Final: 2024/2/6“日本数学会2024 年度年会

英 文

サ

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リ

2024 年 3 月
於大阪公立大学集2024 日 本 数 学 会
年会プログラム期日2024 年 3 月 17 日（ 日 ）〜 3 月 20 日（ 水 ）会場

大阪公立大学杉本キャンパス
大 阪 府 大 阪 市 住 吉 区 杉 本 3–3–138

連 絡 先

大阪公立大学大学院理学研究科〒558-8585
大 阪 府 大 阪 市 住 吉 区 杉 本 3–3–138
E-mail omu24mar mathsoc jp
一般社団法人

第 I 会場

第 II 会場

第 III 会場

第 IV 会場

第 V 会場

第 VI 会場

第 VII 会場

日 本 数 学 会

第 VIII 会場

第 IX 会場

全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟 全学共通教育棟
1 階 810 教室 1 階 811 教室 1 階 812 教室 1 階 813 教室 1 階 814 教室 1 階 815 教室 2 階 820 教室 2 階 821 教室 2 階 822 教室

17 日
（日）

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

数学基礎論
応用数学
および歴史

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

9:30〜11:00

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

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

10:45〜11:45 16:30〜17:30 14:15〜15:15 16:25〜17:25 14:20〜15:20 14:15〜15:15 14:15〜15:15
15:30〜16:30

17:00〜18:00

9:30〜11:40

9:30〜11:45 9:30〜11:10 9:50〜11:20
14:15〜16:10 15:40〜17:30 15:35〜16:30

企画特別講演

13:00〜14:00

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

数学基礎論
応用数学
および歴史

9:30〜12:00

9:15〜12:00

9:30〜12:00

9:30〜11:40 13:00〜14:00

18 日 特 別 講 演 特 別 講 演（月） 13:00〜14:00 13:00〜14:00

特別講演

特別講演 特別講演 特別講演

10:30〜11:30

13:00〜14:00 13:00〜14:00 13:00〜14:00

9:30〜10:00
13:00〜14:00

9:50〜11:20

9:30〜11:00

9:00〜12:00
13:00〜14:00

日本数学会賞授賞式（基礎教育実験棟 1 階 階段教室） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30〜15:00)〃
総 合 講 演（） 日 本 数 学 会 賞 春 季 賞 受 賞 者 · · · · · · (15:15〜16:15)
大理) · · · · · · (16:30〜17:30)
吉 川 謙 一 (京懇
親会（学術情報総合センター 野のはなハウス） · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:00〜20:00)
代 数 学 函数方程式論 統 計 数 学 幾 何 学 トポロジー 実 函 数 論 函数解析学 無限可積分系 応 用 数 学
9:30〜12:00

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

19 日
（火）

20 日
（水）

9:30〜12:00

企画特別講演

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

9:30〜11:30

9:50〜12:00
14:50〜16:30

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

14:40〜15:40 16:15〜17:15
16:00〜17:00

14:20〜15:20 16:30〜17:30 16:00〜17:00 14:15〜15:15 16:45〜17:45

代 数 学 函数方程式論 統 計 数 学 幾 何 学

実函数論

無限可積分系 応 用 数 学

9:00〜12:00 10:00〜12:00 10:00〜11:40
14:15〜18:00 14:15〜15:15

9:30〜12:00
14:15〜15:40

9:30〜11:30

9:20〜10:15

企画特別講演

9:50〜12:00
14:15〜15:25

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

15:30〜16:30 14:15〜15:15 10:30〜11:30
15:30〜16:30

15:45〜16:45
17:00〜18:00

14:15〜15:15 15:40〜16:40

Final: 2024/2/6
3

目次
総合講演

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

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

2

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

5

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

5

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

7

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

11

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

11

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

16

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

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

26

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

26

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

29

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

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

35

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

35

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

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

39

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

39

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

43

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

実函数論

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

53

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

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

62

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

62

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

63

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

統計数学

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

68

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

68

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

70

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Final: 2024/2/6
4

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
応用数学

73

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

76

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

76

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

82

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

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

94

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

94

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

97

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

97

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

97

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

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

101

3 月 19 日（火） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

3 月 20 日（水） . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

Final: 2024/2/6
1

総合講演

総 合

講

演

3 月 18 日（月） 総合講演会場· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:15〜16:15)

日本数学会賞春季賞受賞者

Spring Prize Winner
吉 川 謙 一 (京大理)

Ken-ichi Yoshikawa (Kyoto Univ.)

カラビ・ヤウ型多様体に対する正則解析的捩率 · · · · · · · · · · · (16:30〜17:30)

Holomorphic analytic torsion for manifolds of Calabi–Yau
type

概 要 Holomorphic analytic torsion is a spectral invariant of compact Kähler manifolds introduced by Ray–

Singer in 1973. In the 1990s, as a consequence of mirror symmetry and string duality, two remarkableconjectures concerning the holomorphic analytic torsion of Calabi–Yau threefolds and Enriques surfaces were
proposed by physicists. One is an equivalence of the analytic torsion of Calabi–Yau threefolds and certain
curve counting invariants at genus-one of its mirror manifold (Bershadsky–Cecotti–Ooguri–Vafa), and theother is the coincidence of the analytic torsion of Enriques surfaces and the Borcherds Φ-function, theautomorphic form on the moduli space characterizing the discriminant locus (Harvey–Moore). Following
these conjectures, holomorphic torsion invariants of 2-elementary K3 surfaces and Calabi–Yau threefolds
were introduced and studied by the speaker in the former case and by Fang, Lu and the speaker in thelatter case. In the 2000s, those predictions by physicists concerning the analytic torsion of Enriques surfaces
and quintic mirror threefolds were conﬁrmed. In the late 2010s and beyond, there have been signiﬁcantadvances in the theory of holomorphic torsion invariants, such as the structure theorem of the invariant
for 2-elementary K3 surfaces (S. Ma and the speaker), the construction of a holomorphic torsion invariant
for Calabi–Yau manifolds (BCOV invariant) in higher dimensions and the proof of the genus-one mirror
symmetry for Calabi–Yau hypersurfaces of the projective space of arbitrary dimension (Eriksson–Freixas i
Montplet–Mourougane), and the birational invariance of the BCOV invariant (Fu-Zhang) etc. In the talk,I would like to give an overview of the developments of holomorphic torsion invariants mentioned above,
focusing on 2-elementary K3 surfaces and possibly mirror symmetry at genus one. If time permits, I will
also discuss some recent works in progress.

Final: 2024/2/6
企画特別講演

企

画

特

別

講

2

演

3 月 17 日（日）第 I 会場
特別招待講演 (日本応用数理学会)
関 川
浩 (東 京 理 大 理) 数値数式融合計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Hiroshi Sekigawa (Tokyo Univ. of Sci.)

Symbolic-numeric computation

概 要 Symbolic-numeric computation is a computing methodology that combines ideas from symbolic andnumeric computation. Symbolic computation (a.k.a. computer algebra) is very reliable, but it has thefollowing issues: algorithms in symbolic computation demand signiﬁcant resources, including time andmemory; usual algorithms in symbolic computation break down when applied to inexact values. Symbolicnumeric computation addresses these issues by combining ideas from symbolic and numeric computation.
In this talk, I will explain how to solve algebraic problems with inexact values by using symbolic-numericcomputation through several examples.
第 II 会場
宗 政 昭 弘 ( 東 北 大 情 報)

等角直線族の組合せ論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Akihiro Munemasa (Tohoku Univ.)

Combinatorics of equiangular lines

概 要 The problem of equiangular lines asks how many lines through the origin can be placed in the Euclidean

space while maintaining the pairwise angle of lines to be constant. This problem of metric geometry is
seemingly easier than packing problems in the sphere or the Euclidean spaces, but it is in general open except
for some small dimensions. By Lemmens and Seidel (1973), the problem can be reformulated as a purely
combinatorial problem in terms of switching classes of graphs. In this talk, I will survey recent developmenton this problem in connection with root systems and integral lattices. I will also brieﬂy touch on its complex
analogue, where “lines” mean complex 1-dimensional subspaces, and “angles” mean the absolute values of
the inner product of representing unit vectors. This analogue has been investigated by quantum physicists
under the name SIC-POVM, yet its existence problem is unsolved in general.
第 IV 会場
Junguk Lee(Changwon National Univ.)

Junguk Lee (Changwon National Univ.)

Survey on a geography of Model Theory · · · · · · · · · · · · · · · · (13:00〜14:00)
Survey on a geography of Model Theory

概 要 In this survey talk, we will explore a geography of Model Theory under the guidance of Classiﬁcation

Theory. First, we review basic ﬁrst-order logic and several dividing lines developed in Classiﬁcation Theory.
Second, we will focus on Classiﬁcation Theory for ﬁelds and examine some interactions between Field
Arithmetic and dividing lines.

Final: 2024/2/6
3

企画特別講演

3 月 19 日（火）第 II 会場
仙 葉

隆 ( 福 岡 大 理)

Takasi Senba (Fukuoka Univ.)

対数関数を知覚関数に持つ走化性方程式系の解の挙動について· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Behavior of solutions to chemotaxis systems with logarithmic
sensitivity functions

概 要 In this talk, we consider behavior of solutions to chemotaxis systems with logarithmic sensitivity

functions. In particular, we will talk about blowup and global existence of those solutions. The behaviorof solutions to classical chemotaxis systems is well known. The systems are chemotaxis systems with linear
sensitivity function. The classical chemotaxis systems have Lyapunov functions, which are often used forthe study of solutions to classical chemotaxis system. However, we do not still ﬁnd Lyapunov functions ofchemotaxis system with nonlinear sensitivity functions. This obstacles to the study of those systems. We
will talk some results on blowup and global existence of those solutions.
第 IV 会場
石 川 剛 郎 (北大⋆)Goo Ishikawa (Hokkaido Univ.

⋆)

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

Singular curves of sub-Riemannian spaces and related topics

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

bundle (distribution) over a manifold. Then the notion of geodesics or length minimisers are naturally
deﬁned on sub-Riemannian spaces. Unlike Riemannian case, there appear abnormal geodesics or singularcurves, as sub-Riemannian geodesics, in addition to normal geodesics. It turns out that singular curves
are deﬁned, depending just on the distribution, as critical points of end-point mapping in the context ofcontrol theory, and they are signiﬁcant objects also in geometry and topology in their own right. In thistalk, several topics and results on singular curves of distributions will be explained for speciﬁc cases, say,
(2, 3, 4)-distributions (Engel), in terms of the growth of ranks by taking Lie brackets, (2, 3, 5)-distributions(Cartan), (3, 5)-distributions, (4, 5)-distributions, (3, 6)-distributions, (4, 7)-distributions and so on, with someperspectives.

3 月 20 日（水）第 I 会場千 田 雅 隆 (東京電機大未来)

Masataka Chida (Tokyo Denki Univ.)p 進 Gross–Zagier 公式の高次元化について · · · · · · · · · · · · · · · (13:00〜14:00)
On generalizations of p-adic Gross–Zagier formula

概 要 Gross and Zagier showed a remarkable formula which relates the ﬁrst derivatives of L-functions formodular forms of weight two and heights of Heegner points on modular curves. Perrin-Riou proved a p-adic
analogue of the Gross–Zagier formula. They have many important arithmetic applications including theconjecture of Birch and Swinnerton-Dyer (BSD conjecture). Subsequently, Gan–Gross–Prasad formulated
a conjecture on a generalization of the Gross–Zagier formula to higher dimensional unitary and orthogonal
Shimura varieties, which is known by the arithmetic Gan–Gross–Prasad conjecture. Wei Zhang proposed
an approach to the arithmetic Gan–Gross–Prasad conjecture using relative trace formulas and he also formulated the arithmetic fundamental lemma (conjecture). Recently, Disegni–Zhang proved a p-adic analogue
of arithmetic Gan–Gross–Prasad conjecture for unitary groups using this approach. On the other hand,
Bertolini–Darmon–Prasanna introduced a slightly diﬀerent kind of p-adic Gross–Zagier formula which isa special value formula for p-adic L-functions at a point outside of the interpolation range. It is known
that this kind of formula has some interesting applications to BSD conjecture (more generally, Bloch–Kato
conjecture). For example, Darmon–Rotger proved a BDP type formula for triple products of elliptic modular
forms and it has an application to the equivariant BSD conjecture. In this talk, we will discuss some possible
generalizations of these formulas to higher dimensional cases.

Final: 2024/2/6
企画特別講演

4

第 IV 会場
梶 原 健 司 (九 大 I M I )可積分幾何による美的形状の生成 · · · · · · · · · · · · · · · · · · · · · · · (13:00〜14:00)

Kenji Kajiwara (Kyushu Univ.)

Generation of aesthetic shape by integrable geometry

概 要 We consider log-aesthetic curves (LAC), a family of planar curves developed in industrial design, as

curves that car designers regard as “aesthetic.” We present a new mathematical framework of LAC on thetheory of integrable systems and similarity geometry. Using this framework, LAC is shown to be a similarity
geometry analogue of Euler’s Elastica. Based on this mathematical setting, we present generalizations of
LAC to discrete curves, space curves and surfaces, which may be useful for generating aesthetic shapes.
The surfaces will be regarded as the similarity geometry analogue of the pseudospherical surfaces. We will
mention on some interesting results in the formulation of the 3D space curve and surfaces, such as explicit
formulas and symmetry structure. An interesting example of a classical truss structure called the Michellstructure in architecture in which mechanical optimality, integrability, and aesthetic nature coexist will be
discussed, together with the relationship with the discrete harmonic functions.

Final: 2024/2/6
5

数学基礎論および歴史

数 学

基

礎

論

3 月 17 日（日）

お

よ

び

歴

史

第 VIII 会場

9:30〜11:30
1 静 間 荘 司 ( 阪 府 大 理)Souji Shizuma (Osaka Pref. Univ.)

非同時発言な帽子パズルの一般定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

General theorem for nonsimultaneous hat puzzles

概 要 The prisoner and hat puzzle, also known as the hat problem, is divided into two depending on whether

the prisoners’ statements are simultaneous or non-simultaneous. In this presentation, we will focus on
puzzles with non-simultaneous type and introduce the general theorem.
2 津 久 浦 健 太 ( 法 政 大 理 工)
Kenta Tsukuura (Hosei Univ.)

Prikry 拡大での Namba 強制法の準適性性について · · · · · · · · · · · · · · · · · 15
On semiproperness of Namba forcings in Prikry extensions

概 要 It is known that many kinds of reﬂection principles fail in the extension by Prikry forcing. In

particular, the semistationary reﬂection principle fails, which in turn implies non-semiproperness of someNamba forcings. We ask what cardinal such that Namba forcing over its is not semiproper in Prikry
extension is. In this talk, we introduce Pκ λ-variations of Namba forcings and show that every Namba
forcing above the target of Prikry forcing is not semiproper in the extension.
3 依 岡 輝 幸 ( 静 岡 大 理)

Teruyuki Yorioka (Shizuoka Univ.)

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

Some preservation theorems for forcing notions with models as side conditions

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

by Stevo Todorčević. These forcing notions equip with models as side conditions. In this talk, somepreservation theorems for forcing notions with models as side conditions are introduced.
4 薄 葉 季 路 ( 早 大 理 工)

Toshimichi Usuba (Waseda Univ.)

Uniform ultraﬁlters in a choiceless context · · · · · · · · · · · · · · · · · · · · · · · · 15
Uniform ultraﬁlters in a choiceless context

概 要 We study uniform ultraﬁlters in a choiceless context. We prove that ℵω+1 can be the least cardinal

which carries a unirom ultraﬁlter. We also show that ℵω can be the least cardinal which does not carry auniform ultraﬁlter.
5 吉 信 康 夫 ( 名 大 情 報)

Yasuo Yoshinobu (Nagoya Univ.)

Convex sets and the axiom of choice · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Convex sets and the axiom of choice

概 要 For an R-vector space V , let MC(V ) denote the statement that every subset of V has a maximal

convex subset and MC the statement that MC(V ) holds for all V . Under ZF, we observe that MC isequivalent to the axiom of choice, and that MC(R3 ) is strictly stronger than MC(R2 ), which is equivalent
to the axiom of countable choice for sets of reals.
6 坪 井 明 人 (筑波大⋆)Akito Tsuboi (Univ. of Tsukuba⋆)

Dividing and forking in random structures · · · · · · · · · · · · · · · · · · · · · · · · 15
Dividing and forking in random structures概 要 Dividing and forking are important concepts in model theory, both of which are related to abstract

independence. Although these two concepts are not equivalent in general, in simple theories, they areequivalent. We demonstrate that these concepts diﬀer in random hypergraphs omitting a certain kind of
sub-hypergraphs. This work is a continuation of the study on which I presented at the 2022 fall meeting of
the MSJ.

Final: 2024/2/6
数学基礎論および歴史

7 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⋆)

6

ランダム超グラフと軌道が 1 つの自己同型について · · · · · · · · · · · · · · · · · 15

On random hypergraphs and automorphisms with a single orbit

概 要 Let H(m, l, s) be the class of all ﬁnite m-hypergraphs A such that for any substructure X of A with

|X| = l has less than l Cm − s m-hyperedges. Suppose 0 ≤ s < l Cm . H(m, l, s) has the free amalgamation
property if and only if s < l−2 Cm−2 .
Let M be the random structure for H(m, l, s) (in the case that it exists). Then M has an automorphismwith a single orbit.
11:45〜12:00

数学基礎論および歴史分科会総会

14:30〜17:00
8 池 田 宏 一 郎 ( 法 政 大 経 営)
Koichiro Ikeda(Hosei Univ.)

A note on ω-categorical stable theories · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A note on ω-categorical stable theories

概 要 We show that if α is in (0, 1) with index(α) = ∞ and Kα is a class of ﬁnite graphs which is generated

by an edge graph then a Kα -generic graph is ω-categorical and strictly stable.
9 小 峰

航 (筑波大数理物質)

Wataru Komine (Univ. of Tsukuba)

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

概 要 Pillay and Steinhorn showed that every o-minimal theory has a prime model and it is unique up toisomorphism. We are interested in deﬁnably complete locally o-minimal theory which is generalization ofo-minimal theory, and investigate existence and uniqueness of prime models in deﬁnably complete locallyo-minimal theory. We give an counterexample to existence and some conditions for uniqueness.
10 大 倉 昂 貴 (筑波大数理物質)

Koki Okura (Univ. of Tsukuba)p 進体の拡張構造における Poincaré 級数の有理性 · · · · · · · · · · · · · · · · · · · 15
On rationality of Poincaré series in expansions of the p-adic ﬁelds

概 要 We associate each subset of p-adic integers with a formal power series, which is called its Poincaré

series. Denef showed that the Poincaré series of every set deﬁnable in the p-adic ﬁeld structure is a rational
function. In this talk, we examine the relationship between the rationality of Poincaré series in various
expansions of the p-adic ﬁelds and their stability-theoritic properties. Especially, we will give an example
of NIP expansions without such rationality.
11 米 田 郁 生 (徳 山 工 高 専)

Ikuo Yoneda (Tokuyama Coll. of Tech.)

Weak one-basedness in the eq-structure and the existences of weakcanonical bases in rosy theories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Weak one-basedness in the eq-structure and the existences of weakcanonical bases in rosy theories

概 要 Weak one-basedness is deﬁned in the real sort by Berenstein and Vassiliev. We deﬁne weak one-basedness in the eq-structure, and we show that, in rosy theories, one-basedness is equivalent to weak
one-basedness in the eq-structure with the existences of weak canonical bases.
12 神 谷 德 昭 (会津大⋆)Noriaki Kamiya (Univ. of Aizu⋆)

リー代数という本のタイトルについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the title “Lie algebra” of books published in Japan概 要 In this talk, we exhibit the books of Lie algebra published in Japan, that is, about 1950 2023. It

seems that the notation of Lie algebra is appeared from PRINCETON (USA) of 1934, and soon after, thatcame to JAPAN.

Final: 2024/2/6
7

数学基礎論および歴史

13 平 田 浩 一 (松山大経営・愛媛大⋆)Koichi Hirata(Matsuyama Univ./Ehime Univ.⋆)

算変座標の幾何学的基礎 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Geometric foundations of inversive coordinates of circles

概 要 The inversive coordinates of circles are deﬁned as a coordinate system for studying problems where

many circles touch each other. This coordinate system is suitable for application to Wasan problems, andwe have introduced such applications so far. On the other hand, the geometric foundation of the coordinate
system is also important. In this study, we present the results of the foundation for both σ > 0 and σ < 0cases. We will also introduce the diﬀerences between the two cases.
14 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「省約術」と善光寺算額の関係について · · · · · · · · · · · · · · · · · · · · · 15

A study on the relationship of Takuma school’s book Shouyaku-jutsu
and a mathematical plate dedicated to the Zenkouji temple

概 要 The Takuma school is a school in Osaka, and an important person in the Takuma school is Oka

Shichibei-Yukitada (1791–). Oka left behind many documents. This paper discusses the solution to question
12 of Shouyaku-jutsu[Sinplifying method of equations] (14 questions total). It also investigates and analyzes
the same ﬁgure drawn on the existing Takuma school’s mathematical plate of the Zenkouji temple.
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 (2) · · · · · · · · · · · · · · · · 15

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

Treatment of polynomials in Oka Yukitada’s “Kijutsu Kairohou (Amethod to solve the path to create a formula)” in the Takuma School (2)15 小 川

概 要 The ﬁve (or six) volumes of Kijutsu Kairoho by Oka Yukitada of the Takuma School contain avariety of techniques for processing polynomials. We have already presented the “senshiki (transformationof polynomials)” and “ryakushiki (simpliﬁcation of polynomials).” This presentation will discuss “shouyaku(removal of factors of polynomials)” in the Art of shouyaku. Since “shouyaku” is nothing more than thefactorization of an equation from today’s point of view, it has not received much attention so far. However,“shouyaku” shows a remarkable characteristic in the history of pre-modern Japanese mathematics in that it
actively utilizes the separation of solutions to equations.
17:15〜17:30

歴史部門懇談会

3 月 18 日（月）第 VIII 会場

9:15〜12:00
16 熊 澤 昌 明 (箕面自由学園高)
Masaaki Kumazawa(Mino-Jiyu Gakuen High School)

BCK-代数の中のド・モルガン代数について · · · · · · · · · · · · · · · · · · · · · · · · 15
On De Morgan algebras in BCK-algebras

概 要 We are well known that a bounded commutative BCK-algebra is a De Morgan algebra. In thispresentation, we will deﬁne a new class in BCK-algebras: Involutive bounded BCK-algebras with Condition(I). This class is a proper large class than the class of bounded commutative BCK-algebras. Moreover, we
would like to show that an algebra of this class is also a De Morgan algebra. We predict that this class isthe largest class that is a De Morgan algebra in BCK-algebras.

Final: 2024/2/6
数学基礎論および歴史

17 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.)8

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 scheme

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 investigate the conservation theorem in terms of Rosser provability predicates. We construct
Rosser predicates for which the conservation theorem holds and Rosser predicates for which the theorem
does not hold.
18 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¬□φscheme □n φ → □m φ and the rule
into N. We proved the ﬁnite frame property of N+ Am,n with¬□□φ¬□φrespect to Fitting, Marek, and Truszczyński’s relational semantics. We also proved that the ruleis¬□□φnecessary for the completeness of N+ A0,n for n ≥ 2.
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.)

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

The 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–Löwe 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 倉 橋 太 志 (神戸大システム情報)( Utrecht Univ. )A. Visser

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

理論の不完全性, 決定不能性, 分離不能性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Incompleteness, undecidability, and inseparability of theories

概 要 We studied several notions related to incompleteness, undecidability and inseparability with the

purpose of giving a clear overview of these notions. Firstly, we summarized the historical background ofthese notions. Secondly, we gave alternative proofs of known old results by Cobham, Vaught, and Pour-El.
Finally, we proved that for any consistent RE theory, eﬀective essential hereditary creativity and strong
eﬀective inseparability are equivalent.

Final: 2024/2/6
9

数学基礎論および歴史

21 L. Pacheco(

TU Wien)

Leonardo Pacheco (TU Wien)

A constructive variation of GL · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A constructive variation of GL

概 要 We describe a constructive variation of the provability logic GL. The logic CGL is based on Mendler

and de Paiva’s constructive modal logic CK. The system CGL is obtained by adding Löb’s axiom □(□P →P ) → □P to CK; the CGL models are obtained by adding a reverse well-foundedness condition to the CK
models. We show that CGL is complete over CGL models via a canonical model construction. We also
describe ongoing work on non-classical varieties of GL based on the intuitionistic modal logic IK and theGödel modal logic GK.
22 L. Pacheco(

TU Wien)

Leonardo Pacheco (TU Wien)

Higher-order feedback computation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Higher-order feedback computation

概 要 Feedback Turing machines are Turing machines which can query a halting oracle h :⊆ ω × ω → {↓, ↑},which has information on the convergence or divergence of feedback computations. To avoid a contradiction
by diagonalization, feedback Turing machines have two ways of not halting: they can diverge as standard
Turing machines, or they can freeze. A natural question to ask is: what if we iterate the feedback
construction? We deﬁne αth order feedback Turing machines for each computable ordinal α and describe
the semi-computable sets using inductive deﬁnitions and Gale–Stewart games. (Joint work with Juan P.
Aguilera and Robert S. Lubarsky.)23 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 (2) · · · · · · · · · · · · · · · · · · · · · · · · 15

Equilibria of AND-OR trees without assumptions on tree shapes (2)概 要 The goal of this research is to show nontrivial equations and inequalities on equilibria of AND-OR trees

without assumptions on tree shapes. In the previous meeting, we proved that two equilibria of randomized
directional algorithms coincide. In the current talk, we discuss subsequent development. This work wasdone in collaboration with Fuki Ito.
24 河 村 彰 星 (京 大 数 理 研)
大理)
廣 島 佳 汰 (京Akitoshi Kawamura (Kyoto Univ.)
Keita Hiroshima (Kyoto Univ.)

初等的に追跡される数 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Elementarily traceable numbers

概 要 A function is called elementary if it can be computed in time bounded by a tower of powers of constantheight. A trace function for an irrational number α is a function that maps each rational number r to arational number that is closer to α than r is. We show, as was conjectured by Kristiansen, that there exists
an irrational number that has an elementary trace function but whose continued fraction expansion is notelementary. We also show that there exists an irrational number that has an elementary trace function but
whose sum approximation, i.e., the function that maps each positive integer n to the index of the nth 1 inthe binary expansion of the number, is not elementary.

Final: 2024/2/6
数学基礎論および歴史

25 只 木 孝 太 郎 (中 部 大 工)

Kohtaro Tadaki (Chubu Univ.)

10

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 VIII · · · · · · · 15

A reﬁnement of quantum information theory by algorithmic randomness
VIII

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

In modern mathematics which describes quantum mechanics, however, probability theory means nothingother than measure theory, and therefore any operational characterization of the notion of probability is
still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness,
we presented an operational reﬁnement of the Born rule, called the principle of typicality, for specifying
the property of the results of quantum measurements in an operational way. In this talk, we reﬁne andreformulate the security proof of the BB84 quantum key distribution protocol based on the principle oftypicality, in order to demonstrate how properly our framework works in practical problems in quantum
mechanics.
13:00〜14:00
石 原

特別講演
哉 ( 東 邦 大 理)

Hajime Ishihara (Toho Univ.)

構成的・可述的集合論における逆数学

Reverse mathematics in constructive and predicative set theory

概 要 After quickly reviewing intuitionistic logic and classical Zermelo-Fraenkel set theory (ZF), we look

into constructive Zermelo-Fraenkel set theory (CZF) and its subsystems BCST (Basic constructive set
theory) and ECST (Elementary constructive set theory). Those constructive set theories are predicative
without Powerset and with Separation being restricted, and we see that elementary constructions of sets canbe performed in the theories. We introduce the notions of a set-generated class and NID (Non-deterministic
Inductive Deﬁnition) principles. A class X of subsets of a set S is set-generated if there exists a subset G
Sof X such that α = {β ∈ G | β ⊆ α} for all α ∈ X. A rule on a set S is a pair (a, b) of subsets a and b
of S; it is nullary if a is empty, elementary if a is a singleton and ﬁnitary if a is ﬁnitely enumerable. For aset R of rules on S, a subset α of S is R-closed if for each rule (a, b) in R, a ⊆ α implies ∃x(x ∈ b ∩ α). The
principle NID is that for each set S and each set R of rules on S,
the class of R-closed subsets of S is set-generated;
NID0 , NID1 and NID<ω denote NID restricting R to a set of nullary, elementary and ﬁnitary rules,
respectively. We ﬁrst show (over ECST) that NID0 is equivalent to Fullness, an axiom of CZF, and that
NID1 implies NID0 . Then we show (over ECST) that NID1 , “the category Rel of sets and relations has
weak equalisers” and “the category BP of basic pairs and relation pairs has equalisers” are equivalent.
Finally, we show (over ECST) that NID<ω is equivalent to “the class of models of a geometric theory is
set-generated”.

Final: 2024/2/6
11

代数学

代

数

3 月 17 日（日）学
第 I 会場

9:00〜10:30
潟大⋆)
1 田 島 慎 一 (新小 原 功 任 ( 金 沢 大 理 工)
照 井章 (筑波大数理物質)

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

Jordan 鎖の構造の厳密で効率的な計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Eﬃcient symbolic computation of the structure of Jordan chains概 要 An eﬃcient method for computing the structure of Jordan chains of a matrix of integers or rational

numbers by exact computation is proposed. We have given a method for computing Jordan chains of amatrix with exact computation. However, for deriving just the structure of Jordan chains, the algorithm
can be reduced to increase its eﬃciency. We propose a modiﬁcation of the algorithm for that purpose.
2 辻 栄 周 平 ( 北 教 大 旭 川)
陶 山 大 輔 (日本文理大経営経済)
M. Torielli(Northern Arizona Univ.)

Shuhei Tsujie (Hokkaido Univ. of Edu.)
Daisuke Suyama (Nippon Bunri Univ.)
Michele Torielli(Northern Arizona Univ.)

ゲイングラフから定まる 2 種類の超平面配置の自由性の一致について · · 10

On the coincidence of freeness of two types of hyperplane arrangements
determined from gain graphs

概 要 Two kinds of hyperplane arrangements can be obtained from a gain graph, a graph whose edges arelabeled by elements in a group. Athanasiadis and Bailey have shown that freeness of these hyperplanearrangements sometimes coincide. In this talk, We will report what we know so far about when thesecoincidences occur.
工大)
3 中 島 規 博 (名森友 祐Norihiro Nakashima(Nagoya Inst. of Tech.)
Yusuke Mori

Weyl 配置を変形して得られる配置の特性準多項式 · · · · · · · · · · · · · · · · · · 10
Characteristic quasi-polynomials for deformations of Weyl arrangements

概 要 The characteristic quasi-polynomial is the numbers of elements in the complement of hyperplanearrangements modulo positive integers which is introduced by Kamiya, Takemura, and Terao. In this talk,we compute the characteristic quasi-polynomials for arrangements which contain the Coxeter arrangementof types A, B, C, and D described by the orthonormal basis. In addition, by using this formulas, we also
compute characteristic quasi-polynomials of arrangements obtained by deleting some hyperplanes from the
Coxeter arrangements of types B, C, and D.

Final: 2024/2/6
代数学

4 小 笠 原 匠 (横浜国大環境情報)
原 下 秀 士 (横浜国大環境情報)
大 橋
亮 ( 東 大 情 報 理 工)
坂 田 康 亮 ( 東 大 情 報 理 工)
Takumi Ogasawara(Yokohama Nat. Univ.)
Shushi Harashita(Yokohama Nat. Univ.)
Ryo Ohashi (Univ. of Tokyo)
Kosuke Sakata (Univ. of Tokyo)

12

楕円曲線の二重被覆曲線として得られる種数 4 の超特別曲線 · · · · · · · · · · 15

Superspecial genus-4 double covers of elliptic curves

概 要 In this talk, we study genus-4 curves obtained as double covers of elliptic curves. Firstly we provide

explicit deﬁning equations of such curves with explicit criterion for whether it is nonsingular. We also show
the irreducibility of the singular locus in any characteristic that is not 2 or 3. Secondly as an application
we enumerate the isomorphism classes of superspecial genus-4 double covers of elliptic curves in small
characteristic p (more precisely p is less than or equal to 23). We accomplish this by implementing ouralgorithm in the computer algebra system Magma and executing it. This work deals with a broader classof curves than the case of Howe curves studied by Kudo, Harashita and Howe in 2020.
5 山 本 侑 也 (横浜国大環境情報)
原 下 秀 士 (横浜国大環境情報)
Yuya Yamamoto(Yokohama Nat. Univ.)
Shushi Harashita(Yokohama Nat. Univ.)

The multiplicity-one theorem for the superspeciality of curves of genus
two · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The multiplicity-one theorem for the superspeciality of curves of genus
two

概 要 Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curves in Legendre

form is separable. In this talk, we get an analogous result for curves of genus two in Rosenheim form. Moreprecisely we show that the ideal determining the superspeciality of the curve has multiplicity one at every
superspecial point. Igusa used a Picard–Fucks diﬀerential operator annihilating a Gauss hypergeometricseries. We use Lauricella’s system (of type D) of hypergeometric diﬀerential equations in three variables.
We prove that each entry of the Cartier–Manin matrix satisﬁes the same partial diﬀerential equations andalso various contiguity relations.
6 大 橋

亮 ( 東 大 情 報 理 工)

Ryo Ohashi(Univ. of Tokyo)

On the Rosenhain forms of superspecial genus-2 curves · · · · · · · · · · · · · 15
On the Rosenhain forms of superspecial genus-2 curves

概 要 In this talk, we examine superspecial genus-2 curves C : y 2 = x(x − 1)(x − λ)(x − µ)(x − ν) in

characteristic p ≥ 3. As a main result, we show that the diﬀerence between any two elements in {0, 1, λ, µ, ν}
is a square in Fp2 . In addition, we show that C is maximal or minimal over Fp2 without taking its Fp2 -form(we also give a criterion in terms of p that tells whether C is maximal or minimal). As these applications,
we study the maximality of superspecial hyperelliptic curves of genus 3 and 4 whose automorphism groups
contain Z/2Z × Z/2Z.

Final: 2024/2/6
13

代数学

10:45〜11:45
宮 崎

特別講演
誓 ( 熊 本 大 先 端)

Chikashi Miyazaki (Kumamoto Univ.)

Castelnuovo–Mumford regularity of polynomial ideals and syzygy theoretic approach to vector bundles
Castelnuovo–Mumford regularity of polynomial ideals and syzygy theoretic approach to vector bundles

概 要 The Castelnuovo–Mumford regularity introduced by Mumford generalizing an idea of Castelnuovo is

one of the most important invariants measuring the complexity of the minimal free resolution of polynomial
ideals. In 1980s, the Eisenbud–Goto conjecture, which says the Castelnuovo–Mumford regularity is boundedby degree and codimension of nondegenerate projective variety V , that is, reg V ≤ deg V − codim V + 1, as
crossroads of algebraic geometry and commutative algebra, has interested mathmatician working in relatedﬁelds.
My talk begins with regularity basics and surveys epoch-making results of 1980s and 1990s, especially worksof Gruson–Lazarsfeld–Peskine, Lazarsfeld and Kwak, if possible, in some details of linear projections —secant
lines, Mather’s theory etc. Surprisingly, in 2018, McCullough–Peeva settled down to give counterexamplesof the conjecture.
Focusing on the commutative algebra technique, I have been working from a joint paper with Hoa in 1995,
reg R ≤ a(R) + dim R + 1 for a Buchsbaum graded ring R, which had driven us to study the k-Buchsbaum
property. The uniform position principle immediately implies reg V ≤ d(deg V − 1)/codim V e + 1 for anondegenerate ACM variety. In order to extend our framework, I will explain the relationship between
a-invariant and the Castelnuovo–Mumford regularity, and to get Castelnuovo-type bounds on the regularity
even towards a classiﬁcation of projective varieties —rarional normal scroll, del Pezzo variety.
Finally I am going to talk on the splitting of vector bundles closely related to the syzygy theory frommy point of view. Several proofs are known for the Horrocks theorem, a vector bundle on the projectuve
space having ACM property is isomorphic to a direct sum of line bundles. The one using the Castelnuovo–
Mumford regularity is my favorite. Arising from this idea, we investigate the nonvanishing intermediate
cohomologies and their relation with the regularity to get a characterization of some vector bundles.
14:15〜18:00
7 毛 利 健 太 (関西学院大理工)

Kenta Mori (Kwansei Gakuin Univ.)

Toric rings of perfectly matchable subgraph polytopes · · · · · · · · · · · · · · 10
Toric rings of perfectly matchable subgraph polytopes

概 要 The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope associated with the vertex

sets of matchings in the graph. We study algebraic properties (compressedness, Gorensteinness) of the toricrings of perfectly matchable subgraph polytopes. In particular, we give a complete characterization of agraph whose perfectly matchable subgraph polytope is compressed.
8 宮 下

空 ( 阪 大 情 報)

Sora Miyashita (Osaka Univ.)

半標準的次数付き環における Gorenstein 性の一般化の比較 · · · · · · · · · · · 15

Comparing generalizations of Gorensteinness in semi-standard gradedrings

概 要 Semi-standard graded rings are a generalized notion of standard graded rings. In this talk, we compare

generalized notions of the Gorenstein property in semi-standard graded rings. We discuss the commonalities
between standard graded rings and semi-standard graded rings, as well as elucidate distinctive phenomena
present in semi-standard graded rings that are absent in standard graded rings.

Final: 2024/2/6
代数学

9 松 下 光 虹 ( 阪 大 情 報)宮 下
空 ( 阪 大 情 報)
Koji Matsushita (Osaka Univ.)
Sora Miyashita (Osaka Univ.)

