and Sawano that the dual of generalized Hardy space H p(·) (Rn ) with variable exponent is a generalizedCampanato space with variable growth condition. In this talk we discuss generalized Campanato spaces
with variable growth condition and related topics.
17:00〜18:00 特別講演
川 﨑 敏 治 ( 玉 川 大 工)

Toshiharu Kawasaki (Tamagawa Univ.)

積分の拡張の幾つかの方向性について

On some directions of extension of the integral

概 要 Nowaday, there is no doubt that the Lebesgue integral is usually referred to as an integral. The reason

is that the Lebesgue integral has various useful properties. However, various extensions are conceivable,
such as expanding the domain of integrable functions, changing the range to a vector space, and changing
the measure to a non-additive measure. In this talk, we discuss some directions of extension of the integral.

9 月 23 日（土）第 V 会場

9:30〜12:00
14 赤 木 剛 朗 (東 北 大 理)
中 島 慶 人 ( 東 北 大 理)

非整数階時間微分を含む発展方程式の時間大域解とその減衰レートについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

(Tohoku Univ.)
Goro Akagi
Yoshihito Nakajima (Tohoku Univ.)

Global solutions for evolution eqations involving fractional time-derivatives
and their decay rates

概 要 In this talk, we discuss global-in-time existence of strong solutions to abstract evolution equations (ofgradient flow type for nonconvex energies) involving fractional time-derivatives for small initial data andapply it to degenerate parabolic equations associated with the so-called p-Laplacian as well as fractional
time-derivative. Finally, the optimal decay rate of small strong solutions is determined.
15 森 村 晃 子 (日 本 女 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)
Akiko Morimura(Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

非単調な境界条件を伴う非線形放物型方程式に対する弱解について · · · · 15

Weak solutions for nonlinear parabolic equations with non-monotone
boundary conditions

概 要 In this talk we consider the initial and boundary value problem for the partial differential equations

accompanying non-linear diffusion on the one-dimensional interval. Our research is strongly motivatedfrom the mathematical model describing moisture transport in porous materials. Unknown functions of
the model are distributions of water and air. For the model we assume the air distribution and obtain
the present problem. However, we do not expect existence of strong solutions to the problem since theboundary condition is not monotone. For this problem we define a solution by a weak formulation and proveexistence and uniqueness. The existence is obtained by the standard fix-point argument and our proof of
the uniqueness is based on the dual equation method.

Final: 2023/8/21
実函数論

16 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.)

66

KWC エネルギーに対する擬放物型消散系の適切性 · · · · · · · · · · · · · · · · · · 15
Well-posedness result for a pseudo-parabolic dissipation system of KWC
energy概 要 In this talk, we deal with a system consisting of two pseudo-parabolic PDEs, denoted by (S). Thissystem is based on a dissipation system of Kobayashi–Warren–Carter energy, which was proposed by[Kobayashi et al., Physica D, 140, 141–150(2000)], as a mathematical model of grain boundary motion.
The most characteristic point of (S) is in the point that (S) includes singular diffusion equation, withvariable-dependent mobilities. This brings down non-smoothness of regularity of the solution, and thelack of smoothness leads to the difficulty of well-posedness, especially uniqueness. On the other hand, thepseudo-parabolic structure in our system (S) will encourage smoothness to the solution. Therefore, oursystem (S) can be expected to be a kind of mathematical model of grain boundary motion, that fulfills
the well-posedness. Based on the above, we set the goal of this talk to discuss about the solvability of thesystem, regularity, uniqueness and continuous dependence of the solution, and large-time behavior.
17 磯 部伸 ( 東 大 数 理)

Noboru Isobe (Univ. of Tokyo)

深層ニューラルネットワークの学習過程を記述する, 距離空間上の勾配流と, その全列収束について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On a gradient flow modeling a learning process of deep neural networks
in a metric space and its convergence

概 要 Artificial intelligence (AI) technology, exemplified by Chat-GPT, has advanced in recent years,

astonishing us humans. However, the underlying principle of this technology, deep learning, which possesses
remarkable learning capabilities, still needs to be fully understood. E et al. proposed the formulation ofdeep learning through gradient flow to establish this principle from the standpoint of mathematical andnumerical analysis. Nevertheless, even fundamental mathematical results, such as convergence properties,
have yet to be known for this gradient flow. Therefore, in this talk, we consider the gradient flow of theobjective function in deep learning. In particular, we prove a convergence result of this gradient flow.
18 江 幡 隆 典 (新 潟 大 自 然)
應 和 宏 樹 ( 新 潟 大 理)

Takanori Ebata (Niigata Univ.)
Hiroki Ohwa (Niigata Univ.)

平衡則方程式の解の初期値と流束に関する連続依存性 · · · · · · · · · · · · · · · 15

Continuous dependence on the initial and flux functions for solutions ofbalance laws

概 要 We consider the continuous dependence on the initial and flux functions for the entropy solutions

to the Cauchy problem of balance laws. In general, for the proof, it is necessary to assume that the flux
function is twice continuously differentiable. However, without the assumption that the flux function is
twice continuously differentiable, under only the assumption that the flux is locally Lipschitz continuous, we
prove the continuous dependence on the initial and flux functions for the entropy solutions.

Final: 2023/8/21
67

実函数論

19 千 代 祐 太 朗 (東 京 理 大 理)
菅 原 一 磨 ( 東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

Global existence of classical solutions to an indirect chemotaxis-consumption
model with signal-dependent sensitivity · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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

Global existence of classical solutions to an indirect chemotaxis-consumption
model with signal-dependent sensitivity

概 要 This talk deals with an indirect chemotaxis-consumption model with signal-dependent sensitivity. In

the case that signal-dependent sensitivity is not included, global existence and boundedness were obtained
by Frassu–Viglialoro (Appl. Math. Lett.;132;Paper No. 108108;2022). However, the system including signaldependent sensitivity has not been studied yet. Also, in the literature there is a scope for improvement.
The purpose of this talk is to improve conditions for global existence and boundedness and generalize themto the case that the system includes signal-dependent sensitivity.
20 小 杉 千 春 (山 口 大 創 成)

Chiharu Kosugi (Yamaguchi Univ.)

圧縮性弾性体の伸縮運動を表す初期値境界値問題のエネルギー保存系に対する弱解の一意存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence and uniqueness weak solutions for the energy conservation
system representing motions of elastic curve on the plane

概 要 In this talk, we aim to establish existence and uniqueness of solutions to the energy conservation

system P0 for the beam equation with the nonlinear stress function having singularity. We have alreadyproved existence and uniqueness of the weak solution for the energy dissipative system P µ . The proof idea is
to show that the solution uµ of Pµ converges to the solution of P0 as µ tends to 0. By the energy inequality
for solutions of Pµ , we can obtain uniform estimates independent of µ. The estimates and Aubin’s compact
theorem imply convergence of uµ . The uniqueness is a direct consequence of our previous theorem.
21 奥 村 真 善 美 (甲南大知能情報)
深 尾 武 史 (龍谷大先端理工)

Makoto Okumura (Konan Univ.)
Takeshi Fukao (Ryukoku Univ.)

空間 2 次元の動的境界条件下の Cahn–Hilliard 方程式に対する構造保存
数値解法について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Structure-preserving numerical schemes for the Cahn–Hilliard equation
with dynamic boundary conditions in two spatial dimensions

概 要 Recently, the Cahn–Hilliard equation with dynamical boundary conditions has been proposed byGoldstein–Miranville–Schimperna (GMS) and Liu–Wu (LW). These models have characteristic conservationand dissipation laws. From the perspective of numerical computation, the properties often lead us to stablecomputation. Hence, if the designed schemes retain the properties in a discrete sense, then the schemes are
expected to be stable. In this study, we propose structure-preserving schemes for the two-dimensional GMS
and LW models that retain the conservation and dissipation laws as mentioned above in a discrete sense.
Also, we will talk about the solvability of the proposed scheme for the GMS model and show the results ofnumerical computations in the presentation.

Final: 2023/8/21
実函数論

68

14:15〜16:25
22 赤 川 佳 穂 (岐 阜 工 高 専)
加 納 理 成 ( 高 知 大 教 育)
深 尾 武 史 (龍谷大先端理工)Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)(Kochi Univ.)
Risei Kano
Takeshi Fukao (Ryukoku Univ.)ある完全塑性モデルの連続依存性について · · · · · · · · · · · · · · · · · · · · · · · · · 15

Continuous dependence of a perfect plasticity model

概 要 This paper discusses the continuous dependence of a perfect plasticity model. This model is described

as an evolution inclusion with a constraint. The constraint set is defined by a threshold function and aparallel shift. In previous work, we obtained a continuous dependence respected to outer force and initialvalue. 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 喜 多 航 佑 (早 大 理 工)
大 谷 光 春 ( 早 大 理 工)
Kosuke Kita (Waseda Univ.)Ôtani Mitsuharu (Waseda Univ.)

On global and blow-up solutions to nonlinear heat equations with nonlinear boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On global and blow-up solutions to nonlinear heat equations with nonlinear boundary conditions

概 要 This talk is devoted to studying the global existence and blowing-up of solutions of nonlinear heat

equations with nonlinear boundary conditions. Due to the lack of a homogeneous degree of the functional
associated with Laplacian under nonlinear boundary conditions, it is difficult to apply the method using
a usual potential well. In this talk, we introduce a new definition of a prohibited area, which is available
without the best constant. Moreover, we also discuss the global existence and blow-up for high-energy
solutions.
24 内 田俊 ( 大 分 大 理 工)
大 谷 光 春 ( 早 大 理 工)
(Oita Univ.)
Shun Uchida(
Mitsuharu Ôtani Waseda Univ.)

Sufficient condition of maximality of sum of monotone operators · · · · · 15
Sufficient condition of maximality of sum of monotone operators

概 要 We are concerned with sufficient conditions which assure that the sum of two monotone operators

A, B : H → 2H on the Hilbert space H becomes maximal monotone. In most previous studies, theperturbation term B is assumed to be maximal monotone or single-valued hemi-continuous, and hence wecannot apply them to the cases for the non-maximal perturbation, for instance, differential operators withdegenerate coefficients. In this talk, we propose a new type of sufficient condition where the assumption of
maximality of B is compensated by the level-set compactness of the principal part A and the demiclosednessof the perturbation B.
25 渡 邉紘 ( 大 分 大 理 工)
白 川
健 ( 千 葉 大 教 育)
( Univ. València )J. S. Moll

Hiroshi Watanabe (Oita Univ.)
Ken Shirakawa (Chiba Univ.)
J. Salvador Moll (Univ. València)

結晶粒界現象を記述する 3 次元モデルの時刻無限大における解挙動 · · · · 15

Asymptotic behavior of solutions to a 3D-model associated with grainboundary motion

概 要 We consider a phase-field model of 3D-grain boundary motion with time-dependent external forces.

The model is based on the three dimensional Kobayashi–Warren model for the dynamics of polycrystals. To
formulate our 3D-model, we use a quaternion formulation for the orientation variable. In this talk, we proveglobal existence and asymptotic behavior of solutions to the L2 -gradient descent flow of the constrainedenergy functional with time-dependent external forces. In particular, we show that the ω-limit set of thesolutions is compact and that the ω-limit points satisfy the corresponding elliptic system.

Final: 2023/8/21
69

実函数論

26 熊 崎 耕 太 (京 都 教 育 大)
A. Muntean (Karlstad Univ.)

Kota Kumazaki (Kyoto Univ. of Edu.)
Adrian Muntean (Karlstad Univ.)

多孔質媒体内の湿潤現象を表すマルチスケールモデルの時間大域解の存在· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Global solutions to a multiscale model describing swelling phenomenonin porous materials

概 要 In this talk, we consider a multiscale model describing the swelling phenomenon in porous materials.

This model consists of a diffusion equation for the relative humidity distributed in materials and a freeboundary problem describing the swelling process in microscopic pores. We consider each microscopic poreas a one-dimensional interval and correspond the interval to each point of materials. In our previous results,
for a given relative humidity we showed the well-posedness of the free boundary problem. In this talk,we impose a governing equation for the relative humidity and discuss the existence and uniqueness of a
globally-in-time solution of the model.
27 深 尾 武 史 (龍谷大先端理工)( Univ. of Pavia )P. Colli

Takeshi Fukao (Ryukoku Univ.)
Pierluigi Colli (Univ. of Pavia)

境界上の Cahn–Hilliard 方程式に対する粘性消滅法 · · · · · · · · · · · · · · · · · 15

Vanishing viscosity for the Cahn–Hilliard equation on the boundary

概 要 The well-posedness problem for the Cahn–Hilliard equation with the forward-backward dynamic

boundary conditions was treated in the previous work. We next consider the vanishing viscosity to theCahn–Hilliard equation on the boundary with the auxiliary bulk equation. We prepare two variables ofviscosity, one at the interior and the other at the boundary, and clarify the problem corresponding to each
limit. We also discuss the asymptotic analysis.
28 久 保 雅 弘 (和歌山大システム工)
山 崎 教 昭 ( 神 奈 川 大 情 報)

Masahiro Kubo (Wakayama Univ.)
Noriaki Yamazaki (Kanagawa Univ.)

Elliptic-parabolic quasi-variational evolution equations · · · · · · · · · · · · · · 15
Elliptic-parabolic quasi-variational evolution equations

概 要 We introduce a class of abstract doubly nonlinear evolution equations associated with subdifferential

operators depending on the unknown. This is modeled on quasi-variational inequalities for systems ofelliptic-parabolic partial differential equations that arise from the flows of multi-component fluids in partiallysaturated porous media. We prove the existence of a solution by employing the theory of time-dependent
subdifferential evolution equations and its generalization.
16:45〜17:45

特別講演
宮 本 安 人 ( 東 大 数 理)

優臨界楕円型方程式の球対称解の構造

Yasuhito Miyamoto (Univ. of Tokyo)

Structure of positive radial solutions for supercritical elliptic problems

概 要 We study bifurcation structures of positive radial solutions for supercritical elliptic problems in a ball.

Since the nonlinear term is supercritical, the energy cannot be controlled by an H 1 -norm, and hence it is
not well-defined in an H 1 space. We have to take another approach. In this talk we consider only thecase where the domain is a ball. Then, every classical solution is radially symmetric. Using various ODE
techniques, we clarify bifurcation structures of supercritical elliptic problems.

Final: 2023/8/21
函数解析学

函

数

解

9 月 20 日（水）

析

70

学

第 IV 会場

10:00〜12:00
1 宮 寺 優 斗 ( 埼 玉 大 理 工)

Yuto Miyadera (Saitama Univ.)

弱 Lp ノルムを用いた Lp ノルムの同値公式への注意 · · · · · · · · · · · · · · · · · 15

Remark on the formula for Lp norm characterized by weak Lp norm

概 要 We give a remark on the formula for Lp norm characterized by weak Lp norm which was introduced

by Gu and Yung in 2021. We generalize their formula and discuss relation between them.
2 大 森 祥 輔 (群馬工高専・早大理工)高 橋 淳 一 ( 早 大 理 工)
Shosuke Omori(Gunma Nat. Coll. of Tech./Waseda Univ.)
Junichi Takahashi (Waseda Univ.)

Rigged Hilbert 空間に基づく quasi-Hermitian 作用素のスペクトル分解について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the spectral decomposition of quasi-Hermitian operator based on
rigged Hilbert space

概 要 In my talk, focusing on a quasi-Hermitian operator for a non-Hermitian quantum system with apositive definite metric, its spectral decomposition based on rigged Hilbert space (RHS) is introduced.
First, a RHS associated with the positive definite metric is established. Based on the obtained space, thespectral decomposition for quasi-Hermitian and its bra-ket formalism are shown. As the application to aphysical model, the Swanson model is focused on.
3 川 本 昌 紀 ( 愛 媛 大 理 工)
石 田 敦 英 ( 東 京 理 大 教 養)

Masaki Kawamoto (Ehime Univ.)
Atsuhide Ishida (Tokyo Univ. of Sci.)

Nonexistence of wave operators for sub-quadratic repulsive potential · · 15
Nonexistence of wave operators for sub-quadratic repulsive potential

概 要 In this talk, we consider the Schrödinger operator with sub-quadratic repulsive potentials −σ|x|α .

First prove the new propagation estimates for the time propagator that can be applied to scattering theory.
Second, we prove that the wave operators do not exist if the power is greater than or equal to −(1 − α/2)
and that the threshold expectation of −(1 − α/2) is true using the new propagation estimates.
4 森 岡
悠 ( 愛 媛 大 理 工)
樋 口 健 太 ( 愛 媛 大 理 工)

Hisashi Morioka (Ehime Univ.)
Kenta Higuchi (Ehime Univ.)

量子ウォークにおける形状共鳴の複素平行移動による解析 · · · · · · · · · · · 15

A study of shape resonances for quantum walks via the complex translation method

概 要 Some properties of resonances for multi-dimensional quantum walks are studied. Resonances forquantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo
momentum space. We show some results of existence or nonexistence of resonances in an analogue of shaperesonance models which is a perturbation of a quantum walk with a non-penetrable barrier.

Final: 2023/8/21
71

函数解析学

5 佐
松
泉
井

々
澤
真
村

木
泰
之
航

格 (信 州 大 理) ♭ 対相互作用模型の散乱理論について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
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)

On the scattering theory of the pair interaction model

概 要 We discuss scattering theory of the abstract pair interaction model. The pair interaction model

is a quantum field model which have quadratic interactions of the fields, and can describe nucleonmeson interactions and interacting electron-light systems in the dipole approximation. Since this model isdiagonalized by a Bogoliubov transformation, its scattering theory can also analyzed in detail. It is shownthat the scattering operator in this model is non-trivial. This is in contrast to the van Hove model whichhave trivial scattering operator.
6 V. Louatron( 立 命 館 大 理 工)

Vincent Louatron (Ritsumeikan Univ.)

Semiclassical resonances for matrix Schrödinger operators with vanishing interactions at crossings of classical trajectories · · · · · · · · · · · · · · · · · 15
Semiclassical resonances for matrix Schrödinger operators with vanishing interactions at crossings of classical trajectories

概 要 We study the semiclassical distribution of resonances of a 2 × 2 matrix Schrödinger operator. Theenergy considered is above the energy-level crossing of the two associated classical trajectories, and isrespectively trapping and non-trapping for those trajectories. Under a condition between the contact orderm of the crossings and the vanishing order k of the interaction term at the crossing points, we show
that, asymptotically in the semiclassical limit h → 0+ , the imaginary part of the resonances is of sizeh1+2(k+1)/(m+1) in the general case and shrinks to h1+2(k+2)/(m+1) when both k and m are odd. We also
compute the first term of the associated asymptotic expansions.
7 樋 口 健 太 ( 愛 媛 大 理 工)
Kenta Higuchi(Ehime Univ.)

Local scattering matrix for a degenerate avoided-crossing in the noncoupled regime · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Local scattering matrix for a degenerate avoided-crossing in the noncoupled regime

概 要 A Landau–Zener type formula for a degenerate avoided-crossing is studied in the non-coupled regime.

More precisely, a 2 × 2 system of first order h-differential operator with O(ε) off-diagonal part is consideredin 1D. Asymptotic behavior as εhm/(m+1) → 0+ of the local scattering matrix near an avoided-crossing
is given, where m stands for the contact order of two curves of the characteristic set. A generalization
including the cases with vanishing off-diagonals and non-Hermitian symbols is also given.

