Final: 2023/2/8“ The Mathematical Society of Japan
2023 Annual Meeting

Titles and Short Summaries of the Talks

March, 2023
at Chuo University2023 The Mathematical Society of Japan
ANNUAL MEETING
Dates: March 15th (Wed)–18th (Sat), 2023
Venue: Chuo University
1–13–27 Kasuga, Bunkyo-ku
Tokyo, 112-8551, Japan
Contact to: Faculty of Science and Engineering, Chuo University
1–13–27 Kasuga, Bunkyo-ku
Tokyo, 112-8551, Japan
E-mail chuo23mar mathsoc jp
The Mathematical Society of Japan

15th

I

II

III

IV

V

VI

VII

VIII

IX

5533

5333

5335

5336

5233

5234

5235

5236

5138

AlgebraGeometry

Topology

Functional
Equations

ComplexAnalysis

Functional
Applied Statistics and Found. of Math.
Analysis Mathematics Probability & Hist. of Math.

9:00–12:00
14:15–14:50

9:30–11:40
14:15–16:00

9:30–12:00
15:40–17:30

9:30–12:00
14:15–16:15

9:30–11:45

9:30–12:00
14:15–16:15(Wed)

Featured Invited Talks

9:50–11:50
14:15–15:25

10:00–11:30

9:30–10:15
14:30–16:45

13:00–14:00

Invited Talks Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk Invited Talks Invited Talks
15:00–16:00
16:15–17:15

16:15–17:15

14:20–15:20

16:30–17:30

14:15–15:15
15:30–16:30

16:30–17:30

AlgebraGeometry

Topology

Functional
Equations

ComplexAnalysis

Functional
Applied Statistics and Found. of Math.
Analysis Mathematics Probability & Hist. of Math.

9:10–12:00
13:00–14:10

9:30–12:00

9:30–12:00
13:00–14:00

9:15–12:00

9:30–11:45

9:30–12:00

16th
(Thu)

Invited Talk

Invited Talk Invited Talk Invited Talk

13:00–14:00

13:00–14:00

MSJ Prizes Presentation
Plenary Talks

13:00–14:00

10:00–11:45
13:00–14:10

14:15–15:15
15:30–16:30

10:20–11:10

10:30–11:30
17:00–18:00

9:15–12:15

13:10–14:10(5534, 5F, Bldg. 5) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:30–15:05)(5534, 5F, Bldg. 5) Spring Prize Winner · · · · · · · · · · · · · · · · · · (15:20–16:20)
Takayuki Hibi (Osaka Univ.⋆) · · · · · · · · · · · (16:35–17:35)

AlgebraGeometry

Topology

Functional
EquationsReal
Analysis

9:00–12:00

9:30–11:40
14:15–14:55

9:30–12:00
15:40–17:00

9:30–12:00
14:15–16:15

9:00–11:45
14:15–15:25

17th

15:45–16:45(Fri)

Featured Invited Talks

Functional
Applied Statistics andAnalysis Mathematics Probability

InﬁniteAnalysis

9:30–12:00
14:15–15:30

9:45–10:45

9:50–11:50
14:45–16:30

9:50–11:35

13:00–14:00

Invited Talks Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk Invited Talks Invited Talk
14:40–15:40
16:00–17:00

Algebra9:15–12:00

18th 14:15–16:45(Sat)

15:10–16:10

14:20–15:20

16:30–17:30

15:40–16:40
17:00–18:00

Functional
EquationsReal
Analysis

9:30–12:00
14:15–16:15

9:00–12:00
14:15–16:30

Featured Invited Talks

15:45–16:45

16:45–17:45

14:25–15:25
15:40–16:40

Applied Statistics andMathematics Probability
9:50–11:50
14:15–15:05

10:00–11:10

11:00–12:00

InﬁniteAnalysis
10:00–10:45

13:00–14:00

Invited Talk Invited Talk

Invited Talk

Invited Talk

16:30–17:30

15:20–16:20

11:00–12:00

17:00–18:00

Final: 2023/2/8
3Contents
Plenary Talks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

Foundation of Mathematics and History of Mathematics

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

4March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

8March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

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

20March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

32

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

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

45

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

Functional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

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

60

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

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4

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

66

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

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

77

March 15th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

March 16th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

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

84

March 17th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

March 18th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

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1

Plenary Talks

Plenary Talks
March 16th (Thu) 5534, 5F, Bldg. 5Award Lecture for the 2023 MSJ Spring Prize
Spring Prize Winner····················································(15:20–16:20)

Takayuki Hibi (Osaka Univ.⋆)

Polytopes and Monomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(16:35–17:35)

Summary: The theory of convex polytopes, which has its origins in Euler’s theorem (1752) and Pick’s
formula (1899), is one of the traditional areas of combinatorics. It underwent a dramatic change in trend
around 1970. Backed by the trend from abstract to concrete, a fascinating contact of convex polytopes
with commutative algebra was discovered, and a bridge was built from the abstract theory of commutative
algebra to the concrete theory of convex polytopes. The bridge simultaneously fostered a movement toreimport combinatorial techniques back into commutative algebra, inviting the birth of the rich soil of socalled “commutative algebra and combinatorics” from the mid-1980s, which led to a historic developmentof commutative algebra for monomial ideals. Later, in the 1990s, with the rapid development of computers
and the evolution of software, the theory of convex polytopes took on the color of computational algebra
and benefited from Gröbner bases, which is a treasure trove of techniques. This plenary talk will overview
the trends in convex polytopes and commutative algebra in the last half-century since 1970 and furthermore
report on current of study for reflexive polytopes and Castelnuovo polytopes.

Final: 2023/2/8
Featured Invited Talks

2

Featured Invited Talks
March 15th (Wed)Conference Room I
Guest Talk from the Japan Society for Industrial and Applied Mathematics
Maki Yoshida(Nat. Inst. Information Comm. Tech.)

NewSpace security —Cryptography for space developmentby private companies— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: In the recent NewSpace era, many small satellites have been launched on various academic orcommercial missions.

A low cost yet highly secure wireless communication has been desired for small

satellites and small launch vehicles, for protecting their critical commands and valuable data transmissions. I
would like to first explain requirements that are indispensable in such context and whether the various typesof cryptography used in existing network systems satisfy them or not. I will then show our approach andresults that establish high security and low implementation cost. The latest flight test conducted on July 31,
2021 achieves successful downlink transmission of 34Mbytes at a practical effective bandwidth of 512kbps.
Conference Room VI

Keita Yokoyama (Tohoku Univ.)

Models of arithmetic and reverse mathematics · · · · · · · · · · ·(13:00–14:00)

Summary: Reverse mathematics is an ongoing program in the field of mathematical logic whose aim is toclassify mathematical theorems by their logical strengths. Then, how can we say that one theorem τ islogically different from another theorem σ? One way to show this is to construct a mathematical structure
which satisfies τ (together with some basic axioms) but not σ. In this talk, I will introduce several typesof structures (models) of axioms for the natural number systems (arithmetic) and show some examples ofclassifications of mathematical theorems from the viewpoints of model theory.

March 17th (Fri)
Conference Room I

Yasuaki Hiraoka (Kyoto Univ.)

Persistent homology: theory and application · · · · · · · · · · · · ·(13:00–14:00)

Summary: Topological data analysis (TDA) has emerged in this century and shed new light on data science.
A particularly important tool in TDA is persistent homology, which can provide useful information about”shape of data” in a multi-scale way. Much of the development of theoretical research on persistent homology
has been motivated by applications. This talk will survey the progress of persistent homology from theperspective of both mathematical and applied research.
Conference Room III

Tsukasa Ishibashi (Tohoku Univ.)

Cluster algebras and the topology of surfaces · · · · · · · · · · · ·(13:00–14:00)

Summary: Since its foundation by Fomin–Zelevinsky (2001), the study of cluster algebras has been developedwith fruitful connections with various areas of mathematics, such as topology, representation theory, integrable
systems, mirror symmetry, and so on.

It focuses on a common combinatorial structure, called clustertransformations, which typically arises as coordinate transformations on a certain space, such as the decorated
Teichmueller space of Penner (1987). Its geometric aspect is formulated as cluster varieties by Fock–Goncharov(2006). One of the motivating examples is the moduli space of decorated (twisted) G-local systems on amarked surface, which includes the decorated Teichmueller space in the case G=SL(2).
In this talk, I would like to talk on the interplay between the cluster algebras and the topology of surfaces,with a focus on the geometry and cluster structure of the moduli space mentioned above. I also mention
recent developments on its quantization via the quantum cluster algebra and the relation to the skein theory.

Final: 2023/2/8
3Featured Invited Talks

Conference Room V

Takayoshi Ogawa (Tohoku Univ.) ♭ End point maximal regularity and its application to a criticalnonlinear problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Maximal regularity for the abstract Cauchy problem of evolution equations is well developed in
the Lebesgue-Bochner space Lρ (I; X), where 1 < ρ < ∞, I is a time interval and X is the UMD Banach
space. If X is UMD then it is necessarily reflexive and maximal regularity in non-reflexive Banach spaces
is depending on each setting. In this talk, we consider the end-point case ρ = 1 in the homogeneous Besovsspace X = Ḃp,1(Rn+ ) in the half Euclidean space. We then apply it to the initial boundary value problem ofsome nonlinear evolution equations such as the Navier-Stokes equations.

March 18th (Sat)
Conference Room III

Masahito Yamazaki (Univ. of Tokyo)

Integrability and Chern-Simons Theory · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Integrable models, which are ”exactly solvable”, lie at the intersections of many different topics/areas in mathematics and physics. However, many of the existing results are gradually built up throughdecades of research, and often involve trials and errors. This makes it newcomers (including myself) to learn
the subject. One might therefore hope to find a new conceptual framework for understanding integrable
models from scratch. In this lecture, I will discuss recent developments (in collaboration with Kevin Costelloand Edward Witten, among others) in understanding integrable models from the perspective of the ”fourdimensional Chern-Simons theory.” This is a precise analog to Witten’s explanation of knot invariants fromthe three-dimensional Chern-Simons theory, but is based mostly on perturbative methods of quantum field
theory, which can be formulated mathematically. If time allows, I will also discuss more recent developments
concerning affine Yangians (and quantum toroidal algebras) and five-dimensional version of the Chern-Simons
theory. The developments covered in this lecture give rise to many new mathematical structures, many ofwhich are yet to be fully studied in mathematics.
Conference Room VI
Hideto Asashiba(Shizuoka Univ.⋆/Kyoto Univ./Osaka Metro. Univ.)

Applications of quiver representations to persistence modules: approximations and resolutions by interval modules ·(13:00–14:00)

Summary: In topological data analysis, an input datum is given as a point cloud P , which is a set of points in
Rd for some positive integer d. Then for each r with 0 ≤ r ≤ d an r-th persistent homology H r (P ) of P over a
field k is calculated, which is a representation of an equi-oriented type An quiver Q for some positive integer nover the field k. By Gabriel’s theorem, the “interval” representations VI (I := [a, b], 1 ≤ a ≤ b ≤ n) of Q form
a complete list of indecomposable representations of Q. For each representation M of Q, let dM (I) be themultiplicity of VI in the indecomposable decomposition of M . Then dM := (dM (I))I is a complete invariant
up to isomorphisms of M by the Krull–Schmidt Theorem. The family (H r (P ))0≤r≤d contains information on
P valuable in applications, which is analyzed by the the persistence diagrams dH r (P ) of H r (P ) (0 ≤ r ≤ d).
When P varies with another parameter, say, time, it yields a 2D persistence module. In general, persistence
modules M are understood as modules over the path algebra (or category) A of an acyclic quiver Q with fullcommutativity relations. (Thus A is regarded as the incidence algebra of a poset.) We deal only with thecase where Q is a finite quiver. Unlike the 1-parameter case, there are an infinite number of indecomposablesin the general case, which makes it difficult to use dM in real time. The interval representation above isgeneralized as an interval module VI consisting of k and the identity of k as a representation of Q whose
support I forms a connected and convex subquiver of Q. Instead of using dM , we use approximations of Mby (direct sums of) interval modules in two senses.

Final: 2023/2/8
Foundation of Mathematics and History of Mathematics

4

Foundation of Mathematics and History of Mathematics
March 15th (Wed)Conference Room IX

9:30–10:15
1 Kohtaro Tadaki (Chubu Univ.)

An effectivization of the law of large numbers for algorithmically random
sequences and its absolute speed limit of convergence · · · · · · · · · · · · · · · 15

Summary: In this talk, we show that the law of large numbers can be effectivized for an arbitrary Schnorr
random infinite sequence, with respect to an arbitrary computable Bernoulli measure. Actually, we showthat an absolute speed limit of convergence in this effectivization exists and it equals 2 in a certain sense.
2 Yudai Suzuki (Tohoku Univ.)
Keita Yokoyama (Tohoku Univ.)

On the Weihrauch degrees between Cωω and ATR · · · · · · · · · · · · · · · · · · 15

Summary: A binary relation over the Cantor space 2ω is called a Weihrauch problem. In this talk, we
introduce ω-model reflection for Weihrauch problems and show that the ω-model reflection of ATR2 gives
an upper bound for problems provable from ATR0 in the context of reverse mathematics. We also consider
the complexity of the existence of fixed point for monotone operators (FP) and its variations (LFP) fromthe viewpoint of Weihrauch degrees. We will show that LFPs form a linear hierarchy between the ω-model
reflection of ATR2 and Cωω .
10:30–11:30

Talk Invited by Section on Foundation and History of Mathematics

Makoto Fujiwara (Tokyo Univ. of Sci.)

Hierarchy of semi-classical arithmetic and conservative extension theorems

Summary: It is well-known that classical arithmetic PA is Π2 -conservative over intuitionistic arithmetic HA.
Using a generalized negative translation, we relativize this result with respect to theories of semi-classicalarithmetic, which lie in-between PA and HA. In particular, it follows from our main result that PA isΠk+2 -conservative over HA + Σk -LEM where Σk -LEM is the low-of-excluded-middle scheme for formulasof Σk form. In addition, we show that this conservation theorem is optimal in the sense that for any
semi-classical arithmetic T, if PA is Πk+2 -conservative over T, then T proves Σk -LEM. In the same manner,
we also characterize conservation theorems for other well-studied classes of formulas by fragments of classicalaxioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmeticalhierarchy of classical principles. This is a joint work with Taishi Kurahashi.
14:15–14:30

Mathematics History Team Meeting

14:30–16:45
3 Makoto Tamura (Osaka Sangyo Univ.)
Toshio Harikae (Osaka Sangyo Univ.)

On the equations of “Continuation of Ancient Mathematics” · · · · · · · · 15

Summary: “Continuation of Ancient Mathematics” was written by early Tang dynasty calendarist andmathematician Wang Xiaotong some time after the year 626, and is known as the oldest extant book solving
cubic equations. In this talk, we list up its equations and mention the features of them.
4 Toshio Harikae (Osaka Sangyo Univ.)
Makoto Tamura (Osaka Sangyo Univ.)

On restration of lost chinese text in Continuation of Ancient Mathematics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: “Continuation of Ancient Mathematics” was written by early Tang dynasty calendarist andmathematician Wang Xiaotong some time after the year 626, and was listed as one of the Ten Computational
Canons compiled during Tang dynasty. The aim of this talk is to provide a restration of lost chinese text in“Continuation of Ancient Mathematics.”

Final: 2023/2/8
5Foundation of Mathematics and History of Mathematics

5 Katsushi Waki (Yamagata Univ.)

Evaluation of the accuracy of extracting graphic regions in a WASAN
book · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this presentation, we first present a workflow for extracting graphic regions in a WASAN book,which is necessary for creating a WASAN database, using the Hough transform, and evaluate the accuracyof the extraction. In the latter half of the presentation, we will show how the character “now,” which isthe starting point of the graphic problem, is extracted using artificial intelligence and used to determine thegraphic region for the rectangular combined region, which is a candidate for the graphic region.
6 Tsukane Ogawa (Yokkaichi Univ.)

Problems related to the uniqueness of mathematical thought in Oka
Yukitada’s Collection of Exquisite Formulae · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I present some arguments and summarize the current state of affairs regarding the originality ofthe mathematical thought of Oka Tadayuki (1791-?), that is, whether his mathematical methods and ideas
were unique to him or not. In particular, I suggest that his use of the term “pole” is one clue, even though
no new historical documents have been discovered at present.
7 Hideyuki Majima (Ochanomizu Univ.⋆)

Supplement to the paper “Seki Takakazu, his life and bibliography”· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about some episodes concerning to the discovery of Seki Takakazu’s carrer in the
Kofu clan.
8 Hideyuki Majima (Ochanomizu Univ.⋆)

Theoretical meaning of the calculation of Pi by Seki Takakazu andTakebe Katahiro · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will give some theoretical meaning on the calculation of the number Pi by Seki Takakazu andTakebe Katahiro. Seki found the so-called Aitken’s delta-sequenced process in his theory, but there weresome errors in his calculation and he only claimed that his approximate number of Pi was a little bit lessthan 3.14159265359. Takebe Katahiro followed Seki’s method and discovered another method of calculationof Pi.
9 Hideyuki Majima (Ochanomizu Univ.⋆)

The year 2022, the memorial 314th year of Seki Takakazu and the 300th
anniversary of “Takebe Katahiro’s Tetsujjutsu-Sankei” · · · · · · · · · · · · · · 15

Summary: The author talked about the works of SEKI Takakazu (?-1708), and TAKEBE Katahiro (16641739) on Pi. In this time, we propose to build a stone monument near his tomb in Jorinji Temple, becauseof his significant work concerning to Pi.
10 Noriko Tanaka(Aichi Prefectural Asahigaoka High School)
Nozomu Matsubara (Univ. of Tokyo⋆)

A study on stochastic representations for random motion · · · · · · · · · · · 15

Summary: Regarding the random motion, including Brownian motion, Kiyoshi Ito et al. constructed aprobabilistic representation, based on P. Levy’s point of view. D. Mumford wrote “The Dawning of theAge of Stochasticity”, the basic object of study in probability is the random variable and he argues that itshould be treated as a basic construct, like spaces, groups and functions, and it is artificial and unnatural
to define it in terms of measure theory. This time, based on D. Mumford’s article, we discuss stochasticity
based on its historical background.

Final: 2023/2/8
Foundation of Mathematics and History of Mathematics

17:00–18:00

6

Talk Invited by Section on Foundation and History of Mathematics

Tatsuhiko Kobayashi(Maebashi Inst. of Tech.⋆ /Yokkaichi Univ.)

Finishing the editing of the new Seki Takakazu’s Collected Works

Summary: Seki Takakazu’s life and his mathematical achievements were published in the Takakazu Seki’sCollected Works (Osaka Kyouiku Tosho, 1974), edited by Akira Hirayama and others. In the compilationof historical sources, it is natural to check the content of the descriptions in the documents, but issues
relating to their history and the authenticity of the sources must also be carefully considered. The collected
works by Akira Hirayama and others was carefully compiled based on detailed research. However, a detailed
examination of the documents included in this collected works reveals that the compilation was not based on
sufficient historical criticism. In June 2023, a new edition of the Seki Takakazu’s Collected Works, edited by
Kenji Ueno, Tsukane Ogawa, Tatsuhiko Kobayashi and Kenichi Sato will be published by Iwanami Shoten,
publishers. The new collected works consists of three volumes with approximately 4000 pages. Volume
1 introduces Seki’s life and his mathematical achievements based on new historical documents discovered.
Volume 2 is a collection of transliteration from books and manuscripts which written in classical Chinese
relating to Seki’s mathematical achievements. In preparing these, the editors conducted a comprehensive
survey of relevant sources scattered throughout Japan, and then collated the different editions. Volume 3
is a collection of historical documents related to Seki’s research on calendrical calculations and his life. In
addition, the book contains the writings of his disciples, various records and statements by contemporary
mathematicians. Many aspects of Seki Takakazu’s life and his biography remain unclear. For this reason,
genealogical records relating to the Seki family and him have been included. In this lecture we will introduce
the editorial policy of the new Seki Takakazu’s Collected Works, how the authenticity of Seki’s writings was
judged etc.

March 16th (Thu)

Conference Room IX

9:15–12:15
11 Toshimichi Usuba (Waseda Univ.)

Monotinicity of ultrafilter numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider monotonicity of ultrafilter numbers of infinite cardinals. We show that if there are
cardinals λ < κ with u(κ) < u(λ), then there is an inner model of a large cardinal. Hence the failure ofmonotinicity of ultrafilter numbers has large cardinal strength.
12 Kota Takeuchi (Univ. of Tsukuba)

On the indivisibility of metric structures · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An ifinite L-structure M is said to be indivisible if for any patition M = X0 t X1 there is i < 2such that Xi contains an isomorphic copy of M . Many important structures, such as infinite sets, randomgarphs, countable dense linear order, in model theory has this property. Recently, many structures withmetrics are studied by model theorists using continuous model theory. So it seems that investigating theindivisibility of metric structures are interseting from the point of view of continuous logic. In this talk we
discuss about the indivisibility of Urysohn universal spaces, which was proven by Sauer.
13 Hirotaka Kikyo(Kobe Univ.)

On the structure of Hrushovski’s pseudoplanes · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the structure of Hrushovski’s pseudoplanes. In the definition of the Hrushovski’s
pseudoplanes associated to an irrational number α, good approximations kn /dn of α from the above are
introduced. For each n, a tree Bn with kn nodes, dn edges and dn + 1 vertices is introduced. Bn is abiminimal zero extension of the set of its leaves. Let B∞ be the union of all Bn . Let M be the Hrushovski’s
pseudoplane associated to α. Let Dn < M be a copy of Bn in M . Let a be a node of Dn and Fn the set ofleaves of Dn . The closure of the orbit of a over Fn will be whole M . Let D∞ < M be a copy of B∞ and let
be the set of leaves of D∞ . Let a be a node of D∞ . We discuss the non-superstability of M by considering
the type of a over some finite subset F of F∞ and also discuss on the orbit of a over F∞ .

Final: 2023/2/8
7Foundation of Mathematics and History of Mathematics

14 Akito Tsuboi (Univ. of Tsukuba⋆)

Ramsey’s theorem and coheir sequences · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Ramsey’s theorem is very easy to prove. However, its relation to the notion of coheir sequences,which is quite important in model theory, has not been discussed much. Here we present a result that
illustrates the relationship between the two.
15 Leonardo Pacheco (Tohoku Univ.)
Kazuyuki Tanaka (Tohoku Univ.)

Fixed-points in epistemic logic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The µ-calculus is an extension of modal logic by least and greatest fixed-point operators. Its
alternation hierarchy characterizes formulas by the entanglement of their fixed point operators. While thealternation hierarchy is usually strict, in many settings it may collapse. We study the consequences ofthe strictness or the collapse in epistemic logic. We show that different axioms for knowledge imply in
different numbers of possible degrees of ignorance. We also show that if we consider two or more agentssimultaneously, the alternation hierarchy is strict.
16 Taishi Kurahashi (Kobe Univ.)

Extensions of the Friedman–Goldfarb–Harrington theorem · · · · · · · · · · 15

Summary: We investigate the Friedman–Goldfarb–Harrington theorem. In the frameworks of classical andmodal propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH
theorem.
17 Taishi Kurahashi (Kobe Univ.)
Haruka Kogure (Kanazawa Univ.)

Monotonic modal logics of provability predicates · · · · · · · · · · · · · · · · · · · 15

Summary: We investigate modal logical aspects of provability predicates PrT (x) satisfying the following
condition:
M: If T ` φ → ψ, then T ` PrT (⌜φ⌝) → PrT (⌜ψ⌝).
We proved the arithmetical completeness theorems for monotonic modal logics MN, MN4, MNP, MNP4, and
MND with respect to provability predicates satisfying the condition M.
18 Sohei Iwata(Kobe Univ.)

The cut-elimination theorem for Sacchetti’s logics · · · · · · · · · · · · · · · · · · 15

Summary: Sacchetti showed the modal logics wGLn (Here wGLn is obtained from the provability logic GL
by replacing the axiom □(□A → A) → □A by an weaker one □(□n A → A) → □A.) have the fixed-pointproperty. Moreover, these logics also have desirable properties (for instance, the Lyndon interpolation
property, arithmetical completeness, effective constructibility of fixed-points, etc.). We investigate them inthe point of view of proof theory. We introduce sequent calculi for wGLn and give a purely syntactical
proof of the cut-elimination property for these calculi.
(Chiba Univ.)
19 Yuya Okawa(Kobe Univ.)
Sohei Iwata
Taishi Kurahashi (Kobe Univ.)

The logic IL− (P) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The logic IL− (P) is obtained by adding the persistence principle P : A ▷ B → □(A ▷ B) to
the sublogic IL− of the basic interpretability logic IL. We investigate IL− (P) from several perspectives.
Firstly, we show that IL− (P) has a weak version of fixed-point property. Secondly, we show that IL− (P)is a natural basis for some relational semantics. Thirdly, we introduce a system of sequent calculus forIL− (P), and prove the cut-elimination theorem for it. Finally, we show that IL− (P) is sound and completewith respect to a suitable arithmetical semantics.
12:15–12:30

Research Section AssemblyFinal: 2023/2/8
Algebra8

AlgebraMarch 15th (Wed)Conference Room I

9:00–12:00
1 Daisuke Tambara♭ A linear figure in the Cartesian plane satisfying a condition of rectangle· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We say a subset X of the Cartesian plane R2 satisfies the rectangle condition if for any points(x1 , y1 ), (x1 , y2 ), (x2 , y1 ) of X the point (x2 , y2 ) also belongs to X. We are interested in what restrictions
on the shape of X the condition imposes. We consider the case where X is a linear figure in the sense that
X is a finite union of segments and points. Our result is about the shape of a connected component of X
satisfying the rectangle condition.
2 Toshiyuki Abe (Ehime Univ.)

Harada’s conjecture II and Gramian determinants · · · · · · · · · · · · · · · · · · 10

Summary: We consider Harada’s conjeture II for finite groups G. The conjecture states that the numberh(G) defined as a ratio of the product of all sizes of conjugacy classes and thay of all irreducible degrees of
G is an ineteger. We see that the square h(G)2 is given as a quotient of Gramian determinat for suitablebasis of the center of the group algebra CG by a product of all sizes of centeralizers of representatives ofconjugacy classes. We generalize h(G)2 to numbers µϕ (G) associated to a pair of (Z, ϕ) of central subgroup
Z and its irreducible character ϕ, and give a factrozation theorem of h(G)2 to of these numbers µϕ (G) for
fixed Z. We will show some examples.
3 Kenichiro Tanabe (Tokyo City Univ.)

Fusion rules for the fixed point subalgebra of the vertex algebra associated with a non-degenerate and non-positive definite even lattice by anautomorphism of order 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let VL be the vertex algebra associated with a non-degenerate and non-positive definite evenlattice L and VL+ the fixed point subalgebra of VL under the action of the automorphism induced from the−1-isometry of L. We determine the fusion rules for weak VL+ -modules.
4 Takeshi Suzuki (Okayama Univ.)
Yoshitaka Toyosawa

On hook formulas for cylindric skew diagrams · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present a conjectual hook formula concerning the number of the standard tableaux on“cylindric” skew diagrams. Our formula can be seen as an extension of Naruse’s hook formula for skew
diagrams. Moreover, we prove our conjecture in several cases.
5 Yutaka Yoshii (Ibaraki Univ.)

