Final: 2024/2/9“ The Mathematical Society of Japan
2024 Annual Meeting

Titles and Short Summaries of the Talks

March, 2024
at Osaka Metropolitan University2024 The Mathematical Society of Japan
ANNUAL MEETING
Dates: March 17th (Sun)–20th (Wed), 2024
Venue: Osaka Metropolitan University
3–3–138 Sugimoto, Sumiyoshi-ku
Osaka-shi, 558-8585, Japan
Contact to: Graduate School of Science, Osaka Metropolitan University
3–3–138 Sugimoto, Sumiyoshi-ku
Osaka-shi, 558-8585, Japan
E-mail omu24mar mathsoc jp
The Mathematical Society of Japan
I

II

III

IV

V

VI

VII

VIII

IX

General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg. General Edu. Bldg.
810
811
812
813
814
815
820
821
822

Algebra17th

9:00–10:30
14:15–18:00

Functional Statistics andEquations Probability

Geometry

Topology

ComplexAnalysis

Functional Found. of Math. Applied
Analysis & Hist. of Math. Mathematics

9:30–12:00
14:15–16:15

9:30–11:45
14:15–16:10

9:30–11:10
15:40–17:30

9:50–11:20
15:35–16:30

9:30–11:00

9:30–11:40(Sun)

Featured Invited Talks

9:30–11:30
14:30–17:00

13:00–14:00

Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk Invited Talk Invited Talk

Invited Talk

10:45–11:45

17:00–18:00

16:30–17:30

14:15–15:15
15:30–16:30

16:25–17:25

14:20–15:20

14:15–15:15

14:15–15:15

ComplexAnalysis

Functional Found. of Math. Applied
Analysis & Hist. of Math. Mathematics

9:50–11:20

9:30–11:00

AlgebraFunctional Statistics andEquations Probability

Geometry

Topology

9:30–12:00

9:30–12:00

13:00–14:00

9:30–10:00
13:00–14:00

9:30–11:40

9:15–12:00

18th Invited Talk Invited Talk

Invited Talk

Invited Talk Invited Talk Invited Talk

(Mon) 13:00–14:00

10:30–11:30

13:00–14:00

13:00–14:00

MSJ Prizes Presentation (Auditorium, 1F, Basic Experiment Edu. Bldg.)
Plenary Talks (Auditorium, 1F, Basic Experiment Edu. Bldg.)
Oﬃcial Party (Nonohana House, 1F, Media Center)
Algebra9:30–12:00

19th

Functional Statistics andEquations Probability
9:45–12:00
14:15–16:00

10:00–11:10(Tue)

13:00–14:00

9:00–12:00
13:00–14:00

13:00–14:00· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30–15:00)
Spring Prize Winner · · · · · · · · · · · · · · · · · · (15:15–16:15)
Ken-ichi Yoshikawa (Kyoto Univ.) · · · · · · · (16:30–17:30)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:00–20:00)

Geometry

Topology

9:30–11:45
14:15–17:10

9:30–12:00

Featured Invited Talks

Real
Analysis

Functional
Analysis

InﬁniteAnalysis

AppliedMathematics

9:30–12:00
14:15–16:15

9:30–11:30
14:15–15:45

9:30–11:30

9:50–12:00
14:50–16:30

13:00–14:00

Invited Talks Invited Talk

Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk

14:40–15:40
16:00–17:00

14:20–15:20

Algebra20th

9:00–12:00
14:15–16:50

9:00–12:00
14:15–18:00

16:15–17:15

Functional Statistics andEquations Probability
10:00–12:00
14:15–15:15

10:00–11:40(Wed)

Geometry
9:20–10:15

Featured Invited Talks

16:30–17:30

16:00–17:00

14:15–15:15

16:45–17:45

Real
Analysis

InﬁniteAnalysis

AppliedMathematics

9:30–12:00
14:15–15:40

9:30–11:30

9:50–12:00
14:15–15:25

13:00–14:00

Invited Talk Invited Talks Invited Talk

Invited Talks

Invited Talk Invited Talk

15:30–16:30

15:45–16:45
17:00–18:00

14:15–15:15

14:15–15:15
15:30–16:30

10:30–11:30

15:40–16:40

Final: 2024/2/9
3

Contents
Plenary Talks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Featured Invited Talks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Foundation of Mathematics and History of Mathematics

1
2. . . . . . . . . . . . . . . . . . . .

4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9March 17th (Sun)March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

March 17th (Sun)March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29Functional Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

Real Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44Functional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Statistics and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

Final: 2024/2/9
4

March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Applied Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

March 17th (Sun). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

March 18th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

Inﬁnite Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80March 19th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80March 20th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

March 17th (Sun)Final: 2024/2/9
1

Plenary Talks

Plenary Talks
March 18th (Mon) Auditorium, 1F, Basic Experiment Education Building
Spring Prize Winner····················································(15:15–16:15)

Ken-ichi Yoshikawa (Kyoto Univ.)

Holomorphic analytic torsion for manifolds of Calabi–Yau
type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(16:30–17:30)

Summary: 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: 2024/2/9
Featured Invited Talks

2

Featured Invited Talks
March 17th (Sun)
Conference Room I
Guest Talk from the Japan Society for Industrial and Applied Mathematics
Hiroshi Sekigawa (Tokyo Univ. of Sci.) Symbolic-numeric computation · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Symbolic-numeric computation is a computing methodology that combines ideas from symbolicand numeric computation. Symbolic computation (a.k.a. computer algebra) is very reliable, but it has
the following 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.
Conference Room II

Akihiro Munemasa (Tohoku Univ.)

Combinatorics of equiangular lines · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: 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 asa purely combinatorial problem in terms of switching classes of graphs. In this talk, I will survey recent
development on this problem in connection with root systems and integral lattices. I will also brieﬂy touch onits complex analogue, where “lines” mean complex 1-dimensional subspaces, and “angles” mean the absolutevalues 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.
Conference Room IV

Junguk Lee (Changwon National Univ.)

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

Summary: 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.

March 19th (Tue)
Conference Room II
Takasi Senba (Fukuoka Univ.)

Behavior of solutions to chemotaxis systems with logarithmic
sensitivity functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: 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 willtalk some results on blowup and global existence of those solutions.

Final: 2024/2/9
3

Featured Invited Talks

Conference Room IV

Goo Ishikawa (Hokkaido Univ.⋆)

Singular curves of sub-Riemannian spaces and related topics····················································(13:00–14:00)

Summary: 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.

March 20th (Wed)Conference Room I

Masataka Chida (Tokyo Denki Univ.)

On generalizations of p-adic Gross–Zagier formula · · · · · · · ·(13:00–14:00)

Summary: Gross and Zagier showed a remarkable formula which relates the ﬁrst derivatives of L-functions
for modular forms of weight two and heights of Heegner points on modular curves. Perrin-Riou proved ap-adic analogue of the Gross–Zagier formula. They have many important arithmetic applications including
the conjecture 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 ofarithmetic 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.
Conference Room IV

Kenji Kajiwara (Kyushu Univ.)

Generation of aesthetic shape by integrable geometry · · · · ·(13:00–14:00)

Summary: 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 Michell structurein architecture in which mechanical optimality, integrability, and aesthetic nature coexist will be discussed,
together with the relationship with the discrete harmonic functions.

Final: 2024/2/9
Foundation of Mathematics and History of Mathematics

4

Foundation of Mathematics and History of Mathematics
March 17th (Sun)

Conference Room VIII

9:30–11:30
1 Souji Shizuma (Osaka Pref. Univ.)

General theorem for nonsimultaneous hat puzzles · · · · · · · · · · · · · · · · · · 15

Summary: The prisoner and hat puzzle, also known as the hat problem, is divided into two depending onwhether 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 Kenta Tsukuura (Hosei Univ.)

On semiproperness of Namba forcings in Prikry extensions · · · · · · · · · · 15

Summary: 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 Teruyuki Yorioka (Shizuoka Univ.)

Some preservation theorems for forcing notions with models as side
conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Toshimichi Usuba (Waseda Univ.)

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

Summary: 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 Yasuo Yoshinobu (Nagoya Univ.)

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

Summary: 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 Akito Tsuboi (Univ. of Tsukuba⋆)

Dividing and forking in random structures · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Dividing and forking are important concepts in model theory, both of which are related toabstract independence. Although these two concepts are not equivalent in general, in simple theories, they
are equivalent. We demonstrate that these concepts diﬀer in random hypergraphs omitting a certain kindof sub-hypergraphs. This work is a continuation of the study on which I presented at the 2022 fall meetingof the MSJ.
7 Hirotaka Kikyo (Kobe Univ.)
Akito Tsuboi (Univ. of Tsukuba⋆)

On random hypergraphs and automorphisms with a single orbit · · · · · 15

Summary: 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 freeamalgamation 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.

Final: 2024/2/9
5Foundation of Mathematics and History of Mathematics

11:45–12:00

Research Section Assembly

14:30–17:00
8 Koichiro Ikeda(Hosei Univ.)

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

Summary: 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 Wataru Komine (Univ. of Tsukuba)

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

Summary: Pillay and Steinhorn showed that every o-minimal theory has a prime model and it is unique up
to isomorphism. We are interested in deﬁnably complete locally o-minimal theory which is generalizationof o-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 Koki Okura (Univ. of Tsukuba)

On rationality of Poincaré series in expansions of the p-adic ﬁelds · · · · 15

Summary: 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 Ikuo Yoneda (Tokuyama Coll. of Tech.)

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

Summary: 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 Noriaki Kamiya (Univ. of Aizu⋆)

On the title “Lie algebra” of books published in Japan · · · · · · · · · · · · · · 15

Summary: 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.
13 Koichi Hirata(Matsuyama Univ./Ehime Univ.⋆)

Geometric foundations of inversive coordinates of circles · · · · · · · · · · · · 15

Summary: 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,
and we have introduced such applications so far. On the other hand, the geometric foundation of thecoordinate system is also important. In this study, we present the results of the foundation for both σ > 0
and σ < 0 cases. We will also introduce the diﬀerences between the two cases.
14 Noriko Tanaka (Naragakuen Univ.)
Tsukane Ogawa (Yokkaichi Univ.)

A study on the relationship of Takuma school’s book Shouyaku-jutsu
and a mathematical plate dedicated to the Zenkouji temple · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Foundation of Mathematics and History of Mathematics

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

6

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

Summary: 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

Mathematics History Team Meeting

March 18th (Mon)

Conference Room VIII

9:15–12:00
16 Masaaki Kumazawa(Mino-Jiyu Gakuen High School)

On De Morgan algebras in BCK-algebras · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
17 Haruka Kogure (Kanazawa Univ.)
Taishi Kurahashi (Kobe Univ.)

On the conservation results for local reﬂection principles · · · · · · · · · · · · 15

Summary: For a class Γ of formulas, Γ local reﬂection principle RfnΓ (T ) for a theory T of arithmetic is ascheme formalizing the Γ-soundness of T . Beklemishev proved that for every Γ ∈ {Σn , Πn+1 | n ≥ 1}, thefull 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.
(Kobe Univ.)
18 Yuta Sato
Taishi Kurahashi (Kobe Univ.)

The ﬁnite frame property of some extensions of the pure logic of necessitation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the ﬁnite frame property of some extensions of Fitting, Marek, and Truszczyński’s purelogic of necessitation N. For any natural numbers m, n, we introduce the logic N+ Am,n by adding the axiom¬□φinto N. We proved the ﬁnite frame property of N+ Am,n with
scheme □n φ → □m φ and the rule¬□□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.

Final: 2024/2/9
7Foundation of Mathematics and History of Mathematics(Kobe Univ.)
19 Rihito Takase
Taishi Kurahashi (Kobe Univ.)

The modal logic of provability and forcing · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 to analyze this structure. Hamkins–Löwe studied the forcing accessibility relation on the multiverse.
More precisely, 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
a bimodal logic PF and prove that the modal logic of provability and forcing corresponds to PF.
20 Taishi Kurahashi (Kobe Univ.)
Albert Visser (Utrecht Univ.)

Incompleteness, undecidability, and inseparability of theories · · · · · · · · 15

Summary: 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.
21 Leonardo Pacheco (TU Wien)

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

Summary: 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
the Gödel modal logic GK.
22 Leonardo Pacheco (TU Wien)

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

Summary: 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 acontradiction 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 thefeedback construction? We deﬁne αth order feedback Turing machines for each computable ordinal α anddescribe the semi-computable sets using inductive deﬁnitions and Gale–Stewart games. (Joint work with
Juan P. Aguilera and Robert S. Lubarsky.)
23 Toshio Suzuki (Tokyo Metro. Univ.)

Equilibria of AND-OR trees without assumptions on tree shapes (2)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 ofrandomized directional algorithms coincide. In the current talk, we discuss subsequent development. This
work was done in collaboration with Fuki Ito.

24 Akitoshi Kawamura (Kyoto Univ.)
Keita Hiroshima (Kyoto Univ.)

Elementarily traceable numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A function is called elementary if it can be computed in time bounded by a tower of powers ofconstant height. A trace function for an irrational number α is a function that maps each rational number
r to a rational 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
not elementary. 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
in the binary expansion of the number, is not elementary.

Final: 2024/2/9
Foundation of Mathematics and History of Mathematics

25 Kohtaro Tadaki (Chubu Univ.)

8

A reﬁnement of quantum information theory by algorithmic randomness
VIII · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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

Talk Invited by Section on Foundation and History of Mathematics

Hajime Ishihara (Toho Univ.)

Reverse mathematics in constructive and predicative set theory

Summary: After quickly reviewing intuitionistic logic and classical Zermelo-Fraenkel set theory (ZF), welook 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 ofS
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 a set
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: 2024/2/9
9AlgebraAlgebraMarch 17th (Sun)

Conference Room I

9:00–10:30
1 Shinichi Tajima (Niigata Univ.⋆)
Katsuyoshi Ohara (Kanazawa Univ.)
Akira Terui (Univ. of Tsukuba)

Eﬃcient symbolic computation of the structure of Jordan chains · · · · · 10

Summary: 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 chainsof a matrix 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 Shuhei Tsujie (Hokkaido Univ. of Edu.)
Daisuke Suyama (Nippon Bunri Univ.)
Michele Torielli(Northern Arizona Univ.)