14

重複度に関する条件と almost Gorenstein 性について · · · · · · · · · · · · · · · · 15

Conditions for multiplicities and almost Gorensteinness

概 要 Almost Gorenstein rings have been introduced as a generalization of Gorenstein rings and have been

well studied. In this talk, we show that if Cohen–Macaulay graded rings R1 , R2 and R satisfy appropriate
conditions regarding multiplicity, then almost Gorenstein property of R implies Gorenstein properties forall of R1 , R2 and R. Moreover, we provide its application to semi-standard graded rings.
10 東 谷 章 弘 (阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)

斉次アフィン半群環とその正規化のヒルベルト級数の差について · · · · · · 15

Diﬀerence of Hilbert series of homogeneous aﬃne semigroup ring andits normalization

概 要 Let Q be an aﬃne semigroup, k[Q] the associated semigroup ring, and k[Q] its normalization, where

k is a ﬁeld. In this talk, in the case where k[Q] is homogeneous, a diﬀerence of the Hilbert series ofk[Q] and k[Q] is discussed. More precisely, we prove that if k[Q] satisﬁes Serre’s condition (S2 ), then the
degree of the h-polynomial of k[Q] is always greater than or equal to that of k[Q]. Moreover, we also showcounterexamples of this statement if we drop the assumption (S2 ).
11 木 村 海 渡 (名 大 多 元 数 理)
Kaito Kimura (Nagoya Univ.)

加群の Bass 数の漸近挙動 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Asymptotic behavior of Bass numbers of modules

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

asymptotic behavior of the quotient modules M/I n M of M for large integers n has been actively studied incommutative algebra. We consider the asymptotic Bass numbers of localizations of M/I n M at prime idealsof R. The main result asserts that these have polynomial growth for large integers n that do not dependon the prime ideals when R is local.
12 大 竹 優 也 (名 大 多 元 数 理)
Yuya Otake(Nagoya Univ.)

複体に対する Auslander–Bridger 理論 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Auslander–Bridger theory for complexes

概 要 Let R be a two-sided noetherian ring. Auslander and Bridger developed the theory of the projective

stabilization of the category of ﬁnitely generated R-modules, which is called the stable module theory.
Recently, Yoshino established the stable “complex” theory, i.e., the theory of a certain stabilization of thehomotopy category of complexes of ﬁnitely generated projective R-modules. We introduce higher versionsof several notions introduced by Yoshino, such as the ∗ torsionfreeness and the ∗ reﬂexivity for complexes.
Also, we prove the Auslander–Bridger approximation theorem for complexes.
13 三 船 裕 輝 (名 大 多 元 数 理)
Yuki Mifune(Nagoya Univ.)

分解部分圏および MCM 加群のなす圏の半径の有限性について · · · · · · · 15

On the ﬁniteness of resolving subcategories and the category of MCM
modules概 要 Let R be a commutative noetherian ring. Denote by mod R the category of ﬁnitely generated R-

modules. The concept of the radius of a full subcategory of mod R has been introduced by Dao and
Takahashi in 2014. It has been linked to many well-studied notions such as the dimension of the stable
category of maximal Cohen–Macaulay modules, ﬁnite/countable Cohen–Macaulay representation type andthe uniform Auslander condition. This time we give a partial positive answer to a conjecture of Dao and
Takahashi on the ﬁniteness of radii of resolving subcategories.

Final: 2024/2/6
15

代数学

14 若 杉 直 樹 (名 大 多 元 数 理)
高 橋
亮 ( 名 大 多 元 数 理)

Naoki Wakasugi (Nagoya Univ.)
Ryo Takahashi (Nagoya Univ.)

余有限加群のなす圏と局所コホモロジー加群 · · · · · · · · · · · · · · · · · · · · · · · 15

On the category of coﬁnite modules and local cohomology modules

概 要 Let R be a commutative noetherian ring and I be an ideal of R. In 2021, Bahmanpour proved if thelocal cohomology modules of any ﬁnitely generated R-modules are I-coﬁnite, then the subcategory of Mod R
consisting of I-coﬁnite modules is an abelian subcategory when R is semi-local. We show the converse undercertain assumptions.
15 荒 谷 督 司 (岡 山 理 大 理)
飯 間 圭 一 郎 ( 奈 良 工 高 専)
高 橋
亮 ( 名 大 多 元 数 理)

Tokuji Araya (Okayama Univ. of Sci.)
Kei-ichiro Iima
(Nara Nat. Coll. of Tech.)
Ryo Takahashi (Nagoya Univ.)

On the vanishing of DHKK complexities for singularity categories · · · · 15

On the vanishing of DHKK complexities for singularity categories

概 要 Let R be a commutative noetherian ring. In this talk, we study, for the singularity category of R, thevanishing of the complexity in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich.
16 遠 藤 直 樹 (明 大 政 治 経 済)
Naoki Endo

(Meiji Univ.)

Sally modules of extended canonical ideals and Goto rings · · · · · · · · · · 15
Sally modules of extended canonical ideals and Goto rings

概 要 The aim of this talk is, as part of stratiﬁcation of Cohen–Macaulay rings, to introduce the notionof Goto rings, generalizing the notion of almost Gorenstein rings deﬁned by Barucci and Fröberg for onedimensional analytically unramiﬁed local rings; Goto, Matsuoka, and Phuong for one-dimensional Cohen–
Macaulay local rings; and Goto, Takahashi, and the speaker of this talk for Cohen–Macaulay graded/local
rings of arbitrary dimension. What has dominated the series of researches on almost Gorenstein rings isthe fact that the reduction numbers of extended canonical ideals are at most 2; we deﬁne Goto rings as
Cohen–Macaulay rings admitting such extended canonical ideals.
17 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.)

Normal tangent cone for the maximal ideal of a certain hypersurface· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Normal tangent cone for the maximal ideal of a certain hypersurface

概 要 In this talk, we prove that the normal tangent cone for the maximal ideal of a certain hypersurface is

Cohen–Macaulay. Furthermore, we determine the normal reduction numbers and give a numerical criterion
for Gorensteinness of such a normal tangent cone.

Final: 2024/2/6
代数学

3 月 18 日（月）16

第 I 会場

9:30〜12:00
18 飯 高茂 (学 習 院 大⋆)布中)齋 藤 之 理 (麻Shigeru Iitaka (Gakushuin Univ.⋆)
Yukimasa Saito(Azabu Junior High School)

新世代完全数について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Perfect numbers of new kind

概 要 Let h denote a prime and m an integer.

If a positive integer α satisﬁes X = α − 2ϕ(α), α = X(2hX + m − 1))X, then α is said to be a perfectnumber of new type by Y.Saito.
19 菅 野隼 ( 東 北 大 理)

Hayato Kanno (Tohoku Univ.)

2-1 公式の類似と深さ無限の t-多重ゼータ値 · · · · · · · · · · · · · · · · · · · · · · · · 10
A certain analogue of 2-1 formula and t-MZV of inﬁnite depth

概 要 2-1 formula is an important family of relations between multiple zeta-star values(MZSVs) and half

multiple zeta values(1/2-MZVs). In this talk, we introduce an analogue of 2-1 formula for MZSVs of 2-3-2-1
indices. We also give some special values of t-multiple zeta values of inﬁnite depth.
20 大 塚 瑛 介 (東 北 大 理)
Eisuke Otsuka (Tohoku Univ.)

2 次のフェルマー曲線上の反復積分によって得られる周期について · · · · 15
On the periods obtained by iterated integrals on the Fermat curve ofdegree 2

概 要 In this talk, we deﬁne the periods obtained by iterated integrals on the Fermat curve of degree 2

and discuss their arithmetic properties. The deﬁnition is based on and extended from the iterated integral
representation of multiple zeta values, and includes several other well-known periods. In particular, by using
the theory of motivic iterated integrals given by Deligne, Goncharov et al., it is possible to give a motivic
interpretation of our periods, and we can investigate the Q-linear space spanned by our periods. I would
like to explain this.
21 田 沼 優 佑 (慶 大 理 工)
Yusuke Tanuma(Keio Univ.)

Algebraic independence of the values of a certain family of power series· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Algebraic independence of the values of a certain family of power series

概 要 In this talk, we study the algebraic independence of the values of a certain family of power series

including

P∞

k=0 z

dk ±k

and

P∞

k=1 [kω]zk, where d is an integer greater than 1, ω is a real quadratic irrational

number, and [·] denotes the integral part.
22 行 田 康 晃 (東 大 数 理)
丸 山 修 平 ( 金 沢 大 理 工)

Yasuaki Gyoda (Univ. of Tokyo)
Shuhei Maruyama (Kanazawa Univ.)

一般化マルコフ方程式の一意性予想とその部分的解決 · · · · · · · · · · · · · · · 15

Uniqueness conjecture of generalized Markov equation and its partial
solutions

概 要 The Markov equation x2 + y 2 + z 2 = 3xyz has an open problem called the uniqueness conjecture,

which was introduced by Frobenius in 1913. In this talk, we will introduce a similar conjecture consideredin the generalized Markov equation x2 + y 2 + z 2 + k(yz + zx + xy) = (3 + 3k)xyz with nonnegative integer
k as a parameter and discuss its partial solutions.

Final: 2024/2/6
17

代数学

23 島 田 了 輔 (東 大 数 理)

Ryosuke Shimada (Univ. of Tokyo)

Beyond the cases of Coxeter type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Beyond the cases of Coxeter type

概 要 The notion of aﬃne Deligne–Lusztig variety (ADLV) was ﬁrst introduced by Rapoport, which has been

applied to number theory such as the study of Shimura varieties and a realization of the local Langlands
correspondence. Many of these applications make use of the special cases where the ADLV admits a simple
description. One large class of such cases is the ADLV of Coxeter type, which has been already classiﬁed byGörtz–He–Nie. However, many people (Chan–Ivanov, Howard–Fox–Imai, Trentin,...) have found examples
which are not of Coxeter type but admit a simple description. In this talk, I will explain about recent
progress on this kind of new examples, including my recent work for GLn .
24 中 井 啓 太 (名 大 多 元 数 理)
Keita Nakai(Nagoya Univ.)

Discrete universality theorem for Matsumoto zeta-functions and nontrivial zeros of the Riemann zeta-function · · · · · · · · · · · · · · · · · · · · · · · · · 15
Discrete universality theorem for Matsumoto zeta-functions and nontrivial zeros of the Riemann zeta-function

概 要 In 2017, Garunkštis, Laurinčikas and Macaitienė proved the discrete universality theorem for the

Riemann zeta-function sifted by imaginary part of nontrivial zeros of the Riemann zeta-function. This
discrete universality has been extended in various zeta-functions and L-functions. In this talk, we generalize
this discrete universality for Matsumoto zeta-functions.
25 鈴 木 正 俊 (東工大)Masatoshi Suzuki (Tokyo Tech)

Weil 分布が定めるエルミート形式について · · · · · · · · · · · · · · · · · · · · · · · · 15
On the Hermitian form attached to the Weil distribution

概 要 We study the Hilbert space obtained by completing the space consisting of all smooth and compactly

supported functions on the real line with respect to the Hermitian form attached to the Weil distribution.
As a result, we obtain one novel equivalence condition for the Riemann hypothesis.

Final: 2024/2/6
代数学

18

13:00〜14:00

特別講演
越 川 皓 永 (京 大 数 理 研) ♭ 志村多様体のコホモロジーの消滅定理

Teruhisa Koshikawa (Kyoto Univ.)

Vanishing theorems for the cohomology of Shimura varieties

概 要 Shimura varieties are certain type of locally symmetric spaces, and have canonical structures ofalgebraic varieties. The cohomology of locally symmetric spaces are closely related to automorphic forms,
and it has very rich structure and has been playing an important role for decades in the Langlands
program, which connects automorphic forms and Galois representations. For such study, several typesof vanishing theorems have been proved by several people with many diﬀerent techniques form algebraic
geometry, arithmetic geometry and the theory of automorphic representations, and these results are notjust interesting, but also useful and often essential in the application. Some highlights in recent years are
the proofs of the (potential) modularity and the Sato–Tate conjecture for elliptic curves over CM ﬁelds, andnew cases of the generalized Ramanujan conjecture. These are generalizations of a lot of previous works
starting with the proof of the last theorem of Fermat by Wiles and Taylor–Wiles. Such a generalization
was ﬁrst outlined by Calegari and Geraghty based on some new conjectures related to the cohomology
of locally symmetric spaces. The progresses in recent years basically started by proving variants of theirconjectures in several settings. A key ingredient is a certain vanishing theorem of torsion cohomology classes
for Shimura varieties associated with quasi-split unitary groups. This was ﬁrst proved by Caraiani and
Scholze with several assumptions. I introduced a new technique based on the work of Fargues and Scholzeon the geometrization of the local Langlands correspondence, and was able to drop many assumptions.
These are now further generalized or enhanced by works of Santos, Hamann, Lee, and Zhang. People expect
even more general forms of vanishing theorems, and their conjectural forms are related to the classiﬁcationof automorphic representations and the categorical local Langlands conjecture. There are some works inprogress in such directions. I will survey these results and ideas.

3 月 19 日（火）第 I 会場

9:30〜12:00
26 星
明 考 ( 新 潟 大 理)
大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classiﬁcation for algebraic tori (II) · · · · · · · · · · · · · · · · · · · · · · 10
Birational classiﬁcation for algebraic tori (II)概 要 As a continuation of Part (I) (dimension 3 case), we state main theorems of [HY] which give a stably

birational classiﬁcation of algebraic k-tori of dimension 4.
27 星
明 考 ( 新 潟 大 理)
北 山 秀 隆 ( 和 歌 山 大 教 育)
Akinari Hoshi (Niigata Univ.)
Hidetaka Kitayama (Wakayama Univ.)

Rationality problem of two-dimensional quasi-monomial group actions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Rationality problem of two-dimensional quasi-monomial group actions

概 要 The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by

Hoshi, Kang and Kitayama (2014, J. Algebra). As a generalization, we solve the rationality problem of
two-dimensional quasi-monomial actions under the condition that the actions are deﬁned within the baseﬁeld. In order to prove the theorem, we give a brief review of the Severi-Brauer variety with some examples
and rationality results. We also use a rationality criterion for conic bundles of P1 over non-closed ﬁelds.

Final: 2024/2/6
19

代数学

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

Rationality problem for norm one tori for dihedral extensions · · · · · · · · 7
Rationality problem for norm one tori for dihedral extensions

概 要 We give a complete answer to the rationality problem (up to stable k-equivalence) for norm one tori
(1)

RK/k (Gm ) of K/k whose Galois closures L/k are dihedral extensions with the aid of Endo and Miyata[EM75, Theorem 1.5, Theorem 2.3] and Endo [End11, Theorem 2.1]. By using a similar technique, we give
reﬁnements of the proof of stably rational cases of Endo and Miyata’s theorems.
29 星
明 考 ( 新 潟 大 理)
大理)
山 崎 愛 一 (京Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Rationality problem for norm one tori for A5 and PSL2 (F8 ) extensions······························································ 8
Rationality problem for norm one tori for A5 and PSL2 (F8 ) extensions

概 要 We give a complete answer to the rationality problem (up to stable k-equivalence) for norm one(1)

tori T = RK/k (Gm ) of K/k whose Galois closures L/k are A5 ' PSL2 (F4 ) and PSL2 (F8 ) extensions. In
particular, we prove that T is stably k-rational for G = Gal(L/k) ' PSL2 (F8 ), H = Gal(L/K) ' (C2 )3and H ' (C2 )3 ⋊ C7 where Cn is the cyclic group of order n. Based on the result, we conjecture that T isstably k-rational for G ' PSL2 (F2d ), H ' (C2 )d and H ' (C2 )d ⋊ C2d −1 . Some other cases G ' An , Sn ,GLn (Fpd ), SLn (Fpd ), PGLn (Fpd ), PSLn (Fpd ) and H ⪇ G are also investigated for small n and pd .
30 丹 原 大 介 (弘前大⋆)Daisuke Tambara (Hirosaki Univ.⋆)有限体上の 3 次元可除代数 A の A2 への作用 · · · · · · · · · · · · · · · · · · · · · · · 15Intersection of subspaces Av in A2 for a three-dimensional division algebra A over a ﬁnite ﬁeld

概 要 Let A be a three-dimensional nonassociative division algebra over a ﬁnite ﬁeld. Let A act on A2 by left

multiplication. One of our results states that there exist v, v ′ ∈ A2 such that Av ∩ Av ′ is two-dimensional
if and only if A is isotopic to a commutative algebra.
31 上 山 健 太 (信 州 大 理)

Kenta Ueyama (Shinshu Univ.)

可算 Cohen–Macaulay 表現型非可換次数付き超曲面について · · · · · · · · · 15

On noncommutative graded hypersurfaces of countable Cohen–Macaulay
representation type

概 要 We compute the stable categories of graded maximal Cohen–Macaulay modules over Rε1 and Rε∞ ,which are skew versions of R1 = k[x1 , . . . , xn ]/(x21 + · · · + x2n ) with the standard grading and R∞ =k[x1 , . . . , xn ]/(x21 + · · · + x2n−1 ) with the standard grading, respectively. As a corollary we obtain that Rε1 has
ﬁnite Cohen–Macaulay representation type and Rε∞ has countably inﬁnite Cohen–Macaulay representation
type.
32 松 野 仁 樹 (東京理大教養教育)
板 場 綾 子 (東京理大教養教育)

Masaki Matsuno (Tokyo Univ. of Sci.)
Ayako Itaba (Tokyo Univ. of Sci.)

S 型の 3 次元 2 次 Calabi–Yau AS 正則多元環の次数付き Ore 拡大 · · · · 15
Graded Ore extensions of 3-dimensional quadratic Calabi–Yau AS-regularalgebras of Type S

概 要 In noncommutative algebraic geometry, classiﬁcation of 4-dimensional Artin–Schelter regular (AS-regular) algebras is one of the main interests. It is known that a graded Ore extension of a 3-dimensional
quadratic AS-regular algebra is a 4-dimensional quadratic AS-regular algebra. In this talk, we show thatevery graded Ore extension Λ of a 3-dimensional quadratic AS-regular algebra satisﬁes (G1) condition about
the point scheme of Λ. In particular, for Type S, we give a list of geometric pairs of graded Ore extensionsof 3-dimensional quadratic Calabi–Yau AS-regular algebras. Also, we investigate whether Λ is geometric ornot.

Final: 2024/2/6
代数学

33 淺 井 聡 太 (東 大 数 理)
伊 山
修 ( 東 大 数 理)
(Univ. of Tokyo)
Sota Asai
Osamu Iyama (Univ. of Tokyo)

20

実 Grothendieck 群における M -TF 同値 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

M -TF equivalence in the real Grothendieck group

概 要 Let A be a ﬁnite dimensional algebra over a ﬁeld. Then, the real Grothendieck group K0 (projA)Rof the category of ﬁnitely generated projective A-modules is an Euclidean space whose canonical basis isgiven by the isoclasses of indecomposable projective modules. By using semistable torsion pairs deﬁned by
Baumann–Kamnitzer–Tingley, Asai introduced an equivalence relation on K0 (projA)R called TF equivalence.
For each ﬁnitely generated module M ∈ modA, we have found a method coarsening TF equivalence, andobtained a new equivalence relation on K0 (projA)R called M -TF equivalence. We will talk about thedeﬁnition and some important properties of M -TF equivalence.
14:15〜14:30

2024 年度 (第 27 回) 日本数学会代数学賞授与式

14:40〜15:40 2024 年度 (第 27 回) 日本数学会代数学賞受賞特別講演
浅 芝 秀 人
有限次元代数の表現論とその応用 (導来同値の被覆および区間近似を中(静岡大⋆・京大高等研・阪公大数学研) 心に)
Hideto Asashiba(Shizuoka Univ.⋆/Kyoto Univ./Osaka Metro. Univ.)

Representation theory of ﬁnite-dimensional algebras and its applications(with a focus on coverings of derived equivalences and interval approximations)

概 要 In the ﬁrst part of the lecture, as a topic of representation theory of ﬁnite-dimensional algebras, I will

start with an overview of the derived equivalence classiﬁcation of self-injective algebras, and then outline
the 2-categorical covering theory and its applications to derived equivalences. In the second part, as anapplication of the representation theory to topological data analysis, the interval resolutions and interval
replacements of persistence modules (modules over a ﬁnite poset) will be outlined.
16:00〜17:00 2024 年度 (第 27 回) 日本数学会代数学賞受賞特別講演
中 村 健 太 郎 (佐 賀 大 理 工) 階数 2 の p 進ガロア表現の岩澤理論について

Kentaro Nakamura (Saga Univ.)

Iwasawa theory for rank two p-adic Galois representations

概 要 In this talk, I will explain our main results on Kazuya Kato’s conjectures on the local and theglobal Iwasawa main conjecture for rank two p-adic Galois representations. One result concerns with theexistence of zeta elements for the universal deformations of rank two global p-adic Galois representations.
The other one concerns with the existence of local zeta elements for the universal deformations of rank
two local p-adic Galois representations. For both results, the theory of p-adic (local and global) Langlands
correspondence for GL2 is crucial. I’d like to explain that there exist deep relationships between p-adic
Langlands correspondence and Kato’s conjectures.

3 月 20 日（水）9:00〜12:00
34 助 永 真 之 (広島大先進理工)

Masayuki Sukenaga (Hiroshima Univ.)

第 I 会場

R3 内の種数 3 の滑らかな完全交叉空間トロピカル曲線 · · · · · · · · · · · · · · 15
Smooth tropical complete intersection curves of genus 3 in R3

概 要 We develop a method for describing the tropical complete intersection of a tropical hypersurface and atropical plane in R3 . This involves a method for determining the topological type of a complete intersection
by using a polyhedral complex. As an application, we show that there are no smooth tropical complete
intersection curves in R3 whose skeletons are the lollipop graph of genus 3. This gives a partial answer tothe open question of whether a lollipop graph of genus 3 appears in the skeleton of a tropical curve on atropical plane in R3 .

Final: 2024/2/6
21

代数学

35 澤 原 雅 知 (弘 前 大 教 育)

Masatomo Sawahara (Hirosaki Univ.)

Cylindricity of Du Val del Pezzo surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Cylindricity of Du Val del Pezzo surfaces

概 要 A cylinder in an algebraic variety means its open subset, which is isomorphic to the direct productof the aﬃne line and an algebraic variety. In this talk, we will present the existing condition of polarized
cylinders in Du Val del Pezzo surfaces of degree at least 2 deﬁned over an algebraically closed ﬁeld of
characteristic 0. Moreover, we will also explain the existence criterion of cylinders in Du Val del Pezzo
surfaces deﬁned over an algebraically closed ﬁeld of characteristic 2.
36 渡 邉 健 太 (日 大 理 工)

Kenta Watanabe (Nihon Univ.)

K3 曲面に含まれる曲線上の直線束の持ち上げに関する Donagi–Morrisonの予想とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Donagi–Morrison conjecture concerning lifts of line bundles on curvescontained in a K3 surface and its applications

概 要 Let X be a K3 surface, and let L be a base point free and big line bundle of sectional genus g on X.

Then the polarized K3 surface (X, L) is called Brill–Noether special if there exists a non-trivial line bundle
M on X with M 6= L such that h0 (M )h0 (L ⊗ M ∨ ) ≥ h0 (L) = g + 1. If (X, L) is Brill-Noether special,then any smooth curve C ∈ |L| is Brill–Noether special. Because, the Brill–Noether number of M ⊗ OC isnegative. However, the converse is still open. In this talk, I would like to focus on the Donagi–Morrison
conjecture concerning the existence of lifts of line bundles on curves on a K3 surface and its applications.
37 渡 邉

究 ( 中 大 理 工)

Kiwamu Watanabe (Chuo Univ.)

Contractions and non-free rational curves on Fano varieties · · · · · · · · · · 15
Contractions and non-free rational curves on Fano varieties

概 要 Let X be a complex smooth Fano variety whose minimal anticanonical degree of non-free rational

curves on X is at least dim X − 2. We give a classiﬁcation of extremal contractions of such varieties. As
applications, we obtain a classiﬁcation of Fano fourfolds whose pseudoindex and Picard number are greaterthan one and study the structure of Fano varieties with nef third exterior power of the tangent bundle.
38 鈴 木 香 織 (横 浜 国 大 経 営)

Kaori Suzuki (Yokohama Nat. Univ.)

複素 3 次元 Fano 多様体の Gradede Ring Database と Bogomolov 境界条
件 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Graded Ring Database of Fano 3-folds with Bogomolov condition

概 要 I will talk about the classiﬁcation of Fano 3-fold in Graded Ring Database with some examples.

39 岡 村 郁 弥 (名 大 多 元 数 理)

Fumiya Okamura (Nagoya Univ.)

Rational curves on Fano threefolds with terminal factorial singularities· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Rational curves on Fano threefolds with terminal factorial singularities

概 要 We would like to discuss the space of rational curves on Fano threefolds with terminal factorial

singularities. The project is motivated by the result of the paper by Roya Beheshti, Brian Lehmann, Eric
Riedl, and Sho Tanimoto, regarding the Geometric Manin’s conjecture (GMC) for smooth Fano threefolds.
GMC predicts the asymptotic formula for the number of irreducible components of the Hom scheme
Hom(P1 , X, α) as α ∈ Eﬀ 1 (X) grows positively. One of the main theorems is that GMC holds for terminal
factorial del Pezzo threefolds of Picard rank 1 and (−KX )3 ≥ 24.

Final: 2024/2/6
代数学

40 高

潤 宣 ( 名 大 多 元 数 理)

Runxuan Gao (Nagoya Univ.)

22

The geometric exceptional set in Manin’s conjecture for Batyrev andTschinkel’s example · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The geometric exceptional set in Manin’s conjecture for Batyrev andTschinkel’s example

概 要 Batyrev and Tschinkel’s example is a Fermat cubic surface bundle X which is a Fano 5-fold. It is theﬁrst example for which Manin’s conjecture can never hold for a proper closed exceptional set. Over a ﬁeld
F of characteristic 0, we give the minimal subset Z of X(F ) that contains every rational point coming froma thin map f : Y → X with equal or higher a- and b-values in lexicographical order, which is conjectured tobe the correct exceptional set in Manin’s conjecture. The set Z is a thin set deﬁned by ﬁnitely many thinmaps. Over a number ﬁeld F , we show that every such thin map f factors through the ﬁnitely many ones.
41 野 間淳 (横浜国大環境情報)

Atsushi Noma (Yokohama Nat. Univ.)

Duality for projective morphisms ﬁnite in codimension one and the positivity of double point divisors of general inner projections · · · · · · · · · · 15
Duality for projective morphisms ﬁnite in codimension one and the positivity of double point divisors of general inner projections

概 要 The purpose of this paper is to prove the positivity of double point divisors of general inner projections

for projective S2 -varieties with invertible dualizing sheaves, without assuming the smoothness or thenormality of varieties. As applications, we characterize two types of projective varieties: varieties withtrivial double point divisors and varieties with d − e − 1 ≤ n for dimension n, degree d and codimension e.
42 岩 見 智 宏 (九 工 大 工)

Tomohiro Iwami (Kyushu Inst. of Tech.)Canonical embedding of Clemens–Griﬃths–Kuznetsov components via
three-dimensional Miyaoka–Yau type inequality with the associated third
Chern classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Canonical embedding of Clemens–Griﬃths–Kuznetsov components via
three-dimensional Miyaoka–Yau type inequality with the associated third
Chern classes

概 要 Based on our serial works ([I. 2018 Mar; 2020 Sep]) about three-dimensional Miyaoka–Yau type

inequality with the associated third Chern classes (, abbreviated as (MY) 3,c3 ), and its variant form withdriven by symmetric 2-forms (, as (MY)3,c3 ,S 2 ), on an (extended) three-dimensional extremal neighborhood(X, C) ⊂ C4 ([Mori-Prokhorov 2021], [I. 2019 Sep]) with C reducible, in this talk, we mainly will give:i) to justify “Clemens–Griﬃths–Kuznetsov (CGK) component” CCGK corresponding to Artin–Mumford or
Clemens–Griﬃths properties related to (X, C) via several properties of (MY)3,c3 , (MY)3,c3 ,S 2 ([I. 2019 Sep;
2020 Sep; 2021 Sep; 2022 Mar,Sep; 2023 Mar]), and ii) to give “canonical” embedding Φ of CCGK by(MY)3,c3 ,S 2 , which is an answer to the sect. (2.3) of [Li-Pertushi-Zhao, 2022], on which they mention toneed three-dimesional Bogomolov type inequality with c3 for embedding CGK component, and they use
bounded derived category without it. Here, the word “canonical” means: other than categorical embedding,the target of Φ is not necessary bounded derived category, but occurs to be n(≥ 3)-angulated category with“selective” topologicality given by (MY)3,c3 ,S 2 , which seem to be more ﬂexible than [Li-Pertushi-Zhao,2022].

Final: 2024/2/6
23

代数学

14:15〜18:00
43 金
宮
縫
品

井
本
田
川

和
賢
光
和

貴 (呉
伍 (茨
司 (九
雅 (茨

工 高 専)

有限群の一様巡回群分解とカードベース暗号 · · · · · · · · · · · · · · · · · · · · · · · 15

城 大 工)
大 I M I)
城 大 工)

Kazuki Kanai (Kure Nat. Coll. of Tech.)
Kengo Miyamoto (Ibaraki Univ.)(Kyushu Univ.)
Koji Nuida
Kazumasa Shinagawa (Ibaraki Univ.)

Uniform cyclic group factorization of ﬁnite groups and card-based cryptography

概 要 In this talk, we introduce a kind of factorization of ﬁnite groups called a uniform cyclic groupfactorization. It has an application to card-based cryptography, which is a research ﬁeld that uses a deckof physical cards like playing cards to implement cryptographic techniques. If a group admits a uniform
cyclic group factorization, then a card shuﬄe operation associated with the group can be implemented byrandom cyclic shifts. We believe that our research combines mathematical research on the factorization ofﬁnite groups with cryptographic research on card-based cryptography, providing a new perspective on bothﬁelds.
44 安 東 雅 訓 (奈良学園大人間教育)
青 影 一 哉 ( 有 明 工 高 専)

Masanori Ando (Naragakuen Univ.)
Kazuya Aokage(Ariake Nat. Coll. of Tech.)

対称群と交代群の被覆群における原田予想 II · · · · · · · · · · · · · · · · · · · · · · · 10

Harada conjecture II in the covering groups of symmetric groups andalternating groups

概 要 Harada conjectured that the product of the sizes of all conjugacy classes is divided by the productof the degrees of all irreducible characters for any ﬁnite group. When the group is the symmetric group
Sn and the alternating group An, this conjecture is presented by the hook length properties of the Youngdiagram. We show the conjecture for the covering groups of symmetric groups and alternating groups.
45 田 邊 顕 一 朗 (東京都市大共通教育)

Kenichiro Tanabe (Tokyo City Univ.)

頂点代数上の加群のシュアー・ワイル型双対性 · · · · · · · · · · · · · · · · · · · · · 15

A Schur–Weyl type duality for twisted weak modules over a vertex algebra

概 要 Let V be a vertex algebra of countable dimension, G a subgroup of AutV of ﬁnite order, V G the ﬁxed

point subalgebra of V under the action of G. We show a Schur–Weyl type duality for the actions of an
associative algebra and V G
46 川 節 和 哉 (熊本大先導機構)

Kazuya Kawasetsu (Kumamoto Univ.)

A1 型格子頂点代数の主部分空間の中心化代数について · · · · · · · · · · · · · · 10
On the commutant of the principal subalgebra in the A1 lattice vertex
algebra概 要 The coset (commutant) construction is a fundamental tool to construct vertex operator algebras fromknown vertex operator algebras. The aim of this talk is to provide a fundamental example of the commutantsof vertex algebras ouside vertex operator algebras. Namely, the commutant C of the principal subalgebra
W of the A1 lattice vertex operator algebra VA1 is investigated. An explicit minimal set of generators ofC, which consists of inﬁnitely many elements and strongly generates C, is introduced. It implies that thealgebra C is not ﬁnitely generated. Furthermore, Zhu’s Poisson algebra of C is shown to be isomorphic toan inﬁnite-dimensional algebra C[x1 , x2 , . . .]/(xi xj |i, j = 1, 2, . . .). In particular, the associated variety of C
consists of a point. Moreover, W and C are veriﬁed to form a dual pair in VA1 .

Final: 2024/2/6
代数学

47 㓛 刀 直 子 (東 京 理 大 理)
鈴 木 香 一 ( 東 京 理 大 理)

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

24

有限群の主ブロックの森田型相対安定同値と森田同値 · · · · · · · · · · · · · · · 15

Relative stable equivalences of Morita type and Morita equivalences forthe principal blocks of ﬁnite groups

概 要 Let p be a prime. We consider ﬁnite groups G and G′ having a common central p-subgroup. In 2018,

Wang and Zhang introduced the notion of relative stable equivalence of Morita type for blocks of ﬁnite
groups. In this talk, we give a method of constructing a Morita equivalence between the principal p-blocks
of G and G′ using this notion.
48 小 境 雄 太 (東 京 理 大 理)
酒 井 嵐 士 ( 名 大 多 元 数 理)

Yuta Kozakai (Tokyo Univ. of Sci.)
Arashi Sakai (Nagoya Univ.)

ブリックに関するクリフォードの定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Cliﬀord’s theorem for bricks

概 要 Let G be a ﬁnite group, N a normal subgroup and k an algebraically closed ﬁeld of characteristicp > 0. Cliﬀord’s theorem states that the restricted module of arbitrary simple kG-module to kN is asemisimple module. In this talk, we introduce the brick version of Cliﬀord’s theorem.
49 M. Forsberg Conde(沖縄科学技術大)
Martı́n Forsberg Conde(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

New homomorphisms between Specht modules of the symmetric group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
New homomorphisms between Specht modules of the symmetric group

概 要 Describing the homomorphism spaces between Specht modules of the symmetric groups in positive

characteristic is an important open problem in representation theory. Carter and Payne gave a remarkable
result describing homomorphisms between Specht modules whose associated partitions diﬀer by a single row.
We describe the use of techniques from quiver Hecke algebras to achieve a generalization of the Carter–Payne
theorem.
50 L. Speyer(沖縄科学技術大)

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

Graded decomposition matrices for type C KLR algebras · · · · · · · · · · · 15
Graded decomposition matrices for type C KLR algebras

概 要 Outside of type A, the cyclotomic KLR algebras are still quite mysterious, and have not been studiedin great detail. They have been gaining attention in type C recently, and we now have several usefultools with which we may study their representation theory. These include a theory of Specht modules,
underpinned by combinatorics of multipartitions and tableaux, analogous to the type A situation, andEvseev and Mathas’s recent proof that these algebras are graded cellular. Building on these ideas, in joint
work with Chris Chung and Andrew Mathas, we have calculated graded decomposition matrices in small
ranks. We will explain the techniques used in this endeavour, and point to some interesting examples whose
behaviour look very diﬀerent to what we see in type A.

Final: 2024/2/6
25

代数学

51 河 野 隆 史 (早 大 理 工)
内 藤
聡 ( 東 工 大 理)

Takafumi Kouno (Waseda Univ.)(Tokyo Tech)
Satoshi Naito

C 型旗多様体の同変量子 K 環の Borel 表示 · · · · · · · · · · · · · · · · · · · · · · · · 15
The Borel-type presentation of the equivariant quantum K-ring of the
ﬂag manifold in type C

概 要 We give the Borel-type presentation of the equivariant quantum K-ring of the ﬂag manifold in type C.

The Borel-type presentation is an explicit quotient of a Laurent polynomial ring which is isomorphic to theequivariant quantum K-ring as rings. By specializing the Novikov variables in the Borel-type presentationof the equivariant quantum K-ring to 0, we can obtain the well-known Borel presentation of the equivariant
K-ring of the ﬂag manifold. In this sense, our presentation can be viewed as a quantum analogue of theclassical Borel presentation.
52 木 村 雄 太 (阪 公 大 理)

Yuta Kimura (Osaka Metro. Univ.)

変形前射影代数の傾イデアル · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Tilting ideals for deformed preprojective algebras

概 要 Let K be a ﬁeld and Q a ﬁnite acyclic quiver with n vertices. For an element λ of K n , thedeformed preprojective algebra Π(Q, λ) was introduced and studied by Crawley-Boevey and Holland to
study deformations of Kleinian singularities. If λ = 0, then Π(Q, 0) is the preprojective algebra introducedby Gelfand–Ponomarev, and appears in many areas of mathematics. Among interesting properties ofΠ(Q, 0), the classiﬁcation of tilting ideals of Π(Q, 0) is fundamental and important. In this talk, we classify
tilting ideals of Π(Q, λ) by using a Coxeter group. This is joint work with William Crawley-Boevey.
53 浅 芝 秀 人(静岡大⋆・京大高等研・阪公大数学研)
Hideto Asashiba(Shizuoka Univ.⋆/Kyoto Univ./Osaka Metro. Univ.)

Relative Koszul coresolutions and relative Betti numbers · · · · · · · · · · · · 15
Relative Koszul coresolutions and relative Betti numbers

概 要 Let G be a generator and a cogenerator in the category of ﬁnitely generated right A-modules for aﬁnite-dimensional algebra A over a ﬁled k, and I the additive closure of G. We will deﬁne a I-relative
Koszul coresolution K (V ) of an indecomposable direct summand V of G, and show that for a ﬁnitely
generated A-module M , the I-relative i-th Betti number for M at V is given as the k-dimension of the i-th
homology of the I-relative Koszul complex KV (M ) := HomA (K (V ), M ) of M at V for all i ≥ 0. This isapplied to investigate the minimal interval resolution/coresolution of a persistence module M , e.g., to checkthe interval decomposability of M , and to compute the interval replacement of M .
54 谷 本 龍 二 (静 岡 大 教 育)

Ryuji Tanimoto (Shizuoka Univ.)

Fundamental representations of Ga into SL(3, k) in positive characteristic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Fundamental representations of Ga into SL(3, k) in positive characteristic

概 要 Let k be an algebraically closed ﬁeld of positive characteristic p and let Ga denote the additive groupof k. A representation u : Ga → SL(n, k) is said to be fundamental if u factors through a representationof SL(2, k). In the case where p ≥ 3, Fauntleroy (1977) gave a representation u : Ga → SL(3, k) so thatu is not fundamental. In this talk, we classify fundamental representations of Ga into SL(3, k) in positive
characteristic.

Final: 2024/2/6
幾何学

幾 何
3 月 17 日（日）26

学第 IV 会場

9:30〜11:45
1 上 野
古 畑

龍 (北
仁 (北

大

理)

大

理)

(Hokkaido Univ.)
Ryu Ueno
Hitoshi Furuhata (Hokkaido Univ.)