Some results on certain subalgebras of the hyperalgebra of a simple
algebraic group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let G be a simply connected simple algebraic group defined over a field Fp of p elements, where
p is a prime number. Then G is associated an Fp -algebra U which is called a hyperalgebra. We give someresults on certain Fp -subalgebras of U .
6 Yuichiro Goto

(Osaka Univ.)

A remark on the number of quasi-hereditary structures · · · · · · · · · · · · · 15

Summary: Dlab and Ringel showed that algebras being quasi-hereditary in all total orders for indices ofprimitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary
algebra is again quasi-hereditary. We say that two total orders are equivalent if they induce the same set ofstandard modules. As a matter of fact, if an equivalence class of orders make an algebra be quasi-hereditary,then we call this class a quasi-hereditary structure. Flores, Kimura and Rognerud gave the counting methodof the number of quasi-hereditary structures on path algebras of Dynkin quivers. In this talk, I give a similar
result for path algebras of the quivers Q. Here Q is a quiver whose underlying graph is gotten by adding asingle vertex to type An and a single edge between the new vertex and a vertex originally in An .

Final: 2023/2/8
9Algebra7 Kengo Miyamoto (Ibaraki Univ.)(Tsinghua Univ.)
Qi WangOn τ -tilting finiteness of symmetric algebras of polynomial growth · · · 15

Summary: In this talk, we report on the τ -tilting finiteness of finite dimensional symmetric algebras ofpolynomial growth over an algebraically closed field. It is known that τ -tilting finiteness is preserved underMorita equivalence, but usually not preserved under derived equivalence. However, we have not found any
examples of symmetric algebras which do not preserve τ -tilting finiteness under derived equivalence. In thistalk, any symmetric algebras of polynomial growth preserve τ -tilting finiteness under derived equivalence.
(Osaka Univ.)
8 Sota Asai(
Univ.
of Tokyo)
Osamu Iyama

The rigid parts of the elements of the real Grothendieck groups · · · · · · 15

Summary: Let A be a finite-dimensional algebra over a field K. For any complex X in the homotopy category
Kb (projA) of the complexes over the category of finitely generated projective modules, we can naturally
define the rigid part of X as the maximum presilting direct summand of X. In our study, we found thatthe rigid part of each element θ in the real Grothendieck group K0 (projA)R , which can be identified with an
Euclidean space, is also well-defined. In this talk, I will talk about some key properties to prove our result.
9 Masahisa Sato
(Aichi Univ./Univ. of Yamanashi⋆)On generalized Nakayama–Azumaya’s Lemma · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let R be a ring and J(R) its Jacobson radical. We prove the following lemma. Generalized
Nakayama–Azumaya’s Lemma “Let M be a direct summand of a direct sum of finitely generated right
R-modules. If M satisfies MJ(R) = M, then M = 0.”This unifies the following known results; “Let M be a finitely generated module or a projective module. If
MJ(R)=M, then M=0.”
As an aplication of this lemma, we show existence of a maximal submodule for some kind of modules.
10 Tsutomu Nakamura (Mie Univ.)
Michal Hrbek (Czech Acad. of Sci.)
Jan Šťovı́ček (Charles Univ. in Prague)

Large tilting complexes and homomorphic images of Cohen–Macaulayrings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Tilting theory plays a central role in representation theory of algebras.

Making mutation

operations possible, the notion of tilting objects was extended to silting objects. While they are usuallyassumed to be compact objects in triangulated categories, the definitions have been naturally extended topossibly non-compact objects. In this talk, we give a concrete way to construct (possibly non-compact)silting objects and cosilting objects in the unbounded derived category of a commutative noetherian ring R
by using strictly increasing functions from Spec R to the integers. Then we discuss when they are tilting
objects and cotilting objects. Finally, we relate our construction of (co)tilting objects with a question when
R is a homomorphic image of a Cohen–Macaulay ring.
11 Akihiro Higashitani (Osaka Univ.)

Effectiveness conjecture on equivariant Ehrhart theory and a kind of its
counterexample · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Equivariant Ehrhart theory discusses lattice polytopes admitting a finite group action ρ. Notethat the case where ρ is trivial corresponds to the usual Ehrhart theory. Since every lattice polytope
admits a trivial group action, we can recover the usual Ehrhart theory. In the equivariant Ehrhart theory,
the effectiveness conjecture is one of the central problems. This predicts the following: for any lattice
polytope P , if the H ∗ -series of P , which is a formal power series appearing in the equivariant Ehrhart series,
becomes just a polynomial, then the H ∗ -series becomes effective, i.e., the coefficients really become some
representations. In this talk, we give a kind of a counterexample of this conjecture.

Final: 2023/2/8
Algebra10

14:15–14:50
12 Masamichi Kuroda(Nippon Bunri Univ.)
Kentaro Mitsui (Kobe Univ.)

On the classification of monomial GAPN functions · · · · · · · · · · · · · · · · · 15

Summary: Perfect nonlinear (PN) functions and almost PN (APN) functions over finite fields of characteristic
p have high nonlinearity.

When p = 2, they have been widely studied due to their applications tocryptography and coding theory. Recently, generalized APN (GAPN) functions were defined as an algebraic
generalization of APN functions in characteristic 2 to odd characteristic p > 2 and they have been studied.
In this talk, we introduce some results of the study for the classification of monomial GAPN functions.
13 So Yamagata (Fukuoka Univ.)

On classification of r-sets and a sufficient condition for non-very genericity of arrangements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Manin and Schechtman introduced a family of arrangements of hyperplanes generalizing classicalbraid arrangements, which they called the discriminantal arrangements. Athanasiadis proved a conjecture
by Bayer and Brandt providing a full description of the combinatorics of discriminantal arrangements in thecase of very generic arrangements. Libgober and Settepanella described a sufficient geometric condition forgiven arrangements to be non very generic in terms of the notion of dependency for a certain arrangement.
Settepanella and the author generalized the notion of dependency introducing r-sets and KT -vector sets,
and provided a sufficient condition for non very genericity but still not convenient to verify by hand. In thistalk we give a classification of the r-sets, and a more explicit and tractable condition for non very genericity.
15:00–16:00

Talk Invited by Algebra Section

Naoki Fujita (Kumamoto Univ.)

Schubert calculus and convex polytopes

Summary: A goal of Schubert calculus is to compute the structure constants of the cohomology ring of aflag variety with respect to the basis consisting of Schubert classes. One approach to such computation
is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. In type Acase, monomials in a Schubert polynomial are naturally parametrized by specific faces of a Gelfand–Tsetlin
polytope. These faces are called reduced Kogan faces and appear as the limit of a semi-toric degenerationof a Schubert variety. Since the Gelfand–Tsetlin polytope is a Newton–Okounkov body of the flag variety,
Newton–Okounkov bodies and induced toric degenerations are expected to give a generalization of theories
in Schubert calculus to more general projective varieties. Such generalization has partially developed in thecase of flag varieties in different Lie types. In this talk, some fundamental objects in Schubert calculus will
be explained from the viewpoints of convex polytopes and of Kashiwara crystal bases. We also discuss theirgeneralization to more general projective varieties.

Final: 2023/2/8
11

Algebra16:15–17:15

Talk Invited by Algebra Section

Hiroki Matsui (Tokushima Univ.) ♭ Spectra of triangulated categories and reconstruction of schemes fromtheir derived categories
Summary: For a given noetherian scheme X, it is natural to ask whether we can reconstruct X from its
perfect derived category Dpf (X) or not. This reconstruction problem has been well studied so far in algebraic
geometry. It is known that we cannot reconstruct X from the triangulated category structure of Dpf (X).
For example, Mukai proved that for an abelian variety A, the perfect derived categories of A and A∨ areequivalent as triangulated categories. On the other hand, Balmer proved that we can reconstruct X fromits perfect derived category using its tensor triangulated category structure. For this, Balmer defined theringed space Spec⊗ (T ) for a given tensor triangulated category T , which is called the Balmer spectrum of T .
Using Balmer spectra, Balmer developed tensor triangular geometry and as an application, he proved thatthe Balmer spectrum of Dpf (X) is isomorphic to X as ringed spaces. In this sense, X can be reconstructedfrom the tensor triangulated category structure of Dpf (X).
In this talk, I will introduce another ringed space Spec△ (T ) for a given triangulated category T without
using tensor structure to develop a “tensor-free” analog of tensor triangular geometry. We call Spec △ (T ) the
spectrum of T . Using the spectra of derived categories, we will prove several reconstruction results. Amongthem, we will give an alternative and algebraic proof of Bondal-Orlov-Ballard reconstruction theorem.

March 16th (Thu)

Conference Room I

9:10–12:00
14 Yuya Otake(Nagoya Univ.)

Stable categories of n-spherical modules and n-torisonfree modules · · · 10

Summary: Auslander and Bridger introduced the notions of n-spherical modules and n-torsionfree modules.
In this talk, we study the stable category of n-spherical modules. Moreover, we introduce the notion ofn-G-spherical modules as a G-analogue and give similar results for the stable category of n-G-sphericalmodules. As an application, we prove that if R is a Gorenstein local ring of Krull dimension d > 0, thenthere exists a stable equivalence between the category of (d − 1)-torsionfree R-modules and the category ofd-spherical modules relative to the local cohomology functor.
(Tokyo Tech)
15 Ryo Ishizuka
Kazuma Shimomoto (Nihon Univ.)

An explicit construction of perfectoid almost Cohen–Macaulay algebrain mixed characteristic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The existence and properties of non-Noetherian algebras over a given Noetherian ring play
important roles in commutative algebra. Properties of such algebras are, for example, perfectoid and almost
Cohen–Macaulay. In positive characteristic, the perfect closure has these properties. In this talk, weconstruct an analog of the perfect closure in mixed characteristic and show that it has the same properties.
16 Shinnosuke Ishiro (Nihon Univ.)

The canonical module of a local log-regular ring · · · · · · · · · · · · · · · · · · · 15

Summary: Local log-regular rings are a certain class of Cohen–Macaulay rings that are treated in logarithmic
geometry. This class has similar properties to those toric rings. From this perspective, I determined theform of the canonical module of a local-log regular ring. As an application, we gave the Gorenstein criterionof this class of rings. In this talk, we introduce these results.
17 Koji Matsushita (Osaka Univ.)

Conic divisorial ideals of toric rings and applications to stable set rings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Conic divisorial ideals of toric rings play important roles in the theory of non-commutative
algebraic geometry as well as commutative algebra. In this talk, we introduce an idea to determine a region
representing conic classes in the divisor class group of a toric ring and a description of the conic divisorial
ideals of stable set rings of perfect graphs.

Final: 2023/2/8
Algebra18 Yuki Ishihara (Tokyo Univ. of Sci.)

12

Computation of ideal operations with parameters · · · · · · · · · · · · · · · · · · 15

Summary: Ideal is one of the fundamental concepts in Commutative Algebra and Algebraic Geometry.
For one or more ideals, we consider ideal operations that generate new ideals from them, e.g., the ideal√intersection I ∩ J, the ideal quotient I : J, the saturation I : J ∞ , the radical I, etc., where I and J are
ideals in the polynomial ring C[x1 , . . . , xn ]. In this talk, we consider several algorithms to compute ideal
operations with parameters by using Comprehensive Gröbner Systems. In addition, we present an algorithm
for “feasible” parameterized primary decomposition by utilizing those operations.
19 Kyohei Hattori (Niigata Univ.)
Hideo Kojima (Niigata Univ.)

Rings of nilpotent elements of monomial derivations on polynomial rings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give a classification of Nil D of monomial derivations D on the polynomial ringR[x, y] over a UFD R containing Q. Furthermore, as its application, we show that the minimal number ofgenerators of kernels of derivations on the polynomial ring R[x, y, z] as a R-algebra is unbound.
20 Kaito Kimura (Nagoya Univ.)

Asymptotic depths of localizations of modules · · · · · · · · · · · · · · · · · · · · · 10

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 is an actively studied subject in commutative
algebra. In this talk, we consider the existence of an integer k such that for all integers n ≥ k and all prime
ideals p of R, the depth of (M/I n M )p is equal to the depth of (M/I k M )p .
21 Naoki Endo

(Meiji Univ.)

On the stratification of one-dimensional Cohen–Macaulay rings · · · · · · 15

Summary: The aim of this talk is to discover a good candidate for natural generalizations both of almost
Gorenstein and 2-almost Gorenstein rings from the point of view of Sally modules of canonical ideals. Even
though our results are at this moment restricted within the case of dimension one, we expect that a higher
dimensional notion might be possible after suitable modifications.
22 Tomohiro Okuma (Yamagata Univ.)
Ken-ichi Yoshida (Nihon Univ.)
Kei-ichi Watanabe(Nihon Univ. / Meiji Univ.)

The core of ideals in minimally elliptic singularities · · · · · · · · · · · · · · · · · 15

Summary: A two-dimensional normal local domain is called a minimally elliptic singularity if it is Gorenstein
and its geometric genus is one. For an m-primary integrally closed ideal I in a minimally elliptic singularity(A, m), we represent its core using a cycle on a resolution of the singularity.
23 Ken-ichi Yoshida (Nihon Univ.)
Tomohiro Okuma (Yamagata Univ.)
Kei-ichi Watanabe(Nihon Univ. / Meiji Univ.)

Gorensteinness for normal tangent cones of the maximal ideals inBrieskorn hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let (A, m) be a two-dimensional excellent normal local domain containing an algebraically closed
field. The graded ring defined by all integal closures of powers of an ideal I of A is called the normal tangent
cone of I. We classify all Brieskorn hypersurfaces for which the normal tangent cone of the maximal ideal
m is to be Gorenstein.
13:00–14:10
24 Yoshimune Koreeda (Hiroshima Univ.)

Jet scheme of a singular surface of type D41 in characteristic 2 · · · · · · · 13

Summary: Let k be an algebraically closed field, X a variety over k and m a nonnegative integer. There isa space Xm over X, called the jet scheme of X of order m, parameterizing m-th jets on X. The fiber overthe singular locus of X is called the singular fiber. In this talk, we assume k is of characteristic 2 and X isa singular surface of type D41 . For m  0, we give the irreducible decomposition of the singular fiber of X
and determine the maximal elements among the intersections of two different irreducible components.

Final: 2023/2/8
13

Algebra25 Hiroto Akaike(Osaka Univ.) ♭ Bounds for the order of automorphism groups of cyclic covering fibrations of an elliptic surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: In this talk, we show upper bounds for the order of automorphism groups of primitive cyclic
covering fibrations of an elliptic surface. The upper bound is an explicit function in the genus of the base
curve, the covering degree and the square of relative canonical divisor.
26 Ryosuke Masuya (Tokyo Metro. Univ.)

On weak-bitangents for plane quartics and rational elliptic surfaces · · · 13

Summary: It is well-known that a smooth plane quartic has twenty-eight bitangents. We consider weakbitangents which are generalizations on bitangents for a reduced quartic. We study weak-bitangents fromthe viewpoint of rational elliptic surfaces attached to reduced quartics. In particular, we consider an analogy
of syzygetic triads. As a result, we can give new proofs for some classical results on certain singular plane
quartics and their bitangents.
27 Tatsuki Yamaguchi (Univ. of Tokyo) ♭ Big Cohen–Macaulay test ideals in equal characteristic zero via ultraproducts · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Summary: Schoutens constructed big Cohen–Macaulay (BCM) algebras in equal characteristic zero using
ultraproducts. In this talk, we show that BCM test ideals with respect to Schoutens’ BCM algebras
coincide with multiplier ideals, which define the non-klt loci of normal varieties. As an application, we study
singularities of pure subrings.

March 17th (Fri)

Conference Room I

9:00–12:00
28 Makoto Sakurai (Kaichi Gakuen)

Dimensions of chiral conformal fields and quasi-coherent sheaves · · · · · 13

Summary: The so-called AGT correspondence between 4d gauge theories and 2d conformal field theories
was under discussion. However, despite much effort by mathematicians (and some physicists), the scopeof results is limited, although it is sophisticated. In this report, I will deliver a trial to synthesize themathematical literature of Beilinson and Drinfeld and some of the more “natural” physics for formulae of“anomalies.” Several conventional definitions of “dimensions” will be briefly reviewed. Then I will seek acorrect notion of dimensions for chiral fields in the context of S-duality and the geometrical dimension.
Some more efforts will be on the (non-)quasi-coherent sheaves for chiral algebra theories and D-modules.
29 Tomohiro Iwami (Kyushu Inst. of Tech.)

Majorana double solids for three-dimensional Miyaoka–Yau type inequality with the associated third Chern classes · · · · · · · · · · · · · · · · · · · · 13

Summary: Based on S. Mori’s proof for an three-dimesnional extremal neighborhood (X, C) ⊂ C4 of type
A in the existence of three-dimensional flips, for an extended extremal nbd (X, Cs ) with Cs not necessary
irreducible nor reduced ([I2019Mar]), the author found three-dimesional Miyaoka–Yau type inequality(M Y )3,c3 with the associated c3 ([I2018Mar, I2019Sep]), (M Y )3,c3 with the differential operators ([I2020Sep])fand related ones, moreover introduced an interemdiate Jacobians IJ(X,Cs ) ([I2022Mar]) and found its strong
approximation for its Z-structure ([I2022Sep]). In this talk, as sequel to [I2022Sep], the author will report:fa) to show precise form of strong approximation for IJ(X,Cs ) via the differential operators, b) to giveslightly extended diagonal decomposition ([Bloch–Srinivas 1983]) to introduce real/Majorana spinor by a),and c) to construct Z-structure by gluing this underlying real structure via b) regarding to integral Hodge
conjeture, in order to discuss alternative to [Artin–Mumford 1972].

Final: 2023/2/8
Algebra30 Yuta Takahashi (Chuo Univ.)
Kiwamu Watanabe (Chuo Univ.)

14

Fano 4-folds with nef tangent bundle in positive characteristic · · · · · · · 13

Summary: In characteristic 0, the Campana–Peternell conjecture claims that the only smooth Fano variety
with nef tangent bundle should be homogeneous. In this talk, we present the positive characteristic versionof the Campana–Peternell conjecture. In particular, we give a result for Fano 4-folds with nef tangent
bundle and Picard number greater than one.
31 Taro Yoshino (Univ. of Tokyo)

On the degree of irrationality of complete intersections · · · · · · · · · · · · · · 13

Summary: This is joint work with Lucas Braune. We obtain a lower bound of the degree of irrationalityof very general complete intersections over the complex field from the recent results of Braune and Chen–
Stapleton. For combining these results, we make a minor adjustment of Chen–Stapleton’s method using thetrace map of differential modules.
32 Yuki Mizuno(Waseda Univ.)

Some examples of noncommutative projective Calabi–Yau schemes · · · 13

Summary: We construct some examples of noncommutative projective Calabi–Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare them with commutative
Calabi–Yau varieties and examples by Kanazawa.
33 Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classification for algebraic tori (I) · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: We give a stably birational classification for algebraic k-tori of dimensions 3 and 4 over a field k.
34 Akinari Hoshi (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Birational classification for algebraic tori (II) · · · · · · · · · · · · · · · · · · · · · · 13

Summary: We give a stably birational classification for algebraic k-tori of dimensions 3 and 4 over a field k.
35 Masayuki Sukenaga (Hiroshima Univ.)

Tropical lifting problem for the intersection of plane curves · · · · · · · · · · 13

Summary: Let D be a tropical divisor in the intersection of two tropical plane curves. We study when it
can be realized as the tropicalization of the intersection of two algebraic curves. When a graph theoretic
condition determined by these tropical curves is satisfied, we can algorithmically find algebraic curves suchthat the tropicalization of their intersection is D.
36 Michio Amano (Meisei Univ.)

On kernels of certain homomorphisms of Witt vectors, II · · · · · · · · · · · · 10

Summary: Let W (A) be a Witt group over A and let W n (A) be the product of n of W (A). T. Sekiguchi and
N. Suwa have constructed a certain endomorphism Un of W n (A) related to the deformation group schemefrom the additive group scheme to the multiplicative group scheme. We study the equality of kernels ofcertain homomorphisms related to Un .
37 Daiki Kawabe (Tohoku Univ.)

Chow motives of genus one fibrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Genus 1 fibrations play a central role in the classification of surfaces. Let f : X → C be a genus
1 fibration from a surface to a curve. Then there is a Jacobian genus 1 fibration j : J → C that satisfies
some good properties. In this talk, we prove that the motive of X is isomorphic to the motive of J. As anapplication, we prove motivic finite-dimensionality for surfaces not of general type with geometric genus 0.
This can be regarded as a generalization of Bloch–Kas–Lieberman’s result to arbitrary characteristic.
38 Tetsuya Ando

(Chiba Univ.)

Symmetric quartic extremal inequalities of four variables and K3 surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Let P4,4 be the convex cone of quartic homogeneous polynomials of four variables which is positive
semidefinite. We present a family of symmetric elements of P4,4 . Let f be a such polynomial. Then zero
locus of f in the complex 3-dimensional projective space is a K3 surface which has 10 real A1 type rational
double points.

Final: 2023/2/8
15

Algebra39 Emiko Yorisaki (Tokyo Metro. Univ.)
Shinzo Bannai (Okayama Univ. of Sci.)
Hiro-o Tokunaga (Tokyo Metro. Univ.)

Ramified and Split models of rational elliptic surfaces and bitangent
lines for a quartic curve · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We introduce the notion of ramified and split models of elliptic surfaces. We consider how these
two models are related. In particular, we apply our consideration to rational elliptic surfaces which arise assmooth models of double covers of the projective plane branched along quartics. As a result, we determine
the number of concurrent bitangent lines for irreducible quartics with at most nodes.
14:15–14:30

Presentation Ceremony for the 2023 MSJ Algebra Prize

14:40–15:40

Award Lecture for the 2023 MSJ Algebra Prize

Yoshinori Gongyo (Univ. of Tokyo)

On higher dimensional minimal model theory and its applications

Summary: I will report what I am going on projects related to the minimal model program. First, I will
discuss some new invariants for studies of Fano varieties. We call it the “total index”, which is naturalinvariant mixing Shokurov’s complexities and the usual Fano index. In this study, the Birkar generalizedpair naturally appears. Using this invariant, I propose some conjecture for the characterization of the
product of projective spaces, which is some variant of Mukai’s type conjecture. The methods are to use thelocal–global method from singularities rather than studies of rational curves. To study this conjecture, thenon-vanishing conjecture and characterization of toric varieties are involved. Second, I will explain what I
consider recently on the mainstream of the minimal model theory.
16:00–17:00

Award Lecture for the 2023 MSJ Algebra Prize

Satoshi Wakatsuki (Kanazawa Univ.)

Trace formulas and their applications

Summary: The trace formula is one of the main tools in the study of automorphic forms, and its theory has
been greatly developed by many researchers (Selberg, Arthur, etc.). The trace formula plays an importantrole even today, such as the classification of automorphic representations by stable trace formulas and thestudy of automorphic periods by relative trace formulas. In this talk, I will give an overview of trace
formulas and their applications. After that, I will introduce my recent research on asymptotic behaviors for
dimensions of spaces of automorphic forms.

March 18th (Sat)

Conference Room I

9:15–12:00
40 Shigeru Iitaka (Gakushuin Univ.⋆)

Super perfect numbers of the second kind · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Let m denote translation parameter, and let h denote an odd prime.
Defining A to be σ(a) + m if hσ(A) = 2a(h + 1) − h2 + mh then a is said to be super perfect numbers of thesecond kind. A is called a partner of a.
41 Masato Kobayashi (Kanagawa Univ.)

Balance for the divisor sum function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Let us say finite A ⊆ N is balanced if
XXn∈A d|n,d odd

d=

X

X

d.

n∈A d|n,d, even

For example, {1, 2}, {1, 3, 4}, {3, 6, 8, 9} are balanced.

For each natural number N , does there exist abalanced set A of the cardinality N ? I solved this problem affirmatively in June 2022 with Ramanujan’s
theta function and Jacobi’s triple product idenitity. In this talk, I wish to show details of this.

Final: 2023/2/8
Algebra42 Yuya Kanado(Nagoya Univ.)

16

The relation between a generalized Fibonacci sequence and the lengthof Cunningham chains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Let p be a prime number and α ≥ 3 be an integer. In this talk, a generalized Fibonacci sequencePFα = (Fn )n∈Z is defined as F0 = 0, F1 = 1, Fn+2 = αFn+1 + Fn (n ∈ Z), and Fα σ(n) = d|n,0<d∈Fα d iscalled the divisor function on Fα . Then we obtain that for two prime numbers p and q the fact p = 2q + 1
or 2q − 1 is equivalent to Fα σ(Fα σ(Fp )) = Fα σ(Fq ) for some α.
43 Shun-ichi Kurino (Nihon Univ.)
Masatoshi Nakano(Kesennuma Coll. of Tech.)

The error term in the prime number theorem under the RH · · · · · · · · · 10

Summary: We propose the conjecture that the error term in the prime number theorem under the RH is√o( x).
44 Shingo Sugiyama (Nihon Univ.)
Ade Irma Suriajaya (Kyushu Univ.)

On a weighted density of zeros of Dirichlet L-functions in a family· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Katz and Sarnak suggested a relation between zeros of L-functions in a family and eigenvalues ofrandom matrices in a compact matrix group. In this talk, we consider the analogous conjecture weighted by
L-values and verify this conjecture in the case of the family of Dirichlet L-functions attached to nontrivial
Dirichlet characters of a prime modulus. This is a joint work with Ade Irma Suriajaya (Kyushu University).
45 Yasufumi Hashimoto(Univ. of Ryukyus)

Universality theorem for the Selberg zeta function · · · · · · · · · · · · · · · · · · 13

Summary: In 2013, Drungilas et al. proposed the universality theorem for the Selberg zeta function associatedwith the modular group, which is (probably) the first universality theorem for the zeta function of the orderof more than one. Recently in 2021, Mishou extended it by proving the joint universality theorem for thetuple of Selberg zeta functions associated with principal congruence subgroups. In this talk, we present
the universality theorem (and joint universality theorem) for the Selberg zeta function associated with (notnecessarily congruence) subgroup of the modular group. We also note that our universality theorems areavailable in wider regions than the regions given in the previous works.
46 Takeshi Shinohara (Nagoya Univ.)

On shuffle product of desingularized multiple zeta functions · · · · · · · · · 13

Summary: Furusho, Komori, Matsumoto, and Tsumura introduced the desingularized multiple zeta functions
to resolve all singularities of multiple zeta functions (MZF for short). It is a natural question to ask how
much desingularized MZFs retain the properties of MZFs. As one of the answers, we show that special
values of desingularized MZFs at positive integer points satisfy the shuffle product that holds among special
values of MZFs at positive integer points.
47 Masaki Kato(Toyama Nat. Coll. of Tech.)On q-analogues of zeta functions of root systems · · · · · · · · · · · · · · · · · · · 13

Summary: Komori, Matsumoto and Tsumura introduced zeta functions ζr (s, ∆) associated with root systems∆. In this talk, we introduce q-analogues of functions ζr (s, ∆), denoted by ζr (s, a, ∆; q). We establish
q-extensions of the following properties satisfied by ζr (s, ∆): (a) Integral representations of sums of zetafunctions which have Weyl group symmetries. (b) Explicit expressions of Witten volume formulas. (c)Functional relations including Witten volume formulas. We also introduce elliptic analogues of ζr (s, a, ∆; q),denoted by ζr (s, a, β, ∆; p, q), and investigate their basis properties. To extend the properties (a) and (b)to ζr (s, a, β, ∆; p, q), the factorization formulas of Poincaré polynomials, established by Macdonald, plays
important roles.