Final: 2023/8/21
函数解析学

特別講演
渡 邊 道 之 ( 岡 山 理 大 理)

72

14:15〜15:15

Michiyuki Watanabe(Okayama Univ. of Sci.)

Inverse N-body scattering with the time-dependent Hartree–Fock approximation
Inverse N-body scattering with the time-dependent Hartree–Fock approximation

概 要 The speaker presents a talk on an inverse N-body scattering problem in quantum mechanics. The

problem involves determining two potentials: an external potential acting on all particles and a pairinteraction potential, from the behavior of scattered particles.
The speaker proposes using the time-dependent Hartree–Fock approximation in a three-dimensional setting
to address this inverse scattering problem. Specifically, they focus on high-velocity initial states.
The speaker demonstrates that the leading part of the asymptotic expansion of the scattering operator
allows for the unique reconstruction of the Fourier transform of the pair interaction potential. Additionally,
they find that the second term of the expansion enables the unique reconstruction of the X-ray transform of
the external potential.
In summary, the speaker’s work utilizes the time-dependent Hartree–Fock approximation and asymptotic
analysis to tackle an inverse N-body scattering problem in quantum mechanics. Their findings reveal thatthe asymptotic expansion of the scattering operator for the Hartree–Fock equation provides a means torecover the Fourier transform of the pair interaction potential and the X-ray transform of the externalpotential.

9 月 21 日（木）第 IV 会場

9:30〜11:15
8 岩 田 順 敬 (大阪経法大国際)
Yoritaka Iwata(Osaka Univ. of Economics Law)

非有界作用素の対数表現による無限次元抽象空間におけるキュムラント
母関数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Cumulant generating function in infinite-dimensional abstract spaces
based on the logarithmic representation of unbounded operators

概 要 A mathematical framework for defining cumulant generating function in infinite-dimensional abstract

spaces is presented based on the logarithmic representation of unbounded operators. Much attention is paid
to obtain the abstract evolution equation of moment.
9 田 端

亮 ( 有 明 工 高 専)

Ryo Tabata (Ariake Nat. Coll. of Tech.)

プレシズムに対応する行列関数の恒等式 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Matrix Identities Corresponding to Plethysm

概 要 Plethysm is another type of the product of Schur functions introduced by Littlewood, which originatesfrom the representation theory of the general linear groups. A classical problem to give a combinatorialdescription for plethysm coefficient remains open since the 1940s. Since Schur functions also have an aspectof the representations of the symmetric groups, Robinson constructed the representations corresponding toplethysm in terms of the symmetric groups. In this talk, we design a matrix type of identities which areparallel to plethysm, following Robinson’s construction.

Final: 2023/8/21
73

函数解析学

10 中 田 彬 文 (広島大先進理工)

Akifumi Nakada (Hiroshima Univ.)

The Delsarte theory for probability measures on homogeneous spaces
from compact Gelfand pairs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Delsarte theory for probability measures on homogeneous spaces
from compact Gelfand pairs

概 要 In combinatorial optimization, which aims to find the optimal objects under certain conditions, coding

theory and design theory are both important and active researching themes. The goal of coding theoryis efficient and trustworthy communications, and the goal of design theory is efficient and trustworthy
samplings. The Delsarte theory links these two theories as dual concepts through Fourier analysis, andgive a fundamental tool to study codes and designs. For example, the Delsarte theory for finite subsets on
spheres contributes to the kissing number problem and the sphere packing problem. In this talk, we give aformulation of the Delsarte theory for probability measures.
11 中 濱 良 祐(NTT 基礎数学研究センタ)
Ryosuke Nakahama(NTT Inst. for Funda. Math.)

Symmetry breaking operators of holomorphic discrete series representations for (SU (3, 3), SO∗ (6)) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Symmetry breaking operators of holomorphic discrete series representations for (SU (3, 3), SO∗ (6))

概 要 Let (G, G′ ) be a symmetric pair of tube type, and let H be a holomorphic discrete series representationof scalar type of G. Then the restriction H|G′ is decomposed into a direct sum of unitary representations of
G′ multiplicity-freely, and for each subrepresentation H′ , there exists uniquely (up to scalar multiple) a G′ intertwining operator (symmetry breaking operator) from H|G′ to H′ . In this talk, the speaker presents theresults on explicit construction of symmetry breaking operators for the case (G, G′ ) = (SU (3, 3), SO∗ (6)).
12 長 岡 高 広
和 地 輝 仁 ( 北 教 大 釧 路)
Takahiro Nagaoka
Akihito Wachi (Hokkaido Univ. of Edu.)

相対不変式で生成されるゴレンスタイン環のレフシェッツ性 · · · · · · · · · · 15

The strong Lefschetz property of Gorenstein algebras generated by relative invariants

概 要 We report the strong Lefschetz property for Artinian Gorenstein algebras generated by the relative

invariants F of prehomogeneous vector spaces of commutative parabolic type. In this setting F includes
determinants, determinants of symmetric matrices, pfaffians and so on. The set of Lefschetz elements is
precisely determined, and the annihilator of F is also precisely determined.
13 洞

彰 人 (北大理)Akihito Hora (Hokkaido Univ.)

対称群のスピン Jucys–Murphy 元の動的スピン極限形状への応用 · · · · · 15

Application of spin Jucys–Murphy elements of symmetric groups to dynamical spin limit shapes

概 要 We consider a spin JM element in the group algebra of a representation group of a symmetric groupand show a formula for its moments. As an application, we discuss the problem of dynamical limit shapes
in ensembles of Young diagrams arising from spin representations of symmetric groups.

Final: 2023/8/21
函数解析学

特別講演
東 條 広 一 ( 理 化 学 研)

74

13:15〜14:15

Koichi Tojo

(RIKEN)

スタンダードコンパクト Clifford–Klein 形を持つ既約対称空間の分類

Classification of irreducible symmetric spaces which admit standard
compact Clifford–Klein forms

概 要 Let G be a Lie group, H a closed subgroup of G and Γ a discrete subgroup of G. If Γ acts on G/Hproperly discontinuously and freely, then the double coset space Γ\G/H has a natural manifold structure
and is called a Clifford–Klein form of G/H. Moreover, if G/H is of reductive type and there exists a
reductive subgroup of G containing Γ and acting on G/H properly, Γ\G/H is said to be standard. One
of important problems in this field is “Which homogeneous space G/H admits a compact Clifford–Klein
form?”. In this talk, we consider the subproblem “Classify homogeneous spaces G/H of reductive typewhich admit standard compact Clifford–Klein forms”. More precisely, we give the classification in the classof irreducible symmetric spaces, and see our strategy to obtain the classification.

9 月 22 日（金）第 IV 会場

9:30〜11:00
14 安 藤 浩 志 (千 葉 大 理)
( TU Dresden )A. Thom(Chiba Univ.)
Hiroshi Ando
Andreas Thom (TU Dresden)

Common transversals for coset spaces of compact groups · · · · · · · · · · · · 15
Common transversals for coset spaces of compact groups

概 要 Let G be a Polish group and let H ≤ G be a compact subgroup. We prove that there exists a Borel

set T ⊂ G which is simultaneously a complete set of coset representatives of left and right cosets, provided
that a certain index condition is satisfied. Moreover, we prove that this index condition holds provided that
G is locally compact and G/G◦ is compact or H is a compact Lie group. This generalizes a result which is
known for discrete groups under various finiteness assumptions, but is known to fail for general inclusionsof infinite groups. As an application, we prove that Bohr closed subgroups of countable, discrete groups
admit common transversals.
15 北 村侃 ( 東 大 数 理)

Kan Kitamura (Univ. of Tokyo)

Discrete quantum subgroups of complex semisimple quantum groups · 15
Discrete quantum subgroups of complex semisimple quantum groups

概 要 In this talk, discrete quantum subgroups of the quantum double of a compact quantum group will be

examined. It will be observed that such quantum groups often do not admit a quantum version of lattices.
In the case of the quantum double of q-deformation of a compact semisimple Lie group regarded as its
complexification, we can obtain a classification of its discrete quantum subgroups.
16 田 中 聖 人 (名 大 多 元 数 理)

Masato Tanaka (Nagoya Univ.)

Cocycles on quantum groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Cocycles on quantum groups

概 要 A 1-cocycle on a group is a map which is compatible with a given representation. This map has many

information on a group (e.g. Haargerup property and property (T) etc.) and appears in many areas (e.g.
the theory of the theory of Lévy processes and Popa’s deformation/rigidity theory etc.). In this talk, we
consider consider 1-cocycles on (operator algebraic) quantum groups. In particular, we construct 1-cocycles
on the Drinfeld double of the compact quantum group SUq (2) and on the locally compact quantum groupgq (1, 1).
SUFinal: 2023/8/21
75

函数解析学

17 増 田 俊 彦 (九 大 数 理)

Toshihiko Masuda (Kyushu Univ.)

Actions of discrete amenable groups into the normalizers of full groupsof ergodic transformations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Actions of discrete amenable groups into the normalizers of full groupsof ergodic transformations

概 要 We apply Evans–Kishimoto’s intertwining argument to the classification of actions of discrete amenablegroups into the normalizer of a full group of an ergodic transformation. Our proof does not depend on thetypes of ergodic transformations.
18 渚
勝 ( 立 命 館 大 理 工)大⋆)
綿 谷 安 男 (九Masaru Nagisa (Ritsumeikan Univ.)
Yasuo Watatani (Kyushu Univ.⋆)

コンパクト環上の非線型 Choquet トレース —双対ノルム, 擬ノルム—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Non-linear Choquet traces on compact algebras —dual norms, quasi
norms—

概 要 Let {α(n)}∞n=0 be an increasing sequence with α(0) = 0, which corresponds to a monotone measureon {0, 1, 2, . . .}. Then the Choquet trace on compact operators is functional on compact operators definedP∞by φα (a) = i=1 (α(i) − α(i − 1))λi (a)(∈ [0, ∞]) for a compact positive operator a, where λi (a) means
the i-th eigenvalue of a by the decreasing order. We have already given the equivalent condition that|||a|||α = φα (|a|) satisfies triangle inequality. In this talk, (1) we determine the form of the dual norm of|||a|||α on the algebra of finite rank operators, and (2) we determined the equivalent condition that φα isquasinorm on this algebra.
14:15〜16:00
19 古 市茂 ( 日 大 文 理)

Shigeru Furuichi (Nihon Univ.)

幾何平均とスペクトル幾何平均に関する不等式 · · · · · · · · · · · · · · · · · · · · · 15

Operator inequalities between geometric mean and spectral geometricmean

概 要 Two operator inequalities between geometric mean and spectral geometric mean are shown. Studying

properties of the generalized Kantorovich constant, we determine two bounds superior or inferior.
20 瀬 尾 祐 貴 (大阪教育大教育)
Yuki Seo (Osaka Kyoiku Univ.)

Karcher 幾何平均と Hadamard 積について · · · · · · · · · · · · · · · · · · · · · · · · 15
The Hadamard product of positive invertible operators and Karcher
geometric mean

概 要 In this talk, we estimate the difference between the Hadamard product and the Karcher mean of npositive invertible operators on the Hilbert space in terms of the Specht ratio and the Kantorovich constant.
21 遠 山 宏 明 (前 橋 工 科 大)亀井栄三郎
渡 邉 雅 之 ( 前 橋 工 科 大)Hiroaki Tohyama(Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)Operator valued inequalities based on Young’s inequality · · · · · · · · · · · · 15

Operator valued inequalities based on Young’s inequality

概 要 Various refinements of Young’s inequality have been obtained by many authors. Based on one ofthose refinements we will construct a new operator inequality, which is obtained by generalizing the operator
valued α-divergence.

Final: 2023/8/21
函数解析学

22 森
迪 也
(東大数理・理化学研 iTHEMS)(Univ. of Ljubljana)
P. Šemrl

Michiya Mori (Univ. of Tokyo/RIKEN)Peter Šemrl (Univ. of Ljubljana)76

Nonexpansive and noncontractive mappings on the set of quantum purestates · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Nonexpansive and noncontractive mappings on the set of quantum purestates概 要 Wigner’s theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In

metric geometry nonexpansive maps and noncontractive maps are well studied generalizations of isometries.
We show that under certain conditions Wigner symmetries can be characterized as nonexpansive or noncontractive maps on the set of all projections of rank one. The assumptions required for such characterizations
are injectivity or surjectivity and they differ in the finite and the infinite-dimensional case. We also givea description of nonexpansive maps which satisfy a condition that is much weaker than surjectivity. Suchmaps do not need to be Wigner symmetries. The optimality the results is shown by counterexamples.
23 三 浦毅 ( 新 潟 大 理)
榎 並 優 太 ( 新 潟 大 自 然)
Takeshi Miura (Niigata Univ.)(Niigata Univ.)
Yuta Enami

微分構造をもつ Banach 空間の Tingley 問題 · · · · · · · · · · · · · · · · · · · · · · · 15

Tingley’s problem for Banach spaces with deferential structures

概 要 Let A be a uniformly closed, extremely C-regular subspace of C0 (X) for a locally compact Hausdorff

space X. Let B = A ⊕ℓ1 C and SB the unit sphere of B. We shall prove that each surjective isometry
between SB admits a surjective isometry between the whole space B.
24 羽 鳥

理 (新

潟

大⋆)

Osamu Hatori (Niigata Univ.

⋆)

The Mazur–Ulam property for spaces of harmonic functions · · · · · · · · · 15
The Mazur–Ulam property for spaces of harmonic functions

概 要 We study the Mazur–Ulam property for real Banach spaces including spaces of harmonic functions.

16:15〜17:15

特別講演
大 井 志 穂 ( 新 潟 大 理)

Shiho Oi

(Niigata Univ.)バナッハ環におけるノルム構造, 代数構造, 順序構造の関係

The relationship between norm, algebraic, and order structure of Banach algebras

概 要 The Banach–Stone theorem states that every unital surjective linear isometry on unital commutativeC ∗ -algebras is an algebra isomorphism. Moreover, Gelfand and Kolmogorov, and Kaplansky show thatalgebra isomorphisms and lattice isomorphisms on unital commutative C ∗ -algebras can be represented byweighted composition operators. These imply that the maximal ideal spaces of unital commutative C ∗ algebras are uniquely determined by the isometric structure, the algebraic structure, and the order structure.
Kadison generalized a series of the theorems to unital C ∗ -algebras. This emphasizes the interplay between
these structures and their role in characterizing the underlying space. Motivated by that, we study the
relations between the isometric structure, the algebraic structure, and the order structure on Banach
algebras. Specially, we study Banach algebras of continuous maps or Lipschitz maps which take values inunital C ∗ -algebras. We also study Fourier algebras on locally compact groups. We obtain representationsof several linear preserving maps on the Banach algebras and consider the isometric structure, the algebraic
structure, and the order structure of given Banach algebras.

Final: 2023/8/21
77

統計数学

統 計
9 月 20 日（水）数学第 VII 会場

9:30〜11:30
1 中 川 由 宇 斗 ( 東 北 大 理)

Yuto Nakagawa (Tohoku Univ.)

Left regular band を用いた推移確率行列の固有値と重複度の考察 · · · · · 15
Consideration of eigenvalues and multiplicity of stochastic matrix using
left regular band

概 要 We consider eigenvalues and multiplicity of stochastic matrix. A left-regular band is a semigroup

S that satisfies x2 = x, xyx = xy. A deck of n cards are shuffled by removing the card labeled i withprobability wi and replacing it on top. This process can be considered as a Markov chain on the symmetricgroup, and called Tsetlin library. In this talk, we consider the colored Tsetlin library and q-analog of the
Tsetlin library.
大理)
2 塩 沢 裕 一 (阪(Fujian Normal Univ.)
Jian Wang

Yuichi Shiozawa (Osaka Univ.)
Jian Wang (Fujian Normal Univ.)

Hausdorff dimensions of inverse images and collision time sets for symmetric Markov processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hausdorff dimensions of inverse images and collision time sets for symmetric Markov processes

概 要 In this talk, we establish the Hausdorff dimensions of inverse images and collision time sets for a large

class of symmetric Markov processes on metric measure spaces. We develop the approach of the works by
Hawkes and Jain–Pruitt, and make full use of heat kernel estimates. We apply our results to symmetricdiffusion processes and symmetric jump processes on d-sets.
3 濱 名 裕 治 (筑波大数理物質)

Yuji Hamana (Univ. of Tsukuba)

双曲ベッセル過程の到達時刻について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Hitting times of hyperbolic Bessel processes

概 要 The generalization of the radial part of Brownian motion on a hyperbolic space is called hyperbolic

Bessel process. We give the Laplace transform of its hitting time and the probability that the hitting time
is finite. Moreover we give the limiting value of the expectation of the hitting time under the condition thatthe hitting time is finite.
4 濱 名 裕 治 (筑波大数理物質)
松 本 裕 行 ( 青 学 大 理 工)

Yuji Hamana (Univ. of Tsukuba)
Hiroyuki Matsumoto(Aoyama Gakuin Univ.)

Brownian hitting to spheres · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Brownian hitting to spheres

概 要 We consider linear Brownian motions with constant drifts. The aim is to show explicit formulae bymeans of spherical harmonics for the densities of the joint distributions of the first hitting times to spheres
and the positions. We also study the asymptotic behavior of the distribution function as time tends toinfinity.

Final: 2023/8/21
統計数学

5 綾

朝 弘 (京Tomohiro Aya

大理)(Kyoto Univ.)78

非有界係数を含む楕円型偏微分方程式の確率的均質化の定量的評価 · · · · 15

Quantitative stochastic homogenization of elliptic equations with unbounded coefficients概 要 In this talk, we consider stochastic homogenization of elliptic equations with unbounded and non-uniformly elliptic coefficients. Extending subadditive arguments, we get an estimate for the rate of theconvergence of the solution of the Dirichlet problem under the condition that coefficients in the unit cube
have a certain exponential integrability. For the coefficient field in this talk, we only assume a constantdecrease at a constant distance of the maximal correlation as an assumption of ergodicity, and stationarity
with respect to Zd -translations.
6 濵 口 雄 史 ( 阪 大 基 礎 工)

Yushi Hamaguchi (Osaka Univ.)

確率 Volterra 積分方程式の Markov リフトと漸近的対数 Harnack 不等式· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Markovian lifting and asymptotic log-Harnack inequality for stochastic
Volterra integral equations

概 要 We introduce a new framework of Markovian lifts of stochastic Volterra integral equations (SVIEs for

short) with completely monotone kernels. We define the state space of the Markovian lift as a separable
Hilbert space which incorporates the singularity or regularity of the kernel into the definition. We showthat the solution of an SVIE is represented by the solution of a lifted stochastic evolution equation, which
is a Markov process on the Hilbert space. Furthermore, we establish an asymptotic log-Harnack inequality
and some consequent properties for the Markov semigroup associated with the Markovian lift.
7 蛯 名 真 久 (京大理)Masahisa Ebina (Kyoto Univ.)

Central limit theorems for stochastic wave equations in high dimensions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Central limit theorems for stochastic wave equations in high dimensions

概 要 In this talk, we consider stochastic wave equations in four or more spatial dimensions. We assume

that the driving noise is given by the Gaussian noise that is white in time and has the Riesz kernel as a
spatial correlation. Using the Malliavin–Stein approach, we show that the spatial average of the solution
over a ball converges to the standard normal distribution as the radius of the ball increases to infinity. We
also present the corresponding functional central limit theorem.
8 佐 々 田 槙 子 ( 東 大 数 理)
大工)
魚 住 亮 介 (東Makiko Sasada (Univ. of Tokyo)
Ryosuke Uozumi (Univ. of Tokyo)

Yang–Baxter 写像と独立性保存則 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Yang–Baxter maps and independence preserving property

概 要 We find a surprising relationship between two properties for bijective functions F : X × X → X × X

for a set X which are introduced from very different backgrounds. One of the property is that F is a
Yang–Baxter map, namely it satisfies the set-theoretical Yang–Baxter equation, and the other property is
the independence preserving property (IP property for short), which means that there exist independent
random variables X, Y such that U, V are also independent with (U, V ) = F (X, Y ).