統計 2 重調和写像 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Statistical biharmonic map

概 要 We present statistical biharmonic maps, a new class of mappings between statistical manifolds derived

from a natural variation problem. We give the Euler–Lagrange equation of this problem, and prove that
improper aﬃne spheres induce examples of such maps.
2 本 田 淳 史 ( 横 浜 国 大 理 工)
田 中 千 紗(NTT データフロンティア)
山 内 優 太 ( 横 浜 国 大 理 工)
Atsufumi Honda(Yokohama Nat. Univ.)
Chisa Tanaka(NTT DATA Frontier Corp.)
Yuta Yamauchi (Yokohama Nat. Univ.)

特異点をもつ閉曲線の絶対全曲率 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The total absolute curvature of closed curves with singularities

概 要 In this talk, we give a generalization of Fenchel’s theorem for wave fronts in the n-dimensional

Euclidean space Rn . We prove that, for a closed non-co-orientable 1-dimensional frontal in Rn , its total
absolute curvature is greater than or equal to π. The equality holds if and only if the frontal is a planar
L-convex closed frontal whose rotation index is 12 or − 21 . Furthermore we show that, if the total absolutecurvature is π and if the frontal admits at most cusps, the number N of cusps is an odd integer greater thanor equal to 3, and N = 3 holds if and only if the wave front is a simple closed curve.
3 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.)

3 次元球面から複素射影空間への全実調和写像の分類 · · · · · · · · · · · · · · · · 15

Harmonic totally real maps of the 3-sphere into the complex projective
spaces概 要 I would like to introduce a classiﬁcation result of harmonic totally real maps with constant energy

density of the 3-sphere into the complex projective spaces.
4 岸 田 陸 玖 (東工大情報理工)
Riku Kishida(Tokyo Tech)

共形平坦な多様体の光錐内における体積の変分について · · · · · · · · · · · · · 15

The volume of conformally ﬂat manifolds as hypersurfaces in the lightcone

概 要 In this talk, we focus on a conformally ﬂat Riemannian manifold (M n , g) isometrically immersed into

the light-cone Λn+1 as a hypersurface. We compute the ﬁrst and the second variational formulas on thevolume of such hypersurfaces. Such a hypersurface M n is not only immersed in Λn+1 but also isometricallyrealized as a hypersurface of a certain null hypersurface N n+1 in the Minkowski spacetime, which is diﬀerent
from Λn+1 . Moreover, M n has a volume-maximizing property in N n+1 .

Final: 2024/2/6
27

幾何学

5 佐 々 木 優 ( 宇 都 宮 大 教 育)

Yuuki Sasaki (Utsunomiya Univ.)

四元数対称空間のイソトロピー群作用の軌道 · · · · · · · · · · · · · · · · · · · · · · · 15

Orbits of the isotropy group action on quaternionic symmetric spaces

概 要 A symmetric space which is a quaternionic Kahler manifold is called a quaternionic symmetric space.

We study some properties of orbits of the isotropy group action on a compact quaternionic symmetric spacewith respect to the quaternionic structure. In particular, an orbit is a totally complex submanifold or aquaternionic submanifold if and only if the orbit is a polar. Moreover, many orbits containing principal
orbits satisfy some property which is an analogy of a totally complex submanifolds.
6 梶 ヶ 谷 徹 ( 東 京 理 大 理)

Toru Kajigaya (Tokyo Univ. of Sci.)

非負曲率等質多様体への安定離散写像の非存在 · · · · · · · · · · · · · · · · · · · · · 15

Nonexistence of stable discrete maps into some homogeneous spaces ofnonnegative curvature

概 要 We consider stabilities for the weighted length or energy functional of a discrete map from a ﬁnite

weighted graph (X, mE ) into a smooth Riemannian manifold (M, g). We prove the non-existence of a stablediscrete minimal immersion or a non-constant stable discrete harmonic map from a ﬁnite weighted graphinto certain homogeneous spaces, such as Kähler C-spaces of positive holomorphic sectional curvature andsome simply-connected compact Riemannian symmetric spaces.
7 大 野
Yu Ohno

優 (北

大

理)

(Hokkaido Univ.)

S2 × R と H2 × R の等質構造 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Homogeneous Structures on S2 × R and H2 × R

概 要 We determine all the homogeneous structure tensors on S2 × R and H2 × R. This work together

with previous articles yields a complete classiﬁcation of all the homogeneous structure tensors on threedimensional homogeneous Riemannian manifolds.
14:15〜16:10
8 池 田 憲 明 ( 立 命 館 大 理 工)

Noriaki Ikeda (Ritsumeikan Univ.)

Hamilton Lie algebroids over Dirac structures · · · · · · · · · · · · · · · · · · · · · 15
Hamilton Lie algebroids over Dirac structures

概 要 We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a

generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poissonmanifold. A Hamiltonian Lie algebroid and a momentum section are generalizations of a Hamiltonian
G-space and a momentum map over a symplectic manifold.
9 廣 田 祐 士 ( 麻 布 大 獣 医)池 田 憲 明 ( 立 命 館 大 理 工)
(Azabu Univ.)
Yuji Hirota
Noriaki Ikeda (Ritsumeikan Univ.)

運動量写像の拡張と四元ケーラー対称性 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Expansion of momentum maps, and quaternionic Kähler symmetries

概 要 We expand the notion of homotopy momentum sections in multisymplectic geometry to the one

for bundle-valued multisymplectic manifolds with Lie algebroids. We focus on the momentum map forquaternionic Kähler manifolds introduced by K. Galicki and H. B. Lawson, and describe the condition for
it to be the expanded homotopy momentum section.

Final: 2024/2/6
幾何学

10 西 田 安 寿 菜 (千葉大融合理工)
Azuna Nishida(Chiba Univ.)

28

モースホモトピーを用いた重み付き射影空間のホモロジー的ミラー対称性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Homological mirror symmetry for weighted projective spaces via Morse
homotopy

概 要 We discuss homological mirror symmetry for weighted projective spaces (WPS) based on SYZ con-struction. We consider WPS with a moment map on the complex side and the open dense torus as thetorus ﬁbration over the interior of the moment polytope. On the mirror symplectic side, we consider thedual torus ﬁbration with the same base and a generalization of Fukaya–Oh category of Morse homotopy ofthe polytope on it.
11 山 口 健 太 朗 (都 立 大 理)
Kentaro Yamaguchi(Tokyo Metro. Univ.)

アフィン部分空間から定まるトーリック多様体のトーラス同変埋め込みについて · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Torus-equivalently embedded toric manifolds associated to aﬃne subspaces

概 要 We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus

is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold
is Hamiltonian. In this case, we may think of the embedding of the submanifold as a torus-equivalent
embedding. We show that the image of the moment map for the Hamiltonian subtorus action on our
submanifold coincides with the image of the Delzant polytope of the ambient toric manifold under the
pullback of the inclusion of the tori. The submanifolds constructed in our talk are called torus-equivalently
embedded toric manifolds with respect to the subtorus action.
12 中 西 隼 斗 (千葉大融合理工)

Hayato Nakanishi (Chiba Univ.)

ヒルツェブルフ曲面 Fk の SYZ ミラーとモースホモトピー · · · · · · · · · · · 15

SYZ mirror of Hirzebruch surface Fk and Morse homotopy

概 要 We study homological mirror symmetry for Hirzebruch surface Fk as a complex manifold by using

the Strominger–Yau–Zaslow construction of mirror pair and Morse homotopy. For the Hirzebruch surface
F1 , Futaki–Kajiura proved homological mirror symmetry by using SYZ construction and Morse homotopy.
We extend Futaki–Kajiura’s result of Hirzebruch surface F1 to Fk . In this talk, we construct a quasiisomorphism from the category of Morse homotopy to the DG category of the complex side and discuss theminimality of the category of Morse homotopy.
13 米 原 修 平 (阪大理)Shuhei Yonehara (Osaka Univ.)

coKähler 多様体上の Hamilton 作用と簡約定理 · · · · · · · · · · · · · · · · · · · · · 15
Hamiltonian actions on coKähler manifolds and a reduction theorem

概 要 The notion of cosymplectic manifolds is an odd-dimensional analogue of symplectic manifolds. Albert

introduced the concept of Hamiltonian actions on cosymplectic manifolds and proved a reduction theorem.
In this talk, we reﬁne this theorem in the case of coKähler manifolds, that is, normal almost contact metricmanifolds which have a compatible cosymplectic structure.

Final: 2024/2/6
29

幾何学

16:25〜17:25

特別講演
植 田 一 石 ( 東 大 数 理)

ミラー対称性と退化

Kazushi Ueda (Univ. of Tokyo)

Mirror symmetry and degeneration

概 要 Mirror symmetry is a mysterious relationship between complex geometry and symplectic geometry,

which is inspired by string theory. It suggests that strings perceive the world fundamentally diﬀerently
from particles. Since every compact symplectic manifold comes in a family with varying volumes, a mirrorof a compact symplectic manifold is not a single complex manifold but a degenerating family of complex
manifolds. Studying the limits of degenerating families in various contexts is one of the central problems ingeometry, related to compactiﬁcations of moduli spaces and localization (or concentration) of informationnear singular points. In the talk, I will discuss degenerations from the perspective of mirror symmetry.

3 月 18 日（月）10:10〜10:25

第 IV 会場

2023 年度日本数学会幾何学賞授賞式

10:30〜11:30

2023 年度日本数学会幾何学賞受賞特別講演 (トポロジー分科会と合同)
大理) ♭ ファノ多様体の K 安定性の判定法について
藤 田 健 人 (阪Kento Fujita(Osaka Univ.)

On criteria for the K-stability of Fano varieties

概 要 We survey recent progress on K-stability of Fano varieties.

13:00〜14:00
14 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.)

ケーラー多様体上の特性磁性焦値の評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Estimates on characteristic magnetic focal value on Käher manifold

概 要 A Käher magnetic ﬁelds on a Kähler manifold is a constant multiple of the Kähler form. We study

magnetic Jacobi ﬁelds which are obtained as derivatives of variations of trajectories for Kähler magnetic
ﬁelds. In this talk, we concider a “special” magnetic Jacobi ﬁeld along tarajectory. Since velocity vecor
and accelaration vector span a complex line, we study “special” magnetic Jacobi ﬁelds which are relatedwith such directions. We take auxiliary magnetic Jacobi ﬁeld to estimete. We get estimates of “special”
magnetic Jacobi ﬁeld by comparing magnetic Jacobi ﬁeld on complex space forms.
15 佐 藤 健 治 (玉 川 大 工)
Kenzi Satô (Tamagawa Univ.)

球面三角形と双曲三角形の新しい重心二種 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Two kinds of new centroids of spherical and hyperbolic triangles

概 要 The centroid of a planar triangle satisﬁes many properties, but the points with each property are

diﬀerent for a spherical or hyperbolic triangle. In this talk, the point trisecting the area and the concurrent
point of 3 arcs bisecting the area are considered.
16 V. Pérez-Valdés (東 大 数 理)

Vı́ctor Pérez-Valdés (Univ. of Tokyo)

対 (SO(4,1), SO(3,1)) の主系列表現に対する微分対称性破れ作用素について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Diﬀerential symmetry breaking operators for principal series representations of the pair (SO(4,1), SO(3,1))

概 要 In this talk, we discuss about the problem of constructing and classifying all diﬀerential symmetry

breaking operators for principal series representations of the pair (SO(4,1), SO(3,1))

Final: 2024/2/6
幾何学

3 月 19 日（火）30

第 IV 会場

9:30〜11:45
17 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)

Limit theorems for the total scalar curvature · · · · · · · · · · · · · · · · · · · · · · 15
Limit theorems for the total scalar curvature

概 要 In this talk, we give some W 1,p limit theorems for total scalar curvatures. More precisely, we showthat the lower bound of the total scalar curvatures on a closed n-manifold is preserved under the W 1,pconvergence of the Riemannian metrics for p > n provided that each scalar curvature is nonnegative. We
also give an example which suggests that the W 1,p (p > n) convergence is almost optimal.
18 藤 岡 禎 司 (阪大理)Tadashi Fujioka (Osaka Univ.)

曲率の上界と曲率積分の下界 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Upper curvature bound and the curvature integral

概 要 We prove that the integral of scalar curvature over a Riemannian manifold is uniformly bounded

below in terms of its dimension, upper bounds on sectional curvature and volume, and a lower boundon injectivity radius. This is an analogue of an earlier result of Petrunin for Riemannian manifolds withsectional curvature bounded below. Both proofs rely on the convergence theory of Riemannian manifolds
with one-sided curvature bounds. The parallel structure comes from that of the limit spaces, i.e., Alexandrov
spaces and GCBA spaces.
19 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Improved oscillation estimates and the Hitchin–Thorpe inequality on
compact Ricci solitons · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Improved oscillation estimates and the Hitchin–Thorpe inequality on
compact Ricci solitons

概 要 Stimulated by improved oscillation estimates of the potential function and the scalar curvature oncompact gradient Ricci solitons introduced in a recent work by X. Cheng, E. Ribeiro Jr., and D. Zhou
(Proc. Amer. Math. Soc. Ser. B 10 (2023), 33–45), we give several new suﬃcient conditions for compact
four-dimensional normalized shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality. Our new
conditions reﬁne the validity of the Hitchin–Thorpe inequality obtained by the author (J. Math. Phys. 58(2017), 023503 & J. Math. Phys. 59 (2018), 043507 & Diﬀerential Geom. Appl. 66 (2019), 231–241).
20 只 野誉 ( 山 口 大 理)

Homare Tadano (Yamaguchi Univ.)

Gradient estimates and Harnack inequalities for porous medium and fast
diﬀusion equations via m-Bakry–Émery Ricci curvature with ε-range · 15
Gradient estimates and Harnack inequalities for porous medium and fast
diﬀusion equations via m-Bakry–Émery Ricci curvature with ε-range

概 要 We derive some new local gradient estimates of Li–Yau, Hamilton, Li–Xu types for positive solutions

to porous medium and fast diﬀusion equations associated with the Witten Laplacian on a complete
Riemannian manifold via m-Bakry–Émery Ricci curvature with ε-range. As applications, we give some
Harnack inequalities for positive solutions to porous medium and fast diﬀusion equations associated with
the Witten Laplacian on a complete non-compact Riemannian manifold via m-Bakry–Émery Ricci curvature
with ε-range.

Final: 2024/2/6
31

幾何学

21 見 村 万 佐 人 (東 北 大 理) ♭ 拡張不能な不変擬準同型のなす空間 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
大理)
川 﨑 盛 通 (北(大理)
木 村 満 晃 京
松 下 尚 弘 ( 信 州 大 理)
丸 山 修 平 ( 金 沢 大 理 工)

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

The space of non-extendable invariant quasimorphisms

概 要 We study the space of non-extendable invariant quasimorphisms.

22 見 村 万 佐 人 (東 北 大 理) ♭ scl と粗い群 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
大理)
川 﨑 盛 通 (北大理)
木 村 満 晃 (京松 下 尚 弘 ( 信 州 大 理)
丸 山 修 平 ( 金 沢 大 理 工)

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

scl and coarse groups

概 要 We initiate coarse group theoretic study of scl (stable commutator length).

23 大 島駿 ( 東 北 大 理)

Shun Oshima(Tohoku Univ.)

測度距離空間のオブザーバブル直径と正の測度を持つ点の存在 · · · · · · · · 15

The observable diameter of metric measure spaces and the existence ofpoints with positive measures.

概 要 A metric measure space is a metric space with a Borel measure. This concept was deﬁned when

considering the limit of a sequence of Riemannian manifolds. Currently, there are several deﬁnitions of
metric measure spaces, and one of them is a metric measure space with a probability measure consideredby Gromov. In the theory of this metric measure space, the invariants called the partial diameter and theobservable diameter are often used. We obtained the result that the partial diameter or the observable
diameter equals zero if and only if there exist points that have positive measures (called the atoms).
14:15〜17:10
24 伊 敷 喜 斗 (理化学研 RAP)
Yoshito Ishiki(RIKEN)

距離関数の空間の中の強リジット距離関数 · · · · · · · · · · · · · · · · · · · · · · · · · 15

Strongly rigid metrics in spaces of metrics

概 要 A metric space is said to be strongly rigid if no positive distance is taken twice by the metric. In 1972,

Janos proved that a separable metrizable space has a strongly rigid metric if and only if it is zero-dimensional.
As a development of this result, for a zero-dimensional metrizable space, we prove that the set of all strongly
rigid metrics is dense in the space of metics. Moreover, if the space is the union of countably many compact
subspaces, then that set is comeager. As a consequence, we show that for a strongly zero-dimensional
metrizable space, the set of all metrics possessing no nontrivial (bijective) self-isometry is comeager in thespace of metrics.

Final: 2024/2/6
幾何学

25 清
智 也 ( 東 大 情 報 理 工)
田 中
潮 ( 阪 公 大 理)
Tomonari Sei (Univ. of Tokyo)
Ushio Tanaka (Osaka Metro. Univ.)

32

Stein identity and Poincaré inequality for a discrete metric measurespace · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Stein identity and Poincaré inequality for a discrete metric measurespace

概 要 A Gaussian random variable is characterised in terms of a diﬀerentiable real-valued function. The

characterisation is referred to as Stein identity. Stein identity implies Poincaré inequality in terms ofa random variable. We observe the implication from the point of view of a discrete distribution via
quantiﬁcation. This observation enables us to show Stein identity and Poincaré inequality in terms of thequantiﬁcation. We also argue them to obtain their results on geometric analysis.
26 田 代 賢 志 郎 (東 北 大 理)
(
)
SISSA
S. Borza

Kenshiro Tashiro (Tohoku Univ.)(SISSA)
Samuël Borza

Measure contraction property of the ℓp -Heisenberg group · · · · · · · · · · · · 15
Measure contraction property of the ℓp -Heisenberg group

概 要 We consider the problem whether sub-Finsler manifolds satisfy the measure contraction property

M CP (K, N ), and if so, what is the optimal K and N . It has been considered for sub-Riemannian
Heisenberg groups (and its generalizations), and the optimal N was relevant to the geodesic dimension. We
consider the ℓp -Heisenberg group. We show that for 1 < p < 2, it satisﬁes M CP (K, N ) with non-positive
K and some N which is strictly greater than the geodesic dimension. On the other hand, for 2 < p ≤ ∞, it
has ﬁnite geodesic dimension, but it does not satisﬁes M CP (K, N ) for any numbers.
27 N. Evseev(沖縄科学技術大) ♭ Sobolev curves in an arbitrary metric space · · · · · · · · · · · · · · · · · · · · · · · 15

Nikita Evseev(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Sobolev curves in an arbitrary metric space

概 要 We show that Sobolev curves in a dual Banach space can be characterized in terms of weak derivatives

in a weak* sense. Since every metric space embeds isometrically into a dual Banach space, this implies
a characterization of metric space valued Sobolev curves in terms of such derivatives. Furthermore, weinvestigate for which target spaces Sobolev curves are weak* diﬀerentiable almost everywhere.
28 張

頁 (沖縄科学技術大)

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

Semiconcavity results of squared sub-Riemannian distance on ideal Carnot
groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Semiconcavity results of squared sub-Riemannian distance on ideal Carnot
groups概 要 On Euclidean spaces, the squared distance function | · |2 is a convex function as well as a semiconcave

function. When it comes to Heisenberg group, due to the appearance of the cut locus and the abnormalset, the squared sub-Riemannian distance cannot be locally semiconcave nor locally semiconvex. However,
if we consider the correponding weaker horizontal convexity (or h-convexity in short) on Heisenberg groupinstead, the h-semiconcavity holds for the squared sub-Riemannian distance on Heisenberg group. This
result can be generalized to the case of so-called ideal Carnot groups.

Final: 2024/2/6
33

幾何学

29 成 田 知 将 (名 大 多 元 数 理)

Kazumasa Narita (Nagoya Univ.)

コンパクトケーラー多様体のラプラシアン固有値の最大化問題 · · · · · · · · 15

An extremal eigenvalue problem for the Laplacian on a compact Kähler
manifold

概 要 We study an eigenvalue problem for the Laplacian on a compact Kähler manifold. Considering thek-th eigenvalue λk as a functional on the space of Kähler metrics with ﬁxed volume on a compact complex
manifold, we introduce the notion of λk -extremal Kähler metric. We deduce a condition for a Kähler
metric to be λk -extremal. As examples, we consider product Kähler manifolds and ﬂat complex tori. The
condition for the ﬂat metric on a complex torus to be λk -extremal is also a necessary condition for the ﬂatcomplex torus to admit an isometric minimal immersion into a Euclidean sphere by ﬁrst eigenfunctions.
30 高 橋 雄 也 (名 大 多 元 数 理)

Yuya Takahashi (Nagoya Univ.)

Riemann 面上の SU (2)-平坦接続のモジュライ空間の幾何学的量子化とオペラッド構造 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Operad structures in geometric quantization of the moduli space of ﬂat
SU (2)-connections on a Riemann surface

概 要 The moduli space of ﬂat SU (2)-connections on a Riemann surface is known to contain an open dense

subset which is a symplectic manifold equipped with both Kähler and real polarizations. In this talk, wewill construct morphisms of modular operads fKäh and fre by using the quantum spaces HKäh and Hreassociated to the Kähler and real polarizations respectively. Moreover, we will relate the two morphisms
fKäh and fre , and prove the equality dim HKäh = dim Hre , which is known as the result of Jeﬀrey andWeitsman (1992). This operadic structures are similar to those obtained by Takahashi (2023) in the case of
the moduli space of spatial polygons.
31 瀬 戸樹 ( 明 治 薬 科 大)丸 山 貴 志(NEC Laboratories Europe)

Tatsuki Seto (Meiji Pharm. Univ.)
Takashi Maruyama(NEC Laboratories Europe)n 次元立方体上の自己相似集合における Fredholm 加群について · · · · · · 15

A Fredholm module on self-similar sets built on n-cubes

概 要 We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet

and the Menger sponge. Our construction is a higher dimensional analogue of Connes’ combinatorialconstruction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of operators
induced by the Fredholm module.
32 奥 田 太 夏 (東 京 理 大 理)
佐 古 彰 史 ( 東 京 理 大 理)

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

Star product with separation of variables on G2,4 (C) · · · · · · · · · · · · · · · 15Star product with separation of variables on G2,4 (C)概 要 Deformation quantization with separation of variables for Kähler manifolds has been proposed by

Karabegov. Especially, locally symmetric cases have also been studied by Sako–Suzuki–Umetsu or Hara–
Sako. On the other hand, deformation quantization with separation of variables for complex Grassmannians
has not been explicitly constructed so far, except for CP N . In this work, we explicitly determined the starproduct with separation of variables on G2,4 (C) by using the solution of the recurrence relations given by
Hara–Sako.

Final: 2024/2/6
幾何学

3 月 20 日（水）34

第 IV 会場

9:20〜10:15
33 Joonhyung Kim(Chungnam Nat. Univ.)( Univ. of Crete )I. D. Platis
孫
立 杰 ( 山 口 大 創 成)
Joonhyung Kim(Chungnam Nat. Univ.)
Ioannis D. Platis (Univ. of Crete)
Li-Jie Sun (Yamaguchi Univ.)

On the Kähler cone of the Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · 15

On the Kähler cone of the Heisenberg group

概 要 Starting from the Sasakian structure of the Heisenberg group we construct a Kähler structure of theSiegel domain. We also show other Kähler structures of the Siegel domain and all these are PCR-Kähler
equivalent, that is, essentially the same when restricted to the CR structure.
34 竹 内 有 哉 (筑波大数理物質)

Yuya Takeuchi (Univ. of Tsukuba)

球面的 CR 多様体の Kohn–Rossi コホモロジー · · · · · · · · · · · · · · · · · · · · · 15

Kohn–Rossi cohomology of spherical CR manifolds

概 要 The Kohn–Rossi cohomology is a CR analog of the Dolbeault cohomology and is one of fundamental

invariants in CR geometry. In this talk, we prove some vanishing theorems for the Kohn–Rossi cohomology
of some spherical CR manifolds. To this end, we use a canonical contact form deﬁned via the Patterson–
Sullivan measure and Weitzenböck-type formulae.
35 宮 武 夏 雄 (東北大MathCCS)

Natsuo Miyatake (Tohoku Univ.)

巡回 Higgs 束の Hitchin 方程式の劣調和関数を用いた拡張とその Dirichlet
問題について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Extended Hitchin equation for cyclic Higgs bundles associated with aquasi-subharmonic function, and its Dirichlet problem

概 要 We demonstrate the existence and uniqueness of the solution to the Dirichlet problem for a generaliza-tion of Hitchin’s equation for diagonal harmonic metrics on cyclic Higgs bundles. The generalized equations
are formulated using subharmonic functions. In this generalization, the coeﬃcient exhibits worse regularity
than that in the original equation.
10:30〜11:30

特別講演

糟 谷 久 矢 (阪大理)Hisashi Kasuya (Osaka Univ.)

佐々木多様体上の Higgs 束, 現状とこれから

Vector bundles and Higgs bundles over Sasakian manifolds, present andfuture概 要 The speaker and his collaborators develop the theory of Higgs bundles over compact Sasakian manifolds

as an odd-dimensional analogue of the great works of Corlette, Hitchin and Simpson on Higgs bundles overcompact Kähler manifolds. Sasakian geometry is often qualiﬁed as an odd-dimensional analogy of Kähler
geometry. An important theme on Sasakian geometry is to show that Sasakian geometry is not just an
analogue. The purpose of this talk to give an overview of recent results on Higgs bundles over compact
Sasakian manifolds and suggest future programs for going beyond an analogy of Kähler case.

Final: 2024/2/6
35

函数論

函

数

3 月 17 日（日）論第 VI 会場

9:50〜11:20
1 田 中 清 喜 ( 名 城 大 理 工)
山 路 哲 史 ( 神 戸 工 高 専)
Kiyoki Tanaka (Meijo Univ.)
Satoshi Yamaji(Kobe City Coll. of Tech.)Little Hankel operators on Bloch type spaces · · · · · · · · · · · · · · · · · · · · · · 15
Little Hankel operators on Bloch type spaces

概 要 Axler gave a characterization for bounded or compact Hankel operators with anti holomorphic symbols

on Bergman spaces. Based on Axler’s results, Bonami–Luo gave a characterization for bounded little Hankel
operators with anti holomorphic symbols from Bergman spaces to another Bergman spaces. In this talk,we announce a result of characterization for bounded little Hankel operator with anti holomorphic symbols
on Bloch type spaces.
2 須 川 敏 幸 ( 東 北 大 情 報)
Li-Mei Wang
(Univ. of Int. Business and Econ.)Chengfa Wu (Shenzhen Univ.)

Toshiyuki Sugawa (Tohoku Univ.)
Li-Mei Wang
(Univ. of Int. Business and Econ.)Chengfa Wu (Shenzhen Univ.)

超幾何函数の普遍凸性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On universal convexity of shifted hypergeometric functions

概 要 In this talk, we consider mainly the shifted hypergeometric function f (z) = z2 F1 (a, b; c; z) for realparameters with 0 < a ≤ b ≤ c. Ruscheweyh, Salinas and Sugawa developed in their 2009 paper the theoryof universal prestarlike functions on the slit domain C \ [1, +∞) and showed universal starlikeness of f undersome assumptions on the parameters. We will give conditions on the parameters which lead to universal
convexity of f .
3 小 森 洋 平 ( 早 大 教 育)
Yohei Komori (Waseda Univ.)

On the convergence of Thurston’s hyperbolic circle packing algorithm· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On the convergence of Thurston’s hyperbolic circle packing algorithm

概 要 In this talk we will show the convergence of Thurston’s iterated algorithm for hyperbolic circle packing.

Colin de Verdière proved the convergence for Euclidean case. We will also consider circle pattern case.
4 松 崎 克 彦 ( 早 大 教 育)

Katsuhiko Matsuzaki (Waseda Univ.)

可積分タイヒミュラー空間の実解析的構造について · · · · · · · · · · · · · · · · · 15

On the real-analytic structure of integrable Teichmüller spaces

概 要 For the p-integrable Teichmüller space Tp (p ≥ 1), which is given by p-integrable Beltrami coeﬃcientswith respect to the hyperbolic metric, we describe its real-analytic structure by using Besov spaces.
5 相 川 弘 明 ( 中 部 大 理 工)
Hiroaki Aikawa (Chubu Univ.)

Intrinsic ultracontractivity for planar domains with wide access property· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Intrinsic ultracontractivity for planar domains with wide access property

概 要 Utilizing capacitary width and the parabolic box argument, we unveil analytic notions behind geometriccharacterizations of wide accessible planar domains, those are IU or have ﬁnite lifetime.

Final: 2024/2/6
函数論

特別講演
大 野 貴 雄 (大分大教育福祉)36

14:15〜15:15

Takao Ohno

(Oita Univ.)

極大作用素の有界性と Riesz ポテンシャルに対する Sobolev 型の不等式

Boundedness of maximal operators and Sobolev-type inequalities for
Riesz potentials

概 要 The maximal operator is a classical tool in harmonic analysis and studying Sobolev functions andpartial diﬀerential equations and plays a central role in the study of diﬀerentiation, singular integrals,smoothness of functions and so on. It is well known that the maximal operator is bounded on theLebesgue space if p > 1. One of important applications of the boundedness of the maximal operator is
Sobolev’s inequality for Riesz potentials of functions in the Lebesgue space. My aim in this talk is to talkabout the boundedness of the maximal operator on variable exponent Lebesgue spaces, variable exponent
Morrey spaces, Musielak–Orlicz spaces, Musielak–Orlicz–Morrey spaces and so on. As an application of
the boundedness of the maximal operator, we establish a generalization of Sobolev’s inequality for Riesz
potentials of functions in the above spaces.
15:35〜16:30
6 濱 田 英 隆 ( 九 州 産 大 理 工)
Shaolin Chen
(Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

Riesz type inequalities and a Hardy–Littlewood type theorem on boundedsymmetric domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Riesz type inequalities and a Hardy–Littlewood type theorem on boundedsymmetric domains

概 要 The aim of this talk is to establish some Riesz type inequalities of pluriharmonic functions on boundedsymmetric domains, which extend a theorem due to Kalaj. Also, we observe that similar Riesz type
inequalities do not hold for the pluriharmonic Hardy space PH p (Ω) in the cases p = 1, ∞. We obtain a
Hardy and Littlewood type theorem in the case p = 1.
7 濱 田 英 隆 ( 九 州 産 大 理 工)
Shaolin Chen
(Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

Harmonic functions with smooth moduli · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Harmonic functions with smooth moduli

概 要 Pavlović studied Lipschitz conditions with respect to ψα (t) = tα , 0 < α < 1 on the modulus of

real-valued harmonic functions on the Euclidean unit ball of Rn with n ≥ 2. The aim of this talk is toimprove and extend a Pavlović’s result to a general fast majorant ψ and to real-valued harmonic functions
on an Lψ -extension domain of Rn .
8 濱 田 英 隆 ( 九 州 産 大 理 工)
Shaolin Chen
(Hengyang Normal Univ.)

Holomorphic and pluriharmonic functions with smooth moduli and Hardy–
Littlewood type theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

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

Holomorphic and pluriharmonic functions with smooth moduli and Hardy–
Littlewood type theorems

概 要 In this talk, we discuss the Hardy–Littlewood type theorems and smooth moduli of holomorphic andpluriharmonic functions. Our result improves and extends the corresponding results due to Dyakonov in2004 and Hardy and Littlewood in 1932.

Final: 2024/2/637

函数論

9 濱 田 英 隆 ( 九 州 産 大 理 工)
Shaolin Chen
(Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

Pluriharmonic Lipschitz type spaces and composition operators · · · · · · 15

Pluriharmonic Lipschitz type spaces and composition operators

概 要 The main purpose of this talk is to develop some methods to study the composition operators

between pluriharmonic Lipschitz type spaces. Some characterizations of boundedness and w-compactness ofcomposition operators between the pluriharmonic Lipschitz type spaces will be given. The obtained results
improve and extend some corresponding known results by Madigan in 1993 and Pavlović in 2008.

3 月 18 日（月）第 VI 会場

9:50〜11:20
10 綾 野 孝 則 (阪 公 大 数 学 研)

Takanori Ayano (Osaka Metro. Univ.)

テレスコピック曲線のシグマ関数のべき級数展開に関する改良 · · · · · · · · 15

An improvement on the power series expansion of the sigma function
associated with the telescopic curves

概 要 The sigma function is obtained by modifying the Riemann’s theta function. The sigma function has

some remarkable algebraic properties that it is directly related with the deﬁning equations of an algebraic
curve. Namely, the coeﬃcients of the power series expansion of the sigma function around the origin become
polynomials of the coeﬃcients of the deﬁning equations of the algebraic curve. It is an important problem
to determine the coeﬃcients of the power series expansion of the sigma function. In The MathematicalSociety of Japan Autumn Meeting 2022, I made a presentation on the result of the power series expansionof the sigma function associated with the telescopic curves. In this talk, I will give an improvement of thisresult.
11 孫立 杰 ( 山 口 大 創 成)

Li-Jie Sun(Yamaguchi Univ.)

Geometric structures on the quaternionic Heisenberg group · · · · · · · · · · 15
Geometric structures on the quaternionic Heisenberg group

概 要 Analogous to the pseudohermitian manifold in CR geometry, there exists a quaternionic counterpart

known as the quaternionic contact manifold. A well-known example is the quaternionic Heisenberg group.
Our main focus is to explore the Sasakian 3-structure on the quaternionic Heisenberg group, which isimportant to investigate the geometry on its Riemannian cone.
12 都 丸

正 (群

馬

大⋆)

Tadashi Tomaru (Gunma Univ.

⋆)

Arnold の 14 例外型特異点と虚数乗法をもつ楕円曲線族 · · · · · · · · · · · · · · 15
Arnold’s 14 exceptional singularities and families of elliptic curves withcomplex multiplications

概 要 In my paper in 2013, I introduced the notion of C*-pencil of curves, From the point of view, I will

explain some relations between Arnold’s 14 exceptional singularities and families of elliptic curves withcomplex multiplications.
13 小 池 貴 之 (阪 公 大 理)

Takayuki Koike (Osaka Metro. Univ.)∂ cohomology of the complement of a semi-positive anticanonical divisorof a compact surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
∂ cohomology of the complement of a semi-positive anticanonical divisorof a compact surface

概 要 Let X be a non-singular compact complex surface such that the anticanonical line bundle admits asmooth Hermitian metric with semi-positive curvature. For a non-singular hypersurface Y which deﬁnes ananticanonical divisor, we investigate the ∂ cohomology group H 1 (M, OM ) of the complement M = X \ Y .

Final: 2024/2/6
函数論

38

14 大 沢 健 夫 (名 大 多 元 数 理) ♭ On the Levi problem for locally pseudoconvex bounded domains of regular type with a curvature negativity on the boundary · · · · · · · · · · · · · · 15
Takeo Ohsawa (Nagoya Univ.)

On the Levi problem for locally pseudoconvex bounded domains of regular type with a curvature negativity on the boundary

概 要 Given a bounded locally pseudoconvex domain Ω in a complex manifold M with a complete Kähler

metric and a positive line bundle, it is proved that Ω is holomorphically convex if the canonical bundle of M
is negative on ∂Ω, under a regularity condition on ∂Ω wich is satisﬁed if ∂Ω is a C 2 -smooth hypersurface.
13:00〜14:00

特別講演
久 本 智 之 ( 都 立 大 理)

Tomoyuki Hisamoto(Tokyo Metro. Univ.)

Fano 多様体の最適退化について
Optimal degeneration for a Fano manifold

概 要 The existence problem of the Kähler–Einstein metric for Fano manifolds was solved by Chen–

Donaldson–Sun and by many contributions of other people in the 2010s. In the proof, the uniform lower
bound estimate of the Bergman kernel played a crucial role. While a general Fano manifold does not
admits a Kähler–Einstein metric, its parabolic version, known as the Kähler–Ricci ﬂow, has the long-time
solution and converges to the Kähler–Einstein metric if it exists. In terms of the algebraic geometry theKähler–Ricci ﬂow corresponds to the optimal degeneration of the Fano manifold, which is characterized
as the degeneration with minimal (non-Archimedean) entropy. In this talk I will explain the asymptotic
construction of optimal degeneration using multiplier ideal sheaves. I would also like to touch upon thequantization of the Kähler–Ricci ﬂow, in connection with the above construction.

Final: 2024/2/639函数方程式論函 数

方3 月 17 日（日）

程

式

論

第 II 会場

9:30〜12:00
1 朴

佳 南 ( 鳥 羽 商 船 高 専)

Kanam Park
(Toba Nat. Coll. of Maritime Tech.)(1)

E6 型 q パンルヴェ方程式のラックス形式から得られるアフィンワイル
群の双有理表現 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Birational representations of aﬃne Weyl groups related to a 3 × 3 Lax(1)formalism for the q-Painlevé equation of type E6(1)

概 要 The q-Painlevé equation of type E6

is given as a q-diﬀerence system with an aﬃne Weyl group(1)

symmetry of type E6 . We obtained a 3 × 3 Lax formalism for the equation as a new one. Our goal is(1)
to understand a birational representation of an aﬃne Weyl group symmetry of type E6 as actions on the
3 × 3 Lax formalism. In this talk, we talk about a relation between it and known birational actions of 3
(1)kinds of aﬃne Weyl group of type A22 藤 本 皓 大 (島根大総合理工)

Kodai Fujimoto (Shimane Univ.)

as a partial result.

Minimal set for solutions of ordinary diﬀerential equations involving
p(t)-Laplacian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Minimal set for solutions of ordinary diﬀerential equations involving
p(t)-Laplacian

概 要 We consider the nonlinear diﬀerential equation (a(t)|x′ |p(t)−2 x′ )′ = b(t)|x|q(t)−2 x, where a(t), b(t),and q(t) > 1 are positive continuous, and p(t) > 1 is continuously diﬀerentiable. Nonoscillatory proper
solutions of this equations are categorized into four classes, characterized by speciﬁc integral conditions. Byleveraging these classes, we introduce a minimal set for solutions of this equation, thereby extending theconcept of principal solutions of linear equations. This talk is based on a joint work with Professor ZuzanaDošlá (Masaryk University, Czech Republic).
3 宇 佐 美 広 介 ( 岐 阜 大 工)
前 田 貴 之 ( 岐 阜 大 自 然)
Hiroyuki Usami (Gifu Univ.)
Takayuki Maeda (Gifu Univ.)