On the coincidence of freeness of two types of hyperplane arrangements
determined from gain graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Two kinds of hyperplane arrangements can be obtained from a gain graph, a graph whose edges
are labeled 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.
3 Norihiro Nakashima(Nagoya Inst. of Tech.)
Yusuke Mori

Characteristic quasi-polynomials for deformations of Weyl arrangements· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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.
4 Takumi Ogasawara(Yokohama Nat. Univ.)
Shushi Harashita(Yokohama Nat. Univ.)
Ryo Ohashi (Univ. of Tokyo)
Kosuke Sakata (Univ. of Tokyo)

Superspecial genus-4 double covers of elliptic curves · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study genus-4 curves obtained as double covers of elliptic curves. Firstly weprovide 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 anapplication we enumerate the isomorphism classes of superspecial genus-4 double covers of elliptic curves insmall characteristic p (more precisely p is less than or equal to 23). We accomplish this by implementing
our algorithm in the computer algebra system Magma and executing it. This work deals with a broader
class of curves than the case of Howe curves studied by Kudo, Harashita and Howe in 2020.

Final: 2024/2/9
Algebra5 Yuya Yamamoto(Yokohama Nat. Univ.)
Shushi Harashita(Yokohama Nat. Univ.)

10

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

Summary: Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curves inLegendre form is separable. In this talk, we get an analogous result for curves of genus two in Rosenheim
form. More precisely 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 Gausshypergeometric series. We use Lauricella’s system (of type D) of hypergeometric diﬀerential equations inthree variables. We prove that each entry of the Cartier–Manin matrix satisﬁes the same partial diﬀerential
equations and also various contiguity relations.
6 Ryo Ohashi(Univ. of Tokyo)

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

Summary: 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.
10:45–11:45

Talk Invited by Algebra Section

Chikashi Miyazaki (Kumamoto Univ.)

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

Summary: 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 from mypoint of view. Several proofs are known for the Horrocks theorem, a vector bundle on the projectuve spacehaving 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.

Final: 2024/2/9
11

Algebra14:15–18:00
7 Kenta Mori (Kwansei Gakuin Univ.)

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

Summary: The perfectly matchable subgraph polytope of a graph is a (0,1)-polytope associated with thevertex sets of matchings in the graph. We study algebraic properties (compressedness, Gorensteinness) of
the toric rings of perfectly matchable subgraph polytopes. In particular, we give a complete characterizationof a graph whose perfectly matchable subgraph polytope is compressed.
8 Sora Miyashita (Osaka Univ.)

Comparing generalizations of Gorensteinness in semi-standard gradedrings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 thecommonalities 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.
9 Koji Matsushita (Osaka Univ.)
Sora Miyashita (Osaka Univ.)

Conditions for multiplicities and almost Gorensteinness · · · · · · · · · · · · · 15

Summary: Almost Gorenstein rings have been introduced as a generalization of Gorenstein rings and havebeen 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 for all of R1 , R2 and R. Moreover, we provide its application to semi-standard graded rings.
10 Akihiro Higashitani (Osaka Univ.)

Diﬀerence of Hilbert series of homogeneous aﬃne semigroup ring andits normalization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Kaito Kimura (Nagoya Univ.)

Asymptotic behavior of Bass numbers of modules · · · · · · · · · · · · · · · · · · 15

Summary: 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 in commutative algebra. We consider the asymptotic Bass numbers of localizations of M/I n M atprime ideals of R. The main result asserts that these have polynomial growth for large integers n that do
not depend on the prime ideals when R is local.
12 Yuya Otake(Nagoya Univ.)

Auslander–Bridger theory for complexes · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 stabilizationof the homotopy category of complexes of ﬁnitely generated projective R-modules. We introduce higher
versions of several notions introduced by Yoshino, such as the ∗ torsionfreeness and the ∗ reﬂexivity forcomplexes. Also, we prove the Auslander–Bridger approximation theorem for complexes.

Final: 2024/2/9
Algebra13 Yuki Mifune(Nagoya Univ.)

12

On the ﬁniteness of resolving subcategories and the category of MCM
modules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
14 Naoki Wakasugi (Nagoya Univ.)
Ryo Takahashi (Nagoya Univ.)

On the category of coﬁnite modules and local cohomology modules· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let R be a commutative noetherian ring and I be an ideal of R. In 2021, Bahmanpour proved
if the local cohomology modules of any ﬁnitely generated R-modules are I-coﬁnite, then the subcategoryof Mod R consisting of I-coﬁnite modules is an abelian subcategory when R is semi-local. We show theconverse under certain assumptions.
15 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

Summary: Let R be a commutative noetherian ring. In this talk, we study, for the singularity category of R,
the vanishing of the complexity in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich.
16 Naoki Endo

(Meiji Univ.)

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

Summary: 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 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

Summary: 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.

March 18th (Mon)

Conference Room I

9:30–12:00
18 Shigeru Iitaka (Gakushuin Univ.⋆)
Yukimasa Saito(Azabu Junior High School)

Perfect numbers of new kind · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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.

Final: 2024/2/9
13

Algebra19 Hayato Kanno (Tohoku Univ.)

A certain analogue of 2-1 formula and t-MZV of inﬁnite depth · · · · · · · 10

Summary: 2-1 formula is an important family of relations between multiple zeta-star values(MZSVs) andhalf 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 Eisuke Otsuka (Tohoku Univ.)

On the periods obtained by iterated integrals on the Fermat curve ofdegree 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Yusuke Tanuma(Keio Univ.)

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

Summary: In this talk, we study the algebraic independence of the values of a certain family of power series
P∞P∞kincluding k=0 z d ±k and k=1 [kω]z k , where d is an integer greater than 1, ω is a real quadratic irrational
number, and [·] denotes the integral part.
22 Yasuaki Gyoda (Univ. of Tokyo)
Shuhei Maruyama (Kanazawa Univ.)

Uniqueness conjecture of generalized Markov equation and its partial
solutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
23 Ryosuke Shimada (Univ. of Tokyo)

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

Summary: 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 by Görtz–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 GL n .
24 Keita Nakai(Nagoya Univ.)

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

Summary: 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 Masatoshi Suzuki (Tokyo Tech)

On the Hermitian form attached to the Weil distribution · · · · · · · · · · · · 15

Summary: We study the Hilbert space obtained by completing the space consisting of all smooth andcompactly 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: 2024/2/9
Algebra13:00–14:00

14

Talk Invited by Algebra Section

Teruhisa Koshikawa (Kyoto Univ.) ♭ Vanishing theorems for the cohomology of Shimura varieties
Summary: Shimura varieties are certain type of locally symmetric spaces, and have canonical structuresof algebraic 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.

March 19th (Tue)

Conference Room I

9:30–12:00
26 Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classiﬁcation for algebraic tori (II) · · · · · · · · · · · · · · · · · · · · · · 10

Summary: As a continuation of Part (I) (dimension 3 case), we state main theorems of [HY] which give astably birational classiﬁcation of algebraic k-tori of dimension 4.
27 Akinari Hoshi (Niigata Univ.)
Hidetaka Kitayama (Wakayama Univ.)

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

Summary: The rationality problem of two-dimensional purely quasi-monomial actions was solved completelyby 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.
28 Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

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

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

tori 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.

Final: 2024/2/9
15

Algebra29 Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

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

Summary: 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 Daisuke Tambara (Hirosaki Univ.⋆)

Intersection of subspaces Av in A2 for a three-dimensional division
algebra A over a ﬁnite ﬁeld · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let A be a three-dimensional nonassociative division algebra over a ﬁnite ﬁeld. Let A act on A2 byleft 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 Kenta Ueyama (Shinshu Univ.)

On noncommutative graded hypersurfaces of countable Cohen–Macaulay
representation type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We compute the stable categories of graded maximal Cohen–Macaulay modules over Rε1 andRε∞ , 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 Masaki Matsuno (Tokyo Univ. of Sci.)
Ayako Itaba (Tokyo Univ. of Sci.)

Graded Ore extensions of 3-dimensional quadratic Calabi–Yau ASregular algebras of Type S · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In noncommutative algebraic geometry, classiﬁcation of 4-dimensional Artin–Schelter regular (ASregular) 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.
(Univ. of Tokyo)
33 Sota Asai
Osamu Iyama (Univ. of Tokyo)

M -TF equivalence in the real Grothendieck group · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Algebra14:15–14:30

Presentation Ceremony for the 2024 MSJ Algebra Prize

14:40–15:40

Award Lecture for the 2024 MSJ Algebra Prize

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

16

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

Summary: 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 thenoutline the 2-categorical covering theory and its applications to derived equivalences. In the second part, as
an application 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

Award Lecture for the 2024 MSJ Algebra Prize

Kentaro Nakamura (Saga Univ.)

Iwasawa theory for rank two p-adic Galois representations

Summary: 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.

March 20th (Wed)Conference Room I

9:00–12:00
34 Masayuki Sukenaga (Hiroshima Univ.)

Smooth tropical complete intersection curves of genus 3 in R3 · · · · · · · 15

Summary: We develop a method for describing the tropical complete intersection of a tropical hypersurface
and a tropical 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 tropicalcomplete intersection curves in R3 whose skeletons are the lollipop graph of genus 3. This gives a partial
answer to the open question of whether a lollipop graph of genus 3 appears in the skeleton of a tropicalcurve on a tropical plane in R3 .
35 Masatomo Sawahara (Hirosaki Univ.)

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

Summary: 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 Kenta Watanabe (Nihon Univ.)

Donagi–Morrison conjecture concerning lifts of line bundles on curvescontained in a K3 surface and its applications · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
17

Algebra37 Kiwamu Watanabe (Chuo Univ.)

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

Summary: 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 Kaori Suzuki (Yokohama Nat. Univ.)

Graded Ring Database of Fano 3-folds with Bogomolov condition · · · · 15

Summary: I will talk about the classiﬁcation of Fano 3-fold in Graded Ring Database with some examples.
39 Fumiya Okamura (Nagoya Univ.)

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

Summary: 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.
40 Runxuan Gao (Nagoya Univ.)

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

Summary: Batyrev and Tschinkel’s example is a Fermat cubic surface bundle X which is a Fano 5-fold. It
is the ﬁrst example for which Manin’s conjecture can never hold for a proper closed exceptional set. Overa ﬁeld F of characteristic 0, we give the minimal subset Z of X(F ) that contains every rational point
coming from a thin map f : Y → X with equal or higher a- and b-values in lexicographical order, whichis conjectured to be the correct exceptional set in Manin’s conjecture. The set Z is a thin set deﬁned byﬁnitely many thin maps. Over a number ﬁeld F , we show that every such thin map f factors through theﬁnitely many ones.
41 Atsushi Noma (Yokohama Nat. Univ.)

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

Summary: The purpose of this paper is to prove the positivity of double point divisors of general innerprojections for projective S2 -varieties with invertible dualizing sheaves, without assuming the smoothness or
the normality 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 Tomohiro Iwami (Kyushu Inst. of Tech.)Canonical embedding of Clemens–Griﬃths–Kuznetsov components via
three-dimensional Miyaoka–Yau type inequality with the associatedthird Chern classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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: 2024/2/9
Algebra18

14:15–18:00
43 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 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Masanori Ando (Naragakuen Univ.)
Kazuya Aokage(Ariake Nat. Coll. of Tech.)Harada conjecture II in the covering groups of symmetric groups andalternating groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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 Kenichiro Tanabe (Tokyo City Univ.)

A Schur–Weyl type duality for twisted weak modules over a vertex
algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let V be a vertex algebra of countable dimension, G a subgroup of AutV of ﬁnite order, V G theﬁxed point subalgebra of V under the action of G. We show a Schur–Weyl type duality for the actions ofan associative algebra and V G
46 Kazuya Kawasetsu (Kumamoto Univ.)

On the commutant of the principal subalgebra in the A1 lattice vertex
algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The coset (commutant) construction is a fundamental tool to construct vertex operator algebras
from known vertex operator algebras. The aim of this talk is to provide a fundamental example of thecommutants of 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 ofgenerators of C, which consists of inﬁnitely many elements and strongly generates C, is introduced. It
implies that the algebra C is not ﬁnitely generated. Furthermore, Zhu’s Poisson algebra of C is shown
to be isomorphic to an inﬁnite-dimensional algebra C[x1 , x2 , . . .]/(xi xj |i, j = 1, 2, . . .). In particular, theassociated variety of C consists of a point. Moreover, W and C are veriﬁed to form a dual pair in VA1 .
47 Naoko Kunugi (Tokyo Univ. of Sci.)
Kyoichi Suzuki (Tokyo Univ. of Sci.)

Relative stable equivalences of Morita type and Morita equivalences forthe principal blocks of ﬁnite groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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

Cliﬀord’s theorem for bricks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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.

Final: 2024/2/9
19

Algebra49 Martı́n Forsberg Conde(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

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

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

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

Summary: Outside of type A, the cyclotomic KLR algebras are still quite mysterious, and have not beenstudied in 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.
51 Takafumi Kouno (Waseda Univ.)(Tokyo Tech)
Satoshi Naito

The Borel-type presentation of the equivariant quantum K-ring of the
ﬂag manifold in type C · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give the Borel-type presentation of the equivariant quantum K-ring of the ﬂag manifoldin type C. The Borel-type presentation is an explicit quotient of a Laurent polynomial ring which isisomorphic to the equivariant quantum K-ring as rings. By specializing the Novikov variables in the Boreltype presentation of the equivariant quantum K-ring to 0, we can obtain the well-known Borel presentationof the equivariant K-ring of the ﬂag manifold. In this sense, our presentation can be viewed as a quantum
analogue of the classical Borel presentation.
52 Yuta Kimura (Osaka Metro. Univ.)

Tilting ideals for deformed preprojective algebras · · · · · · · · · · · · · · · · · · 15

Summary: 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 introduced by
Gelfand–Ponomarev, and appears in many areas of mathematics. Among interesting properties of Π(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 Hideto Asashiba(Shizuoka Univ.⋆/Kyoto Univ./Osaka Metro. Univ.)