Final: 2023/8/21
79

統計数学

14:15〜15:15

特別講演
松 浦 浩 平 (筑波大数理物質)

Kouhei Matsuura (Univ. of Tsukuba)

領域の分割上のマルコフ連鎖による反射壁ブラウン運動の離散近似

Discrete approximation of reflected Brownian motions by Markov chainson partitions of domains

概 要 Discrete approximation of a space is one of the problems that appear in many areas of mathematics.

In probability theory, this is often studied in relation to the scaling limits of random walks or Markov chains.
One of the most typical examples is approximating the Brownian motion on the d-dimensional Euclidean
space Rd by the simple random walks on the scaled lattices n−1 Zd , n ∈ N, and this result has been extended
in a wide range of directions.
In this talk, we will consider discrete approximation of the reflected Brownian motion (RBM) on a domain
D ⊂ Rd . Our approximation is given by Markov chains on a sequence of general partitions of D whose
sizes converge to 0 in an appropriate sense. A typical example of such partitions is the Voronoi partition
associated with uniformly distributed independent random points in D. In this kind of situation, it is a
non-trivial problem to construct appropriate Markov chains approximating RBM because partitions are
inhomogeneous. We will explain how to construct a specific Markov chain on each partition in such a waythat the inhomogeneity is taken into consideration and prove that its distribution converges weakly to RBM
in the Skorohod space. This is a joint work with Masanori Hino and Arata Maki.
15:30〜16:30

特別講演

難 波 隆 弥 ( 京 都 産 大 理)

ベキ零被覆グラフ上のランダムウォークの極限定理

Ryuya Namba (Kyoto Sangyo Univ.)

Limit theorems for random walks on nilpotent covering graphs

概 要 A nilpotent covering graph is an infinite covering graph of a finite graph whose covering transformationgroup is finitely generated and nilpotent. In this talk, we discuss recent progress in limit theorems for random
walks on nilpotent covering graphs, by putting emphasis on geometric features of underlying graphs. In
particular, we focus on central limit theorems including their rates of convergences, large and moderate
deviation principles, and laws of the iterate logarithm for non-symmetric random walks on nilpotent coveringgraphs. Some possible directions of these topics are discussed as well.

9 月 21 日（木）第 VII 会場

9:30〜11:30
9 駒 場
敦 ( 山 梨 大 医)城 野 悠 志 ( 山 梨 大 医)中 本 和 典 ( 山 梨 大 医)Atsushi Komaba (Univ. of Yamanashi)
Hisashi Johno (Univ. of Yamanashi)
Kazunori Nakamoto(Univ. of Yamanashi)

1 次元単純ランダムウォークの範囲における鏡像法の応用 · · · · · · · · · · · · 15

An application of the method of images in calculations on the range ofa one-dimensional simple random walk概 要 It is known that the general term of Catalan numbers can be derived with the method of images, atool to solve some differential and difference equations. In this study, we apply this method in calculations
on the range Dn of a one-dimensional simple random walk {Si }ni=0 , defined as S0 = 0, Si = Si−1 + Xi
(i = 1, . . . , n), and Dn = #{S0 , . . . , Sn }, where X1 , . . . , Xn are independent random variables which takethe values ±1 with probability 1/2 each. We think of infinite reflections by two parallel mirrors, which gives
us an expression for Pr(Dn ≤ d, Sn = 0) where d is a positive integer.

Final: 2023/8/21
統計数学

10 河 本 野 恵 (北大理)

Noe Kawamoto (Hokkaido Univ.)

80

Rate of convergence of the critical point of the memory-τ self-avoiding
walk in dimensions d > 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Rate of convergence of the critical point of the memory-τ self-avoiding
walk in dimensions d > 4

概 要 We consider the spread-out models of the self-avoiding walk and its finite-memory version, called

the memory-τ walk. For both models, each step is uniformly distributed over the d-dimensional box{x ∈ Zd : ∥x∥∞ ≤ L}. The critical point pτc for the memory-τ walk converges to the critical point p∞c for
the self-avoiding walk as τ ↑ ∞. By using the lace expansion, we show that for d > 4 and L sufficiently
large,
τp∞c − pc =where Σ2U =R
x∈Rd :∥x∥∞ ≤1

2
d−2



d
2πΣ2U

 d2

L−d τ − 2

d−2




d−2
1 + O(L−1 ) + O(1/(τ 2 log τ ))|x|2 dd x.

11 久 保 田 直 樹 (日 大 理 工)
竹 居 正 登 ( 横 浜 国 大 工)
Naoki Kubota (Nihon Univ.)
Masato Takei (Yokohama Nat. Univ.)

Bernoulli first-passage percolation における極限形状の比較 · · · · · · · · · · 10
Comparison of limit shapes for Bernoulli first-passage percolation

概 要 We consider Bernoulli first-passage percolation on the d-dimensional hypercubic lattice with d ≥ 2.

The passage time of edge e is 0 with probability p and 1 with probability 1 − p, independently of each other.
Let pc be the critical probability for percolation of edges with passage time 0. When 0 ≤ p < pc , there exists
a nonrandom, nonempty compact convex set Bp such that the set of vertices to which the first-passage timefrom the origin is within t is well-approximated by tBp for all large t, with probability one. The aim of thispaper is to prove that for 0 ≤ p < q < pc , the Hausdorff distance between Bp and Bq grows linearly in q − p.
12 小 川 重 義 (立 命 館 大 理 工)

Shigeyoshi Ogawa (Ritsumeikan Univ.)

Noncausal calculus approach to Wong–Zakai’s theorem on the approximation of SDE · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Noncausal calculus approach to Wong–Zakai’s theorem on the approximation of SDE

概 要 The aim of the present talk is two-fold: First point is to show extended results for Wong–Zakai’s

theorem in two directions: one is sharper than Wong–Zakai’s theorem and the second is a noncausal versionof the first result. The second point is that we do it in the framework of the noncausal stochastic calculus.
This way of study gives us many merits. For instance, in that framework we can treat the subject in thosedifferent two cases in a unified manner, Besides we can give proofs of those theorems in a much simpler
way than in Wong–Zakai’s paper. Whole discussions being developed in that framework, for the details
about materials and related facts we would refer to “Noncausal Stochastic Calculus” by Ogawa, S., (2017,
Springer).
13 世 良Toru Sera

透 (阪

大

理)

(Osaka Univ.)

間欠力学系の逆正弦法則に関連する大偏差評価 · · · · · · · · · · · · · · · · · · · · · 15

Large deviations related to arcsine laws for intermittent maps

概 要 Interval maps with indifferent fixed points are called intermittent maps. They are typical examples

of infinite ergodic transformations. Many researchers have studied various probabilistic limit theorems forintermittent maps, such as Darling–Kac type limit theorem and Dynkin–Lamperti type arcsine laws. In
this talk, we study large deviations related to Dynkin–Lamperti type arcsine laws for intermittent maps.

Final: 2023/8/21
81

統計数学

14 中 島 由 人 (慶 大 理 工)
Yuto Nakajima(Keio Univ.)

フラクタル n 角形のマンデルブロ集合と冪級数の零根について · · · · · · · 15

Mandelbrot set for fractal n-gons and zeros of power series

概 要 We give a framework to study the connectedness of the set of zeros of power series with coefficients ina finite subset G ⊂ C. We prove that the set of zeros in the unit disk is connected and locally connected ifsome graph on the set G of coefficients is connected. Furthermore, we apply this result to the study of theMandelbrot set Mn for fractal n-gons. We prove that Mn is connected and locally connected for any n.
15 植 田 優 基 (北 教 大 旭 川)
O. Arizmendi ( CIMAT )大理)
藤 江 克 徳 (北Yuki Ueda (Hokkaido Univ. of Edu.)
Octavio Arizmendi (CIMAT)
Katsunori Fujie (Hokkaido Univ.)

Limit theorems and new combinatorial identities in finite free probability theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Limit theorems and new combinatorial identities in finite free probability theory

概 要 In 2010s, the finite free probability theory was initiated by Marcus, Spielman and Srivastava toshow link between recent theory via the polynomial convolutions introduced by Szegő and free probability
theory. Moreover, Arizmendi and Perales introduced the finite version of free cumulants to understandfinite free probability via the combinatorial theory. In this talk, we will give the limit theorems for thefinite free multiplicative convolution. More strictly, we investigate the finite free analogue of Sakuma andYoshida’s free limit theorem and give an alternative proof of Kabluchko’s limit theorem for free unitary
normal distribution which was introduced by Biane. To prove them, we need to get rigorous combinatorial
identities for partitions of a finite set, so we explain these results obtained from our works. This is a joint
work with Octavio Arizmendi (CIMAT) and Katsunori Fujie (Hokkaido University).
16 寺 田 知 幸 (金 沢 工 大)
井 手 勇 介 ( 日 大 文 理)
今 野 紀 雄(立命館大理工・横浜国大⋆)Tomoyuki Terada(Kanazawa Inst. of Tech.)(Nihon Univ.)
Yusuke Ide
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)

パスグラフ上のランダムウォーク・量子ウォークの再帰確率 · · · · · · · · · · 15

Return probabilities for random walks and quantum walks on the pathgraph

概 要 In this talk, we focus on discrete-time random walks (DTRWs) on the path graph with reflecting walls.

Also we consider the corresponding continuous-time random walks (CTRWs), discrete-time quantum walks(DTQWs) and continuous-time quantum walks (CTQWs). We give formulas for the return probabilitiesof these four walks (DTRWs, CTRWs, DTQWs, CTQWs) at the boundary point of the path graph anddiscuss their relationships.
11:30〜12:00

統計数学分科会総会

9 月 22 日（金）第 VII 会場

9:30〜11:30
17 若 木 宏 文 (広 島 大 理)

Hirofumi Wakaki (Hiroshima Univ.)

経時データに関する混合線形モデルのモデル選択規準について · · · · · · · · 15

On model selection criteria for mixed linear models for longitudinal data.

概 要 The models treated are polynomial regression models in which some partial regression coefficients are

random variables. The maximum likelihood estimators of the covariance parameters and the asymptotic
expansion of the bias of the AIC are derived. We consider the correction of the bias.

Final: 2023/8/21
統計数学

18 増 田 弘 毅 (東 大 数 理)
藤 永 雄 基 ( 九 大 数 理)

Hiroki Masuda (Univ. of Tokyo)
Yuki Fujinaga (Kyushu Univ.)

82

Asymptotic inference for a non-Gaussian location-scale mixed-effects
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic inference for a non-Gaussian location-scale mixed-effects
model

概 要 Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class oflocation-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying
generalized hyperbolic distribution. We first study the local maximum-likelihood asymptotics and reveal
the instability in the numerical optimization of the log-likelihood. Then, we construct an asymptoticallyefficient estimator based on the Newton–Raphson method based on the original log-likelihood function with
the initial estimator being naive least-squares-type. Numerical experiments are conducted to show that the
proposed one-step estimator is not only theoretically efficient but also numerically much more stable andmuch less time-consuming compared with the maximum-likelihood estimator.
19 吉 田 拓 真 (鹿 児 島 大 理)

Takuma Yoshida (Kagoshima Univ.)

Asymptotic properties of generalized additive models in extreme value
theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Asymptotic properties of generalized additive models in extreme value
theory概 要 The classical approach to analyzing extreme value data is the generalized Pareto distribution (GPD).

When the GPD is used to explain a target variable with the large dimension of covariates, the shape andscale function of covariates included in GPD are sometimes modeled using the generalized additive models(GAM). In contrast to many results of application, there are no theoretical results on the hybrid techniqueof GAM and GPD, which motivates us to develop its asymptotic theory. We provide the rate of convergenceof the estimator of shape and scale functions, as well as its local asymptotic normality.
20 栗 田 絵 梨 (東 京 理 大 理)
瀬 尾
隆 ( 東 京 理 大 理)

Eri Kurita (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

Multivariate kurtosis test for multivariate normality with monotone
missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Multivariate kurtosis test for multivariate normality with monotone
missing data

概 要 A sample measure of multivariate kurtosis under general monotone missing data is provided. Thisdefinition is an extension of the multivariate sample kurtosis under two and three-step monotone missing
data that were already given. To test a multivariate normality on the monotone missing data, we derive
the evaluation of the expectation and variance of the sample measure of multivariate kurtosis by asymptotic
expansion procedure. The expectation and variance are used to standardized the multivariate sample
kurtosis and we propose test statistics. The statistics asymptotically follow a standard normal distribution
under the null distribution. Finally, the normal approximation for the null distribution of the test statistics
is investigated via Monte Carlo simulation.
21 仲 北 祥 悟 (東 大 総 合 文 化)

Shogo Nakakita (Univ. of Tokyo)

非対数凹非平滑分布に対する Langevin 型モンテカルロアルゴリズム · · · 15

Langevin-type Monte Carlo algorithm for non-log-concave non-smooth
distributions

概 要 We propose a Langevin-type Monte Carlo algorithm for sampling from non-log-concave non-smooth

distributions. A basic idea of the algorithm is empirical mollification; we mollify the gradient of the potentialfunction of a target distribution by a Monte Carlo method and run the unadjusted Langevin algorithm. The
proposed algorithm can approximate target distributions satisfying mild conditions with arbitrary precisionsin 2-Wasserstein distance.

Final: 2023/8/21
83

統計数学

22 仲 北 祥 悟 (東 大 総 合 文 化)

Shogo Nakakita (Univ. of Tokyo)

ジャンプ付き確率微分方程式クラスのエルゴード性に対する一様評価 · · 15

Uniform estimates for the ergodicity of a class of stochastic differential
equations with jumps

概 要 We consider uniform estimates of total variation distances between Markov kernels of ergodic solutionsof stochastic differential equations in a class and its invariant probability measures. Our main result is
simple sufficient conditions for such estimates with exponential or sub-exponential decay. We apply it to
non-asymptotic risk bounds for estimation of stochastic differential equations under discrete observations.
23 田 中 輝 雄 (広 島 市 大 情 報)

Teruo Tanaka (Hiroshima City Univ.)

ある分数型評価基準の最適停止問題について · · · · · · · · · · · · · · · · · · · · · · · 10

On some fractional optimal stopping problems

概 要 We give the formulation of discrete time optimal stopping problems with the criterion of a fractional

reward. Using the standard mathematical arguments in the theory of mathematical programming, we provethe existence of optimal stopping times for these problems under the certain assumption on the regularityof the stochastic process.
24 藤 田 敏 治 (九 工 大 工)

確率環境下における分岐・合流型決定過程 —状態発生順序が不確実な場
合— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Toshiharu Fujita(Kyushu Inst. of Tech.)

Stochastic decision process model with feedforward loop system —Uncertain
state occurrence order—

概 要 In this study, we consider a stochastic decision process model with a feedforward loop system which

is one of the nonserial transition systems. When the order of state occurrence is uncertain, we introduce
recursive equations by using dynamic programming technique.
14:15〜15:15

特別講演
栗 栖 大 輔 (東 大CSIS)

Daisuke Kurisu (Univ. of Tokyo)

非定常空間データのモデリングと統計的推測

Modeling and statistical inference for nonstationary spatial data

概 要 In this talk, we will begin by introducing various models for (nonstationary) spatial data and thendelve into the topic of statistical inference for nonstationary spatial data.
In the first part of the talk, we begin with reviewing autoregressive and moving average (ARMA) processes
and consider continuous ARMA (CARMA) random fields, which serve as an extension of ARMA processes
specifically designed for spatial data on d-dimensional Euclidean space. Furthermore, we will discuss theextension of CARMA random fields to nonstationary cases by introducing locally stationary Levy-driven
moving average random fields.
In the second part of the talk, we will address three problems related to statistical inference of nonstationary
spatial data. Specifically, we will focus on the following areas: (1) high-dimensional central limit theorems
and bootstrap for high-dimensional spatial data, (2) nonparametric inference of spatial trend function, and(3) nonparametric regression for locally stationary spatial data.
By covering these topics, we aim to provide an overview of the challenges and approaches involved instatistical inference for nonstationary spatial data.

Final: 2023/8/21
統計数学

特別講演
坂 田 綾 香 ( 統 計 数 理 研)

グラフィカルモデルを用いた確率推論の回帰問題における展開

Ayaka Sakata (Inst. of Stat. Math.)

Probabilistic inference with graphical models for regression problems

84

15:30〜16:30

概 要 Since the end of 2000, approximate probabilistic inference on graphical models has witnessed significant

advancements. One notable algorithm that has emerged in this context is approximate message passing(AMP). Originally proposed for sparse estimation, AMP not only offers tractability as a polynomial timealgorithm but also enables theoretical analysis, including convergence conditions under certain assumptions.
In this talk, we will focus on applying the AMP algorithm to regression problems. We will begin byintroducing a graphical model representation of regression problems and demonstrate how the AMP algorithm can be used to obtain marginalized posterior distributions. Our presentation will showcase two key
results. Firstly, we will explore the efficient calculation of the model selection criterion using the AMP
algorithm, employing a perturbative approach. Secondly, we will derive the convergence condition of the
AMP algorithm for nonconvex regularizations.
By examining these findings, we aim to shed light on the potential of the AMP algorithm in addressing
regression problems.

9 月 23 日（土）第 VII 会場

9:30〜11:30
25 中 村 慶 太 (横 浜 市 大 医)中 川 智 之(明星大データサイエンス)
田 畑 耕 治 (東京理大創域理工)Keita Nakamura(Yokohama City Univ.)
Tomoyuki Nakagawa (Meisei Univ.)
Kouji Tahata (Tokyo Univ. of Sci.)

Aitchison 幾何を用いた正方分割表の準対称性と幾何周辺同等性 · · · · · · · 15

Quasi-symmetry and geometric marginal homogeneity in square contingency tables using Aitchison geometry

概 要 We consider square contingency tables with the same row and column classifications. The set ofindependent probability tables and the set of symmetric probability tables are identified as linear subspacesof the simplex with Aitchison geometry. As a result, we can orthogonally decompose a simplex into fourparts and express quasi-symmetry and geometric marginal homogeneity using their combinations. We
propose measures of departure from quasi-symmetry and geometric marginal homogeneity and present thearrays which express the strength and direction of departure from quasi-symmetry and geometric marginal
homogeneity.

Final: 2023/8/21
85

統計数学

26 岡 原 久 也 (東京理大創域理工)藤 澤 健 吾 (山口東京理大工)田 畑 耕 治 ( 東 京 理 大 理 工)

Hisaya Okahara (Tokyo Univ. of Sci.)
Kengo Fujisawa(Tokyo Univ. of Sci., Yamaguchi)
Kouji Tahata (Tokyo Univ. of Sci.)