射的問題について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On target shooting problems

概 要 Mathematical Analysis for target shooting problems is given. We consider the diﬀerential systems

describing the motion of an objective thrown at the target. We assume that the air resistance is proportional
to the square of the magnitude of its velocity. We can determine whether or not the objective hits thetarget in some cases.
4 柴 田 徹 太 郎 (広島大先進理工)

Tetsutaro Shibata (Hiroshima Univ.)

The ﬁrst eigenvalue and eigenfunction of the nonlocal one-dimensional
elliptic eigenvalue problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The ﬁrst eigenvalue and eigenfunction of the nonlocal one-dimensional
elliptic eigenvalue problem

概 要 We consider the one-dimensional nonlinear eigenvalue problem of Kirchhoﬀ type. We obtain the ﬁrst

eigenvalue µ1 of this problem explicitly by using a simple time map method. We also obtain the ﬁrst
eigenfunction associated with µ1 .

Final: 2024/2/6函数方程式論5 西 口 純 矢 (東 北 大 A I M R )Junya Nishiguchi (Tohoku Univ.)40

線型遅延微分方程式の「軟解」概念について · · · · · · · · · · · · · · · · · · · · · · · 15

On the notion of “mild solutions” to linear delay diﬀerential equations

概 要 The delay diﬀerential equations (DDEs), in which the time derivative of the unknown function also

depends on the past information determine inﬁnite-dimensional dynamical systems as the time evolution of
the history segments of solutions, even when the independent variables of the unknown function are only
time variable. While this inﬁnite-dimensionality can cause complicated behavior of solutions to DDEs, theactual complexity of the dynamics depends on the “size of the time-lag.” To facilitate such an understanding,
it is necessary to develop a treatment of DDEs. In this talk, for retarded functional diﬀerential equations(RFDEs), which give a mathematical formulation of DDEs, we introduce a notion of “mild solutions” tolinear RFDEs for a purpose of dealing with “discontinuous history functions”, which is a barrier to thestudy of RFDEs.
6 西 口 純 矢 (東 北 大 A I M R )Junya Nishiguchi (Tohoku Univ.)

線型遅延微分方程式の解の基本系と基本行列解 · · · · · · · · · · · · · · · · · · · · · 15

Fundamental systems of solutions and fundamental matrix solutions tolinear delay diﬀerential equations

概 要 For a non-homogeneous linear RFDE, we consider how the solutions are expressed by using thesolutions to the homogeneous equation and the forcing term. By an analogy to non-homogeneous linear
ODEs, we call such a formula the variation of constants formula and ask “What is the fundamental matrix
solutions to the linear RFDE?” This is of course a fundamental question, and there is a long history of overﬁfty years. However, it is known that there is a conceptual diﬃculty which is peculiar to RFDEs. In thistalk, we resolve the diﬃculty by deﬁning fundamental matrix solutions to the linear RFDE as matrix-valued
milds solutions having discontinuous matrix-valued functions in their initial histories.
7 濱 本 直 樹 ( 阪 公 大 理)

Naoki Hamamoto (Osaka Metro. Univ.)

半平面上の渦なし場に対する Hardy 定数 · · · · · · · · · · · · · · · · · · · · · · · · · · 12

The Hardy’s constant for curl-free vector ﬁelds on the half-plane
R

R

|u|2
dx with the best constant C =RN |x|2
2
N
N∞(N − 2) /4 is well known when the test vector ﬁeld u : R → R is in Cc (RN ) and unconstrained. We are

概 要 The N -dimensional Hardy’s inequality

RN|∇u|2 dx ≥ Cinterested in how C can be improved when u is constrained by the curl-free condition curlu ≡ 0; however,when N = 2 such an improvement cannot be obtained. On the other hand, when the support of u is2
contained in the half space RN+ the best constant is known to be N /4 for unconstrained ﬁelds. In thissituation we treat the problem how C can be improved when u is a two-dimensional curl-free ﬁeld whose
support is contained in the half-plane R2+ .
8 勝 呂 剛 志 (熊 本 大 先 端) ♭ ある拡張エントロピーに対する対数型 Sobolev の不等式の安定性評価と不確定性関係への応用について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Takeshi Suguro (Kumamoto Univ.)

Stability estimates for the logarithmic Sobolev inequality for a generalized entropy and an application to the uncertainty relation inequality

概 要 We consider the logarithmic Sobolev inequality for the Tsallis entropy, which is a generalization of the

Boltzmann–Shannon entropy. We show the stability estimate for the logarithmic Sobolev inequality via the
Gagliardo–Nirenberg inequality. Moreover, we derive an extension of the uncertainty relation inequality.

Final: 2024/2/641函数方程式論

14:15〜16:15
9 只 野 之 英 ( 東 京 理 大 理)
中 村
周 ( 学 習 院 大 理)
三 上 渓 太 (理化学研iTHEMS)

Yukihide Tadano (Tokyo Univ. of Sci.)
Shu Nakamura (Gakushuin Univ.)(RIKEN)
Keita Mikami

Continuum limit for discretized elliptic operators on square lattice · · · 15

Continuum limit for discretized elliptic operators on square lattice概 要 In this talk, we consider the discretization of elliptic operators P = −Pj,k ∂xj aj,k (x)∂xk + V (x) on

Rd onto the square lattice hZd with mesh size h. We show that under the strictly ellipticity of aj,k anda certain assumption where V is not necessarily bounded, the above discretized operators converge to P
in the continuum limit. We also show that as an application the spectra and eigenfunctions of P can beapproximated by those of its discretization.
10 鈴 木貴 (阪 大 M M D S )渡 辺 一 雄 (北里大一般教育)
Takashi Suzuki (Osaka Univ.)
Kazuo Watanabe (Kitasato Univ.)

微分形式の界面消滅 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·5Interface vanishing of diﬀerential forms

概 要 We introduce d − δ systems on diﬀerential forms in Euclidean spaces and show the interface vanishingof the solution. This result generalizes the previous theorems on stationary and non-stationary Maxwell’sequation.
11 牧 田 慎 平 (北
中 安
淳 (京

大

理)

大

理)

Shimpei Makida (Hokkaido Univ.)
Atsushi Nakayasu (Kyoto Univ.)

Stability of metric viscosity solutions under Hausdorﬀ convergence · · · 15
Stability of metric viscosity solutions under Hausdorﬀ convergence

概 要 Recently, the domain perturbation problem for the Hamilton–Jacobi equation has been studied. In

this talk we investigate the stability of viscosity solutions of the Hamilton–Jacobi equations for a sequenceof domains that are not necessarily monotone. The proof is based on the relaxed half semilimit and acharacterization of the metric viscosity solutions in terms of squared distance functions.
12 上 野 竜 也 (神 奈 川 大 理)

Tatsuya Ueno (Kanagawa Univ.)

連立非線形キルヒホッフ・シュレディンガー方程式の劣臨界・臨界指数の場合の正値解の存在 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Existence of positive ground state solution of coupled nonlinear Kirchhoﬀ–
Schrödinger system for a subcritical and critical case

概 要 In this talk, we prove the existence of positive ground state solution of a nonlinear Kirchhoﬀ–

Schrödinger system with constant potentials for a subcritical case and critical case. We use a variational
technique, in particular, we consider a minimization problem on the Nehari–Pohozaev manifold corresponding
to the problem.
13 宮 本 安 人 (東 大 数 理)

Yasuhito Miyamoto (Univ. of Tokyo)

Exact Morse index of radial solutions for semilinear elliptic equations
with critical exponent on annuli · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Exact Morse index of radial solutions for semilinear elliptic equations
with critical exponent on annuli

概 要 We consider a Dirichlet problem of the Henon equation with a critical exponent on annuli. This

problem has exactly two radial solutions with n nodal domains. When the domain is a ball, the problem
has no positive solution due to Pohozaev identity. Therefore, it is interesting to study the case where theinner radius goes to zero. In this talk we study the Morse index of radial solutions. In particular, an exact
Morse index can be determined when the inner radius is small. Several estimates of the Morse index arealso obtained.

Final: 2024/2/6函数方程式論14 竹 村 春 希 (東 大 数 理)
宮 本 安 人 ( 東 大 数 理)
若 狭
徹 ( 九 工 大 工)Haruki Takemura (Univ. of Tokyo)
Yasuhito Miyamoto (Univ. of Tokyo)
Tohru Wakasa (Kyushu Inst. of Tech.)42

スカラーフィールド方程式の線形化問題における固有値の明示的表示 · · 15

Asymptotic formulas of the eigenvalues for the linearization of the scalarﬁeld equation

概 要 We give asymptotic formulas for all the eigenvalues of the linearization problem of the Neumann

problem for the scalar ﬁeld equation ε2 uxx − u + u3 = 0. The eigenvalues are classiﬁed into three categories.
The eigenvalues in the three categories respectively converge to −3, 0 and 1 as ε → 1. The number ofthe eigenvalues which converge to −3 is equal to the number of the interior and boundary peaks of thesolution of Neumann problem u. The number of the eigenvalues which converge to 0 is equal to the numberof the interior peaks of u. In this study, complete elliptic integrals and Jacobi’s elliptic functions play animportant role.
15 中 村 謙 太(熊本大数理科学総合教育センター)

Kenta Nakamura (Kumamoto Univ.)

分数階放物型 De Giorgi クラスの局所的性質 · · · · · · · · · · · · · · · · · · · · · · · 10

Local properties of fractional parabolic De Giorgi classes

概 要 This talk studies fractional parabolic De Giorgi classes of order s, p and renders the local boundedness

and the nonlocal weak Harnack estimate. I will present a brief sketch of the proof of my results as long as
time permits.
16 佐 藤 光 汰 朗 (東 北 大 理)
Kotaro Sato

(Tohoku Univ.)

準静的発展方程式の解の長時間挙動について · · · · · · · · · · · · · · · · · · · · · · · 15

Long-time behavior of solutions to some quasistatic evolution equation

概 要 We investigate long-time dynamics of strong solutions of the initial-boundary value problem for

diﬀerential equations of doubly-nonlinear type in this talk. More precisely, we characterize the stationary
limits of the global-in-time L2 -solutions as a solution to the corresponding stationary problem. Here, thelayer structure (or so-called comparison principle) of the equations plays an important role in the proof ofthe characterization of the limit.
16:30〜17:30

特別講演
後 藤 良 彰 ( 小 樽 商 大)

Yoshiaki Goto
(Otaru Univ. of Commerce)

超幾何積分とホモロジー・コホモロジー

Hypergeometric integrals —homology and cohomology

概 要 Hypergeometric integrals are deﬁned as integrals of the product of complex powers of polynomials. We

study hypergeometric integrals by using homology and cohomology groups with local coeﬃcients, so-called
twisted homology and cohomology groups. Many types of relations between hypergeometric functions canbe regarded as relations in (co)homology groups. Further, the intersection forms on (co)homology groups
are also useful tools. In this talk, I would like to show some examples that hypergeometric integrals arestudied by using twisted (co)homology groups and intersection forms.

Final: 2024/2/643函数方程式論

3 月 18 日（月）第 II 会場

9:30〜12:00
17 草 場 竜 之 介 (早 大 理 工)
小 澤
徹 ( 早 大 理 工)

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

Higher order asymptotic expansions for the complex Ginzburg–Landau
type equation in the supercritical case · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Higher order asymptotic expansions for the complex Ginzburg–Landau
type equation in the supercritical case

概 要 We present explicit asymptotic proﬁles with parabolic self-similarity of global solutions to the Cauchy

problem for the complex Ginzburg–Landau type equation in the super Fujita-critical case. Our approachis based on the integral representation of the CGL semigroup and Taylor expansions with respect to theboth space and time variables. We also discuss the optimal decay rate in time of the remainder for theasymptotic expansion.
18 小 波 津 晶 平 (東 京 理 大 理)

Shohei Kohatsu (Tokyo Univ. of Sci.)

Immediate smoothing of measure-valued population densities in a Keller–
Segel system with ﬂux limitation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Immediate smoothing of measure-valued population densities in a Keller–
Segel system with ﬂux limitation

概 要 We deal with a Keller–Segel system with ﬂux limitation. For the one-dimensional Keller–Segel system,

it is known that given any nonnegative measure-valued initial data, the system admits a global classicalsolution which is continuous at t = 0. The purpose is to show this immediate smoothing in the system forany dimension with the aid of eﬀect of ﬂux limitation.
19 石 田 祥 子 (千 葉 大 理)
横 田 智 巳 ( 東 京 理 大 理)
Sachiko Ishida (Chiba Univ.)
Tomomi Yokota (Tokyo Univ. of Sci.)

N 次元癌浸潤モデルに対する最大正則性原理を用いた大域可解性 · · · · · 10
Global solvability for N -dimensional tumor invasion models via themaximum Sobolev regularity

概 要 We consider the initial-boundary value problem for a degenerate chemotaxis model arising from tumor

invasion, in which the ﬁrst equation is ut = ∇ · (f (u, w)∇u − g(u)∇v). The diﬀusivity and the sensitivity
are assumed to fulﬁll f (u, w) ≥ um−1 (m > 1), 0 ≤ g(u) ≤ u(u + 1)α−1 (α ∈ R). It is shown that if
α + 1 = m + N4 (N ≥ 3), then for any initial data with small mass, the system possesses a global bounded
weak solution.
20 細 野 竜 也 (東 北 大 理) ♭ Global existence and boundedness of solutions to the 4D fully parabolic
P. Laurençotchemotaxis system with indirect signal production · · · · · · · · · · · · · · · · · 15
(CNRS・Univ. Savoie Mont Blanc)

Tatsuya Hosono (Tohoku Univ.)
Philippe Laurençot(CNRS/Univ. Savoie Mont Blanc)

Global existence and boundedness of solutions to the 4D fully parabolic
chemotaxis system with indirect signal production

概 要 We consider the Cauchy problem for the 4 dimensional fully parabolic chemotaxis system with indirect

signal production. In this talk, we show that the solution exists globally in time provided that the initial
mass is less than the value (8π)2 , known as the 4 dimensional threshold value whether the blow-up ofsolutions occurs or not. Furthermore some condition on the initial mass ensuring the boundedness ofsolutions is also obtained. This talk is based on a joint work with Philippe Laurençot (CNRS & Université
Savoie Mont Blanc).

Final: 2024/2/6函数方程式論21 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)

44

Convergence to traveling waves of predator-prey type reaction-diﬀusion
systems with equal diﬀusivity by utilizing a relative entropy · · · · · · · · · 15
Convergence to traveling waves of predator-prey type reaction-diﬀusion
systems with equal diﬀusivity by utilizing a relative entropy

概 要 Our aim is to construct a general framework to derive the asymptotic stability of traveling waves.

This method is universal in the sense that it works well for waves in many reaction-diﬀusion systems withequal diﬀusivities.
22 下 條 昌 彦 (都 立 大 理)
郭忠 勝 (Tamkang Univ.)郭珈 妤 (Providence Univ.)
Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)
Karen Guo (Providence Univ.)

Stability of monostable traveling waves in diﬀusive three-species competition systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Stability of monostable traveling waves in diﬀusive three-species competition systems

概 要 We discuss the asymptotic stability of traveling waves of diﬀusive three-species competition systems

under certain perturbations of initial data.
23 谷 口 雅 治 (岡山大異分野基礎研)
二 宮 広 和 ( 明 大 総 合 数 理)

Masaharu Taniguchi (Okayama Univ.)
Hirokazu Ninomiya (Meiji Univ.)

Traveling front solutions of dimension n generate entire solutions ofdimension (n − 1) in reaction-diﬀusion equations · · · · · · · · · · · · · · · · · · · 15
Traveling front solutions of dimension n generate entire solutions ofdimension (n − 1) in reaction-diﬀusion equations

概 要 Multidimensional traveling front solutions and entire solutions of reaction-diﬀusion equations havebeen studied intensively. To study the relationship between multidimensional traveling front solutions andentire solutions, we study the reaction-diﬀusion equation with a bistable nonlinear term. It is well known
that there exist multidimensional traveling front solutions with every speed that is greater than the speed ofa one-dimensional traveling front solution connecting two stable equilibria. In this paper, we show that thelimit of the n-dimensional multidimensional traveling front solutions as the speeds go to inﬁnity generates
an entire solution of the same reaction-diﬀusion equation in the (n − 1)-dimensional space.
24 谷 口 雅 治 (岡山大異分野基礎研)

Masaharu Taniguchi (Okayama Univ.)

Entire solutions with and without radial symmetry in balanced bistable
reaction-diﬀusion equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Entire solutions with and without radial symmetry in balanced bistable
reaction-diﬀusion equations

概 要 Let n ≥ 2 be a given integer. In this paper, we assert that an n-dimensional traveling front converges

to an (n − 1)-dimensional entire solution as the speed goes to inﬁnity in a balanced bistable reactiondiﬀusion equation. As the speed of an n-dimensional axially symmetric or asymmetric traveling front goesto inﬁnity, it converges to an (n − 1)-dimensional radially symmetric or asymmetric entire solution in abalanced bistable reaction-diﬀusion equation, respectively. We conjecture that the radially asymmetric
entire solutions obtained in this paper are associated with the ancient solutions called the Angenent ovals
in the mean curvature ﬂows.

Final: 2024/2/645函数方程式論13:00〜14:00
柳特別講演
青 (沖縄科学技術大)

Qing Liu(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Monge solutions of eikonal equations in metric spaces
Monge solutions of eikonal equations in metric spaces

概 要 In recent years, there has been rapid progress in the study of nonlinear partial diﬀerential equations ingeneral metric spaces, driven by applications in optimal transport, traﬃc ﬂows, control theory, data sciences
and many others. This talk provides a summary of recent results on the ﬁrst order Hamilton–Jacobi
equations in metric spaces, with emphasis on a special case of the eikonal equation.
We begin with a brief review of the theory of viscosity solutions, a well-established powerful tool for fully
nonlinear partial diﬀerential equations in the Euclidean space. We next discuss several recently developed
approaches to tackle the well-posedness of Hamilton–Jacobi equations in metric spaces. Our focus will beplaced on the notion of so-called Monge solutions to the eikonal equation, which was originally introduced
by Newcomb–Su (1995) as an equivalent alternative of viscosity solutions in the Euclidean case. We extend
their idea to metric spaces. Compared to other known notions of metric viscosity solutions, its advantage
lies in the convenience that it does not require any smooth test functions, whose existence is a signiﬁcantobstacle in general metric spaces.
It is possible to adapt this method to further study eikonal equation with a discontinuous or even only
integrable inhomogeneous term. In the last part of the talk, we present our recent results concerning thisproblem in metric measure spaces.

3 月 19 日（火）第 II 会場

9:45〜12:00
25 國 分 海 斗 (東 京 理 大 理)

Kaito Kokubu (Tokyo Univ. of Sci.)

On solitary wave solutions to dispersive equations with double power
nonlinearities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On solitary wave solutions to dispersive equations with double power
nonlinearities

概 要 We study semilinear elliptic equations with the fractional Laplacian in dimension 1. The equations

with single power nonlinearities have been observed by Weinstein (1987), Frank–Lenzmann (2013), and soon. We focus on the equations with double power nonlinearities and consider the existence of ground states.
26 中 橋渉 ( 東 京 理 大 理)
加 藤 圭 一 ( 東 京 理 大 理)
只 野 之 英 ( 東 京 理 大 理)

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

Non-smoothness of the fundamental solutions for Schrödinger equations
with super-quadratic and spherically symmetric potentials · · · · · · · · · · 15
Non-smoothness of the fundamental solutions for Schrödinger equations
with super-quadratic and spherically symmetric potentials

概 要 We consider non-smoothness of the fundamental solution for the Schrödinger equation with a spheri-

cally symmetric and super-quadratic potential in the sense that V (x) ≥ C|x|2+ε at inﬁnity with constants
C > 0 and ε > 0. Yajima(1996) has shown that if V is super-quadratic and the spatial dimension is one,then the fundamental solution E(t, x, y) is not smooth anywhere with respect to (t, x, y). In this talk, weshow that the fundamental solution E(t, x, y) does not belong to C 1 as a function of (t, x, y) if V is aspherically symmetric and super-quadratic potential, the spatial dimension is larger than or equals to 4.

Final: 2024/2/6函数方程式論27 瀧 澤駿 ( 東 京 理 大 理)

Shun Takizawa (Tokyo Univ. of Sci.)

46

Short-time asymptotics of the fundamental solutions for Schrödinger
equations with non-smooth potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Short-time asymptotics of the fundamental solutions for Schrödinger
equations with non-smooth potentials

概 要 We consider short-time asymptotic behaviors of the fundamental solutions for Schrödinger equations

with potentials which are time-dependent and at most quadratic growth. Fujiwara (1980) has studied
asymptotic behaviors of the fundamental solutions in the case where potentials are smooth. The purposeof this talk is to show in the case where potentials are non-smooth.
28 波 多 間 備 (京 大 数 理 研)
山 本 拓 人 ( 京 大 数 理 研)
Sonae Hadama (Kyoto Univ.)
Takuto Yamamoto (Kyoto Univ.)

無限量子系に対する Hartree 方程式の殆ど確実な局所解の存在 · · · · · · · · 15

Almost sure existence of local solutions to the Hartree equation forinﬁnite quantum systems

概 要 This talk focuses on the Cauchy problem of the Hartree equation for inﬁnite quantum systems. The

Strichartz estimates for orthonormal systems play an essential role in this problem. The initial data is givenin the Schatten classes, and the orthonormal Strichartz estimates determine the optimal Schatten exponents
α. Consequently, when relying solely on deterministic estimates to manage the initial data terms, we cannot
construct any solutions for initial data in Schatten classes with exponents greater than α. However, we cango beyond this limitation by introducing a randomization of initial data. In this talk, we will ﬁrst establish
probabilistic Strichartz estimates and then apply them to the Hartree equation. Finally, we obtain local
solutions for initial data in bigger Schatten classes than the deterministic Strichartz estimates allow.
29 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.)

3 次元 Dirac 方程式の平滑化評価式の最良定数 · · · · · · · · · · · · · · · · · · · · · 15
Optimal constants of smoothing estimates for the 3D Dirac equation

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 optimal constants for the 3-dimensional free Dirac equation.
30 田 中 智 之 (同 志 社 大 理 工)
( Univ. Tours )L. Molinet

Tomoyuki Tanaka (Doshisha Univ.)(Univ. Tours)
Luc Molinet

Improved bilinear Strichartz estimates with application to the wellposedness of periodic generalized KdV type equations · · · · · · · · · · · · · · 15
Improved bilinear Strichartz estimates with application to the wellposedness of periodic generalized KdV type equations

概 要 We consider the Cauchy problem for one-dimensional dispersive equations of KdV type on the torus.

Our main new ingredient is the replacement of improved Strichartz estimates with improved bilinear
estimates so as to treat the worst resonant interactions. As a result, we obtain the unconditional wellposedness for the generalized KdV equation in H s (T) for s > 1/2. Our result also holds for more generalequations whose dispersive operator behaves for high frequencies as a Fourier multiplier with the symboli|ξ|α ξ for 1 ≤ α ≤ 2. We remark that our methods work for the real line case as well.

Final: 2024/2/647函数方程式論31 佐 藤 拓 也 (熊 本 大 先 端) ♭ Optimal L2 -decay rate of solutions to dissipative nonlinear Schrödinger
equations in the analytic class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Takuya Sato (Kumamoto Univ.)

Optimal L2 -decay rate of solutions to dissipative nonlinear Schrödinger
equations in the analytic class

概 要 We consider the Cauchy problem of one dimensional dissipative nonlinear Schrödinger equations witha critical power nonlinearity. In this talk, we show that L2 -decay rate obtained in the previous work is
optimal in the analytic class.
14:15〜16:00
32 川 上 隼 平 (京大理)Jumpei Kawakami (Kyoto Univ.)

Scattering and blow up for nonlinear Schrödinger equation with theaveraged nonlinearity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Scattering and blow up for nonlinear Schrödinger equation with theaveraged nonlinearity

概 要 We consider a 3-dimensional nonlinear Schrödinger equation with average nonlinearity. This is a

generalized model of the resonant system of an NLS with a partial harmonic oscillator in terms of nonlinear
power. We provide a new proof for the conservation law of kinetic energy and remove the restriction on
nonlinearity. Moreover, in the focusing, super-quintic, and sub-nonic cases, we construct a ground-statesolution and classify the behavior of the solutions below the ground state. We demonstrate a sharp thresholdfor scattering and blow-up.
33 宮 﨑 隼 人 (香 川 大 教 育)
川 本 昌 紀 ( 愛 媛 大 理 工)

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

時間減衰する調和振動子を持つ非線形シュレディンガー方程式の修正散乱作用素について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Modiﬁed scattering operator for nonlinear Schrödinger equations witha time-decaying harmonic potential

概 要 We consider nonlinear Schrödinger equations with a time-decaying harmonic potential. The nonlin-

earity is gauge-invariant of the long-range critical order. Kawamoto and Muramatsu show that the equation
admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in theframeworks of both the ﬁnal state problem and the initial value problem. Also, in the equation without
the potential, Hayashi and Naumkin establish the existence of a modiﬁed scattering operator. In thistalk, we construct a modiﬁed scattering operator for our equation by utilizing a generator of the Galileantransformation.
34 北 村 駿 介 (東 北 大 理) ♭ 非コンパクト台の初期値を持つ空間変数重み付き半線形波動方程式の古典解の lifespan 評価 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Shunsuke Kitamura (Tohoku Univ.)

Lifespan of solutions of one dimensional semilinear wave equations withspatial weights and not-compactly supported data

概 要 In this talk,I will report on the lifespan estimates of time-local classical solutions of semilinear wave

equations with spatial weights and non-compactly supported data in one space dimension. Lifespan means
the maximum existence time of solutions. There are cases where no time-local solution exists due to thespatial weight of the nonlinear term and the decay of the initial data.

Final: 2024/2/6函数方程式論35 肥田野久二男 (三 重 大 教 育)横 山 和 義 (北海道科学大工)(Mie Univ.)
Kunio Hidano
Kazuyoshi Yokoyama(Hokkaido Univ. of Sci.)

48

Global existence for a 2-speed and 3-component semilinear system ofwave equations in 3D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Global existence for a 2-speed and 3-component semilinear system ofwave equations in 3D

概 要 This talk is concerned with global existence of small solutions to a two-speed and three-component

system with quadratic nonlinear terms in 3D that so far has fallen beyond the capability of existing
techniques. At the price of assuming radial symmetry, we resort to a point-wise estimation approach.
The proof of global existence is based on the iteration argument using only weighted sup norms. Our
weight functions are useful in observing that gain of time decay occurs in the product of derivatives of two
components with diﬀerent propagation speeds. This gain compensates for a small loss of decay of a certain
component. Gain of time decay is observed also for “the tangential derivatives”, and we thereby allow forsome null forms in the nonlinear terms.
大理)
36 岡 本葵 (阪P. de Roubin (Univ. of Edinburgh)

Mamoru Okamoto (Osaka Univ.)
Pierre de Roubin (Univ. of Edinburgh)

粘性効果を含む非線形波動方程式の初期値問題の非適切性 · · · · · · · · · · · 15

Ill-posedness of the Cauchy problem for the viscous nonlinear wave equation

概 要 We consider the Cauchy problem for the viscous nonlinear wave equation. We show the ill-posedness

in negative Sobolev spaces of the Cauchy problem for polynomial nonlinearity. In particular, we prove anorm inﬂation result above the scaling critical regularity in some cases.
37 M. A. Hamza(Imam Abdulrahman Bin Faisal Univ.)
若 杉 勇 太 (広島大先進理工)吉 川 周 二 ( 大 分 大 理 工)
Mohamed Ali Hamza(Imam Abdulrahman Bin Faisal Univ.)
Yuta Wakasugi (Hiroshima Univ.)
Shuji Yoshikawa (Oita Univ.)

Asymptotic proﬁles for the Cauchy problem of damped beam equation
with two variable coeﬃcients and derivative nonlinearity · · · · · · · · · · · · 10

Asymptotic proﬁles for the Cauchy problem of damped beam equation
with two variable coeﬃcients and derivative nonlinearity

概 要 We study the asymptotic behavior of solutions to the Cauchy problem of nonlinear damped beam

equation with time-dependent coeﬃcients. We give a conjecture of the classiﬁcation of the asymptotic
behavior of solutions depending on the coeﬃcients, and show a partial answer for the case of parabolic-type
behavior.

Final: 2024/2/649

函数方程式論

16:15〜17:15

2023 年度 (第 22 回) 日本数学会解析学賞受賞特別講演
太 田 雅 人 (東 京 理 大 理) ♭ 非線形シュレディンガー方程式に対する定在波の強不安定性解析

Masahito Ohta (Tokyo Univ. of Sci.)

Strong instability analysis of standing waves for nonlinear Schrödinger
equations概 要 A typical equation considered in this talk is the following nonlinear Schrödinger equation (NLS):i∂t u = −∆u + |x|2 u − |u|2 u,(t, x) ∈ R × R3 .

It is known that for any ω ∈ (−3, ∞) there exists a unique positive solution (ground state) ϕω (x) of thestationary problem −∆ϕ + |x|2 ϕ + ωϕ − |ϕ|2 ϕ = 0 in the energy space X := {v ∈ H 1 (R3 ) : |x|v ∈ L2 (R3 )}.
A standing wave solution eiωt ϕω (x) of (NLS) is said to be stable if for any ε > 0 there exists δ > 0such that if ku0 − ϕω kX < δ then the solution u(t) of (NLS) with u(0) = u0 exists globally and satisﬁes
inf{ku(t) − eiθ ϕω kX : θ ∈ R} < ε for all t ∈ [0, ∞). Otherwise, eiωt ϕω (x) is said to be unstable. On
the other hand, eiωt ϕω (x) is said to be strongly unstable if for any ε > 0 there exists u0 ∈ X such thatku0 − ϕω kX < ε and the solution u(t) of (NLS) with u(0) = u0 blows up in ﬁnite time. In this talk, we will
review the strong instability of standing wave solutions for some nonlinear Schrödinger equations.

3 月 20 日（水）第 II 会場

10:00〜12:00
38 高 山 正 宏 (慶 大 理 工)
井 口 達 雄 ( 慶 大 理 工)

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

吊り下げられた紐の運動に対する解のアプリオリ評価 · · · · · · · · · · · · · · · 15

A priori estimates for solutions to the motion of an inextensible hanging
string

概 要 We consider the initial boundary value problem to the motion of an inextensible hanging string ofﬁnite length under the action of the gravity. In this problem, the tension of the string is also an unknown
quantity. It is determined as a unique solution to a two-point boundary value problem, which is derived fromthe inextensibility of the string together with the equation of motion, and degenerates linearly at the freeend. We derive a priori estimates for solutions to the initial boundary value problem in weighted Sobolev
spaces under a natural stability condition. The necessity for the weights results from the degeneracy of thetension. Uniqueness of solution is also proved.
39 江 口 太 一 (早 大 理 工)
Taichi Eguchi (Waseda Univ.)

The energy equality of the magnetohydrodynamic system in the framework of Lorentz–Besov spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The energy equality of the magnetohydrodynamic system in the framework of Lorentz–Besov spaces

概 要 We ﬁnd a new criterion of the Lorentz–Besov spaces to establish the energy equality of the incompress-

ible magnetohydrodynamic (MHD) system in R3 . In the Navier–Stokes equations, Cheskidov–Luo (2020)
obtained the energy equality if the weak solution belongs to the class of the Lorentz–Besov spaces that are
1/3

not contained in the classical Onsager space L3 (0, T ; B3,∞ ). Motivated by Cheskidov–Luo (2020), we obtaina new criterion of the Lorentz–Besov spaces to establish the energy equality of the MHD system. We may
regard our criterion on the MHD system as a generalization of the criterion of Cheskidov–Luo (2020).

Final: 2024/2/6函数方程式論50(TU Darmstadt)
40 T. Binz
飯 田 祥 樹 ( 早 大 理 工)

Uniqueness of weak solutions to the primitive equations in some anisotropic
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

(TU Darmstadt)(Waseda Univ.)

Uniqueness of weak solutions to the primitive equations in some anisotropic
spacesTim Binz
Yoshiki Iida

概 要 We consider the three dimensional primitive equations for large scale oceanic and atmospheric dynam-

ics. The uniqueness of weak solutions to the system is still open. In this talk, based on regularity in termsof Besov spaces, we give a new class in which the uniqueness holds, and compare with the known result by
Tachim Medjo (2010). The proof of our result is basically relied on Littlewood–Paley theory argument.
41 顧
仲 陽 ( 東 大 数 理)コ
キ ン ( 東 大 数 理)
米 田
剛 ( 一 橋 大 経 済)Zhongyang Gu (Univ. of Tokyo)(Univ. of Tokyo)
Xin Hu(Tsuyoshi Yoneda Hitotsubashi Univ.)

Anomalous smoothing eﬀect on the incompressible Navier–Stokes–Fourier
limit from Boltzmann with periodic velocity · · · · · · · · · · · · · · · · · · · · · · · 10
Anomalous smoothing eﬀect on the incompressible Navier–Stokes–Fourier
limit from Boltzmann with periodic velocity

概 要 Adding a nontrivial term composed from a microstructure, we prove the existence of a global-in-timeweak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier–Stokes–Fouriersystem for arbitrary initial data. It cannot be expected to directly derive the energy inequality for this new
system of equations. The main idea is to employ the hydrodynamic limit from the Boltzmann equation
with periodic velocity and a specially designed collision operator.
42 小 泉 祐 太 (早 大 理 工)
Yuta Koizumi (Waseda Univ.)

Convergence of approximating solutions of the Navier–Stokes equations
in higher ordered Sobolev norms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Convergence of approximating solutions of the Navier–Stokes equations
in higher ordered Sobolev norms

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

Kato (1984) with the initial data u(0) ∈ Lnσ (Rn ) converge to the local strong solution u in the topology of
W k,q (Rn ) for all k ∈ N provided the convergence in the scaling invariant norm in Lq (Rn ) with the timeweight holds. As an application of our convergence, it is clariﬁed that the approximation of the pressure isestablished in W k+1,q (Rn ).
43 中 塚 智 之 (松 山 大 経 済)
Tomoyuki Nakatsuka(Matsuyama Univ.)

Existence of time-periodic strong solutions to the Navier–Stokes equation in the whole space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence of time-periodic strong solutions to the Navier–Stokes equation in the whole space

概 要 In this talk, the existence of time-periodic strong solutions to the Navier–Stokes equation in Rn isestablished under a suitable smallness condition on the external force. Our analysis is based on splitting
periodic solutions into steady and purely periodic parts. One advantage of this decomposition is theavailability of slightly more regularity in time of the purely periodic part. We apply this property toconstruct time-periodic solutions of the Navier–Stokes equation with information on the classes of theirsteady and purely periodic parts.

Final: 2024/2/651函数方程式論

14:15〜15:15
44 牛 越 惠 理 佳(横浜国大環境情報・阪大基礎工)
岡 部 考 宏 ( 阪 大 基 礎 工)
菅 野 晴 瑠 (横浜国大環境情報)
Erika Ushikoshi(Yokohama Nat. Univ./Osaka Univ.)
Takahiro Okabe (Osaka Univ.)
Haru Kanno (Yokohama Nat. Univ.)

時間依存領域における Helmholtz–Weyl 分解と Navier–Stokes 方程式の時間周期解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Helmholtz–Weyl decomposition on a time dependent domain for time
periodic Navier–Stokes ﬂow

概 要 We consider the Helmholtz–Weyl decomposition on a time dependent bounded domain Ω(t) in R3 .

Especially, we investigate the domain dependence of each component in the decomposition, namely, theharmonic vector ﬁelds (i.e., div and rot free vectors), vector potentials, and scalar potentials equipped withsuitable boundary conditions, when Ω(t) moves along to t ∈ R. As an application, we construct a time
periodic solution of the incompressible Navier–Stokes equations for some large boundary data with non-zero
ﬂuxes.
45 寺 本 惠 昭
西 田 孝 明 ( 京 大 情 報)
Yoshiaki Teramoto
Takaaki Nishida (Kyoto Univ.)

Decay of solutions to the initial boundary value problem of the Stokes
system in the halfspace · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Decay of solutions to the initial boundary value problem of the Stokes
system in the halfspace

概 要 The initial boundary value problem of the Stokes system in the 3D halfspace is considered. The

boundary condition subject on x3 = 0 is the balance of stress. Under certain conditions on the initial value
we derive the rate of decay in time of L2 norm of solutions to this problem. The solutions to an auxiliaryboundary value are estimated by residue analysis.
46 郭
柔 均 ( 早 大 理 工)大⋆)
柴 田 良 弘 (早Jou-chun Kuo (Waseda Univ.)
Yoshihiro Shibata (Waseda Univ.⋆)

L1 approach to the compressible viscous ﬂuid ﬂows in the half-space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
L1 approach to the compressible viscous ﬂuid ﬂows in the half-space

概 要 This talk is devoted to proving the local well-posedness for the Navier–Stokes equations describing theisotropic motion of the compressible viscous ﬂuid ﬂows in the half-space with non-slip boundary conditions.
s+1s
We construct a unique strong solution in the L1 in time and Bq,1
× Bq,1in space maximal regularity class.

Here, 1 < q < ∞ and −1 + N/q ≤ s < 1/q, where N ≥ 2 is the space dimension. The approach is by meansof the analytic semigroup theory and we use Lagrange transformation in order to eliminate the convection
term v · ∇ρ.

Final: 2024/2/6函数方程式論15:30〜16:30

52

特別講演

橋本伊都子
(金沢大理工・阪公大数学研)

流体方程式の球対称問題に関する流入及び流出問題について

Itsuko Hashimoto(Kanazawa Univ./Osaka Metro. Univ.)

Inﬂow and outﬂow problem on radially symmetric solution for ﬂuid
equation

概 要 We consider the boundary value problem of radially symmetric solutions for the multi-dimensional

Burgers equation and compressible Navier–Stokes equation on the exterior domain, where the boundary
and far ﬁeld conditions are prescribed. In this talk, we ﬁrst consider the existence of radially symmetricstationary solutions for both inﬂow and outﬂow problems. We also comment for the asymptotic stability ofthe obtained stationary solutions for both Burgers equation and compressible Navier–Stokes equation. Next
we consider the inviscid limit problem of the radially symmetric stationary solutions to compressible Navier–Stokes equation. In this consideration, we investigate the corresponding Euler equation and boundary layer
equation and their relations. Finally we clear the diﬀerence of the inviscid limit state between Inﬂow andoutﬂow problem.