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

Summary: Let G be a generator and a cogenerator in the category of ﬁnitely generated right A-modules fora ﬁnite-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 .

Final: 2024/2/9
Algebra54 Ryuji Tanimoto (Shizuoka Univ.)

20

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

Summary: Let k be an algebraically closed ﬁeld of positive characteristic p and let Ga denote the additive
group of 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: 2024/2/9
21

Geometry

Geometry
March 17th (Sun)

Conference Room IV

9:30–11:45(Hokkaido Univ.)
1 Ryu Ueno
Hitoshi Furuhata (Hokkaido Univ.)

Statistical biharmonic map · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 provethat improper aﬃne spheres induce examples of such maps.
2 Atsufumi Honda(Yokohama Nat. Univ.)
Chisa Tanaka(NTT DATA Frontier Corp.)
Yuta Yamauchi (Yokohama Nat. Univ.)

The total absolute curvature of closed curves with singularities · · · · · · 15

Summary: 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 − 12 . 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 Isami Koga
(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Yasuyuki Nagatomo (Meiji Univ.)

Harmonic totally real maps of the 3-sphere into the complex projective
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Riku Kishida(Tokyo Tech)

The volume of conformally ﬂat manifolds as hypersurfaces in the lightcone · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 .
5 Yuuki Sasaki (Utsunomiya Univ.)

Orbits of the isotropy group action on quaternionic symmetric spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: A symmetric space which is a quaternionic Kahler manifold is called a quaternionic symmetricspace. We study some properties of orbits of the isotropy group action on a compact quaternionic symmetricspace with respect to the quaternionic structure. In particular, an orbit is a totally complex submanifold ora quaternionic 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 Toru Kajigaya (Tokyo Univ. of Sci.)

Nonexistence of stable discrete maps into some homogeneous spaces ofnonnegative curvature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Geometry

7 Yu Ohno(Hokkaido Univ.)

22

Homogeneous Structures on S2 × R and H2 × R · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Noriaki Ikeda (Ritsumeikan Univ.)

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

Summary: We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure asa 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.
(Azabu Univ.)
9 Yuji Hirota(
Noriaki Ikeda Ritsumeikan Univ.)

Expansion of momentum maps, and quaternionic Kähler symmetries· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
10 Azuna Nishida(Chiba Univ.)

Homological mirror symmetry for weighted projective spaces via Morse
homotopy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss homological mirror symmetry for weighted projective spaces (WPS) based on SYZ
construction. 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 Kentaro Yamaguchi(Tokyo Metro. Univ.)

Torus-equivalently embedded toric manifolds associated to aﬃne subspaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Hayato Nakanishi (Chiba Univ.)

SYZ mirror of Hirzebruch surface Fk and Morse homotopy · · · · · · · · · · 15

Summary: We study homological mirror symmetry for Hirzebruch surface Fk as a complex manifold byusing the Strominger–Yau–Zaslow construction of mirror pair and Morse homotopy. For the Hirzebruchsurface 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 constructa quasi-isomorphism from the category of Morse homotopy to the DG category of the complex side anddiscuss the minimality of the category of Morse homotopy.
13 Shuhei Yonehara (Osaka Univ.)

Hamiltonian actions on coKähler manifolds and a reduction theorem· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 metric manifolds which have a compatible cosymplectic structure.

Final: 2024/2/9
23

Geometry

16:25–17:25

Talk Invited by Geometry Section

Kazushi Ueda (Univ. of Tokyo)

Mirror symmetry and degeneration

Summary: 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.

March 18th (Mon)

Conference Room IV

10:10–10:25

Presentation Ceremony for the 2023 MSJ Geometry Prize

10:30–11:30

Award Lecture for the 2023 MSJ Geometry Prize

Kento Fujita(Osaka Univ.) ♭ On criteria for the K-stability of Fano varieties

Summary: We survey recent progress on K-stability of Fano varieties.
13:00–14:00
14 Yusei Aoki (Nagoya Inst. of Tech.)Toshiaki Adachi (Nagoya Inst. of Tech.)

Estimates on characteristic magnetic focal value on Käher manifold· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 andaccelaration vector span a complex line, we study “special” magnetic Jacobi ﬁelds which are related withsuch 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 Kenzi Satô (Tamagawa Univ.)

Two kinds of new centroids of spherical and hyperbolic triangles · · · · · 15

Summary: 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 Vı́ctor Pérez-Valdés (Univ. of Tokyo)

Diﬀerential symmetry breaking operators for principal series representations of the pair (SO(4,1), SO(3,1)) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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))

March 19th (Tue)

Conference Room IV

9:30–11:45
17 Shota Hamanaka(Mitsubishi Electric Corp. Adv. Tech. R&D Center)

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

Summary: In this talk, we give some W 1,p limit theorems for total scalar curvatures. More precisely, weshow that 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.

Final: 2024/2/9
Geometry

18 Tadashi Fujioka (Osaka Univ.)

24

Upper curvature bound and the curvature integral · · · · · · · · · · · · · · · · · 15

Summary: 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 Homare Tadano (Yamaguchi Univ.)

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

Summary: Stimulated by improved oscillation estimates of the potential function and the scalar curvature
on compact 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 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

Summary: 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.
21 Masato Mimura (Tohoku Univ.) ♭ The space of non-extendable invariant quasimorphisms · · · · · · · · · · · · · 15
Morimichi Kawasaki (Hokkaido Univ.)
Mitsuaki Kimura (Kyoto Univ.)
Takahiro Matsushita (Shinshu Univ.)
Shuhei Maruyama (Kanazawa Univ.)
Summary: We study the space of non-extendable invariant quasimorphisms.
22 Masato Mimura (Tohoku Univ.) ♭ scl and coarse groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Morimichi Kawasaki (Hokkaido Univ.)
Mitsuaki Kimura (Kyoto Univ.)
Takahiro Matsushita (Shinshu Univ.)
Shuhei Maruyama (Kanazawa Univ.)
Summary: We initiate coarse group theoretic study of scl (stable commutator length).
23 Shun Oshima(Tohoku Univ.)

The observable diameter of metric measure spaces and the existence ofpoints with positive measures. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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).

Final: 2024/2/9
25

Geometry

14:15–17:10
24 Yoshito Ishiki(RIKEN)

Strongly rigid metrics in spaces of metrics · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 iszero-dimensional. As a development of this result, for a zero-dimensional metrizable space, we prove thatthe set of all strongly rigid metrics is dense in the space of metics. Moreover, if the space is the union ofcountably 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 the space of metrics.
25 Tomonari Sei (Univ. of Tokyo)
Ushio Tanaka (Osaka Metro. Univ.)

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

Summary: 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 termsof a 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 Kenshiro Tashiro (Tohoku Univ.)(SISSA)
Samuël Borza

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

Summary: 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 andsome 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.
♭ Sobolev curves in an arbitrary metric space · · · · · · · · · · · · · · · · · · · · · · · 15
27 Nikita Evseev(Okinawa Inst. of Sci. and Tech. Grad. Univ.)
Summary: We show that Sobolev curves in a dual Banach space can be characterized in terms of weakderivatives 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,
we investigate for which target spaces Sobolev curves are weak* diﬀerentiable almost everywhere.
28 Ye Zhang(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Semiconcavity results of squared sub-Riemannian distance on ideal
Carnot groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: On Euclidean spaces, the squared distance function | · |2 is a convex function as well as asemiconcave function. When it comes to Heisenberg group, due to the appearance of the cut locus and theabnormal set, 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
group instead, 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.
29 Kazumasa Narita (Nagoya Univ.)

An extremal eigenvalue problem for the Laplacian on a compact Kähler
manifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We study an eigenvalue problem for the Laplacian on a compact Kähler manifold. Considering
the k-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 aKähler 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 theﬂat complex torus to admit an isometric minimal immersion into a Euclidean sphere by ﬁrst eigenfunctions.

Final: 2024/2/9
Geometry

30 Yuya Takahashi (Nagoya Univ.)

26

Operad structures in geometric quantization of the moduli space of ﬂat
SU (2)-connections on a Riemann surface · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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,we will 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 Tatsuki Seto (Meiji Pharm. Univ.)
Takashi Maruyama(NEC Laboratories Europe)

A Fredholm module on self-similar sets built on n-cubes · · · · · · · · · · · · 15

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

Star product with separation of variables on G2,4 (C) · · · · · · · · · · · · · · · 15

Summary: 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.

March 20th (Wed)Conference Room IV

9:20–10:15
33 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

Summary: Starting from the Sasakian structure of the Heisenberg group we construct a Kähler structure of
the Siegel 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 Yuya Takeuchi (Univ. of Tsukuba)

Kohn–Rossi cohomology of spherical CR manifolds · · · · · · · · · · · · · · · · · 15

Summary: 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 thePatterson–Sullivan measure and Weitzenböck-type formulae.
35 Natsuo Miyatake (Tohoku Univ.)

Extended Hitchin equation for cyclic Higgs bundles associated with aquasi-subharmonic function, and its Dirichlet problem · · · · · · · · · · · · · · 15

Summary: We demonstrate the existence and uniqueness of the solution to the Dirichlet problem for ageneralization 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.

Final: 2024/2/9
27

Geometry

10:30–11:30

Talk Invited by Geometry Section

Hisashi Kasuya (Osaka Univ.)

Vector bundles and Higgs bundles over Sasakian manifolds, present andfutureSummary: 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 over compact Kähler manifolds. Sasakian geometry is often qualiﬁed as an odd-dimensional analogyof Kähler geometry. An important theme on Sasakian geometry is to show that Sasakian geometry is notjust an analogue. The purpose of this talk to give an overview of recent results on Higgs bundles overcompact Sasakian manifolds and suggest future programs for going beyond an analogy of Kähler case.

Final: 2024/2/9
Complex Analysis

28

Complex Analysis
March 17th (Sun)

Conference Room VI

9:50–11:20
1 Kiyoki Tanaka (Meijo Univ.)
Satoshi Yamaji(Kobe City Coll. of Tech.)Little Hankel operators on Bloch type spaces · · · · · · · · · · · · · · · · · · · · · · 15

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

On universal convexity of shifted hypergeometric functions · · · · · · · · · · 15

Summary: 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 Yohei Komori (Waseda Univ.)

On the convergence of Thurston’s hyperbolic circle packing algorithm· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 patterncase.

4 Katsuhiko Matsuzaki (Waseda Univ.)

On the real-analytic structure of integrable Teichmüller spaces · · · · · · · 15

Summary: For the p-integrable Teichmüller space Tp (p ≥ 1), which is given by p-integrable Beltrami
coeﬃcients with respect to the hyperbolic metric, we describe its real-analytic structure by using Besov
spaces.
5 Hiroaki Aikawa (Chubu Univ.)

Intrinsic ultracontractivity for planar domains with wide access property· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Utilizing capacitary width and the parabolic box argument, we unveil analytic notions behindgeometric characterizations of wide accessible planar domains, those are IU or have ﬁnite lifetime.

14:15–15:15

Talk Invited by Complex Analysis Section(Oita Univ.) Boundedness of maximal operators and Sobolev-type inequalities for
Takao Ohno
Riesz potentials

Summary: The maximal operator is a classical tool in harmonic analysis and studying Sobolev functions
and partial 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.

Final: 2024/2/9
29

Complex Analysis

15:35–16:30
6 Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

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

Summary: The aim of this talk is to establish some Riesz type inequalities of pluriharmonic functions onbounded symmetric 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 obtaina Hardy and Littlewood type theorem in the case p = 1.
7 Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

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

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

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

Summary: In this talk, we discuss the Hardy–Littlewood type theorems and smooth moduli of holomorphic
and pluriharmonic functions. Our result improves and extends the corresponding results due to Dyakonovin 2004 and Hardy and Littlewood in 1932.
9 Hidetaka Hamada(Kyushu Sangyo Univ.)
Shaolin Chen (Hengyang Normal Univ.)

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

Summary: 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.

March 18th (Mon)

Conference Room VI

9:50–11:20
10 Takanori Ayano (Osaka Metro. Univ.)

An improvement on the power series expansion of the sigma function
associated with the telescopic curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 todetermine the coeﬃcients of the power series expansion of the sigma function. In The Mathematical Societyof Japan Autumn Meeting 2022, I made a presentation on the result of the power series expansion of thesigma function associated with the telescopic curves. In this talk, I will give an improvement of this result.
11 Li-Jie Sun(Yamaguchi Univ.)

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

Summary: 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
is important to investigate the geometry on its Riemannian cone.

Final: 2024/2/9
Complex Analysis

12 Tadashi Tomaru (Gunma Univ.⋆)

30

Arnold’s 14 exceptional singularities and families of elliptic curves withcomplex multiplications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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

Summary: Let X be a non-singular compact complex surface such that the anticanonical line bundle admits
a smooth Hermitian metric with semi-positive curvature. For a non-singular hypersurface Y which deﬁnes
an anticanonical divisor, we investigate the ∂ cohomology group H 1 (M, OM ) of the complement M = X \ Y .
14 Takeo Ohsawa (Nagoya Univ.) ♭ On the Levi problem for locally pseudoconvex bounded domains ofregular type with a curvature negativity on the boundary · · · · · · · · · · · 15
Summary: Given a bounded locally pseudoconvex domain Ω in a complex manifold M with a completeKähler metric and a positive line bundle, it is proved that Ω is holomorphically convex if the canonicalbundle 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

Talk Invited by Complex Analysis Section

Tomoyuki Hisamoto(Tokyo Metro. Univ.)

Optimal degeneration for a Fano manifold

Summary: 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: 2024/2/931Functional Equations

Functional Equations
March 17th (Sun)

Conference Room II

9:30–12:00
1 Kanam Park
(Toba Nat. Coll. of Maritime Tech.)

Birational representations of aﬃne Weyl groups related to a 3 × 3 Lax(1)formalism for the q-Painlevé equation of type E6 · · · · · · · · · · · · · · · · · 15
(1)

Summary: The q-Painlevé equation of type E6(1)symmetry of type E6 .

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

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 A2 as a partial result.
2 Kodai Fujimoto (Shimane Univ.)