順序カテゴリをもつ多元分割表における f -divergence に基づいた非対称モデルについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An asymmetry model based on f -divergence for multi-way contingency
tables with ordered categories

概 要 For the analysis of multi-way contingency tables with ordered categories, Yamamoto, Iwashita, andTomizawa (2007) proposed and discussed an asymmetry model, which is thought to fit well if it is reasonable
to assume an underlying multivariate normal distribution. In this presentation, an asymmetry model basedon f-divergence is proposed for multi-way contingency tables with ordered categories. The nature of the
proposed model allows for a new information-theoretic interpretation of the model by Yamamoto et al.
(2007). Additionally, by using the proposed model, necessary and sufficient conditions for the symmetry
model to hold are provided.
27 松 原 和 樹 (埼 玉 大 教 育)

Kazuki Matsubara (Saitama Univ.)

A new method for constructing additive BIB designs · · · · · · · · · · · · · · · 15
A new method for constructing additive BIB designs

概 要 Some existence, construction methods, and applications of additive BIB designs, denoted byAB(v, k, λ), have been discussed in Sawa et al. (2007). This talk is devoted to providing a new construction method of AB(v, k, k − 1) using affine resolvable semi-regular group divisible designs.
28 地 嵜 頌 子 (大 阪 工 大 情 報)
波
大⋆)
藤 原
良 (筑
宮 本 暢 子 ( 東 京 理 大 理 工)

Shoko Chisaki (Osaka Inst. of Tech.)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

A construction of regular spanning bipartite block designs · · · · · · · · · · · 10

A construction of regular spanning bipartite block designs

概 要 It is usually to design an experiment using treatments and its blocks in the design of experiments.

Consider a set of edges of a complete bipartite graph as a treatments set and suppose the treatments havea structure. Then, we proposed a spanning bipartite block design (SBBD) to achieve better estimation
accuracy. In this talk, we introduce a construction for SBBDs which of design matrix is A-optimal, using a
BIBD with prime power number of blocks and an ordered design.
29 盧
暁 南 ( 岐 阜 大 工)
三 嶋 美 和 子 ( 岐 阜 大 工)
宮 本 暢 子 ( 東 京 理 大 理 工)
神 保 雅 一 ( 統 計 数 理 研)
(Gifu Univ.)
Xiao-Nan Lu
Miwako Mishima (Gifu Univ.)
Nobuko Miyamoto (Tokyo Univ. of Sci.)
Masakazu Jimbo (Inst. of Stat. Math.)

An algebraic sufficient condition for a circulant almost orthogonal array
to be D-optimal · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An algebraic sufficient condition for a circulant almost orthogonal array
to be D-optimal

概 要 Circulant almost orthogonal arrays (CAOAs) are a type of circulant arrays used for statistical designsof fMRI experiments that generalize circulant orthogonal arrays. This talk specifically focuses on binary
CAOAs with strength 2 designed for n treatments, where n ≡ 2 (mod 4). Our main aim is to characterize
D-optimal CAOAs and investigate their constructions. In this regard, this talk presents a new sufficientcondition for a CAOA to be D-optimal, which relies on the existence of specific negacyclic matrices as
substructures within the CAOAs.

Final: 2023/8/21
統計数学

30 江 頭 健 斗 (東 京 理 大 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)

86

高次元小標本における k-means 法と階層的クラスタリングについて · · · 15

High-dimensional asymptotic properties of k-means and hierarchicalclustering

概 要 k-means has been approved as a useful methodology for analysis of high-dimensional, low-sample-size

data. But k-means is not sufficiently studied theoretically under high dimensional settings. In this talk,we show the asymptotic properties of k-means under mild and practical settings for HDLSS data. We
also introduce a result for high dimensional data about hierarchical clustering and compare k-means withhierarchical clustering. At last, we present numerical simulation studies that demonstrate the performanceof k-means for high dimensional data, discussing the achieved results.
31 巖
矢
石
青

名 佑 務 (筑波大数理物質)
田 和 善 (筑波大数理物質)
井晶 ( 東 京 理 大 理 工)嶋誠 (筑波大数理物質)

Strongly spiked eigenvalue モデルにおける高次元相関行列の検定について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Yumu Iwana (Univ. of Tsukuba)
Kazuyoshi Yata (Univ. of Tsukuba)
Aki Ishii (Tokyo Univ. of Sci.)
Makoto Aosima (Univ. of Tsukuba)

Correlation test for high-dimensional correlation matrix under the strongly
spiked eigenvalue model

概 要 In this talk, we consider a test for the high-dimensional correlation matrix. Aoshima and Yata (2018)

proposed two eigenvalue models for high-dimensional data and constructed two-sample test procedures.
One is called strongly spiked eigenvalue (SSE) model and the other one is called non-SSE (NSSE) model.
Yata and Aoshima (2016) constructed a test for the high-dimensional correlation matrix under the NSSE
model. We focus on the SSE model that is often seen when we analyze the microarray data set. We give a
new test procedure by using the extended cross data method given by Yata and Aoshima (2013).
32 佃
康 司 ( 九 大 数 理)
松 浦
峻 ( 慶 大 理 工)
Koji Tsukuda (Kyushu Univ.)
Shun Matsuura (Keio Univ.)

高次元の設定における allometric extension モデルの仮説検定について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On testing the hypothesis of the allometric extension model in highdimensional settings

概 要 Considering two populations, if the directions of the first principal component vectors of the two

populations coincide and they also coincide with the direction of the difference of the mean vectors, then the
populations are called to form an allometric extension. In this presentation, we suppose a high-dimensionalsetting with an assumption that some eigenvalues of the covariance matrices are strongly spiked. Under
this setting, we construct a test statistic for the allometric extension model that is asymptotically normally
distributed and discuss properties of the test.
14:15〜16:20
33 間 野 修 平 (統 計 数 理 研)
廣 瀬 雅 代 (九 大 I M I )Shuhei Mano (Inst. of Stat. Math.)
Masayo Y. Hirose (Kyushu Univ.)

推定に現れる 1 階準線形偏微分方程式とその微分幾何的解法について · · 15

On a quasi-linear partial differential equation of the first order appears
in estimation and the solution with differential geometry

概 要 Integration of a quasi-linear partial differential equation of the first order with the aid of differential

geometry is discussed. The partial differential equation appears in a procedure for asymptotic bias reductionof maximum likelihood estimates of a function of parameters. The procedure for statistical model manifolds
with equiaffine connections is discussed as a special case.

Final: 2023/8/21
87

統計数学

34 藤 森洸 ( 信 州 大 経 法)佃康 司 ( 九 大 数 理)
Kou Fujimori (Shinshu Univ.)
Koji Tsukuda (Kyushu Univ.)

The Dantzig selector for semiparametric models of stochastic processes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The Dantzig selector for semiparametric models of stochastic processes

概 要 We consider the sparse estimation for stochastic processes with possibly infinite-dimensional nuisanceparameters, by using the Dantzig selector which is a sparse estimation method similar to Z-estimation. Whena consistent estimator for a nuisance parameter is obtained, it is possible to construct an asymptoticallynormal estimator for the parameter of interest under appropriate conditions. Motivated by this fact,
we establish the asymptotic behavior of the Dantzig selector for models of ergodic stochastic processes
with high-dimensional parameters of interest and possibly infinite-dimensional nuisance parameters. The
applications for ergodic diffusion processes and ergodic time series including integer-valued autoregressivemodels are presented.
35 野 村昇 ( 高 知 大 理 工)

Noboru Nomura (Kochi Univ.)

角度に基づく座標系を用いた象限確率の計算 · · · · · · · · · · · · · · · · · · · · · · · 15

Integral calculation for orthant probability with polar coordinates

概 要 Evaluation of probability that vectors distributed with elliptical distribution falls in orthant byintegration with polar coordinate system is considered. The probability is evaluated by repeating splitting
regions and calculating one dimensional integration. Coordinate system used in the process affect roughnessof functions which appear in the process. Numerical experiments were carried out and showed that theprocedure using polar coordinate systems gave satisfactory results and functions appear in the computation
process are smooth.
36 仲 北 祥 悟 (東 大 総 合 文 化)
P. Alquier(ESSEC Business School)
今 泉 允 聡 ( 東 大 総 合 文 化)

Shogo Nakakita (Univ. of Tokyo)
Pierre Alquier (ESSEC Business School)
Masaaki Imaizumi (Univ. of Tokyo)

Dimension-free concentration inequalities for sums of weakly dependent
random matrices · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Dimension-free concentration inequalities for sums of weakly dependent
random matrices

概 要 We study dimension-free concentration inequalities for sums of random matrices and operators under

weak dependence. The derivation of our results is based on a duality formula for moment-generating
functions. We apply the results to the estimation of covariance matrices of dependent processes.
37 曾
小 強 ( 北 大 経 済)
柿 沢 佳 秀 ( 北 大 経 済)

Xiaoqiang Zeng (Hokkaido Univ.)
Yoshihide Kakizawa (Hokkaido Univ.)

ADCINAR(1) 過程における二段階, 条件付き最小二乗推定の再考察 · · · 15
On two-step CLS estimation in stationary ADCINAR(1) process, revisited概 要 Asymptotic normality of two-step conditional least squares estimator is revisited for a new parameterin the stationary alternative dependent counting nonnegative integer-valued autoregressive process of thefirst-order, under a general innovation. It is shown through the stochastic expansion that plugging aconsistent estimator for the parameter α affects the resulting asymptotic variance, compared to the casewhere α is known.

Final: 2023/8/21
統計数学

38 後 藤 佑 一 (九 大 数 理)
Xuze Zhang (Maryland Univ.)(Maryland Univ.)
B. Kedem(Maryland Univ.)
Shuo Chen(Kyushu Univ.)
Yuichi Goto
Xuze Zhang (Maryland Univ.)
Benjamin Kedem (Maryland Univ.)
Shuo Chen (Maryland Univ.)

88

Test for the existence of the residual spectrum · · · · · · · · · · · · · · · · · · · · · 15

Test for the existence of the residual spectrum

概 要 Coherence is a similarity measure between two time series and takes the form of the time series

extension of Pearson’s correlation. However, only a linear relationship between two time series can bemeasured by coherence. In this talk, we introduce a residual spectrum in order to measure non-linear
relationships and show the existence and uniqueness of the residual spectrum by decomposing the regression
model we consider into orthogonal processes. Moreover, we propose a test for the existence of the residual
spectrum and show that our proposed test has asymptotically correct size and is consitent.
39 劉言 (早 大 理 工) ♭ Semiparametric empirical likelihood for circular distributions · · · · · · · · 15
( 早 大 理 工)
U Lan(
谷 口 正 信 早 大 理 工)
(Waseda Univ.)
Yan Liu(Waseda Univ.)
U Lan
Masanobu Taniguchi (Waseda Univ.)

Semiparametric empirical likelihood for circular distributions

概 要 We consider the empirical likelihood of the data coming from the circular distribution. Many circular

distributions have probability densities proportional to ones among the ARMA spectra family. These
circular models have shown promising potential for analyzing and interpreting circular data. However,many parameters of interest do not have explicit forms. This reveals a significant challenge arises in thestatistical inference due to the loss of explicit forms of normalizing constants in these circular models. We
propose a semiparametric empirical likelihood method for statistical inference for circular distributions. The
empirical likelihood ratio has a chi-squared limiting distribution. The theoretical results are illustrated bynumerical simulations and real data analysis.
40 明 石 郁 哉 (東 大 経 済)Fumiya Akashi (Univ. of Tokyo)

多変量中央値に基づく低ランク VAR モデルの推定 · · · · · · · · · · · · · · · · · · 15

Multivariate median based estimation methods for low-rank VAR models

概 要 In this talk, we consider estimation problems of the coefficient matrices of vector autoregressive models.

The innovation process is assumed to have zero-multivariate median, and the model can represent both
finite and infinite variance processes. We consider self-weighted least distance and GMM based reduced
rank estimators and derive the limit distributions of the proposed estimators. By comparing the asymptotic
covariance matrices of the estimators, we discuss the asymptotic relative efficiency of the estimators.

Final: 2023/8/21
89

応用数学

応 用
9 月 20 日（水）数学第 VIII 会場

9:30〜11:50
1 松 本 直 己 ( 琉 球 大 教 育)中 上 川 友 樹 ( 湘 南 工 科 大)Naoki Matsumoto (Univ. of Ryukyus)
Tomoki Nakamigawa(Shonan Inst. of Tech.)

グラフのゲーム連結度 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Game connectivity of graphs

概 要 We introduce a new game invariant of graphs, called game connectivity, which is related to theconnectivity of graphs. We investigate many fundamental and significant topics of the game connectivityof graphs, and propose many open problems and conjectures. In this talk, we introduce some of them.
2 善 本

潔 ( 日 大 理 工)

Kiyoshi Yoshimoto (Nihon Univ.)

辺着色グラフの連結性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On connectivities of edge-colored graphs

概 要 Let (G, c) be an edge-colored graph where c : E(G) → N is an edge-coloring. The color of the edge

incident to an end vertex x of a path P in G is denoted by cx (P ). For any vertices x, y ∈ V (G), if there
exist two properly colored paths P, Q joining x and y such that cx (P ) ̸= cx (Q) and cy (P ) ≠ cy (Q), thenwe say (G, c) is color-connected. Color-connectivity is a generalization of strong connectivity of digraphs.
In this talk, we discuss structures and properties of color-connected graphs, comparing strong connecteddigraphs.
3 安 藤

清 ( 国 立 情 報 学 研)

Kiyoshi Ando (Nat. Inst. of Informatics)

A constructive characterization of 4-connected 4-regular graphs · · · · · · 15
A constructive characterization of 4-connected 4-regular graphs

概 要 We introduce two new operations on a 4-connected 4-regular graph G. (I) Delete a vertex x from G,(II) Add K4 to G − x, (III) Add a perfect matching between V (K4 ) and NG (x). We call this operation“K4 -expansion”. (I) Delete independent 2 edges e1 , e2 from G, (II) Add K4 to G − e1 − e2 , (III) Add aperfect matching between V (K4 ) and V (e1 ) ∪ V (e2 ), where V (ei ) stands for the set of end vertices of ei for
i = 1, 2. We call this operation “K4 -edge-binding”.
Theorem Every 4-connected 4-regular graph can be obtained from K5 or K4,4 by repeated applications ofedge-bindings, K4 -expansions and K4 -edge-bindings.
4 高 橋 大 樹 (横浜国大環境情報)

Daiki Takahashi (Yokohama Nat. Univ.)

3-連結平面的グラフの 2-連結全域部分グラフ · · · · · · · · · · · · · · · · · · · · · · · 15
2-Connected spanning subgraphs of 3-connected planar graph

概 要 Kaneko et al. proved that every 3-connected planar graph G has a 2-connected spanning subgraph

K such that |E(K)| ≤ 43 (|V (G)| − 1), and they also conjectured that the constant of the estimation canbe improved to 43 (|V (G)| − 2). To prove the result, they showed the statement for circuit graphs, which is
obtained from a 3-connected planar graph by deleting one vertex, and the theorem is best possible for circuit
graphs. In this paper, we give a characterization of a circuit graph G each of whose 2-connected spanning
subgraph K of G requires |E(K)| ≥ 34 (|V (G)| − 1) and then we improve the bound for the 3-connectedplanar case.

Final: 2023/8/21
応用数学

5 久 保 田 匠 ( 大 阪 工 大 情 報)

Sho Kubota (Osaka Inst. of Tech.)90

Mixed strongly regular graphs to induce periodic quantum walks · · · · · 15
Mixed strongly regular graphs to induce periodic quantum walks

概 要 We derive combinatorial necessary conditions for discrete-time quantum walks defined by regular

mixed graphs to be periodic. One useful necessary condition is that if a k-regular mixed graph with nvertices is periodic, then 2n/k must be an integer. As an application of this work, we determine periodicityof mixed complete graphs and mixed graphs with a prime number of vertices. Furthermore, we study
periodicity of mixed strongly regular graphs and several classes of mixed distance-regular graphs, andextend existing results to mixed graphs.
6 吉 江 佑 介 ( 石 川 工 高 専)
Yusuke Yoshie(Ishikawa Nat. Coll. of Tech.)

Grover walk の周期性とグラフ幾何 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Periodicity of the Grover walk and graph structure

概 要 We study periodicity of the Grover walk and see relation between structure of the underlying graph.

By combinations of matchings and cycles of the underlying graph, we completely characterize the graphs
admitting an odd-periodic Grover walk. Through such characterization, we see relation between quantum
walks and geometric information of graph.
7 関 藤 寛 人 (横浜国大環境情報)
久 保 田 匠 ( 大 阪 工 大 情 報)
吉 野 聖 人 ( 広 島 工 大 情 報)

Hiroto Sekido (Yokohama Nat. Univ.)
Sho Kubota (Osaka Inst. of Tech.)
Kiyoto Yoshino(Hiroshima Inst. of Tech.)

偶数周期のグローヴァーウォークを誘導する正則グラフ · · · · · · · · · · · · · 15

Regular graphs to induce Grover walks with even period

概 要 The purpose of this presentation is a characterization of graphs that induce periodic Grover walks

with given periods. In previous studies, Yoshie has shown that the only graphs that induce odd periodic
Grover walks are cycle graphs. However, this problem is largely unsolved for even periods. In this study,
using spectral graph theory and Galois theory, we calculate eigenvalues of a graph and their multiplicities
and sum of eigenvalues, and then characterize graphs. As a result, we show that regular graphs that induce
2l-periodic Grover walks are also restricted to cycle graphs in most cases, where l is an odd number.
8 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⋆)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.⋆)
Iwao Sato (Oyama Nat. Coll. of Tech.)

Bipartite walks on bipartite graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Bipartite walks on bipartite graphs

概 要 Recently, a bipartite walk on a bipartite graph was introduced, and the periodicity of its time evolution

matrix was discussed. We resent a formula for the time evolution matrix of the bipartite walk, and so giveits spectra. As an application, we provide a formula for the time evolution matrix of the bipartite walk on
a semiregular bipartite graph, and show its spectra. Furthermore, we treat a relation between the Grover
walk and the bipartite walk on a bipartite graph. Finally, we present a formula for the time evolution
matrix of the bipartite walk on a regular covering of a bipartite graph.

Final: 2023/8/21
91

応用数学

14:15〜16:10
9 穂 坂 大 将 (横浜国大環境情報)
今 野 紀 雄(立命館大理工・横浜国大⋆)Taisuke Hosaka (Yokohama Nat. Univ.)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)

量子ウォークによる量子探索のパロンドゲーム · · · · · · · · · · · · · · · · · · · · · 10

Parrondo’s game of quantum search based on quantum walk概 要 In this talk, we introduce a Parrondo’s game of quantum search based on quantum walks. Parrondo’s

game is the game that a winning strategy is constructed a combination of losing strategies. This situation iscalled Parrondo’s paradox. Unlike the previous model, the paradox is defined by the average of probabilityof finding marked vertex. We show that the paradox exists for our model by numerical simulations on thecycle and the 2-dimensional torus. Moreover, we give the range in which the paradox occurs is symmetric
about the origin on the d-dimensional torus with even vertices and one marked vertex.
10 成 松 明 廣(福知山公大数理・データサイエンスセンター)
井 手 勇 介 ( 日 大 文 理)
Akihiro Narimatsu(Univ. of Fukuchiyama)(Nihon Univ.)
Yusuke Ide

Path 上の相関付ランダムウォークの固有値解析 · · · · · · · · · · · · · · · · · · · · 15

A spectral analysis of the Correlated Random Walk

概 要 In this talk, we consider a spectral analysis of the Correlated Random Walk. We obtain the result for

the isospectral coin cases by using the Jacobian Matrix.
11 遠 藤 隆 子 (東 北 大 工)
松 本 洋 平 (信州大総合医理工)鈴 木 章 斗 ( 信 州 大 工)
Takako Endo (Tohoku Univ.)
Yohei Matsumoto (Shinshu Univ.)
Akito Suzuki (Shinshu Univ.)