Final: 2024/2/6
53

実函数論

実 函

数

3 月 19 日（火）論第 VI 会場

9:30〜12:00
1 伊 東 由 文
Yoshifumi Ito

公理的集合論 I の定義と存在定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Deﬁnition and existence theorem of the axiomatic set theory I

概 要 In this lecture, we give the complete system of axioms of the set theory I.

This is the combined system of axioms ZFC and the axiom of the ordinal numbers and the axiom of thetranscendental construction. Here the system of axioms of the set theory I is given in the new formulation.
We prove the existence theorem of the set theory I by constructing its model.
This is the ﬁnal and complete solution of the problem of the axiomatic set theory.
2 伊 東 由 文
Yoshifumi Ito

ユークリッド幾何学の定義と存在定理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10Deﬁnition and existence theorem of Euclidean geometry

概 要 In this lecture, we deﬁne Euclidean geometry and prove its existence theorem by using the axiomatic

method.
In the present time, we know the complete set theory.
Thereby we can deﬁne the plane in the exact sense. Thus we use the notion of the point, the straight linein the plane.
Thereby we give the complete solution of the problem of the foundation of Euclidean geometry.
3 川 﨑 敏 治
拡張積分可能関数全体の空間構造について (II) · · · · · · · · · · · · · · · · · · · · · 15
(玉川大工・千葉大法経・千葉大理)
Toshiharu Kawasaki(Tamagawa Univ./Chiba Univ./Chiba Univ.)

On the structure of space of all extended integrable functions, II

概 要 In this talk, we expand the concept of integration and further discuss the structure of space of extended

integrable functions.
4 福 田 亮 治 ( 大 分 大 理 工)
本 田 あ お い ( 九 工 大 情 報 工)
岡 崎 悦 明 (ファジィシステム研)(Oita Univ.)
Ryoji Fukuda(
KyushuInst.
of Tech.)Aoi Honda
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

非加法的測度が導く L0 上の一様構造 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Uniform topogies on L0 with respect to a non-additive measure

概 要 Let L0 be a space of all measurable functions deﬁned on a non-additive measure space (Ω, µ). We

discuss the uniform topology on L0 , which is given by entourages Vε = {(f, g) | µ(|f − g| > ε) ≤ ε}(ε > 0). We give some equivalent conditions for this uniformness and these also equivalent conditions forthe uniformness of the measure algebra, which is naturally included in L0 .

Final: 2024/2/6
実函数論

5 山 口 哲 志 ( 茨 城 大 理 工)

Satoshi Yamaguchi (Ibaraki Univ.)

54

Bi-preduals of generalized Morrey spaces with variable growth condition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Bi-preduals of generalized Morrey spaces with variable growth condition

概 要 Let Lp,λ (Rd ) be the Morrey space. In 2015 Rosenthal and Triebel gave the proof that∞ (Rd )
Ccomp

Lp,λ (Rd ) ′′= Lp,λ (Rd ).

We consider generalized Morrey spaces Lp,ϕ (Rd ) with variable growth function ϕ : Rd × (0, ∞) → (0, ∞).
∞ (Rd )In this talk we extend the duality to Lp,ϕ (Rd ). Moreover, we characterize Ccomp

Lp,ϕ (Rd )by the meanvalue of functions in Lp,ϕ (Rd ).
6 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

A characterization of boundedness of composition operators on Orlicz–
Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A characterization of boundedness of composition operators on Orlicz–
Morrey spaces

概 要 In this talk, we introduce our recent result about the necessary condition on boundedness of compo-

sition operators to the Orlicz–Morrey space, which extends the result about the Morrey space by Hatano,
Ikeda, Ishikawa and Sawano in 2021. The composition operator is also called the Koopman operator and has
been applied to data science and dynamical system extensively. To show the necessary condition we provethe boundedness of the composition operator from a Orlicz–Morrey space to itself, which was introduced in
MSJ Autumn Meeting 2023 at Tohoku University. Next, we show that the product of the singular valuesof a Jacobi matrix is a positive constant. Finally, we ﬁnd a function in Orlicz–Morrey space satisfying theprevious step.
7 水 口 洋 康 (関西大システム理工)

Hiroyasu Mizuguchi (Kansai Univ.)

2 次元ノルムにより Pythagorean orthogonality を一般化する関係式 · · · 15
generalized relation of Pythagorean orthogonality by two-dimensionalnorms

概 要 The orthogonality relation in inner product spaces is simple, fruitful and interesting. When moving tonormed spaces, we have many possibilities to extend this notion. Pythagorean orthogonality is one of them.
The condition of Pythagorean orthogonality can be expressed by usual ℓ2 -norm k · k2 on R2 . So we consider
the generalized relation of Pythagorean orthogonality by two-dimensional norms. Similar to Pythagorean
orthogonality or other orthogonalities, we obtain three existence theorems on this generalized relation.
8 厚 芝 幸 子 (東京女大現代教養)
Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Approximation of ﬁxed points of monotone nonexpansive-type mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Approximation of ﬁxed points of monotone nonexpansive-type mappings

概 要 In this talk, we prove weak and strong convergence theorems for monotone nonexpansive-type map-

pings. We also study the asymptotic behavior of orbits of some nonlinear mappings.

Final: 2024/2/6
55

実函数論

14:15〜16:15
9 米 田

剛 ( 一 橋 大 経 済)

Tsuyoshi Yoneda (Hitotsubashi Univ.)

フーリエ変換の不確定性原理と機械学習の数理構造 · · · · · · · · · · · · · · · · · 15

Fourier uncertainty principle and mathemetial analysis on machine learning

概 要 Reservoir Computing (RC) is a type of recursive neural network (RNN), and there can be no doubtthat the RC will be more and more widely used for building future prediction models for time-series data,with low training cost, high speed and high computational power. In this talk, we clarify hidden structuresof input and recurrent weight matrices in RC neural networks, and show that such structures are closely
related to the Fourier uncertainty principle.
10 近 藤 恵 夢 (奈良女大人間文化)
森 藤 紳 哉 ( 奈 良 女 大 自 然)

Emu Kondo (Nara Women’s Univ.)
Shinya Moritoh (Nara Women’s Univ.)

非増加関数に対する重み付き Hardy の不等式と doubling condition について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weighted Hardy’s inequality for nonincreasing functions and the doubling condition for weights

概 要 The aims of my talk are to state a limiting case of weighted Hardy’s inequality and to give a simple

proof of it by using the doubling condition for weights.
11 原 田 真 衣 (神 奈 川 大 工)
山 崎 教 昭 ( 神 奈 川 大 情 報)
Mai Harada (Kanagawa Univ.)
Noriaki Yamazaki (Kanagawa Univ.)

再感染を考慮した SIRS モデルの時間周期解の存在について · · · · · · · · · · 15

On the existence of time periodic solutions for the SIRS model with theseasonally-dependent transmission rate

概 要 We consider periodic problems for SIRS models with the seasonally-dependent transmission rate.

Then, we prove the existence of time-periodic solutions to our problems.
12 鵜 飼 直 孝 (千 葉 大 教 育)
水 野 大 樹 (千葉大融合理工)白 川
健 ( 千 葉 大 教 育)(George Mason Univ.)
H. Antil(Chiba Univ.)
Naotaka Ukai
(Chiba Univ.)
Daiki Mizuno
Ken Shirakawa (Chiba Univ.)
Harbir Antil (George Mason Univ.)

画像処理問題における方位調整を考慮する エネルギー勾配流 · · · · · · · · · 15

Anisotropic energy gradient system associated with image denoisingprocess with orientation adjustment

概 要 In this talk, we consider a gradient system of a non-convex functional, based on a governing energy

for anisotropic image denoising, as developed in [Berkels et al., SFB 611, 2006]. A characteristic of ourgradient system lies in the nonstandard part ∂γ ◦ R, which consists of the (set-valued) subdiﬀerential ∂γof an anisotropic metric γ ∈ W 1,∞ (R2 ), and a rotation matrix R ∈ C ∞ (R; R2×2 ). This part plays a keyrole in the orientation adjustment within the image denoising process. Under appropriate settings, we will
provide some mathematical observations for the gradient system using the time-discretization approach.

Final: 2024/2/6
実函数論

13 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.)

56

凝固現象を考慮した結晶粒界運動の擬放物型フェーズ・フィールドモデル· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Pseudo-parabolic phase-ﬁeld model of grain boundary motion with solidiﬁcation eﬀect

概 要 In this talk, we deal with a coupling system consisting of Allen–Cahn equation with singular typediﬀusion and Kobayashi–Warren–Carter type system with pseudo-parabolicity. This system is based on theϕ-η-θ model, which is proposed by [Kobayashi, RIMS Kokyuroku, 1210, 68–77 (2001)] as a mathematicalmodel of grain boundary motion with solidiﬁcation. In this system, the main characteristics are the strong
singularity in the diﬀusions and variable-dependent mobilities, and these characteristics make it diﬃcult
to guarantee important mathematical properties, including the uniqueness of solutions. To address these
problems, we consider a system modiﬁed by introducing pseudo-parabolic structure, which delivers bettersmoothness to the solution. Based on the above, we set our goal to discuss solvability, uniqueness, andregularity results of the system.
14 山 崎 教 昭 (神 奈 川 大 情 報)
( Univ. of Pavia )P. Colli
M. H. Farshbaf-Shaker
(
)
WIAS
白 川
健 ( 千 葉 大 教 育)

Noriaki Yamazaki (Kanagawa Univ.)
Pierluigi Colli (Univ. of Pavia)
M. Hassan Farshbaf-Shaker (WIAS)Ken Shirakawa (Chiba Univ.)

Approximate methods for optimal control problems of the Frémondmodel for shape memory alloys · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Approximate methods for optimal control problems of the Frémondmodel for shape memory alloys

概 要 In this talk, we consider optimal control problems for the one-dimensional Frémond model for shapememory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potentialof dissipation. The state problem is expressed by a system of partial diﬀerential equations involving thebalance equations for energy and momentum. We prove the existence of an optimal control that minimizes
the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary conditionof the optimal pair by using optimal control problems for approximating systems.
16:30〜17:30

特別講演

松 下 慎 也
(秋田県立大システム科学技術)

不動点アルゴリズムとその応用

Shin-ya Matsushita (Akita Pref. Univ.)

Fixed point algorithms and their applications

概 要 The main purpose of this talk is to present some current progress about the ﬁxed point algorithms.

This talk consists of two parts. The ﬁrst part deals with the theory of nonexpansive mapping in Hilbert
spaces and some ﬁxed point algorithms. The second part focuses on the many diﬀerent interpretations ofnonexpansve mappings and algorithms, and describes their connections to many other topics in optimization
and applied mathematics.

Final: 2024/2/6
57

実函数論

3 月 20 日（水）第 VI 会場

9:30〜12:00
15 赤 川 佳 穂 (岐 阜 工 高 専)
松 井 一 徳 ( 成 蹊 大 理 工)
Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)
Kazunori Matsui (Seikei Univ.)

ある弾塑性モデルを記述する仮似変分不等式の閾値関数の非負値性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Nonnegativity of the threshold function in an elastoplasticity model
based on quasi-variational inequality

概 要 This paper discusses the nonnegativity of the threshold function in the elastoplasticity model based on

quasi-variational inequality. In the previous work, the existence of a solution is proved under the assumptionthat the threshold function is strictly positive. In physical terms, it is natural that the threshold function
is nonnegative. Therefore, it is meaningful to discuss the well-posedness under the weaker assumption. To
prove the existence of a solution to the elastoplasticity model, we construct the concrete projection of theconstraint set.
16 垣 内花 ( 日 本 女 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)

Hana Kakiuchi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

放物型方程式の連立系に対する自由境界問題の可解性について · · · · · · · · 15

Solvability of free boundary problems for the parabolic equation system

概 要 We consider a free boundary problem for a system of two parabolic equations on the one-dimensional

space interval. The problem has been proposed as a mathematical model for a baking bread process in a
hot oven. In the modeling we assume that the region consists of crumb, crust, and the evaporation front.
The unknown functions of the problems are the position of the evaporation front which is regarded as thefree boundary, the temperature ﬁeld, and the mass distribution. Here, the temperature ﬁeld and the mass
distribution satisfy the standard parabolic equations in the crumb and crust regions, which are separated
by the free boundary. We discuss about solvability of the approximation problem in the present talk.
17 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.)

水分移動モデルに対する有限体積法を用いた数値解の収束 · · · · · · · · · · · 15

Convergence of approximation solutions obtained by the ﬁnite volume
method in moisture transport model

概 要 We consider the initial boundary value problem for nonlinear parabolic equations with non-monotone

boundary conditions. The problem was already investigated as a mathematical model for moisture transportphenomena in porous materials. In our recent work, we have established existence and uniqueness of weaksolutions by the Schauder ﬁxed point theorem and the dual equation method, respectively. Since the proof
for the existence is not constructive, it is important to show convergence of numerical solutions. In thepresent result, by applying the ﬁnite volume method, we approximate the partial diﬀerential equations andprove that the sequence of approximation solutions converges to the weak solution. The key to the proof isa compact theorem for discretized functions.

Final: 2024/2/6
実函数論

18 小 杉 千 春 (山 口 大 理)
愛 木 豊 彦 ( 日 本 女 大 理)

Chiharu Kosugi (Yamaguchi Univ.)
Toyohiko Aiki (Japan Women’s Univ.)58

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強解の存在について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Existence of strong solutions for the energy conservation system representing motions of incompressible elastic curve on the plane

概 要 In this talk, we consider the energy conservation system for the beam equation with the nonlinear

stress function having singularity. In the previous meeting, we established existence and uniqueness of the
weak solution to this problem. Also, existence and uniqueness of the solution for the energy dissipative
system were already obtained. We note that the dissipative property is characterized by the viscosity
coeﬃcient. In this talk by showing that the sequence of the strong solution of the conservation system as
the viscosity coeﬃcient tends to 0, we prove the existence of the solution to the conservation system. In
our proof the well-known compact theorem plays an important role.
19 菅 原 佑 也 (東 京 理 大 理)
田 中 悠 也 ( 東 京 理 大 理)
横 田 智 巳 ( 東 京 理 大 理)

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

Regularizing property of a Keller–Segel system with density-dependent
sensitivity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Regularizing property of a Keller–Segel system with density-dependent
sensitivity

概 要 This talk deals with a parabolic–parabolic Keller–Segel system with density-dependent sensitivity. In

a Keller–Segel system with logistic source, Lankeit (2021) constructed global classical solutions for initial
data in L1 × W 1,2 . The purpose of this talk is to show existence of global classical solutions for initial datain L2 × (W 2,q ∩ W 1,2 ) with some q > 1 in a parabolic–parabolic Keller–Segel system with density-dependent
sensitivity.
20 小 波 津 晶 平 (東 京 理 大 理)

Shohei Kohatsu (Tokyo Univ. of Sci.)

Boundedness and blow-up of weak solutions to a chemotaxis systemwith ﬂux limitation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Boundedness and blow-up of weak solutions to a chemotaxis systemwith ﬂux limitation

概 要 We consider boundedness and ﬁnite-time blow-up in a chemotaxis system with ﬂux limitation.

When there is no logistic term, Tello (Comm. Partial Diﬀerential Equations; 2022; 47; 307–345) obtained
a condition such that ﬁnite-time blow-up occurs, however, the condition could still be improved. We
improved the condition for ﬁnite-time blow-up in the system within the framework of weak solutions. Also,
we established boundedness and ﬁnite-time blow-up of weak solutions to a chemotaxis system with ﬂux
limitation and logistic source.
21 千 代 祐 太 朗 (東 京 理 大 理)
F. G. Düzgün (Hecettepe Univ.)( Cagliari Univ. )S. Frassu
G. Viglialoro ( Cagliari Univ. )Yutaro Chiyo (Tokyo Univ. of Sci.)
Fatma Gamze Düzgün(Hecettepe Univ.)
Silvia Frassu (Cagliari Univ.)
Giuseppe Viglialoro (Cagliari Univ.)

Global existence and boundedness in a fully parabolic chemotaxis system with nonlocal source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Global existence and boundedness in a fully parabolic chemotaxis system with nonlocal source

概 要 This talk deals with a fully parabolic chemotaxis system with nonlocal source. In the case thatthe second equation is simpliﬁed by the elliptic one, global existence and boundedness have already beenobtained by Bian, Chen and Latos (Nonlinear Anal.; 2018; 176; 178–191). The purpose of this talk is toderive global existence and boundedness in the case that the second equation is parabolic.

Final: 2024/2/6
59

実函数論

( Univ. of Pavia )22 P. Colli
来 間 俊 介 ( 東 京 理 大 理)
L. Scarpa(Politecnico di Milano)
Pierluigi Colli (Univ. of Pavia)
Shunsuke Kurima (Tokyo Univ. of Sci.)
Luca Scarpa (Politecnico di Milano)

Convergence of a nonlocal phase ﬁeld system with inertial term · · · · · · 15

Convergence of a nonlocal phase ﬁeld system with inertial term

概 要 There are some studies on nonlocal-to-local convergence of evolution equations. For example, Davoli–

Scarpa–Trussardi (2021) and Abels–Terasawa (2022) have studied nonlocal-to-local convergence of Cahn–
Hilliard equations. On the other hand, regarding phase ﬁeld systems, in the case of a conserved phase ﬁeld
system related to entropy balance, nonlocal-to-local convergence has already been conﬁrmed (K. (2022)). In
this talk, we focus on convergence of a nonlocal phase ﬁeld system with inertial term to a parabolic-hyperbolic
phase ﬁeld system.
23 伊 藤 昭 夫
Akio Ito

Quasi-variational structural evolution inclusion with perturbation on areal Hilbert space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Quasi-variational structural evolution inclusion with perturbation on areal Hilbert space

概 要 We consider a Cauchy problem of a quasi-variational structural evolution inclusion on an abstract

real Hilbert space. The main purpose of this talk is to establish the abstract perturbation theory forevolution inclusions on real Hilbert spaces with quasi-variational structures by showing the existence ofstrong solutions on any ﬁnite interval, not strong global-in-time solutions. Moreover, it is applicable tothe tumor invasion system with quasi-variational degenarate diﬀusion for the movement of tumor cells,
which is treated in the paper, Quasi-variational Structure Approach to Systems with Degenerate Diﬀusions,
Rendiconti del Seminario Matematico della Universita di Padova, 147 (2022), 169–235.
14:15〜15:40
24 白 川健 ( 千 葉 大 教 育)
水 野 大 樹 (千葉大融合理工)(George Mason Univ.)
H. AntilKen Shirakawa (Chiba Univ.)(Chiba Univ.)
Daiki Mizuno(
GeorgeMason Univ.)
Harbir Antil

Optimal control problems governed by pseudo-parabolic gradient systems for KWC type energies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Optimal control problems governed by pseudo-parabolic gradient systems for KWC type energies

概 要 In this talk, we consider a class of optimal control problems governed by KWC type systems withpseudo-parabolicity. Here, KWC type system means a gradient system associated with KWC energy,
which was a free-energy of grain boundary motion proposed by [Kobayashi–Warren–Carter, Physica D,
140 (2000)]. In this study, we should be note that our state system admits a unique solution, evenunder unknown-dependent mobilities. Indeed, in previous works, unknown-dependent mobilities broughtsigniﬁcant diﬃculties in the observations of uniqueness and linearization for the KWC type system. In
view of this, we set the objective of this talk to establish a mathematical theory for optimization problems
governed by the KWC type system. The main focuses of this talk will be on the existence of the optimal
control, and the necessary conditions for the optimal control.

Final: 2024/2/6
実函数論

25 池 田 正 弘(理化学研 AIP・慶大理工)内 田俊 ( 大 分 大 理 工)
深 尾 武 史 (龍谷大先端理工)

Masahiro Ikeda (RIKEN/Keio Univ.)(Oita Univ.)
Shun Uchida
Takeshi Fukao (Ryukoku Univ.)

60

An approximation of evolution equation with clique expansion of hypergraph Laplacian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

An approximation of evolution equation with clique expansion of hypergraph Laplacian概 要 Hypergraph G is the triplet consisting of a ﬁnite set V , a family E ⊂ 2V , and w : E → (0, ∞).

We are concerned with an ODE governed by some nonlinear set-valued operator deﬁned on RV , whichis called “hypergraph Laplacian”. This ODE can be interpreted as a model of “heat” diﬀusion in the
network represented by hypergraph. In this talk, we consider the case where the heat at some vertices of
the hypergraph is given, and discuss the existence of solution and the continuous dependence of solution on
given data.
26 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.)

一般の平衡則方程式のエントロピー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 entropy
solutions of general balance laws

概 要 We consider the continuous dependence on the initial and ﬂux functions for the entropy solutions

to the Cauchy problem of general balance laws. In general, for the proof, it is necessary to assume thatthe ﬂux and source functions are continuously diﬀerentiable. However, without the assumption that thefunctions are continuously diﬀerentiable, under only the assumption that the functions are locally Lipschitz
continuous, we prove the continuous dependence on the initial and ﬂux functions for the entropy solutions.
27 熊 崎 耕 太 (京 都 教 育 大)
A. Muntean (Karlstad Univ.)

Kota Kumazaki (Kyoto Univ. of Edu.)
Adrian Muntean (Karlstad Univ.)

あるマルチスケールモデルの解の時間大域的挙動について · · · · · · · · · · · 15

Large-time behavior of a solution to a multiscale model

概 要 In this talk, we consider a multiscale model describing nonlinear phenomena in porous materials. Thismodel consists of a diﬀusion equation for the relative humidity distributed in materials and a free boundary
problem describing the water-ﬁlling process in microscopic pockets. We consider each microscopic pocket
as a one-dimensional interval and correspond the interval to each point of materials. In the previous result,
we have proved the existence and uniqueness of a globally-in-time solution to the model. In this talk, we
discuss the large-time behavior of a solution and investigate the steady state in each pocket.
28 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)

空間 4 階の動的境界条件を課した Allen–Cahn 方程式への発展方程式論
的接近 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Allen–Cahn equations with dynamic boundary conditions of fourthorder

概 要 In this study, we consider the initial and boundary value problem of the second-order parabolic

Allen–Cahn equation with the dynamic boundary condition of fourth-order Cahn–Hilliard type. As an
approximation problem, we consider an evolution equation governed by a subdiﬀerential and discuss thelimiting procedure approaching the target problem.

Final: 2024/2/6
61

実函数論

15:45〜16:45

2023 年度 (第 22 回) 日本数学会解析学賞受賞特別講演
田 中 直 樹 (静 岡 大 理) 発展方程式に対する抽象理論 —加藤による準線形理論に関連する話題を中心に—
Naoki Tanaka (Shizuoka Univ.) Abstract theory for evolution equations
概 要 This presentation provides an overview of recent advances in abstract theory for evolution equations,with a focus on topics related to the abstract quasi-linear theory pioneered by Kato. The signiﬁcant theme
is to explore strategies for weakening or eliminating stability, continuity with respect to the time variable,
and denseness of domains of operators imposed in Kato’s theory.
The discussion will begin by relaxing the strong continuity condition on the time variable, and our result
obtained under Carathéodory’s condition will be explained. Subsequently, a new concept of stability will be
proposed, and Kōmura’s conjecture regarding the well-posedness of an abstract degenerate wave equation
will be discussed.
Future topics, such as the well-posedness of an abstract quasi-linear evolution equation governed by a familyof non-densely deﬁned operators in a reﬂexive Banach space and the approximate solvability of diﬀerential
equations in a complete metric space, will be outlined. The former necessitates investigating a family of
operators that do not satisfy the known stability conditions. The latter is related not only to mutational
analysis but also to QDE theory, which is associated with product formulas for semigroups of operators.
17:00〜18:00

特別講演

黒 田 紘 敏 (北大理)Hirotoshi Kuroda (Hokkaido Univ.)

4 階の全変動流方程式の解の挙動について
On the behaviour of solutions to the fourth order total variation ﬂow
equation

概 要 We consider the fourth order total variation ﬂow equation. In the case of the second order, many

results are known. Typical results are presented for comparison with the case of the fourth order. We
characterize the solution in terms of what is called the Cahn–Hoﬀman vector ﬁeld for the fourth order case.
Next, we introduce a notion of calibrability of a set in our fourth order setting to explain the behaviourof solutions. This notion is related to whether a characteristic function preserves its form throughout theevolution. These concepts are used to discuss the relationship between the behaviour of solutions and spatial
dimensions and boundary conditions.

Final: 2024/2/6
函数解析学

函

数

解

3 月 17 日（日）

析

62

学

第 VII 会場

9:30〜11:00
1 渡 辺 秀 司 ( 群 馬 大 理 工)

Shuji Watanabe (Gunma Univ.)

外部磁場のあるときの超伝導の BCS 理論における Bogoliubov 変換とギャップ方程式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

The Bogoliubov transformation and the gap equation in the BCS modelof superconductivity with external magnetic ﬁeld

概 要 Under a simple condition, we derive the Bogoliubov transformation and the gap equation in the BCS

model of superconductivity with external magnetic ﬁeld.
2 佐
松
泉
井

々
澤
真
村

木
泰
之
航

格 ( 信 州 大 理)
道 ( 信 州 大 教 育)介 ( 信 州 大 理)
太 (長野県富士見高)

Itaru Sasaki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Shinnosuke Izumi (Shinshu Univ.)
Kouta Imura(Nagano Pref. Fujimi High School)

対相互作用模型の基底状態の収束半径について · · · · · · · · · · · · · · · · · · · · · 15

On the radius of convergence of the ground state in a pair interactionmodel

概 要 A year ago at the Mathematical Society of Japan we reported that the ground state and ground stateenergy of a pair interaction model are analytic with respect to the coupling constant. However, it was notenough to estimate the coupling constants such that the Maclaurin series converges. We have improved theproof and extended it to what we consider to be the best possible value.
3 只 野 之 英 ( 東 京 理 大 理)
中 村
周 ( 学 習 院 大 理)
三 上 渓 太 (理化学研iTHEMS)

Yukihide Tadano (Tokyo Univ. of Sci.)
Shu Nakamura (Gakushuin Univ.)(RIKEN)
Keita Mikami

Continuum limit for Laplace operators on lattices · · · · · · · · · · · · · · · · · · 15

Continuum limit for Laplace operators on lattices

概 要 We consider Laplace operators deﬁned on lattices with mesh size h and those operators with per-turbations of potentials. We prove that the above operators converge to certain elliptic operators in thecontinuum limit from the view point of spectral theory. We obtain as an application the asymptotic behaviorof the spectra and eigenfunctions of the above operators.
4 廣 島 文 生 ( 九 大 数 理)

Fumio Hiroshima (Kyushu Univ.)

Positivity improving for the Nelson model with nonzero total momenta· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Positivity improving for the Nelson model with nonzero total momenta

概 要 It is shown that the strongly continuous semigroup generated by the Nelson Hamiltonian with zero

total momentum zero is positivity improving. It is also shown that the strongly continuous semigroup
generated by the Nelson Hamiltonian with nonzero total momentum zero is also positivity improving.
Moreover the similar results are obtained for the relativistic Nelson Hamiltonian.

Final: 2024/2/6
63

函数解析学

5 和 田 和 幸 ( 北 教 大 旭 川)
Kazuyuki Wada
(Hokkaido Univ. of Edu.)

量子ウォークの離散固有値に付随する固有関数の指数減衰性 · · · · · · · · · · 15

Exponential decay for eigenfunctions associated with discrete spectra ofquantum walks

概 要 In this talks, we show that eigenfunctions associated with discrete spectra of quantum walks posesses

exponential decay property. First, we estabsish the abstract theorem for unitary operators whose eigenvector
associated with discrete spectra has exponential decay property. We consider the d-dimensional 2d-state
quantum walks as an application.
14:15〜15:15

特別講演

A. Galtbayar(National Univ. of Mongolia)
Artbazar Galtbayar(National Univ. of Mongolia)

The Lp -boundedness of the wave operators for bi-Schrödinger operators
on R4
The Lp -boundedness of the wave operators for bi-Schrödinger operators
on R4

概 要 We prove that the wave operators for the fourth order Schrödinger operator ∆ 2 + V (x) in R4 arebounded in Lp (R4 ) for the set of p’s of (1, ∞) depending on the kind of spectral singularities of H at zero
which can be described by the space of bounded solutions of (∆2 + V (x))u(x) = 0.

3 月 18 日（月）第 VII 会場

9:30〜11:00
6 青 山 天 馬 ( 東 大 数 理)

Temma Aoyama (Univ. of Tokyo)

BenSaı̈d–Kobayashi–Ørsted 理論にもとづく熱核と Wiener 測度の変形· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Deformation of heat kernels and Wiener measures from the viewpointof BenSaı̈d–Kobayashi–Ørsted’s Laguerre semigroup theory

概 要 The BenSaı̈d–Kobayashi–Ørsted theory gives a generalization of the theory of metaplectic represen-tations, and metaplectic representations relate to a classical harmonic analysis including heat ﬂow. From
this perspective, we may consider a deformation of classical heat theory. In this talk, we examine whichbasic properties of the classical heat theory can be generalized and, by using these properties, we discuss aconstruction of a deformed Wiener measure.
7 久 保 利 久 ( 龍 谷 大 経 済)
( Aarhus Univ. )B. ØrstedToshihisa Kubo (Ryukoku Univ.)(Aarhus Univ.)
Bent Ørsted

The classiﬁcation and construction of projectively covariant diﬀerential
operators on RP2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
The classiﬁcation and construction of projectively covariant diﬀerential
operators on RP2

概 要 In contrast to conformal geometry, in which there are a large number of works on conformally covariant

diﬀerential operators, only a few results are known for projectively covariant diﬀerential operators. For
instance, the classiﬁcation of such diﬀerential operators for RP2 seems not in the literature, although thecase for RP1 was done by G. Bol in 1949. In this talk, we shall discuss the classiﬁcation and explicit
construction of projectively covariant diﬀerential operators on RP2 .

Final: 2024/2/6
函数解析学

8 甘 中 一 輝 ( 理 化 学 研)
(RIKEN)

Kazuki Kannaka

64

半単純 Lie 群の固有作用と Hurwitz–Radon 数 I · · · · · · · · · · · · · · · · · · · · · 15

Proper actions of semisimple Lie groups and the Hurwitz–Radon number I

概 要 Let G/H be a homogeneous space of reductive type and L a reductive Lie subgroup of G. We consider

the natural left action of L on G/H. When H is non-compact, the properness of this action often imposes
serious constraints on L.
In this talk, we introduce a certain condition for classical G/H (of possibly higher corank). Then I would
like to discuss a type of theorem stating that there are almost no semisimple Lie subgroups L that act
properly on G/H satisfying this condition. This talk is based on a joint work with Koichi Tojo (RIKEN).
9 東 條 広 一 ( 理 化 学 研)
(RIKEN)

Koichi Tojo

半単純 Lie 群の固有作用と Hurwitz–Radon 数 II · · · · · · · · · · · · · · · · · · · · 15

Proper actions of semisimple Lie groups and the Hurwitz–Radon number II

概 要 Let G ⊂ GL(N, C) be a classical Lie group and G/H a homogeneous space satisfying ”very evencondition”. We show that for ﬁxed n ∈ N, the condition that G/H admits a Spin(n, 1) proper action canbe described by the Hurwitz–Radon number (or its analogues) of the size N . This talk is based on a joint
work with Kazuki Kannaka (RIKEN).
10 笹 木 集 夢 (東 海 大 理)
Atsumu Sasaki(Tokai Univ.)

Weyl group of pseudo-Riemannian symmetric space · · · · · · · · · · · · · · · · 15
Weyl group of pseudo-Riemannian symmetric space

概 要 It is well-known that the Weyl group of a non-compact real semisimple Lie group coincides with the

Weyl group of the restricted root system of its Lie algebra. This talk considers the Weyl group W (G/H) ofpseudo-Riemannian symmetric space G/H. We show that W (G/H) is the same as the Weyl group of the
Lie group associated to G/H.
13:00〜14:00

特別講演

田 内 大 渡 ( 青 学 大 理 工)

Relationship between multiplicities of induced representations and orbit
decomposition on real and complex ﬂag varieties

Taito Tauchi (Aoyama Gakuin Univ.)

Relationship between multiplicities of induced representations and orbit
decomposition on real and complex ﬂag varieties

概 要 Let G be a real reductive algebraic group and H its real reductive algebraic subgroup. It was proved

by T. Kobayashi and T. Oshima that the ﬁniteness of the multiplicities of irreducible G-representations
in C ∞ (G/H) is equivalent to the real sphericity of G/H. Moreover, they also proved that the uniform
boundedness of the multiplicities in C ∞ (G/H) is equivalent to the sphericity of GC /HC , where GC andHC are complexiﬁcations of G and H, respectively. These theorems indicate a relationship between themultiplicities in C ∞ (G/H) and the orbit decomposition of the real and complex full ﬂag varieties withrespect to the action of H and HC , respectively. In this talk, a variant of this relationship will be discussed
by replacing the full ﬂag varieties with partial ﬂag varieties.

3 月 19 日（火）第 VII 会場

9:30〜11:30
11 渡 邉 恵 一 (新 潟 大 理)

Keiichi Watanabe (Niigata Univ.)

複素内積空間の開球におけるジャイロ演算について · · · · · · · · · · · · · · · · · 15

On gyro operations in open balls of complex inner product spaces

概 要 We present some results on structures which should be called as Moebius or Einstein gyrovector

spaces. They are introduced into an open balls centered at the origin of complex inner product spaces.

Final: 2024/2/6
65

函数解析学

潟
大⋆)
12 羽 鳥理 (新阿 部 敏 一 ( 茨 城 大 工)Osamu Hatori (Niigata Univ.⋆)
Toshikazu Abe (Ibaraki Univ.)

A Mazur–Ulam theorem on a GGV and its application · · · · · · · · · · · · · 15
A Mazur–Ulam theorem on a GGV and its application

概 要 We show a Mazur–Ulam theorem on a GGV and a revised proof. As an application, we show a rather

short proof of a known result about a characterization of the Thompson isometry on the positive cone ofthe positive invertible elements in a unital C ∗ -algebra.
13 森

迪 也 ( 東 大 数 理)

Michiya Mori (Univ. of Tokyo)

On the Scottish Book Problem 155 by Mazur and Sternbach · · · · · · · · · 15
On the Scottish Book Problem 155 by Mazur and Sternbach

概 要 Problem 155 of the Scottish Book asks whether every bijection U : X → Y between two Banach spaces

X, Y with the property that, each point of X has a neighborhood on which U is isometric, is globallyisometric on X. We prove that this is true under the additional assumption that X is separable and theweaker assumption of surjectivity instead of bijectivity.
14 瀬 尾 祐 貴 (大阪教育大教育)
Yuki Seo (Osaka Kyoiku Univ.)

幾何平均に関する数域半径不等式について · · · · · · · · · · · · · · · · · · · · · · · · · 15

On numerical radius inequalities related to geometric means

概 要 In this talk, we show numerical radius inequalities releted to geometric means of real power for positive

invertible operators, which estimates the upper and lower bounds of the α-geometric means in terms of thegeneralized Kantorovich constant.
15 伊 藤 公 智 (前 橋 工 科 大)Masatoshi Ito (Maebashi Inst. of Tech.)

Inequalities among the weighted Heinz mean and related ones · · · · · · · 15
Inequalities among the weighted Heinz mean and related ones

概 要 Recently Furuichi, Minculete and Moradi got an improvement of the weighted arithmetic-logarithmic-

geometric mean inequality. In this talk, as an extension of their result, we obtain inequalities among theweighted Heinz mean and related ones. Our approach is to consider the notion of a transpose symmetricpath of weighted means.
16 大 坂 博 幸 (立 命 館 大 理 工)
(Univ. of Bojnord)
M. Kian
M. S. Moslehian(Ferdowsi Univ. of Mashhad)

Hiroyuki Osaka (Ritsumeikan Univ.)
Mohsen Kian (Univ. of Bojnord)
Mohammad Sal Moslehian(Ferdowsi Univ. of Mashhad)

On characterization of matrix monotone decreasing functions · · · · · · · · 15

On characterization of matrix monotone decreasing functions

概 要 Relating to ﬁnding possible upper bounds for the probability of error for discriminating between two

quantum states, it is well-known thattr(A + B) − tr|A − B| ≤ 2tr(f (A)g(B))
holds for every positive-valued matrix monotone function f , where g(x) = x/f (x), and all positive deﬁnite
matrices A and B. In this talk, we present a characterization of matrix monotone decreasing functions
based on a matrix version of the above inequality.

Final: 2024/2/6
函数解析学

17 山 崎 丈 明 (東 洋 大 理 工)
大 坂 博 幸 ( 立 命 館 大 理 工)

Takeaki Yamazaki (Toyo Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)

66

The induced Aluthge sequence of compact operators · · · · · · · · · · · · · · · · 15
The induced Aluthge sequence of compact operators

概 要 We shall introduce convergence properties of iteration of the induced Aluthge transforms. In thistalk, we shall consider compact, AN and AM operators.
14:15〜15:45
18 磯 野 優 介 (京 大 数 理 研)
Yusuke Isono(Kyoto Univ.)

Haagerup and Størmer’s conjecture for pointwise inner automorphisms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Haagerup and Størmer’s conjecture for pointwise inner automorphisms

概 要 In 1988, Haagerup and Størmer conjectured that any pointwise inner automorphism of a type III 1

factor is a composition of an inner and a modular automorphism. We study this conjecture and provethat any type III1 factor with trivial bicentralizer indeed satisﬁes this condition. In particular, this showsthat Haagerup and Størmer’s conjecture holds in full generality if Connes’ bicentralizer problem has anaﬃrmative answer. Our proof is based on Popa’s intertwining theory and Marrakchi’s recent work on
relative bicentralizers.
19 後 藤 聡 史 (上 智 大 理 工)
Satoshi Goto

(Sophia Univ.)Ocneanu の ADE Dynkin 図形間 connection system の一般化 · · · · · · · · · 15
A generalization of Ocneanu’s ADE inter-Dynkin connection systems

概 要 We generalize Ocneanu’s ADE inter-Dynkin connection systems to the case of an arbitrary ﬁnite depth

subfactor with its maximal atlas. We also discuss how to determine the intermediate subfactor lattice of anirreducible subfactor arising from an irreducible bimodule in the maximal atlas. Kawahigashi’s “Quantum
Galois correspondence” and “a characterization of a ﬁnite-dimensional commuting square producing a
subfactor of ﬁnite depth” play a key role in this generalization.
20 曽 我 部 太 郎 (京大理) ♭ A duality of KK-theory and its application to the extensions of C*-

algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Taro Sogabe(Kyoto Univ.)