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

Summary: 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 Hiroyuki Usami (Gifu Univ.)
Takayuki Maeda (Gifu Univ.)

On target shooting problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 the target
in some cases.
4 Tetsutaro Shibata (Hiroshima Univ.)

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

Summary: We consider the one-dimensional nonlinear eigenvalue problem of Kirchhoﬀ type. We obtain theﬁrst eigenvalue µ1 of this problem explicitly by using a simple time map method. We also obtain the ﬁrst
eigenfunction associated with µ1 .
5 Junya Nishiguchi (Tohoku Univ.)

On the notion of “mild solutions” to linear delay diﬀerential equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 evolutionof 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.

Final: 2024/2/9
Functional Equations

6 Junya Nishiguchi (Tohoku Univ.)

32

Fundamental systems of solutions and fundamental matrix solutions tolinear delay diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Naoki Hamamoto (Osaka Metro. Univ.)

The Hardy’s constant for curl-free vector ﬁelds on the half-plane · · · · · 12

RR2
Summary: The N -dimensional Hardy’s inequality RN |∇u|2 dx ≥ C RN |u||x|2 dx with the best constant C =(N − 2)2 /4 is well known when the test vector ﬁeld u : RN → RN is in Cc∞ (RN ) and unconstrained. We areinterested 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 Takeshi Suguro (Kumamoto Univ.) ♭ Stability estimates for the logarithmic Sobolev inequality for a generalized entropy and an application to the uncertainty relation inequality· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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.
14:15–16:15
9 Yukihide Tadano (Tokyo Univ. of Sci.)
Shu Nakamura (Gakushuin Univ.)(RIKEN)
Keita Mikami

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

Summary: 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 Takashi Suzuki (Osaka Univ.)
Kazuo Watanabe (Kitasato Univ.)

Interface vanishing of diﬀerential forms · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: We introduce d − δ systems on diﬀerential forms in Euclidean spaces and show the interface
vanishing of the solution. This result generalizes the previous theorems on stationary and non-stationary
Maxwell’s equation.
11 Shimpei Makida (Hokkaido Univ.)
Atsushi Nakayasu (Kyoto Univ.)

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

Summary: 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.

Final: 2024/2/9
33

Functional Equations

12 Tatsuya Ueno (Kanagawa Univ.)

Existence of positive ground state solution of coupled nonlinear Kirchhoﬀ–
Schrödinger system for a subcritical and critical case · · · · · · · · · · · · · · · 10

Summary: 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 Yasuhito Miyamoto (Univ. of Tokyo)

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

Summary: 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.
14 Haruki Takemura (Univ. of Tokyo)
Yasuhito Miyamoto (Univ. of Tokyo)
Tohru Wakasa (Kyushu Inst. of Tech.)

Asymptotic formulas of the eigenvalues for the linearization of the scalarﬁeld equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 of theeigenvalues which converge to −3 is equal to the number of the interior and boundary peaks of the solutionof Neumann problem u. The number of the eigenvalues which converge to 0 is equal to the number of theinterior peaks of u. In this study, complete elliptic integrals and Jacobi’s elliptic functions play an importantrole.
15 Kenta Nakamura (Kumamoto Univ.)

Local properties of fractional parabolic De Giorgi classes · · · · · · · · · · · · 10

Summary: 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 Kotaro Sato

(Tohoku Univ.)

Long-time behavior of solutions to some quasistatic evolution equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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

Talk Invited by Functional Equations Section

Yoshiaki Goto
(Otaru Univ. of Commerce)Hypergeometric integrals —homology and cohomology

Summary: 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, socalled twisted homology and cohomology groups. Many types of relations between hypergeometric functions
can be 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
are studied by using twisted (co)homology groups and intersection forms.

Final: 2024/2/9
Functional Equations

March 18th (Mon)34

Conference Room II

9:30–12:00
17 Ryunosuke Kusaba (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

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

Summary: 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
approach is based on the integral representation of the CGL semigroup and Taylor expansions with respect
to the both space and time variables. We also discuss the optimal decay rate in time of the remainder forthe asymptotic expansion.
18 Shohei Kohatsu (Tokyo Univ. of Sci.)

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

Summary: We deal with a Keller–Segel system with ﬂux limitation. For the one-dimensional Keller–Segelsystem, it is known that given any nonnegative measure-valued initial data, the system admits a globalclassical solution which is continuous at t = 0. The purpose is to show this immediate smoothing in thesystem for any dimension with the aid of eﬀect of ﬂux limitation.
19 Sachiko Ishida (Chiba Univ.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Global solvability for N -dimensional tumor invasion models via themaximum Sobolev regularity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial-boundary value problem for a degenerate chemotaxis model arising fromtumor invasion, in which the ﬁrst equation is ut = ∇ · (f (u, w)∇u − g(u)∇v). The diﬀusivity and thesensitivity 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 Tatsuya Hosono (Tohoku Univ.) ♭ Global existence and boundedness of solutions to the 4D fully parabolic
Philippe Laurençotchemotaxis system with indirect signal production · · · · · · · · · · · · · · · · · 15
(CNRS/Univ. Savoie Mont Blanc)
Summary: We consider the Cauchy problem for the 4 dimensional fully parabolic chemotaxis system withindirect signal production. In this talk, we show that the solution exists globally in time provided that theinitial mass is less than the value (8π)2 , known as the 4 dimensional threshold value whether the blow-up
of solutions 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).
21 Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)

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

Summary: 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 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

Summary: We discuss the asymptotic stability of traveling waves of diﬀusive three-species competition
systems under certain perturbations of initial data.

Final: 2024/2/935Functional Equations

23 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

Summary: 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 Masaharu Taniguchi (Okayama Univ.)

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

Summary: 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
reaction-diﬀusion equation. As the speed of an n-dimensional axially symmetric or asymmetric travelingfront goes to inﬁnity, it converges to an (n − 1)-dimensional radially symmetric or asymmetric entire solution
in a balanced 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.
13:00–14:00

Talk Invited by Functional Equations Section

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

Monge solutions of eikonal equations in metric spaces

Summary: In recent years, there has been rapid progress in the study of nonlinear partial diﬀerential
equations in general 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.

March 19th (Tue)

Conference Room II

9:45–12:00
25 Kaito Kokubu (Tokyo Univ. of Sci.)

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

Summary: 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.

Final: 2024/2/9
Functional Equations

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

36

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

Summary: We consider non-smoothness of the fundamental solution for the Schrödinger equation with aspherically symmetric and super-quadratic potential in the sense that V (x) ≥ C|x|2+ε at inﬁnity withconstants 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 thistalk, we show that the fundamental solution E(t, x, y) does not belong to C 1 as a function of (t, x, y) if V isa spherically symmetric and super-quadratic potential, the spatial dimension is larger than or equals to 4.
27 Shun Takizawa (Tokyo Univ. of Sci.)

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

Summary: 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 purpose ofthis talk is to show in the case where potentials are non-smooth.
28 Sonae Hadama (Kyoto Univ.)
Takuto Yamamoto (Kyoto Univ.)

Almost sure existence of local solutions to the Hartree equation forinﬁnite quantum systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 given in 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 thanα. However, we can go beyond this limitation by introducing a randomization of initial data. In thistalk, 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 Makoto Ikoma (Nagoya Univ.)
Soichiro Suzuki (Chuo Univ.)

Optimal constants of smoothing estimates for the 3D Dirac equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 thistalk, we give optimal constants for the 3-dimensional free Dirac equation.
30 Tomoyuki Tanaka (Doshisha Univ.)(Univ. Tours)
Luc Molinet

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

Summary: We consider the Cauchy problem for one-dimensional dispersive equations of KdV type on thetorus. 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.
31 Takuya Sato (Kumamoto Univ.) ♭ Optimal L2 -decay rate of solutions to dissipative nonlinear Schrödinger
equations in the analytic class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider the Cauchy problem of one dimensional dissipative nonlinear Schrödinger equations
with a critical power nonlinearity. In this talk, we show that L2 -decay rate obtained in the previous work is
optimal in the analytic class.

Final: 2024/2/9
37Functional Equations

14:15–16:00
32 Jumpei Kawakami (Kyoto Univ.)

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

Summary: 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 Hayato Miyazaki (Kagawa Univ.)
Masaki Kawamoto (Ehime Univ.)Modiﬁed scattering operator for nonlinear Schrödinger equations witha time-decaying harmonic potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider nonlinear Schrödinger equations with a time-decaying harmonic potential.

The

nonlinearity is gauge-invariant of the long-range critical order. Kawamoto and Muramatsu show that theequation admits a nontrivial solution that behaves like a free solution with a logarithmic phase correction in
the frameworks 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 Shunsuke Kitamura (Tohoku Univ.) ♭ Lifespan of solutions of one dimensional semilinear wave equations withspatial weights and not-compactly supported data · · · · · · · · · · · · · · · · · · 15
Summary: 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. Lifespanmeans the maximum existence time of solutions. There are cases where no time-local solution exists due tothe spatial weight of the nonlinear term and the decay of the initial data.
(Mie Univ.)
35 Kunio Hidano
Kazuyoshi Yokoyama(Hokkaido Univ. of Sci.)

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

Summary: 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.
36 Mamoru Okamoto (Osaka Univ.)
Pierre de Roubin (Univ. of Edinburgh)Ill-posedness of the Cauchy problem for the viscous nonlinear wave
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the Cauchy problem for the viscous nonlinear wave equation. We show the illposedness in negative Sobolev spaces of the Cauchy problem for polynomial nonlinearity. In particular, we
prove a norm inﬂation result above the scaling critical regularity in some cases.

Final: 2024/2/9
Functional Equations

37 Mohamed Ali Hamza(Imam Abdulrahman Bin Faisal Univ.)
Yuta Wakasugi (Hiroshima Univ.)
Shuji Yoshikawa (Oita Univ.)

38

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

Summary: 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.
16:15–17:15

Award Lecture for the 2023 MSJ Analysis Prize

Masahito Ohta (Tokyo Univ. of Sci.) ♭ Strong instability analysis of standing waves for nonlinear Schrödinger
equations
Summary: 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 that ku0 − ϕω kX < εand 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.

March 20th (Wed)Conference Room II

10:00–12:00
38 Masahiro Takayama (Keio Univ.)(Keio Univ.)
Tatsuo Iguchi

A priori estimates for solutions to the motion of an inextensible hanging
string · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial boundary value problem to the motion of an inextensible hanging stringof ﬁnite 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 Taichi Eguchi (Waseda Univ.)

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

Summary: We ﬁnd a new criterion of the Lorentz–Besov spaces to establish the energy equality of theincompressible 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
1/3

that are not contained in the classical Onsager space L3 (0, T ; B3,∞ ). Motivated by Cheskidov–Luo (2020),
we obtain a 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: 2024/2/9
39

Functional Equations

40 Tim Binz
Yoshiki Iida

(TU Darmstadt)(Waseda Univ.)

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

Summary: We consider the three dimensional primitive equations for large scale oceanic and atmospheric
dynamics. The uniqueness of weak solutions to the system is still open. In this talk, based on regularity
in terms of 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 Zhongyang Gu (Univ. of Tokyo)(Univ. of Tokyo)
Xin HuTsuyoshi Yoneda (Hitotsubashi Univ.)

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

Summary: Adding a nontrivial term composed from a microstructure, we prove the existence of a global-intime weak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier–Stokes–
Fourier system for arbitrary initial data. It cannot be expected to directly derive the energy inequality forthis 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 Yuta Koizumi (Waseda Univ.)

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

Summary: We show that the approximating solutions {uj }∞j=0 of the Navier–Stokes equations constructedby Kato (1984) with the initial data u(0) ∈ Lnσ (Rn ) converge to the local strong solution u in the topologyof 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 Tomoyuki Nakatsuka(Matsuyama Univ.)

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

Summary: In this talk, the existence of time-periodic strong solutions to the Navier–Stokes equation in
Rn is established 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 decompositionis the availability of slightly more regularity in time of the purely periodic part. We apply this property
to construct time-periodic solutions of the Navier–Stokes equation with information on the classes of theirsteady and purely periodic parts.
14:15–15:15
44 Erika Ushikoshi(Yokohama Nat. Univ./Osaka Univ.)
Takahiro Okabe (Osaka Univ.)
Haru Kanno (Yokohama Nat. Univ.)

Helmholtz–Weyl decomposition on a time dependent domain for time
periodic Navier–Stokes ﬂow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: 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,
the harmonic vector ﬁelds (i.e., div and rot free vectors), vector potentials, and scalar potentials equippedwith suitable 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.

Final: 2024/2/9
Functional Equations

45 Yoshiaki Teramoto
Takaaki Nishida (Kyoto Univ.)

40

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

Summary: 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 Jou-chun Kuo (Waseda Univ.)
Yoshihiro Shibata (Waseda Univ.⋆)

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

Summary: This talk is devoted to proving the local well-posedness for the Navier–Stokes equations describing
the isotropic motion of the compressible viscous ﬂuid ﬂows in the half-space with non-slip boundarys+1sin space maximal
conditions. We construct a unique strong solution in the L1 in time and Bq,1
× Bq,1

regularity class. Here, 1 < q < ∞ and −1 + N/q ≤ s < 1/q, where N ≥ 2 is the space dimension. The
approach is by means of the analytic semigroup theory and we use Lagrange transformation in order toeliminate the convection term v · ∇ρ.
15:30–16:30

Talk Invited by Functional Equations Section

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

Inﬂow and outﬂow problem on radially symmetric solution for ﬂuid
equation

Summary: 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: 2024/2/9
41

Real Analysis

Real Analysis
March 19th (Tue)

Conference Room VI

9:30–12:00
Deﬁnition and existence theorem of the axiomatic set theory I · · · · · · · 15

1 Yoshifumi Ito

Summary: 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.
Deﬁnition and existence theorem of Euclidean geometry · · · · · · · · · · · · 10

2 Yoshifumi Ito

Summary: In this lecture, we deﬁne Euclidean geometry and prove its existence theorem by using theaxiomatic 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 Toshiharu Kawasaki(Tamagawa Univ./Chiba Univ./Chiba Univ.)