Final: 2023/2/8
17

Algebra48 Masahiro Mine (Sophia Univ.)

Weak denseness theorem for the Hurwitz zeta-function with quadratic
irrational parameter · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: In this talk, we consider the value-distribution of the Hurwitz zeta-function with algebraic
irrational parameter. The main result is that any complex number can be approximated by values of the
Hurwitz zeta-function for arbitrary quadratic irrational parameters but with finite exceptions.
49 Keita Nakai(Nagoya Univ.)

Universality for the iterated integrals for the logarithm of L-functionsin the Selberg class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 1975, Voronin proved the Universality theorem for the Riemann zeta-function and in 2022,
Endo generalized this theorem for the iterated integrals for the logarithm of the Riemann zeta-function.
In this talk, we give a more generalization of this theorem for the iterated integrals for the logarithm ofL-functions in the Selberg class.
50 Kazunari Sugiyama(Chiba Inst. of Tech.)

The modularity of Siegel’s zeta functions · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic
properties such as analytic continuations and functional equations. We discuss the modularity of Siegel’s
zeta functions on the basis of converse theorems.
14:15–16:45
51 Wataru Takeda (Tokyo Univ. of Sci.)
Maki Nakasuji(Sophia Univ. / Tohoku Univ.)
Yoshinori Yamasaki (Ehime Univ.)

Quadratic relations for 9th variation Schur functions involving Plücker
relations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: The 9th variation of Schur polynomial is known to satisfy determinant formulas such as Jacobi–
Trudi, Gambelli, and Hamel–Goulden identities. In this talk, we apply the Plücker relations to theseidentities. These relations are known to give algebraic dependencies among the determinants of the various
minors of an arbitrary matrix. Applying them to the n × n minors of an n × 2n matrix, we give somequadratic relations between the 9th variation of Schur polynomials.
52 Genki Shibukawa (Kobe Univ.)
Yoshiaki Goto
(Otaru Univ. of Commerce)

Some monotonic properties of special values of the bivariate complete
homogeneous symmetric polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove some monotonic properties of special values of the bivariate complete homogeneous
symmetric polynomials.
53 Akinari Hoshi (Niigata Univ.)
Kazuki Kanai (Niigata Univ.)
Aiichi Yamasaki (Kyoto Univ.)

Hasse norm principle for M11 extensions · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Let k be a field and T be an algebraic k-torus. In 1969, over a global field k, Voskresenskii provedthat there exists an exact sequence 0 → A(T ) → H 1 (k, Pic X)∨ → Sha(T ) → 0 where A(T ) is the kernel of
the weak approximation of T , Sha(T ) is the Shafarevich–Tate group of T , X is a smooth k-compactificationof T , Pic X is the Picard group of X = X ×k k. On the other hand, in 1963, Ono proved that for the norm
(1)

one torus T = RK/k (Gm ) of K/k, Sha(T ) = 0 if and only if the Hasse norm principle holds for K/k. We(1)determine H 1 (k, Pic X) for norm one tori T = RK/k (Gm ) when the Galois group Gal(L/k) of the Galois
closure L/k of K/k is isomorphic to the Mathieu group M11 of degree 11. We also give a necessary andsufficient condition for the Hasse norm principle for such extensions K/k with Gal(L/k) ' M11 .

Final: 2023/2/8
Algebra54 Tomoyoshi Ibukiyama (Osaka Univ.⋆)

18

Dimensions of paramodular forms with involutions · · · · · · · · · · · · · · · · · 10

Summary: Paramodular forms are a part of Siegel modular forms. For degree two case, they are importantfor Shimura–Taniyama conjecture for abelian surfaces and the new form theory of Roberts and Schmidt.
Here we give explicit dimension formulas for paramodular forms of any vector valued weight det3 Sym(j)with k ≥ 3 of prime level p with fixed sign of the Atkin–Lehner involution. It is known that such forms
have a good correspondence with certain algebraic modular forms up to endoscopic part and old forms. We
calculate dimensions of the corresponding algebraic modular forms and apply it to paramodular case.
55 Tomoyoshi Ibukiyama (Osaka Univ.⋆)

Differential operators on Siegel modular forms and Laplace transforms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: The talk has two aims. One is to give a new special basis of the polynomial ring C[T ] incomponents of n × n symmetric matrix T . The basis P (T ) is characterized by the action of P (∂Z ) ondet(CZ + D)s , where ∂Z is the matrix of partial derivatives of the variable of the Siegel upper half spaceand det(CZ + D) is the automorphy factor. Everything is described explicitly. For example, the basis isobtained as coefficients of certain explicitly described generating series. The second aim is to apply thisto the so-called pullback formula of the Siegel Eisenstein series of degree 2n and determine all appearing
constants.
56 Yuichi Sakai (Kurume Inst. of Tech.)

On modular-form solutions of a certain modular linear differential equations for cocompact groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: In this talk, we give a modular linear differential equation of second order for a cocompact groupof discriminant 6, and we also give its solutions. Furthermore we prove a relation between supersingularpolynomials and certain polynomials derived from solutions of the modular linear differential equation.
57 Shingo Sugiyama (Nihon Univ.)
Kenji Sakugawa (Shinshu Univ.)

Integrality of Hecke eigenvalues of Hilbert and Siegel modular forms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we prove the integrality of Hecke eigenvalues of Hilbert modular forms and Siegel
modular forms in a general setting. As applications, we estimate the degrees of Hecke fields of cuspidal
automorphic representations of GL(2d) with a prime number d and Sp(2n).
58 Yuki Kato (Ube Nat. Coll. of Tech.)Almost mathematics and its algebraic K-theory from non-unital algebras viewpoint · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: While almost mathematics has various applications to arithmetic geometry, Quillen mentioned
linear algebra over non-unital rings which is the same as almost mathematics introduced by Faltings; andGabber and Ramero. Quillen’s work is more conceptional in the sense of using categorical language: in his
work, almost mathematics is characterized as bilocalization of an abelian category of modules. By using thetheory of bilocalization, we define the derived category (or stable ∞-category) of almost perfect complexes,
enabling us to obtain the K-theory of almost modules. Furthermore, by modifying K-theory of almost
algebra, we prove that the modified K-groups decompose into the almost algebraic K-theory and the almost
acyclic part of them. The main result of almost K-theory is that the almost K-theory of A is represented
by the modified K-theory of the corresponding the idempotent non-unital algebra.
59 Norihiko Minami(Nagoya Inst. of Tech.)

SBNR (stably birationalized unramified sheaf) and Gersten type resolution for any motivic generalized cohomology theory · · · · · · · · · · · · · · · 13

Summary: Suppose the base field is perfect. Then, for any generalized motivic cohomology theory, I shalldiscuss its Zariski sheafifcation which turns out to be unramified in Morel’s sense and a Nisnevich sheaf inthis particular case.
Amongst of all, I shall emphasize the existence of its Gersten type resolution as Zariski sheaves and its
SBNR - stably birationalized Nisnevich subsheaf of the unramified sheaf.

Final: 2023/2/8
19

Algebra60 Norihiko Minami♭ Higher codimensional irrationality of counter examples of the integral(Nagoya Inst. of Tech.) Hodge conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13
Summary: Some necessary condition for a non-singular complex projective manifold X to be a counterexample for the codimension k integral Hodge conjecture Z 2k (X) 6= 0 is given.
Our necessary condition is stated as codimension ck irrationality for some ck , which grows as k increases.
This may suggest that counter-examples to the integral Hodge conjecture become ubiquitous as k increases.

Final: 2023/2/8
Geometry

20

Geometry
March 15th (Wed)Conference Room II

9:30–11:40
1 Antoni Kijowski(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Asymptotically mean value harmonic functions · · · · · · · · · · · · · · · · · · · · 15

Summary: The Blaschke–Privaloff–Zaremba theorem gives rise to a recently investigated concept of theasymptotic mean value harmonic function on a metric measure space X. For a function u ∈ L1loc (X) define
the r-laplacian of u as:

uBr (x) − u(x),r2
where uBr (x) stands for the mean-value of u over a ball Br (x). We say that u is amv-harmonic if its∆r u(x) :=r-laplacian converges to 0 in an appropriate sense as r → 0. In my talk I will present known results focusing
on regularity, blow ups and characterization of these functions in the following settings: weighted Euclidean
domains, Carnot groups and RCD spaces.
2 Shigeaki Yokota (Tohoku Univ.)

Geometry of geometric data set · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Gromov originated a geometric theory of metric measure spaces based on the phenomenon ofconcentration of measure and the theory of the collapsing of Riemannian manifolds; Pestov pointed out theconnection of Gromov’s theory with the curse of dimensionality in statistics. To improve time complexity,
Hanika, Schneider, Stumme proposed to generalize metric measure space to ‘geometric data set’. The
total set of the metric measure spaces has two natural distance functions, the observable and box distancefunctions, and their topological properties are well known, but the properties of the total set of the geometricdata set are almost unknown. In this talk, we extend these results of metric measure space to the total setof geometric data sets.
3 Daisuke Kazukawa (Kyushu Univ.)
Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)

Topological aspects of the space of metric measure spaces · · · · · · · · · · · 15

Summary: Gromov introduced two distance functions, the box distance and the observable distance, on thespace of isomorphism classes of metric measure spaces and developed the convergence theory of metricmeasure spaces. We investigate several topological properties on the space equipped with these distancefunctions toward a deep understanding of convergence theory.
4 Daisuke Kazukawa (Kyushu Univ.)
Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)

Principal bundle structure of the space of metric measure spaces · · · · · 10

Summary: We study the topological structure of the space X of isomorphism classes of metric measure spaces
equipped with the box or concentration topologies. We consider the scale-change action of the multiplicative
group R+ of positive real numbers on X , which has a one-point metric measure space, say ∗, as only
one fixed point. We prove that the R+ -action on X \ {∗} admits the structure of nontrivial and locallytrivial principal R+ -bundle over the quotient space. A similar statement is obtained for the pyramidal
compactification of X , where we completely determine the structure of the fixed-point set of the R+ -action
on the compactification.

Final: 2023/2/8
21

Geometry

5 Takumi Matsuka (Tokyo Metro. Univ.)

Free products of metric spaces and the coarse Baum–Connes conjecture· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce the notion of free products of metric spaces. When X and Y are coarsely convex,
the free product X ∗ Y is coarsely convex. In particular, the free product X ∗ Y satisfies the coarse Baum–
Connes conjecture. This talk is based on a ongoing joint work with Tomohiro Fukaya (Tokyo Metropolitan
University).
6 Yoshito Ishiki(RIKEN)

Continua in the Gromov–Hausdorff space · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We first prove that for all compact metrizable spaces, there exists a topological embedding of
the compact metrizable space into each of the sets of compact metric spaces which are connected, pathconnected, geodesic, or CAT(0), in the Gromov–Hausdorff space with finite prescribed values. As its
application, we show that the sets prescribed above are path-connected and their non-empty open subsets
have infinite topological dimension. By the same method, we also prove that the set of all proper CAT(0)spaces is path-connected and its non-empty open subsets have infinite topological dimension with respect
to the pointed Gromov–Hausdorff distance.
7 Yoshito Ishiki(RIKEN)

Metric trees in the Gromov–Hausdorff space · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topologicalembedding of the compact metrizable space into the set of all metric trees in the Gromov–Hausdorff spacewith finite prescribed values. As its application, we show that the set of all metric trees is path-connected
and its all non-empty open subsets have infinite topological dimension.
14:15–16:00
8 Kentaro Yonemura (Kyushu Univ.)

Embedding smooth quandles in Lie groups · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We deal with embedding smooth quandles in Lie groups in this talk.
9 Yuuki Sasaki (Tokyo Nat. Coll. of Tech.)Some submanifolds of the associative Grassmann manifold · · · · · · · · · · 15

Summary: We construct a totally complex immersion from almost complex submanifolds of the 6-dimensional
sphere into the associative Grassmann manifold. Also, as an analogy of almost complex immersions weconstruct a CR immersion from 3-dimensional CR submanifolds of the 6-dimensional sphere into theassociative Grassmann manifold. Moreover, in the associative Grassmann manifold we show that many
orbits of the action of the isotropy subgroup of the isometry group are the image of some CR immersions.
10 Taro Kimura(Nat. Inst. of Tech., Tsuruoka Coll.)
Katsuya Mashimo (Hosei Univ.)

Biharmonic Cartan embeddings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we determine all the proper biharmonic submanifolds in compact Lie groups which
are the image of Cartan embeddings defined by automorphism of order 4. Moreover we show that if the
Cartan embedding defined by automorphism of order 3 is biharmonic, then it is harmonic.
11 Osamu Ikawa (Kyoto Inst. Tech.)
Katsuya Mashimo (Hosei Univ.)

The geometry of orbits of σ-action induced by triality automorphism ofSpin(8) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The universal covering group Spin(8) of the special orthogonal group SO(8) has an outerautomorphism σ of order 3 called the triality automorphism. From this σ, the action of Spin(8) on Spin(8)itself, called the σ-action, is determined. This action is a hyperpolar action of cohomogeneity (= codimensionof maximum-dimensional orbit) 2. We report on the orbit space and properties of orbits of this action.

Final: 2023/2/8
Geometry

12 Kazumi Tsukada (Ochanomizu Univ.⋆)

22

The complexification of Lie sphere geometry and totally complex submanifolds of the real Grassmann manifold · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The real Grassmann manifold Gr4 (Rn ) of all 4-dimensional subspaces in Rn is known to havethe quaternionic Kähler structure. We consider the set H2 (C n ) of all 2-dimensional complex subspaces in
C n that are isotropic with respect to the standard complex inner product. H2 (C n ) is a complex manifoldof dimension 2n − 7 and has the holomorphic contact structure. The natural projection of H2 (C n ) onto
Gr4 (Rn ) is a twistor fibration. Through H2 (C n ), we show the relation between the geometry regarded as
the complexification of Lie sphere geometry and that of totally complex submanifolds of Gr4 (Rn ).
13 Yusuke Sakane (Osaka Univ.⋆)

Existence and non-existence of Einstein metrics on compact homogeneous manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The study of existence and non-existence of Einstein metrics on G/H is started by Wang and
Ziller in 1986. More general results for non-existence are obtained by Böhm in 2005. One of his results isthat G/H = SU (n + k1 + · · · + kp )/S(SO(n)U (1) × U (k1 ) × · · · × U (kp )) (where SO(n)U (1) ⊂ U (n)) does not
admit G-invariant Einstein metrics, if n > (k1 + · · · + kp )2 + 2. He has obtained the results by considering“traceless” part of Ricci tensor. For G/H = SO(2n + k1 + · · · + kp )/SO(n)U (1) × SO(k1 ) × · · · × SO(kp )(where SO(n)U (1) ⊂ U (n) ⊂ SO(2n)), we can not apply his method directly. In this talk, we will show
that, if n ≥ 5(k1 + · · · + kp ) (ki ≥ 3), G/H does not admit G-invariant Einstein metrics. We also discuss
existence of Einstein metrics for compact homogeneous manifolds G/H above.
16:15–17:15

Talk Invited by Geometry Section

Daisuke Tarama (Ritsumeikan Univ.)

On integrable geodesic flows over a semi-simple Lie group

Summary: This talk deals with the geodesic flow of a semi-simple Lie group equipped with a left-invariant
metric. After a short review over the geometric settings for general left-invariant Hamiltonian systems on
the cotangent bundle to a Lie group, a class of left-invariant metrics is considered on a semi-simple Liegroup, following Mishchenko and Fomenko. These metrics have been known to give rise to completely
integrable geodesic flows since late 1970’s. It is however rather recent that their equilibrium points arestudied mostly on the basis of techniques in symplectic/Poisson geometry. In the talk, these developments
are briefly reviewed. Then, as a main result, the classification of Williamson types of relative equilibrium
points for a large subclass of above integrable geodesic flows is explained in terms of root systems. Related
studies and remaining problems are also mentioned.

March 16th (Thu)

Conference Room II

9:30–12:00
14 Masaya Kawamura(Kagawa Nat. Coll. of Tech.)

On a k-th Gauduchon metric on compact almost Hermitian manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce some results about k-th Gauduchon metrics on compact almost
Hermitian manifolds. We have shown that if both the conformally k-th Gauduchon condition and theconformally semi-Kähler condition are satisfied, then it becomes conformally quasi-Kähler.

Also, wecharacterize the k-th Gauduchon condition and by applying its characterization, we have shown somegeometric conditions for negative Kodaira dimension on compact almost Hermitian manifolds.

Final: 2023/2/8
23

Geometry

15 Natsuo Miyatake (Kyushu Univ.)
Hisashi Kasuya (Osaka Univ.)

Uniformization of compact Sasakian manifolds using basic Higgs bundles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Simpson introduced the notion of uniformizing variation of Hodge structure (VHS) and showedthat the universal covering of a compact Kähler manifold is isomorphic to a bounded symmetric domain
if and only if there exists a uniformizing VHS on the Kähler manifold. In this talk, on compact Sasakian
manifolds, we consider an analogy of this. We can formulate an analogy of the uniformizing VHS also on
compact Sasakian manifolds. However, even if there exists a uniformizing VHS on a compact Sasakian
manifold, the constructed map collapses all the points on each leaf of the foliation of the universal covering
into one point and can never be an isomorphism. I will explain how to properly take the lift of this map
and construct an isomorphism from the universal covering to a homogeneous space.
16 Natsuo Miyatake (Kyushu Univ.)

Restriction of Donaldson’s functional to diagonal metrics on Higgs
bundles with not-holomorphic Higgs filelds · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A Higgs bundle over a compact Kähler manifold X is the pair (E, θ) consisting of a holomorphic
V1,0
vector bundle E → X and a holomorphic section θ of EndE ⊗satisfying θ ∧ θ = 0. The holomorphic
section θ is called a Higgs field. Usually, Higgs fields are assumed to be holomorphic. However, in this talk,I will consider Higgs bundles with not holomorphic Higgs fields. I will suppose that the holomorphic vector
bundle E decomposes into a direct sum of holomorphic line bundles, and I will give some necessary andsufficient conditions for Donaldson’s functional to attain a minimum over diagonal metrics concerning thedecomposition. I will also slightly extend the theorem for not-holomorphic splittings of the vector bundle.
17 Natsuo Miyatake (Kyushu Univ.)

Some generalizations of the Hermitian–Einstein equation of cyclic Higgs
bundles and their parabolic equations and the Dirichlet problem · · · · · 15

Summary: In this talk, I will introduce some generalizations of the Hermitian–Einstein equation of cyclic
Higgs bundles on Riemann surfaces. For such generalized equations, I will show the existence and theuniqueness of the time-global solution of the parabolic equations and I will also show the existence and theuniqueness of the solution to the Dirichlet problem.
18 Koki Matsuzaka (Hokkaido Univ.)
Masao Jinzenji (Okayama Univ.)

Recursion relation on moduli space of quasimaps in the case of Calabi–
Yau hypersurface in CP N −1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In computing of B-model in classical mirror symmetry, Picard–Fuchs equation is very important.
In the case of Calabi–Yau hypersurface in CP N −1 , its solutions are used in a mirror map, and it is known that
gp0,2 (N, d) of quasimaps
a generating function of intersection numbers w(OhN −3 Oh0 )0,d of moduli space M
from CP 1 with 2 marked points to CP N −1 coincides with the mirror map. In our previous work, we provedthat the solutions are written by using a term d · w(σj (OhN −2−j )Oh−1 )0,d + w(σj−1 (OhN −1−j )Oh−1 )0,d , whereσj corresponds to the Mumford–Morita–Miller class. In this talk, we see that the above term can be
gp0,2|1 (N, d) of quasimaps from CP 1 with 2 + 1 marked
obtained from a recursion relation on moduli space M
points to CP N −1 .
19 Kazushi Kobayashi (Osaka Univ.)

A gerby deformation of complex tori and the homological mirror symmetry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let (X, X̌) be a mirror pair of a complex torus X and its mirror partner X̌. This mirror pair is
described as the trivial special Lagrangian torus fibrations X → B and X̌ → B on the same base space B
by SYZ construction. Then, we can associate a holomorphic line bundle E(s, L) → X to a pair (s, L) of a
Lagrangian section s of X̌ → B and a unitary local system L along it. In this talk, we first construct the
deformation XG of X by a certain flat gerbe G and its mirror partner X̌G from the mirror pair (X, X̌), anddiscuss deformations of objects E(s, L) and (s, L) over the deformed mirror pair (XG , X̌G ).

Final: 2023/2/8
Geometry

20 Hayato Nakanishi (Chiba Univ.)

24

Homological mirror symmetry of toric Fano surfaces via Morse homotopy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Strominger–Yau–Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus
fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss thehomological mirror symmetry, where we consider Morse homotopy of the moment polytope instead of the
Fukaya category.
21 Yuto Yamamoto(IBS-CGP)

Period integrals of hypersurfaces via tropical geometry · · · · · · · · · · · · · · 15

Summary: Let {Zt }t be a one-parameter family of complex toric hypersurfaces of dimension d ≥ 1. We
compute asymptotics of period integrals for {Zt }t by applying the method of Abouzaid–Ganatra–Iritani–
Sheridan, which uses tropical geometry. As integrands, we consider Poincaré residues of meromorphic(d + 1)-forms on the ambient toric variety, which have poles along the hypersurface Zt . The cycles overwhich we integrate them are spheres and tori which correspond to tropical (0, d)-cycles and (d, 0)-cycles on
the tropicalization of {Zt }t respectively.
13:00–14:00

Talk Invited by Geometry Section

Yoshinori Hashimoto♭ Recent developments on constant scalar curvature Kähler metrics with
(Osaka Metro. Univ.) cone singularities along a divisor
Summary: We present some recent results concerning constant scalar curvature Kähler metrics with cone
singularities along a divisor, henceforth abbreviated as cscK cone metrics. One of the main results is that theexistence of cscK cone metrics implies various stability conditions of the underlying pair of the manifold andthe divisor, including G-uniform K-stability and K-polystability. We also prove that any Kähler manifold
admits a cscK cone metric if the divisor is a generic member of the linear system defined by a sufficiently
large multiple of the polarisation, and point out an analogy to the twisted constant scalar curvature Kähler
metrics. This talk is based on a joint work with Takahiro Aoi and Kai Zheng.

March 17th (Fri)

Conference Room II

9:30–11:40
22 Hiroaki Izumi (Hiroshima Univ.)

Significance of game theory and formulization of in-phase and anti-phasecircadian rhythms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we explain the significance of game theory, which frees a system of differential
equations from the spell of integrability conditions. Also using it, we present the system of equations ofin-phase and anti-phase circadian rhythms from the viewpoint of variational principle. In addition, thegeneral formulization of the mathematical structure of phase transition and synchronization is carried out.
23 Yoshiki Jikumaru (Kyushu Univ.)
Kentaro Hayakawa (Kyoto Univ.)
Kazuki Hayashi (Kyoto Univ.)
Kenji Kajiwara (Kyushu Univ.)
Yohei Yokosuka (Kagoshima Univ.)

On the Michell truss-like structure and discrete log-aesthetic curves
based on integrable geometry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The truss structure minimizing the product of axial forces and lengths for a given load and a
support condition is called Michell truss, which is classically known in the field of structural mechanics.
In this presentation, we have an analytical construction of Michell truss-like structure described by adiscrete holomorphic function (discrete conformal map) in the context of discrete integrable systems.
The validity of the structure is demonstrated by the result of structural analysis. Moreover, we show
the truss structure is composed of so-called discrete log-aesthetic curves. This structure connects threeobjects (discrete holomorphic functions, discrete log-aesthetic curves, and classical truss structures) having
completely different origins which were achieved through the collaboration of mathematics and architecture.

Final: 2023/2/8
25

Geometry

24 Yoshihiko Suyama (Fukuoka Univ.)
Nozomu Matsuura(Kurume Inst. of Tech.)

Extension and approximation of curvature surfaces in generic conformally flat hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We talk about curvature surfaces of generic conformally flat analytic-hypersurfaces in the Euclidean 4-space.
25 Satoshi Ishiwata (Yamagata Univ.)
Hiroshi Kawabi (Keio Univ.)

A discretization of a non-symmetric diffusion on a Riemannian manifold· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give a graph discretized approximation of the diffusion for a Schrödinger operator
with drift on a complete Riemannian manifold.
26 Ye Zhang(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Gradient estimates for the heat semigroup on step-two Carnot groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is well-known that we can characterize the lower bound of the Ricci curvature by the boundfor the gradient of the heat semigroup. However, on a nonabelian nilpotent Lie group endowed with aleft-invariant Riemannian metric, there exists a direction of strictly negative Ricci curvature. This implies
the gradient bound has exponential growth. In this talk, I will present how to improve the gradient boundto the constant in the setting of step-two Carnot groups on which the H.-Q. Li inequality holds.
27 Yuichiro Taketomi(Osaka Metro. Univ.)

A maximal element of a moduli space of Riemannian metrics · · · · · · · · 15

Summary: For a given smooth manifold X, we consider the moduli space of Riemannian metrics on X up toisometry and scaling. One can define a preorder on the moduli space by the size of isometry groups. We
call a Riemannian metric that attains a maximal element with respect to the preorder a maximal metric.
Maximal metrics give nice examples of self-similar solutions for various metric evolution equations such as
the Ricci flow. In this talk, we construct many examples of maximal metrics on Euclidean spaces.
28 Yoshihiko Matsumoto (Osaka Univ.)

Renormalized energy of maps and conformal geodesics · · · · · · · · · · · · · · 15

Summary: We introduce a certain renormalized energy of maps between asymptotically hyperbolic Einsteinmanifolds. Then, it is used to give a holographic description of conformal geodesics on the boundary at
infinity, in a way deeply inspired by a work of Fine and Herfray on renormalized area minimization andconformal geodesics.
14:15–14:55
29 Tomoshige Yukita (Waseda Univ.)

On nerves and growth rates of 2-dimensional Coxeter systems · · · · · · · 15

Summary: For a Coxeter system (Γ, S), the nerve L(Γ, S) is a simplicial complex defined via the structureof finite parabolic subgroups of Γ. The dimension of (Γ, S) is defined by dim L(Γ, S) + 1. In this talk, we
consider the relationship between the combinatorial structure of L(Γ, S) and the arithmetic properties of
the growth rate of (Γ, S). We show that the growth rate of a 2-dimensional Coxeter system (Γ, S) withvanishing (resp. positive) Euler characteristic χ(L(Γ, S)) is a Salem (resp. Pisot) number. This is a joint
work with Naomi Bredon.
30 Akira Ushijima (Univ. of Hyogo)

Ceva’s and Menelaus’ theorems in the hyperbolic plane as Cayley–Klein
geometry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Using the construction of the hyperbolic plane as Cayley–Klein geometry, we will demonstrate
how to obtain Ceva’s and Menelaus’ theorems in the hyperbolic plane from their corresponding theorems in
the real projective plane.