A duality of KK-theory and its application to the extensions of C*algebras

概 要 KK-theory gives a tool to understand the morphisms of operator algebras and if the K-groups of theoperator algebras are ﬁnitely generated one has a duality for the KK-groups which is called the Spanier–Whitehead K-duality. Many variants of this duality are studied in the context of the Poincare duality,
Paschuke’s duality and the dual algebras due to N. Higson. In this talk, I would like to talk about somecategorical description of this duality and its application to the theory of extensions of C*-algebras. I will
explain how to understand a duality of extensions of C*-algebras introduced by K. Matsumoto from theviewpoint of the Spanier–Whitehead K-duality.
21 縄 田 紀 夫 (阪 大 情 報)
Norio Nawata(Osaka Univ.)

W-absorbing actions of ﬁnite abelian groups · · · · · · · · · · · · · · · · · · · · · · · 15
W-absorbing actions of ﬁnite abelian groups

概 要 The Razak–Jacelon algebra W is the simple separable nuclear monotracial Z-stable C∗ -algebra which

is KK-equivalent to {0}. We say that an action γ of a ﬁnite group on W is W-absorbing if there exist
a simple separable nuclear monotracial C∗ -algebra A and an action α on A such that γ is conjugate toα ⊗ idW . In this talk, we shall show a classiﬁcation theorem for certain outer W-absorbing actions of ﬁnite
abelian groups.

Final: 2024/2/6
67

函数解析学

22 小 沢 登 高 (京 大 数 理 研)

Narutaka Ozawa (Kyoto Univ.)

Quasi-local operators and ﬁnite-propagation operators · · · · · · · · · · · · · · 15
Quasi-local operators and ﬁnite-propagation operators

概 要 This talk is about an operator theoretic aspect of Coarse Geometry. Every operator on (the ℓ2

space on) a uniformly locally ﬁnite metric space X that is approximable by ﬁnite-propagation operators is
quasi-local. Since introduced by J. Roe in 90s, it has been questioned whether the converse also holds true.
It is indeed the case, by Spakula and Zhang’s theorem (2018), if the metric space X is suﬃciently nice(namely, satisfying Yu’s property A). In this talk, I will report that the converse does not hold if the metricspace X contains a sequence of expanders.
16:00〜17:00

特別講演
武 石 拓 也 (京都工繊大基盤)

Takuya Takeishi (Kyoto Inst. Tech.)

代数体から構成される C*-環と関連する代数体の完全不変量について

C*-algebras constructed from number ﬁelds and related complete invariants of number ﬁelds

概 要 The study of C*-algebras from number theory originates from the work of Bost and Connes, but today

there are several other known constructions. The interesting point is that for certain classes of C*-algebras
from number theory, it is possible to show that those C*-algebras are isomorphic if and only if original
ﬁelds are isomorphic. In this talk, we summarize those kind of rigidity results. As a consequence of rigidity
results, we can see that the topological full groups of several groupoids from number theory are complete
invariants of number ﬁelds. We summarize recent developments on the homology of the topological fullgroup for a certain class.

Final: 2024/2/6
統計数学

統

計

3 月 17 日（日）9:30〜11:40
1 星 野 浄 生 ( 阪 公 大 数 学 研)

Kiyoiki Hoshino (Osaka Metro. Univ.)

数

68

学
第 III 会場

Characterization of the stochastic integral by the Riemann sum · · · · · · 15
Characterization of the stochastic integral by the Riemann sum

概 要 We consider the Riemann sum of the same type we introduced at the MSJ autumn meeting in 2020and discuss approximation and characterization of the stochastic integral with respect to a local martingale
by the Riemann sum. We extend the preceding result given at the meeting mentioned above mainly inthe following respect: (1) on the weight measures deﬁning the Riemann sum, (2) on the continuity of theintegrator and (3) on the uniform Riemann approximation of the stochastic integral.
2 山 戸 康 祐 (筑波大数理物質)
野 場
啓 ( 統 計 数 理 研)

Kosuke Yamato (Univ. of Tsukuba)
Kei Noba (Inst. of Stat. Math.)

Existence of quasi-stationary distributions of standard processes withno negative jumps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Existence of quasi-stationary distributions of standard processes withno negative jumps

概 要 I will talk about the existence of quasi-stationary distributions for standard processes with no negative

jumps killed at the boundaries. Quasi-stationary distributions are a kind of equilibrium state for Markov
processes with killing. For standard processes with no negative jumps, we can deﬁne a function called thescale function, which provides a simple representation of the exit times and the potential density. Using thescale function, we can generalize the methods that have been used for one-dimensional diﬀusions and Lévy
processes and provide necessary and suﬃcient conditions for the existence of quasi-stationary distributions.
3 甲 斐 大 貴 (京Hirotaka Kai

大理)(Kyoto Univ.)

Long time behavior of Lévy processes on manifolds · · · · · · · · · · · · · · · · · 15
Long time behavior of Lévy processes on manifolds

概 要 Applebaum constructs a Lévy process on Riemannian manifolds by projecting the solution to the

Marcus type stochastic diﬀerential equation on the orthonormal frame bundle, so called Elles–Elworthy–
Malliavin construction. In this talk, we will show that how the curvature of a Riemnnain manifold aﬀects
the properties of aLévy process. We reveal these eﬀects by introducing some estimates for the radial partof a Lévy process.
4 西 森 康 人 ( 阿 南 工 高 専)
Yasuhito Nishimori(Nat. Inst. of Tech., Anan Coll.)

Limiting distributions for particles near the frontier of spatially inhomogeneous branching symmetric stable processes · · · · · · · · · · · · · · · · · · · 15
Limiting distributions for particles near the frontier of spatially inhomogeneous branching symmetric stable processes

概 要 We discuss on the maximal displacement of the branching symmetric α-stable processes. Here, we

assume the branching rate measure is in the Kato class and it has a compact support on d-dimensional
Euclidean space. We show that the maximal displacement exponentially grows and its order is determinedby the index α and the spectral bottom of the corresponding Schrödinger-type operator. Then, we consider
the evolution of particles near the frontier and determine the limiting distribution of these particles.
5 濱 名 裕 治 (筑波大数理物質)

Yuji Hamana (Univ. of Tsukuba)

ブラウン運動の到達時刻と到達位置の末尾確率の漸近展開について · · · · 10

Asymptotic expansion for the tail probability of the hitting time andsite of Brownian motion

概 要 We consider the large time asymptotics for the tail probabitity of the ﬁrst hitting time of Brownian

motion with the ﬁxed arrival site. We give the ﬁrst three terms in the three dimensional cases. In the twodimensional case, we show that the tail probability admits an asymptotic expanson in powers of 1/ log t.

Final: 2024/2/6
69

統計数学

6 簗 島
瞬 ( 都 立 大 理)
石 谷 謙 介 ( 都 立 大 理)

Shun Yanashima (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

2 曲線間に留まるよう条件付けられたランダムウォーク橋に対する不変原
理 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An invariance principle for random walk bridges conditioned to stay
between two curves

概 要 Brownian house-moving is a stochastic process that plays an important role in computing higher-

order Greeks for barrier options. It was introduced by Ishitani, Hatakenaka, and Suzuki (2020). In thispresentation, we construct Brownian house-moving in a diﬀerent way from their previous work. Speciﬁcally,
we construct Brownian house-moving as the weak limit of Gaussian random walk bridges conditioned tostay between two curves.
7 西 野 颯 馬 ( 都 立 大 理)
石 谷 謙 介 ( 都 立 大 理)

Soma Nishino (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

Higher order integration by parts formulae for Wiener measures on apath space between two curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Higher order integration by parts formulae for Wiener measures on apath space between two curves

概 要 The ﬁrst order integration by parts formulae for Wiener measures on a path space between two

curves are already known. In this talk, we extend this result to the higher order integration by parts.
In the case of higher order, non-trivial boundary terms, which are absent in the conventional ﬁrst ordercase, appear additionally. Furthermore, in the proof of this result, a construction method using random
walk approximation of stochastic processes called Brownian excursion and Brownian house-moving becomes
necessary. In the proof, we introduce the notion of ﬁrst-order and second-order inﬁnitesimal probabilities.
We will explain that this concept is useful in organizing the integration by parts formulae.
8 星 野 壮 登 ( 阪 大 基 礎 工)
I. Bailleul(Univ. Bretagne Occidentale)
Masato Hoshino (Osaka Univ.)
Ismaël Bailleul(Univ. Bretagne Occidentale)

Random models on regularity-integrability structures · · · · · · · · · · · · · · · 15

Random models on regularity-integrability structures

概 要 In the study of singular SPDEs, it has been a challenging problem to obtain a simple proof of a generalprobabilistic convergence result (BPHZ theorem). Diﬀerently from Chandra and Hairer’s Feynman diagram
approach, Linares, Otto, Tempelmayr, and Tsatsoulis recently proposed an inductive proof based on the
spectral gap inequality by using their multiindex language. Inspired by their approach, Hairer and Steele
also obtained an inductive proof by using the regularity structure language. In this talk, we introduce anextension of the regularity structure including integrability exponents and provide a simpler proof of BPHZ
theorem. This talk is based on a joint work with Ismael Bailleul (Univ Brest).
14:15〜15:15

特別講演濵 口 雄 史 ( 阪 大 基 礎 工)

確率 Volterra 方程式の無限次元 Markov リフト

Yushi Hamaguchi (Osaka Univ.)

Inﬁnite dimensional Markovian lifts of stochastic Volterra equations

概 要 Stochastic Volterra equations (SVEs for short) are useful to model dynamics with hereditary properties,

memory eﬀects and roughness of the path, which cannot be described by standard SDEs. However, theanalysis of SVEs is much more diﬃcult than the SDEs case since the solutions are no longer Markovian orsemimartingales in general. In this talk, we introduce an inﬁnite dimensional framework which captures
Markov and semimartingale structures behind SVEs. We show that an SVE can be “lifted” to an inﬁnite
dimensional stochastic evolution equation (SEE for short) and that the solution of the SEE becomes a
Markov process on a Hilbert space. Furthermore, we establish asymptotic properties and well-posedness
results for lifted SEEs, and then apply them to the original SVEs.

Final: 2024/2/6
統計数学

15:30〜16:30 特別講演
永 沼 伸 顕 ( 熊 本 大 先 端)

Nobuaki Naganuma (Kumamoto Univ.)70

非整数 Brown 運動により駆動される確率微分方程式の近似理論

Approximation theory of SDEs driven by fractional Brownian motion

概 要 In this talk, we will consider approximation of solutions to stochastic diﬀerential equations (SDEs)

driven by fractional Brownian motions. In particular we focus on asymptotic error distributions. In
preceding results, several schemes (e.g. Euler–Maruyama scheme, Milstein scheme, Crank–Nicolson schemeand so on) to approximate the solutions were proposed and studied in several situations, which are classiﬁed
by continuity and dimensions of the driving processes. To obtain such results, we use rough path theory
to formulate SDEs and use the fourth moment theorem to identify limit distributions of error distributions.
We will give an overview of them and introduce preceding results and recent developments.

3 月 18 日（月）9:30〜11:40
9 田 端 操 樹 ( 立 命 館 大 理 工)

Misaki Tabata (Ritsumeikan Univ.)

第 III 会場

An inﬁnite-dimensional Hawkes process · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An inﬁnite-dimensional Hawkes process

概 要 We construct an inﬁnite-dimensional stochastic process using the Hawkes process, speciﬁcally by

establishing a compound Hawkes process. In this construction, we introduce a Poisson random measure to
the process, thereby creating an inﬁnite-dimensional stochastic process from a measure-theoretic perspective.
For the constructed process, we derive suﬃcient conditions for the existence of L1 , L2 moments and theLaplace transform. In particular, for L2 moment and the Laplace transform, we use a compensated Poisson
measure to derive these conditions for the inﬁnite-dimensional stochastic process we have constructed.
10 中 島誠 ( 名 大 多 元 数 理)

Makoto Nakashima (Nagoya Univ.)

1 点相互作用をもつ 3 次元熱方程式に関する Feynman–Kac 表現 · · · · · 15
Feynman–Kac representation for three-dimensional heat equation with
one-center point interaction

概 要 In this talk, we consider the heat equation associated with the Schrödinger operator with one-center

point interaction Hλ := −∆ + λδ0 , where δ0 is a Dirac measure at 0. This expression of the operator isthe formal one but Hλ is mathematically deﬁned via the norm-resolvent convergence of the Schrödinger
operators with short-range interaction. We give a kind of Feynman–Kac representation of the heat equation
associated with Hλ .
11 中 島誠 ( 名 大 多 元 数 理)
大理)
楠 岡 誠 一 郎 (京梁
松 ( 早 大 教 育)
アルベベリオセルジオ( Univ. of Bonn )Makoto Nakashima (Nagoya Univ.)
Seiichiro Kusuoka (Kyoto Univ.)(Waseda Univ.)
Song Liang
Sergio Albeverio (Univ. of Bonn)

3 次元 Edwards 測度に対する確率過程量子化 · · · · · · · · · · · · · · · · · · · · · · 15

Stochastic quantization of the three-dimensional Edwards measure

概 要 In this talk, we focus on the Edwards model formally given byνλ (dω) =Z 1Z t1
δ0 (ωt − ωs )dsdt ν0 (dω)
exp −λZλ00for λ ≥ 0, where Zλ is a normalizing constant. The formal random variable J(ω) =

R1Rt
0

0

δ0 (ωt − ωs )dsdt

is called a self-intersection local time, that measures a random set T (ω) = {(s, t) : ωs = ωt }. We will talkabout the stochastic quantization of νλ via the Dirichlet form.

Final: 2024/2/6
71

統計数学

12 上 木 直 昌 (京 大 人 間 環 境)
Naomasa Ueki

(Kyoto Univ.)

Positivity of small ball probabilities of a Gaussian random ﬁeld, and its
applications to random Schrödinger operators · · · · · · · · · · · · · · · · · · · · · 15
Positivity of small ball probabilities of a Gaussian random ﬁeld, and its
applications to random Schrödinger operators

概 要 The spectrum of a Schrödinger operator with a Gaussian random potential is R. This is a theorem

appeared in a book by Pastur and Figotin, and is proven by the theory on small ball probabilities, which
had been extensively developed for Gaussian random ﬁelds. In this talk, some remarks are given on the
proof, and similar facts are proven for a Schrödinger operator with a Gaussian random magnetic ﬁeld.
13 田 中 晴 喜 (鳴 門 教 育 大)
Haruyoshi Tanaka(Naruto Univ. of Edu.)

Higher-order asymptotic behaviours of pressure functionals and statistical representations of the coeﬃcients · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15Higher-order asymptotic behaviours of pressure functionals and statistical representations of the coeﬃcients概 要 We study the higher-order asymptotic behaviour of the pressure functional ϵ 7→ P (φ + ϵψ) withpotentials φ and ψ on a countable Markov shift X, where P (f ) means the topological pressure of f . In
this talk, we give a condition for obtaining the n-order asymptotic expansion of ϵ 7→ P (φ + ϵψ). Moreover,
R
Pm−1
i k
i=0 (ψ − X ψ dµ) ◦ σ ) ) as m → ∞ with the Gibbs

we have an explicit formula for the behaviour of µ((measure µ of φ and the shift σ. As a corollary, it turns out that the 3-th coeﬃcient of the expansion has alimit representation that looks like the asymptotic variance well.
14 大 井 拓 夢 (京 大 数 理 研)
上 村 稔 大 (関西大システム理工)(Kyoto Univ.)
Takumu Ooi
Toshihiro Uemura (Kansai Univ.)

Dynkin games for Markov processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Dynkin games for Markov processes

概 要 We consider Dynkin games for Markov processes associated with semi-Dirichlet forms. Dynkin games

are the optimal stopping games introduced as the models of zero-sum games by two players. We prove thatthe solution to the certain variational inequality with two obstacles is the equilibrium price of the Dynkingame. Moreover, we obtain the saddle point of the game.
15 篠 崎 裕 司 (日本銀行・東工大理)
二 宮 祥 一 ( 東 工 大 理)
Yuji Shinozaki(Bank of Japan / Tokyo Tech)
Syoiti Ninomiya (Tokyo Tech)

再結合測度法の誤差評価とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Error estimation of high-order recombination and its application

概 要 Those algorithms to perform the patch dividing which are necessary when weakly approximating

SDEs using the recombination method developed in [C. Litterer T. Lyons, 2012] are proposed. Reﬁning
Litterer–Lyon’s error estimation provides the patch radius criteria on which these algorithms are based.
Numerical examples of the calculation of option prices under the Heston model are also presented.

Final: 2024/2/6
統計数学

16 植 田 優 基 (北 教 大 旭 川)

Yuki Ueda (Hokkaido Univ. of Edu.)

72

Uniform convergence towards extreme value distributions in free probability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Uniform convergence towards extreme value distributions in free probability

概 要 In probability theory, there had been an interest in the uniform convergence to an extreme value

distribution. Extreme value distributions are classiﬁed into three types: Fréchet, Weibull, and Gumbel
types, and the uniform convergence rate for Fréchet type was obtained by Smith and Omey. Later,
Bartholmé and Swan obtained a new convergence rate from Stein’s method in the Fréchet case. In 2020,
Kusumoto and Takeuchi similarly used the Stein method to obtain an estimate of the Gumbel case. In thistalk, we will report the results obtained on the uniform convergence to the free extreme value distribution
using the Stein method as in the classical case. In free case, we will point out that information on the left
tail of the distribution, which does not appear in the classical case, becomes important.
11:40〜12:10

統計数学分科会総会

3 月 19 日（火）第 III 会場

10:00〜11:10
17 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 —連続時間の場合— · · · · · 10

Certain fractional optimal stopping problems —continuous time case—

概 要 We give the formulation of optimal stopping problems which combined a continuous time stochastic

process and the criterion of a fractional reward. Using standard arguments in the theory of mathematicalprogramming, we prove the existence of optimal stopping times under certain assumptions on the regularityof the stochastic processes.
18 藤 田 敏 治 (九 工 大 工)
Toshiharu Fujita(Kyushu Inst. of Tech.)

確率環境下における分岐・合流型決定過程 —最小型評価— · · · · · · · · · · · 15

Stochastic decision process with feedforward loop system —Minimum
reward system—

概 要 We consider minimum reward system on a stochastic decision process model with a feedforward loop

system, which is one of the nonserial branch systems. We apply invariant imbedding approach to our modeland introduce recursive equations by dynamic programming technique.
19 谷 野 憲 司 (神戸大システム情報)
平 尾 将 剛 (愛知県立大情報)澤正 憲 (神戸大システム情報)(Kobe Univ.)
Kenji Tanino(
Aichi
Pref. Univ.)
Masatake Hirao
Masanori Sawa (Kobe Univ.)

B 型鏡映群不変な球面デザインの単体的特徴付けと Hilbert 恒等式 · · · · 15

Research on the strength of Bd -invariant weighted spherical design using
simplicial characterization and Hilbert’s identity

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). To achive this goal,
we focus on the equivalence of designs on the simplex and on the sphere. In addition to this, we also
pay attention to the equivalence between the design on sphere and a certain type of Hilbert’s identity. In
particular, the former allows us to evaluate the upper bound of the design, and this is precisely our main
result. We also discuss the best possibility of our bound in low dimensions.

Final: 2024/2/6
73

統計数学

20 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 (東京理大創域理工)

Hisaya Okahara (Tokyo Univ. of Sci.)
Kengo Fujisawa(Tokyo Univ. of Sci., Yamaguchi)
Kouji Tahata (Tokyo Univ. of Sci.)

多元分割表における対称性に関する分離可能モデル · · · · · · · · · · · · · · · · · 15

Separable models related to symmetry for multi-way contingency tables

概 要 We consider multi-way contingency tables with the same ordered classiﬁcations and propose an

asymmetry model based on f -divergence, which extends a previous model. In this talk, we show theasymptotic properties of test statistics. Additionally, we also oﬀer insights into the previous model fromthe perspective of the proposed model. Finally, we present numerical experiments as a validation of theobtained results.

3 月 20 日（水）第 III 会場

10:00〜11:40
21 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.)

Mardia による多変量歪度に対する検定統計量 · · · · · · · · · · · · · · · · · · · · · · 15
A test statistic for Mardia’s multivariate skewness

概 要 In this talk, we consider a test statistic for Mardia’s multivariate skewness related to the test for

multivariate normality. Mardia (1970) gave the deﬁnitions of the multivariate skewness and the sample
measure of multivariate skewness, and the test statistic was given by using the expectation and varianceof asymptotic approximate statistic for the multivariate sample skewness. In this talk, we consider an
improvement on Mardia’s result. In particular, we derive exact results, instead of asymptotic Mardia’s
results for the expectation and variance. From the exact results, we propose a new test statistic with agood chi-squared approximation. Finally, we compare our result with that of Mardia (1970) and investigate
the accuracy of chi-squared approximation by a Monte Carlo simulation.
22 佃康 司 ( 九 大 数 理)
松 浦
峻 ( 慶 大 理 工)
Koji Tsukuda (Kyushu Univ.)
Shun Matsuura (Keio Univ.)

多変量 allometric 回帰モデルにおける第一主成分の推定について · · · · · · 15

Estimation of the leading principal component in the multivariate allometric regression model

概 要 The multivariate allometric regression model is a multivariate multiple regression model which imposesthat the diﬀerence of mean vectors of two observations is always parallel to the leading eigenvector of thecovariance matrix of observations. For this model, we consider the estimation problem for the leading
eigenvector. Considering a class of estimators which includes conventional estimators, we evaluate estimation
accuracies of the estimators contained in this class. Moreover, some estimators based on a preliminary testare proposed.

Final: 2024/2/6
統計数学

23 藤 森洸 ( 信 州 大 経 法)佃康 司 ( 九 大 数 理)
Kou Fujimori (Shinshu Univ.)
Koji Tsukuda (Kyushu Univ.)

74

Two step estimations via the Dantzig selector for ergodic time seriesmodels · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Two step estimations via the Dantzig selector for ergodic time seriesmodels概 要 We consider the estimation problems for conditionally heteroskedastic ergodic time series models withhigh-dimensional and sparse parameters and possibly inﬁnite- dimensional nuisance parameters. We ﬁrst
establish the asymptotic behavior of the Dantzig selector based on the least squares method to estimate
the unknown parameter of interest. Then, using the Dantzig selector and a consistent estimator for thenuisance parameter, we propose the asymptotically normal estimator for the non-zero components of theparameter of interest. Applications to the integer-valued autoregressive models are also presented in thistalk.
24 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)

高次元小標本におけるカーネル k-means 法について · · · · · · · · · · · · · · · · · 15

Asymptotic properties of kernel k-means for high-dimension, low-samplesize data

概 要 Substantial works about clustering on high-dimension, low-sample-size (HDLSS) data have been

performed. Particularly, asymptotic behaviors of hierarchical clustering are investigated without assuming
normality. On the other hand, asymptotic properties of k-means on behalf of partitional clustering in the
HDLSS settings seem to have not been studied suﬃciently. Especially, while the kernel method with somemethodologies is investigated, a theoretical result of kernel k-means is not obtained. In this talk, we show
the asymptotic properties of k-means for HDLSS data. Then, we introduce kernel k-means and show its
eﬀectiveness. At last, we present numerical simulation studies that demonstrate the performance of k-means
and kernel k-means for high dimensional data, discussing the achieved results.
25 矢 田 和 善 (筑波大数理物質)
青 嶋
誠 (筑波大数理物質)

Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Reconstruction of a low-rank matrix by singular value decompositions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Reconstruction of a low-rank matrix by singular value decompositions

概 要 In this talk, we consider the problem of recovering a signal (low-rank) matrix in high-dimensionalsettings. We ﬁrst consider the conventional PCA to recover the signal matrix and show that the estimationof the signal matrix holds consistency properties under severe conditions. The conventional PCA is heavily
subjected to a noise. In order to remove the noise, we apply the cross-data-matrix (CDM) methodology andpropose a new estimation of the signal matrix. We show that the proposed estimation by the CDM method
holds the consistency properties under mild conditions and improves the error rate of the conventional PCA
eﬀectively.
26 柿 沢 佳 秀 (北 大 経 済)

Yoshihide Kakizawa (Hokkaido Univ.)

シリンダーデータに対する密度推定 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Density estimation for cylinder data

概 要 For the data supported on [0, ∞) or [0, 1], the so-called boundary bias problem is one of the interests.

Instead of the location-scale kernel k((x − ·)/h)/h, we have recently developed asymmetric kernel method tosolve the boundary bias problem. In this talk, we consider the problem of estimating the density for cylinder
data, using the asymmetric kernel and von Mises kernel. This is a ﬁrst step, so that some related works
in this direction will be expected by combining the circular distribution theory with the nonparametricmethod.

Final: 2024/2/6
75

統計数学

14:15〜15:15

2023 年度 (第 22 回) 日本数学会解析学賞受賞特別講演
島
大⋆) 高次元統計解析における情報量規準に基づくモデル選択
藤 越 康 祝 (広Yasunori Fujikoshi (Hiroshima Univ.⋆)

Model selection based on information criteria in high-dimensional statistical analysis

概 要 In this talk we consider model selection methods based on information criteria such as AIC, BIC and

Cp in high-dimensional statistical analysis. First we point in multivariate regression (Fujikoshi, Sakurai
and Yanagihara (2014), Yanagihara, Wakaki and Fujikoshi (2015), Bai, Choi, Fujikoshi and Hu (2022)) thatwithin the framework of large-sample and high-dimension data AIC and Cp are asymptotically consistent,
but there exists a case that BIC is not asymptotically consistent. This is a remarkable result, since it was
known that AIC and Cp are not asymptotically consistent under the large sample case. Existence of thecase that BIC is not asymptotically consistent but AIC is asymptotically consistent can be seen for theother situation as in estimating the dimensionality in principal component analysis, multivariate regression
analysis and discriminant analysis. There is a faulty in the use of AIC and the like in a variable selection
problem, since the amount of computation becomes numerous as the number of variables to choose is large.
In order to avoid this diﬃculty, we discuss KOO (kick-one-out) methods. As a result, it is shown that themethods have asymptotic high-dimensional consistency in multivariate regression and discriminant analysis
models under certain conditions (Fujikoshi (2022)).
15:30〜16:30

特別講演

中 川 智 之(明星大データサイエンス)

ダイバージェンスを用いたロバストな一般化ベイズ法とその応用

Tomoyuki Nakagawa (Meisei Univ.)

Robust Bayesian inference using the divergences and its applications

概 要 In Bayesian statistics, the robustness against outliers is one of important issues. It is well known thatan ordinary Bayesian inference is strongly inﬂuenced by outliers. As one of the solutions to this problem,
Bayesian inference using heavy-tailed distributions has been used for a long time and has been studied
extensively in recent years. However, the heavy-tailed distributions require a model to be constructed foreach problem, and it is often diﬃcult to deal with complex models. On the other hand, Bayesian inference
using the divergence has the advantage of being ﬂexible applied to a variety of models, and has beendeveloped by numerous studies in recent years. In this presentation, we consider that the robustness ofBayesian inference using the density power and gamma divergences. In addition, we show the performanceof these Bayesian inferences which applied to several models in simulation studies.

Final: 2024/2/6
応用数学

応

用

3 月 17 日（日）

数

76

学
第 IX 会場

9:00〜12:00
1 赤
今
岡
佐
田

堀
野
本
藤
村

次 郎 ( 立 命 館 大 理 工)
紀 雄 (立 命 館 大⋆)
陸 希 ( 立 命 館 大 理 工)
巖 ( 小 山 工 高 専)
勇 真 ( 立 命 館 大 理 工)

Jiro Akahori (Ritsumeikan Univ.)
Norio Konno (Ritsumeikan Univ.⋆)
Rikuki Okamoto (Ritsumeikan Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)
Yuma Tamura (Ritsumeikan Univ.)

サイクル上の量子ウォークに対する絶対ゼータ関数と周期性 · · · · · · · · · · 15

Absolute zeta functions and periodicity of quantum walks on cycles

概 要 The absolute zeta function can be considered as a zeta function over F1 and the quantum walk is aquantum counterpart of the classical random walk. We showed a connection between the quantum walk andthe absolute zeta function. Then we focused Grover walks and Hadamard walks on cycle graphs, which are
typical models of quantum walks, and using cyclotomic polynomials, we calculated the periods and absolutezeta functions of such quantum walks. Especially, our result includes other proofs of some known results
which showed such periods in some cases.
2 岡
今
佐
赤

本 陸 希 ( 立 命 館 大 理 工)
野 紀 雄 (立 命 館 大⋆)
藤巌 ( 小 山 工 高 専)
堀 次 郎 ( 立 命 館 大 理 工)

Rikuki Okamoto (Ritsumeikan Univ.)
Konno Norio (Ritsumeikan Univ.⋆)
Sato Iwao (Oyama Nat. Coll. of Tech.)Akahori Jiro (Ritsumeikan Univ.)

量子ウォークのゼータ関数に対する絶対ゼータ関数 · · · · · · · · · · · · · · · · · 15

Absolute zeta functions of zeta functions of quantum walks

概 要 We consider the absolute zeta function of zeta functions of quantum walks. First, we deﬁne the matrix

zeta function for square matrix. The zeta function of quantum walk is a matrix zeta function for the Grover
matrix that determines quantum walk on a graph. The zeta function of quantum walk has an absoluteautomorphic form of weight depending on the number of edges of the graph. We can consider the absolutezeta function of zeta function of quantum walk by this absolute automorphy. Especially, we calculate theabsolute zeta function of zeta functions of quantum walks on a complete graph.
3 穂 坂 大 将 (横浜国大環境情報)
瀬 川 悦 生 (横浜国大環境情報)
今 野 紀 雄 (立 命 館 大⋆)

Taisuke Hosaka (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)
Norio Konno (Ritsumeikan Univ.⋆)

QW-search/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

QW-search/Zeta correspondence

概 要 In this talk, we introduce the zeta function for the search model based on quantum walk. For thecycle, we give an expression of the zeta function in the case where the position and number of the marked
vertices are general. Moreover we deal with the d-dimensional torus in the two special case of the positionof the marked vertices, ﬁxing the number of marked vertices is half.

Final: 2024/2/6
77

応用数学

4 佐
遠
小
今

藤
巖 ( 小 山 工 高 専)
藤 隆 子 ( 東 北 大 工)松尭 ( 山 梨 大 工)
野 紀 雄 (立 命 館 大⋆)

Iwao Sato (Oyama Nat. Coll. of Tech.)
Takako Endo (Tohoku Univ.)
Takashi Komatsu (Univ. of Yamanashi)
Norio Konno (Ritsumeikan Univ.⋆)

Weighted alternating Walk/Zeta 対応 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weighted alternating Walk/Zeta correspondence

概 要 We deﬁne a generalized second weighted alternating zeta function of a graph, and express thegeneralized second weighted alternating zeta function of a vertex-transitive regular graph by spectra of thetransition probability matrix of the symmetric simple random walk on it and its Laplacian. Furthermore,
we present an integral expression for the limit of the generalized second weighted alternating zeta functionsof a series of vertex-transitive regular graphs. As an example, we treat the generalized second weighted
alternating zeta functions of a ﬁnite torus.
5 山 岸 弘 幸 ( 産 業 技 術 高 専)
衛大)
渡 辺 宏 太 郎 (防(永 井
敦 津 田 塾 大 学 芸)
Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)(Tsuda Coll.)
Atsushi Nagai

完全グラフに対応する 2 種類の 離散 ℓp ソボレフ不等式の最良定数 · · · · 15

The best constants of two types of discrete ℓp Sobolev inequalities on acomplete graph概 要 Let p be a positive real number. We determine the best constants of two types of discrete ℓp Sobolev

inequalities on a complete graph KN . The discrete ℓp Sobolev inequality shows that the maximum of |u(i)|p isestimated from above by constant multiples of the potential energy for vector u = t (u(0), · · · , u(N −1)) ∈ CN .
The potential energy is the ℓp norm of u with dumping coeﬃcicent a. In addition, we also have the best
constant of the discrete ℓp Sobolev inequality in the case of a = 0.
丞
(福岡大情報基盤センター)
白 石 修 二 ( 福 岡 大 理)

On the generation of all Euler trails in an Eulerian graph · · · · · · · · · · · 10

Sho Fujimura (Fukuoka Univ.)
Shuji SHIRAISHI (Fukuoka Univ.)

On the generation of all Euler trails in an Eulerian graph

6 藤 村

概 要 Fujimura and Shiraishi showed that all Euler trails of G are obtained in parallel for any Euleriangraph with 2n edges. In this paper, we generalize this result for an arbitrary Eulerian graph G by an ideaof adding a dummy padding path to G.
7 B. Jackson(Queen Mary Univ. of London)
善 本
潔 ( 日 大 理 工)Bill Jackson(Queen Mary Univ. of London)
Kiyoshi Yoshimoto (Nihon Univ.)

Spanning even trees of graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Spanning even trees of graphs

概 要 A tree T is said to be even if all pairs of vertices of degree one in T are joined by a path of evenlength. We conjecture that every r-regular non-bipartite connected graph G has a spanning even tree andverify this conjecture when G has a 2-factor. Well-known results of Petersen and Hanson et al. imply thatthe only remaining unsolved case is when r is odd and G has at least r bridges. We investigate this casefurther and propose some related conjectures.

Final: 2024/2/6
応用数学

8 前 澤 俊 一 ( 東 京 理 大 理)斎 藤
明 ( 日 大 文 理)
Shun-ichi Maezawa(Tokyo Univ. of Sci.)(Nihon Univ.)
Akira Saito

78

虹色禁止部分グラフが誘導する前順序について · · · · · · · · · · · · · · · · · · · · · 15

On a preorder induced by rainbow forbidden subgraphs

概 要 A subgraph H of an edge-colored graph G is rainbow if all the edges of H receive diﬀerent colors. If

G does not contain a rainbow subgraph isomorphic to H, we say that G is rainbow H-free. For connected
graphs H1 and H2 , if every rainbow H1 -free complete graph edge-colored in suﬃciently many colors is
rainbow H2 -free, we write H1 ≤ H2 . The binary relation ≤ is a preorder. Cui et al. (2021) characterized
the pairs (H1 , H2 ) with H1 ≤ H2 when either H1 or H2 is a subgraph of the other. Motivated by theirresult, we are currently searching for such pairs under the condition that neither H1 nor H2 is a subgraphof the other. In this talk, We give a progress report of this study.
9 小 沢
誠 ( 駒 澤 大 総 合)
M. Eudave-Muñoz(Univ. Nacional Autónoma de México)

Makoto Ozawa (Komazawa Univ.)
Mario Eudave-Muñoz(Univ. Nacional Autónoma de México)

Characterization of critical complexes which have a form (G × S 1 ) ∪ H· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Characterization of critical complexes which have a form (G × S 1 ) ∪ H

概 要 A simplicial complex is said to be critical for the 3-sphere S 3 if it cannot be embedded in S 3 but after

removing any one point, it can be embedded. We show the following theorem:
Let X = (G × S 1 ) ∪ H be a critical complex, where G and H are graphs. Then (G × {0}) ∪ H has a minorG′ ∪ H ′ which is one of the following.
(1) G′ ∪ H ′ is K5 , where H ′ = K1,4 .
(2) G′ ∪ H ′ is K5 , where H ′ = K3 .
(3) G′ ∪ H ′ is K3,3 , where H ′ = K1,3 .
10 小 沢誠 ( 駒 澤 大 総 合)
M. Eudave-Muñoz(Univ. Nacional Autónoma de México)

Makoto Ozawa (Komazawa Univ.)
Mario Eudave-Muñoz(Univ. Nacional Autónoma de México)

Partially ordered set of complexes by embeddings and the existence of
critical subcomplexes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Partially ordered set of complexes by embeddings and the existence of
critical subcomplexes

概 要 A simplicial complex is said to be critical for the 3-sphere S 3 if it cannot be embedded in S 3 but after

removing any one point, it can be embedded. There exist complexes which cannot be embedded in S 3 , butthey do not contain any critical complexes. From the property of those examples, we deﬁne an equivalence
relation on all simplicial complexes C and a partially ordered set of complexes (C/ ∼; ⫅), and reﬁne thedeﬁnition of critical. According to the reﬁned deﬁnition of critical, we show that if a complex X cannot beembedded in S 3 , then there exists [X ′ ] ⫅ [X] such that [X ′ ] is critical for [S 3 ].
11 田 中 康 平 (信 州 大 経 法)
Kohei Tanaka (Shinshu Univ.)

Directed topological complexity for CW complexes · · · · · · · · · · · · · · · · · 15
Directed topological complexity for CW complexes

概 要 The topological complexity of a space is a numerical homotopy invariant closely related to the robot

motion planning problem. If robot motions are required to go along with certain direction, the directed
topological complexity plays an important role to control directed algorisms. This talk will focus on the
directed topological complexity of a space decomposed by a poset.

Final: 2024/2/6
79

応用数学

12 東 谷 章 弘 (阪 大 情 報)

Akihiro Higashitani (Osaka Univ.)

正則マトロイドに付随する反射的多面体と γ 非負性 · · · · · · · · · · · · · · · · · 15

Reﬂexive polytopes arising from regular matroids and γ-nonnegativity

概 要 The symmetric edge polytope (SEP) of a graph is a centrally symmetric reﬂexive polytope whose

vertices are deﬁned by the edges of the graph. SEPs have been studied extensively in the past twenty
years. Recently, a generalized version of SEPs has been introduced from graphs (i.e. graphic matroids) toregular matroids, which is characterized by totally unimodular matrices. Generalized SEPs are known tohave palindromic Ehrhart h∗ -polynomials. On the other hand, it is conjectured that (ordinary) SEPs havenonnegative γ-vectors. In this talk, we show that the conjecture on the nonnegativity of γ-vectors of SEPs
does not hold for generalized SEPs.
14:15〜16:50
13 永 並 健 吾 (成 蹊 大 理 工)
大野由美子
(横浜国大研究推進機構)(Seikei Univ.)
Kengo Enami
Yumiko Ohno (Yokohama Nat. Univ.)