On the structure of space of all extended integrable functions, II · · · · · 15

Summary: In this talk, we expand the concept of integration and further discuss the structure of space ofextended integrable functions.
(Oita Univ.)
4 Ryoji Fukuda
Aoi Honda (Kyushu Inst. of Tech.)
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

Uniform topogies on L0 with respect to a non-additive measure · · · · · · 15

Summary: 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 .
5 Satoshi Yamaguchi (Ibaraki Univ.)

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

Summary: 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
dvalue of functions in Lp,ϕ (R ).

Lp,ϕ (Rd )by the mean

Final: 2024/2/9
Real Analysis

6 Ryota Kawasumi(RIKEN)
Masahiro Ikeda(
Ehime Univ.)
Isao Ishikawa

42

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

Summary: In this talk, we introduce our recent result about the necessary condition on boundedness ofcomposition operators to the Orlicz–Morrey space, which extends the result about the Morrey space byHatano, 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 prove the boundedness of the composition operator from a Orlicz–Morrey space to itself, which wasintroduced in MSJ Autumn Meeting 2023 at Tohoku University. Next, we show that the product of thesingular values of a Jacobi matrix is a positive constant. Finally, we ﬁnd a function in Orlicz–Morrey spacesatisfying the previous step.
7 Hiroyasu Mizuguchi (Kansai Univ.)

generalized relation of Pythagorean orthogonality by two-dimensional
norms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The orthogonality relation in inner product spaces is simple, fruitful and interesting. When
moving to normed 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 Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

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

Summary: In this talk, we prove weak and strong convergence theorems for monotone nonexpansive-type
mappings. We also study the asymptotic behavior of orbits of some nonlinear mappings.
14:15–16:15
9 Tsuyoshi Yoneda (Hitotsubashi Univ.)

Fourier uncertainty principle and mathemetial analysis on machinelearning · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Reservoir Computing (RC) is a type of recursive neural network (RNN), and there can be no
doubt that 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
structures of input and recurrent weight matrices in RC neural networks, and show that such structures areclosely related to the Fourier uncertainty principle.
10 Emu Kondo (Nara Women’s Univ.)
Shinya Moritoh (Nara Women’s Univ.)

Weighted Hardy’s inequality for nonincreasing functions and the doubling condition for weights · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Mai Harada (Kanagawa Univ.)
Noriaki Yamazaki (Kanagawa Univ.)

On the existence of time periodic solutions for the SIRS model with theseasonally-dependent transmission rate · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
43

Real Analysis(Chiba Univ.)
12 Naotaka Ukai
(Chiba Univ.)
Daiki Mizuno
Ken Shirakawa (Chiba Univ.)
Harbir Antil (George Mason Univ.)

Anisotropic energy gradient system associated with image denoisingprocess with orientation adjustment · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a gradient system of a non-convex functional, based on a governingenergy for anisotropic image denoising, as developed in [Berkels et al., SFB 611, 2006]. A characteristic ofour gradient system lies in the nonstandard part ∂γ ◦ R, which consists of the (set-valued) subdiﬀerential∂γ of 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.
(Chiba Univ.)
13 Daiki Mizuno
Ken Shirakawa (Chiba Univ.)

Pseudo-parabolic phase-ﬁeld model of grain boundary motion withsolidiﬁcation eﬀect · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 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

Summary: In this talk, we consider optimal control problems for the one-dimensional Frémond model forshape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudopotential of dissipation.

The state problem is expressed by a system of partial diﬀerential equations

involving the balance 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 thenecessary condition of the optimal pair by using optimal control problems for approximating systems.
16:30–17:30

Talk Invited by Real Analysis Section

Shin-ya Matsushita (Akita Pref. Univ.)

Fixed point algorithms and their applications

Summary: 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: 2024/2/9
Real Analysis

March 20th (Wed)44

Conference Room VI

9:30–12:00
15 Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)
Kazunori Matsui (Seikei Univ.)

Nonnegativity of the threshold function in an elastoplasticity model
based on quasi-variational inequality · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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 assumption that the threshold function is strictly positive. In physical terms, it is natural that thethreshold function is nonnegative. Therefore, it is meaningful to discuss the well-posedness under the weakerassumption. To prove the existence of a solution to the elastoplasticity model, we construct the concrete
projection of the constraint set.
16 Hana Kakiuchi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

Solvability of free boundary problems for the parabolic equation system· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a free boundary problem for a system of two parabolic equations on the onedimensional space interval. The problem has been proposed as a mathematical model for a baking breadprocess in a hot oven. In the modeling we assume that the region consists of crumb, crust, and theevaporation front. The unknown functions of the problems are the position of the evaporation front whichis regarded as the free boundary, the temperature ﬁeld, and the mass distribution. Here, the temperatureﬁeld 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 inthe present talk.
17 Akiko Morimura(Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

Convergence of approximation solutions obtained by the ﬁnite volume
method in moisture transport model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial boundary value problem for nonlinear parabolic equations with nonmonotone boundary conditions.

The problem was already investigated as a mathematical model formoisture transport phenomena in porous materials. In our recent work, we have established existence
and uniqueness of weak solutions 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 convergenceof numerical solutions. In the present result, by applying the ﬁnite volume method, we approximate thepartial diﬀerential equations and prove that the sequence of approximation solutions converges to the weaksolution. The key to the proof is a compact theorem for discretized functions.
18 Chiharu Kosugi (Yamaguchi Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

Existence of strong solutions for the energy conservation system representing motions of incompressible elastic curve on the plane · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
45

Real Analysis

19 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

Summary: 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 Shohei Kohatsu (Tokyo Univ. of Sci.)

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

Summary: 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 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

Summary: 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.
22 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

Summary: 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 ofCahn–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 aparabolic-hyperbolic phase ﬁeld system.
23 Akio Ito

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

Summary: 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.

Final: 2024/2/9
Real Analysis

46

14:15–15:40
24 Ken Shirakawa (Chiba Univ.)(Chiba Univ.)
Daiki Mizuno
Harbir Antil (George Mason Univ.)

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

Summary: In this talk, we consider a class of optimal control problems governed by KWC type systems
with pseudo-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.
25 Masahiro Ikeda (RIKEN/Keio Univ.)(Oita Univ.)
Shun Uchida
Takeshi Fukao (Ryukoku Univ.)

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

Summary: 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 Takanori Ebata (Niigata Univ.)
Hiroki Ohwa (Niigata Univ.)

Continuous dependence on the initial and ﬂux functions for entropy
solutions of general balance laws · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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

Large-time behavior of a solution to a multiscale model · · · · · · · · · · · · · 15

Summary: In this talk, we consider a multiscale model describing nonlinear phenomena in porous materials.
This model consists of a diﬀusion equation for the relative humidity distributed in materials and a freeboundary 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 Takeshi Fukao (Ryukoku Univ.)
Pierluigi Colli (Univ. of Pavia)

Allen–Cahn equations with dynamic boundary conditions of fourthorder · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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: 2024/2/9
47

Real Analysis

15:45–16:45

Award Lecture for the 2023 MSJ Analysis Prize

Naoki Tanaka (Shizuoka Univ.)

Abstract theory for evolution equations

Summary: 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 tothe 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

Talk Invited by Real Analysis Section

Hirotoshi Kuroda (Hokkaido Univ.)

On the behaviour of solutions to the fourth order total variation ﬂow
equation

Summary: 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: 2024/2/9
Functional Analysis

48

Functional Analysis
March 17th (Sun)

Conference Room VII

9:30–11:00
1 Shuji Watanabe (Gunma Univ.)

The Bogoliubov transformation and the gap equation in the BCS modelof superconductivity with external magnetic ﬁeld · · · · · · · · · · · · · · · · · · 15

Summary: Under a simple condition, we derive the Bogoliubov transformation and the gap equation in the
BCS model of superconductivity with external magnetic ﬁeld.
2 Itaru Sasaki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Shinnosuke Izumi (Shinshu Univ.)
Kouta Imura(Nagano Pref. Fujimi High School)

On the radius of convergence of the ground state in a pair interaction
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A year ago at the Mathematical Society of Japan we reported that the ground state and groundstate energy of a pair interaction model are analytic with respect to the coupling constant. However, it was
not enough to estimate the coupling constants such that the Maclaurin series converges. We have improved
the proof and extended it to what we consider to be the best possible value.
3 Yukihide Tadano (Tokyo Univ. of Sci.)
Shu Nakamura (Gakushuin Univ.)(RIKEN)
Keita Mikami

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

Summary: We consider Laplace operators deﬁned on lattices with mesh size h and those operators with
perturbations of potentials. We prove that the above operators converge to certain elliptic operators in
the continuum limit from the view point of spectral theory. We obtain as an application the asymptotic
behavior of the spectra and eigenfunctions of the above operators.
4 Fumio Hiroshima (Kyushu Univ.)

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

Summary: It is shown that the strongly continuous semigroup generated by the Nelson Hamiltonian withzero 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.
5 Kazuyuki Wada
(Hokkaido Univ. of Edu.)

Exponential decay for eigenfunctions associated with discrete spectraof quantum walks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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

Talk Invited by Functional Analysis Section

Artbazar Galtbayar(National Univ. of Mongolia)

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

Summary: 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.

Final: 2024/2/9
49

Functional Analysis

March 18th (Mon)

Conference Room VII

9:30–11:00
6 Temma Aoyama (Univ. of Tokyo)

Deformation of heat kernels and Wiener measures from the viewpointof BenSaı̈d–Kobayashi–Ørsted’s Laguerre semigroup theory · · · · · · · · · 15

Summary: The BenSaı̈d–Kobayashi–Ørsted theory gives a generalization of the theory of metaplectic representations, 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 Toshihisa Kubo (Ryukoku Univ.)(Aarhus Univ.)
Bent Ørsted

The classiﬁcation and construction of projectively covariant diﬀerential
operators on RP2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In contrast to conformal geometry, in which there are a large number of works on conformallycovariant 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
the case 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 .
8 Kazuki Kannaka(RIKEN)

Proper actions of semisimple Lie groups and the Hurwitz–Radon number I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 Koichi Tojo

(RIKEN)

Proper actions of semisimple Lie groups and the Hurwitz–Radon number II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: 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 Atsumu Sasaki(Tokai Univ.)

Weyl group of pseudo-Riemannian symmetric space · · · · · · · · · · · · · · · · 15

Summary: 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)
of pseudo-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

Talk Invited by Functional Analysis Section
Taito Tauchi (Aoyama Gakuin Univ.) Relationship between multiplicities of induced representations and orbit
decomposition on real and complex ﬂag varieties
Summary: 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 Grepresentations in C ∞ (G/H) is equivalent to the real sphericity of G/H. Moreover, they also proved thatthe uniform boundedness of the multiplicities in C ∞ (G/H) is equivalent to the sphericity of GC /HC , where
GC and HC are complexiﬁcations of G and H, respectively. These theorems indicate a relationship between
the multiplicities 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.

Final: 2024/2/9
Functional Analysis

March 19th (Tue)50

Conference Room VII

9:30–11:30
11 Keiichi Watanabe (Niigata Univ.)

On gyro operations in open balls of complex inner product spaces · · · · 15

Summary: 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.
12 Osamu Hatori (Niigata Univ.⋆)
Toshikazu Abe (Ibaraki Univ.)

A Mazur–Ulam theorem on a GGV and its application · · · · · · · · · · · · · 15

Summary: We show a Mazur–Ulam theorem on a GGV and a revised proof. As an application, we showa rather short proof of a known result about a characterization of the Thompson isometry on the positive
cone of the positive invertible elements in a unital C ∗ -algebra.
13 Michiya Mori (Univ. of Tokyo)

On the Scottish Book Problem 155 by Mazur and Sternbach · · · · · · · · · 15

Summary: 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 Yuki Seo (Osaka Kyoiku Univ.)

On numerical radius inequalities related to geometric means · · · · · · · · · 15

Summary: 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 termsof the generalized Kantorovich constant.
15 Masatoshi Ito (Maebashi Inst. of Tech.)

Inequalities among the weighted Heinz mean and related ones · · · · · · · 15

Summary: Recently Furuichi, Minculete and Moradi got an improvement of the weighted arithmeticlogarithmic-geometric mean inequality. In this talk, as an extension of their result, we obtain inequalities
among the weighted Heinz mean and related ones. Our approach is to consider the notion of a transpose
symmetric path of weighted means.
16 Hiroyuki Osaka (Ritsumeikan Univ.)
Mohsen Kian (Univ. of Bojnord)
Mohammad Sal Moslehian(Ferdowsi Univ. of Mashhad)

On characterization of matrix monotone decreasing functions · · · · · · · · 15

Summary: 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.
17 Takeaki Yamazaki (Toyo Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)

The induced Aluthge sequence of compact operators · · · · · · · · · · · · · · · · 15

Summary: We shall introduce convergence properties of iteration of the induced Aluthge transforms. In thistalk, we shall consider compact, AN and AM operators.

Final: 2024/2/9
51

Functional Analysis

14:15–15:45
18 Yusuke Isono(Kyoto Univ.)

Haagerup and Størmer’s conjecture for pointwise inner automorphisms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In 1988, Haagerup and Størmer conjectured that any pointwise inner automorphism of a typeIII1 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 Satoshi Goto

(Sophia Univ.)

A generalization of Ocneanu’s ADE inter-Dynkin connection systems· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 ofan irreducible 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 Taro Sogabe(Kyoto Univ.) ♭ A duality of KK-theory and its application to the extensions of C*algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: KK-theory gives a tool to understand the morphisms of operator algebras and if the K-groupsof the operator 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 aboutsome categorical 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 fromthe viewpoint of the Spanier–Whitehead K-duality.
21 Norio Nawata(Osaka Univ.)

W-absorbing actions of ﬁnite abelian groups · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
22 Narutaka Ozawa (Kyoto Univ.)

Quasi-local operators and ﬁnite-propagation operators · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Functional Analysis

16:00–17:00

52

Talk Invited by Functional Analysis Section

Takuya Takeishi (Kyoto Inst. Tech.)