Final: 2023/2/8
Geometry

15:10–16:10

26

Talk Invited by Geometry Section

Harish Seshadri(Indian Inst. of Sci., Bangalore)

On the diameter of Kähler manifolds with positive bisectional curvature

Summary: I will discuss the Kähler analogues of the classical Bishop volume inequality and Myers–Bonnet
diameter bound for Riemannian manifolds. In particular, I will outline the proof of diameter rigidity(an analogue of Cheng’s theorem in the Riemannian case) for compact Kähler n-manifolds (M, ω) withbisectional curvature BK ≥ 1. It is known from the work of Li–Wang that diam (M ) ≤ diam (CP n ) forsuch manifolds, where CP n is endowed the Fubini–Study metric. In joint work with V. Datar, we provedthat if diam (M ) = diam (CP n ), then M is isometric to CP n .

Final: 2023/2/8
27Complex Analysis

Complex Analysis
March 15th (Wed)Conference Room V

9:30–11:45
1 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Complex analysis and theory of reproducing kernels · · · · · · · · · · · · · · · · 10

Summary: The theory of reproducing kernels is very fundamental, beautiful and will have many applicationsin analysis, numerical analysis and data sciences. Based on a draft paper, I would like to give a global
viewpoint for the relation of complex analysis and the theory of reproducing kernels. I listed the basic
references on the topics.
2 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Complex analysis and division by zero calculus · · · · · · · · · · · · · · · · · · · · 15

Summary: Based on a draft book manuscript, I would like to introduce the basic and essential relations ofcomplex analysis and division by zero calculus. Basic references are cited in the references.
3 Takanori Ayano (Osaka Metro. Univ.)
Victor M. Buchstaber(Steklov Inst. of Math.)

A relationship between hyperelliptic functions of genus 3 and elliptic
functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the nineteenth century, the reductions of hyperelliptic integrals to elliptic integrals were studied
actively and many examples of the reductions were obtained. They are closely related to coverings of curves,
split Jacobians, and automorphism groups of curves.

This knowledge is applied to the isogeny-based

cryptography. In our previous work, by using this knowledge, we derived the relationships between thehyperelliptic functions of genus 2 and the elliptic functions when the curve of genus 2 admits a morphism ofdegree 2 to an elliptic curve. In this talk, we will derive a relationship between the hyperelliptic functionsof genus 3 and the elliptic functions when the hyperelliptic curve of genus 3 admits a morphism of degree 2
to an elliptic curve.
4 Shingo Sugiyama (Nihon Univ.)

The existence of equivariant functions and the Schwarzian derivative· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Equivariant functions associated to a 2-dimensional representation of a Fuchsian group was
introduced by Saber and Sebbar. They are regarded as a generalization of automorphic functions. We
prove the existence of equivariant functions associated to any generic 2-dimensional representation of any
Fuchsian group. We prove such existence by using the Schwarzian derivative.
5 Yoshikazu Yamagishi (Ryukoku Univ.)
Takuro Uezono (Mars Networks Corp.)
Takamichi Sushida (Salesian Polytech.)

Voronoi tiling and circle packing on spiral lattices with rotational symmetry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices withrotational symmetry is graph-theoretically dual to the bifurcation diagram of Voronoi tessellations, by using
the relative metric. If the rotation parameter (called divergence angle) is badly approximable, then the
aspect ratio of the quadrilateral Voronoi cells is bounded. If the divergence angle is linearly equivalent to
the golden section, then the shape of the quadrilateral cells tend to square as the plastochron ratio tends to1.

Final: 2023/2/8
Complex Analysis

6 Shun Kumagai (Tohoku Univ.)

28

Voronoi decomposition of origamis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Edwards–Sanderson–Schmidt method uses the Voronoi decomposition to present an excellent
criterion for the equivalence class and the Veech group of a finite translation surface. The key argument of
their method includes a complicated combinatorial structure. An origami is a typical example of a translation
surface defined combinatorially. This talk discusses the Voronoi decomposition of a half-translation versionof origami.
7 Shinpei Baba

(Osaka Univ.)

Bending maps of Teichmüller spaces and character varieties · · · · · · · · · 15

Summary: The space holomorphic quadratic differentials on a compact Riemann surface is a complex vector
space. By the holonomy map of complex projective structures, this vector space properly embeds into thePSL(2, C)-character variety of the base surface. We construct certain analogues of such an embedding fromthe viewpoint of Thurston’s parametrization of complex projective structures.
8 Yohei Komori (Waseda Univ.)

Applications of canonical polygons of Zieschang–Vogt–Coldewey · · · · · 15

Summary: As applications of canonical polygons of Zieschang–Vogt–Coldewey, we will show that (1) 6g-6
angles between geodesics on Riemann surfaces of genus g globally parametrize Teichmuller space of genus
g surfaces. (2) Mapping classes of genus 2 surface can be represented by the cut and paste argument ofcanonical polygons.
9 Masashi Kisaka (Kyoto Univ.)

Polynomial-like mappings and transcendental entire functions with irrationally indifferent fixed points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, by using the theory of polynomial-like mappings, we construct various kinds oftranscendental entire functions with irrationally indifferent fixed points. This talk is based on the joint workwith Hiroto Naba.
14:15–15:15

Talk Invited by Complex Analysis Section

Toshihiro Nakanishi (Shimane Univ.)

Teichmüller space of the genus two surface and Kleinian groups

Summary: In this talk the Teichmüller space is a deformation space of marked Fuchsian groups of finite type,in most cases, genus two Fuchsian groups. We deal with (1) trace functions as parameters for a Teichmüller
space, (2) matrix representation of the genus two surface group, (3) mapping classes represented by rationaltransformations. These materials are used to produce some examples of Kleinian groups related to surface
groups.

Final: 2023/2/8
29Complex Analysis

15:30–16:30

Award Lecture for the 2022 MSJ Analysis Prize

Katsuhiko Matsuzaki (Waseda Univ.)

Curves and function spaces of absolutely continuous Teichmüller spaces

Summary: The universal Teichmüller space is the total space containing all quasiconformal Teichmüller
spaces and it can be regarded as the space of normalized quasisymmetric functions f on the real line.
According to the regularity of these functions f , there are two different directions of subspaces included in
the universal Teichmüller space: Teichmüller spaces of Riemann surfaces are typically in the direction of
totally singular f , and Teichmüller spaces of function spaces are absolutely continuous f .
Teichmüller spaces can be represented by quasisymmetric homeomorphisms mentioned above, and in otherways, they can be represented by the complex dilatations of quasiconformal mappings, the Schwarzian or
pre-Schwarzian derivatives of conformal mappings, and the quasicircles given as the images of the circle.
Fundamental studies of particular Teichmüller spaces are composed by the investigation of the relationshipbetween these different representations and structures. In addition, if we deal with absolutely continuous
Teichmüller spaces, the derivative f ′ or log f ′ defines the corresponding function spaces, and by using them,
we can introduce simpler structures to these Teichmüller spaces.
In this talk, we exhibit several important examples of absolutely continuous Teichmüller spaces and explain
how the identification of different representations works. The examples include Weil–Petersson Teichmüller
spaces, BMO Teichmüller spaces and the space of chord-arc curves between them. One technical tool is thesimultaneous uniformization imported from the theory of quasifuchsian spaces. We represent the space ofparticular quasicircles by the product of the corresponding Teichmüller spaces and consider biholomorphic
correspondence between this parameter space and the complex function space. Furthermore, we apply
this method to see (dis)continuous dependence of the Riemann mapping parametrizations of the family of
Weil–Petersson curves and chord-arc curves to their arc-length parametrizations.

March 16th (Thu)

Conference Room V

9:30–11:45
10 Kohei Ueno

(Daido Univ.)

Dynamics of superattracting skew products · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the dynamics of a holomorphic skew product with a superattracting fixed point. We
proved that it is generally conjugate to a monomial map on an invariant wedge whose closure contains
the fixed point. In this talk we provide several kinds of plurisubharmonic functions on the complement ofspecific fibers in the attracting basin, which describe the vertical dynamics well.
11 Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Jian-Feng Zhu (Huaqiao Univ.)

Lipschitz constant of harmonic Bloch functions and composition operators on Bloch and Hardy type spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The main purpose of this talk is to discuss Hardy type spaces, Bloch type spaces and thecomposition operators of complex-valued harmonic functions. We first establish a sharp estimate of the
Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudohyperbolic metric, which gives an answer to an open problem. Then some classes of composition operators
on Bloch and Hardy type spaces will be investigated. The obtained results improve and extend somecorresponding known results.

Final: 2023/2/8
Complex Analysis

12 Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)
Mirela Kohr (Babeş-Bolyai Univ)

30

Fekete–Szegö problem for univalent mappings in one and higher dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will give the Fekete–Szegö inequality for the mappings f in various subclassesof normalized univalent mappings which are the first elements of g-Loewner chains on the unit disc U in
C and also on the unit ball B of a complex Banach space. As an application, we give the estimation of
the third coefficient for f under the condition that the second coefficient of f is zero. This result gives ageneralization of the estimation of the third coefficient for odd univalent functions on the unit disc U. We
also give the Fekete–Szegö inequality for the images of the first elements of g-Loewner chains on U under
the Roper–Suffridge type extension operators.
13 Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Loewner PDE in infinite dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we generalize the existence and uniqueness result for the solutions of the Loewnerpartial differential equation (Loewner PDE) from Cn to the case of separable reflexive complex Banach
spaces.
14 Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)

Some sharp Schwarz–Pick type estimates and their applications ofharmonic and pluriharmonic functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The purpose of this talk is to study the Schwarz–Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimatesof the norm of harmonic functions from the Euclidean unit ball in Rn into the unit ball of the real ℓp space.
Next, we give several sharp Schwarz–Pick type inequalities for pluriharmonic functions from the Euclidean
unit ball in Cn or from the unit polydisc in Cn into the unit ball of the ℓp space. Furthermore, we establish
some sharp coefficient type Schwarz–Pick inequalities for pluriharmonic functions defined in the ℓp space.
Finally, we use the obtained Schwarz–Pick type inequalities to discuss the Schwarz–Pick type lemmas ofarbitrary order and the Bohr phenomenon of harmonic or pluriharmonic functions.
15 Shaolin Chen (Hengyang Normal Univ.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Saminathan Ponnusamy(Indian Inst. of Tech. Madras)
Ramakrishnan Vijayakumar(Indian Inst. of Tech. Madras)

Schwarz type lemmas and their applications in Banach spaces · · · · · · · 15

Summary: The main purpose of this talk is to develop some methods to investigate the Schwarz typelemmas of holomorphic mappings and pluriharmonic mappings in Banach spaces. Initially, we extend theclassical Schwarz lemmas of holomorphic mappings to Banach spaces, and then we apply to establish a
sharp Bloch type theorem for pluriharmonic mappings on homogeneous unit balls of Cn and to obtain somesharp boundary Schwarz type lemmas for holomorphic mappings in Banach spaces. Next, we improve andgeneralize the classical Schwarz lemmas of planar harmonic mappings into the sharp forms of Banach spaces
and give some applications to sharp boundary Schwarz type lemmas for pluriharmonic mappings in Banach
spaces. Finally, we give some sharp Schwarz-Pick type estimates of pluriharmonic mappings in JB ∗ -triples.

Final: 2023/2/8
31Complex Analysis

16 Yuta Watanabe (Univ. of Tokyo)

L2 -type Dolbeault isomorphisms and vanishing theorems for logarithmic
sheaves twisted by multiplier ideal sheaves · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this speech, we first establish an L2 -type Dolbeault isomorphism for the sheaf of logarithmic
differential forms twisted by the multiplier ideal sheaf. By using this isomorphism and L2 -estimates equippedwith a singular Hermitian metric, we obtain logarithmic vanishing theorems involving multiplier ideal sheaves
on compact Kähler manifolds with simple normal crossing divisors.
17 Takeo Ohsawa (Nagoya Univ.) ♭ On the Levi problem on Kähler manifolds under the negativity ofcanonical bundles on the boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: It is proved that a bounded smooth pseudoconvex domain D in a Kähler manifold M can bemapped onto a locally closed analytic set in a complex number space holomorphically and properly withconnected fibers if the caninical bundle of M is negative on a neighborhood of the boundary of D. A similar
result holds for Zariski open domains of compact manifolds.
13:00–14:00

Talk Invited by Complex Analysis Section

Makoto Abe (Hiroshima Univ.)

Domains over a Stein manifold satisfying the Oka–Grauert principle

Summary: We discuss the pseudoconvexity and the Steinness of a complex manifold or a complex space undersome conditions. Among others, we announce the recent joint research with Sugiyama on the Steinness ofa domain over a Stein manifold that satisfies the Oka–Grauert principle for a complex Lie group of positive
dimension and some additional cohomological conditions.

Final: 2023/2/8
Functional Equations

32

Functional Equations
March 15th (Wed)Conference Room IV

9:30–12:00
1 Yumiko Takei(Ibaraki Nat. Coll. of Tech.)On the expression of Voros coefficients for the hypergeometric differential equation of type (1,1,1,2) in terms of the topological recursion, andits applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Voros coefficients are important objects in the exact WKB analysis for the global study ofsolutions of differential equations. In this talk I will report that the Voros coefficients for the hypergeometricdifferential equation of type (1,1,1,2) are given by the generating functions of free energies defined in termsof Eynard and Orantin’s topological recursion.
2 Saiei-Jaeyeong Matsubara-Heo(Kumamoto Univ.)
Yoshiaki Goto
(Otaru Univ. of Commerce)

The signature of the invariant hermitian form for a regular holonomic
GKZ system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Frits Beukers and Carlos Verschoor conjectured that the signature of the monodromy invariant
hermitian form for a regular holonomic GKZ system has an explicit formula. We prove that this conjectureis true, by computing the intersection matrix of the twisted homology group associated to Euler type integral
representation of a solution to GKZ system.
3 Hidekazu Ito (Kanagawa Univ.)

Birkhoff normalization of a family of symplectic maps and superintegrability of Hamiltonian systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Integrability of a Hamiltonian system is defined by the existence of sufficiently many (Poissoncommuting) integrals. The Liouville–Arnold theorem gives description of the orbit structure near a compact
regular level set of those integrals, however, is not valid near singularities of those integrals. The aim of thistalk is to clarify the orbit structure of a super (noncommutatively) integrable system near singularities of
its integrals. For this purpose, Birkhoff normalization for a family of symplectic maps plays a key role. We
show that there exists a convergent Birkhoff normalization if a family of 2n-dimensional analytic symplectic
maps has n + q integrals near a fixed point of resonance degree q.
♭ Two-component solitons via an energy dependent inverse scattering · · 12
4 Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.⋆)Summary: An extended KdV hierarchy is discussed. Based upon an inverse scattering method on an energy
dependent Schroedinger operator, soliton solutions in the hierarchy are constructed in a unified manner.
5 Yuki Hata (Osaka Pref. Univ.)
Hideaki Matsunaga(Osaka Metro. Univ.)

Asymptotic stability in a linear differential equation with two delays· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This study is devoted to the investigation of the effect of delays on the asymptotic stability of alinear differential equation with two delays x′ (t) = −ax(t) − bx(t − τ ) − cx(t − 2τ ), t ≥ 0, where a, b, and c
are real numbers and τ > 0. We establish some explicit conditions for the zero solution of the equation to
be asymptotically stable.
6 Masakazu Onitsuka(Okayama Univ. of Sci.)

On Ulam stability of two-dimensional linear differential systems · · · · · · 10

Summary: The main purpose of this talk is to classify the Ulam stability of the linear differential equationu′ = Au, where A is a real-valued constant 2 × 2 matrix. The best Ulam constant is obtained for somespecial cases of A.

Final: 2023/2/8
33

Functional Equations

7 Hiroyuki Usami(Gifu Univ.)

Study on nonexistence results of positive solutions of ODEs without
assuming monotonicities on nonlinear terms · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Sufficient conditions for the existence of positive solutions of quasilinear ODEs are given. Usually,such results are proved under the monotonicity conditions of nonlinear terms. However, in this talk we will
give such results without assuming monotonicities on nonlinear terms.
8 Tetsutaro Shibata (Hiroshima Univ.)

Global and asymptotic behaviors of bifurcation curves of one-dimensional
nonlocal elliptic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the global behavior of the bifurcation curves and solution curves of one-dimensional
nonlocal elliptic eigenvalue problems. We know that the bifurcation curve λ is a continuous function of the
maximum norm α = kuλ k∞ such as λ(α). Here, uλ is the positive solution associated with λ. Our purpose
here is to establish the asymptotic formulas for λ(α) and uλ as λ → ∞.
9 Naoki Hamamoto (Osaka Metro. Univ.)

The Poincaré constant for curl-free vector fields on a ball · · · · · · · · · · · 12

Summary: We investigate the best value of the constant in classical Poincaré inequality
ZZ|∇u|2 dx ≥ C|u|2 dx
BNBNfor a class of vector fields u with u|∂B N = 0 on the unit ball B N ⊂ RN which are subject to the curl-freeconstraint. We find that the best value of C turns out to be the square of the first zero of Bessel functionof the (N/2)-th order.
10 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Functional equations and theory of reproducing kernels · · · · · · · · · · · · · 10

Summary: By a survey paper, we shall introduce the basic relations of functional equations and the theoryof reproducing kernels, globally, as a summary of the topics. In particular, I would like to introduce typicalresults with their principles in some concrete way based on the draft paper.
The general theory of reproducing kernels will give the basic tool of these widespread problems.
11 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)

Representations of quotients g/f =h in terms of g=fh · · · · · · · · · · · · · · · 12

Summary: We are considering the simple functional equation hf=g. By the paper (REPRESENTATIONSOF QUOTIENTS g/f = h IN TERMS OF g = fh, International Journal of Reproducing Kernels Vol. 2 No.
1 (2023)), we shall introduce quotients g/f of general functions f and g in some deep and natural meanings,
in a natural setting.
14:15–16:15
12 Toshio Horiuchi (Ibaraki Univ.)

On general Caffarelli–Kohn–Nirenberg type inequalities involving nondoubling weights · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: By introducing W (R+ ) = P (R+ ) ∪ Q(R+ ) = ∪a∈[0,∞] Wa (R+ ) as a class of weight functions, wewill establish the Caffarelli–Kohn–Nirenberg type inequalities for p ≥ 1 involving non-doubling weights in
W (R+ ). The classical Caffarelli–Kohn–Nirenberg type inequalities are categorized into non-critical andcritical cases, and it is known that there is some kind of mysterious relationship between them. Interestingly
the new framework in this treatise allows them to be integrated and reveals the meaning of mysterious
relationships. A function w(t) on (0, ∞) is said to be a doubling weight if there exists a positive number
C such that we have C −1 w(t) ≤ w(2t) ≤ Cw(t)(0 < t < ∞), where C is independent of each t ∈ (0, ∞).

When w(t) does not possess this property, w(t) is said to be a non-doubling weight in the talk.

Final: 2023/2/8
Functional Equations

13 Ryuji Kajikiya(Osaka Electro-Comm. Univ.)

34

Boundedness of critical points in the symmetric mountain pass lemma· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the boundedness of critical points defined by the symmetric mountain pass lemma. We
construct three types of functionals, which have an unbounded sequence of critical values. For the first one,the set of all critical points is bounded and the set of critical values is unbounded. The second one has bothan unbounded sequence and a bounded sequence of critical points. For the last one, the set of critical points
is countably infinite and unbounded.
(Tohoku Univ.)
14 Goro Akagi
Hiroki Miyakawa (Tohoku Univ.)

Maximal regularity of distributional solutions to degenerate elliptic
systems for locally integrable data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk is concerned with degenerate elliptic equations involving the p-Laplacian and absorptionin unbounded domains. Main results consist of the existence of distributional solutions and their maximal
regularity (estimates) for locally integrable forcing terms beyond the duality.
15 Goro Akagi
Kotaro Sato

(Tohoku Univ.)(Tohoku Univ.)

On some quasistatic evolution equation arising from fracture mechanics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk deals with some quasistatic evolution equation, which relates fracture mechanics and isalso written as an evolutionary variational inequality. The main result of this talk is concerned with theexistence of strong solutions complying with three qualitative properties, that is, irreversibility, unilateralequilibrium and energy conservation, which were originally proposed in a phase-field model for brittle
fracture.
16 Tomoyuki Oka (Univ. of Tokyo)

Corrector results for space-time homogenization of fast diffusion equations without assumptions for smoothness of coefficients · · · · · · · · · · · · 12

Summary: In this talk, we shall discuss a space-time homogenization problem for fast diffusion equations
with periodically oscillating (in space and time) coefficients. The main purpose of this talk is to present
a corrector result, i.e., strong convergence of gradient of the solution with a corrector term. The proof isbased on the unfolding method and the strong two-scale convergence theory.
17 Takashi Suzuki (Osaka Univ.)

Mathematical analysis for Brownian particle gas · · · · · · · · · · · · · · · · · · · 5

Summary: We study Streater’s model on Brownian particle gas in statistical mechanics on bounded domain
in Rn . If n ≤ 2, there is a solution global in time, provided that the entropy production is bounded.
18 Koichi Taniguchi (Tohoku Univ.)
Noboru Chikami (Nagoya Inst. of Tech.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Slim Tayachi (Univ. de Tunis El Manar)

Unconditional uniqueness and non-uniqueness of solutions for Hardy–
Hénon parabolic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we study the problems of uniqueness for Hardy–Hénon parabolic equations, which
are semilinear heat equations with the singular potential (Hardy type) or the increasing potential (Hénontype) in the nonlinear term. To deal with the Hardy–Hénon type nonlinearities, we employ the weighted
Lorentz spaces as the solution space. The purpose of this talk is to prove unconditional uniqueness andnon-uniqueness for Hardy–Hénon parabolic equations in the weighted Lorentz spaces.
19 Masahiko Shimojo(Tokyo Metro. Univ.)
Jong Shenq Guo (Tamkang Univ.)
Amy Ai-Ling Poh (Univ. of Tokyo)

Spreading behavior of an SIR model with non-local dispersal · · · · · · · · 10

Summary: We explain a Liouville type of theorem on the positive bounded entire solution of a class ofreaction- diffusion systems with nonlocal dispersal. Some application from epidemiology is also given.

Final: 2023/2/8
35Functional Equations

20 Masahiko Shimojo(Tokyo Metro. Univ.)
Jong Shenq Guo (Tamkang Univ.)

Spreading behavior of a predator-prey system with fractional Laplacian· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We establish a Liouville theorem on the positive bounded entire solution of a class of reactiondiffusion systems with fractional diffusion. As an application, we investigate the spreading phenomena of apredator-prey system with fractional diffusion. More precisely, by a suitable limiting argument along with
the Liouville-type theorem, we prove that the solution converges to the unique positive co-existence statebehind the spreading front.
16:30–17:30

Award Lecture for the 2022 MSJ Analysis Prize
Masaru Ikehata (Hiroshima Univ.) Development of the time domain enclosure method
Summary: This talk is concerned with a reconstruction method in inverse problems formulated by using thesolutions of various partial differential equations. Such equations are called the governing equations and theobservation data are described by the solutions. The object to be reconstructed or extracted from the datais the discontinuity such as obstacles, inclusions, cracks etc.
The probe and enclosure methods are general ideas to extract information about unknown discontinuity
embedded in a known background medium from the observation data. The data are given by the far field
pattern of the scattered field, the Dirichlet-to-Neumann map or its partial knowledge at the boundary of
the medium. The methods were introduced by the speaker and it has already been passed more than twenty
years. The methods have been applied to several inverse problems, e.g., an inverse boundary value problem
related to EIT(electrical impedance tomography), elasticity and inverse obstacle scattering problems ofacoustic wave at a fixed wave number, whose governing equations are time-independent.
The next challenge and interest of the speaker were to extend the enclosure method to cover inverse problems
governed by time-dependent PDEs. However, as a result of research over the last ten years, it has been foundthat the enclosure method is also effective for various time-dependent PDEs, such as the heat equation,
the wave equation, a system of equations in thermoelasticity, the Maxwell system and quite recently thefractional diffusion equation.
This talk will give a brief history of probe and enclosure method and then describe some of recent
developments of enclosure methods in the time domain.

March 16th (Thu)

Conference Room IV

9:15–12:00
21 Masaaki Mizukami(Kyoto Univ. of Edu.)
Yuya Tanaka (Tokyo Univ. of Sci.)

Non-simultaneous blow-up in a two-species chemotaxis-competition
model with single production · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In a two-species chemotaxis-competition model, blow-up of solutions was shown in a previous
paper. In this model, the production term seems to promote blow-up phenomena; this implies that the lackof the production term makes the solution likely to be bounded. Thus, it is expected that the model without
one of the production terms has a solution such that the species which does not produce the chemical
substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that
this conjecture is true.
22 Yuya Tanaka (Tokyo Univ. of Sci.)

Finite-time blow-up in a degenerate parabolic–elliptic Keller–Segel system with logistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk deals with a degenerate parabolic–elliptic Keller–Segel system with logistic source. In
the case of nondegenerate diffusion, Black, Fuest and Lankeit (Z. Angew. Math. Phys.; 2021; 72; no. 96, 23
pp.) obtained a condition such that finite-time blow-up occurs. The purpose of this talk is to show that
finite-time blow-up occurs also in the case of degenerate diffusion.

Final: 2023/2/8
Functional Equations

23 Yutaro Chiyo (Tokyo Univ. of Sci.)
Masaaki Mizukami(Kyoto Univ. of Edu.)

36

Boundedness of solutions to a chemotaxis system for tumor angiogenesis· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk deals with a chemotaxis system for tumor angiogenesis. When the third equation is
simplified by the elliptic one and the sensitivity functions are constants, global existence and boundedness
were proved by Tao and Winkler (Nonlinear Analysis; 2021; 112324; 16 pp). However, the case that thesensitivity functions are not constants and the third equation is parabolic seems not to have been studied
yet. The purpose of this talk is to establish global existence and boundedness in a fully parabolic chemotaxis
system for tumor angiogenesis with sensitivity functions.
24 Takeshi Suguro (Kyoto Univ.) ♭ Well-posedness of the Cauchy problem of a parabolic-elliptic Keller–
Segel system in uniformly local spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the Cauchy problem of the parabolic-elliptic Keller–Segel system on Euclidean space.
This system is one of the diffusion equation involving a nonlocal term. It is interesting whether this problem
is well-posed in function spaces containing the non-decaying function. We show that the Cauchy problem ofa Keller–Segel system is well-posed in uniformly local Lebesgue spaces.
25 Tatsuya Hosono (Tohoku Univ.) ♭ Global existence of solutions to the 4D attraction-repulsion chemotaxis
Takayoshi Ogawa (Tohoku Univ.) system and applications of Brezis–Merle inequality · · · · · · · · · · · · · · · · · 12
Summary: We consider the Cauchy problem for an attraction-repulsion chemotaxis system in the four spacedimension. One of main topics in the study of such a system is the presence of L1 threshold. In fact,
the critical mass phenomenon called 8π-problem is well-known in the 2-dimensional setting. In this talk,using the Brezis–Merle type inequality and rearrangement arguments, we will show that the solution exists
globally in time when the initial mass is less than 4-dimensional L1 threshold value (8π)2 .
26 Kiichi Tashiro(Tokyo Tech)

On the construction of canonical generalized mean curvature flow byelliptic regularization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider a generalized mean curvature flow constructed by elliptic regularization.
Elliptic regularization is a method invented by Tom Ilmanen to construct an approximation of the generalized
mean curvature flow using real analytic functional. We will show that the area change of the region movedby this flow is given by equality using the generalized mean curvature. The key to the proof is to establish
approximate velocity and estimate it in L2 .
27 Tatsuya Miura (Tokyo Tech)
Kensuke Yoshizawa (Kyushu Univ.)