原点に摂動をもつ非ユニタリ量子ウォークのスペクトル · · · · · · · · · · · · · 15

Spectra of non-unitary one-dimensional quantum walks with a perturbation at the origin.

概 要 The quantum walk (QW) is a quantum version of the classical random walk (RW) and is known as oneof the fundamental elements of quantum algorithms. In this study, eigenvalues are derived for one-defective
non-unitary QWs with perturbations at the origin using the transfer matrix method.
12 神 吉 知 博 (松 江 工 高 専)
名 倉
誠 (大阪電通大基礎理工)大 谷 信 一 (関東学院大理工)
Tomohiro Kamiyoshi(Matsue Coll. of Tech.)
Makoto Nagura(Osaka Electro-Comm. Univ.)
Otani Shin-ich (Kanto Gakuin Univ.)

指数型 recursive matrix から得られる統一スターリング数の関係式について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On some equations of unified Stirling numbers obtained from exponential recursive matrices

概 要 We propose a generalization of a unified Stirling numbers introduced by Hsu and Shiue and thebivariate generating functions of exponential generating functions by using the Roman factorial. As aconsequence, we conclude that a horizontal generating function of generalized Stirling numbers with certain
parameters is simply the principal part of the Laurent series of the vertical generating function withreciprocal parameters. Moreover, by specializing the parameters of generalized Stirling numbers, we canobtain some equations concerning the fourth quadrant of the exponential recursive matrix.

Final: 2023/8/21
応用数学

13 吉 田 裕 哉 (名工大)Yuuya Yoshida (Nagoya Inst. of Tech.)92

有限体上の部分空間に含まれる線型独立な product vector の個数について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the number of linearly independent product vectors in subspaces
over finite fields

概 要 Let n ≥ 2 and d1 , . . . , dn ≥ 2 be integers, and F be a field. A vector u ∈ F d1 ⊗ · · · ⊗ F dn is calleda product vector if u = u[1] ⊗ · · · ⊗ u[n] for some u[1] ∈ F d1 , . . . , u[n] ∈ F dn . In this talk, we estimate thenumber of linearly independent product vectors in subspaces over finite fields. This result is an extensionof our previous work from the case of infinite fields to that of finite fields.
大⋆)14 坂 内 英 一 (九栗 原 大 武 ( 山 口 大 創 成)
( 京 大 情 報)
Da Zhao(
上 海 理 工 大)
Yan Zhu

Eiichi Bannai (Kyushu Univ.⋆)
Hirotake Kurihara (Yamaguchi Univ.)(Kyoto Univ.)
Da Zhao
Yan Zhu(Univ. of Shanghai for Sci. Tech.)

多変数 P - ,Q- 多項式アソシエーションスキームについて · · · · · · · · · · · · 15

Multivariate P - and/or Q-polynomial association schemes

概 要 The classification problem of P - and Q-polynomial association schemes has been one of the central

problems in algebraic combinatorics. Generalizing the concept of P - and Q-polynomial association schemes
to multivariate cases has been tried by some authors, but it seems that so far, there were neither very
well-established definition nor results. Very recently, Bernard, Crampé, d’Andecy, Vinet, and Zaimi definedbivariate P -polynomial association schemes, as well as bivariate Q-polynomial association schemes. In thistalk, we study these concepts and propose a new modified definition concerning a general monomial order,
which is more general and more natural and also easy to handle. We prove that there are many interesting
families of examples of multivariate P - and/or Q-polynomial association schemes.
15 辻 栄 周 平 (北 教 大 旭 川)
Hung Manh Tran
(National Univ. of Singapore)
Tan Nhat Tran
(Leibniz Univ. Hannover)

Shuhei Tsujie (Hokkaido Univ. of Edu.)
Hung Manh Tran
(National Univ. of Singapore)
Tan Nhat Tran
(Leibniz Univ. Hannover)

自由グラフ超平面配置の MAT 分割と局所正則ヴァインの対応について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On correspondence between MAT partitions of free graphic hyperplanearrangements and local regular vines

概 要 There is a close relationship between MAT-free graphic arrangements, derived from the theory of

hyperplane arrangements, and strongly chordal graphs, derived from graph theory. In this talk, we willfurther study the correspondence with locally regular vines, which are objects derived from statistics.
16:30〜17:30

特別講演
土 屋 翔 一 ( 専 修 大 ネ ッ ト)

HIST と Halin graphShoichi Tsuchiya (Senshu Univ.)

HISTs and Halin graphs

概 要 A spanning tree with no vertices of degree 2 is called a homeomorphically irreducible spanning tree

(HIST). The structure of a HIST is sometimes used as an essential tool to construct an explicit class ofedge-minimal 3-connected plane graphs (such graphs are called Halin graphs). In this talk, we introduce
theorems, problems and open problems on HISTs and Halin graphs with a particular focus on conjectures
which are solved in last about 10 years.

Final: 2023/8/21
93

応用数学

9 月 21 日（木）第 VIII 会場

9:30〜11:30
16 藤 田 慎 也(横浜市大データサイエンス)
飯田礼美子(横浜市大データサイエンス)
前 澤 俊 一 ( 東 京 理 大 理)

Shinya Fujita (Yokohama City Univ.)
Remiko Iida (Yokohama City Univ.)
Shun-ichi Maezawa(Tokyo Univ. of Sci.)

頂点重み付き木における properly ordered coloring を実現する辺の向き付けについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Orientations for properly ordered coloring on vertex weighted trees

概 要 Let (G,w) be a vertex weighted graph, where w is a weight function on V(G) such that w: V–>

1,2,.... A vertex coloring c: V–>0,1,2,... is called properly ordered coloring (POC) of (G,w), if for everyedge e=uv in E(G), c(u)>c(v) if w(u)>w(v) and c(u) is different from c(v) if w(u)=w(v). In this talk, we
discuss giving an orientation on E(G) such that the in-degrees of vertices of the resulting digraph D achieve
a POC on (G,w) for the case where G is a tree T and w: V–>1,2.
17 横 村 国 治(東海大理系教育センター)

Kuniharu Yokomura (Tokai Univ.)

Semi-balanced 3 部グラフの Hamiltonian 性について · · · · · · · · · · · · · · · · 15
On degree conditions of semi-balanced 3-partite Hamiltonian graphs

概 要 A k-partite graph is said to be a semi-balanced k-partite graph if each partite set has either n or mvertices. We obtain a degree condition of a semi-balanced 3-partite Hamiltonian graph. We also show adegree condition of a semi-balanced 3-partite pancyclic graph.
18 才 川 隆 文 (名 大 多 元 数 理)辻陽 介 ( 北 見 工 大 工)
松 田 一 徳 ( 北 見 工 大 工)

Takafumi Saikawa (Nagoya Univ.)
Yosuke Tsuji (Kitami Inst. of Tech.)
Kazunori Matsuda(Kitami Inst. of Tech.)

Coq によるマッチング理論の形式化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Formalization of matching theory in Coq

概 要 We formalize the notions of matching, maximal matching, induced matching and related invariants.

19 佐 藤巖 ( 小 山 工 高 専)
小 松
尭 ( 山 梨 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)Iwao Sato (Oyama Nat. Coll. of Tech.)Takashi Kmatsu (Univ. of Yamanashi)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)

CTM/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

CTM/Zeta correspondence

概 要 In our previous work, we investigated the relation between zeta functions and discrete-time models

including random and quantum walks. We introduce a zeta function for the continuous-time model (CTM)
and consider CTMs including the corresponding random and quantum walks on the d-dimensional torus.

Final: 2023/8/21
応用数学

20 佐 藤 宏 平 (小 山 工 高 専)
小 松
尭 ( 山 梨 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)佐 藤
巌 ( 小 山 工 高 専)

Kohei Sato (Oyama Nat. Coll. of Tech.)Takashi Komatsu (Univ. of Yamanashi)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Iwao Sato (Oyama Nat. Coll. of Tech.)

94

Ronkin/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Ronkin/Zeta correspondence

概 要 We present a new relation between the Ronkin function and the logarithmic zeta function for several

random walks and quantum walks. Fortunately, the Laurent polynomials were obtained through those
Ronkin functions. Finally, we describe some properties about them by using the terminology of tropicalgeometry.
21 小 松尭 ( 山 梨 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)佐 藤
巖 ( 小 山 工 高 専)
田 村 駿 也 ( 横 浜 国 大 理 工)

Takashi Komatsu (Univ. of Yamanashi)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)
Iwao Sato (Oyama Nat. Coll. of Tech.)Shunya Tamura (Yokohama Nat. Univ.)

Mahler/Zeta correspondence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mahler/Zeta correspondence

概 要 The Mahler measure was introduced by Mahler in the study of number theory. It is known that theMahler measure appears in different areas of mathematics and physics. On the other hand, we have been
investigated a new class of zeta functions for various kinds of walks including quantum walks by a seriesof our previous work on Zeta Correspondence. In this talk, we present a new relation between the Mahler
measure and our zeta function for quantum walks. Our results bridge between the Mahler measure and thezeta function via quantum walks for the first time.
22 坂 本光 ( 神 奈 川 大 工)
今 野 紀 雄(立命館大理工・横浜国大⋆)齋 藤
渓 ( 神 奈 川 大 工)

Hikari Sakamoto (Kanagawa Univ.)
Norio Konno(Ritsumeikan Univ./Yokohama Nat. Univ.⋆)(Kanagawa Univ.)
Kei Saito

今野分布に従う確率変数の和の性質 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A property of the summation of random variables determined by the
Konno distribution

概 要 The state-space model for time-series analysis typically uses a white noise given by the Gaussian

distribution. This means that the noise follows a random walk on the one-dimensional lattice. In thisstudy, we report the results obtained for the noise containing quantum effects, i.e., when the noise follows
a quantum walk determined by the Konno distribution. In particular, we consider a property of a sum ofrandom variables determined by the Konno distribution.

Final: 2023/8/21
95

応用数学

13:00〜14:15
23 粟 田 円 佳 (早 大 理 工)

Madoka Awada (Waseda Univ.)

Isodual 2 元符号と t-design について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A note on t-designs in isodual codes

概 要 Shells of the extended binary quadratic residue code Cℓ are known to support combinatorial 2-designs.

In the present talk, by computing Jacobi polynomials and harmonic weight enumerators, we show thatCℓ ∪ (C ⊥ )ℓ is a 3-design whenever Cℓ ∪ (C ⊥ )ℓ is non-empty.
24 平 尾 将 剛 (愛知県立大情報)野 崎
寛 (愛知教育大教育)
田 坂 浩 二 (愛知県立大情報)

Masatake Hirao (Aichi Pref. Univ.)
Hiroshi Nozaki (Aichi Univ. of Edu.)
Koji Tasaka (Aichi Pref. Univ.)

Spherical designs and modular forms of the D4 lattice · · · · · · · · · · · · · · 15

Spherical designs and modular forms of the D4 lattice概 要 In this talk, we study shells of the D4 lattice with the concept of spherical design of harmonic index T(spherical T -design for short). We first introduce that the 2m-shell of D4 is an antipodal spherical {10, 4, 2}design on the 3-sphere. In addition, the 2-shell, which is the D4 root system, is a tight {10, 4, 2}-design,using the linear programming method. Moreover, we introduce the the uniqueness of the D4 root system as
an antipodal spherical {10, 4, 2}-design with 24 points. Finally, we give two applications of the uniqueness.
25 谷 野 憲 司 (神戸大システム情報)澤正 憲 (神戸大システム情報)
平 尾 将 剛 (愛知県立大情報)(Kobe Univ.)
Kenji Tanino
Masanori Sawa (Kobe Univ.)
Masatake Hirao (Aichi Pref. Univ.)

B 型鏡映群不変なある球面デザインの強さの評価について · · · · · · · · · · · 15

An upper bound for the degree of a certain type of Bd -invariant weighted
spherical designs

概 要 In this talk we give an upper bound for the degree of a certain type of Bd -invariant weighted sphericaldesigns, as a generalization of Bajnok(2007), Heo–Xu (2001) and Sawa–Xu (2014). We also discuss the best
possibility of our bound in low dimensions.
26 三 島 輝 之 (神 戸 大 工)澤正 憲 (神戸大システム情報)
内 田 幸 寛 ( 都 立 大 理)

Teruyuki Mishima (Kobe Univ.)
Masanori Sawa (Kobe Univ.)
Yukihiro Uchida (Tokyo Metro. Univ.)

中心対称的な有理デザインの存在問題 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The problem of the existence of centrally symmetric rational designs

概 要 In this talk we consider the existence of rational quadrature for Hermite polynomials and Chebyshev

polynomials of the first kind, which originally goes back to a work by Hausdorff (1909) concerning Waring
problem in number theory. We show some nonexistence theorems for quadrature with small number of points
and then provide existence results, together with explicit constructions and individual curious examples.
Our proof is based on elementary number-theoretic techniques and elementary geometric considerations.

Final: 2023/8/21
応用数学

9 月 22 日（金）96

第 VIII 会場

9:30〜12:00
27 伊 藤昇 ( 茨 城 工 高 専)

Noboru Ito (Ibaraki Nat. Coll. of Tech.)Integrating curvature and quantizating Arnold strangeness invariant · · 15
Integrating curvature and quantizating Arnold strangeness invariant

概 要 There are three classical Arnold invariants for plane curves. Two of them have been quantized by Viro

(1996) and by Lanzat–Polyak (2013), respectively. Although the quantization of the Arnold strangeness St
remained unrealized. In this talk, we express a quantization of St by integrating curvatures multiplied by
non-trivial densities. This integral indues a polynomial of variable q. This quantized Arnold strangenesspolynomial includes the rotation number, the original Arnold strangeness St, and the Tabachnikov invariants
as coefficients in its Taylor expansion.
28 インタウォンカモンパット( 茨 城 工 高 専)
Kamolphat Intawong(Ibaraki Nat. Coll. of Tech.)

Application of linking number theory to authentication technology · · · 15
Application of linking number theory to authentication technology

概 要 In this study, we introduce the application of linking number theory of knot theory in mathematics

to information security technology. Firstly, we introduce new variations of Milnor’s triple linking number.
Secondly, we define a notion of the multiple linking number, which implies two kinds of invariants. Lastly,
we apply a multiple linking number to the authentication technology.
29 中 川 卓 也 (立 命 館 大 理 工)

Takuya Nakagawa (Ritsumeikan Univ.)

Existence of density functions for the running maximum of SDEs by
non-truncated pure-jump Lévy processes. · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence of density functions for the running maximum of SDEs by
non-truncated pure-jump Lévy processes.

概 要 We verify the existence of density functions of the running maximum of a stochastic differential

equation driven by a Brownian motion and a non-truncated stable process. This is proved by the existenceof density functions of the running maximum of Wiener–Poisson functionals resulting from Bismut’s approach
to Malliavin calculus for jump processes.
30 渡 辺樹 ( 早 大 理 工)

Itsuki Watanabe (Waseda Univ.)

Markov chain approximation for Hamilton–Jacobi–Bellman equation
with absorbing boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Markov chain approximation for Hamilton–Jacobi–Bellman equation
with absorbing boundary

概 要 In this talk, we consider the infinite horizon optimal control problems of the controlled Markov process.

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.

Final: 2023/8/21
97

応用数学

31 E. G. Escolar (神戸大人間発達環境)
湯 浅 正 洋 (神戸大人間発達環境)

Emerson Gaw Escolar (Kobe Univ.)
Masahiro Yuasa (Kobe Univ.)

A topological analysis of the space of recipes · · · · · · · · · · · · · · · · · · · · · · 15
A topological analysis of the space of recipes

概 要 In recent years, the use of data-driven methods has provided insights into underlying patterns andprinciples behind culinary recipes. In this work, we introduce the use of persistent homology, a tool in
topological data analysis that can describe the multiscale holes in data, in the study of culinary recipes. In
particular, persistent homology analysis provides a set of recipes surrounding holes in the space of existing
recipes. We then propose a method to generate novel ingredient combinations using this topologicalinformation with combinatorial optimization. We made biscuit-like baked goods using the novel ingredient
combinations. Our findings indicate that persistent homology has the potential for suggesting novel culinary
recipes.
32 本 永 翔 也(立命館大総合科学技術研究機構)
矢 ヶ 崎 一 幸 ( 京 大 情 報)

Shoya Motonaga (Ritsumeikan Univ.)
Kazuyuki Yagasaki (Kyoto Univ.)

近可積分系の正則レベル集合近傍における非可積分性 · · · · · · · · · · · · · · · 15

Nonintegrability of nearly integrable dynamical systems near regularlevel sets

概 要 We study the existence of real-analytic first integrals and real-analytic integrability for perturbations ofintegrable systems including non-Hamiltonian ones in the sense of Bogoyavlenskij such that the first integrals
and commutative vector fields depend analytically on the small parameter. We compare our results withthe classical results of Poincaré and Kozlov for systems written in action and angle coordinates and discuss
their relationships with the subharmonic and homoclinic Melnikov methods for periodic perturbations of
single-degree-of-freedom Hamiltonian systems. Moreover, we apply our theory to the periodically forced
Duffing oscillator and reveal that the perturbed systems can be real-analytically nonintgrable even if there
exists no transverse homoclinic orbit to a periodic orbit.
33 榊 原 航 也 (金沢大理工・理化学研)
高 津 飛 鳥 (都立大理・理化学研)
保 國 惠 一 (筑波大システム情報)
Koya Sakakibara(Kanazawa Univ. / RIKEN)
Asuka Takatsu(Tokyo Metro. Univ. / RIKEN)
Keiichi Morikuni (Univ. of Tsukuba)

有限集合間の最適輸送の Bregman ダイバージェンスによる正則化 · · · · · 15

Regularization by Bregman divergence of optimal transport on finitesets

概 要 In this talk, we consider regularizing the optimal transport problem using Bregman divergence andpresent the results of the error estimate. We also show that there exists a Bregman divergence that converges
faster than the commonly used regularization by Shannon entropy and provide an actual example.

Final: 2023/8/21
応用数学

34 徐
百 歌 ( 神 戸 大 理)
谷 口 隆 晴 ( 神 戸 大 理)
片 山 義 雄 ( 神 戸 大 医)(Kobe Univ.)
Baige Xu
Takaharu Yaguchi (Kobe Univ.)
Yoshio Katayama (Kobe Univ.)98

末梢血造血幹細胞動員データ解析のためのグレブナー基底による変数分
類手法 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classification of variables using Groebner basis for analysis of peripheral
blood hematopoietic stem cell mobilization data

概 要 In this study, we propose a variable classification method based on the Groebner basis, motivated by

the analysis of peripheral blood hematopoietic stem cell mobilization data. This data analysis requires theextraction of particularly important variables from the given data, but the hidden algebraic relationships
make it difficult to identify the important variables. We attempt to extract hidden algebraic equations fromthe data and classify the variables by rearranging these equations using a computational algebraic method.
35 石 渡 哲 哉(芝浦工大システム理工)
榊 原 航 也 ( 金 沢 大 理 工)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)
Koya Sakakibara (Kanazawa Univ.)

離散正則性とコーシーの積分表示の離散版 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Discrete holomorphicity and a discrete version of Cauchy’s integral formula

概 要 In this talk, we introduce a new definition of discrete holomorphic functions and a discrete circum-

scription. And we report a theorem of the discrete version of Cauchy’s integral representation obtained inour setting.
14:15〜16:30
36 大 野 航 太 (中 大 理 工)
小 川 知 之 ( 明 大 総 合 数 理)
(Chuo Univ.)
Kota Ohno
Toshiyuki Ogawa (Meiji Univ.)