C*-algebras constructed from number ﬁelds and related complete invariants of number ﬁelds

Summary: 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 ofC*-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 consequenceof rigidity results, we can see that the topological full groups of several groupoids from number theory arecomplete invariants of number ﬁelds. We summarize recent developments on the homology of the topologicalfull group for a certain class.

Final: 2024/2/9
53

Statistics and Probability

Statistics and Probability
March 17th (Sun)

Conference Room III

9:30–11:40
1 Kiyoiki Hoshino (Osaka Metro. Univ.)

Characterization of the stochastic integral by the Riemann sum · · · · · · 15

Summary: We consider the Riemann sum of the same type we introduced at the MSJ autumn meetingin 2020 and 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 in the following respect: (1) on the weight measures deﬁning the Riemann sum, (2) on the continuityof the integrator and (3) on the uniform Riemann approximation of the stochastic integral.
2 Kosuke Yamato (Univ. of Tsukuba)
Kei Noba (Inst. of Stat. Math.)

Existence of quasi-stationary distributions of standard processes withno negative jumps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will talk about the existence of quasi-stationary distributions for standard processes with nonegative jumps killed at the boundaries. Quasi-stationary distributions are a kind of equilibrium state forMarkov processes with killing. For standard processes with no negative jumps, we can deﬁne a function
called the scale function, which provides a simple representation of the exit times and the potential density.
Using the scale function, we can generalize the methods that have been used for one-dimensional diﬀusionsand Lévy processes and provide necessary and suﬃcient conditions for the existence of quasi-stationary
distributions.
3 Hirotaka Kai(Kyoto Univ.)

Long time behavior of Lévy processes on manifolds · · · · · · · · · · · · · · · · · 15

Summary: 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 part ofa Lévy process.
4 Yasuhito Nishimori(Nat. Inst. of Tech., Anan Coll.)

Limiting distributions for particles near the frontier of spatially inhomogeneous branching symmetric stable processes · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Yuji Hamana (Univ. of Tsukuba)

Asymptotic expansion for the tail probability of the hitting time andsite of Brownian motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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.
6 Shun Yanashima (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

An invariance principle for random walk bridges conditioned to stay
between two curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Brownian house-moving is a stochastic process that plays an important role in computing higherorder 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.

Final: 2024/2/9
Statistics and Probability

7 Soma Nishino (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

54

Higher order integration by parts formulae for Wiener measures on apath space between two curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Masato Hoshino (Osaka Univ.)
Ismaël Bailleul(Univ. Bretagne Occidentale)

Random models on regularity-integrability structures · · · · · · · · · · · · · · · 15

Summary: In the study of singular SPDEs, it has been a challenging problem to obtain a simple proof of ageneral probabilistic convergence result (BPHZ theorem). Diﬀerently from Chandra and Hairer’s Feynman
diagram approach, Linares, Otto, Tempelmayr, and Tsatsoulis recently proposed an inductive proof basedon the spectral gap inequality by using their multiindex language. Inspired by their approach, Hairer andSteele also obtained an inductive proof by using the regularity structure language. In this talk, we introduce
an extension 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

Talk Invited by Statistics and Probability Section

Yushi Hamaguchi (Osaka Univ.)

Inﬁnite dimensional Markovian lifts of stochastic Volterra equations

Summary: Stochastic Volterra equations (SVEs for short) are useful to model dynamics with hereditaryproperties, memory eﬀects and roughness of the path, which cannot be described by standard SDEs.
However, the analysis of SVEs is much more diﬃcult than the SDEs case since the solutions are no longer
Markovian or semimartingales 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 becomesa 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.
15:30–16:30

Talk Invited by Statistics and Probability Section

Nobuaki Naganuma (Kumamoto Univ.)

Approximation theory of SDEs driven by fractional Brownian motion

Summary: 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.

Final: 2024/2/9
55

Statistics and Probability

March 18th (Mon)

Conference Room III

9:30–11:40
9 Misaki Tabata (Ritsumeikan Univ.)

An inﬁnite-dimensional Hawkes process · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Makoto Nakashima (Nagoya Univ.)

Feynman–Kac representation for three-dimensional heat equation with
one-center point interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the heat equation associated with the Schrödinger operator with onecenter point interaction Hλ := −∆ + λδ0 , where δ0 is a Dirac measure at 0. This expression of the operator
is the 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 Makoto Nakashima (Nagoya Univ.)
Seiichiro Kusuoka (Kyoto Univ.)(Waseda Univ.)
Song Liang
Sergio Albeverio (Univ. of Bonn)

Stochastic quantization of the three-dimensional Edwards measure · · · 15

Summary: In this talk, we focus on the Edwards model formally given by
Z 1Z t1
νλ (dω) =exp −λδ0 (ωt − ωs )dsdt ν0 (dω)
Zλ00for 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.
12 Naomasa Ueki

(Kyoto Univ.)

Positivity of small ball probabilities of a Gaussian random ﬁeld, and its
applications to random Schrödinger operators · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Haruyoshi Tanaka(Naruto Univ. of Edu.)

Higher-order asymptotic behaviours of pressure functionals and statistical representations of the coeﬃcients · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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
we have an explicit formula for the behaviour of µ(( i=0 (ψ − X ψ dµ) ◦ σ i )k ) as m → ∞ with the Gibbs
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.

Final: 2024/2/9
Statistics and Probability(Kyoto Univ.)
14 Takumu Ooi
Toshihiro Uemura (Kansai Univ.)

56

Dynkin games for Markov processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider Dynkin games for Markov processes associated with semi-Dirichlet forms. Dynkingames are the optimal stopping games introduced as the models of zero-sum games by two players. We
prove that the solution to the certain variational inequality with two obstacles is the equilibrium price of
the Dynkin game. Moreover, we obtain the saddle point of the game.
15 Yuji Shinozaki(Bank of Japan / Tokyo Tech)
Syoiti Ninomiya (Tokyo Tech)

Error estimation of high-order recombination and its application · · · · · 15

Summary: 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.
16 Yuki Ueda (Hokkaido Univ. of Edu.)

Uniform convergence towards extreme value distributions in free probability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 this talk, wewill 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

Research Section Assembly

March 19th (Tue)

Conference Room III

10:00–11:10
17 Teruo Tanaka (Hiroshima City Univ.)

Certain fractional optimal stopping problems —continuous time case—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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 Toshiharu Fujita(Kyushu Inst. of Tech.)

Stochastic decision process with feedforward loop system —Minimum
reward system— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 ourmodel and introduce recursive equations by dynamic programming technique.

Final: 2024/2/9
57

Statistics and Probability(Kobe Univ.)
19 Kenji Tanino
Masatake Hirao (Aichi Pref. Univ.)
Masanori Sawa (Kobe Univ.)

Research on the strength of Bd -invariant weighted spherical design using
simplicial characterization and Hilbert’s identity · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we give an upper bound for the degree of a certain type of Bd -invariant weighted
spherical designs, as a generalization of Bajnok (2007), Heo–Xu (2001) and Sawa–Xu (2014). To achive thisgoal, 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.
20 Hisaya Okahara (Tokyo Univ. of Sci.)
Kengo Fujisawa(Tokyo Univ. of Sci., Yamaguchi)
Kouji Tahata (Tokyo Univ. of Sci.)

Separable models related to symmetry for multi-way contingency tables· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

March 20th (Wed)Conference Room III

10:00–11:40
21 Eri Kurita (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

A test statistic for Mardia’s multivariate skewness · · · · · · · · · · · · · · · · · · 15

Summary: 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 a goodchi-squared approximation. Finally, we compare our result with that of Mardia (1970) and investigate theaccuracy of chi-squared approximation by a Monte Carlo simulation.
22 Koji Tsukuda (Kyushu Univ.)
Shun Matsuura (Keio Univ.)

Estimation of the leading principal component in the multivariate allometric regression model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The multivariate allometric regression model is a multivariate multiple regression model which
imposes that the diﬀerence of mean vectors of two observations is always parallel to the leading eigenvectorof the covariance 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: 2024/2/9
Statistics and Probability

23 Kou Fujimori (Shinshu Univ.)
Koji Tsukuda (Kyushu Univ.)

58

Two step estimations via the Dantzig selector for ergodic time seriesmodels · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the estimation problems for conditionally heteroskedastic ergodic time series models
with high-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 Kento Egashira (Tokyo Univ. of Sci.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Asymptotic properties of kernel k-means for high-dimension, low-samplesize data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Reconstruction of a low-rank matrix by singular value decompositions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Yoshihide Kakizawa (Hokkaido Univ.)

Density estimation for cylinder data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For the data supported on [0, ∞) or [0, 1], the so-called boundary bias problem is one of theinterests. Instead of the location-scale kernel k((x − ·)/h)/h, we have recently developed asymmetric kernel
method to solve 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 somerelated works in this direction will be expected by combining the circular distribution theory with the
nonparametric method.

Final: 2024/2/9
59

Statistics and Probability

14:15–15:15

Award Lecture for the 2023 MSJ Analysis Prize

Yasunori Fujikoshi (Hiroshima Univ.⋆)

Model selection based on information criteria in high-dimensional statistical analysis

Summary: 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

Talk Invited by Statistics and Probability Section

Tomoyuki Nakagawa (Meisei Univ.)

Robust Bayesian inference using the divergences and its applications

Summary: In Bayesian statistics, the robustness against outliers is one of important issues.

It is wellknown that an ordinary Bayesian inference is strongly inﬂuenced by outliers. As one of the solutions tothis 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 beconstructed for each 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 been developed by numerous studies in recent years. In this presentation, we consider that therobustness of Bayesian inference using the density power and gamma divergences. In addition, we show theperformance of these Bayesian inferences which applied to several models in simulation studies.

Final: 2024/2/9
Applied Mathematics

60

Applied Mathematics
March 17th (Sun)

Conference Room IX

9:00–12:00
1 Jiro Akahori (Ritsumeikan Univ.)
Norio Konno (Ritsumeikan Univ.⋆)
Rikuki Okamoto (Ritsumeikan Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)
Yuma Tamura (Ritsumeikan Univ.)

Absolute zeta functions and periodicity of quantum walks on cycles· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The absolute zeta function can be considered as a zeta function over F1 and the quantum walk isa quantum counterpart of the classical random walk. We showed a connection between the quantum walkand the 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 andabsolute zeta functions of such quantum walks. Especially, our result includes other proofs of some known
results which showed such periods in some cases.
2 Rikuki Okamoto (Ritsumeikan Univ.)
Konno Norio (Ritsumeikan Univ.⋆)
Sato Iwao (Oyama Nat. Coll. of Tech.)Akahori Jiro (Ritsumeikan Univ.)

Absolute zeta functions of zeta functions of quantum walks · · · · · · · · · · 15

Summary: We consider the absolute zeta function of zeta functions of quantum walks. First, we deﬁne thematrix 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
absolute automorphic form of weight depending on the number of edges of the graph. We can consider
the absolute zeta function of zeta function of quantum walk by this absolute automorphy. Especially, we
calculate the absolute zeta function of zeta functions of quantum walks on a complete graph.
3 Taisuke Hosaka (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)
Norio Konno (Ritsumeikan Univ.⋆)

QW-search/Zeta correspondence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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.
4 Iwao Sato (Oyama Nat. Coll. of Tech.)
Takako Endo (Tohoku Univ.)
Takashi Komatsu (Univ. of Yamanashi)
Norio Konno (Ritsumeikan Univ.⋆)

Weighted alternating Walk/Zeta correspondence · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
61

Applied Mathematics

5 Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)(Tsuda Coll.)
Atsushi Nagai

The best constants of two types of discrete ℓp Sobolev inequalities on acomplete graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let p be a positive real number. We determine the best constants of two types of discreteℓp Sobolev inequalities on a complete graph KN .

The discrete ℓp Sobolev inequality shows that the

maximum of |u(i)|p is estimated from above by constant multiples of the potential energy for vectoru = 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.
6 Sho Fujimura (Fukuoka Univ.)
Shuji SHIRAISHI (Fukuoka Univ.)

On the generation of all Euler trails in an Eulerian graph · · · · · · · · · · · 10

Summary: 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 Bill Jackson(Queen Mary Univ. of London)
Kiyoshi Yoshimoto (Nihon Univ.)

Spanning even trees of graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
8 Shun-ichi Maezawa(Tokyo Univ. of Sci.)(Nihon Univ.)
Akira Saito

On a preorder induced by rainbow forbidden subgraphs · · · · · · · · · · · · · 15

Summary: 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 thepairs (H1 , H2 ) with H1 ≤ H2 when either H1 or H2 is a subgraph of the other. Motivated by their result,
we are currently searching for such pairs under the condition that neither H1 nor H2 is a subgraph of theother. In this talk, We give a progress report of this study.
9 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

Summary: 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 .

Final: 2024/2/9
Applied Mathematics

10 Makoto Ozawa (Komazawa Univ.)
Mario Eudave-Muñoz(Univ. Nacional Autónoma de México)62

Partially ordered set of complexes by embeddings and the existence of
critical subcomplexes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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 , but they do not contain any critical complexes. From the property of those examples, we deﬁne anequivalence relation on all simplicial complexes C and a partially ordered set of complexes (C/ ∼; ⫅), andreﬁne the deﬁnition of critical. According to the reﬁned deﬁnition of critical, we show that if a complex X
cannot be embedded in S 3 , then there exists [X ′ ] ⫅ [X] such that [X ′ ] is critical for [S 3 ].
11 Kohei Tanaka (Shinshu Univ.)

Directed topological complexity for CW complexes · · · · · · · · · · · · · · · · · 15

Summary: The topological complexity of a space is a numerical homotopy invariant closely related to therobot motion planning problem. If robot motions are required to go along with certain direction, thedirected 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.
12 Akihiro Higashitani (Osaka Univ.)

Reﬂexive polytopes arising from regular matroids and γ-nonnegativity· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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(Seikei Univ.)
13 Kengo Enami
Yumiko Ohno (Yokohama Nat. Univ.)

Diﬀerence of facial achromatic numbers between two triangular embeddings of a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A facial 3-complete k-coloring of a triangulation G on a surface is a vertex k-coloring such thatevery 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 Daiki Takahashi (Yokohama Nat. Univ.)
Atsuhiro Nakamoto(Yokohama Nat. Univ.)