Complete classification of planar p-elasticae · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Euler’s elastica is defined by a critical point of the total squared curvature under the fixed length
constraint, and its Lp -counterpart is called p-elastica. In our talk, we completely classify all p-elasticae inthe plane and obtain their explicit formulae as well as optimal regularity. To this end we introduce new
types of p-elliptic functions which streamline the whole argument and result. As an application we alsoclassify all closed planar p-elasticae.
28 Takeyuki Nagasawa (Saitama Univ.)

A lower estimate of the life-span and a blow-up rate for non-local
curvature flows for plane curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Several non-local curvature flows for plane curves with general rotation number are consideredhere. The flows include the area-preserving flow and the length-preserving flow. Previously, we showedsufficient conditions for finite-time blow-up, and gave an upper bound of the blow-up time. Here, we give
estimates for solutions including at least two important applications. As the first one, it gives a lower boundof the life span, which is a lower bound of the blow-up time for blow-up solutions. Secondly, our estimate
also improves the blow-up rate of blow-up solutions.

Final: 2023/2/8
37Functional Equations

29 Tatsu-Hiko Miura (Hirosaki Univ.)

Error estimate for classical solutions to the heat equation in a moving
thin domain and its limit equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Neumann type problem of the heat equation in a moving thin domain around a
given closed moving hypersurface. Our main result is an estimate in the sup-norm for the difference of aclassical solution to the heat equation in the moving thin domain and a classical solution to a limit equationon the moving hypersurface which appears in the thin-film limit of the heat equation. To prove that error
estimate, we construct a suitable approximate solution to the heat equation from a classical solution to thelimit equation and then estimate the difference of a classical solution and the approximate one to the heat
equation based on the maximum principle.
30 Hirokazu Ninomiya (Meiji Univ.)

Example of pattern formation by equal diffusion · · · · · · · · · · · · · · · · · · · 12

Summary: In 1952, Turing proposed the mechanism of pattern formation in which a stable equilibrium ofsome kinetic system is destabilized by diffusion. In the case of two-component reaction-diffusion systems,
however, the diffusion coefficients should be different. Conversely, there exist several chemical models
that produce the stable patterns even though the diffusion coefficients are equal. To study the patternformation by equal diffusion, this talk presents an example of a kinetic system with a asymptotically stableequilibrium, while the corresponding reaction-diffusion system has a family of unstable stationary solutions
that is arbitrarily close to the homogeneous stationary solution.
31 Hirokazu Ninomiya (Meiji Univ.)

Dynamics of area-preserving curvature flow of a convex plane curve in
an inhomogeneous medium · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In 1986, Gage studied the area-preserving curvature flows in a two-dimensional homogeneous
medium. He showed that an initially convex closed curve remains convex and converges to a circle as timegoes to infinity. However, in many applications, the medium is not homogeneous. In this talk, we consider
the area preserving flow in an inhomogeneous medium when the area enclosed by the interface is small. The
reduced equation of its center will be explained.
13:00–14:00

Talk Invited by Functional Equations Section

Takeyuki Nagasawa (Saitama Univ.)

The decomposition of the Möbius energies and wave maps

Summary: The Möbius energy for knots is known as a functional invariant under Möbius transformations.
There is an energy for links having the same properties. For the energies for knots and two-component
links, there exists a Möbius invariant decomposition, that is, each decomposed part is still invariant underMöbius transformations.
Recently, the author found two new expressions of decomposition using Gauss maps of knots and links. One
is an “indirect expression”, the other is a “direct expression.”
Using the indirect expression, we can regard the decomposition as the parallelogram law of the Möbius
energy. Furthermore, the cosine formula of the Möbois energy for knots is generalized to decomposedenergies.
It has been known that the first decomposed energy relates to an energy of fractional harmonic maps. We
can see from the direct expression that the second one does to an energy of wave maps. As an application,
we show the existence or non-existence of knots and links which Gauss maps are wave maps.

Final: 2023/2/8
Functional Equations

March 17th (Fri)38

Conference Room IV

9:30–12:00
32 Yohei Sato

(Saitama Univ.)

Even ground state for nonlinear Schrödinger systems with repulsive
interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: It is known that the nonlinear Schrödinger systems with repulsive interaction has no groundstates. Here ground state means a positive solution that attains a minimizing problem on the Nehari set
with two constrains. On the other hand, when the minimizing problem is restricted to even functions, one
calls a positive minimizer as an even ground state. We show the existence of even ground states of nonlinear
Schrödinger systems with repulsive interaction. The keys of the proof are estimates of minimizing level anda classificaton of Palais-Smale sequences of even functions. In particular, the case N = 1 requires moredetailed estimates than N = 2, 3.
33 Hiroyuki Hirayama (Univ. of Miyazaki)
Masahiro Ikeda (RIKEN/Keio Univ.)

Existence and stability of ground states for the system of nonlinear
Schrödinger equations with derivative nonlinearity · · · · · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem of the system of nonlinear Schrödinger equations with derivative
nonlinearlity. The well-posedness of this system in the Sobolev space H 1 is obtained by the previous works.
But the long time behavior of the solution of this system is not well known. In this talk, we prove theexistence of ground state solutions of this system. Furthermore, for 1 dimensional case, we also prove thestability of ground states by using the variational method.
34 Noriyoshi Fukaya (Tokyo Univ. of Sci.)
Masayuki Hayashi(Univ. di Pisa / Waseda Univ.)

Instability of stationary solutions for double power nonlinear Schrödinger
equations in one dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider a double power nonlinear Schrödinger equation in one dimension and L2 -subcriticalsetting. The equation has the algebraically decaying stationary solution ϕ0 as well as exponentially decaying
standing waves eiωt ϕω (x) with positive frequency. It is known from the general theory that the standing wave
with positive frequency is stable if M ′ (ω) > 0 and unstable if M ′ (ω) < 0, where M (ω) := 21 kϕω k2L2 . In thistalk we prove the instability of the stationary solution under the condition M ′ (0) := limω↓0 M ′ (ω) ∈ [−∞, 0).
The key in the proof is the costruction of the one-sided derivative of ω 7→ ϕω at ω = 0, which is effectively
used to construct the unstable direction.
35 Yuji Sagawa (Chiba Inst. of Tech.)Takuya Sato (Tohoku Univ.)
Shota Kawakami (Saitama Univ.)

Finite time blow up solutions to the nonlinear Schrödinger equation
with harmonic potential for arbitrary small initial data · · · · · · · · · · · · · 12

Summary: We construct finite time blow up solutions to the power type nonlinear Schrödinger equation withharmonic potential for arbitrary small initial data in the positive time direction. We simultaneously observethat those solutions exist globally in time and its mass decays in the negative time direction. This part isan improvement of the previous work by Antonelli, Carles and Sparber.
36 Hiroyuki Hirayama (Univ. of Miyazaki)
Shinya Kinoshita (Saitama Univ.)
Mamoru Okamoto (Osaka Univ.)

Well-posedness of the Cauchy problem for the two dimensional quadratic
nonlinear Schrödinger equation with angular regularity · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem for the two dimensional nonlinear Schrödinger equation with thequadratic nonlinearity |u|2 . In the Sobolev space H s (R2 ), it is known that s = − 41 is the threshold for the
Cauchy problem to be well-posed. We prove the well-posedness in H s (R2 ) for − 12 < s < − 41 by assumingsome angular regularity on initial data.

Final: 2023/2/8
39

Functional Equations

37 Shun Tsuhara (Tohoku Univ.) ♭ Global well-posedness for the Sobolev critical nonlinear Schrödinger
Takayoshi Ogawa (Tohoku Univ.) system in four space dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the Cauchy problem of the system of nonlinear Schrödinger equations with cubic
nonlinearity in four space dimensions. We prove the existence of the ground state solution and the global
well-posedness for the system below the ground state solution under the mass resonance condition. We
also show that the ground state solution is written by Aubin–Talenti function. The proof of the gloval
well-posedness result is following the well-known results due to Kenig–Merle (2006).
38 Takuya Sato (Tohoku Univ.) ♭ The initial boundary value problem of nonlinear Schrödinger equations
Nakao Hayashi (Tohoku Univ.) with a nonlinear Neumann boundary condition · · · · · · · · · · · · · · · · · · · · 12
Takayoshi Ogawa (Tohoku Univ.)
Summary: We consider the initial-boundary value problem of the nonlinear Schrödinger equation on the halfline with a nonlinear Neumann boundary condition. After establishing the boundary Srtichartz estimate in
L2 , we consider the time local well-posedness of the problem in the lower regularity spaces as L2 .
39 Yuki Osada (Tokyo Metro. Univ.)

Existence of a minimizer for a nonlinear Schrödinger system with three
wave interaction under non-symmetric potentials · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we show the existence of a minimizer for the L2 -constrained minimization problem
associated with a nonlinear Schrödinger system with three wave interaction without assuming symmetry forpotentials by using interaction estimates.
40 Masahiro Ikeda (RIKEN/Keio Univ.)
Takahisa Inui
(Osaka Univ./Univ. of British Columbia)
Masaru Hamano (Waseda Univ.)(Osaka Univ.)
Ikkei Shimizu

Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the nonlinear Schrödinger equations on the star graph with the Kirchhoff boundary
and the repulsive Dirac delta boundary at the origin. In this talk, we show scattering-blowup dichotomy
result below the mass-energy of the ground state on the real line. The proof of the scattering part is basedon a concentration compactness and rigidity argument. Our main contribution is to give a linear profile
decomposition on the star graph by using a new idea of decomposition of functions on the star graph.
41 Jumpei Kawakami (Kyoto Univ.)

Averaging of strong magnetic nonlinear Schrödinger equations in energy
space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider nonlinear Schrödinger equation with strong magnetic field in 3-dimension. To analyze
this, R L. Frank, F. Méhats, C. Sparber derived two nonlinear Schrödinger type models. One model isderived by spatial scaling and the other model is obtained by averaging the aforesaid spatial scaled modelin time. We study these two models in energy space and obtain global solutions for some cases. We
also prove that the time averaged model is energy-critical when this model has the nonic nonlinear power.
Furthermore, we improve the previous result that the solution to the spatial scaled model converges to thesolution to the time averaged model.
14:15–16:15
42 Kenjiro Ishizuka (Kyoto Univ.)

Long-time asymptotics of the one-dimensional damped nonlinear Klein–
Gordon equation with a potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we consider the one-dimensional nonlinear focusing damped Klein–Gordon equation
with a potential. When a potential is good conditon, it follows from standard arguments that the Cauchy
problem for this equation is locally well-posed in the energy space. When a potential is zero, Cote–Martel–
Yuan (2021) proved the full soliton resolution. Anywaw we consider soliton resolution for this equation.
Especially we will mainly talk the case that a potential is a repulsive delta potential.

Final: 2023/2/8
Functional Equations

43 Satoshi Masaki (Osaka Univ.)
Jun-ichi Segata (Kyushu Univ.)
Kota Uriya (Okayama Univ. of Sci.)40

On classification of cubic nonlinear systems · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we introduce the classification of cubic nonlinear systems. The critical ingredient is
to introduce a matrix representation of a system. It turns out that the rank of the matrix is an invariant
quantity that describes the number of linearly independent conserved quantities. We give a classification ofsystems that have two distinct conserved quantities.
44 Satoshi Masaki (Osaka Univ.) ♭ On classification of complex-valued cubic nonlinear systems · · · · · · · · · 12
Summary: In this talk, we introduce the classification of complex-valued gauge-invariant cubic systems. The
critical ingredient is the matrix-vector representation of a system. This clarifies the effect of the changeof variables and describes the systems’ Hamiltonian structure. In particular, the rank of the matrix part
denotes the number of the conserved quantities, and hence reflects the system’s complexity. We show theclassification of systems that have only one conserved quantity.
45 Kimitoshi Tsutaya (Hirosaki Univ.) ♭ Blow up of solutions of semilinear wave equations with time-dependent
Yuta Wakasugi (Hiroshima Univ.) damping · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the Cauchy problem for nonlinear wave equations with time-dependent damping.
We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as
upper bounds of the lifespan of blow-up solutions. We also show the same results for the space derivative
nonlinear term.
46 Ikki Fukuda (Shinshu Univ.)
Hiroyuki Hirayama (Univ. of Miyazaki)

Large time behavior and optimal decay estimate for solutions to the
Cauchy problem for the generalized KP–Burgers equation in 2D · · · · · 10

Summary: In this talk, we consider the Cauchy problem for the generalized KP–Burgers equation in 2D. Thisis one of the nonlinear dispersive-dissipative type equations, which has a spatial anisotropic dissipative term.
Under some suitable regularity assumptions on the initial data u0 , especially the condition ∂x−1 u0 ∈ L1 (R2 ),it is known that the solution to this problem decays at the rate of t− 4 in the L∞ -sense. In this study, we7

investigate the more detailed large time behavior of the solution and construct the approximate formula forthe solution at t → ∞. Moreover, we obtain a lower bound of the L∞ -norm of the solution and prove thatthe decay rate t− 4 of the solution given in the previous work to be optimal.
7

47 Slim Ibrahim (Univ. of Victoria)(Osaka Univ.)
Ikkei Shimizu

Phase transition threshold and stability of magnetic skyrmions · · · · · · 12

Summary: We examine the stability of vortex-like configuration of magnetization in magnetic materials,
so-called the magnetic skyrmion. These correspond to critical points of the Landau–Lifshitz energy with
the Dzyaloshinskii–Moriya interactions. In this talk, we prove that there is an explicit critical value of theparameter in the energy above which the skyrmion is unstable, while stable below this threshold. This
mathematically explains the occurrence of phase transition observed in some experiments. We also showthat in the unstable regime, the infimum of energy is not bounded below.
48 Masashi Ohnawa(Tokyo Univ. of Marine Sci. and Tech.)
Masahiro Suzuki (Nagoya Inst. of Tech.)On the shallow water systems under periodic boundary conditions · · · 12

Summary: We consider stationary flows over periodic topography modeled by one-dimensional shallow waterequation. We first show the nonexistence of stationary solutions with discontinuities as well as the conditions
on the existence of continuous subsonic/supersonic stationary solutions. We also claim that the subsonicstationary solutions are not asymptotically stable.

Final: 2023/2/8
41Functional Equations

49 Takashi Furuya (Shimane Univ.)

Inverse medium scattering problems with Kalman filter techniques · · · 10

Summary: We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous
medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed
and nonlinear, and the iterative optimization method is often adapted. A natural iterative approach tothis problem is to place all available measurements and mappings into one long vector and mapping,respectively, and to iteratively solve the linearized large system equation. However, this is computationallyexpensive because we must construct the larger system equations when the number of available measurements
increases. In this talk, we propose the reconstruction algorithm based on the Kalman filter, which avoids
the construction of a large system equation and retains the information of past updates.
16:30–17:30

Talk Invited by Functional Equations Section
Naoyasu Kita (Kumamoto Univ.) ♭ On behaviors of solutions to nonlinear Schrödinger equations with complex coefficient in its nonlinearity

Summary: We consider the Cauchy problem of nonlinear Schrodinger equations. Unlike the conservative
system, the equation contains a complex coefficient in its nonlinearity. The physical background of sucha non-conservative system is coming from the optical fiber engineering, where nonlinear Ohm’s law andnonlinear amplification are applied. My talk consists of two parts. The first part treats a problem ofglobal existence and asymptotic behavior of solutions without size restriction on the initial data, where
Hayashi–Naumkin’s theory basically contributes to the result. The second part treats a construction of
blowing-up solutions. Combining the former result on asymptotic behavior of solutions, we can obtainblowing-up solutions even for small initial data. Recently, the result on the blowing-up solutions has been
generalized by Cazenave–Martel–Zhao, Cazenave–Han–Martel and Kawakami–Machihara. If time permits,these recent progresses will be also presented.

March 18th (Sat)

Conference Room IV

9:30–12:00
50 Naoyuki Iwata (Nagoya Inst. of Tech.)
Masahiro Suzuki (Nagoya Inst. of Tech.)

Stationary solutions of the Vlasov–Poisson system for a multicomponent
plasma · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we mathematically investigate the formation of a plasma sheath, and analyze theBohm criterion which is required for the formation. In 1995, Riemann derived the Bohm criterion fromthe stationary Vlasov–Poisson system which describes the motion of a multicomponent plasma. We study
the solvability of boundary value problems of the system, and show that the Bohm criterion is a necessary
condition but not a sufficient condition for the solvability.
51 Masahiro Suzuki (Nagoya Inst. of Tech.)
Masahiro Takayama (Keio Univ.)
Katherine Zhiyuan Zhang(New York Univ.)

Stability and instability of stationary solutions of the Vlasov–Poisson
system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov–Poisson system on a half-line with the completely absorbing boundary condition. The solvability of thestationary problem has been established. In this talk, we study the nonlinear stability and instability ofthese stationary solutions of the Vlasov–Poisson system.
52 Taichi Eguchi (Waseda Univ.)

Energy equality of MHD system under a weaker condition on magnetic
field · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We prove the energy equality of MHD system in the space founded by Cheskidov–Constantin
Friedlander–Shvydkoy (2008) and Berselli–Chiodaroli (2020). It is clarified that the energy equality isestablished for a lager class of the magnetic filed than that of velocity field. Our result covers most ofprevious theorems on validity of the energy equality on the Navier–Stokes equations.

Final: 2023/2/8
Functional Equations

42

53 Ryosuke Nakasato (Waseda Univ.) ♭ Asymptotic stability for quasi-linear plasma models with Hall effects
via energy methods on Fourier–Herz spaces · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the initial-value problem for the compressible Hall-magnetohydrodynamic systemwith quantum effects in the 3-dimensional Euclidean space R3 . The aim of this talk is to obtain timedecay estimates for solutions as a perturbation from a constant equilibrium state (1, 0, B̄) in a critical Lp
framework. Here B̄ ∈ R3 is denoted by constant magnetic fields. To obtain such a result, we establish energyb p introduced by Grünrock (2004). By combining L
b p energy methods andmethods on Fourier–Herz spaces L
b p -Lb p/2 typea transformation of the momentum equation given by the effective velocity, we will derive the L
time-decay estimate without the smallness requirement of low frequencies for initial data.
54 Sonae Hadama (Kyoto Univ.)

Stability of Fermi gas at zero temperature for the Hartree equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Hartree equation describing the time evolution of wave functions of infinitely
many fermions interacting with each other. The Hartree equation can be formulated in terms of theoperators on L2 (Rd ). It has infinitely many stationary solutions, and several authors have studied theirstability, for example, Lewin–Sabin(2014), Chen–Hong–Pavloić(2018), and Collot–de Suzzoni(2020, 2022).
However, the stability of Fermi gas at zero temperature, one of the most important stationary solutions
from the physics point of view, was left open. In this talk, we report that it is stable; that is, any small
perturbation from Fermi gas at zero temperature scatters.
55 Hajime Koba

(Osaka Univ.)

Mathematical modeling of inviscid multiphase flow system with surface
flow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the governing equations for the motion of the inviscid fluids in moving domains andsurface from an energetic point of view. We employ an energetic variational approach to derive multiphaseflow system with surface flow and tension. We make use of the feature of the barotropic fluid to derive thesurface pressure and tension of the compressible fluid in the surface.
56 Hajime Koba

(Osaka Univ.)

Mathematical modeling of inviscid multiphase flow system with phasetransition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the governing equations for the motion of the fluid particles near air-water interface
from an energetic point of view. We employ an energetic variational approach to derive inviscid multiphaseflow system with phase transition, where a phase transition means a jump condition. We apply our energetic
variational approach and jump condition to study the dominant equations for the densities of the fluids inmoving domains.
57 Ken Furukawa(RIKEN)

Data assimilation of the primitive equations in maximal Lp -Lq settings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We discuss about data assimilation to the primitive equations in maximal Lp -Lq settings in amathematically rigorous way. The primitive equations describe the flow in a thin domain. The equations
combined with some data assimilation methods are used in meteorology and ocean physics for predictions
for phenomena. Our results are that the solution to data assimilation equations of the primitive equations
converges to the solution to the primitive equations in maximal Lp -Lq spaces at t → ∞.
58 Kei Noda

(Kyoto Univ.)

Analyticity in space-time of solutions to evolution equations with multilinear operator based on maximal regularity · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this presentation, we introduce a method to prove space-time analyticity for evolution equations
with nonlinear terms represented by multilinear operators via the parameter trick. By extending the caseof bilinear operators in the previous work, this method is expected to be applicable not only to theNavier–Stokes equations but also to the equations of Fujita type.

Final: 2023/2/8
43Functional Equations

59 Yoshiki Iida

(Waseda Univ.)

Energy equality for the 3D inhomogeneous Navier–Stokes equations inLorentz–Besov spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We establish the energy equality for Leray–Hopf weak solutions of the 3D incompressible inhomogeneous Navier–Stokes equations in Lorentz–Besov spaces. This result may be regarded as an extensionof that by Cheskidov and Luo (2020).
14:15–16:15
60 Motofumi Aoki (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

On the ill-posedness for the full system of the compressible Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem for the equations of the ideal gas in the three space dimensions.
In the critical Besov spaces, it is known that the Cauchy problem is uniquely solvable for all 1 < p < 3 andill-posed for all p > 3. We study the threshold case p = 3. We prove that the Cauchy problem is ill-posedby constructing a sequence of the initial data such that the solution map is discontinuous.
61 Dáithı́ Ó hAodha (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

Optimality of the decay estimate of solutions to the linearised curl-freecompressible Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov
norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations,in the homogeneous case. We prove that our estimate is optimal in the L∞ -norm by showing that the norm
is bounded from below by the same decay rate. This is the first time such a bound from below has beenobtained for the compressible Navier–Stokes equation.
62 Takahiro Okabe (Osaka Univ.)
Lorenzo Brandolese (Univ. Lyon 1)

Forced rapidly dissipative Navier–Stokes flows · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the asymptotic behavior of the solution to the incompressible Navier–Stokes equationon the whole space. By an action of a forcing term we control the nonlinear term of the flow and derive a
rapid time decay. This talk is based on the joint work with Lorenzo Brandolese (Univ. Lyon 1).
63 Tomoyuki Nakatsuka(Matsuyama Univ.)

On solvability of the time-periodic problem for the Navier–Stokes equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we consider the existence of time-periodic solutions to the Navier–Stokes equation in
the whole space. We decompose periodic solutions into steady and purely periodic parts, and we analyze
the equations they should satisfy. Based on the analysis of the purely periodic solutions represented by
the Fourier transform to the Stokes equation, their additional property can be obtained and we use it toconstruct a time-periodic solution of the Navier–Stokes equation.
64 Yuta Koizumi (Waseda Univ.)
Toya Taniguchi (Waseda Univ.)

Convergence of approximating solutions of the Navier–Stokes equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

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 2,n (Rn ) provided the convergence in the scaling invariant norm in Lp (Rn ) with the time weight holds.
65 Hiroki Ohyama (Kyushu Univ.)
Keiji Yoneda (Kyushu Univ.)

Fast rotation limit for the magnetohydrodynamics equations in a 3D
layer · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial value problem for the incompressible magnetohydrodynamics systemwith the Coriolis force in a three-dimensional infinite layer.

We prove the unique existence of global

solutions for initial data in the scaling invariant space when the speed of rotation is sufficiently high.
Moreover, we show that the global solution converges to that of the coupled system of the 2D incompressible
magnetohydrodynamics equations and the 3D incompressible Maxwell equations as the rotation speed tends
to infinity.

Final: 2023/2/8
Functional Equations

66 Takanari Egashira (Kyushu Univ.)
Ryo Takada (Univ. of Tokyo)

44

Large time behavior of solutions to the 3D rotating Navier–Stokes
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the large time behavior of the solutions for the initial value problem of the Navier–Stokes equations with the Coriolis force in the three-dimensional whole space. We show the temporal decay
estimates with the dispersion effect of the Coriolis force for the global solutions. Moreover, we prove thelarge time asymptotic expansion of the solutions behaving like the first-order spatial derivatives of theintegral kernel of the corresponding linear solution.
67 Mikihiro Fujii (Kyushu Univ.)

Global strong solutions to the compressible Navier–Stokes equation with
the Coriolis force · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we consider the global solvability for the compressible Navier–Stokes equation with
the Coriolis force in the scaling critical Besov space. Despite many studies on the weak solutions, theexistence of global strong solutions has been an open problem. Unlike the incompressible case, the Coriolis
force causes the linear solutions to behave like a semigroup {e−t∆ }t>0 , which creates difficulties in nonlinear2

estimates in the low frequency part. In this research, we propose a new idea of the low frequency analysis
and overcome these difficulties.
68 Hirokazu Saito(Univ. of Electro-Comm.)

On decay properties of solutions to the two-phase Stokes equations withsurface tension and gravity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

N
Summary: In this talk, we consider the two-phase Stokes equations with surface tension in ṘN = RN
+ ∪ R−and in the presence of a uniform gravitational field acting vertically downward. Let ρ± be positive constants
describing the densities of fluids occupying RN± . It is well-known that the Rayleigh-Taylor instability occurs
when the upper fluid is heavier than the lower one, i.e., when ρ+ > ρ− . On the other hand, this talk aims
to introduce time decay estimates of solutions to the two-phase Stokes equations under the condition thatthe lower fluid is heavier than the upper one, i.e., ρ− > ρ+ .
16:30–17:30

Talk Invited by Functional Equations Section

Youhei Tsutsui (Kyoto Univ.) ♭ Convergence to the initial data and weighted estimates for the incompressible Navier–Stokes equations
Summary: We discuss conditions on data for which ensure the solution to the incompressible Navier–Stokes
equations strongly converges to the initial data from weak Ln space on the whole space. We also consider
weighted estimates for the solutions.

Final: 2023/2/8
45

Real Analysis

Real Analysis
March 17th (Fri)

Conference Room V

9:00–11:45
1 Masashi Toyoda (Toho Univ.)

Fixed point theorem in a ball space and Caristi fixed point theorem· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The purpose of this talk is to introduce a fixed point theorem in a ball space, which is proved
without the Axiom of Choice. Moreover, using the fixed point theorem in a ball space, we prove Caristi’s
fixed point theorem. Therefore the proof of Caristi’s fixed point theorem in this paper does not depend on
the Axiom of Choice.
2 Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Convergence theorems for families of monotone nonexpansive mappingsin orderd Banach spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we prove weak and strong convergence theorems for monotone nonexpansive mappingsand convergence theorems for monotone nonexpansive semigroups in Banach spaces endowed with a partial
order.
3 Yasunori Kimura (Toho Univ.)

Approximation of common fixed points by modified shrinking projection
methods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This study deals with the approximation of fixed points for nonexpansive and other types ofmappings. Using a modified shrinking projection method, we obtain the delta-convergence of generated
approximation sequence to a fixed point of the mapping. We also consider a family of mappings and show
a convergence theorem to their common fixed point.
4 Koji Aoyama(Chiba Univ.)

Mean convergence theorems with respect to attractive points in a
Hilbert space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show a mean convergence theorem for a mapping with an attractive point in a Hilbert
space by using a quasinonexpansive extension of the mapping and a mean convergence theorem for aquasinonexpansive mapping. Then using the theorem, we establish a mean convergence theorem for a
λ-hybrid mapping in the sense of Aoyama, Iemoto, Kohosaka, and Takahashi (2010).
5 Naoya Hatano(Chuo Univ.)