結合振動子におけるリミットサイクルの特性とキメラの発達度について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The characteristic of the limit cycle and the growth of the chimera state
in coupled oscillator system

概 要 Coupled oscillator systems have been studied in various fields of physical and biological phenomena.

Among them, systems of nonlocally coupled oscillators can exhibit chimera states, which consist of spatiallycoherent and incoherent states. However, chimera states’ stability and bifurcation origin has not been
understood. In this study, we investigate the relationship between the characteristic of the limit cycle andthe growth of the chimera state. We consider the control principle and bifurcation origin for the chimera
state.

Final: 2023/8/21
99

応用数学

37 相
市
鎌
加
小
坂
山
矢

澤
田
谷
藤
菅
元
田
崎

ゆ
史
美
孝
莉
成

守 ( 明 大 理 工)
優 (明大研究・知財)き ( 明 大 理 工)
織 ( 明 大 理 工)
南 ( 明 大 理 工)
志 ( 明 大 理 工)
花 ( 明 大 理 工)
俊 ( 明 大 理 工)

Mamoru Aizawa (Meiji Univ.)(Meiji Univ.)
Yu Ichida(Meiji Univ.)
Yuki Kamaya(Meiji Univ.)
Shiori KatoMinami Kosuge (Meiji Univ.)
Takashi Sakamoto (Meiji Univ.)(Meiji Univ.)
Rika Yamada
Shigetoshi Yazaki (Meiji Univ.)

ペースト状人工骨の材料特性を表現する数理モデル · · · · · · · · · · · · · · · · · 15

Mathematical model to describe the material properties of paste-likeartificial bone

概 要 A mathematical model for expressing the material properties of paste-like artificial bone constructedbased on biomaterials experiments and a discussion on the validity of the model based on the simulation andexperimental results are presented. The model is based on an experiment comparing calcium cement using
IP6 with pure water and adopts the Allen–Cahn equation. In this talk, we will present the experimentsthat led to the construction of the model, the experiments for the construction of the model, and the model,
as well as the results obtained in cooperation with the experiments.
38 市 田優 (明大研究・知財)
坂 元 孝 志 ( 明 大 理 工)
(Meiji Univ.)
Yu Ichida
Takashi Sakamoto (Meiji Univ.)ある退化放物型方程式の進行波の分類とそれを特徴付ける無限遠の分岐· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Classification of traveling wave solutions for certain degenerate parabolic
equations and the bifurcation at infinity

概 要 This talks reports results on the classification of traveling wave solutions, including nonnegative weaksense, in the spatial 1D degenerate parabolic equation. These are obtained through dynamical systems
theory and geometric approaches (in particular, Poincaré compactification). The results examine a different
range of parameters included in the equation, using the same techniques as discussed in the earlier mywork. In a clear departure from this previous work, the classification results obtained in this paper
and the successful application of known transformation also yield results for the classification of (weak)nonnegative traveling wave solutions for spatial 1D porous medium equations with special nonlinear terms
and the simplest porous medium equation. Finally, the bifurcations at infinity occur in the two-dimensional
ordinary differential equations that characterize these traveling wave solutions are shown.

Final: 2023/8/21
応用数学

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 理 工)
Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Takeo Ushijima (Tokyo Univ. of Sci.)100ある準線形放物型偏微分方程式に対する進行波解に関する一考察 · · · · · · 15

A Remark on traveling wave solutions for a quasi-linear parabolic partial
differential equation

概 要 Blow-up phenomena of curvatures on cusp singularities in contractions of convex immersed curves with

self-crossing points have been studied by many authors. They deal with blow-up solutions of a quasi-linear
parabolic equation and a rescaled one. In their analysis, particularly in estimating the blow-up rate, theslowly traveling wave solutions play a significant role. Our purpose of this talk is to investigate the behaviorof slowly traveling wave solutions.
40 Junyong Eom (北 大 電 子 研)
中 村
玄 ( 北 大 電 子 研)
西 村 吾 朗 ( 北 大 電 子 研)
Chunlong Sun(Nanjing Univ. of Aeronautics and Astronautics)

Junyong Eom (Hokkaido Univ.)
Nakamura Gen (Hokkaido Univ.)
Goro Nishimura (Hokkaido Univ.)
Chunlong Sun(Nanjing Univ. of Aeronautics and Astronautics)

Local analysis for locating a single point target in time-domain fluorescence diffuse optical tomography · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Local analysis for locating a single point target in time-domain fluorescence diffuse optical tomography

概 要 The time-domain fluorescence diffuse optical tomography (FDOT) problem is to recover the dis-tribution of fluorophores in biological tissue from the time-domain measurement on the boundary. The
measurement is conducted by several pairs (S-D pairs) of a point source and a point detector. In thistalk, we identify the location of the fluorophore over a point, refer as a point target. We first expressa solution for the forward problem in a dimensionless form and derive its asymptotic behavior when the
point target is far from the boundary. Based on the asymptotic behavior, we show local solvability andmake a numerical inversion scheme for locating a single point target. Further we discuss about locatingwell-separated multiple point targets.
41 田 中 吉 太 郎 (公立はこだて未来大)村 川 秀 樹 (龍谷大先端理工)Yoshitaro Tanaka(Future Univ.-Hakodate)
Hideki Murakawa (Ryukoku Univ.)

1 次元有界領域上の非局所 Fokker–Planck 方程式に対する Keller–Segel型近似 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Keller–Segel type approximation for nonlocal Fokker–Planck equations
in one-dimensional bounded domain

概 要 To describe biological phenomena such as cell migration and cell adhesion many evolutional equations

are proposed in which an advective convolution term with a suitable integral kernel is imposed. It is wellknown that such nonlocal equations can reproduce various behaviors depending on the shape of the integral
kernel. These nonlocal evolutional equations are often difficult to analyze, and the analytical method isdeveloping. In the light of these background we approximate the nonlocal Fokker–Planck equations by the
combination of a Keller–Segel system which is a typical local dynamics. We will show that the solution of
the nonlocal Fokker–Planck equation with any even continuous integral kernel can be approximated as a
singular limit of the Keller–Segel system by controlling parameters.

Final: 2023/8/21
101

応用数学

42 池 田 幸 太 (明 大 総 合 数 理)
小 川 知 之 ( 明 大 総 合 数 理)菅徹 ( 阪 公 大 理)
(Meiji Univ.)
Kota Ikeda
Toshiyuki Ogawa (Meiji Univ.)
Toru Kan (Osaka Metro. Univ.)

連続 OV モデルにおける進行波解の存在 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence of traveling wave solutions in continuous OV models

概 要 In the field of traffic flow, self-organized wave propagation, which characterizes congestion, has been

reproduced in both macro and micro models. Hydrodynamic models, a type of macro-model, include thosethat can be derived from micro-level car-following models, and the relationship between the two has been
investigated. However, since most of them have been verified by numerical methods and formal analysis,
analytical approaches are also necessary to rigorously guarantee their validity. The aim of this research is to
discuss the relationship between macro and micro models through the properties of solutions corresponding
to congestion with sparse and dense waves. Specifically, we will show the existence of traveling wave
solutions in the macro model and investigate their properties.
43 森 田 善 久 (龍谷大⋆)Yoshihisa Morita (Ryukoku Univ.⋆)

Time backward profile of entire solutions to the bistable reaction-diffusion
equation on unbounded metric graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Time backward profile of entire solutions to the bistable reaction-diffusion
equation on unbounded metric graphs

概 要 We deal with the bistable reaction-diffusion equation on an unbounded metric graph consisting ofhalf-lines Li (1 ≤ i ≤ m) joined at a point (junction). Assume that on R the equation has a monotone
decreasing traveling front wave ϕ(x − ct) with c > 0 connecting the two stable constant steady states andset Li = {−∞ < xi < 0} (1 ≤ i ≤ k) with k ≤ m. Then we prove that given numbers θi (1 ≤ i ≤ k), there
exists an entire solution which converges to the front profile ϕ(xi − ct − θi ) on each Li as t → −∞.
16:45〜17:45

2022 年度日本数学会応用数学賞受賞特別講演大理) パターン形成問題とその縮約について
栄 伸 一 郎 (北Shin-ichiro Ei (Hokkaido Univ.)

On pattern formation problem and its contraction

概 要 There are three major stages in the process of pattern formation. The process of pattern generation,in which various patterns are generated from small initial perturbations, and convergence of individual
patterns to a specific pattern, such as a stationary state or a traveling wave, and the pattern interaction
process, in which multiple formed patterns converge to a final shape through the interaction between them.
In this talk, I will focus on the phenomena described by the reaction-diffusion type model equations, andapply the method of contraction to the mathematical analysis for the behavior of solutions in each process
involved in pattern formation.

Final: 2023/8/21
応用数学

9 月 23 日（土）9:30〜12:00
44 今 川 真 城 (京 大 情 報)
川 越 大 輔 ( 京 大 情 報)

Masaki Imagawa (Kyoto Univ.)
Daisuke Kawagoe (Kyoto Univ.)

102

第 VIII 会場

定常移流方程式に対する楕円型正則化の収束率 · · · · · · · · · · · · · · · · · · · · · 15

Convergence rates of an elliptic regularization applied to a stationary
advection equation

概 要 Elliptic regularization is a method of capturing a solution to a partial differential equation by adding an

elliptic operator with a small parameter. In this talk, we consider a boundary value problem of a stationary
advection equation with the homogeneous inflow boundary condition in a bounded domain with Lipschitz
boundary, and consider its perturbation by ε∆, where ε is a positive parameter and ∆ is the Laplacian,as an example of elliptic regularization. We discuss convergence rates assuming H 1 or H 2 regularity fororiginal solutions. A key observation is that the convergence rate depends on boundary conditions posed tothe perturbed equation, the regularity of original solutions, and a relation between the boundary and theadvection vector field.
45 田 﨑 創 平 (北大理)Sohei Tasaki (Hokkaido Univ.)

2 次元円盤領域における線形弾性作用素の固有値・固有関数 · · · · · · · · · · 15
Eigenpairs of the linear elasticity operator on the disk

概 要 Although the linear elasticity operator is an important elliptic operator that describes the core of thedeformation theory of elastic bodies, the form of its eigenfunctions, even the first eigenfunction, seems to be
not well understood. This is due to the fact that the conservation of ordered structure, such as the maximum
principle, is not obvious in vector fields. Another difficulty is the existence of non-diagonal components of
the operator. Therefore, the next step is to find eigenvalues and eigenfunctions on the two-dimensional disk
domain, which seems to be the simplest case where the non-diagonal components essentially play a role. In
this talk, we report all eigenvalues and eigenfunctions of the linear elastic operator on the disk.
46 坂 上 貴 之 (京
辻
裕 太

大

理)

Takashi Sakajo (Kyoto Univ.)
Yuta Tsuji

ランダム偏微分方程式で記述される一次元乱流モデルの統計則 · · · · · · · · 15

Statistical laws of a one-dimensional turbulence model as a random PDE

概 要 We propose a one-dimensional model of turbulent flows generating the cascade of the conserved

quantity. We show the global existence of a unique global solution of the equation subject to random
forcing functions that are chosen from a given distribution. Moreover, we numerically investigate thesolutions’ statistical laws such as enstrophy spectra and structure functions by Galerkin approximation of
random variables with generalized Polynomial Chaos.
大理)
47 坂 上 貴 之 (京V. Krishnamurthy(Indian Inst. of Tech. Hyderabad)

Takashi Sakajo (Kyoto Univ.)
Vikas Krishnamurthy(Indian Inst. of Tech. Hyderabad)

二重周期領域上のグリーン関数と点渦力学 · · · · · · · · · · · · · · · · · · · · · · · · · 15

The hydrodynamic Green’s function and point vortex dynamics in a
doubly periodic domain

概 要 We consider the evolution of N point vortices in a doubly-periodic rectangle. In this talk, we provide

the analytic formula of the hydrodynamic Greeb’s function in the domain utilizing the Schottky–Klein
prime function associated with an annular domain. With the conformal mapping approach, we have derived
the governing equation from the analytic representation. In the derivation, the sum of vortex strengths
doesn’t necessarily vanish, which is not covered by the previous works. Utilizing the equation, we show a
Hamiltonian structure for the equation and discuss the integrability of the system. We also find new latticeequilibria arranged in doubly-periodic rectangular and parallelograms.

Final: 2023/8/21
103

応用数学

大⋆)
48 西 田 孝 明 (京藤 原 宏 志 ( 京 大 情 報)夏俊 雄(National Taiwan Univ.)

Takaaki Nishida (Kyoto Univ.⋆)
Hiroshi Fujiwara (Kyoto Univ.)
Chun-Hsiung Hsia
(National Taiwan Univ.)

Thermohaline convections in the horizontal layer with non-uniform heat
supply · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Thermohaline convections in the horizontal layer with non-uniform heat
supply概 要 Viscous salt water motion under gravity with non-uniform heat supply in a long horizontal strip

domain is considered. An existence theorem of stationary solutions and some numerical computations areshown.
49 緒 方 秀 教 (電通大情報理工)
Hidenori Ogata(Univ. of Electro-Comm.)

数値計算における IMT 型変数変換の利用 · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The usage of the IMT-type variable transformation in numerical computations

概 要 We propose the usage of the IMT-type variable transformation, which is used in the IMT-typenumerical integration formula, in various numerical computation such as numerical indefinite integral,numerical solution of ordinary differential equations, and so on. Recently, the DE (double exponential)
transformation, which is used in the DE numerical integration formula, has been applied to various numericalcomputations coupled with the Sinc approximation. We show that the IMT-type transformation can beapplied as the DE one coupled with the Sinc approximation for periodic functions.
50 古 賀 一 基 (東工大情報理工)
Kazuki Koga

(Tokyo Tech)

球面とその離散化との間の弱い比較について · · · · · · · · · · · · · · · · · · · · · · · 15

On weak comparisons between the sphere and its approximations

概 要 We propose a novel algorithm for quantitative comparisons between compact surfaces embedded in

the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface
measures and compute a weak distance between them using the Fourier transform on the ambient space. In
particular, the Sobolev norm of negative order for a difference between two surface measures is evaluated via
the Plancherel theorem. This approach amounts to approximating a weighted integral norm of smooth dataon the frequency space and allows several advantages in terms of accuracy and efficiency. As a validation,
we present numerical experiments where the 2-sphere is compared with its icosahedral discretization andobserve that the piecewise linear approximations converge to the smooth object.
51 坂 口 文 則 (福 井 大 工)Fuminori Sakaguchi (Univ. of Fukui)

常微分方程式整数型解法の平均 2 乗誤差の直接評価 · · · · · · · · · · · · · · · · · 15

Direct evaluation of the mean squares errors of an integer-type algorithm
for ODEs

概 要 In this study, we evaluate directly the mean square errors in numerical solutions by an integer-

type high-accuracy algorithm for linear higher-order ODEs using quasi-orthogonalizations of integer-valued
vectors which was proposed recently by the author and M. Hayashi. Their direct evaluation is very difficult
by usual methods, since the accuarcy of this algorithm is very high while we have hardly a simple method
for calculating the true values of the expansion coefficients with a very high accuracy in usual cases. In thisstudy, we show how we can execute the direct evaluation by means of the recurrence relation among the
expansion coefficients.

Final: 2023/8/21
応用数学

52 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)

104

On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation · · · · · · · 15
On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation

概 要 We introduce a capillary Chambolle type scheme for mean curvature flow with prescribed contact

angle. Our scheme includes a capillary functional instead of just the total variation. We show that thescheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang
type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of thisscheme based on the split Bregman method instead of a duality method.
14:15〜16:00
53 竹 村 春 希 (東 大 数 理)
柏 原 崇 人 ( 東 大 数 理)

Haruki Takemura (Univ. of Tokyo)
Takahito Kashiwabara (Univ. of Tokyo)

1 次元移流方程式における CIP 法の収束証明 · · · · · · · · · · · · · · · · · · · · · · · 15
Convergence analysis of CIP method for the one-dimensional advection
equation

概 要 Cubic Interpolated Pseudo-particle (CIP) scheme is a semi-Lagrangian method for numerical calcu-

lation of hyperbolic partial differential equations. The CIP method has low numerical diffusion and highaccuracy. It is observed by experiments that the CIP scheme for the one-dimensional advection equation
has third-order accuracy in time and space. We present convergence analysis of the CIP scheme for the
one-dimensional advection equation. Since the scheme can be interpreted as the repetition of translationand the Hermite interpolation, properties of the piecewise Hermite interpolation play an important role in
the proof.
54 遠 藤 凌 輝 (新 潟 大 自 然)劉雪 峰 ( 新 潟 大 理)
Ryoki Endo
Xuefeng Liu(Niigata Univ.)(Niigata Univ.)クラスターを成す Laplace 作用素の固有値に対する形状微分の厳密計算法· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Verified computation for shape derivative of the Laplacian eigenvalues

概 要 The shape derivative of Laplacian eigenvalues with respect to domain deformations was studied

theoretically by Hadamard in the early 20th century. In this study, we propose a verified computation
method for the shape derivative of clustered eigenvalues using guaranteed computation of both eigenvalues
and eigenfunctions.
55 千 葉 悠 喜 (東 大 数 理)
齊 藤 宣 一 ( 東 大 数 理)
Yuki Chiba (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

滑らかな領域上の Robin 境界値問題に対する Nitsche 法 · · · · · · · · · · · · · 15

Nitsche’s method for a Robin boundary value problem in a smoothdomain

概 要 The Robin boundary value problem (BVP) is interpreted as the classical penalty method with thepenalty parameter ε. The optimal choice of the mesh size h relative to ε is a non-trivial issue. In thistalk, we carefully examine the dependence of ε on error estimates and prove several optimal-order error
estimates for a Nitsche’s method applied to an inhomogeneous Robin BVP for the Poisson equation definedin a smooth bounded domain.

Final: 2023/8/21
応用数学

105

56 水
中
橋
関
大

口
尾
本
根
石

充
弘
晃
進

信 ( 中 大 理 工)
宏 ( 早 大 理 工)
治 ( 中 村 学 園 大)
太 ( 千 葉 工 大)
一 ( 早 大 理 工)

Makoto Mizuguchi (Chuo Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)
Kouji Hashimoto(Nakamura Gakuen Univ.)
Kouta Sekine (Chiba Inst. of Tech.)
Shin’ichi Oishi (Waseda Univ.)