Quadrangulations of a polygon with outer Steiner points · · · · · · · · · · · · 15

Summary: Given an n-sided polygon P on the plane with n ≥ 4, we consider a problem whether P
is quadrangulatable 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 canbe put in any position in 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.

Final: 2024/2/9
63

Applied Mathematics

15 Kenta Noguchi (Tokyo Univ. of Sci.)
Gunnar Brinkmann (Ghent Univ.)
Heidi Van den Camp (Ghent Univ.)

Embedding of complete graphs so that the dual has a 1-cut · · · · · · · · · 15

Summary: In 2022, Bokal, Brinkmann, and Zamﬁrescu considered the problem of the connectivity of thedual and they 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 forc ≥ k ≥ 1 and they determined the exact value when k ≥ 3 or c ≤ 6. In this talk, we determine the exact
value of δ2 (c) for all c and give an upper bound for δ1 (c), which is one apart from the best, for inﬁnitely
many c.
16 Hideki Matsumura (Keio Univ.)
Masanori Sawa (Kobe Univ.)

On a complex analogue of central symmetry of weighted designs · · · · · 15

Summary: A quadrature formula is a formula computing a deﬁnite integration by evaluation at a set ofﬁnitely many points (design). Examining the existence of certain rational quadrature formulas leads toapplications to interesting problems such as Waring’s problem and spherical designs. A central symmetricquadrature is a central research object in the real case. Sawa and Uchida proved the existence and thenon-existence of 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 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 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 geometricconsiderations.
18 Eiichi Bannai (Kyushu Univ.⋆)
Hirotake Kurihara (Yamaguchi Univ.)(Kyoto Univ.)
Da Zhao
Yan Zhu(Univ. of Shanghai for Sci. Tech.)On the bivariate Q-polynomiality of certain association schemes. · · · · · 15

Summary: 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 Madoka Awada (Waseda Univ.)

3-designs constructed by using quadratic residue codes · · · · · · · · · · · · · · 15

Summary: 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: 2024/2/9
Applied Mathematics

20 Reina Ishikawa (Waseda Univ.)

64

Exceptional designs in some extended quadratic residue codes · · · · · · · 15

Summary: 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
codes of 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 for theextended ternary quadratic residue code of length 14 and the extended quaternary quadratic residue codeof length 18. By using these results, we prove our examples through logical reasoning.
21 Hiroaki Taniguchi(Yamato Univ./Kagawa Nat. Coll. of Tech.⋆)On quadratic APN functions F (x) + T r(x)L(x) · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 ∈ F2n−1 with e0 ∈ Fn2 \Fn−1.
2
Next we specialize this characterization to the case when f is quadratic and g(x) = f (x) + L(x) for somelinearized polynomial L. Lastly for a quadratic APN (n, n)-function F and a linearized polynomial L,
we give a characterization of 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

Talk Invited by Applied Mathematics Section(Gifu Univ.) Combinatorial structures for group testing and combinatorial testingXiao-Nan Lu
Summary: Group testing (GT) is a method for identifying defective items within a large population bypooling samples together for joint testing. Combinatorial structures in GT, commonly represented bybinary matrices like separable matrices and disjunct matrices, serve as crucial mathematical frameworks forformulating eﬃcient testing strategies. Combinatorial testing (CT) focuses on the identiﬁcation and locationof faults arising from interactions among a small number of factors, not just independent items. Test
case designs in 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.

March 18th (Mon)

Conference Room IX

9:00–12:00
22 Jun Sato (Tokyo Polytechnic Univ.)
Yuki Ishiguro (Univ. of Tokyo)
Katsuhiro Nishinari (Univ. of Tokyo)

Exact stationary state of the inhomogeneous ASEP · · · · · · · · · · · · · · · · 15

Summary: 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 Shuhei Kamioka (Osaka Seikei Univ.)

An integrable algorithm for randomly sampling plane partitions · · · · · · 15

Summary: 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
is about 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.

Final: 2024/2/9
65

Applied Mathematics

24 Toshitaka Aoki (Kobe Univ.)
Emerson Gaw Escolar (Kobe Univ.)
Shunsuke Tada (Kobe Univ.)

Computing bipath persistent homology · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Hideaki Morita (Muroran Inst. of Tech.)On the regular covering of a ﬁnite digraph · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 digraph can 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 of a digraph.
26 Ayaka Ishikawa (Yamagata Univ.)

A graph zeta function of periodic paths and its determinant expression· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Tatsuya Tsurii(Tokyo Univ. of Information Sci.)
Naoharu Ito (Nara Univ. of Edu.)
Toyoki Matsuyama(Nara Univ. of Edu.)

A study on periodicity of Grover walk using group structures obtained
from its evolution matrix · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In our previous paper [1], we have shown that Grover walk on complete graphs with n vertices
and a self-loop at each vertex has period 2n. The method of the proof is focus on the eigenvalues ofthe evolution matrix U . In this talk, we show another proof of the above problem by focusing on groupstructures obtained from the evolution matrix U .
28 Daiju Funakawa (Hokkai-Gakuen Univ.)(Kanagawa Univ.)
Kei Saito

The existence of eigenvalues in one-dimensional two-state open quantum
walks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Quantum walks are mathematical models that are said to be quantum version of random walks
and are 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.

Final: 2024/2/9
Applied Mathematics

29 Masahiro Sanka
Katsuhiro Ota(Keio Univ.)(Keio Univ.)

66

Toughness, forbidden induced paths and hamiltonicity of graphs · · · · · 15

Summary: 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.
30 Kuniharu Yokomura (Tokai Univ.)

On degree conditions of balanced 3-partite Hamiltonian-connected graphs· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 give some conditions for balanced 3-partite graphs to be Hamiltonian-connected.
31 Shinya Fujita (Yokohama City Univ.)

On monochromatic connectivity in edge-colored graphs · · · · · · · · · · · · · 10

Summary: We consider edge-colored graphs. Let G be an edge-colored graph. If, for any two vertices inG, 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 Kiyoshi Ando (Nat. Inst. of Informatics)

A constructive characterization of 5-edge-connected 5-regular multigraphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We deal with multi-graphs with no self-loops. By introducing a new operation “quasi- edgebinding”, we give a generating theorem for 5-edge-connected 5-regular multi-graphs. This is a 5-edgeconnected analogue of Korzig–Simmons result on 2k-edge-connected 2k-regular multi-graphs.
13:00–14:00
33 Satoru Fukasawa (Yamagata Univ.)
Tsuyoshi Miezaki (Waseda Univ.)

Galois points for a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Tsuyoshi Miezaki (Waseda Univ.)
Yuusaku Nishimura (Waseda Univ.)
Akihiro Munemasa (Tohoku Univ.)
Tadashi Sakuma (Yamagata Univ.)
Shuhei Tsujie (Hokkaido Univ. of Edu.)

A generalization of the chromatic symmetric function · · · · · · · · · · · · · · · 15

Summary: The present talk aims to give a generalization of the chromatic symmetric function. We call thisthe Kneser chromatic function and show that the set of Kneser chromatic functions is a complete invariant
for graphs. Further, we give three graph invariants and discuss some of their properties.

Final: 2024/2/9
67

Applied Mathematics

35 Yusaku Nishimura (Waseda Univ.)

A simple random walk and equitable partition · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Yuho Tanaka(Waseda Univ.)

On the average hitting times of directed Cayley graphs · · · · · · · · · · · · · 15

Summary: 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}).

March 19th (Tue)

Conference Room IX

9:50–12:00
37 Koji Nuida(Kyushu Univ.)

A proof of Zorn’s Lemma from elementary properties of partially orderedsets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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 Tetsuya Nagano (Univ. of Nagasaki)

Finsler encryption · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Inspired by previous work with the ﬁrst example proposed at SecITC 2020, we give a generaldescription of Finsler encryption that is based on a Finsler space, which uses a kind of a diﬀerentiablegeometry on a 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.
39 Ryoko Tomiyasu (Kyushu Univ.)

Packing theory derived from phyllotaxis and products of linear forms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Applied Mathematics

40 Tomoharu Suda

(RIKEN)68

A categorical perspective on the relationship between discrete andcontinuous time dynamical systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
41 Tomoyuki Miyaji (Kyoto Univ.)
Kazuya Okamoto (Waseda Univ.)
Akiyasu Tomoeda (Kansai Univ.)

Neimark–Sacker bifurcation with discrete rotational symmetry and traveling waves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Neimark–Sacker bifurcation, a codimension-one bifurcation for a ﬁxed point of a map witha pair of complex eigenvalues on the unit circle, leads to the appearance of an invariant closed curve. We
show that 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 Mikio Murata(Tokyo Univ. of Agri. and Tech.)

Turing patterns appearing in Gray–Scott cellular automaton · · · · · · · · 15

Summary: A cellular automaton constructed by positive value diﬀerentiation and ultradiscretization of theGray–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 will report the results of numerical simulations of a two-dimensional Gray–Scott cellular automaton byreplacing diﬀusion parameters, initial concentration, and neighborhoods and grids.
43 Itsuki Watanabe (Waseda Univ.)

High density limit for nonlocal cross-diﬀusion model with self-diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The deterministic limit of a stochastic model of nonlocal cross-diﬀusion with self-diﬀusion isconsidered. The stochastic model is given by two types particle system where the diﬀusion rate depends onthe density of both particle types. In this talk, we reveal its deterministic limit, and show the existence ofsolution of nonlocal cross-diﬀusion equation by Markov chain approximation method.
(RIKEN)
44 Ken Furukawa
Hiroyuki Kitahata (Chiba Univ.)

Drift-diﬀusion equations under dynamic boundary conditions for ﬁltration phenomena · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 ona one-dimensional 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 theboundary conditions, unlike the Dirichlet, the Neumann, and the Robin boundary conditions. In this model,
the dynamic boundary condition with the fourth boundary condition is considered. This study is based on
joint research with Professor Hiroyuki Kitahata of Chiba University.

Final: 2024/2/9
69

Applied Mathematics

14:15–14:40

Presentation Ceremony for the 2023 Applied Mathematics Prize

14:50–16:30
45 Yoshihisa Morita (Ryukoku Univ.⋆)
Shuichi Jimbo (Hokkaido Univ.)

Front propagation and blocking for the bistable reaction-diﬀusion equation on tree-like metric graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Takeo Ushijima (Tokyo Univ. of Sci.)

A Remark on the blow-up rates of curvatures in the area-preserving
curvature ﬂow in the plane · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We deal with the area-preserving curvature ﬂow in the plane, particularly the blow-up phenomenaof curvatures 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.
47 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.)

Unique existence of weak solution and asymptotic behavior of Zenertype viscoelastic wave equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
(Chuo Univ.)
48 Kota Ohno
Toshiyuki Ogawa (Meiji Univ.)

Process to reach consensus in Deﬀuant model · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Opinion dynamics, one of the ﬁelds of social science, is a multidisciplinary ﬁeld and has beenstudied 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 the criticalpoint through variations of this ratio. Furthermore, we also discuss the process to reach consensus in themodiﬁed Deﬀuant model where distance is introduced for the agent placement.

Final: 2024/2/9
Applied Mathematics

49 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.)

70

Numerical simulation to reproduce morphogenesis of hair follicles · · · · 15

Summary: 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 Sungrim Seirin Lee(Kyoto Univ. / Kyoto Univ.)

Mathematical dermatology linking eruption morphology and in vivo
pathology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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

Talk Invited by Applied Mathematics Section

Yoshitaro Tanaka(Future Univ.-Hakodate)

Nonlocal evolution equations and approximations by system of partial
diﬀerential equations

Summary: 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,
we approximate 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: 2024/2/9
71

Applied Mathematics

March 20th (Wed)Conference Room IX

9:50–12:00
51 Takashi Furuya (Shimane Univ.)

Globally injective and bijective neural operators · · · · · · · · · · · · · · · · · · · 10

Summary: Recently, there has been great interest in neural operators, which learn operators between
inﬁnite-dimensional function spaces. Given their discretization-invariance property, neural operators havebeen remarkably 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 Jumpei Nagase(Univ. of Electro-Comm.)

ReLU function representability by piecewise nonlinear functions · · · · · · 15

Summary: 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 the activation function is representable of the ReLU function, then the deep neural network model ispossible to transform any linear connection into a multilayer perceptron model. And since it is possible
to express the design 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 Takeshi Gotoda (Tokyo Tech)

Numerical study of enstrophy variation on ﬁltered-Euler ﬂows · · · · · · · 15

Summary: We investigate enstrophy variation in an incompressible and inviscid ﬂow through point-vortex
solutions 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 solutionsof 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 Yuuki Shimizu (Univ. of Tokyo)

Impact of curvature on a point vortex · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Towards quantifying the impact of curvature variations on a point vortex, we discuss somedynamical properties of the point vortex on continuously diﬀerentiable surfaces obtained by gluing two
diﬀerent constant-curvature surfaces.
55 Takehiko Kinoshita (Saga Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

Regarding the matrix 2-norm of real 2 × 2 matrices and improved
convergence order of norm for approximate inverse operetors · · · · · · · · 15

Summary: We report that we have improved the convergence order of norm for approximate inverse operetors
reported in [1].
56 Takeshi Terao (Kyushu Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Katsuhisa Ozaki(Shibaura Inst. of Tech.)

Numerical veriﬁcation method of the approximate inverse operator norm
for inﬁnite-dimensional linear operators · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
Applied Mathematics

57 Makoto Okumura (Konan Univ.)

72

On the regularity of a matrix appearing in the proof of the solvabilityof a structure-preserving scheme under dynamic boundary conditions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
58 Tetsuya Ishiwata(Shibaura Inst. of Tech.)Daisuke Ito (Shibaura Inst. of Tech.)
Taichi Shiga

Monotonicity-preserving numerical scheme for fractional advection equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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
59 Fumio Kikuchi (Univ. of Tokyo⋆)
Xuefeng Liu(Tokyo Woman’s Christian Univ.)

Techniques for hypercircle-based error estimation of ﬁnite element solutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 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.)