Diﬀerence of facial achromatic numbers between two triangular embeddings of a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Diﬀerence of facial achromatic numbers between two triangular embeddings of a graph

概 要 A facial 3-complete k-coloring of a triangulation G on a surface is a vertex k-coloring such that every

triple of the colors appears on the boundary of some face of G. The facial 3-achromatic number ψ3 (G)of G is the maximum integer k such that G has a facial 3-complete k-coloring. We show an upper boundfor diﬀerence of facial 3-achromatic numbers between two triangular embeddings of the same graph on asurface.
14 高 橋 大 樹 (横浜国大環境情報)
中 本 敦 浩 (横浜国大環境情報)

Daiki Takahashi (Yokohama Nat. Univ.)
Atsuhiro Nakamoto(Yokohama Nat. Univ.)

Outer Steiner point を用いた多角形の四角形分割 · · · · · · · · · · · · · · · · · · · 15
Quadrangulations of a polygon with outer Steiner points

概 要 Given an n-sided polygon P on the plane with n ≥ 4, we consider a problem whether P is quadran-gulatable or not by adding straight segments into the interior. We can easily ﬁnd a non-quadrangulatable
polygon P and hence we introduce Steiner points, which are auxiliary points which can be put in any positionin the interior or exterior of P . In our talk, we estimate the number of Steiner points for quadrangulating
P using the notion “spirality” of P which measures how far P is from being convex polygon in a sense.
15 野 口 健 太 (東 京 理 大 理 工)
G. Brinkmann ( Ghent Univ. )H. Van den Camp ( Ghent Univ. )Kenta Noguchi (Tokyo Univ. of Sci.)
Gunnar Brinkmann (Ghent Univ.)
Heidi Van den Camp (Ghent Univ.)

双対グラフが 1-点カットをもつような完全グラフの埋め込み · · · · · · · · · 15

Embedding of complete graphs so that the dual has a 1-cut

概 要 In 2022, Bokal, Brinkmann, and Zamﬁrescu considered the problem of the connectivity of the dual andthey deﬁned a function δk (c) as the smallest genus s which allows a simple c-connected graph G embedded
in an orientable surface Ss with a simple dual G∗ with a k-cut. This function is well-deﬁned for c ≥ k ≥ 1
and they determined the exact value when k ≥ 3 or c ≤ 6. In this talk, we determine the exact value ofδ2 (c) for all c and give an upper bound for δ1 (c), which is one apart from the best, for inﬁnitely many c.

Final: 2024/2/6
応用数学

16 松 村 英 樹 (慶 大 理 工)澤正 憲 (神戸大システム情報)

Hideki Matsumura (Keio Univ.)
Masanori Sawa (Kobe Univ.)80

重み付きデザインの中心対称性の複素類似について · · · · · · · · · · · · · · · · · 15

On a complex analogue of central symmetry of weighted designs

概 要 A quadrature formula is a formula computing a deﬁnite integration by evaluation at a set of ﬁnitely

many points (design). Examining the existence of certain rational quadrature formulas leads to applications
to interesting problems such as Waring’s problem and spherical designs. A central symmetric quadrature
is a central research object in the real case. Sawa and Uchida proved the existence and the non-existenceof central symmetric rational quadrature formulas for Hermite polynomials. In this talk, we consider an
extension of the above results to Bessel polynomials and discuss complex analogues of central symmetry
with examples. This is a joint work with Masanori Sawa.
17 三 島 輝 之 (神澤正 憲 (神内 田 幸 寛 (都盧暁 南 (岐戸 大 工)

有理的 interval design の明示的構成法と Hilbert Kamke 問題 · · · · · · · · 15

戸 大 工)
立 大 理)
阜 大 工)

Teruyuki Mishima (Kobe Univ.)
Masanori Sawa (Kobe Univ.)
Yukihiro Uchida (Tokyo Metro. Univ.)(Gifu Univ.)
Xiao-Nan Lu

Explicit construction of rational interval design and Hilbert–Kamke
problem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.
大⋆)18 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.)

あるアソシエーションスキームの 2 変数 Q-多項式性について · · · · · · · · · 15

On the bivariate Q-polynomiality of certain association schemes.

概 要 The classiﬁcation problem of P - and Q-polynomial association schemes has been one of the central

problems in algebraic combinatorics. The deﬁnition of the multivariate version of P - and/or Q-polynomial
association schemes was reported at the last meeting. In this talk, we show that the non-binary Johnson
scheme and the association scheme obtained from attenuated spaces are bivariate Q-polynomial association
schemes.
19 粟 田 円 佳 (早 大 理 工)

Madoka Awada (Waseda Univ.)

平方剰余符号を用いた 3-design 構造について · · · · · · · · · · · · · · · · · · · · · · · 15

3-designs constructed by using quadratic residue codes

概 要 The transitivity argument shows that shells of the extended quadratic residue codes of length p + 1

e q,p+1 )ℓ , support combinational 2-designs. In the present talk, by computing Jacobi polynomials
over Fq , (Qe q,p+1 )ℓ ∪ ((Qe q,p+1 )⊥ ) (6= ∅) is a 3-design. In addition,and harmonic weight enumerators, we show that (Qℓe r2 ,p+1 , which does not follow from the
we introduce the way to construct inﬁnite series of 3-designs in Q
transitivity argument.

Final: 2024/2/6
81

応用数学

20 石 川 麗 菜 (早 大 理 工)

Reina Ishikawa (Waseda Univ.)

拡大平方剰余符号から得られる例外的デザイン構造 · · · · · · · · · · · · · · · · · 15

Exceptional designs in some extended quadratic residue codes

概 要 In general, a non-empty set of all codewords with a weight of ℓ in extended quadratic residue codes has a

combinatorial 2-design. Bonnecaze–Sóle (2021) demonstrated that extended binary quadratic residue codesof length 42 has a 3-design. However, this result was obtained only through electronic calculations. The
goal of this presentation is to provide additional examples in the extended ternary and quaternary quadratic
residue codes with logical proofs. We compute Jacobi polynomials and harmonic weight enumerators forthe extended ternary quadratic residue code of length 14 and the extended quaternary quadratic residue
code of length 18. By using these results, we prove our examples through logical reasoning.
21 谷 口 浩 朗(大和大教育・香川高専⋆)
Hiroaki Taniguchi(Yamato Univ./Kagawa Nat. Coll. of Tech.⋆)2 次的な APN 関数 F (x) + T r(x)L(x) について · · · · · · · · · · · · · · · · · · · · 15
On quadratic APN functions F (x) + T r(x)L(x)

概 要 We ﬁrst characterize how two (n−1, m) functions f and g can be combined into an APN (n, m)-function

F of the form F (x) = f (x) and F (x + e0 ) = g(x) for x ∈ Fn−1
with e0 ∈ Fn2 \Fn−1. Next we specialize
22this characterization to the case when f is quadratic and g(x) = f (x) + L(x) for some linearized polynomial
L. Lastly for a quadratic APN (n, n)-function F and a linearized polynomial L, we give a characterizationof APN-ness for (n, n)-function F (x) + T r(x)L(x). With some computational experiments, we see that
CCZ-inequivalent APN functions F (x) + T r(x)L(x) can be obtained from F using this construction.
17:00〜18:00
盧特別講演

暁 南 ( 岐 阜 大 工)

Xiao-Nan Lu(Gifu Univ.)

グループテスト・組合せテストにおける組合せ構造について

Combinatorial structures for group testing and combinatorial testing概 要 Group testing (GT) is a method for identifying defective items within a large population by poolingsamples together for joint testing. Combinatorial structures in GT, commonly represented by binary matrices
like separable matrices and disjunct matrices, serve as crucial mathematical frameworks for formulatingeﬃcient testing strategies. Combinatorial testing (CT) focuses on the identiﬁcation and location of faults
arising from interactions among a small number of factors, not just independent items. Test case designsin CT employ combinatorial structures, such as covering arrays, locating arrays, and detecting arrays.
Remarkably, GT can be viewed as specialized CT models under particular conditions.
In both GT and CT, constructions and characterizations of combinatorial structures are closely related to
extremal combinatorics, combinatorial designs, and coding theory. The practical applications of GT and
CT have also impacted the advancements in combinatorial design theory. This talk aims to introduce thefundamental mathematical frameworks through key combinatorial structures for GT and CT. Moreover,recent research focusing on variations and extensions of classical GT and CT using novel combinatorial
structures will be discussed.

Final: 2024/2/6
応用数学

3 月 18 日（月）82

第 IX 会場

9:00〜12:00
22 佐 藤純 ( 東 京 工 芸 大 工)
石 黒 裕 樹 ( 東 大 物 性 研)
西 成 活 裕 ( 東 大 先 端 研)

Jun Sato (Tokyo Polytechnic Univ.)
Yuki Ishiguro (Univ. of Tokyo)
Katsuhiro Nishinari (Univ. of Tokyo)

非一様な非対称単純排他過程の厳密な定常状態 · · · · · · · · · · · · · · · · · · · · · 15

Exact stationary state of the inhomogeneous ASEP

概 要 We ﬁnd the exact stationary state of the asymmetric simple exclusion process, where the hopping

rates are dependent on the position of the lattice site.
23 上 岡 修 平(大阪成蹊大データサイエンス)

Shuhei Kamioka (Osaka Seikei Univ.)

可積分系に基づく平面分割の乱択アルゴリズム · · · · · · · · · · · · · · · · · · · · · 15

An integrable algorithm for randomly sampling plane partitions

概 要 An algorithm for random sampling of plane partitions is proposed. The algorithm is based on an

integrable system, called the discrete two-dimensional Toda equation. The complexity of the algorithm isabout the same as a conventional fast method. In addition, the probability distribution for sampling isdetermined by a solution to the integrable system. For this property, we can perform the sampling from a
nontrivial distribution in the same manner as the uniform one.
24 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.)

Computing bipath persistent homology · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Computing bipath persistent homology

概 要 In topological data analysis, persistent homology provides a compact descriptor of the birth anddeath scales of the topological features of data. In particular, the descriptor, the persistence diagram,can be algebraically understood using interval decompositions of persistence modules. In a previous work,
we characterized all posets whose persistence modules are guaranteed to be interval decomposable. In
addition to the classical setting of zigzag persistence, this includes what we call the bipath poset and bipath
persistence, as a generalization of the persistent homology of ﬁltrations. In this work, we provide algorithms
to compute the interval decompositions and thus construct persistence diagrams for bipath persistence.
25 森 田 英 章 (室 蘭 工 大 工)

Hideaki Morita (Muroran Inst. of Tech.)

有限有向グラフの正則被覆について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the regular covering of a ﬁnite digraph概 要 We consider the regular covering of a ﬁnite digraph which allows multi-arcs ans multi-loops. We deﬁne

the notion “inverse arcs” for such a digraph. In addition, we will see that the regular covering of the digraphcan be constructed as the induced digraph with respect to the ordinary voltage assignment corresponding
to the group action, including the behaviors of those inverse arcs of them. This enables one to consider the
problem which describes decomposition of the generalized weighted zeta function for the regular covering ofa digraph.

Final: 2024/2/6
83

応用数学

26 石 川 彩 香(山形大データサイエンス教育研究推進センター)

Ayaka Ishikawa (Yamagata Univ.)

周期経路に対するグラフゼータ函数とその行列式表示 · · · · · · · · · · · · · · · 15

A graph zeta function of periodic paths and its determinant expression

概 要 In general, a graph zeta function is deﬁned for ordinary paths. On the other hand, there also exists

a graph zeta function deﬁned for alternating paths. These can be expressed in the Ihara representation,
similar to the case of ordinary paths. In this talk, we will deﬁne more general paths and present the Ihara
expression of the graph zeta function.
27 釣 井 達 也 (東京情報大総合情報)
伊 藤 直 治 (奈良教育大教育)
松 山 豊 樹 (奈良教育大教育)
Tatsuya Tsurii(Tokyo Univ. of Information Sci.)
Naoharu Ito (Nara Univ. of Edu.)
Toyoki Matsuyama(Nara Univ. of Edu.)

発展行列から得られる群構造を用いた Grover walk の周期性に関する研究· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A study on periodicity of Grover walk using group structures obtained
from its evolution matrix

概 要 In our previous paper [1], we have shown that Grover walk on complete graphs with n vertices and aself-loop at each vertex has period 2n. The method of the proof is focus on the eigenvalues of the evolution
matrix U . In this talk, we show another proof of the above problem by focusing on group structures
obtained from the evolution matrix U .
28 船 川 大 樹 (北 海 学 園 大 工)齋 藤
渓 ( 神 奈 川 大 工)

Daiju Funakawa (Hokkai-Gakuen Univ.)(Kanagawa Univ.)
Kei Saito

1 次元 2 状態の開放系量子ウォークにおける固有値の存在 · · · · · · · · · · · · 15
The existence of eigenvalues in one-dimensional two-state open quantumwalks

概 要 Quantum walks are mathematical models that are said to be quantum version of random walks andare applied to topological insulators. In recent years, open quantum walks, in which the ﬂow of particles
are controlled, have been studied actively. For closed systems, topological invariants are described using thedimension of the eigenspace of the time evolution operator. For this reason, the analysis of the eigenvaluesof the time evolution operator is important in the study of quantum walks. In this talk, we will analyze thebirth eigenvalues of the Mochizuki–Kim–Obuse model, which is an example of an open quantum system.
29 三 家 雅 弘 (慶 大 理 工)
太 田 克 弘 ( 慶 大 理 工)
Masahiro Sanka
Katsuhiro Ota(Keio Univ.)(Keio Univ.)

グラフのハミルトン性とタフネスおよび禁止誘導部分パスの条件 · · · · · · 15

Toughness, forbidden induced paths and hamiltonicity of graphs

概 要 For a real number t > 0, we say that a graph G is t-tough if for any set S with G − S disconnected,

the number of components of G − S is at most |S|/t. In 1973, Chvátal conjectured that there exists a
constant t0 such that every t0 -tough graph is hamiltonian. In this talk, the result on 2-tough 2K2 -freegraphs provided by Ota and the presenter is introduced. To show the result, the theorem saying that every
2-tough graph has a 2-factor is useful. On the other hand, it is also known that every 3/2-tough 2K2 -freegraph has a 2-factor. In this talk, the result on forbidden induced paths for a 3/2-tough graph to have a2-factor is also introduced.

Final: 2024/2/6
応用数学

30 横 村 国 治(東海大理系教育センター)

Kuniharu Yokomura (Tokai Univ.)

84

Balanced 3 部グラフの Hamiltonian-connected 性について · · · · · · · · · · · 15
On degree conditions of balanced 3-partite Hamiltonian-connected graphs

概 要 For a graph G and u, v ∈ V (G), a path in G from u to v is called a (u, v)-path, and if (u, v)-path is a

Hamiltonian path from u to v, then (u, v)-path is called a (u, v)-Hamiltonian path. A graph G is said to be
Hamiltonian-connected if there exists a (u, v)-Hamiltonian path between any two vertices u, v. A k-partite
graph is said to be a balanced k-partite graph if each partite set has the same number of vertices. We givesome conditions for balanced 3-partite graphs to be Hamiltonian-connected.
31 藤 田 慎 也(横浜市大データサイエンス)

Shinya Fujita (Yokohama City Univ.)

辺着色グラフにおける単色連結構造について · · · · · · · · · · · · · · · · · · · · · · · 10

On monochromatic connectivity in edge-colored graphs

概 要 We consider edge-colored graphs. Let G be an edge-colored graph. If, for any two vertices in G, there

exists a monochromatic path connecting them, then we say that G is monochromatic connected. Some
recent results on monochromatic connectivity in edge-colored graphs will be reviewed.
32 安 藤清 ( 国 立 情 報 学 研)

Kiyoshi Ando (Nat. Inst. of Informatics)

A constructive characterization of 5-edge-connected 5-regular multigraphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A constructive characterization of 5-edge-connected 5-regular multigraphs

概 要 We deal with multi-graphs with no self-loops. By introducing a new operation “quasi- edge-binding”,

we give a generating theorem for 5-edge-connected 5-regular multi-graphs. This is a 5-edge-connected
analogue of Korzig–Simmons result on 2k-edge-connected 2k-regular multi-graphs.
13:00〜14:00
33 深 澤知 ( 山 形 大 理)
三 枝 崎 剛 ( 早 大 理 工)Satoru Fukasawa (Yamagata Univ.)
Tsuyoshi Miezaki (Waseda Univ.)

グラフのガロア点について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Galois points for a graph概 要 In this talk, we introduce the notion of a Galois point for a ﬁnite graph, using the theory of linear

systems of divisors for graphs discovered by Baker and Norine. We present a new characterization ofcomplete graphs in terms of Galois points.
34 三
西
宗
佐
辻

枝
村
政
久
栄

崎
優
昭
間
周

剛 ( 早 大 理 工)
作 ( 早 大 理 工)
弘 ( 東 北 大 情 報)
雅 ( 山 形 大 理)
平 ( 北 教 大 旭 川)

Tsuyoshi Miezaki (Waseda Univ.)
Yuusaku Nishimura (Waseda Univ.)
Akihiro Munemasa (Tohoku Univ.)
Tadashi Sakuma (Yamagata Univ.)
Shuhei Tsujie (Hokkaido Univ. of Edu.)

彩色対称関数の一般化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A generalization of the chromatic symmetric function

概 要 The present talk aims to give a generalization of the chromatic symmetric function. We call this the

Kneser chromatic function and show that the set of Kneser chromatic functions is a complete invariant forgraphs. Further, we give three graph invariants and discuss some of their properties.

Final: 2024/2/6
85

応用数学

35 西 村 優 作 (早 大 理 工)

Yusaku Nishimura (Waseda Univ.)

シンプルランダムウォークの期待到達時間と equitable partition · · · · · · 15

A simple random walk and equitable partition

概 要 It is known that the average hitting times of simple random walks from any vertex to any othervertex in distance-regular graphs are determined by their intersection array. In this paper, we introduce a
new graph classiﬁcation called f -equitable, utilizing both the equitable partition and the function f , which
represents one of the generalizations of distance-regular graphs. We determine the average hitting times
from any vertex to any other vertex in f -equitable graphs by using their parameter, referred to as thequotient matrix. Furthermore, we establish the existence of a function (f1 , f2 ) such that the Cartesian
product of two strongly regular graphs is (f1 , f2 )-equitable. We then calculate the quotient matrix for thesegraphs and determine the average hitting times from any vertex to any other vertex in these graphs.
36 田 中 優 帆 (早 大 理 工)
Yuho Tanaka(Waseda Univ.)

有向 Cayley グラフ上の乱歩における期待到達時間の解析 · · · · · · · · · · · · 15

On the average hitting times of directed Cayley graphs

概 要 The exact formula for the average hitting time of simple random walks from one vertex to any

other vertex on Cay(ZN , {±1, ±2}) was given by Y. Doi et al. [Discrete Applied Mathematics, 313 (2022)
18-28]. Y. Doi et al. give a simple formula for the average hitting times of simple random walks on
Cay(ZN , {±1, ±2}) by using an elementary method. In this talk, using an elementary method also used by
Y. Doi et al. [Discrete Applied Mathematics, 313 (2022) 18-28], we give a simple formula for average hitting
times of simple random walks on Cay(ZN , {+1, +2}). Furthermore, we also give the exact formula for the
average hitting times of random walks on the weighted Cayley graph Cay(ZN , {+1, +2}).

3 月 19 日（火）第 IX 会場

9:50〜12:00
37 縫 田 光 司 (九 大 I M I)
Koji Nuida(Kyushu Univ.)

半順序集合の初等的性質による Zorn の補題の証明 · · · · · · · · · · · · · · · · · · 10

A proof of Zorn’s Lemma from elementary properties of partially orderedsets

概 要 Zorn’s Lemma is stated purely in terminology of posets (partially ordered sets), but its standard proof

relies on transﬁnite recursion, which is a non-elementary set-theoretic machinery. In this talk, we show a
new simple proof of Zorn’s Lemma that only uses (besides Axiom of Choice) basic properties of posets. In
contrast to the existing similar proofs, our proof is more elementary in the sense that it even does not use
the notion of well-ordered sets.
38 永 野 哲 也(長崎県立大情報システム)

Tetsuya Nagano (Univ. of Nagasaki)

フィンスラー暗号 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Finsler encryption

概 要 Inspired by previous work with the ﬁrst example proposed at SecITC 2020, we give a general descriptionof Finsler encryption that is based on a Finsler space, which uses a kind of a diﬀerentiable geometry ona smooth manifold, with appropriate quantization as the security parameter. Key generation, encryption
and decryption algorithms are introduced in outline, and a further example is presented. Then we analyse
security properties of Finsler encryption. First, as the dimension (as another security parameter) increases,
the length of the secret key also increases, and hence the computational hardness becomes stronger. Second,
we prove indistinguishability against chosen-plaintext attacks.

Final: 2024/2/6
応用数学

39 富 安 亮 子 (九 大 I M I)

Ryoko Tomiyasu (Kyushu Univ.)

86

葉序と線形式の積に由来するパッキング理論 · · · · · · · · · · · · · · · · · · · · · · · 15

Packing theory derived from phyllotaxis and products of linear forms

概 要 Parastichies are spiral patterns observed in plants and numerical patterns generated using golden angle

method. We generalize this method by using Markoﬀ theory and the theory of product of linear forms,
to obtain packings on Riemannian manifolds with a locally diagonalizable metric. Using this method, we
prove that it is possible to generate packings on any real analytic Riemannian surfaces with the packing
density bounded below by approximately 0.7. For 3-manifolds, the lower bound for the packing density isapproximately 0.38.
40 須 田 智 晴 (理 化 学 研)
Tomoharu Suda

(RIKEN)A categorical perspective on the relationship between discrete and continuous time dynamical systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
A categorical perspective on the relationship between discrete and continuous time dynamical systems

概 要 Dynamical systems are broadly categorized into two types: discrete and continuous time systems.

While it is commonly acknowledged that analogies exist between these two types, formalizing and proving
this correspondence in a mathematically rigorous manner poses a challenge. This study aims to explore
the relationship between these categories in the light of category theory. The main result of this researchestablishes a connection between discrete and continuous dynamical systems via classical constructs, namely
the Poincaré map and suspension ﬂow. This result not only elucidates the relationship between the two
types of systems but also validates the natural relevance of these constructs in the study of dynamicalsystems.
大理)
41 宮 路 智 行 (京
(
早
大
理
工)
岡 本 和 也友 枝 明 保 (関西大総合情報)

Tomoyuki Miyaji (Kyoto Univ.)
Kazuya Okamoto (Waseda Univ.)
Akiyasu Tomoeda (Kansai Univ.)

離散回転対称性をもつ Neimark–Sacker 分岐と進行波 · · · · · · · · · · · · · · · 15

Neimark–Sacker bifurcation with discrete rotational symmetry and traveling waves

概 要 The Neimark–Sacker bifurcation, a codimension-one bifurcation for a ﬁxed point of a map with a pairof complex eigenvalues on the unit circle, leads to the appearance of an invariant closed curve. We showthat a branch of traveling waves, which form invariant closed curves, bifurcates by the Neimark–Sacker
bifurcation of a homogeneous ﬁxed point provided that the map commutes with the action of the cyclic
group. In addition, we discuss a method of numerical continuation of the bifurcating traveling waves andapplication to a system of delay diﬀerence equations proposed by the present authors as a traﬃc ﬂow model.
42 村 田 実 貴 生 (東 京 農 工 大 工)
Mikio Murata(Tokyo Univ. of Agri. and Tech.)

グレイ–スコットセル・オートマトンに現れるチューリングパターン · · · 15

Turing patterns appearing in Gray–Scott cellular automaton

概 要 A cellular automaton constructed by positive value diﬀerentiation and ultradiscretization of the Gray–

Scott model generates various non-uniform spatiotemporal patterns through numerical simulation. This
spatiotemporal pattern can be considered a Turing pattern in a broad sense. In this presentation, we willreport the results of numerical simulations of a two-dimensional Gray–Scott cellular automaton by replacing
diﬀusion parameters, initial concentration, and neighborhoods and grids.

Final: 2024/2/6
87

応用数学

43 渡 辺樹 ( 早 大 理 工)

Itsuki Watanabe (Waseda Univ.)

High density limit for nonlocal cross-diﬀusion model with self-diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15High density limit for nonlocal cross-diﬀusion model with self-diﬀusion

概 要 The deterministic limit of a stochastic model of nonlocal cross-diﬀusion with self-diﬀusion is considered.

The stochastic model is given by two types particle system where the diﬀusion rate depends on the densityof both particle types. In this talk, we reveal its deterministic limit, and show the existence of solution of
nonlocal cross-diﬀusion equation by Markov chain approximation method.
44 古 川賢 ( 理 化 学 研)
北 畑 裕 之 ( 千 葉 大 理)
(RIKEN)Ken Furukawa
Hiroyuki Kitahata (Chiba Univ.)

動的境界条件下での移流拡散方程式と濾過現象について · · · · · · · · · · · · · 15

Drift-diﬀusion equations under dynamic boundary conditions for ﬁltration phenomena

概 要 We introduce a mathematical model describing the microbial ecosystem in an aquarium. We present

a mathematical analysis of the model and numerical simulation results. The model is based on a onedimensional advection-diﬀusion equation, a predator-prey model, and dynamic boundary conditions. Dynamic boundary conditions are a type of boundary conditions that include time derivatives in the boundary
conditions, unlike the Dirichlet, the Neumann, and the Robin boundary conditions. In this model, thedynamic boundary condition with the fourth boundary condition is considered. This study is based on joint
research with Professor Hiroyuki Kitahata of Chiba University.
14:15〜14:40

2023 年度日本数学会応用数学賞・応用数学研究奨励賞授賞式

14:50〜16:30
45 森 田 善 久 (龍神 保 秀 一 (北

谷

大⋆)

大

理)

Yoshihisa Morita (Ryukoku Univ.⋆)
Shuichi Jimbo (Hokkaido Univ.)

Front propagation and blocking for the bistable reaction-diﬀusion equation on tree-like metric graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Front propagation and blocking for the bistable reaction-diﬀusion equation on tree-like metric graphs

概 要 We deal with the bistable reaction-diﬀusion equation on an unbounded metric graph, comprisinghalf-lines and triple junctions, referred to as a tree-like metric graph. Our analysis focuses on the behaviorof the entire solution displaying front propagation from the inﬁnity end of a primary branch (half-line).
We establish conditions for the existence of standing front solutions that block the front propagation. This
blocking depends on not only conditions at the junctions but also the length between neighboring junctions.
Additionally, we prove the stability/instability of the standing fronts.
46 穴 田 浩 一 (早 大 高 等 学 院)
石 渡 哲 哉
(芝浦工大システム理工)
牛 島 健 夫 (東京理大創域理工)
Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Takeo Ushijima (Tokyo Univ. of Sci.)

面積保存型曲率流における曲率の爆発レートに関する一考察 · · · · · · · · · · 15

A Remark on the blow-up rates of curvatures in the area-preserving
curvature ﬂow in the plane

概 要 We deal with the area-preserving curvature ﬂow in the plane, particularly the blow-up phenomena ofcurvatures on cusp singularities in contractions of convex immersed curves with self-crossing points. For
Abresch–Langer type curves with highly symmetric properties, it has been known that the maximum ofcurvatures blows up at a ﬁnite time under some assumptions. In this talk, we consider the blow-up rates inthis case.

Final: 2024/2/6
応用数学

47 木
李
劉
中
野
上

村 正
敬
逸
村
津 裕
田 好

人 ( 金 沢 大 理 工)
潼 ( 金 沢 大 自 然)
大
理)
侃 (京
玄 (北大理・北大電子研)
史 ( 金 沢 大 理 工)
寛 ( 神 戸 大 海 事)

Masato Kimura (Kanazawa Univ.)
Jingtong Li (Kanazawa Univ.)(Kyoto Univ.)
Yikan LiuGen Nakamura(Hokkaido Univ./Hokkaido Univ.)
Hirofumi Notsu (Kanazawa Univ.)
Yoshihiro Ueda (Kobe Univ.)

88

Zener 型粘弾性波動方程式の弱解の一意存在と漸近挙動 · · · · · · · · · · · · · · 15

Unique existence of weak solution and asymptotic behavior of Zenertype viscoelastic wave equation

概 要 We consider a Zener-type viscoelastic wave equation in a bounded domain, which consists of n

Maxwell-type viscoelastic components connected in parallel and a dumping term. Based on a physicallynatural energy dissipation identity, we establish the unique existence of a weak solution and a stability
estimate. The proof of the existence of the solution is performed by a compactness argument for thetime-discretized solution as the time increment tends to zero. Furthermore, we prove an exponential decay
property of the energy as time tends to inﬁnity even for the case without the dumping term.
48 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.)

Deﬀuant model における合意形成過程 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Process to reach consensus in Deﬀuant model

概 要 Opinion dynamics, one of the ﬁelds of social science, is a multidisciplinary ﬁeld and has been studied

using the mathematical model. Among them, the Deﬀuant model is widely known, which simply models
changes in the opinions of multiple agents. Both consensus and split states are seen as locally stableequilibriums. In this study, we introduce the “non-consensus ratio” to describe the behavior near thecritical point through variations of this ratio. Furthermore, we also discuss the process to reach consensus
in the modiﬁed Deﬀuant model where distance is introduced for the agent placement.

Final: 2024/2/6
89

応用数学

49 香 川 渓 一 郎 (北 大 電 子 研)
奥 村 真 善 美 (甲南大知能情報)
小 林 康 明 ( 北 大 電 子 研)
D. Wuergezhen (理化学研 BDR)
森 田 梨 津 子 ( 阪 大 生 命 機 能)
藤 原 裕 展 (理化学研 BDR)
長 山 雅 晴 ( 北 大 電 子 研)

Keiichiro Kagawa (Hokkaido Univ.)
Makoto Okumura (Konan Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Duligengaowa Wuergezhen (RIKEN)
Ritsuko Morita (Osaka Univ.)
Hironobu Fujiwara (RIKEN)
Masaharu Nagayama (Hokkaido Univ.)

毛包の形態形成の再現を目指した数値シミュレーション · · · · · · · · · · · · · 15

Numerical simulation to reproduce morphogenesis of hair follicles

概 要 In this study, we focus on the morphogenesis of hair follicles, one of the appendages of the skin,in which a two-dimensional placode is transformed into a cylindrical structure. We use a mathematicalmodel incorporating signal diﬀusion from ﬁbroblasts and plastic deformation of the basement membrane toinvestigate how the signal aﬀects the mechanical properties of the basement cells and membrane to reproduce
the phenomenon of invagination. We hypothesize that only in regions where the signal is strong, basal
cells deform vertically and that the basement membrane and dermis are more easily deformed, successfully
reproducing the sinking phenomenon. This model will be the basis for future studies on avian hair follicles
with projecting geometry and other skin appendages such as the mammary gland.
50 李

聖 林 (京大高等研・京大医)Sungrim Seirin Lee(Kyoto Univ. / Kyoto Univ.)

皮疹の形と生体内をつなぐ数理皮膚医学 · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Mathematical dermatology linking eruption morphology and in vivo
pathology

概 要 Chronic spontaneous urticaria (CSU) is one of the most intractable human-speciﬁc skin diseases.

However, as no experimental animal model exists, the mechanism underlying disease pathogenesis in vivo
remains unclear, making the establishment of a curative treatment challenging. Here, using a novel approachcombining mathematical modeling, in vitro experiments and clinical data analysis, we demonstrate that thepathological state of CSU patients can be inferred by geometric features of the skin eruptions. Our study
not only demonstrates that pathological states of diseases can be deﬁned by geometric features but will also
facilitate more accurate decision-making to manage CSU in the clinical setting.
16:45〜17:45

特別講演
田 中 吉 太 郎 (公立はこだて未来大)

非局所発展方程式と偏微分方程式系近似について

Yoshitaro Tanaka(Future Univ.-Hakodate)

Nonlocal evolution equations and approximations by system of partial
diﬀerential equations

概 要 Many evolutional equations with spatial convolution using suitable integral kernel have been proposed.

This type of equation is called the nonlocal evolution equation. Nonlocal evolution equations are analyzed
for dispersion of animals and plants, pigmentation patterns in the animal epidermis, and cell migration,and so on. To reveal the relationship between the nonlocal evolution equations and local systems, weapproximate the nonlocal evolution equations by systems of partial diﬀerential equations. We show thatthe nonlocal evolution equations with two types of convolution can be approximated by a multi-component
reaction-diﬀusion system and Keller–Segel system, respectively. From this theory, we explain that dealing
with a nonlocal interaction is in a sense equivalent to dealing with local dynamical system.

Final: 2024/2/6
応用数学

3 月 20 日（水）90

第 IX 会場

9:50〜12:00
51 古 屋 貴 士(島根大数理・データサイエンス教育研究センター)

Takashi Furuya (Shimane Univ.)

Globally injective and bijective neural operators · · · · · · · · · · · · · · · · · · · 10
Globally injective and bijective neural operators

概 要 Recently, there has been great interest in neural operators, which learn operators between inﬁnite-

dimensional function spaces. Given their discretization-invariance property, neural operators have beenremarkably successful, especially in learning solution operators for partial diﬀerential equations (PDEs). In
this talk, we show that injective neural operators are universal approximators of continuous operators. This
holds substantial relevance to inverse problems in PDEs, as injective neural operators can serve invertible
surrogate models for solution operators, which, in general, is not injective due to ill-posnedss of inverse
problems. This is joint work with Michael Puthawala (South Dakota State University), Matti Lassas(University of Helsinki), and Maarten V. de Hoop (Rice University).
52 長 瀬 准 平(電通大データ教育センター)
Jumpei Nagase(Univ. of Electro-Comm.)

区分非線型関数による ReLU 関数設計可能性 · · · · · · · · · · · · · · · · · · · · · · · 15

ReLU function representability by piecewise nonlinear functions

概 要 As a discussion on the representability of deep neural network models, we discuss the condition that

the ReLU function can be represented by a composition of non-linear functions and aﬃne functions. If theactivation function is representable of the ReLU function, then the deep neural network model is possible totransform any linear connection into a multilayer perceptron model. And since it is possible to express thedesign of that model architecture down as a parameter constraint, representability of the ReLU function is
an important concept in the systematic discussion of deep neural network models. Speciﬁc conditions are
the case by linear combination of functions and the case by composition of functions.
53 後 藤 田 剛 (東工大情報理工)
Takeshi Gotoda (Tokyo Tech)

Numerical study of enstrophy variation on ﬁltered-Euler ﬂows · · · · · · · 15
Numerical study of enstrophy variation on ﬁltered-Euler ﬂows

概 要 We investigate enstrophy variation in an incompressible and inviscid ﬂow through point-vortex solu-

tions of the 2D ﬁltered Euler equations, which are a regularized 2D Euler equations. The preceding results
have shown that there exist three point-vortex solutions converging to self-similar collapsing solutions of
the point-vortex system and dissipate the enstrophy in the zero limit of a ﬁlter scale. In this study, we
numerically show that the enstrophy dissipation could occur for certain four and ﬁve point-vortex solutionsin that limit.
54 清 水 雄 貴 (東 大 数 理)

Yuuki Shimizu (Univ. of Tokyo)

曲率変化の点渦への作用の定量化 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Impact of curvature on a point vortex

概 要 Towards quantifying the impact of curvature variations on a point vortex, we discuss some dynamical

properties of the point vortex on continuously diﬀerentiable surfaces obtained by gluing two diﬀerent
constant-curvature surfaces.

Final: 2024/2/6
91

応用数学

55 木 下 武 彦 (佐 賀 大 理 工)
渡 部 善 隆(九大情報基盤研究開発センター)
中 尾 充 宏 ( 早 大 理 工)

Takehiko Kinoshita (Saga Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

実 2 × 2 行列の 2 ノルムと近似逆作用素ノルムの収束オーダーの改善について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Regarding the matrix 2-norm of real 2 × 2 matrices and improved convergence order of norm for approximate inverse operetors

概 要 We report that we have improved the convergence order of norm for approximate inverse operetors

reported in [1].
56 寺 尾 剛 史(九大情報基盤研究開発センター)
渡 部 善 隆(九大情報基盤研究開発センター)
尾 崎 克 久(芝浦工大システム理工)
Takeshi Terao (Kyushu Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Katsuhisa Ozaki(Shibaura Inst. of Tech.)

無限次元線形作用素の近似逆作用素ノルムに対する精度保証付き特異値
計算 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Numerical veriﬁcation method of the approximate inverse operator norm
for inﬁnite-dimensional linear operators

概 要 In this talk, we present a veriﬁed singular value estimation, especially an enclosure of the spectral

norm for the approximate inverse operator norm for inﬁnite-dimensional linear operators. Enclosures of thespectral norm give important information in the computation of rigorous error bounds for the solution ofordinary and partial diﬀerential equations.
57 奥 村 真 善 美 (甲南大知能情報)

Makoto Okumura (Konan Univ.)

動的境界条件下のある構造保存スキームの可解性の証明に現れる行列の正則性について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

On the regularity of a matrix appearing in the proof of the solvabilityof a structure-preserving scheme under dynamic boundary conditions

概 要 Recently, the Cahn–Hilliard equation with dynamic boundary conditions that consider the Cahn–

Hilliard equation even on the boundary has been proposed by Goldstein–Miranville–Schimperna (GMS).
This model has characteristic conservation and dissipation laws. In the previous study, we proposed astructure-preserving scheme for the two-dimensional GMS model that retained the above laws in a discrete
sense and proved its solvability. In the proof, it is necessary to show the regularity of a certain matrix,
which was derived conditionally. Concretely, we clariﬁed at least how small the time mesh size should beaccording to the space mesh sizes to make the mapping well-deﬁned. In this study, we have unconditionallyproved the regularity of the matrix in a particular case. In this talk, we talk about the result.