放物型方程式の全離散近似解に対する定量的な誤差評価 · · · · · · · · · · · · · 15

The quantitative error estimates for a full-discrete approximate solution

概 要 We consider constructive error estimates for a full discrete approximate solution of the heat equation

with the Dirichlet boundary condition. In particular, we mainly focus on formulas for obtaining the values ofthe error constants. The formulas giving sharp estimates for the constants improve the numerical verification
methods. The previous formula requires some large-size complicated matrices to get the values. We leada formula constructed by only the error constants for the Ritz-projections in a domain and a time interval
without the matrices. The effectiveness of the formula will be introduced in this talk.
57 G. W. Duchesne ( McGill Univ. )J.-P. Lessard ( McGill Univ. )高 安 亮 紀 (筑波大システム情報)

Gabriel W. Duchesne (McGill Univ.)
Jean-Philippe Lessard (McGill Univ.)
Akitoshi Takayasu (Univ. of Tsukuba)

半線形放物型方程式の時間大域解の計算機援用証明 · · · · · · · · · · · · · · · · · 15

Computer-assisted proofs for global existence of solutions to semilinear
parabolic equations

概 要 We propose a strategy to prove the global existence (in time) of solutions to initial value problemsof semilinear parabolic PDEs via the mechanism of convergence towards an asymptotically stable nontrivial equilibrium solution. Our method is based on the pseudo-diagonalization of the Fréchet derivativeat a non-trivial equilibrium using Gershgorin’s approach, which gives access to the “eigenvalues” of theequilibrium. Then, by constructing a trapping region of the asymptotically stable equilibrium, we perform
rigorous integration so that the solution goes into the trapping region. Therefore, we conclude that thesolution exists globally in time and it converges to the non-trivial equilibrium.
58 渡 部 善 隆(九大情報基盤研究開発センター)
大理)
宮 路 智 行 (京Yoshitaka Watanabe (Kyushu Univ.)
Tomoyuki Miyaji (Kyoto Univ.)

精度保証付き数値計算による Proudman–Johnson 方程式の単峰性解の存
在検証 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Computer-assisted proofs of unimodality of solutions for Proudman–Johnson equation

概 要 This talk presents a computer-assisted proof of the existence and unimodality of steady-state solutions

for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed
approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is anotherproof by Miyaji and Okamoto (2019). Verification results show the validity of both proofs.

Final: 2023/8/21
応用数学

特別講演
石 本 健 太 ( 京 大 数 理 研)

Jeffery の解と流体力学的な生き物の「かたち」

Kenta Ishimoto (Kyoto Univ.)

Jeffery’s orbits and hydrodynamic shape of life106

16:15〜17:15

概 要 When observing fluid flow, our perception of its motions often relies on tracking the movements ofsmall particles within the fluid. In this talk, we will discuss the dynamics of microscopic objects, particularly
those capable of self-propulsion, such as living organisms. Nearly a century ago, G. B. Jeffery derived anexact solution to the Stokes equation for a spheroidal object in simple shear, revealing that its orientation
vector traces a closed, time-periodic trajectory now referred to as Jeffery’s orbit. By introducing the conceptof hydrodynamic symmetry, based on the equation of motion, we extend Jeffery’s equation to encompass
general chiral axisymmetric objects. Further, we will demonstrate by a classical multi-scale perturbation
theory that various complex self-propelling motions can be explained by generalized asymptotic Jeffery’s
equation.

Final: 2023/8/21
トポロジー

107

ト ポ

ロ

9 月 20 日（水）ジー第 III 会場

9:30〜12:00
1 鈴 木 正 明 ( 明 大 総 合 数 理)
森 藤 孝 之 ( 慶 大 経 済)
Masaaki Suzuki (Meiji Univ.)
Takayuki Morifuji (Keio Univ.)

結び目の最小位数について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On the minimal order of knots

概 要 Based on a vanishing theorem for non-fibered knots due to Friedl and Vidussi, we define the minimalorder of a knot to be the order of the smallest finite group such that the corresponding twisted Alexanderpolynomial is zero. In this talk, we report that the lower bound of the minimal order of every knot is
24. This is the best possible in the sense that there exists a knot whose minimal order attains the bound.
Moreover, we provide several explicit values for the minimal order of knots with 10 or fewer crossings.
戸大⋆)2 中 西 康 剛 (神佐 藤
進 ( 神 戸 大 理)

Yasutaka Nakanishi (Kobe Univ.⋆)(Kobe Univ.)
Shin SatohColors of virtual tangles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Colors of virtual tangles

概 要 For Fox n-colorings of virtual tangles, we consider a condition on colors of endpoints of tangles.

3 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 Wada

Virtualized ∆-moves for virtual knots and links · · · · · · · · · · · · · · · · · · · · 10

Virtualized ∆-moves for virtual knots and links

概 要 In this talk, we introduce a local deformation for virtual knots and links, called the v∆-move, as a

virtualized version of the ∆-move. We show that the v∆-move is an unknotting operation for virtual knots,
and then define the v∆-unknotting number of a virtual knot K as the minimal number of v∆-moves needed
to transform K into the trivial knot. For any positive integer m, we construct a family of infinitely many
virtual knots with v∆-unknotting number m. Moreover we give a classification of virtual links of two or
more components up to v∆-moves.
4 水 澤 篤 彦 ( 早 大 非 常 勤)
小 鳥 居 祐 香 (広島大理・理化学研)

Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii(Hiroshima Univ. / RIKEN)

空間グラフの component-homotopy 類の分類 · · · · · · · · · · · · · · · · · · · · · · 15

A classification of the component-homotopy classes of spatial graphs

概 要 Two links are called link-homotopic if they are transformed to each other by a sequence of self-crossingchanges and ambient isotopies. Two spatial graphs are called component-homotopic if they are transformed
to each other by a sequence of self-crossing changes and ambient isotopies. The set of the link-homotopy
classes of links were classified as the set of the link-homotopy classes of string links modulo certain relations
by Habegger and Lin. We give new relations for the set of the link-homotopy classes of “colored” string
links and classify the set of the component-homotopy classes of spatial graphs.

Final: 2023/8/21
トポロジー

5 柳 田 幸 輝 ( 東 工 大 理)
Koki Yanagida(Tokyo Tech)108

絡み目の parabolic Dijkgraaf–Witten 不変量 · · · · · · · · · · · · · · · · · · · · · · · 15

Parabolic Dijkgraaf–Witten invariants of links

概 要 The Dijkgraaf–Witten invariant is a topological invariant of closed orientable 3-manifolds. Based on

this invariant, we define a new invariant of links in the 3-sphere and call it the parabolic Dijkgraaf–Witten
invariant. Considering covering spaces branched over links or quandle theory, we establish two procedures
to compute parabolic Dijkgraaf–Witten invariants of links. In this talk, we introduce the definition of theparabolic Dijkgraaf–Witten invariant and some computational results.
6 村 上

順 ( 早 大 理 工)

Jun Murakami (Waseda Univ.)

ボトムタングルから Aq 多項式へ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

From bottom tangle to Aq polynomial

概 要 Construct a quantization of the fundamental group of a knot complement by using the bottom tangle.

Then applying the Kauffman bracket skein relation, we obtain the skein module of the knot complement.
The boundary of a knot is a torus, and the skein algebra of the torus acts to the skein module of the knot
complement. Investigating this action, we get a recurrence relation of the colored Jones polynomial.
7 久 保 田 肇 (京大理)Hajime Kubota (Kyoto Univ.)

Knot Floer homology の連結和公式の組み合わせ的な証明 · · · · · · · · · · · 15
A combinatorial proof of the connected sum formula for knot Floer
homology

概 要 Grid homology is a combinatorial reconstruction of knot Floer homology. We research the extended

grid homology for transverse spatial graphs and show that grid homology vanishes if the underlying graphhas a cut edge as a spatial graph. Then as a corollary, we give a combinatorial proof of the connected sum
formula for knot Floer homology.
8 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.)

ロンジチュードの像が自明となるメリディアンを保つ曲面束結び目群の間の全射準同型の構成について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A construction of epimorphisms between groups of fibered knots that
preserve a meridian but the image of its longitude is killed

概 要 We study epimorphisms between knot groups, especially focusing on the case that these epimorphisms

are induced by a map of degree zero. We construct a family of infinitely many fibered knots that each knot
group maps to the knot group of the figure eight knot by an epimorphism, and these epimorphisms are
induced by maps that preserve its meridian but the image of its longitude is killed in the knot group of the
figure eight knot.
14:20〜15:20

特別講演
北 野 晃 朗 (創 価 大 理 工) ♭ 結び目群の間の全射準同型写像から見た結び目の幾何的構造や不変量についてTeruaki Kitano (Soka Univ.) Epimorphisms between knot groups and relations to geometric struc-tures and invariants of a knot
概 要 Let K be a knot in S 3 and G(K) = π1 (S 3 \ K) its knot group. Here we assume that an epimorphism

maps a meridian to a meridian. It is well known that a degree one map between knot exteriors induces an
epimorphism which preserves a pair of a meridian and a longitude. However, there are a lot of epimorphism
between knot groups which preserve a meridian but a longitude to the trivial element. In this talk, we
discuss the following: if there exists a meridian preserving epimorphism from G(K1 ) onto G(K2 ), then what
we can see geometric structures or invariants of K1 and K2 ? Mainly we will discuss the genus, twisted
Alexander polynomials, symmetric union, and character varieties. This talk will be partially based on
several joint works with Michel Boileau, Steven Sivek, Raphael Zentner, Yuta Nozaki, and Yasuharu Nakae.

Final: 2023/8/21
109

トポロジー

15:40〜17:30
9 藤 井 道 彦 ( 琉 球 大 理)
逆 井 卓 也 ( 東 大 数 理)

Michihiko Fujii (Univ. of Ryukyus)
Takuya Sakasai (Univ. of Tokyo)

The spherical growth series of amalgamated free products of infinite
cyclic groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The spherical growth series of amalgamated free products of infinite
cyclic groups

概 要 Let n be an integer greater than 1. Then we consider an amalgamated free product G of n infinite

cyclic groups. The group G is geometrically realized as the fundamental group of a Seifert fiber space overthe 2-dimensional disk with n cone points. We present a formula for the spherical growth series of the group
G with respect to its standard generating set, from which a rational function expression for the spherical
growth series of G is derived concretely.
10 地 引 知 栄 (東 工 大 理)
Chihaya Jibiki(Tokyo Tech)

融合積の帰納極限における左順序 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Left-orderings on inductive limits of amalgamated free products

概 要 We study left orderings on countably generated groups. In particular, we construct left orderings of

inductive limits of amalgamated free products by using isolated left orderings of the groups appearing in
the inductive system. Moreover, we show that they are no longer isolated orderings.
11 高 野 暁 弘 (東 大 数 理)
児 玉 悠 弥 ( 都 立 大 理)

Akihiro Takano (Univ. of Tokyo)
Yuya Kodama (Tokyo Metro. Univ.)

The p-colorable subgroup of Thompson’s group F · · · · · · · · · · · · · · · · · · 15
The p-colorable subgroup of Thompson’s group F

概 要 Recently, Jones introduced a method of constructing knots and links from elements of Thompson’sgroup F by using its unitary representations. He also defined a subgroup of F as the stabilizer subgroup,
called the 3-colorable subgroup. We proved that all knots and links obtained from non-trivial elements ofthis group are 3-colorable. In this talk, we extend this result to any odd integer p greater than two. Namely,
we define the p-colorable subgroup of F whose non-trivial elements yield p-colorable knots and links andshow it is isomorphic to the certain Brown–Thompson group.
12 児 玉 悠 弥 (都 立 大 理)
高 野 暁 弘 ( 東 大 数 理)

Yuya Kodama (Tokyo Metro. Univ.)
Akihiro Takano (Univ. of Tokyo)

Alexander’s theorem for stabilizer subgroups of Thompson’s group · · · 15
Alexander’s theorem for stabilizer subgroups of Thompson’s group

概 要 Recently, Jones introduced a method of constructing knots and links from elements of Thompson’sgroup F by using its unitary representations. He also showed that this construction is surjective. Namely,
any knot or link can be obtained from F . To understand this construction well, we focus on subgroups of
F . In this talk, we show that almost all stabilizer subgroups (under the natural action on [0, 1]) also give
all knots and links.

Final: 2023/8/21
トポロジー

9 月 21 日（木）110

第 III 会場

9:30〜11:30
13 加 藤諒 ( 高 知 工 科 大)知大)
下 村 克 己 (高下 村 磨 生 将 (高知大総合人間自然)

Ryo Kato (Kochi Univ. of Tech.)
Katsumi Shimomura (Kochi Univ.)
Maonosuke Shimomura (Kochi Univ.)

1
The first cohomology of the monochromatic comodule Mn−1
at anyprime · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 101
The first cohomology of the monochromatic comodule Mn−1
at anyprime

1
概 要 We determined the structure of the first cohomology of the monochromatic cohomodule Mn−1
at anyprime.
14 岡 島 宏 樹
加 藤諒 ( 高 知 工 科 大)知大)
下 村 克 己 (高Hiroki Okajima
Ryo Kato (Kochi Univ. of Tech.)
Katsumi Shimomura (Kochi Univ.)

W -originated elements in the stable homotopy groups of spheres · · · · · 10

W -originated elements in the stable homotopy groups of spheres

概 要 We prove new result around W -originated elements in the stable homotopy groups of spheres.

15 加 藤諒 ( 高 知 工 科 大)

Ryo Kato (Kochi Univ. of Tech.)Deformed cohomological Bousfield classes · · · · · · · · · · · · · · · · · · · · · · · · · 10
Deformed cohomological Bousfield classes

概 要 We prove that deformed cohomological Bousfield classes form a set.

16 加 藤諒 ( 高 知 工 科 大)

Ryo Kato (Kochi Univ. of Tech.)

A relation between Picard groups of some local categories · · · · · · · · · · · 10
A relation between Picard groups of some local categories

概 要 We give a new relation between Picard groups of some stable homotopy categories.

17 石 黒 賢 士 (福 岡 大 理)
山 縣
真 ( 福 岡 大 理)

Kenshi Ishiguro (Fukuoka Univ.)
Makoto Yamagata (Fukuoka Univ.)

Genus problem of the classifying spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Genus problem of the classifying spaces

概 要 We consider the spaces that their p-completions are homotopy equivalent to the classifying space BG

of a compact connected Lie group G at any prime p. Such spaces are said to be in the genus set of BG.
Particularly we investigate the case of G being a product of the 3-dimennsional spheres. We will generalize
some previous results.
18 森 吉 仁 志 (名 大 多 元 数 理)
夏 目 利 一 ( 名 工 大 工)

Hitoshi Moriyoshi (Nagoya Univ.)
Toshikazu Natsume(Nagoya Inst. of Tech.)

カントール集合に対するコロナ指数定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Corona index theorem for Cantor sets

概 要 Let X a topological space with its corona the Cantor set. We choose as X either a binary tree

or a binary tube. An index formula on X developed, which connect the index class in K∗ (C ∗ Xtop ) to a
topological invariant obtained from the Cantor set.

Final: 2023/8/21
111

トポロジー

衛
大)
19 知 念 直 紹 (防山 内 貴 光 ( 愛 媛 大 理 工)
Naotsugu Chinen(Nat. Defense Acad. of Japan)
Takamitsu Yamauchi (Ehime Univ.)

On equivariant asymptotic dimension of actions of discrete groups on
non-compact Hausdorff spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On equivariant asymptotic dimension of actions of discrete groups on
non-compact Hausdorff spaces

概 要 We extend F-eq-asdim(Γ ↷ X) to F-eq-asdimﬁn (Γ ↷ X) of actions on (not necessarily compact)

Hausdorff spaces satisfying that F-eq-asdim(Γ ↷ X) = F-eq-asdimﬁn (Γ ↷ X) whenever X is a compact
Hausdorff space. And we also give a characterization theorem for F-eq-asdimﬁn (Γ ↷ X) in terms of maps
into ℓ1 (V ), which is a generalization of it due to Guentner, Willett and Yu.

9 月 21 日（木）11:40〜12:00

第 I 会場2023 年度日本数学会幾何学賞受賞者発表

9 月 21 日（木）第 III 会場

13:00〜14:00
20 武 田 雅 広 (京 大 ILAS)
岸 本 大 祐 ( 九 大 数 理)

Masahiro Takeda (Kyoto Univ.)
Daisuke Kishimoto (Kyushu Univ.)

Torsion in the space of commuting elements in a Lie group · · · · · · · · · · 15
Torsion in the space of commuting elements in a Lie group

概 要 Let Hom(Z m , G) denote the space of commuting m-tuples in a Lie group G. This space is identified

with the based moduli space of flat bundles over a torus, so it is an important object not only in topology
but also in geometry and physics. I will talk about torsion in the homology of Hom(Z m , G). We provethat for m ≥ 2, Hom(Z m , SU (n)) has p-torsion in homology if and only if p ≤ n. The proof includes a newhomotopy decomposition of Hom(Z m , G) in terms of a homotopy colimit. This talk is based on the joint
work with Daisuke Kishimoto.
21 秋 田 利 之 (北大理)Toshiyuki Akita (Hokkaido Univ.)

Alexander カンドルの共役カンドルへの埋め込み · · · · · · · · · · · · · · · · · · · 10
Embeddings of Alexander quandles into conjugation quandles

概 要 For any twisted conjugate quandle X, and in particular any Alexander quandle, there exists a group

G such that X is embedded into the conjugation quandle of G.
22 狩 野 隼 輔 (東北大MathCCS)

Shunsuke Kano (Tohoku Univ.)

Train track combinatorics and cluster algebras · · · · · · · · · · · · · · · · · · · · · 15
Train track combinatorics and cluster algebras

概 要 The concepts of train track was introduced by W. P. Thurston to study the measured folia-

tions/laminations and the pseudo-Anosov mapping classes on a surface. In this talk, I will translate
some concepts of train tracks into the language of cluster algebras using the Goncharov–Shen’s potentialfunction. Moreover, I will explain the sign stability of the general pseudo-Anosov mapping classes by using
this translation.

Final: 2023/8/21
トポロジー

9 月 22 日（金）112

第 III 会場

9:30〜12:00
23 鈴 木 龍 正 (東 工 大 理)

Tatsumasa Suzuki (Tokyo Tech)

概単純線形グラフを持つ Brieskorn ホモロジー球面の d 不変量 · · · · · · · · 15

The d-invariants of the Brieskorn homology spheres with almost simple
linear graphs

概 要 In 2003, Ozsváth and Szabó introduced an invariant of rational homology spin c cobordisms called ad-invariant. One of the most fundamental and important classes of 3-dimensional homology spheres is theBrieskorn homology sphere Σ(p, q, r). It is not clear how to calculate the d-invariant for Σ(p, q, r) uniformly
and concretely. In 2020, Karakurt and Şavk investigated the d-invariant of Σ(p, q, r) with pq + pr − qr = 1,
a class of Brieskorn homology spheres with almost simple linear graphs. They derived concrete calculation
results with p even and a formula with p odd. In this talk, we find a sharper evaluation formula when p is
odd and present some sufficient conditions for the equality of this formula. Furthermore, we see an infinite
number of examples showing phenomena that cannot occur when p is even.
24 鈴 木 龍 正 (東 工 大 理)
丹 下 基 生 (筑波大数理物質)

Tatsumasa Suzuki (Tokyo Tech)
Motoo Tange (Univ. of Tsukuba)

Brieskorn ホモロジー球面の d 不変量 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The d-invariant of any Brieskorn homology sphere概 要 One of the most important problems in the topology of 3-manifolds is the question of which 3-homology

sphere bounds a 3-homology ball. In 2003, Ozsváth and Szabó introduced an invariant of rational homology
spinc cobordisms called a d-invariant. Karakurt constructed a formula for the invariants of the Brieskorn
homology spheres, one of the most important classes of 3-homology spheres. From this formula, we can findthe correspondence between the invariants of these homology spheres and those of lens spaces. In this talk,
we introduce a reciprocity law which is effective for obtaining the invariant of any lens space. Furthermore,
we explain that by combining these results, we can specifically calculate the invariants of some Brieskorn
homology spheres.
25 鈴 木 龍 正 (東 工 大 理)
丹 下 基 生 (筑波大数理物質)

Tatsumasa Suzuki (Tokyo Tech)
Motoo Tange (Univ. of Tsukuba)

リボン 2 次元結び目に沿うポシェット手術 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Pochette surgery along any ribbon 2-knot

概 要 The pochette is the boundary sum P = S 1 × D 3 ♮D 2 × S 2 of S 1 × D 3 and D 2 × S 2 . Pochette surgery

on a 4-manifold X is an operation of removing the interior of P from X and gluing P by a diffeomorphismof ∂P . In this talk, we show that for any non-trivial ribbon 2-knot there exists a non-trivial cord suchthat any pochette surgery yielding a homology S 4 gives the double of a homology D4 without 3-handles.
Furthermore, we give infinitely many examples of pochette surgeries on S 4 with a non-trivial core sphereand a non-trivial cord such that the surgeries give S 4 . We also show that there exists the non-trivial
fundamental group of the homology S 3 by a Dehn surgery on a knot, which can be constructed along aribbon 2-knot by that of pochette operations on S 4 .
26 菅 原 朔 見 (北大理)Sakumi Sugawara (Hokkaido Univ.)