A ﬁnite element scheme for a multiphase ﬂow model · · · · · · · · · · · · · · · · 15

Summary: 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 the common pressure, where N is the number of ﬂuid phases. After introducing an energy estimate of
the model, a stability result of the scheme and two-dimensional numerical results are also presented.

Final: 2024/2/9
73

Applied Mathematics

61 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

Summary: We consider a sharp interface formulation for the multi-phase Mullins–Sekerka ﬂow. Making useof a 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 Karel Svadlenka (Tokyo Metro. Univ.)

On an approximation scheme for anisotropic interfacial motion on obstacle · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider L2 gradient ﬂow of anisotropic surface energy in the presence of an obstacle andpossibly 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 as stability, convergence and Gamma-convergence of the corresponding approximate energies. We also
show numerical simulations of motions involving topology changes.
15:40–16:40
Yikan Liu

Talk Invited by Applied Mathematics Section(Kyoto Univ.)

On solution dynamics of coupled systems and semilinear problems oftime-fractional diﬀusion equations

Summary: The last decade has witnessed explosive developments and gradual saturation of nonlocal models
from various 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: 2024/2/9
Topology

74

Topology
March 17th (Sun)

Conference Room V

9:30–11:10
1 Takahiro Oba (Osaka Univ.)
Myeonggi Kwon
(Jeonbuk National Univ.)

Symplectic ﬁllings of unit cotangent bundles of spheres · · · · · · · · · · · · · 15

Summary: 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 Naoyuki Monden (Okayama Univ.)
Anar Akhmedov (Univ. of Minnesota)

Geography of symplectic 4-manifolds admitting Lefschetz ﬁbrations · · 15

Summary: 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 Naoyuki Monden (Okayama Univ.)
Anar Akhmedov (Univ. of Minnesota)

Ruled surfaces and indecomposable Lefschetz ﬁbrations · · · · · · · · · · · · · 15

Summary: 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 thisrelation, we obtain a condition for a Lefschetz ﬁbration to be ﬁber sum indecomposable. Moreover, we giveﬁber sum indecomposable Lefschetz ﬁbrations on minimal total spaces.
4 Tatsumasa Suzuki (Tokyo Tech)
Motoo Tange (Univ. of Tsukuba)

Pa,b -surgery on 4-manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In 2004, Iwase and Matsumoto introduced pochette surgery. In 2018, Nakamura introduced ageneralization of pochette surgery called Pa,b -surgery. A Pa,b -surgery on a 4-manifold X is an operationof 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 isisomorphic to the fundamental group of a Pa,b -surgery on a simply connected 4-manifold.
5 Tsukasa Isoshima (Tokyo Tech)

Trisections of the doubles of some Mazur type 4-manifolds · · · · · · · · · · 15

Summary: A trisection is roughly a decomposition of a closed, oriented, smooth 4-manifold into three 4dimensional 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.

Final: 2024/2/975Topology

6 Masaki Ogawa (Tohoku Univ.)

Weinstein trisections of trivial surface bundles · · · · · · · · · · · · · · · · · · · · · 10

Summary: 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

Research Section Assembly

14:20–15:20

Talk Invited by Topology Section

Masaaki Ue(Kyoto Univ.⋆)

Constraints on intersection forms of 4-manifolds with given boundary
in terms of Gauge theoretical invariants

Summary: 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 Atsuhide Mori (Osaka Dent. Univ.)

A model of linguistic minimalism · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Teruaki Kitano
Marina Shibata(Soka Univ.)(Soka Univ.)

On linear representations of a surface group of genus 2 into SL(2; Z[1/2])
with a nontrivial real Euler class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Milnor proved that there exists a ﬂat real R2 -vector bundle over a closed orientable surface ofgenus 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.).
9 Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)

Generating sets for the level d mapping class group of a compact nonorientable surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The level d mapping class group Md (S) of a surface S is the subgroup of the mapping class groupof S consisting of mapping classes acting trivially on H1 (S; Zd ). In this work, we gave a normal generating
set of 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.

Final: 2024/2/9
Topology

10 So Yamagata (Fukuoka Univ.)

76

Presentation of the pure braid group and section of the braid arrangement · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 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

Summary: Vaughan Jones motivated by an attempt to develop new conformal ﬁeld theory, obtained asequence of results related to Thompson’s groups F. One of the results is the concrete construction of knots
and links 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
and they 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 Haru Negami(Chiba Univ.)

Generalization of the twisted Long–Moody construction · · · · · · · · · · · · · 15

Summary: The Long–Moody construction is a method for obtaining a representation of the braid groupfrom a given representation of the semidirect product of the free group and the braid group deﬁned byArtin representation. Artin representation has a geometric realization such as the transformation of theloops 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.

March 18th (Mon)

Conference Room V

9:30–10:00
13 Toshiyuki Akita (Hokkaido Univ.)
Sota Takase (Hokkaido Univ.)

Groups having Wirtinger presentations and the second group homology· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Kuz’min (1996) characterized groups having Wirtinger presentations in relation to their second
group homology. We further reﬁne the connections between these groups and their second group homology.
14 Masahiko Yoshinaga (Osaka Univ.)
Yu Tajima (Hokkaido Univ.)

Causal order complex and magnitude homotopy type · · · · · · · · · · · · · · · 15

Summary: 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.

Final: 2024/2/9
77Topology

March 18th (Mon)
10:10–10:25

Conference Room IV

Presentation Ceremony for the 2023 MSJ Geometry Prize

10:30–11:30

Award Lecture for the 2023 MSJ Geometry Prize(Osaka Univ.) ♭ On criteria for the K-stability of Fano varieties
Kento Fujita
Summary: We survey recent progress on K-stability of Fano varieties.

March 18th (Mon)

Conference Room V

13:00–14:00
15 Naotsugu Chinen(Nat. Defense Acad. of Japan)
Takamitsu Yamauchi (Ehime Univ.)

Equivariant asymptotic dimension, asymptotic dimension and covering
dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)

Weak D-space properties on products with metric spaces · · · · · · · · · · · · 15

Summary: In this talk, we discuss weak D-space properties on products with metric spaces. We obtain the
result that 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.
17 Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima (Kanagawa Univ.⋆)

Weak D-space properties on inﬁnite products · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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
the real line, (2) if κ is an inﬁnite cardinal such that there is no weakly inaccessible cardinal ≤ κ, then Nκ
is irreducible, where N = {0, 1, 2, · · · } is the countable discrete space.

March 19th (Tue)

Conference Room V

9:30–12:00
18 Katsumi Ishikawa (Kyoto Univ.)
Takayuki Morifuji (Keio Univ.)
Masaaki Suzuki (Meiji Univ.)

Twisted Alexander vanishing order of knots · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We deﬁne the twisted Alexander vanishing order of a knot to be the order of the smallest ﬁnite
group such that the corresponding twisted Alexander polynomial is zero. In this talk, we show its basic
properties.
19 Hiroshi Goda
(Tokyo Univ. of Agri. and Tech.)Takayuki Morifuji (Keio Univ.)

Chirality of hyperbolic knots and twisted Alexander polynomials · · · · · 10

Summary: 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
of ﬁnite 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.

Final: 2024/2/9
Topology

20 Shun Sawabe(Waseda Univ.)

78

On the annihilating polynomial of the colored Jones polynomial for theWhitehead link · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: An annihilating polynomial of the colored Jones polynomial for a knot is conjectured to produce
the A-polynomial when made into a commutative polynomial by putting q = 1 (AJ conjecture). In this talk,we give 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.
21 Kokoro Tanaka (Tokyo Gakugei Univ.)
Yuta Taniguchi (Osaka Univ.)

The second quandle homology group of the knot n-quandle · · · · · · · · · · 10

Summary: 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 thatit characterizes the unknot. In this talk, we compute the second quandle homology group of the knot
n-quandle for each 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 isfound to have more information than that of the latter.
22 Keisuke Himeno (Hiroshima Univ.)

Hyperbolic knots whose knot Floer complex is stably equivalent to thatof a (3, q)-torus knot · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Two (full) knot Floer complexes are called stably equivalent if they can be made to become
ﬁltered chain 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 constructinﬁnitely many mutually non-concordant hyperbolic knots whose knot Floer complex is stably equivalent tothat 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 Han Yoshida(Gunma Nat. Coll. of Tech.)Commensurators of Löbell polyhedra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a non-arithmetic Kleinian group Γ < Isom(H3 ), the commensurator C(Γ) < Isom(H3 ) isthe (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 Kengo Kawamura (Osaka Sangyo Univ.)

Solvability of an integral region choice problem for a link projection· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Mahito Kobayashi (Akita Univ.)
Takashi Sano (Hokkai-Gakuen Univ.)
Minoru Yamamoto (Hirosaki Univ.)

Panorama views of closed piecewise linear curves in R2 for shape study· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a closed piecewise linear (PL) curve in R2 , a geometric transformation called a panorama
view is applied to show two basic formulae on the shape of the curve by Crofton and by Banchoﬀ. We
note that for a simple PL curve, a sequence of polygons can be obtained by which one can describe theorganizations of so called hollows of the curve.

Final: 2024/2/9
79Topology

26 Sachiko Saito (Hokkaido Univ. of Edu.)−
Strongly mixed weighted homogeneous polynomials of type J10· · · · · · 10

Summary: 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

Talk Invited by Topology Section

Mayuko Yamashita (Kyoto Univ.) ♭ Topological Modular Forms and supersymmetric quantum ﬁeld theories
Summary: 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 isan 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: 2024/2/9
Inﬁnite Analysis

80

Inﬁnite Analysis
March 19th (Tue)

Conference Room VIII

9:30–11:30
1 Mizuki Mori (Ochanomizu Univ.)
Kouichi Takemura (Ochanomizu Univ.)

Three-term recurrence relations and Heun equations · · · · · · · · · · · · · · · · 15

Summary: Heun’s diﬀerential equation is a standard form of the second order Fuchsian diﬀerential equation
with four 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 coeﬃcientsare polynomials on the accessory parameter and they satisfy a three-term recurrence relation.
2 Yumi Arai (Ochanomizu Univ.)

Solutions to q-hypergeometric equations associated with q-middle convolution · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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-hypergeometricseries. We show the correspondence between these integral solutions and solutions obtained through othermethods. We also show the linear relationships among the integral solutions.
3 Takahiko Nobukawa (Kobe Univ.)(Kobe Univ.)
Taikei Fujii

Connection problem for the variant of q-hypergeometric equation ofdegree three · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 geta three term relation for the very-well-poised q-hypergeometric function 8 W7 .
4 Sanefumi Moriyama(Osaka Metro. Univ.)

ABJM matrix models and q-Painlevé equations · · · · · · · · · · · · · · · · · · · · 15

Summary: 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.
5 Yousuke Ohyama (Tokushima Univ.)

Mano’s decomposition and q-Painlevé equations · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Lax pairs.
6 Tetsu Masuda (Aoyama Gakuin Univ.)

An explicit formula for the discriminants of the Umemura polynomialsof the Painlevé V equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present a combinatorial formula for the discriminants of the Umemura polynomials associatedwith a family of rational solutions to the Painlevé V equation.

Final: 2024/2/9
81

Inﬁnite Analysis

14:15–15:15

Talk Invited by Inﬁnite Analysis Special Session

Ryo Okawa(Osaka Metro. Univ./Kyoto Univ.)

Non-stationary diﬀerence equation and aﬃne Laumon space

Summary: 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 Painlevé VI equation proposed by Hasegawa. It is also identiﬁed with the quantum Knizhnik–(1)
Zamolodchikov(q-KZ) equation for Uq (A1 ). In the latter half of the talk, we would like to introduce thejoint work with Shiraishi, and point out the similarity between the Shakirov equation and the wall-crossing
formula.

March 20th (Wed)Conference Room VIII

9:30–11:30
7 Masahiko Yoshinaga (Osaka Univ.)
Misha Feigin (Univ. of Glasgow)
Zixuan Wang (Hokkaido Univ.)

Integral expressions of logarithmic vector ﬁelds for multiarrangements· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The explicit construction of the logarithmic vector ﬁelds for hyperplane arrangements withmultiplicity is a hard problem in general. In this talk, we will discuss integral expression of them.
8 Saburo Kakei(Rikkyo Univ.)

Solutions to the KP hierarchy with an elliptic background · · · · · · · · · · · 15

Summary: 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.
9 Genki Shibukawa (Kobe Univ.)
Masatoshi Noumi (Rikkyo Univ.)

Ruijsenaars-type identities and their applications · · · · · · · · · · · · · · · · · · 15

Summary: We prove some identities, which we call Ruijsenaars-type identities, and show their applications
such as 1) commutativity of some diﬀerence operators and 2) Weyl group symmetry of the Tableau
representation of interpolation polynomials.
10 Ryo Takenaka (Osaka Metro. Univ.)

On exponents associated with Y-systems · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 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 Ryota Akagi(Nagoya Univ.)

Ordered product expressions of rank 2 cluster scattering diagrams · · · · 15

Summary: We focus on cluster scattering diagrams, which were introduced in recent years.

They areclosely related to cluster algebras. By Nakanishi’s study, it was clariﬁed that dilogarithm elements play
an important 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 productof dilogarithm elements. In this talk, we show some result for these ordered products.

Final: 2024/2/9
Inﬁnite Analysis(Chiba Univ.)
12 Rei Inoue
Atsuo Kuniba (Univ. of Tokyo)
Yuji Terashima (Tohoku Univ.)

82

Quantum cluster algebras and 3D integrability · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct new solutions to the tetrahedron equation and the 3D reﬂection equation, bydeveloping the recent study by Sun and Yagi on the tetrahedron equation applying quantum cluster
algebras.
14:15–15:15

Talk Invited by Inﬁnite Analysis Special Session

Katsushi Ito(Tokyo Tech)

ODE/IM correspondence and exact WKB analysis in quantum mechanics

Summary: 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 theexact WKB analysis of one-dimensional quantum mechanics and the Thermodynamic Bethe Ansatz (TBA)
equation in two-dimensional quantum integrable theory. The Voros symbols in the exact WKB analysis
correspond to 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 a generalization to higher-order ODE.