Proper embedding for Morrey–Lorentz spaces · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The embeddings for Morrey–Lorentz spaces have been previously introduced by Ragusa. This
paper describes the major differences between these embedding types.
6 Denny Ivanal Hakim(Bandung Inst. of Tech.)(Chuo Univ.)
Naoya Hatano
Toru Nogayama (Chuo Univ.)
Yoshihiro Sawano (Chuo Univ.)

Bourgain–Morrey spaces and its applications · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce the Bourgain–Morrey space which is a one generalization of Morrey
spaces. By using this space, it is showed that we can refine the Strichartz estimate for Schrödinger equations.
We consider some properties of this space from the viewpoints of harmonic analysis and functional analysis.
7 Toru Nogayama (Chuo Univ.)

Complex interpolation for mixed Morrey spaces · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the complex interpolation for mixed Morrey spaces via the Calderónproduct. The mixed Morrey space Mpq⃗ (Rn ) is a function space which is a generalization of Morrey spaces.
The results in this talk are extensions for classical Morrey spaces.

Final: 2023/2/8
Real Analysis

8 Koichi Taniguchi (Tohoku Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)(Ehime Univ.)
Isao Ishikawa

46

Boundedness of composition operators on Besov spaces · · · · · · · · · · · · · 15s
Summary: In this talk we consider boundedness of composition operators on Besov spaces Bp,qon onedimensional Euclidean space. The boundedness has been well studied in the lower derivative case 0 < s < 1.

In contrast, there is almost no research on the higher order case s ≥ 1, and many problems remain unsolved.
The purpose of this talk is to give necessary and sufficient conditions for the boundedness when s > 1 + 1/p.
Similar results for composition operators on Triebel–Lizorkin spaces are provided.
9 Takanobu Hara (Hokkaido Univ.)

Strong barriers for weighted quasilinear equations · · · · · · · · · · · · · · · · · · 15

Summary: We construct strong barriers for weighted quasilinear elliptic equations. There are two applications: (i) solvability of Poisson-type equations with boundary singular data, and (ii) a geometric version of
Hardy inequality.
14:15–15:25
10 Toshiharu Kawasaki(Tamagawa Univ./Chiba Univ./Chiba Univ.)

On the difference between the families of extended integrable functions
and extended primitive functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss the difference between the families of extended integrable functions andextended primitive functions.
On topologically invariant means and almost convergence · · · · · · · · · · · 15

11 Ryoichi Kunisada

Summary: In this talk, we discuss applications of topologically invariant means and almost convergence forthe theory of analytic functions on the half plane.
(Tokyo Tech)
12 Takumi Terae
Toshiaki Murofushi (Tokyo Tech)

An equality condition for supremum increments of distorted measuresin non-additive measure theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In non-additive measure theory, there exist two definitions of null sets, which are weak null sets
and strong null sets. Several theorems in measure theory such as the Egoroff theorem and the Lebesgue
theorem are described by using the concept of null sets, therefore there exist weak forms and strong formsof these theorems as definitions in non-additive measure theory. The concept of supremum increment
is important for studying about the strong forms of them. This paper has an argument that gives anecessary and sufficient condition for two different distorted measures having an equal supremum increment
for a simple case. In addition, we define the concept of strong supremum increments in preparation forgeneralizing this argument.
13 Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)(Oita Univ.)
Ryoji Fukuda
Aoi Honda (Kyushu Inst. of Tech.)Fréchet–Nikodym uniformity on a ring determined by a non-additive
measure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Fréchet–Nikodym difference on a measure ring R determined by a non-additive measure µ is
defined by µ(AB).

We prove that if µ is quasi-monotone and satisfies (p.g.p)-condition, then theentourages {(A, B) | µ(Aring R.

B) ≤ ϵ}, ϵ > 0 is a basis of entourages of a uniform structure on the measureFinal: 2023/2/8
47

Real Analysis

15:40–16:40

Award Lecture for the 2022 MSJ Analysis Prize

Eiichi Nakai(Ibaraki Univ.)

Generalized Campanato spaces with variable growth condition andrelated topics

Summary: Generalized Campanato spaces with variable growth condition were introduced by Nakai andYabuta in 1985 to characterize the space of pointwise multipliers on BMO(Rn ). This characterization was
extended from Rn to spaces of homogeneous type in 1997, to probability spaces with filtration in 2014,
and, to Rn with non-doubling measures in 2018. On the other hand, this characterization was used by
Lerner in 2005 to study the class P(Rn ) of functions p(·) for which the Hardy-Littlewood maximal operator
is bounded on the Lebesgue spaces Lp(·) (Rn ) with variable exponent, and positively solve a conjecture of
Deining in 2005 saying that there are discontinuous functions belonging to P(Rn ). Moreover, in 2012 it was
discovered by Nakai and Sawano that the dual of generalized Hardy space H p(·) (Rn ) with variable exponent
is a generalized Campanato space with variable growth condition. In this talk we discuss generalizedCampanato spaces with variable growth condition and related topics.
17:00–18:00

Talk Invited by Real Analysis Section

Hitoshi Tanaka(Tsukuba Univ. of Tech.)Dyadic cubes analysis, dyadic rectangles analysis

Summary: After reviewing a history of the dyadic cubes analysis, with rectangular doubling weight, ageneralized Hardy–Littlewood–Sobolev inequality for rectangular fractional integral operators is verified.
The result is a nice application of M -linear embedding theorem for dyadic ractangles.

March 18th (Sat)

Conference Room V

9:00–12:00(Tohoku Univ.)
14 Goro Akagi
Yoshihito Nakajima (Tohoku Univ.)

Solvability of evolution equations involving time-fractional derivatives
and applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is concerned with local and global in time solvability of abstract evolution equations
involving time-fractional derivatives as well as subdifferential operators. An application to the initialboundary value problem for degenerate parabolic equations involving time-fractional derivatives as well as
blow-up nonlinearity will also be discussed.
15 Kosuke Kita (Waseda Univ.)Ôtani Mitsuharu (Waseda Univ.)

Mosco convergence of functionals associated with Laplacian under nonlinear boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is devoted to studying the convergence of functionals associated with Laplacian under
nonlinear boundary conditions and the asymptotic behavior of solutions to nonlinear evolution equations
governed by subdifferential operators of the functionals. To be more precise, we show the continuous
dependence of the solution on the power of the nonlinear term of boundary conditions. The proof is basedon some modifications of the argument of Mosco convergence by Attouch.

Final: 2023/2/8
Real Analysis

16 Takanori Kuroda (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

48

Asymptotic behaviors of complex solutions for the semilinear heat equation with arbitrarily large initial energy · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the semilinear heat equation (P):ut − ∆u − |u|q−2 u = 0,u(0) = u0

and the semilinear elliptic equation (E), which corresponds to the stationary problem of (P):−∆u − |u|q−2 u = 0,
with the hohogeneous Dirichlet boundary condition in bounded domains Ω ⊂ RN , (N ≥ 3) which areradially symmetric with respect to the first two variables. We seek solutions which takes complex values ofthe following form:uk (x1 , x2 , x̃) = eikθ vk (r, x̃),

(x1 , x2 , x̃) = (r cos θ, r sin θ, x̃) ∈ Ω,k ∈ N.

We show the energy of solutions uk of (E) tends to infinity as k → ∞. Making use of this fact, for initial
data of arbitrarily large energy, we construct two kinds of sets, i.e., stable set W and blow-up set V suchthat if u0 ∈ W (resp. u0 ∈ V ), then u can be continued globally up to (0, ∞) (resp. u blows up in finitetime).
17 Shohei Kohatsu (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Behavior of weak solutions to a Keller–Segel system with gradientdependent chemotactic coefficient · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider behavior of weak solutions to a Keller–Segel system with gradient dependent chemotactic coefficient:u = ∆u − χ∇ · (u|∇v|p−2 ∇v),tv = ∆v − v + u,twhere χ > 0, p ∈ (1, ∞).
18 Yutaro Chiyo (Tokyo Univ. of Sci.)

Boundedness and stabilization in a quasilinear attraction-repulsion
chemotaxis system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with a quasilinear parabolic–parabolic–elliptic attraction-repulsion chemotaxis
system. In the case that the second equation is simplified by the elliptic one, boundedness and stabilization
have already been obtained. The purpose of this talk is to derive boundedness and stabilization in the casethat the second equation is parabolic.
19 Tobias Black (Paderborn Univ.)
Mario Fuest (Leibniz Univ. Hannover)
Johannes Lankeit(Leibniz Univ. Hannover)
Masaaki Mizukami(Kyoto Univ. of Edu.)

Possible points of blow-up in a chemotaxis system with environmental
dependent logistic source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the influence of possible spatial inhomogeneities in the coeffcients of logistic source
terms in parabolic–elliptic chemotaxis-growth systems in two-dimensional smoothly bounded domains.
Assuming that the coeffcient functions is nonnegative, we prove that finite-time blow-up of the classicalsolution can only occur in points where the coefficient function is zero.

Final: 2023/2/8
49

Real Analysis

20 Yoshiho Akagawa(Gifu Nat. Coll. of Tech.)(Kochi Univ.)
Risei Kano
Takeshi Fukao (Kyoto Univ. of Edu.)

A quasi-variational inequality in plasticity model · · · · · · · · · · · · · · · · · · · 15

Summary: This paper discusses the a quasi-variational inequality in plasticity model. In phys- ical terms, it isnatural that the threshold function depends on some unknown variable. This model is expected to describe
plastic deformation due to the time-nonlocal depen- dence of the constraint on the unknown function. Thisis a difference from the perfect plasticity model. To prove the existence of a solution of the plastity model,
Banach fixed point theorem is applied, taking care to choose the test function.
21 Akiko Morimura(Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

On existence and uniqueness of solutions to the moisture transportmodel in porous materials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial-boundary value problems for nonlinear parabolic equations describing
moisture transport in a porous material occupying a one-dimensional interval. Our problem is obtained bysimplification of the model proposed by Green, Dabiri and Weinaug. Precisely, their system consists of two
equations corresponding to conservation law for water in air and liquid regions, and in our problem thewater distribution in air is given. The unknown function of the problem indicates the chemical potential ofwater. Also, we approximate the equation which is type of elliptic-parabolic, originally, as a first step inthis research. The aim of this talk is to establish existence and uniqueness of solutions to the approximate
problem by applying the standard fixed-point argument.
22 Chiharu Kosugi (Japan Women’s Univ.)
Toyohiko Aiki (Japan Women’s Univ.)

Omega-limit sets for the strong solutions to initial and boundary value
problems for compressible elastic curves · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We talk about omega-limit sets for strong solutions to the initial and boundary value problem forthe beam equation with the viscosity term and the nonlinear stress function having a singularity. Thanks
to the singularity, we obtained the uniform estimate of lower bounds for the strain, and already proved
existence and uniqueness of weak and strong solutions. By effect of the viscosity, it seems to be natural thatthe solution converges to the stationary solution. On this conjecture we show existence of a subsequenceof the orbit {u(t)|t ≥ 0} such that it converges to a strong solution to the steady problem. We note thatsimilar result on the weak solutions was reported at the previous meeting.
23 Kota Kumazaki (Nagasaki Univ.)
Adrian Muntean (Karlstads Univ.)

A multiscale model describing the wetting-drying phenomenon in porous
materials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we propose a multiscale model describing the wetting-drying phenomenon in porous
materials. This model consists of a diffusion equation for the relative humidity distributed in materials
and a free boundary problem describing the wetting-drying process in microscopic pores. We consider
each microscopic pore as a one-dimensional interval and correspond the interval to each point of materials.
In our previous results, for a given relative humidity we showed the well-posedness of the free boundary
problem. In this talk, we impose a governing equation for the relative humidity and discuss the existence
and uniqueness of a locally-in-time solution of this model.

Final: 2023/2/8
Real Analysis

50

14:15–16:30(Chiba Univ.)
24 Daiki Mizuno
Ken Shirakawa (Chiba Univ.)

Well-posedness and regularity results for a class of total variation flows
of pseudo-parabolic types · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, a class of initial-boundary value problems of total variation flows of pseudo-parabolic
types is considered. Total variation flow has been adopted as governing equation of various nonlinear
phenomena, such as grain boundary motion, image denoising, and so on. The principal characteristic of
our problem is in the velocity term of diffusion flux, and the velocity would bring stronger regularity thatthat as in standard parabolic PDE. Meanwhile, our total variation flow contains singular diffusion, andthe singularity would degenerate the regularity of solution. The objective of this paper will be to clarify
the power balance between these conflicted effects. Consequently, the mathematical results concerned withwell-posedness and regularity of solution will be discussed in the Main Theorems of this talk.
25 Shodai Kubota (Kanagawa Univ.)

Periodic solutions for Warren– Kobayashi–Lobkovsky–Carter type systems of grain boundary motions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider teh periodic solutions for the parabolic PDE systems denoted by (S).
Each system (S) is associated with the phase field model of grain boundary motion, proposed by [Warren,
et al.; Acta Materialia, 51(20): 6035–6058, 2003]. Under suitable assumptions, the existence of the periodic
solution to the system (S) will be reported as the main theorem of this talk.
26 Hiroshi Watanabe (Oita Univ.)
Ken Shirakawa (Chiba Univ.)
Salvador Moll (Univ. València)

Existence of solutions to a phase-field model of 3D-grain boundary
motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a phase-field model of 3D-grain boundary motion. The model is based on the three
dimensional Kobayashi–Warren model for the dynamics of polycrystals. To formulate our 3D-model, we
use a quaternion formulation for the orientation variable. In this talk, we obtain existence of solutions
to the L2 -gradient descent flow of the constrained energy functional via several approximating problems.
Moreover, we also obtain an invariance principle for the orientation variable.
27 Takeshi Fukao (Kyoto Univ. of Edu.)
Pierluigi Colli (Univ. of Pavia)
Luca Scarpa (Politecnico di Milano)

The Cahn–Hilliard system of LW model with forward-backward dynamic boundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For Cahn–Hilliard equations with forward-backward dynamical boundary conditions, we consider
the vanishing viscosity approach from LW model. In the previous study, the approach from GMS model
was discussed. The same idea is used for the LW model. Since the regularity of the solution is lowered in
the limit equations, we define a weak solution using the subdifferential with suitable function spaces. In the
LW model unlike the GMS model, it is subject to the mass conservations at the bulk and the boundary,respectively, which makes some difficulty. In this talk, we will especially introduce the idea of the uniform
estimate.
28 Noriaki Yamazaki (Kanagawa Univ.)
Nobuyuki Kenmochi (Chiba Univ.⋆)
Ken Shirakawa (Chiba Univ.)

Approximation of singular optimal control problems for doubly quasivariational evolution inclusions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we establish an approximate procedure for singular optimal control problems for
abstract doubly quasi-variational evolution inclusions governed by time-dependent subdifferentials withthe unknown-dependent constraints. Indeed, we consider the parameter-dependent state inclusion and its
control problems. Then, we show the relationship between the original control problem and its approximateone.

Final: 2023/2/8
51

Real Analysis

29 Akio Ito

Tumor invasion model with quasi-variational structural porous medium
diffusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider an initial-boundary value problem of a tumor invasion of Chaplain–Anderson type, inwhich the coefficient of random motility of tumor cells depends on the extracellular matrix and the diffusion
flux of tumor cells is porous medium type whose power depends upon the extracellular matrix. Form thesepoints of view, the Cauchy problem considered in this talk has a quasi-variational structure and this fact
makes it more difficult and complicate to analyze this model mathematically. The aim of this talk, we givethe global existence of strong solutions by using the general theory, which was established in the paper,
Evolution inclusion on a real Hilbert space with quasi-variational structure for inner products, Journal ofConvex Analysis, 26 (2019), No. 4, 1185–1252.
30 Toshitaka Matsumoto (Shizuoka Univ.)
Naoki Tanaka (Shizuoka Univ.)

Generation of evolution operators under a generalized stability condition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A generation theorem of a linear evolution operator on a Banach spaces is given under a generalizedstability condition for a difference scheme. The denseness and the time-independence of the domains ofgenerators are not assumed. A differentiablity theorem of an evolution operator is also given.
17:00–18:00

Talk Invited by Real Analysis Section

Shunsuke Kurima (Tokyo Univ. of Sci.)

Time discretization methods for phase field systems

Summary: The speaker has studied approaches by time discretization to a phase field system of Caginalp
type and a singular phase field system of conserved type with Pierluigi Colli. The time discretization method
is a method of capturing the derivative with respect to time with the limit of the difference quotient, andit has the advantage that evolution equations can be reduced to stationary problems of elliptic equations.
In this talk, for phase field systems with inertial term which has already been proved to have solutions,
we will confirm if we can apply time discretization methods to show existence of solutions and derive error
estimates for the time step. Also, in this talk, for singular nonlocal phase field systems with inertial term
which has not yet been proved to have solutions, we will show existence of solutions by time discretization
methods.

Final: 2023/2/8
Functional Analysis

52

Functional Analysis
March 15th (Wed)Conference Room VI

9:30–12:00
1 Yoritaka Iwata (Kansai Univ.)

Generalization of von Neumann equation based on the logarithmic
representation of unbounded operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, by replacing the commutator product by the logarithmic representation of unbounded operators [1-9], the generalized/unbounded version of von Neumann equation is presented. The
proposed equation is general enough to be valid to bounded situations (i.e., classical mechanics). By taking
some concrete examples in the quantum mechanics, the derivation of generalized von Neumann equation is
explained.
2 Shuji Watanabe (Gunma Univ.)

A new operator-theoretical treatment of the BCS gap equation of superconductivity and its application to the second-order phase transition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a new operator-theoretical proof of the existence, uniqueness and smoothness of thesolution to the BCS-Bogoliubov gap equation of superconductivity and apply the results to the second-orderphase transition.
3 Takashi Aoki (Kindai Univ.⋆)
Ryuichi Ishimura (Chiba Univ.⋆)
Yasunori Okada (Chiba Univ.)

Differential operator representations of continuous homomorphisms onsome spaces of entire functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The space of entire functions at most of a given order and of normal type (resp. minimal type)is endowed with a locally convex topology as an inductive limit (resp. projective limit) of Banach spaces.
Continuous endomorphisms of such spaces include differential operators, translations, dilations, etc., andthey can be represented as formal differential operators of infinite order satisfying suitable conditions. We
consider continuous homomorphisms between spaces of entire functions with growth given by proximate
orders instead of orders, and give their differential operator representations. We also reveal the merits oftreating proximate orders and homomorphisms from the view point of inductive and projective descriptions.
4 Fumio Hiroshima (Kyushu Univ.)

Positivity improving for the translation invariant Nelson model · · · · · · 15

Summary: Let H(P) be the renormalized Nelson Hamiltonian with total momentum P. We show thatexp(-TH(P)) is positivity improving for any P.
5 Itaru Sasaki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Shinnosuke Izumi (Shinshu Univ.)
Kota Imura(Nagano Pref. Fujimi High School)

Analyticity of the ground state for the pair interaction model · · · · · · · · 15

Summary: We consider the pair interaction model which is a models in the quantum field theory. In ourprevious work, we diagonalize its Hamiltonian by a Bogoliubov transformation. As a consequence, theexistence and uniqueness of the ground states are proven. In addition, the explicit formula for the groundstate energy has been given. In this talk, we show that the ground state and the ground state energy are
analytic in the coupling constant. Their radii of convergence are always finite.

Final: 2023/2/8
53

Functional Analysis

6 Naoya Yoshida (Ritsumeikan Univ.)

Bohr–Sommerfeld quantization condition for self-adjoint Dirac operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the eigenvalue problem for self-adjoint Dirac operators. It is known that, near anenergy level where the square of the potential makes a simple well, the eigenvalues are approximated by a
Bohr–Sommerfeld type quantization rule. A remarkable difference from the Schroedinger case appears in
the Maslov correction term. This fact was recently found by Hirota (2017) under the analyticity conditionof the potential using a complex WKB method. In this talk, we approach this problem with a microlocal
technique focusing on the asymptotic behavior of the eigenfunction along the characteristic set to generalize
the result to smooth potentials.
7 Kyohei Itakura (Univ. of Tokyo)

On resonances for inverted harmonic oscillators · · · · · · · · · · · · · · · · · · · · 15

Summary: We characterize resonance free domain for semiclassical inverted harmonic oscillators by employing
method of Briet–Combes–Duclos. For fixed non-zero energy E, we assume a certain non-trapping condition;
the whole domain can be split into the classically forbidden region and region where virial is bounded bynegative constant from above. Then we obtain the absence of resonances in a complex neighborhood of E.
8 Kota Ujino(Kyushu Univ.)

Exact Hausdorff dimension of the spectral measure for the graph Laplacian on a sparse tree · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that Schroedinger operators with sparse potentials have singular continuous spectrum.
The graph Laplacian on a sparse tree is identified with one-dimensional discrete Schroedinger operators, andhas singular continuous spectrum. The intermittency function describes the behavior of the time averaged
momentum and gives the upper bound of the Hausdorff dimension of the spectral measure. We show theintermittency function explicitly and give the Hausdorff dimension of the spectral measure for the graphLaplacian on a sparse tree.
9 Kota Ujino(Kyushu Univ.)

No eigenvectors embedded in the singular continuous spectrum ofSchrödinger operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that the spectrum of Schrödinger operators with sparse potentials consists of singular
continuous spectrum. We give a sufficient condition so that the edge of the singular continuous spectrum
is not an eigenvalue and construct examples with singular continuous spectrum which have no eigenvalues
and which have a single negative eigenvalue.
14:15–16:15
10 Hiroki Yagisita (Kyoto Sangyo Univ.) ♭ Variational formulation and self-adjointness of Laplace operator in infinite dimensional space R∞ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In a variational method like Lax–Milgram theorem, we define Laplacian on the infinite directQ
product space R∞ := n∈N R and show that it is a self-adjoint operator. Here, the most important thingis to define Hilbert space that corresponds to Sobolev space H 1 (R∞ ). To do it, we use square root of
density introduced by Hormander in context of Fourier integral operator theory. However, here, we use
a measure-theoretic method rather than a geometric method to give a very elementary introduction atleast for analyst (inspired by statistical interpretation of quantum mechanical wave function by Born and
Heisenberg) of square root of density. All in all, only basic knowledge of analysis (as it is quite possible tostudy undergraduate) is required.

Final: 2023/2/8
Functional Analysis

54

11 Hiroki Yagisita (Kyoto Sangyo Univ.) ♭ Analytic semigroup of infinite dimensional interacting Brownian motion
on R∞ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
Summary: We define the generator of a holomorphic semigroup for a countably infinite interacting BrownianQ
particle system on a countable direct product space R∞ := n∈N R as a maximal monotone self-adjointP∞
operator k=1 ((− ∂x∂ k + Hk )( ∂x∂ k + Hk )). At first glance, this may seem like a pretty difficult problem, but
it is not too difficult because ∂x∂ k on R∞ can be defined as just a (generalized) partial derivative. The mostimportant thing is to define a H-partial derivative ∂H,k := ∂x∂ k + Hk as a closed operator for a sequence∞{Hk }∞
k=1 of measurable functions whose domain are measurable “subsets” of R . As with the previous talk,

only basic knowledge of analysis (and part of the previous talk) is required.
12 Kiyoshi Mochizuki(Chuo Univ./Tokyo Metro. Univ.⋆)
Hideo Nakazawa(Nippon Medical School)

The principle of limiting amplitude for dissipative wave equations inmagnetic fields · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The dissipative wave propagation problem with magnetic Laplacian in an exterior domain isconsidered.The uniform estimates and Hölder conditions of the resolvent are studied for the reduced wave
operator without dissipation. Based on these results, the validity of the principle of limiting amplitude isproved for wave propagation problem with dissipation. As byproduct, the result by Mizohata–Mochizuki in
1966 are improved.
13 Hirokazu Ohya (Salesian Polytech.)

Embedding properties for some Weighted Sobolev spaces with growing
weight · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we are concerned with the embedding properties for several kind of functional spaces
in RN . We will consider the functional spaces called as Weighted Sobolev space with some weight function.
If we choose some suitable growing functions in the weight functions, we can derive the continuity andcompact embedding for these functional spaces. We also obtain the sufficient conditions for the weightfunctions to show the above properties. Our method is mainly owed to usual Sobolev’s inequality.
14 Kenta Higuchi (Ehime Univ.)
Takuya Watanabe (Ritsumeikan Univ.)

Two-level adiabatic transition probability for small avoided crossings
generated by tangential intersections · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a first order ordinary differential system with two small parameters, which are an
adiabatic parameter and an interaction one. This system is a model of a time-dependent Schrödinger
equation which describes that two energy-levels with tangential intersections avoid crossings. In this talk,we give asymptotic expansion of the transition probability between avoided crossings as two parameters
tend to zero as well as their ratio determined by the tangential order does.
15 Yoshihisa Miyanishi (Shinshu Univ.)

Spectrum of the Neumann–Poincaré operator on thin domains · · · · · · · 10

Summary: The Neumann–Poincaré operator (abbreviated by NP) is a boundary integral linear operator
known as one of the important tools associated with boundary value problems in the field of partial
differential equations. Our purpose here is to introduce the spectral structure of the NP operator. In an
asymptotic sense, the NP spectrum distributed in the interval [-1/2, 1/2) as the domains become longer in
2D. In an asymptotic sense, we also find that the NP spectrum densely distributed in the interval [-1/2,
1/2) (resp. [0, 1/2)), as the domains which are defined by spheroids become flatter (resp. longer) in 3D.

Final: 2023/2/8
55

Functional Analysis

16 Yoshihiro Anahara(Yokohama Nat. Univ.)
Norio Konno (Yokohama Nat. Univ.)
Morioka Hisashi (Ehime Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

Limit theorem for quantum walk on one dimensional lattice with inflows
and outflows · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: To obtain a stationary state of quantum walks on the finite path, we set the sink and source tothe boundaries of the path so that the internal path receives the inflow and raditas the outflow at every
time step. In this talk we consider one dimensional lattice as finite graph and we show the weak convergence
theorem for the scaled limit distribution of the comfortability in the limit of the length of the path.
17 Kenta Higuchi (Ehime Univ.)
Hisashi Morioka (Ehime Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

Resonance expansion for finitely perturbed free quantum walks on theline · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce resonances to a class of quantum walks on the line as poles inside the unit circleof the outgoing resolvent. With each resonance, a resonant state which behaves like an eigenvector isassociated. We show that the time evolution with an initial state with compact incoming support exactly
coincides with the evolution of a sum of resonant states in each compact set after a finite length of time
has passed. Consequently, the exponential decay rate of the time evolution is given by the modulus ofresonances. We note that in the special case where a resonance is algebraically multiple, the decay becomespolynomially slower.
16:30–17:30

Talk Invited by Functional Analysis Section

Toshimitsu Takaesu (Gunma Univ.)

On the spectral analysis of interacting quantum field systems

Summary: In this talk, interacting systems of quantum field models are investigated. We mainly consider thesystem of quantum electrodynamics, which is the interaction system of a Dirac field and the radiation fieldin the Coulomb gauge, but the Yukawa model and ϕ4 model are also considered. By introducing momentum
and spatial cutoffs, the Hamiltonians are self-adjoint operators on a Hilbert space. Focusing on groundstates, the spectral analysis of these systems will be explained.