Final: 2024/2/6
応用数学

58 石 渡 哲 哉(芝浦工大システム理工)
伊 藤 大 将 ( 芝 浦 工 大 理 工)
志 賀 大 知Tetsuya Ishiwata(Shibaura Inst. of Tech.)Daisuke Ito (Shibaura Inst. of Tech.)
Taichi Shiga92

時間非整数階移流方程式に対する空間単調性保存スキーム · · · · · · · · · · · 15

Monotonicity-preserving numerical scheme for fractional advection equation

概 要 The fractional advection equation is a time nonlocal equation that refers to the solution history;

that is, it is a delay partial diﬀerential equation. In this talk, we propose a ﬁnite diﬀerence scheme that
reproduces the monotonicity of the solution to the fractional advection equation and show theoretical results
and some numerical demonstrations.
14:15〜15:25
大⋆)59 菊 地 文 雄 (東劉雪 峰 ( 東 京 女 大 数 理)

Fumio Kikuchi (Univ. of Tokyo⋆)
Xuefeng Liu(Tokyo Woman’s Christian Univ.)

Techniques for hypercircle-based error estimation of ﬁnite element solutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Techniques for hypercircle-based error estimation of ﬁnite element solutions

概 要 Kikuchi and H.Saito once proposed an a priori error estimation method for ﬁnite element solutions

using P1 and Raviart–Thomas H(div) triangular elements. Recently, we have found that improved results
can be obtained and simpliﬁed technique introduced there is justiﬁed. We explain outline of the theory
with its analysis and give numerical results for a few sample problems. Reasonable coincidence between
theory and numerical results is observed, so that the proposed method and techniques are really eﬀective.
Our methodology is applicable to higher degree triangular and rectangular elements and also a posteriori
estimation.
60 A. N. F. Rudiawan( 金 沢 大 理 工)
A. Žák(Czech Tech. Univ. in Prague)
M. Beneš
(Czech Tech. Univ. in Prague)
木 村 正 人 ( 金 沢 大 理 工)
野 津 裕 史 ( 金 沢 大 理 工)
Aufa Numan Fadhilah Rudiawan(Kanazawa Univ.)
Alexandr Žák(Czech Tech. Univ. in Prague)
Michal Beneš(Czech Tech. Univ. in Prague)
Masato Kimura (Kanazawa Univ.)
Hirofumi Notsu (Kanazawa Univ.)

混相流モデルのための有限要素スキーム · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A ﬁnite element scheme for a multiphase ﬂow model

概 要 A numerical scheme for a multi-phase ﬂow model describing sedimentation phenomena is presented.

The unknown functions of the model are the velocities and the volume fractions of the N-phases and thecommon pressure, where N is the number of ﬂuid phases. After introducing an energy estimate of themodel, a stability result of the scheme and two-dimensional numerical results are also presented.

Final: 2024/2/6
93

応用数学

61 江 藤 徳 宏 (東 大 数 理)
(Univ. of Regensburg)
H. Garcke(
R. Nürnberg Univ. of Trento)
Tokuhiro Eto (Univ. of Tokyo)
Harald Garcke (Univ. of Regensburg)
Robert Nürnberg (Univ. of Trento)

A structure-preserving parametric ﬁnite element method for the multiphase Mullins–Sekerka problem with triple junctions · · · · · · · · · · · · · · · · 15
A structure-preserving parametric ﬁnite element method for the multiphase Mullins–Sekerka problem with triple junctions

概 要 We consider a sharp interface formulation for the multi-phase Mullins–Sekerka ﬂow. Making use ofa variational formulation, we introduce a fully discrete ﬁnite element method. Our discretization featuresa parametric approximation of the moving interfaces that is independent of the discretization used for theequations in the bulk. The scheme can be shown to be unconditionally stable and to satisfy an exact volumeconservation property. Moreover, an inherent tangential velocity for the vertices on the discrete curves leads
to asymptotically equidistributed vertices, meaning no remeshing is necessary in practice. Several numericalexamples, including a convergence experiment for the three-phase Mullins–Sekerka ﬂow, demonstrate thecapabilities of the introduced method.
62 シュワドレンカカレル( 都 立 大 理)

Karel Svadlenka (Tokyo Metro. Univ.)

障害物上の非等方的な界面運動に対する近似スキームについて · · · · · · · · 15

On an approximation scheme for anisotropic interfacial motion on obstacle

概 要 We consider L2 gradient ﬂow of anisotropic surface energy in the presence of an obstacle and possibly a

volume constraint. With the twofold purpose of existence proof and numerical implementation, we introduce
a thresholding approximation scheme employing anisotropic kernels, and investigate its properties, such asstability, convergence and Gamma-convergence of the corresponding approximate energies. We also show
numerical simulations of motions involving topology changes.
15:40〜16:40
劉

特別講演
大
逸 侃 (京Yikan Liu理)

非整数階拡散方程式の結合系と半線形問題の解のダイナミクスについて(Kyoto Univ.)

On solution dynamics of coupled systems and semilinear problems oftime-fractional diﬀusion equations

概 要 The last decade has witnessed explosive developments and gradual saturation of nonlocal models fromvarious practical backgrounds. As a popular representative, partial diﬀerential equations with fractional
derivatives in time have gathered considerable attentions among applied mathematicians. Recently, linear
theory for fractional diﬀusion equations with time derivatives in (0, 1) has been well established, followed byextensive researches on related numerical methods and inverse problems. This motivates the generalizationsof studies from single equations to coupled systems and from linear to nonlinear problems.
Started with a brief survey on existing results on time-fractional partial diﬀerential equations, this talkis concerned with the solution dynamics of their coupled and semilinear counterparts. For coupled timefractional diﬀusion systems, we obtain a sharp estimate for the long-time asymptotic behavior of solutions
by the Laplace transform. Further, we discover a new decay pattern by the coupling of non-fractionaland fractional diﬀusion equations. For time-fractional diﬀusion equation with superlinear convex semilinear
terms including Fujita type nonlinearity up , we show the blow-up of solutions and provide upper estimatesof the blow-up times by a comparison principle.

Final: 2024/2/6
トポロジー

ト

ポ

ロ

3 月 17 日（日）

ジ

94

ー

第 V 会場

9:30〜11:10
大理)
1 大 場 貴 裕 (阪Myeonggi Kwon
(Jeonbuk National Univ.)

Takahiro Oba (Osaka Univ.)
Myeonggi Kwon
(Jeonbuk National Univ.)

球面の単位余接バンドルのシンプレクティック充填について · · · · · · · · · · 15

Symplectic ﬁllings of unit cotangent bundles of spheres

概 要 This talk is concerned with symplectic ﬁllings of contact manifolds. After brieﬂy giving an overview

of results on the topology of symplectic ﬁllings, I will present joint work with Myeonggi Kwon, in which we
give some topological restrictions on symplectic ﬁllings of unit cotangent bundles of spheres S n and show
the uniqueness of diﬀeomorphism types of them, under some condition, for the case n = 3. Also, I will
explain an application of our result to exact symplectic cobordisms.
2 門 田 直 之 ( 岡 山 大 理)
A. Akhmedov (Univ. of Minnesota)

Naoyuki Monden (Okayama Univ.)
Anar Akhmedov (Univ. of Minnesota)

Geography of symplectic 4-manifolds admitting Lefschetz ﬁbrations · · 15
Geography of symplectic 4-manifolds admitting Lefschetz ﬁbrations

概 要 Ruled surfaces play an important role in the theory of Lefschetz ﬁbrations. In fact, Lefschetz

ﬁbrations on blow-ups of ruled surfaces have given many interesting examples. In this talk, using them, wegive Lefschetz ﬁbrations on minimal symplectic 4-manifolds with arbitrary ﬁnitely presented fundamentalgroups that violate the Noether inequality.
3 門 田 直 之 ( 岡 山 大 理)
A. Akhmedov (Univ. of Minnesota)

Naoyuki Monden (Okayama Univ.)
Anar Akhmedov (Univ. of Minnesota)

Ruled surfaces and indecomposable Lefschetz ﬁbrations · · · · · · · · · · · · · 15
Ruled surfaces and indecomposable Lefschetz ﬁbrations

概 要 In this talk, we give a relation among the genus of the base space of blow-ups of a ruled surface

admitting a Lefschetz ﬁbration, the number of blow-ups and the genus of the Lefschetz ﬁbration. Using
this relation, we obtain a condition for a Lefschetz ﬁbration to be ﬁber sum indecomposable. Moreover, wegive ﬁber sum indecomposable Lefschetz ﬁbrations on minimal total spaces.
4 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)

4 次元多様体上の Pa,b -surgery · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Pa,b -surgery on 4-manifolds

概 要 In 2004, Iwase and Matsumoto introduced pochette surgery. In 2018, Nakamura introduced a general-

ization of pochette surgery called Pa,b -surgery. A Pa,b -surgery on a 4-manifold X is an operation of removing
the interior of the boundary sum Pa,b = ♮a S 2 × D2 ♮b S 1 × D3 of a S 2 × D2 and b S 1 × D3 embedded in X
from X and gluing Pa,b to X − int Pa,b by a diﬀeomorphism of ∂Pa,b . P1,1 -surgery is nothing but pochette
surgery. In this talk, we introduce identiﬁcation factors of the diﬀeomorphism type of any Pa,b -surgery on
any 4-manifold by Nakamura. Furthermore, we compute the homology groups of any Pa,b -surgery of the
4-sphere with a trivial embedding. We also show that any ﬁnitely generated group is isomorphic to thefundamental group of a Pa,b -surgery on a simply connected 4-manifold.

Final: 2024/2/6
95

トポロジー

5 磯 島

司 ( 東 工 大 理)

Tsukasa Isoshima (Tokyo Tech)

Trisections of the doubles of some Mazur type 4-manifolds · · · · · · · · · · 15
Trisections of the doubles of some Mazur type 4-manifolds

概 要 A trisection is roughly a decomposition of a closed, oriented, smooth 4-manifold into three 4-

dimensional 1-handlebodies. A trisected 4-manifold can be described by a trisection diagram that consistsof a closed, oriented surface and certain three kinds of cut systems on the surface. A Mazur type 4-manifold
is a compact, contractible, smooth 4-manifold admits a handle decomposition that consists of only single 0-,1-, and 2-handle. It is known that the double of each Mazur type is diﬀeomorphic to S 4 . In this talk, weshow that certain trisection diagrams of the doubles of the Mazur types introduced by Akbulut and Kirby
are standard.
6 小 川 将 輝 (東北大MathCCS)
Masaki Ogawa (Tohoku Univ.)

Weinstein trisections of trivial surface bundles · · · · · · · · · · · · · · · · · · · · · 10
Weinstein trisections of trivial surface bundles

概 要 Trisection is a decomposition of a closed, oriented 4-manifold. Recently, a trisection which has

a symplectic property is introduced by Lambert-Cole, Meier and Starkston. This trisection is called a
Weinstein trisection. They showed that any closed 4-manifold with symplectic structure admits a Weinstein
trisection. But there only a few example of Weinstein trisection. In this talk, I introduce Weinstein
trisections of product of two closed surfaces.
11:20〜12:00

トポロジー分科会総会

14:20〜15:20
上特別講演
正 明 (京Masaaki Ue

大⋆)Constraints on intersection forms of 4-manifolds with given boundary
in terms of Gauge theoretical invariants(Kyoto Univ.⋆)

Constraints on intersection forms of 4-manifolds with given boundary
in terms of Gauge theoretical invariants

概 要 For any closed 3-manifold Y , there exists a compact 4-manifold X bounded by Y . We discuss

constraints on the intersection form of X (in particular when X is spin) in terms of several invariants ofY derived from Gauge theory, including Seiberg–Witten and Heegaard Floer theories. We mainly focus on
Manolescu’s κ-invariant of Y .
15:40〜17:30
7 森

淳 秀 ( 大 阪 歯 大 歯)Atsuhide Mori (Osaka Dent. Univ.)

極小主義言語学のモデル · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

A model of linguistic minimalism

概 要 In this presentation, I will propose an easy topological model of what the external and internal merges

in the generative linguistics are doing in the real brain and examine the need for formal techniques in a
recent development of linguistic minimalism.
8 北 野 晃 朗 ( 創 価 大 理 工)
柴 田 茉 莉 奈 ( 創 価 大 理 工)
Teruaki Kitano
Marina Shibata(Soka Univ.)(Soka Univ.)

種数 2 の曲面の基本群の Euler 類の引き戻しが非自明となる SL(2; Z[1/2])への線型表現について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

On linear representations of a surface group of genus 2 into SL(2; Z[1/2])
with a nontrivial real Euler class

概 要 Milnor proved that there exists a ﬂat real R2 -vector bundle over a closed orientable surface of genus

g > 1 with non-trivial Euler number in 1958. This was proved by giving a representation from thefundamental group of a surface in SL(2; R). Here SL(2; R) acts on the plane linearly and then does on
the unit circle. Hence the above result implies that the real Euler class is nontrivial on SL(2; R), which isdeﬁned originally in the homeomorphism group of the circle. Further as Sullivan mentioned in 1975, Milnor’s
construction was done implicitly on SL(2; Z[1/2]). In this talk, we give concrete examples of representations
in SL(2; Z[1/2]) with nontrivial Euler number. This is a joint work with Marina Shibata(Soka univ.).

Final: 2024/2/6
トポロジー

9 小 林 竜 馬 ( 石 川 工 高 専)
Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)96

コンパクトな向き付け不可能曲面のレベル d 写像類群の生成系 · · · · · · · 15

Generating sets for the level d mapping class group of a compact nonorientable surface

概 要 The level d mapping class group Md (S) of a surface S is the subgroup of the mapping class group of

S consisting of mapping classes acting trivially on H1 (S; Zd ). In this work, we gave a normal generating setof Md (Ng,n ) for a genus g ≥ 4 compact non-orientable surface Ng,n with n ≥ 0 boundaries. In addition,
we can construct a ﬁnite generating set of Md (Ng,n ) for n ≥ 1, from a ﬁnite generating set of Md (Ng,0 ) by
induction on n.
10 山 形颯 ( 福 岡 大 理)

So Yamagata (Fukuoka Univ.)

純組紐群の表示と組紐配置の切断について · · · · · · · · · · · · · · · · · · · · · · · · · 15

Presentation of the pure braid group and section of the braid arrangement

概 要 In1891, Hurwitz introduced the (pure) braid group as the fundamental group of the conﬁguration

space of points in the complex plane.
Later, in 1925, Artin studied the algebraic and geometric perspectives of braids. In particular, he gave apresentation of the braid group, which is now recognized as a standard one. He also studied the pure braid
group and gave its presentation. However, it is much more complicated than the one of the braid group.
Thus, there is nothing better than to have a simple to look and intuitive presentation of the pure braid
group.
In my talk, even though there is no new presentation, we connect two diﬀerent approaches to the puregroup: from group theory and from hyperplane arrangement.
11 盛

小 冰 (沖縄科学技術大)Xiaobing Sheng(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Some experimental results on knots and links constructed from Thompson’s group F a la Jones · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Some experimental results on knots and links constructed from Thompson’s group F a la Jones

概 要 Vaughan Jones motivated by an attempt to develop new conformal ﬁeld theory, obtained a sequenceof results related to Thompson’s groups F. One of the results is the concrete construction of knots andlinks from Thompson’s group F and the oriented Thompson’s group as an analogue of the results on braid
groups. Aiello and Baader investigated knots and links constructed from certain positive words in F andthey proved that the so-called positive oriented Thompson links are arborescent.
We present a sequence of computational results on certain sequences of knots from certain sequences ofwords and we also provide a way of estimating the number of crossings from the group theoretic property.
12 根 上春 (千葉大融合理工)

Haru Negami(Chiba Univ.)

Generalization of the twisted Long–Moody construction · · · · · · · · · · · · · 15
Generalization of the twisted Long–Moody construction

概 要 The Long–Moody construction is a method for obtaining a representation of the braid group froma given representation of the semidirect product of the free group and the braid group deﬁned by Artin
representation. Artin representation has a geometric realization such as the transformation of the loops
on a closed disk with n points. Wada generalized the Artin representation, which is called Wada-type
representation, and obtained the group invariants of links.
We extended the Long–Moody construction to obtain an inﬁnite series of representations of the braid groups
and named it as twisted Long–Moody construction. In this talk, we further extend the method to some of
the Wada-type representations. We then discuss the connection between this construction and the unitarityof the representation.

Final: 2024/2/6
97

トポロジー

3 月 18 日（月）9:30〜10:00
13 秋 田 利 之 (北高 瀬 壮 太 (北

大

理)

大

理)

Toshiyuki Akita (Hokkaido Univ.)
Sota Takase (Hokkaido Univ.)

第 V 会場

Wirtinger 表示を持つ群と 2 次の群ホモロジー · · · · · · · · · · · · · · · · · · · · · · 10Groups having Wirtinger presentations and the second group homology

概 要 Kuz’min (1996) characterized groups having Wirtinger presentations in relation to their second grouphomology. We further reﬁne the connections between these groups and their second group homology.
14 吉 永 正 彦 (阪
田 嶌
優 (北

大

理)

大

理)

Masahiko Yoshinaga (Osaka Univ.)
Yu Tajima (Hokkaido Univ.)

因果順序複体とマグニチュードホモトピー型 · · · · · · · · · · · · · · · · · · · · · · · 15

Causal order complex and magnitude homotopy type

概 要 The magnitude homology group of a metric space was introduced by Hepworth, Willerton, Leinster

and Shulman. In this talk, for a given metric space, we construct a pair of simplicial complexes whose
homology group is isomorphic to the magnitude homology group. The construction is based on the causal
order on the metric space-time and its order complex.

3 月 18 日（月）10:10〜10:25

第 IV 会場

2023 年度日本数学会幾何学賞授賞式

10:30〜11:30 2023 年度日本数学会幾何学賞受賞特別講演 (幾何学分科会と合同)
大理) ♭ ファノ多様体の K 安定性の判定法について
藤 田 健 人 (阪Kento Fujita(Osaka Univ.)

On criteria for the K-stability of Fano varieties

概 要 We survey recent progress on K-stability of Fano varieties.

3 月 18 日（月）13:00〜14:00
衛
大)
15 知 念 直 紹 (防
(
愛
媛
大
理
工)
山 内 貴 光Naotsugu Chinen(Nat. Defense Acad. of Japan)
Takamitsu Yamauchi (Ehime Univ.)

第 V 会場

Equivariant asymptotic dimension, asymptotic dimension and covering
dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Equivariant asymptotic dimension, asymptotic dimension and covering
dimension

概 要 We consider the following question. For a free action Γ ↷ X of a discrete group Γ on a normal

space X with ead(Γ ↷ X) < ∞, does the inequality ead(Γ ↷ X) ≤ asdim Γ+ dim X hold? We give thefollowing positive partial answer. If Γ is locally ﬁnite, then ead(Γ ↷ X) ≤ dim X(without the assumptionead(Γ ↷ X) < ∞). In particular, if X is the n-dimensional sphere, then ead(Γ ↷ X) = n.
16 平 田 康 史 (神 奈 川 大 工)
矢 島 幸 信 (神 奈 川 大⋆)

Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)

距離空間との積における弱い D-空間性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weak D-space properties on products with metric spaces

概 要 In this talk, we discuss weak D-space properties on products with metric spaces. We obtain the resultthat for each normal product space X × Y with a metric space Y , (1) if X is a collectionwise Hausdorﬀ
aD-space, then X × Y is an aD-space, (2) if X is an irreducible space, then X × Y is irreducible.

Final: 2024/2/6
トポロジー

17 平 田 康 史 (神 奈 川 大 工)
矢 島 幸 信 (神 奈 川 大⋆)

Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)98

無限積空間における弱い D-空間性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Weak D-space properties on inﬁnite products

概 要 In this talk, we discuss weak D-space properties on inﬁnite products. We obtain the result that (1)the Σ-product of arbitrary many copies of I is dually discrete, where I = [0, 1] is the closed interval in thereal line, (2) if κ is an inﬁnite cardinal such that there is no weakly inaccessible cardinal ≤ κ, then Nκ isirreducible, where N = {0, 1, 2, · · · } is the countable discrete space.

3 月 19 日（火）第 V 会場

9:30〜12:00
18 石 川 勝 巳 (京 大 数 理 研)
森 藤 孝 之 ( 慶 大 経 済)
鈴 木 正 明 ( 明 大 総 合 数 理)

Katsumi Ishikawa (Kyoto Univ.)
Takayuki Morifuji (Keio Univ.)
Masaaki Suzuki (Meiji Univ.)

Twisted Alexander vanishing order of knots · · · · · · · · · · · · · · · · · · · · · · · 10

Twisted Alexander vanishing order of knots

概 要 We deﬁne the twisted Alexander vanishing order of a knot to be the order of the smallest ﬁnite groupsuch that the corresponding twisted Alexander polynomial is zero. In this talk, we show its basic properties.
19 合 田洋 ( 東 京 農 工 大 工)
森 藤 孝 之 ( 慶 大 経 済)
Hiroshi Goda
(Tokyo Univ. of Agri. and Tech.)Takayuki Morifuji (Keio Univ.)

双曲結び目の chirality とねじれ Alexander 多項式 · · · · · · · · · · · · · · · · · · 10

Chirality of hyperbolic knots and twisted Alexander polynomials

概 要 In this talk, we report a relationship between the chirality of knots and higher-dimensional twisted

Alexander polynomials associated with holonomy representations of hyperbolic 3-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic 3-cone-manifold ofﬁnite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist
knots, according to our criterion, using low-dimensional irreducible representations.
20 沢 辺俊 ( 早 大 理 工)

Shun Sawabe(Waseda Univ.)

On the annihilating polynomial of the colored Jones polynomial for theWhitehead link · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
On the annihilating polynomial of the colored Jones polynomial for theWhitehead link

概 要 An annihilating polynomial of the colored Jones polynomial for a knot is conjectured to produce theA-polynomial when made into a commutative polynomial by putting q = 1 (AJ conjecture). In this talk, wegive an annihilating polynomial of the colored Jones polynomial for the Whitehead link. We observe thata kind of A-polynomial appears when we make the annihilating polynomial into a commutative polynomial
as in the AJ conjecture. We also give another annihilating polynomial for the Whitehead link that isalternating under the transposition of colors.

Final: 2024/2/6
99

トポロジー

21 田 中心 ( 東 京 学 大 教 育)大理)
谷 口 雄 大 (阪Kokoro Tanaka (Tokyo Gakugei Univ.)
Yuta Taniguchi (Osaka Univ.)

結び目 n-カンドルのカンドル二次ホモロジー群 · · · · · · · · · · · · · · · · · · · · · 10

The second quandle homology group of the knot n-quandle

概 要 The knot quandle is known to be a complete invariant for oriented classical knots up to orientation.

Eisermann computed the second quandle homology group of the knot quandle and showed that it characterizes the unknot. In this talk, we compute the second quandle homology group of the knot n-quandle foreach integer n > 1, where the knot n-quandle is a certain quotient of the knot quandle. Although the knot
n-quandle is weaker than the knot quandle, the second homology group of the former is found to have more
information than that of the latter.
22 姫 野 圭 佑 (広島大先進理工)

Keisuke Himeno (Hiroshima Univ.)

結び目フレア複体が (3, q) 型トーラス結び目と安定同値な双曲結び目 · · 10Hyperbolic knots whose knot Floer complex is stably equivalent to thatof a (3, q)-torus knot

概 要 Two (full) knot Floer complexes are called stably equivalent if they can be made to become ﬁlteredchain homotopy equivalent by adding an acyclic complex to each complex. Hom showed that if two knots
are concordant, then their knot Floer complexes are stably equivalent. In this talk, we construct inﬁnitely
many mutually non-concordant hyperbolic knots whose knot Floer complex is stably equivalent to that of a(3, q)-torus knot. In particular, the upsilon invariant of such knots is convex. This gives a new answer to
Borodzik and Hedden’s question of for which knots is the upsilon invariant a convex function.
23 吉 田 は ん (群 馬 工 高 専)
Han Yoshida(Gunma Nat. Coll. of Tech.)Commensurators of Löbell polyhedra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Commensurators of Löbell polyhedra

概 要 For a non-arithmetic Kleinian group Γ < Isom(H3 ), the commensurator C(Γ) < Isom(H3 ) is the(unique) maximal group commensurable with Γ. Few examples of computation of commensurators ofcocompact Kleinian groups are known. Let Ln be the Löbell polyhedron, which is a compact polyhedron
with 2n + 2 faces, and Γ(Ln ) the subgroup of Isom(H3 ), generated by the reﬂections in the faces of Ln . In
this talk, I will show the calculation of the commensurators C(Γ(Ln )) for n ≥ 61.
24 河 村 建 吾(大阪産大全学教育機構)

Kengo Kawamura (Osaka Sangyo Univ.)

絡み目射影図に対する整数値領域選択問題の可解性 · · · · · · · · · · · · · · · · · 15

Solvability of an integral region choice problem for a link projection

概 要 Ahara and Suzuki proved that an integral region choice problem for a knot projection is solvable.

This result does not hold for replacing “knot projection” with “link projection”. In this talk, we introduce
a diagrammatic characterization to solve an integral region choice problem for a link projection.
25 小 林 真 人 (秋 田 大 理 工)
佐 野 貴 志 ( 北 海 学 園 大 工)
山 本
稔 ( 弘 前 大 教 育)

Mahito Kobayashi (Akita Univ.)
Takashi Sano (Hokkai-Gakuen Univ.)
Minoru Yamamoto (Hirosaki Univ.)

閉折れ線の全周投影変換を用いた幾何公式の証明 · · · · · · · · · · · · · · · · · · · 15

Panorama views of closed piecewise linear curves in R2 for shape study

概 要 For a closed piecewise linear (PL) curve in R2 , a geometric transformation called a panorama view isapplied to show two basic formulae on the shape of the curve by Crofton and by Banchoﬀ. We note thatfor a simple PL curve, a sequence of polygons can be obtained by which one can describe the organizationsof so called hollows of the curve.

Final: 2024/2/6
トポロジー

26 齋 藤 幸 子 (北 教 大 旭 川)

Sachiko Saito (Hokkaido Univ. of Edu.)

100

−
J10
型の強義混合擬斉次多項式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10−
Strongly mixed weighted homogeneous polynomials of type J10

概 要 We consider a strongly mixed weighted homogeneous polynomial f := f2,2,1,2,1,4 (k = 3) = z22 z̄2 −−6z12 z2 z̄2 + 11z12 z̄12 z2 − 6z14 z̄12 of type J10. We ﬁrst show that f := f2,2,1,2,1,4 (k = 3) is strongly Newton

non-degenerate. We next consider the toric modiﬁcation π̂ : X → C2 associated with the regular simplicial
cone subdivision Σ∗ which is admissible for the dual Newton diagram Γ∗ (f ) of f . Then it is concluded
that the strict transform Ṽ via the toric modiﬁcation π̂ of the mixed hypersurface singularity V := f −1 (0)is not only a real analytic manifold outside of Ṽ ∩ π̂ −1 (0) but also a real analytic manifold as a germ atṼ ∩ π̂ −1 (0).
14:20〜15:20

特別講演
大山 下 真 由 子 (京理) ♭ Topological Modular Forms and supersymmetric quantum ﬁeld theories

Mayuko Yamashita (Kyoto Univ.)

Topological Modular Forms and supersymmetric quantum ﬁeld theories

概 要 In this talk I will explain my works with Y. Tachikawa and T. Johnson-Freyd to give a bridge between

physics and homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E∞
ring spectrum which has deep and rich structure from homotopy-theoretical viewpoints. On the other hand,
TMF is relevant in physics because it is conjectured by Stolz and Teichner to classify two-dimensional
supersymmetric quantum ﬁeld theories (SQFTs). We originally started from applying TMF to a problem
in superstring theory, but investigating it further, we have found many interesting mathematical results on
TMF out of physical motivations.
In the ﬁrst work (https://arxiv.org/abs/2108.13542) with Tachikawa we used TMF to prove the vanishingof anomalies in heterotic string theory. After that, N. Kawazumi suggested considering a secondarytransformation of spectra arising from the vanishing result. This idea turns out to be crucial; we found thatthe secondary transformation coincides the Anderson duality of TMF. This result allows us to detect subtle
torsion phenomena in TMF by diﬀerential-geometric ways, and leads us to new conjectures on the relation
between VOAs and TMF (https://arxiv.org/abs/2305.06196). Moreover, in the work-in-progress with T.
Johnson-Freyd, we found a new explanation of the mysterious 576-periodicity in TMF and SQFTs. In thetalk, I explain this exciting interplay between physics and mathematics.

Final: 2024/2/6
101

無限可積分系無 限

可3 月 19 日（火）

積

分

系

第 VIII 会場

9:30〜11:30
1 森 み ず き
(お茶の水女大人間文化)
竹 村 剛 一 (お茶の水女大基幹)

Mizuki Mori (Ochanomizu Univ.)
Kouichi Takemura (Ochanomizu Univ.)

ホインの微分方程式に関連する三項間漸化式 · · · · · · · · · · · · · · · · · · · · · · · 15

Three-term recurrence relations and Heun equations概 要 Heun’s diﬀerential equation is a standard form of the second order Fuchsian diﬀerential equation withfour singularity, and it has an accessory parameter. We investigate the coeﬃcients of the local holomorphic
solution to Heun’s diﬀerential equation around the origin. We use the facts that the coeﬃcients arepolynomials on the accessory parameter and they satisfy a three-term recurrence relation.
2 新 井 由 美
(お茶の水女大人間文化)
Yumi Arai (Ochanomizu Univ.)

Solutions to q-hypergeometric equations associated with q-middle convolution · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Solutions to q-hypergeometric equations associated with q-middle convolution

概 要 We investigate the integral representations of solutions to q-hypergeometric equation and its variant

obtained through q-middle convolution by using transformation formulas for q-hypergeometric series. We
show the correspondence between these integral solutions and solutions obtained through other methods.
We also show the linear relationships among the integral solutions.
3 信 川 喬 彦 ( 神 戸 大 理)
藤 井 大 計 ( 神 戸 大 理)

Takahiko Nobukawa (Kobe Univ.)(Kobe Univ.)
Taikei Fujii

q 超幾何方程式の 3 次の変異版の接続問題 · · · · · · · · · · · · · · · · · · · · · · · · · 15
Connection problem for the variant of q-hypergeometric equation ofdegree three

概 要 The variant of q-hypergeometric equation of degree three is introduced by Hatano–Matsunawa–Sato–

Takemura (Funkcial. Ekvac., 2022) from the viewpoint of quantum integrable systems. Euler-type integral
solutions and hypergeometric series solutions are obtained by Fujii–Nobukawa (arXiv:2207.12777). The
main purpose of this talk is to give linear relations for the integral solutions. As an application, we get athree term relation for the very-well-poised q-hypergeometric function 8 W7 .
4 森 山 翔 文 ( 阪 公 大 理)
Sanefumi Moriyama(Osaka Metro. Univ.)

ABJM 行列模型と q パンルヴェ方程式 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
ABJM matrix models and q-Painlevé equations

概 要 It was known that sometimes Painlevé equations have solutions of matrix models. We conjecturethat a certain matrix model solves the sixth q-Painlevé equation. This matrix model originates from athree-dimensional superconformal Chern–Simons theory which describes multiple M2-branes in M-theory.
The partition function of this theory reduces to a matrix model using the localization theorem. Aftermoving to the grand canonical ensemble by introducing the fugacity dual to the overall rank, we ﬁnd the
grand canonical partition function serves as the tau function and solves the 40 bilinear relations of qPVI.
This talk is based on works with Tomoki Nosaka, JHEP08(2023)191.

Final: 2024/2/6
無限可積分系

5 大 山 陽 介 ( 徳 島 大 理 工)

Yousuke Ohyama (Tokushima Univ.)

102

Mano’s decomposition and q-Painlevé equations · · · · · · · · · · · · · · · · · · · · 15
Mano’s decomposition and q-Painlevé equations

概 要 We study connection formula of several types of q-Painlevé equations. Mano’s decomposition, which

is a q-analogue of Jimbo’s decomposition theorem, is a powerful tool to study global theory on q-Painlevé
equations. We show existence of solutions given by formal double power series for the q-Painlevé equations.
In degenerated cases, some conﬂuent basic hypergeometric functions appear after decomposing the Laxpairs.
6 増 田

哲 ( 青 学 大 理 工)

Tetsu Masuda (Aoyama Gakuin Univ.)

Painlevé V 方程式の梅村多項式の判別式 · · · · · · · · · · · · · · · · · · · · · · · · · · 15
An explicit formula for the discriminants of the Umemura polynomialsof the Painlevé V equation

概 要 We present a combinatorial formula for the discriminants of the Umemura polynomials associatedwith a family of rational solutions to the Painlevé V equation.
14:15〜15:15

特別講演

大 川
領
(阪公大数学研・京大数理研)

Non-stationary diﬀerence equation and aﬃne Laumon space

Ryo Okawa(Osaka Metro. Univ./Kyoto Univ.)

Non-stationary diﬀerence equation and aﬃne Laumon space

概 要 In the ﬁrst half of the talk, we will introduce the joint work with Awata, Hasegawa, Kanno, Shakirov,

Shiraishi, and Yamada. We explain the theorem that the aﬃne Laumon partition function is a solution of
the Shakirov equation. The Shakirov equation is gauge equivalent to the quantized q-diﬀerence PainlevéVI equation proposed by Hasegawa. It is also identiﬁed with the quantum Knizhnik–Zamolodchikov(q-KZ)(1)equation for Uq (A1 ). In the latter half of the talk, we would like to introduce the joint work with Shiraishi,
and point out the similarity between the Shakirov equation and the wall-crossing formula.

3 月 20 日（水）第 VIII 会場

9:30〜11:30
大理)
7 吉 永 正 彦 (阪( グ ラ ス ゴ ー 大)
M. Feigin
大理)
Zixuan Wang (北Masahiko Yoshinaga (Osaka Univ.)
Misha Feigin (Univ. of Glasgow)
Zixuan Wang (Hokkaido Univ.)

重複度付き超平面配置の対数的ベクトル場の積分表示 · · · · · · · · · · · · · · · 15

Integral expressions of logarithmic vector ﬁelds for multiarrangements

概 要 The explicit construction of the logarithmic vector ﬁelds for hyperplane arrangements with multiplicity

is a hard problem in general. In this talk, we will discuss integral expression of them.
8 筧三 郎 ( 立 教 大 理)

Saburo Kakei(Rikkyo Univ.)

楕円関数を背景場とする KP 階層の解 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Solutions to the KP hierarchy with an elliptic background概 要 A class of “elliptic soliton” solutions of the Kadomtsev–Petviashvili hierarchy, which includes a

determinantal solution of Li and Zhang, is described in terms of pseudo-diﬀerential operator formulation.
Real-valued solutions are discussed and various examples that display web-like patterns are presented.

Final: 2024/2/6
103

無限可積分系

9 渋 川 元 樹 ( 神 戸 大 理)
野 海 正 俊 ( 立 教 大 理)

Genki Shibukawa (Kobe Univ.)
Masatoshi Noumi (Rikkyo Univ.)

Ruijsenaars 型恒等式とその応用 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Ruijsenaars-type identities and their applications

概 要 We prove some identities, which we call Ruijsenaars-type identities, and show their applications suchas 1) commutativity of some diﬀerence operators and 2) Weyl group symmetry of the Tableau representationof interpolation polynomials.
10 武 中亮 ( 阪 公 大 理)

Ryo Takenaka (Osaka Metro. Univ.)

Y-system に付随する指数について · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
On exponents associated with Y-systems

概 要 Let g be a ﬁnite dimensional simple Lie algebra and X be its Dynkin diagram. Associated with X

and a positive integer ℓ such that ℓ ≥ 2, Kuniba and Nakanishi introduced a system of algebraic relations
called Y-system. It has been proved that solutions of the Y-system have periodicity. Based on this result,
Mizuno introduced a notion of exponent and gave a conjectual formula expressing the exponents for any(X, ℓ). He also gave a proof for (A1 , ℓ) and (Ar , 2). In this talk, we show results for some other Dynkintypes and level ℓ = 2.
11 赤 木 亮 太 (名 大 多 元 数 理)
Ryota Akagi(Nagoya Univ.)

ランク 2 団散乱図の整列積表示について · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Ordered product expressions of rank 2 cluster scattering diagrams

概 要 We focus on cluster scattering diagrams, which were introduced in recent years. They are closely

related to cluster algebras. By Nakanishi’s study, it was clariﬁed that dilogarithm elements play animportant role in cluster scattering diagrams. In particular, for rank 2 cases, every cluster scattering
diagram is recovered by a (possibly inﬁnite) product of dilogarithm elements, which is called ordered
product of dilogarithm elements. In this talk, we show some result for these ordered products.
12 井 上玲 ( 千 葉 大 理)
国 場 敦 夫 ( 東 大 総 合 文 化)寺 嶋 侑 二 ( 東 北 大 理)
(Chiba Univ.)
Rei Inoue
Atsuo Kuniba (Univ. of Tokyo)
Yuji Terashima (Tohoku Univ.)

量子クラスター代数と 3 次元可積分性 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Quantum cluster algebras and 3D integrability

概 要 We construct new solutions to the tetrahedron equation and the 3D reﬂection equation, by developing

the recent study by Sun and Yagi on the tetrahedron equation applying quantum cluster algebras.
14:15〜15:15

特別講演
伊 藤 克 司 ( 東 工 大 理)

Katsushi Ito(Tokyo Tech)

ODE/IM 対応と量子力学における完全 WKB 解析
ODE/IM correspondence and exact WKB analysis in quantum mechanics

概 要 The ODE/IM correspondence, which was found by P. Dorey and R. Tateo in 1998, provides a non-trivial relation between the spectral problem of ordinary diﬀerential equations and the functional relation
approach in the quantum integrable system. This relation clariﬁes also the relation between the exact WKB
analysis of one-dimensional quantum mechanics and the Thermodynamic Bethe Ansatz (TBA) equationin two-dimensional quantum integrable theory. The Voros symbols in the exact WKB analysis correspondto the Y-functions. In this talk, we review the ODE/IM correspondence for the Schrödinger equation
with polynomial potential. The associated TBA equations show the wall-crossing phenomena under the
deformation of the potential, which describes a detailed structure of the correspondence. We also discuss ageneralization to higher-order ODE.