平面代数曲線の補集合のハンドル分解と Kirby 図式 · · · · · · · · · · · · · · · · · 15

Handle decompositions and Kirby diagrams for the complements ofplane algebraic curves

概 要 The complements of plane algebraic curves are well studied from topological and algebro-geometricviewpoints. In this talk, we will describe the explicit handle decompositions and the Kirby diagrams forthe complement of plane algebraic curves. The method is based on the notion of braid monodromy. We
refined this technique to obtain handle decompositions and Kirby diagrams.

Final: 2023/8/21
113

トポロジー

27 谷 口 南 海 (東 工 大 理)

Minami Taniguchi (Tokyo Tech)

曲面結び目の Kirby–Thompson 不変量 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Kirby–Thompson invariants for knotted surfaces

概 要 The Kirby–Thompson invariant for a knotted surface was defined in 2021 using the bridge trisection

for the knotted surface and the pants complex or the dual curve complex of the trisection surface. In thistalk, we review the definition of bridge trisections of knotted surfaces and the Kirby–Thompson invariants
for them. Moreover, we determine some Kirby–Thompson invariants for distant sums of finitely many
standard knotted surfaces.
28 福 田 瑞 季(産総研・東北大数理先端材料モデリングOIL)
石 川 昌 治 ( 慶 大 経 済)

Mizuki Fukuda (AIST–Tohoku Univ.)
Masaharu Ishikawa (Keio Univ.)

基本群を用いた branched twist spin の分類について · · · · · · · · · · · · · · · · 15

Distinguishing branched twist spins by fundamental groups

概 要 A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin.

A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely.
Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental groupsof the complements of branched twist spins. In this talk, by using such fundamental groups, we give someconditions to distinguish branched twist spins.
29 磯 島司 ( 東 工 大 理)

Tsukasa Isoshima (Tokyo Tech)Infinitely many standard trisection diagrams for Gluck twisting · · · · · · 15
Infinitely many standard trisection diagrams for Gluck twisting概 要 Gay and Meier asked whether a trisection diagram for Gluck twisting on the spin or the twist spin of

a non-trivial knot in the 3-sphere constructed by using its doubly pointed Heegaard diagram is standard.
The diagram is a potential counterexample of so called 4-dimensional Waldhausen’s conjecture. In this talk,we depict the trisection diagram explicitly in the case of the spin of the (p + 1, −p)-torus knot, where p ≥ 2,
and show that the trisection diagram is standard for all p.
30 高 橋 夏 野 (阪 大 情 報)

Natsuya Takahashi (Osaka Univ.)

境界付き 4 次元多様体のエキゾチック対に対するトライセクション種数· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Trisection genera for an exotic pair of 4-manifolds with boundary

概 要 A trisection is a decomposition of a 4-manifold into three 1-handlebodies. The notion of a trisection isa natural 4-dimensional analogue of Heegaard splittings for 3-manifolds. A trisection genus is a fundamental
invariant of smooth 4-manifolds defined by trisections. In this talk, we show that there exists an exotic pairof 4-manifolds with boundary whose trisection genera are 4. We also show genus-3 relative trisections forthe infinite family {W ± (l, k)}l,k∈Z of contractible 4-manifolds introduced by Akbulut and Kirby.
14:20〜15:20

特別講演
安 井 弘 一 ( 阪 大 情 報)

Kouichi Yasui(Osaka Univ.)

4 次元多様体の微分構造と種数関数
Smooth structures on 4-manifolds and genus functions

概 要 The genus function of a smooth oriented 4-manifold is the function that maps a second homology

class to the minimal genus of an embedded closed oriented surface representing the class. This function issensitive to the smooth structure of a 4-manifold and has many applications to low dimensional topology.
In this talk, I will briefly review genus functions, and give applications to exotic smooth structures andproperties of smooth 4-manifolds such as the geometric simple connectivity and the (mod 2) simple typeconjecture. I will also discuss a limitation of genus functions and its applications.

Final: 2023/8/21
トポロジー

114

15:40〜17:00
31 大 森 源 城 (東 京 理 大 理 工)

Genki Omori (Tokyo Univ. of Sci.)

Quasitoric 組み紐群の最小生成系について · · · · · · · · · · · · · · · · · · · · · · · · · 10
A minimal generating set for the quasitoric braid group

概 要 A toric braid is a braid whose closure is a torus link in R3 . Manturov generalized toric braids thatis called quasitoric braids and showed that the subset of quasitoric braids in the classical braid group isa subgroup of the braid group. We call this subgroup the quasitoric braid group. In this talk, we give aminimal generating set for the quasitoric braid group.
32 小 林 竜 馬 (石 川 工 高 専)
井 本 奈 緒Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)
Nao Imoto

SL(n; Z) のレベル d 主合同部分群 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
The level d principal congruence subgroup of SL(n; Z)

概 要 The abelianization of the level d principal congruence subgroup Γd (n) of SL(n; Z) was determined by

Lee–Szczarba. By this result and a result of Tits, we can obtain a minimal generating set for Γ d (n). In
this work, we gave three theorems about Γd (n).
33 小 林 竜 馬 (石 川 工 高 専)
Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)

向き付け不可能閉曲面のレベル d 写像類群 · · · · · · · · · · · · · · · · · · · · · · · · 10

The level d mapping class group of a non-orientable closed surface

概 要 Let Ng be a genus g non-orientable closed surface. We explain about relations on the level d mappingclass group Md (Ng ) of Ng and the level d principal congruence subgroup of GL(g − 1; Z). As applications,
we can give a normal generating set of Md (Ng ) and a finite generating set of M2l (Ng ) for g ≥ 4.

Final: 2023/8/21
115

無限可積分系

無 限

可積

9 月 20 日（水）分

系

第 VI 会場

9:30〜12:00
1 Wenda Fang

( 京 大 数 理 研)

Wenda Fang

(Kyoto Univ.)

Generalized AKS scheme of integrability via vertex algebra · · · · · · · · · · 15
Generalized AKS scheme of integrability via vertex algebra

概 要 It is well-known that the affine Kac–Moody vertex algebra at the critical level has a large center called

the Feigin–Frenkel center. Also, Victor Kac and his collaborators showed that Poisson vertex algebra plays
an important role in studying infinite-dimensional Hamiltonian systems. In this talk, we define the classicalR-matrix of Lie conformal algebra. By using the Feigin–Frenkel center and the classical R-matrix of Lieconformal algebra we give a new integrability scheme.
2 大 山 陽 介 ( 徳 島 大 理 工)

Yousuke Ohyama (Tokushima Univ.)

Global theory on q-Painlevé equations and special solutions · · · · · · · · · 15
Global theory on q-Painlevé equations and special solutions

概 要 We study the space of connection matrices of the Lax pair of the q-Painlevé VI equation. The spaceis the Segre surface, which is the del Pezzo surface of degree four. We observe that a holomorphic solutionof the q-Painlevé VI equation corresponds to an intersection of two lines of the Segre surface. This result isa q-analogue of Kaneko’s solutions of the Painlevé VI equation, which correspond to an intersection of twolines of the Fricke cubic.
3 竹 村 剛 一 (お茶の水女大基幹)

Kouichi Takemura (Ochanomizu Univ.)

Kernel function, q-integral transformation and q-Heun equations · · · · · 15
Kernel function, q-integral transformation and q-Heun equations

概 要 We find kernel functions of the q-Heun equation and its variants. We apply them to obtain q-integral

transformations of solutions to the q-Heun equation and its variants.
4 増 田
哲 ( 青 学 大 理 工)
津 田 照 久 ( 青 学 大 理 工)

Tetsu Masuda (Aoyama Gakuin Univ.)
Teruhisa Tsuda (Aoyama Gakuin Univ.)(1)

E7 型 q-Painlevé 系の有理解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(1)

Rational solutions to the q-Painlevé system of type E7(1)

概 要 We explain a construction of a family of rational solutions to the q-Painlevé system of type E7 .

5 長 尾 秀 人 ( 明 石 工 高 専)

Hidehito Nagao (Akashi Coll. of Tech.)(1)

D4 型アフィンワイル群対称性をもつ加法差分パンルヴェ方程式の多変数化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Multivariable generalization of the additive difference Painlevé equation(1)
with the affine Weyl group symmetry of type D4

概 要 We construct a multivariable generalization of the additive difference Painlevé equation with the affine(1)Weyl group symmetry of type D4

and give three representations of the Lax forms. Also, we show somerelations to additive difference Painlevé equations and the q-Garnier system (given as the multivariable(1)

generalization of the q-Painlevé equation with the affine Weyl group symmetry of type D5 ). In this talk,we present the results.

Final: 2023/8/21
無限可積分系

116

6 信 川 喬 彦 ( 神 戸 大 理)
藤 井 大 計 ( 神 戸 大 理)

q 超幾何方程式の 3 次の変異版の積分解と級数解 · · · · · · · · · · · · · · · · · · · · 15

Takahiko Nobukawa (Kobe Univ.)(Kobe Univ.)
Taikei Fujii

Integral solutions and series solutions for the variant of the q-hypergeometricequation of degree three

概 要 Papperitz’s differential equation is essentially obtained by applying a Moebius transformation toGauss’ hypergeometric system, thus it has Euler type integral solutions and series solutions in terms of Gausshypergeometric function 2 F1 . The variant of the q-hypergeometric equation of degree three, introduced by
Hatano–Matsunawa–Sato–Takemura (Funkcial. Ekvac., 2022) from the viewpoint of quantum integrable
systems, is a linear q-difference system of rank 2. It can be regarded as a q-analog of Papperitz’s equation,and from this aspect we give Euler type Jackson integral solutions and series solutions in terms of very-wellpoised q-hypergeometric function 8 W7 for the above q-difference systems. As an application, we obtain new
relations among those integrals and series.
7 渋 川 元 樹 ( 神 戸 大 理)
土 見 怜 史 ( 神 戸 大 理)

Genki Shibukawa (Kobe Univ.)
Satoshi Tsuchimi (Kobe Univ.)

The generalized Zwegers’ µ-function and transformation formulas forthe bilateral basic hypergeometric series · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The generalized Zwegers’ µ-function and transformation formulas forthe bilateral basic hypergeometric series

概 要 By applying Slater’s transformation formulas for the bilateral basic hypergeometric series 2 ψ2 , we derive

three-type translation formulas for the generalized Zwegers’ µ-function (“continuous q-Hermite function”)
which was introduced by Shibukawa–Tsuchimi (SIGMA, 2023). From some Bailey’s transformation formulaof 2 ψ2 , we also give a formula for the expression of the generalized Zwegers’ µ-function by some Very-WellPoised bilateral basic hypergeometric series.
8 粟 田 英 資 ( 名 大 多 元 数 理)
長 谷 川 浩 司 ( 東 北 大 理)
菅 野 浩 明 ( 名 大 多 元 数 理)
大 川
領
(阪公大数学研・京大数理研)(Univ. of Geneva)
S. Shakirov
白 石 潤 一 ( 東 大 数 理)
山 田 泰 彦 ( 神 戸 大 理)

Hidetoshi Awata (Nagoya Univ.)
Koji Hasegawa (Tohoku Univ.)
Hiroaki Kanno (Nagoya Univ.)
Ryo Okawa(Osaka Metro. Univ./Kyoto Univ.)
Shamil Shakirov (Univ. of Geneva)
Jun’ichi Shiraishi (Univ. of Tokyo)
Yasuhiko Yamada (Kobe Univ.)

Non-stationary difference equation, affine Laumon space and quantization of discrete Painlevé equation 1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Non-stationary difference equation, affine Laumon space and quantization of discrete Painlevé equation 1

概 要 We clarify relation between the non-stationary difference equations proposed by Shakirov and thequantized discrete Painleve VI equations proposed by Hasegawa.

Final: 2023/8/21
117

無限可積分系

9 粟 田 英 資 ( 名 大 多 元 数 理)
長 谷 川 浩 司 ( 東 北 大 理)
菅 野 浩 明 ( 名 大 多 元 数 理)
大 川
領
(阪公大数学研・京大数理研)(Univ. of Geneva)
S. Shakirov
白 石 潤 一 ( 東 大 数 理)
山 田 泰 彦 ( 神 戸 大 理)

Hidetoshi Awata (Nagoya Univ.)
Koji Hasegawa (Tohoku Univ.)
Hiroaki Kanno (Nagoya Univ.)
Ryo Okawa(Osaka Metro. Univ./Kyoto Univ.)
Shamil Shakirov (Univ. of Geneva)
Jun’ichi Shiraishi (Univ. of Tokyo)
Yasuhiko Yamada (Kobe Univ.)

Non-stationary difference equation, affine Laumon space and quantization of discrete Painlevé equation 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Non-stationary difference equation, affine Laumon space and quantization of discrete Painlevé equation 2

概 要 We conjecture that the instanton partition function coming from the affine Laumon space provides asolution to Shakirov’s equation. We show that this conjecture is true in a special limit of parameters.
14:15〜15:15

特別講演

松 原 宰 栄(熊本大先端・熊本大教育)

代数方程式系と超幾何系

Saiei-Jaeyeong Matsubara-Heo(Kumamoto Univ./Kumamoto Univ.)

Algebraic equations and hypergeometric equations

概 要 It has been decades since Gelfand, Graev, Kapranov, and Zelevinsky shed new light on the theory of

hypergeometric systems. They discovered that it is intimately related to a system of algebraic equations,especially the theory of discriminants. This is the theory of GKZ systems. We highlight that rich combinatorics of discriminants reveals analytic properties of GKZ hypergeometric functions. A more interesting,yet challenging, function arises in the context of Feynman integrals. It is beyond GKZ system, but it is still
hypergeometric. We introduce a new approach to understanding such integrals. The key is again a systemof algebraic equations, called likelihood equations.

9 月 21 日（木）第 VI 会場

9:30〜10:45
10 桑 野 泰 宏(鈴鹿医療科学大医用工)Yas-Hiro Quano(Suzuka Univ. of Med. Sci.)

統計的因果推論における反事実の確率公式 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Causal inference in statistics and probability formulae for counterfact

概 要 In this talk I shall reprot some probability formulae for counterfact.

Final: 2023/8/21
無限可積分系

11 A. J. Gerrard(お茶の水女大ソフトマター教育研究センター)
Allan John Gerrard(Ochanomizu Univ.)

118

Fundamentals of the nested algebraic Bethe ansatz · · · · · · · · · · · · · · · · · 15
Fundamentals of the nested algebraic Bethe ansatz

概 要 The algebraic Bethe ansatz is a well-known technique used for constructing eigenvectors of integrable

models, most notably the Heisenberg XXX and XXZ spin chains. It was pioneered by Soviet mathematiciansin the 1970s, and has since undergone countless generalisatons. Among these generalisations, the nested
Bethe ansatz has been used to tackle integrable models with higher rank Lie symmetry than the SU (2) ofthe XXX model. However, these implementations have generally been considered on a case-by-case basis.
In this talk I would like to unify the theory for rational closed spin chains into a single formalism based on
the theory of Yangians in the RTT presentation.
12 田 中 聖 人 (名 大 多 元 数 理)

Masato Tanaka (Nagoya Univ.)

A cocycle on the quantum deformation of the special linear group · · · · 15
A cocycle on the quantum deformation of the special linear group

概 要 In 2021, De Commer–Talla constructed a quantum deformation SLq (2, R) of SL(2, R). To reveal

properties of groups, we consider interesting maps called 1-cocycles, for example. In the case of (operator
algebraic quantum) groups, we can give characterization of Haargerup property and property (T) via thelanguages of 1-cocycles and 1-cocycles appear in many areas (e.g. the theory of Lévy processes and Popa’s
deformation/rigidity theory). In this talk, we construct a 1-cocycle on SLq (2, R) and introduce someproperties SLq (2, R) has.
13 山 根 宏 之 (富 山 大 理)
井 上 鷹 斗 ( 富 山 大 理 工)

Hiroyuki Yamane (Univ. of Toyama)
Takato Inoue (Univ. of Toyama)

ワイル亜群のケイリーグラフのハミルトン閉路 · · · · · · · · · · · · · · · · · · · · · 15

Hamiltonian cycles of Cayley graphs of Weyl groupoids

概 要 We show an existence of Hamiltonian cycles of Cayley graphs of almost Weyl groupoids.

14 尾 角 正 人 (阪 公 大 理)
Jae-Hoon Kwon (Seoul National Univ.)
Sin-Myung Lee (Seoul National Univ.)

Masato Okado (Osaka Metro. Univ.)
Jae-Hoon Kwon (Seoul National Univ.)
Sin-Myung Lee (Seoul National Univ.)

量子アフィン orthosymplectic 超代数の振動子表現 · · · · · · · · · · · · · · · · · · 15

Oscillator representations of quantum affine orthosymplectic superalgebras

概 要 We introduce a category of q-oscillator representations over the quantum affine superalgebras of type

D and construct a new family of its irreducible representations. Motivated by the theory of super duality, we(1)show that these irreducible representations naturally interpolate q-oscillator representations of type Xn and(1)

finite-dimensional representations of type Ynfor (X, Y ) = (C, D), (D, C) under exact monoidal functors.

This can be viewed as a quantum affine analogue of the correspondence between irreducible oscillator andirreducible finite-dimensional representations of classical Lie algebras arising from Howe’s reductive dual
pairs (g, G), where g = sp2n , so2n and G = Ol , Sp2l .

Final: 2023/8/21
119

無限可積分系

11:00〜12:00

特別講演
佐 々 田 槙 子 ( 東 大 数 理)

離散可積分系への確率論的アプローチ

Makiko Sasada (Univ. of Tokyo)

Discrete integrable systems from probabilistic perspectives

概 要 The box-ball system (BBS) was introduced by Takahashi and Satsuma as a simple discrete model inwhich solitons (i.e. solitary waves) could be observed, and it has since been shown that it can be derived fromthe classical Korteweg–de Vries equation, which describes waves in shallow water by a proper discretization.
The last few years have seen a growing interest in the study of the BBS and related discrete integrable
systems started from random initial conditions. Particular aims include characterizing probability measuresthat are invariant for the dynamics, exploring the soliton decompositions of random configurations, andestablishing (generalized) hydrodynamic limits. These studies have generated new research topics in bothprobability theory and integrable systems, as well as given new perspectives on classical results. In thistalk, I will explain some recent progress in this direction. This talk is based on joint works with David
Croydon, Tsuyoshi Kato, Matteo Mucciconi, Tomohiro Sasamoto, Hayate Suda, Satoshi Tsujimoto, andRyosuke Uozumi.