March 16th (Thu)

Conference Room VI

9:30–12:00
18 Takashi Satomi (Univ. of Tokyo)

Inequality for the convolutions on unimodular locally compact groups
and the optimal constant of related inequalities · · · · · · · · · · · · · · · · · · · · 15

Summary: Let µ be the Haar measure of a unimodular locally compact group G and m(G) be the infimum ofRRthe volumes of all open subgroups of G. The main result is that G f ◦(ϕ1 ∗ ϕ2 ) (g) dg ≤ R f ◦(ϕ∗1 ∗ ϕ∗2 ) (x) dx
holds for any measurable functions ϕ1 , ϕ2 : G → R≥0 with µ(supp ϕ1 ) + µ(supp ϕ2 ) ≤ m(G) and any convex
function f : R≥0 → R with f (0) = 0. Here ϕ∗ is the rearrangement of ϕ.
Let YO (P, G) and YR (P, G) denote the optimal constants of Young’s and the reverse Young’s inequality,
respectively, on G for the pair of the exponents P = (p1 , p2 ) under the assumption µ(supp ϕ1 )+µ(supp ϕ2 ) ≤m(G). Then we have YO (P, G) ≤ YO (P, R) and YR (P, G) ≥ YR (P, R) as a corollary of the main result.
Thus, we obtain that m(G) = ∞ holds if and only if H(p, G) ≤ H(p, R) in the case of p′ := p/(p − 1) ∈ 2Z,
where H(p, G) is the optimal constant of the Hausdorff–Young inequality on G for the exponent p.

Final: 2023/2/8
Functional Analysis

19 Toshihisa Kubo (Ryukoku Univ.)

56

On the standardness of homomorphisms between generalized Vermamodules for sl(3, C) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let g be a finite dimensional complex simple Lie algebra and b a Borel subalgebra. Let p ⊃ b
be a standard parabolic subalgebra. In 1977, Lepowsky showed that a homomorphism φ : Mb (ν) → Mb (ζ)
between Verma modules induces a map φstd : Mp (ν) → Mp (ζ) between the corresponding generalized Vermamodules, provided that ν and ζ satisfy a certain integral condition. He called such a map φstd standard.
It was also observed that the standard map φstd could be zero and even in the case there could be a
non-zero homomorphism φnonstd : Mp (ν) → Mp (ζ). Any map that is not standard is called non-standard.
The classification of standard/non-standard maps is still an open problem.
In this talk, for g = sl(3, C) with a maximal parabolic subalgebra p, we shall show that all non-zero
homomorphisms ψ : Mp (ν) → Mp (ζ), where Mp (ζ) is of scalar type, are standard.
20 Hiroshi Oda (Takushoku Univ.)

Inversion formula for Opdam–Cherednik transform associated with aroot system of type BC · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give the inversion formula and the Plancherel formula for Opdam–Cherednik transform
associated with a root system of type BC, when the multiplicity parameters are not necessarily nonnegative.
21 Koichi Kaizuka(Nippon Medical School)

Some remarks on the Dirac operator on symmetric spaces · · · · · · · · · · · 15

Summary: We develop the spectral analysis for the Dirac operator on symmetric spaces of noncompact typebased on harmonic analysis on Lie groups. In this talk, we compute the continuous spectrum of the Dirac
operator on irreducible symmetric spaces of noncompact type. We show that the continuous spectrum has aspectral gap if and only if the symmetric space is isomorphic to a coset space of the special pseudo-unitarygroup of odd matrix size. Furthermore, we give a uniform weighted resolvent estimate for the Dirac operator
under a certain assumption on the symmetric space.
22 Ryosuke Nakahama(NTT Inst. for Funda. Math.)

Computation of weighted Bergman inner products on block off-diagonal
matrices in bounded symmetric domains for Sp(2r, R) · · · · · · · · · · · · · · 15

Summary: Let (G, G1 ) = (G, (Gσ )0 ) be a symmetric pair of holomorphic type, and we consider a pair of
Hermitian symmetric spaces D1 = G1 /K1 ⊂ D = G/K, realized as bounded symmetric domains in complex
e of G acts unitarily on
vector spaces p+ := (p+ )σ ⊂ p+ respectively. Then the universal covering group G
1

the weighted Bergman space Hλ (D) ⊂ O(D) = Oλ (D) on D for sufficiently large λ. Its restriction to thee 1 decomposes discretely and multiplicity-freely, and its branching law is given in terms of thesubgroup Ge
K1 -decomposition of the space P(p+ ) of polynomials on p+ := (p+ )−σ ⊂ p+ . Our goal is to understand the22e 1 -typedecomposition of the restriction Hλ (D)|Ge1 by studying the weighted Bergman inner product on each K
in P(p+2 ) ⊂ Hλ (D). Today we deal with the symmetric pair (G, G1 ) = (Sp(2r, R), Sp(r, R) × Sp(r, R)).

23 Yuichiro Tanaka (Univ. of Tokyo)

A unitary trick for the multiplicity-freeness property · · · · · · · · · · · · · · · 15

Summary: With the aim of uniform treatment of multiplicity-free representations of Lie groups including
infinite-dimensional representations, T. Kobayashi introduced the notion of visible actions on complex
manifolds. In this talk I would like to show a trick for obtaining the multiplicity-freeness property of
infinite-dimensional representations of real semisimple Lie groups from that of finite-dimensional ones ofcompact Lie groups through visible actions on flag varieties.
24 Vı́ctor Pérez-Valdés (Univ. of Tokyo)

Construction and classification of conformally equivariant differential
symmetry breaking operators from a vector bundle over S 3 to a line
bundle over S 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we explain about the construction and classification problems of all differential
symmetry breaking operators D : C ∞ (S 3 , Vλ2N +1 ) → C ∞ (S 2 , Lm,ν ) between the section spaces of Vλ2N +1 →S 3 , a rank 2N + 1 vector bundle over S 3 , and Lm,ν → S 2 , a line bundle over S 2 .

Final: 2023/2/8
57

Functional Analysis

25 Hideto Nakashima (Inst. of Stat. Math.)

Decomposition formulas for gamma matrices of zeta functions associatedwith homogeneous cones · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Associated with homogeneous cones, we are able to construct solvable prehomogeneous vector
spaces. In the previous paper, we calculate gamma matrices of the associated zeta functions explicitly. In
this talk, we show that the gamma matrices can be decomposed into variable-wise matrices. Moreover,under suitable condition, we show that the associated zeta functions admit a kind of completion forms.
13:10–14:10

Talk Invited by Functional Analysis Section
Takashi Hashimoto (Tottori Univ.) Qunatization of the moment map on symplectic vector spaces andminimal representation
Summary: Let G be Sp(n, R), U(p, q), or O∗ (2n), which acts on a symplectic vector space W in a Hamiltonian
way with moment map µ. The purpose of this talk is twofold: the first one is to show that the canonicalquantization of µ with a choice of a Lagrangian subspace of W provides the oscillator representations of G,
which have been extensively studied in relation to the Howe duality and to minimal representations. The
second one is to construct the minimal representation of O(p, q) by applying this method to O(p, q) andusing the fact that (O(p, q), SL2 (R)) is a Howe’s dual pair.

March 17th (Fri)

Conference Room VI

9:30–12:00
26 Shiho Oi(Niigata Univ.)

Algebraic reflexivity of isometry groups of Lipschitz algebras · · · · · · · · 15

Summary: We consider Banach algebras of Lipschitz maps taking the values in a Banach algebra of complex
matrices of degree n. The unital subjective linear isometries on the Banach algebras have been obtained. In
this talk, we study the algebraic reflexivity of the set of subjective linear isometries. The subset S of the setof all bounded linear operators from A1 into A2 is called algebraically reflexive if a bounded linear operator
T : A1 → A2 which satisfies T a ∈ Sa for every a ∈ A1 implies T ∈ S. We show the set of unital subjective
linear isometries is algebraic reflexivity.
(Niigata Univ.)
27 Yuta Enami
Takeshi Miura (Niigata Univ.)

Surjective isometries on the Banach algebra of analytic functions with
C n -boundary values · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Let D, D and T be the open unit disk, closed unit disk and unit circle in the complex plane
C. The disk algebra A(D) is the algebra of all continuous functions on D that is holomorphic in D. We
consider the subalgebra An (D) consisting of all f ∈ A(D) whose restrictions f |T are of class C n . For eachf ∈ An (D), we denote by Dk (f ) the k-th derivative of f |T . The algebra An (D) is a Banach algebra, with thePnnorm kf kΣ = k=0 kDk (f )k∞ /k!, where kgk∞ = supz∈T |g(z)|. We characterized surjective, not necessarily
linear, isometries on An (D) with respect to the norm k · kΣ .
28 Takeshi Miura (Niigata Univ.)
Daisuke Hirota (Niigata Univ.)

Tingley’s problem for uniformly closed function algebras · · · · · · · · · · · · 15

Summary: Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces X andY , respectively. We shall present a positive answer to Tingley’s problem for A and B. More explicitly,
we prove that every surjective isometry between the unit spheres, S(A) and S(B), of A and B admits anextension to a surjective real linear isometry between whole spaces A and B.
29 Takashi Sano (Yamagata Univ.) ♭ Inertia of Kraus matrices · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Kazuki Takeuchi (Yamagata Univ.)
Summary: Let r, p0 , p1 < · · · < pn be positive numbers. We consider the n × n matrix whose (i, j) entry is
prj − pr0 
1  pri − pr0
given as−. We call this a Kraus matrix associated with tr . We show the inertia
p i − p j pi − p0
pj − p0of this Kraus matrix.

Final: 2023/2/8
Functional Analysis

30 Masaru Nagisa(Ritsumeikan Univ./Chiba Univ.)

58

The p-norm of some matrices · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We compute the operator p-norm of some n × n complex matrices, which can be seen as
bounded linear operators on the n-dimensional Banach space ℓp (n). In particular, a p-norm of a matrix


8 1 6


A = 3 5 7 which corresponds to a magic square is 15 for any p ∈ [1, ∞].
4 9 2
31 Hiroaki Tohyama(Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)Operator inequalities related to Young’s inequality · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we show several operator inequalities concerning Young’s inequality by using relative
operator entropies and operator valued α-divergence. One of them is partially a refinement of Young’s
inequality.
32 Takeaki Yamazaki (Toyo Univ.)
Hiroyuki Osaka (Ritsumeikan Univ.)

Limit of iterated induced Aluthge transformations of centered operators· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall discuss on bounded linear operators on a complex Hilbert space. We will
introduce convergence property of an operator sequence which is generated by iteration of the induced
Aluthge transformation. In this talk, we consider the case of centered operators.
33 Hiroyuki Osaka (Ritsumeikan Univ.)
Tomasz Mlynik (Univ. of Gdanśk)
Marcin Marciniak (Univ. of Gdanśk)

On a class of K-entanglement witnesses · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, Yang et al.showed that each 2-positive map acting from M3 (C) into itself is decomposable. It is equivalent to the statement that each PPT state on C3 ⊗ C3 has Schmidt number at most 2. It isa generalization of Perez–Horodecki criterion which states that each PPT state on C2 ⊗ C2 or C2 ⊗ C3 has
Schmidt rank 1 i.e. is separable. Natural question arises whether the result of Yang at al. stays true for
PPT states on C3 ⊗ C4 . This question can be considered also in higher dimensions. We construct a positive
maps which is suspected for being a counterexample. More generally, we provide a class of positive maps
between matrix algebras whose k-positivity properties can be easily controlled.
34 Yuki Seo (Osaka Kyoiku Univ.)

On data processing inequality for quantum ♮α -Rényi divergences of
positive order · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we show some fundamental properties of quantum ♮α -Rényi divergences of real order.
In particular, we show that the data processing inequality holds for all α > 0.
14:15–15:30
35 Hiroshi Inoue (Kyushu Sangyo Univ.)

An unbounded generalization of Tomita’s observable algebras II · · · · · · 15

Summary: In a previous talk we tried to build the basic theory of unbounded Tomita’s observable algebras
called T † -algebras which are related to unbounded operator algebras, especially unbounded Tomita–Takesaki
theory, operator algebras on Krein spaces, studies of positive linear functionals on ∗-algebras and so on.
And we defined the notions of regularity, semisimplicity and singularity of T † -algebras and characterized
them. In this talk we shall proceed further studies of T † -algebras and investigate whether a T † -algebra isdecomposable into a regular part and a singular part.

Final: 2023/2/8
59

Functional Analysis(Univ. of Tokyo)

36 Kei Ito

Cartan subalgebras of C*-algebras associated with complex dynamicalsystems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Deaconu and Muhly was defined C ∗ -algebras associated with branched coverings. But their
algebras lack information of branch points.

Kajiwara and Watatani tried to modify Deaconu–Muhly∗

algebras and defined C -algebras associated with complex dynamical systems. Let R be a rational function
and J be its Julia set. It is known that the C ∗ -algebra C(J) of complex-valued continuous functions on J isa Cartan subalgebra of the Deaconu–Muhly algebra for the dynamical system (J, R), but it was not known
whether C(J) is a Cartan subalgebra of the Kajiwara–Watatani algebra for (J, R) or not. In this talk, I
explain that C(J) may not be a Cartan subalgebra of the Kajiwara–Watatani algebra for (J, R).
37 Ryoya Arimoto (Kyoto Univ.)

On the type of the von Neumann algebra of an open subgroup of the
Neretin group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Neretin group is the totally disconnected locally compact group consisting of almost automorphisms of the tree. In 2021, P.-E. Caprace, A. Le Boudec, and N. Matte Bon proved that the Neretingroup is not of type I. We prove that a distinguished open subgroup of the Neretin group is not of type I
either.
38 Satoshi Goto

(Sophia Univ.)

On flat part commuting squares · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: When a non-degenerate commuting square is given, we can construct a hyperfinite II 1 subfactor
N ⊂ M generated by the tower of the given non-degenerate commuting squares.

From the originalcommuting square, we can also construct the flat part commuting squares. If the subfactor N ⊂ M is offinite depth, we will show that the composite connection of the original and the flat part ones (in the senseof N. Sato) produces a subfactor which is isomorphic to N ⊂ M . We also show an application of this result.
15:45–16:45

Talk Invited by Functional Analysis Section

Masaru Nagisa(Ritsumeikan Univ./Chiba Univ.)

Non-linear traces on the algebra of compact operators and majorization

Summary: We study non-linear traces of Choquet type and Sugeno type on the algebra of compact operators.
They have certain partial additivities. We show that these partial additivities charactererize non-linear tracesof both Choquet type and Sugeno type respectively. There exists a close relation between non-linear tracesof Choquet type and majorization theory. We study trace class operators for non-linear traces of Choquet
type. More generally we discuss Schatten–von Neumann p-class operators for non-linear traces of Choquet
type. We determine when they form Banach spaces. This is an attempt of non-commutative integration
theory for non-linear traces of Choquet type on the algebra of compact operators. We also consider the
triangle inequality for non-linear traces of Sugeno type.

Final: 2023/2/8
Statistics and Probability

60

Statistics and Probability
March 15th (Wed)Conference Room VIII

10:00–11:30
1 Naoki Kubota(Nihon Univ.)

Lipschitz-tiype estimates for the time constant of the frog model · · · · · 15

Summary: We consider the frog model on the multidimensional lattice, whose initial configuration is according
to a Bernoulli distribution. The main object of interest is the so-called time constant, which describes the
speed of the spread of frogs. The time constant depends on the parameter of the Bernoulli distribution.
Hence, in this talk, we discuss how the change in the parameter of the Bernoulli distribution affects thetime constant. More precisely, we provide some Lipschitz-type estimates for the time constant.
2 Takumu Ooi(Kyoto Univ.)

Convergence of time-changed α-stable processes by GMC · · · · · · · · · · · 15

Summary: We consider Gaussian fields whose covariance kernels are 1-order green functions of d-dimensional
symmetric α-stable processes, Gaussian multiplicative chaos (GMC) and time-changed α-stable processes
by GMC. In the case of both d and α are 2, these are the Gaussian free field, the Liouville measure andthe Liouville Brownian motion, respectively. In this talk, we explain weak convergence of the time-changed
α-stable processes by GMC with Skorokhod’s topology.
3 Mikio Hirokane (Osaka Univ.)
Masaaki Fukasawa (Osaka Univ.)

A limit theorem for generalized tempered stable processes and theirquadratic variations with stable index tending to two · · · · · · · · · · · · · · · 15

Summary: Motivated by Yoshida’s martingale expansion theory, we study the limit of the joint distributionof a multidimensional Generalized Tempered Stable (GTS) process and its quadratic covariation process
when the stable index tends to two. Under a proper scaling, the GTS processes converges to a Brownian
motion that is a stable process with stable index two. We renormalize their quadratic covariation processes
so that they have a nondegenerate limit distribution. We show that the limit is a stable process with stableindex one and is independent of the limit Brownian motion of the GTS processes.
(Keio Univ.)
4 Yuki Suzuki
Hiroshi Takahashi (Keio Univ.)
Yozo Tamura

A diffusion process with a symmetric stable potential on the negativeside in R · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We investigate a diffusion process with a symmetric stable potential on the negative side in R. In
the case of a Brownian potential on the negative side, this process was examined by Kawazu, Suzuki andTanaka (2001, 2006). We study a long-time behavior of our process by a different method from theirs. We
use a method based on a theory of bi-generalized diffusion processes studied by Ogura (1989).
5 Yuki Suzuki(Keio Univ.)

Limit theorems for a diffusion process with a non-selfsimilar random
potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study a one-dimensional diffusion process with a non-selfsimilar random potential. The typeof the potential is different on the left and the right hand sides of the origin. We show that the long-time
behavior of the process is different from the behaviors of any other previous models.

Final: 2023/2/8
61

Statistics and Probability

6 Shigeyoshi Ogawa (Ritsumeikan Univ.)

Another representation of the mean value theorem for noncausal stochastic integrals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This is the follow up to the preceding lecture “Mean value theorems for the noncausal stochastic
integral” that was presented at the 2022 annual meeting of Math Society of Japan held in Sappro, in Octobre
2022. There we showed a basic fact about the validity of a mean value theorem for the noncausal stochastic
Rtintegral, also called ogawa integral, with respect to Brownian motion Wt of the form s f (Xr )d∗ Wr whereRt
Xt is an Itô process, We derived formulae of mean value theorem for Itô integral s f (Xr )d0 Wr and for theRtnoncausal integral s f (X̃r )d∗ Wr where X̃t (ø) is a noncausal variation of Xt .
The aim of the present talk is to give an elementary but important comment on the basic result and show
another formula of mean value theorem for each of three cases mentioned above.
14:15–15:15

Talk Invited by Statistics and Probability Section
Shuta Nakajima (Meiji Univ.) First-passage percolation and its related topics
Summary: In this talk, we discuss recent progress on First-passage percolation (FPP). FPP was originallyintroduced by Hammersley and Welsh as a model of the spread of fluid in a random medium. The model
also can be regarded as a dynamic version of percolation. In FPP, a graph with random weights is given,
and we consider the optimization problem of the passage time between two fixed vertices. The minimum
value is called the first passage time and it represents the time when the fluid reaches from one point to theother. From the viewpoint of an optimization problem, properties of the optimal path that attains minimum
value are also of interest. Over 50 years, many mathematical techniques have been developed to study theseobjects. This talk mainly focuses on the fluctuations and the large deviations of the first passage times, andthe geometric properties of geodesics. We also discuss related models such as the chemical distance.

15:30–16:30

Talk Invited by Statistics and Probability Section(Waseda Univ.) A mechanical model of Brownian motion
Song Liang
Summary: We provide a connection between Brownian motion and a classical Newton mechanical system.
Brownian motion is a well-known physical phenomenon concerning the erratic motion of a small particle
immersed into a fluid in equilibrium. The physical explanation of Brownian motion is often presented in
the following way: since the massive particle is interacted by a large number of very light environmental
particles, if we could assume that the interactions from each light particle at each time are independent,
then by the central limit theorem for the sums of i.i.d. random variables, this will give in a suitable limit

the Brownian motion. We notice that this assumption of independence can hardly be justified, even ina collision model, because of the possibility of re-collisions. This becomes a more evident and significant
drawback when considering the model of interactions caused by potentials.
In this talk, we consider a mechanical model consisting of a massive particle in an ideal gas, evolved
according to non-random Newton mechanical principles, via interaction potentials. We prove that undercertain conditions, the (position, velocity)-process of the massive particle converges to a diffusion process,when the mass of the environmental particles converges to 0, while the density and the velocities of them
go to infinity promptly. The precise expression of the limiting process is also given.

March 16th (Thu)

Conference Room VIII

10:20–11:10
7 Haruyoshi Tanaka(Wakayama Med. Univ.)

On dimension estimates in nonconformal graph iterated function systems via asymptotic perturbation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider infinite graph-directed iterated function systems (GIFSs) whose contraction mappings
are nonconformal. As our main result, we formulate asymptotic perturbations from conformal GIFSs tononconformal GIFSs, and give the asymptotic behaviour of the Hausdorff dimension of the limit set of theperturbed system. We also investigate perturbed self-affine sets as special cases.

Final: 2023/2/8
Statistics and Probability

8 Ryoji Takano(Osaka Univ.)

62

Large deviation principle for the Lyons–Victoir extension · · · · · · · · · · · 15

Summary: We study the large deviation principle for the Lyons–Victoir extension.

The Lyons–Victoir

extension is known as a method to lift a general continuous path of finite p-variation to a geometricq-variation rough path, where q is grater than p. We use the Lyons–Victoir extension as a method for lifting
continuous stochastic processes to geometric rough paths. The main idea of this study is that by using the
Lyons–Victoir extension, lifting the large deviation principle for continuous stochastic processes to that forgeometirc rough paths. To do so, we will prove the boundedness of the Lyons–Victoir extension map. As
consequence of this, the large deviation principle for rough differential equation driven by the Lyons–Victoir
extenstion can be obtained.
9 Hiroki Yagisita (Kyoto Sangyo Univ.) ♭ Any Gibbs measure on infinite-dimensional space R∞ defines a regular
Dirichlet form with local property on compact space (R ∪ {∞})∞ · · · · 10
Summary: For Gibbs measure µ on R∞ , we consider a classical symmetric form formally denotedRPµ∂f1 ∂f2
ECD(f1 , f2 ) :=k∈N R∞ ∂xk ∂xk dµ. Following, for example, Albeverio, Kondratiev, Rockner, etc., weadopt definition of Gibbs measure by establishment of integration by parts formula. In our main result, “µdetermines a regular Dirichlet form with local property”, there are no constraints other than that µ is (what
we say) Gibbs measure. It seems that Gibbs measure (as we call it) also includes fairly marginal probability
measure in that it is “spatially spread out”. Note that we see R∞ as a direct product of Riemannian
manifolds.
10 Yuta Nakagawa (Kyoto Univ.)

Density of states for Schrödinger operators associated with Gibbs point
processes and nonpositive potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the random Schrödinger operator for the potential generated by the
nonpositive single site potential and the points randomly located according to the Gibbs point process forthe pairwise interaction. We determine the leading term of the asymptotic behavior of the integrated densityof states (IDS) for the Schrödinger operator. This IDS vanishes much faster near −∞ than the IDS for the
Poisson point process, of which asymptotic behavior is known.
11:20–11:50

Research Section Assembly

March 17th (Fri)

Conference Room VIII

9:50–11:35
11 Teruo Tanaka (Hiroshima City Univ.)

Prophet inequalities for finite stage multiparameter optimal stopping
problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the optimal stopping problem for discrete time multiparameter stochastic processes.
In the classical optimal stopping problems, the comparisons between the expected reward of a player withcomplete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet
inequalities, have been studied by many authors. We shall study the prophet inequalities for optimal
stopping problems for finite stage multiparameter stochastic processes.
12 Toshiharu Fujita(Kyushu Inst. of Tech.)Markov decision process with converging branch system —Multiplicative
reward system— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider multiplicative reward system on a certain finite-stage stochastic converging decision
process model. Converging decision process has converging transition, which is one of the nonserial branchsystems proposed by Nemhauser. We apply bidecision approach to our model and give a recursive methodby dynamic programming technique.

Final: 2023/2/8
63

Statistics and Probability

13 Hayato Takahashi (Random Data Lab.)

Posterior distributions weakly converge to Martin-Löf random parameters · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In parametric models estimators that are consistent at all parameters are concerned, while in
Bayes models those that are consistent at almost all parameters are concerned. The identification of thepoints at which the posterior distributions weakly converge constitutes the problem (Diaconis and Freedman
1986). We show that for joint probabilities on complete separable metric spaces, the posterior distributions
are consistent at almost all parameters if and only if the posterior distributions are consistent at MLrandom parameters. Reference: Hayato Takahashi, Bayesian definition of random sequences with respect toconditional probabilities, preprint
14 Hayato Takahashi (Random Data Lab.)

Some explicit formulae for the distributions of words · · · · · · · · · · · · · · · 15

Summary: Bassino et al. 2010 and Regnier et al. 1998 showed generating functions of the distributionsof words for all sample sizes. Robin et al. 1999 presented generating functions of the distributions forthe return time of words and demonstrated a recurrence formula for these distributions. These generating
functions are rational functions; except for simple cases, it is difficult to expand them into power series. In
this paper, we study finite-dimensional generating functions of the distributions of nonoverlapping words
and some overlapping words for each fixed sample size, respectively and demonstrate the explicit formulae
for the distributions of words for the Bernoulli models.
15 Shoko Chisaki (Osaka Inst. of Tech.)Shinji Kuriki (Osaka Pref. Univ.⋆)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

Optimality of spanning bipartite block designs II · · · · · · · · · · · · · · · · · · · 15

Summary: It is usually to design an experiment using treatments and its blocks in the design of experiments.
Consider a set of edges of a complete bipartite graph as a treatments set and suppose the treatments havea structure. Then, we proposed a spanning bipartite block design (SBBD) to achieve better estimation
accuracy. In this talk, using an SBBD as a statistical model, we prove that the design matrix of an SBBD
is A-optimal under some conditions.
16 Nobuhiro Taneichi(Hokkaido Univ. of Edu.)
Yuri Sekiya (Hokkaido Univ. of Edu.)

An index for selecting the multinomial goodness-of-fit test statistics andits applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For the goodness-of-fit test for a multinomial distribution, we consider phi-divergence family of
goodness-of-fit test statistics. Members of phi-divergence family of statistics all have an equivalent limiting
chi-square distribution under the null hypothesis. We consider a second-order correction term as an index
whether the distribution of statistic is close to the limiting chi-square distribution. We derive important
properties of the index for selecting a phi-divergence goodness-of-fit statistic. We also discuss an applicationof the index to the other kinds of tests.
17 Eri Kurita (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

On the null distribution of multivariate normality test statistics using
multivariate skewness · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider on the null distribution of multivariate normality test statistic using
multivariate skewness. Although there are several definitions of multivariate skewness and kurtosis, thistalk focuses on Mardia’s multivariate skewness and proposes a new chi-square approximation with adjusted
degrees of freedom for the null distribution of the normality test statistic using it. Finally, some simulation
results are presented to investigate the accuracy of the chi-square approximation of the test statistic proposedin this talk.

Final: 2023/2/8
Statistics and Probability

14:25–15:25

64

Talk Invited by Statistics and Probability Section

Takeru Matsuda(Univ. of Tokyo / RIKEN)

Shrinkage estimation: from vector to matrix

Summary: In the estimation of a normal mean vector under the quadratic loss, the maximum likelihood
estimator (MLE) is inadmissible and dominated by shrinkage estimators (e.g. James–Stein estimator) when
the dimension is greater than or equal to three (Stein’s paradox). In particular, generalized Bayes estimatorswith respect to superharmonic priors (e.g. Stein’s prior) are minimax and dominate MLE. Note that afunction is said to be superharmonic if its average value on a hypersphere is always not greater than its
value at the center.
In this talk, I will introduce recent studies on generalizations of the above results to matrices. First,
we develop a superharmonic prior for matrices that shrinks singular values, which can be viewed as anatural generalization of Stein’s prior. This prior is motivated from the Efron–Morris estimator, which
is an extension of the James–Stein estimator to matrices. The generalized Bayes estimator with respect
to this prior is minimax and dominates MLE under the Frobenius loss. In particular, since it shrinks
to the space of low-rank matrices, it attains large risk reduction when the unknown matrix is close to
low-rank (e.g. reduced-rank regression). Next, we construct a theory of shrinkage estimation under the“matrix quadratic loss”, which is a matrix-valued loss function suitable for matrix estimation. A notion of“matrix superharmonicity” for matrix-variate functions is introduced and the generalized Bayes estimatorwith respect to a matrix superharmonic prior is shown to be minimax under the matrix quadratic loss. The
matrix-variate improper t-priors are matrix superharmonic and this class includes the above generalizationof Stein’s prior. Applications include matrix completion and nonparametric estimation.
15:40–16:40

Talk Invited by Statistics and Probability Section

Yuma Uehara(Kansai Univ.)

Information criteria for jump diffusion models

Summary: In this talk, we consider ergodic jump diffusion models with high-frequency observations. We
mainly focus on the model selection problem for the models. More specifically, our interest is to select all
drift and diffusion coefficients, and jump distribution among candidates. For such a problem, the thresholdbased transition density approximation which corresponds to the case where at most one jump occur within
one observation interval is useful. We evaluate such an approximation, and propose explicit AIC-type
information criterion constructed by the threshold based quasi-likelihood function.

March 18th (Sat)

Conference Room VIII

10:00–11:10
18 Ayaka Yagi (Tokyo Univ. of Sci.)
Toya Ozaki (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

On the test for adequacy in growth curve model with two-step monotone
missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the test for adequacy in growth curve model when the data set has a two-stepmonotone missing pattern. For the complete data case, to test the adequacy hypothesis, Hotelling’s T 2
statistic is presented in Fujikoshi, Ulyanov and Shimizu (2010). In this talk, we propose a test statistic
for the adequacy hypothesis with two-step monotone missing data based on the above result. Further, wegive the approximation to the upper percentile of this statistic. Finally, we investigate the accuracy of theapproximation by Monte Carlo simulation.

Final: 2023/2/8
65

Statistics and Probability

19 Yuta Koike (Univ. of Tokyo)
Xiao Fang(Chinese Univ. of Hong Kong)

A high-dimensional central limit theorem for sums of i. i. d log-concave
random vectors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the problem of bounding the normal approximation error over rectangles for a sumof n independent d-dimensional random vectors. Here, our aim is to establish such a bound with polylogarithmic dependence on the dimension d. It is known that such a bound is available with a nearly n−1/2
convergence rate when the covariance matrix of the sum is non-degenerate. In this talk, we show that, if therandom vectors are i.i.d. and log-concave, we can derive an error bound with a nearly n−1/2 convergence
rate and poly-log dependence on d without any restriction on the covariance matrix.
20 Koichi Yamagata(Nat. Inst. of Informatics)
Akio Fujiwara (Osaka Univ.)

Efficiency of estimators for locally asymptotically normal quantum statistical models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We herein establish an asymptotic representation theorem for locally asymptotically normal
quantum statistical models.

This theorem enables us to study the asymptotic efficiency of quantum

estimators such as quantum regular estimators and quantum minimax estimators, leading to a universal
tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum
contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105–2141],
providing a solid foundation of the theory of weak quantum local asymptotic normality.
21 Keita Nakamura (Tokyo Univ. of Sci.)
Tomoyuki Nakagawa(Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)

Symmetry in square contingency tables using aitchison geometry · · · · · 15

Summary: The probability table obtained from a contingency table can be viewed as an element in thesimplex. Symmetric probability tables are identified as a linear subspace using the Aitchison geometry of
the simplex. Given a probability table, we can obtain the closest symmetric table by orthogonal projection
onto the symmetric subspace. The original probability table is decomposed into the symmetric and theskew-symmetric tables that are orthogonal to each other. A procedure to test symmetry of a contingency
table, based on a multinomial simulation, is developed and examples of tests carried out are given.

Final: 2023/2/8
Applied Mathematics

66

Applied Mathematics
March 15th (Wed)Conference Room VII

9:50–11:50
1 Yuho Tanaka (Waseda Univ.)
Tsuyoshi Miezaki (Waseda Univ.)
Manabu Oura (Kanazawa Univ.)
Himadri Shekhar Chakraborty(Shahjalal Univ. of Sci. Tech.)

Jacobi polynomials and design theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: There are Jacobi polynomials as an analogue to Jacobi forms as a powerful generalization of theta
series of Lattices. It is a generalization of weight enumerators that M. Ozeki introduced for codes. A.
Bonnecaze et al. constructed various types of designs and did some studies to establish a relationship between
Jacobi polynomials and designs by focusing on weight enumerators, Jacobi polynomials, and the Molien
series. In this talk, we introduce the concept of multiple Jacobi polynomials and give the MacWilliams type
duality for them. We also give generalizations and analogies of some results in their paper. In addition, we
introduce a criterion for the existence of (generalized) designs using Jacobi polynomials.
2 Sho Suda (Nat. Defense Acad. of Japan)
Alexander L. Gavrilyuk(Shimane Univ.)

Uniqueness of an association scheme related to the 4-(11, 5, 1)-design· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It follows from the Delsarte theory that the Witt 4-(11, 5, 1) design gives rise to a (Q-polynomial)
association scheme W defined on the set of its blocks. In this talk, we observe that W is unique, i.e., defined
up to isomorphism by its parameters.
3 Norifumi Ojiro (Toyota Tech. Inst.)
Hajime Matsui (Toyota Tech. Inst.)

LCD property and reversiblity in quasi-cyclic codes · · · · · · · · · · · · · · · · 15

Summary: We show a necessary and sufficient condition for which quasi-cyclic codes represented by polynomial matrices are to be LCD (Linear Complimentary Dual), and using this result, a connection between
LCD quasi-cyclic codes and reversible quasi-cyclic codes is investigated.
(Meiji Univ.)
4 Shohei Satake(
YokohamaNat. Univ.)
Hyungrok Jo

On high-girth arc-transitive expander graphs · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Expander graphs are highly-connected sparse graphs which have fruitful connections to mathematics, computer science and cryptography. One of the fundamental problems about expander graphs is
to construct explicit high-girth expander graphs, which can be applied for designing cryptographic hashfunctions, for example. In this talk we introduce new explicit constructions of high-girth expander graphsthat are arc-transitive.
5 Shinya Fujita (Yokohama City Univ.)

Connectivity keeping paths in highly connected graphs · · · · · · · · · · · · · 15

Summary: Some recent results concerning connectivity keeping paths in highly connected graphs will be
reviewed.
6 Sho Fujimura (Fukuoka Univ.)
Shuji SHIRAISHI (Fukuoka Univ.)

On the generation of all Euler trails for an Eulerian graph with 2n edges· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For an Eulerian graph G with 2n edges, we give a new method of generating all Euler trails in G
in parallel efficiently by using 2-chain cover of G.

Final: 2023/2/8
67

Applied Mathematics

7 Tomoya Machide(Nat. Inst. of Informatics)

An application of systems of Boolean polynomial equations to list color
problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will talk an application of systems of Boolean polynomial equations to list color problems, inwhich not only vertex-coloring conditions but also edge-coloring conditions are imposed under Grünbaum
method.
8 Tadashi Takahashi (Konan Univ.)
Tomohiro Washino (Konan Univ.)

On the proof of lemma in the learning model using Groebner basis· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the statistical model of three-layer neural network with H hidden units. By using
taylor expansion of activation function , the set of parameters that true density function is realizable bya statistical model is a common zero points defined by finite polynomials. First, in this case H = 2, we
calculate equations define the algebraic set. The algebraic set is the set of parameters that true density
function is realizable by a statistical model with one or zero hidden unit. Next, we determine equations
define the algebraic set. The algebraic set is the set of parameters that true density function is realizable bya statistical model with H0 < H hidden unit. We prove the lemma in the learning model applying Hilbert’sbasis theorem using Groebner basis.
14:15–15:25
9 Shuhei Tsujie (Hokkaido Univ. of Edu.)
Ryo Uchiumi (Hokkaido Univ.)

Graph embedding and the product of transpositions associated withedges · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Given a graph, we associate each edge with the transposition which exchanges the endvertices.
Fixing a linear order on the edge set, we obtain a permutation of the vertices. Dénes proved that the
permutation is a full cyclic permutation for any linear order if and only if the graph is a tree.
In this article, we characterize graphs having a linear order such that the associated permutation is a full
cyclic permutation in terms of graph embeddings.
10 Yumi Yamada (Univ. of Tsukuba)
Masahiro Hachimori(Univ. of Tsukuba)
Akihiro Higashitani (Osaka Univ.)

The root distributions of Ehrhart polynomials of free sums of lattice
polytopes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study the root distributions of Ehrhart polynomials of free sums of certain lattice
polytopes. We investigate cases where the roots of the Ehrhart polynomials of the free sums of A∗d ’s or Ad ’s
lie on the canonical line Re(z) = −1/2 on the complex plane C, where Ad denotes the root polytope of type
A of dimension d and A∗d denotes its polar dual. For example, it is proved that A∗m ⊕ A∗n with min{m, n} ≤ 1
or m + n ≤ 7, A∗2 ⊕ (A∗1 )⊕n and A∗3 ⊕ (A∗1 )⊕n for any n satisfy this property.
11 Akihiro Higashitani (Osaka Univ.)
Kenta Ueyama (Hirosaki Univ.)

Classification of skew polynomial algebras by switching of matrices andits associated simplicial complexes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Classifying skew polynomial rings is important in noncommutative algebraic geometry because askew polynomial ring can be regarded as a noncommutative version of the homogeneous coordinate ring of
the projective space. In this talk, we focus on a particular class of skew polynomial rings and discuss whether
the classification of such skew polynomial rings up to equivalence of their graded module categories can bedone by using the switching of matrices and the simplicial complexes associated to switching equivalenceclasses. We prove that we can do it if the sizes of the matrices are relatively small.
12 Hirotake Kurihara (Yamaguchi Univ.)
Takahiro Hashinaga (Saga Univ.)

Construction of homogeneous Lagrangian subalgebras using rooted trees· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the construction and classification problems of homogeneous Lagrangiansubmanifolds of the noncompact Hermitian symmetric space M = Sp(n, R)/U(n) of rank n. We give thatrooted trees contribute to the classification of homogeneous Lagrangian submanifolds in M = Sp(n, R)/U(n).

Final: 2023/2/8
Applied Mathematics

15:45–16:45

68

Talk Invited by Applied Mathematics Section

Kenta Noguchi (Tokyo Univ. of Sci.)

Graphs on closed surfaces, expressly triangulations and quadrangulations

Summary: Graphs on closed surfaces are widely studied in the literature. We have been interested in andstudied the triangulations and quadrangulations, which are important classes of such graphs. Specifically,
we have been investigated the relationship between them to reveal their several properties, such as thechromatic number and the related topics. In this talk, we will present the basic background and someproblems, and give recent results on the extension from a quadrangulation to a triangulation and spanning
quadrangulation subgraphs of triangulations.

March 16th (Thu)

Conference Room VII

10:00–11:45
13 Iwao Sato (Oyama Nat. Coll. of Tech.)(Nihon Univ.)
Yusuke Ide
Takashi Komatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Norio Konno (Yokohama Nat. Univ.)

Metzler/Zeta correspondence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present an explicit formula for the determinant on the Metzler matrix of a digraph D.
Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix of the symmetricdigraph of a finite torus, and express its limit formula by using the integral expression.
14 Iwao Sato (Oyama Nat. Coll. of Tech.)Takashi Kmatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)
Norio Konno (Yokohama Nat. Univ.)

Alternating walk/Zeta correspondence · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We express the alternating zeta function of a graph G by using the Ihara zeta function of G.
Next, we define a generalized alternating zeta function of a graph, and express it of a vertex-transitive
regular graph by spectra of the transition probability matrix of the symmetric simple random walk on it andits Laplacian. Furthermore, we present an integral expression for the limit of the generalized alternating
zeta functions of a series of vertex-transitive regular graphs. As an example, we treat the generalized
alternating zeta functions of a finite torus. Finally, we treat the relation between the Mahler measure andthe alternating zeta function of a graph.
15 Yoshihiro Anahara(Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)
Morioka Hisashi (Ehime Univ.)

Convergence speed for quantum walks on one dimensional lattice withinflows and outflows · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For quantum walks on finite graphs whose time evolution is unitary operator, it is difficult tofind a stationary state which is not equal to the initial state. We can consider a quantum walk model witha stationary state on a connected finite graph by introducing infinite length tails and inserting a quantum
walker into the internal graph at every time step from the tail. In this talk focusing on the finite path as theinternal graph, and also on the spectrum of the truncated submatrix of the unitary time evolution operator
with respect to the internal graph, we estimate a convergence speed to the stationary state.

Final: 2023/2/8
69

Applied Mathematics

16 Akihiro Narimatsu(Univ. of Fukuchiyama)(Nihon Univ.)
Yusuke Ide

Perfect state transfer, equitable partition and continuous-time quantum
walk based search · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a continuous-time quantum walk based search algorithm. We introduce equitablepartition of the graph and perfect state transfer on it. By these two methods, we can calculate the successprobability and the finding time of the search algorithm. In addition, we gave some examples of graphs that
we can calculate the success probability and the finding time.
17 Satoshi Yabuoku(Kitakyushu Nat. Coll. of Tech.)(Kyushu Univ.)
Taro Hasui
Tomoyuki Shirai (Kyushu Univ.)

Enumeration of connected bipartite graphs with given Betti number· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G = (V, E) be a simple connected bipartite graph with bipartition V = V1 t V2 , and f (r, s, q)
denote the number of Gs such that |V1 | = r, |V2 | = s and |E| = q. In this talk, we focus on the valuesf (r, s, r + s + k − 1) for given Betti number k. For k = 0, this is the number of spanning trees on Kr,s ,and Scoins proved f (r, s, r + s − 1) = rs−1 sr−1 . By recurrence equation, we obtain the explicit form of
exponential generating functions of f (r, s, r + s + k − 1) for general k, and we derive the asymptotic behaviorof their coefficients. We also give another expression of the generating functions as the summation of rational
functions of those for the number of bipartite rooted spanning trees.
18 Hiroyuki Yamagishi(Tokyo Metro. Coll. of Ind. Tech.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)

The best constant of the discrete ℓp Sobolev inequality on the completegraph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We assume a classical mechanical model of the complete graph KN with N vertices. We put the
N atoms on vertices of KN . Its neighboring two atoms are connected to a linear spring. The spring constantis 1. Let p and q be real numbers satisfying 1/p + 1/q = 1 (p, q > 1). If u(i) takes a real value, then u(i)represents a deviation from the steady state. The discrete ℓp Sobolev inequality shows that the maximumof deviation |u(i)|p is estimated in a constant multiple of the potential energy on KN . Hence, the best
contants represent the rigidity of the mechanical model on KN .
13:00–14:10
19 Xiao-Nan Lu(Gifu Univ.)

Covering arrays guaranteeing a passing test · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Covering arrays (CAs) are a kind of combinatorial designs proposed for applications in combinatorial testing (CT). For adaptive decoding algorithms in CT using CAs, it is required that a passing test
should be contained in the CA. In this talk, a few results on such binary CAs that guarantee at least one
passing test are introduced. In particular, it is shown that for no more than two faulty interactions, theknown optimal construction for binary CAs is good enough. Then, a general sufficient condition for such
CAs in terms of domination numbers of graphs associated to the CAs is proposed.

Final: 2023/2/8
Applied Mathematics

20 Akira Saito
Shingo Degawa
Aiki Masuda
Hiroki Nishida(Nihon Univ.)(Nihon Univ.)(Nihon Univ.)(Nihon Univ.)

70

Two upper bounds on secure domination number · · · · · · · · · · · · · · · · · · 15

Summary: A set of vertices S in a graph G is a dominating set if every v ∈ V (G) − S satisfies NG (v) ∩ S 6= ∅.
A dominating set S is secure if for every v ∈ V (G) − S, there exists x ∈ S such that (S − {x}) ∪ {v}
is a dominating set. The order of a smallest secure dominating set of G is called the secure domination
number of G and denoted by γs (G). In this talk, we report an upper bound γs (G) ≤ 53 |G| for a graph G ofminimum degree at least 2. Then we generalize the notion of a secure dominating set. A dominating set
S = {x1 , . . . , xk } in G is weakly secure if for every v ∈ V (G) − S, there exists yi ∈ NG (xi ) ∪ {xi } for each
i with 1 ≤ i ≤ k such that {y1 , . . . , yk } is a dominating set and v ∈ {y1 , . . . , yk }. The order of a smallest
weakly secure dominating set of G is called the weakly secure domination number and denoted by γws (G).
We report γws (G) ≤ d|G|/2e for every onnected graph G of minimum degree at least 1.
21 Yuichi Yoshida (Kitami Inst. of Tech.)
Kazunori Matsuda(Kitami Inst. of Tech.)On the three graph invariants related to matching of finite simple graphs· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We determine the relationship between the matching number,the minimum matching number,theinduced matching number and the number of vertices.
22 Robert E. L. Aldred (Univ. of Otago)(Keio Univ.)
Jun Fujisawa

Distance restricted matching extension in 5-connected graphs on surfaces which are not triangulation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we show the following result. Let G be a 5-connected graph of even order which is
2-cell embedded in a surface F 2 with sufficiently
 large face-width, and let M be a matching of G such that2)+25
any two edges in M are at distance at least 2 20 − 12χ(F|M |in the face subdivision G. Then G has aperfect matching containing M .

March 17th (Fri)

Conference Room VII

9:50–11:50
23 Hironari Miyoshi (Saitama Univ.)

Derivation of Brownian motion from the Goldstein–Taylor model · · · · · 15

Summary: In this lecture, we consider a random walk associated with the initial value problem of theGoldstein–Taylor model. First, we show the existence of the solution for a scaled Goldstein–Taylor modelby using the corresponding telegraph equation. Next, we find the probability density function pε (x, t)
associated with a random process of particles for the Goldstein–Taylor model. Finally, we prove that thescaling limit of the cumulative distribution function for pε (x, t) converges to the Brownian motion in thesense of distributions.
24 Itsuki Watanabe (Waseda Univ.)

High-density limit of controlled density-dependent Markov processes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the high-density type scaling limit of the controlled stochastic model. The stochastic
model can be constructed as a particle system with birth and death events whose transition rate depends
on its density and control. In this talk, we reveal that the scaling limit of this model is governed by thecontrolled stochastic differential equation by showing the relative compactness and using the continuous
mapping theorem.

Final: 2023/2/8
71

Applied Mathematics

25 Antoine Diez

(Kyoto Univ.)

Scaling limits and emergent phenomena in a system of body-oriented
particles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Biological phenomena such as the flock of birds or the swarm of bacteria and other active cells
reveal that complex self-organized patterns can emerge from active particle systems when the number ofparticles becomes very large. In this talk, I will describe a modelling framework based on classical tools
developed in the mathematical kinetic theory of gas. The core idea is the derivation of PDE models fromstochastic many-particle systems. I will illustrate these ideas with a system of so-called body-oriented
particles and explain how the behavior of many-particle systems can be inferred by looking at appropriatescaling limits. In particular, this work demonstrates the influence of stochasticity and geometry on selforganization.
26 Jumpei Nagase(Shibaura Inst. of Tech./ZOZO Research)
Yuki Saito (ZOZO Research)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)

Permutation invariant deep neural network model for representing hierarchical sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Deep neural network models, which have been rapidly developing and expanding their range ofapplication in recent years, need to be applied to structured data. Specifically, there is a wide range ofapplications such as face recognition, set matching, and point cloud segmentation. A set data is interpreted
as structured data, and representations of a set data based on permutations equivalence / invarianceproperties are known. In particular, Renhao et al. have made a mathematical discussion of a machinelearning model that satisfies equivalence / invariance for hierarchical group actions by introducing the ideaof Wreath product. In this paper, we focus on the results of Renhao et al. especially for hierarchical set
data, and discuss the representation of hierarchical sets by specifically discussing hierarchical permutationequivalence / invariance.
27 Tsuyoshi Yoneda (Hitotsubashi Univ.)

Pointwise convergence theorem of mini-batch gradient descent in termsof deep neural network · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The theoretical understanding of deep neural network (DNN) has not yet been fully understood.
Nevertheless, even in this recent circumstance, Imaizumi-Fukumizu (2019) and Suzuki (2019) clarified thatthe learning ability of DNN is superior to the previous theories when the target function is non-smoothfunctions. In this talk we give a convergence problem in more practical setting. More precisely, we provethat a certain prescribed function pointwisely converges to a step function provided by mini-batch gradientdescent process with ReLU DNN.
28 Makoto Okumura (Hokkaido Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Masaharu Nagayama (Hokkaido Univ.)
Hironobu Fujiwara (RIKEN)
Yasugahira Yusuke (Hitachi, Ltd.)(Chuo Univ.)
Kota Ohno

Numerical simulations of a mathematical model of hair follicle formation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: As an appendage of the skin, a hair follicle is the source of the hair. Moreover, the hair follicle
has a cylinder-like structure. In this study, we attempt to examine the mechanism of hair follicle formationfrom a mathematical viewpoint by applying a mathematical model of the basement membrane, whichenables us to describe plastic deformation. In this presentation, we will introduce numerical examples ofour mathematical model and discuss what assumptions play an essential role in shaping the cylinder shapeof the hair follicle. If possible, we will also present the numerical results that consider the epithelium,
while previous mathematical models have considered only the basal layer, basement membrane, and dermal
structure.

Final: 2023/2/8
Applied Mathematics

29 Karel Svadlenka (Kyoto Univ.)

72

Variational analysis of finite strain elastoplasticity for structured materials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Structured materials, such as metallic alloys with atomic-scale layers, show peculiar deformation
patterns, which may have significant implications on material properties. In this talk, we discuss one
possible approach to modeling and understanding of this kind of pattern formation through the so-called
rate-independent evolution in the variational setting of finite-strain elastoplasticity. Besides mentioning
connections to homogenization via Gamma-convergence, we present the underlying mathematical theory
and show numerical simulations in comparison to experimental measurements.
14:15–14:40

Presentation Ceremony for the 2022 Applied Mathematics Prize

14:45–16:30
30 Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Makoto Nakamura (Osaka Univ.)

Numerical accuracy and stability of semilinear Klein–Gordon equationin de Sitter spacetime · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Klein–Gordon equation is known as the fundamental wave equation in relativistic phenomena
such as near light speed phenomena. We perform numerical simulations of this equation using the structurepreserving scheme in the de Sitter spacetime. The discretization equation proposed in our previous work
(J. Comput. Appl. Math. 361 pp.364–412) has good accuracy but poor numerical stability. In this talk,we propose a new discretization equation with the structure-preserving scheme and show numerical resultswith high-accuracy and high-stability.
31 Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Makoto Nakamura (Osaka Univ.)

On behaviors of solutions of semilinear Klein–Gordon equation in contracting de Sitter spacetime · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: de Sitter spacetime is a well-known model of expanding or contracting universes.

In thisspacetime, we investigate numerical solutions of the semilinear Klein–Gordon equation. In particular, in thecase of contracting spacetime, it is difficult to investigate the behaviors of the solutions even by numericalcalculations because of the blow-up solutions. Therefore, we apply the structure-preserving scheme to the
Klein–Gordon equation to obtain accurate and stable numerical solutions and show the behaviors of thesolutions.
(Kyoto Univ.)
32 Kota Takeda
Takashi Sakajo (Kyoto Univ.)

Computing an invariant measure of the N -vortex problem on the sphereby Hamiltonian Monte Carlo · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Hamiltonian Monte Carlo (HMC) is a stochastic method to approximate high-dimensional integrals
by the samples from the target distribution, efficiently by utilizing the Hamiltonian dynamics. In general, theefficiency of HMC is characterized by a geometric convergence rate of the associated Markov chain, known
as a property ‘geometric ergodicity’. For a class of target distributions on the Euclidean space, geometricergodicity for HMC has been established, however, that has not yet been established on manifolds. Hence,
we prove geometric ergodicity for HMC on compact manifolds. As an application, we consider the sampling
problem from the invariant measure of the N -vortex problem on the sphere, which is relevant to twodimensional turbulence on geophysical fluid.

Final: 2023/2/8
73

Applied Mathematics

33 Hiroshi Fujiwara (Kyoto Univ.)
Kamran Sadiq(Johann Radon Inst. for Comput. Appl. Math.)
Alexandru Tamasan(Univ. Central Florida)

On a Cauchy-type singular integral equation for x-ray computerized
tomography with partial measurement · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we propose a direct numerical reconstruction procedure for x-ray tomography withpartial measurement. The proposed method is based on Bukhgeim–Cauchy boundary integral formuladeveloped for an inverse source problem of the transport equation, and is characterized by a singular
integral equation with Cauchy kernel for the considering partial measurement case. We also show its
quantitative stability in terms of the condition number with a particular discretization for reliable numericalreconstruction.
34 Toshimasa Ishige (Chiba Univ.)
Akitoshi Takayasu (Univ. of Tsukuba)

Rigorous numerics for finding the monodromy of Picard–Fuchs differential equations for a family of K3 toric hypersurfaces · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce a method for finding monodromy matrices of linear differential equations
with finite-dimensional solution spaces using rigorous numerics. We also provide a result of computer-assisted
proof that yields monodromy matrices of Picard–Fuchs differential equations for a certain family of K3 toric
hypersurfaces.
35 Takehiko Kinoshita (Saga Univ.)
Yoshitaka Watanabe (Kyushu Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

Convergence order estimations of approximate inverse operator norm
for second-order elliptic linear operators · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the convergence order of the approximate inverse operator norm for√second-order elliptic linear operators. We show that the general order of convergence is O( h), and give
concrete computable error bounds for achieving the same order.
16:45–17:45

Talk Invited by Applied Mathematics Section

Koya Sakakibara(Okayama Univ. of Sci. / RIKEN)

Structure-preserving numerical analysis of interfacial phenomena

Summary: Soap bubbles, falling water droplets, and other phenomena that deform from moment to moment
are all around us. The problem of mathematically investigating these phenomena is known as the moving
boundary problem, which has been studied in mathematics, physics, and various other fields. Numericalanalysis of interfacial phenomena is more complicated than the usual numerical analysis of differential
equations on a fixed domain because the problem domain changes from moment to moment. In this talk,we will review what has been known about attempts to design structure-preserving numerical methods formathematical models describing interfacial phenomena. Further directions of research development will also
be discussed.

March 18th (Sat)

Conference Room VII

9:50–11:50
36 Toshikazu Kuniya (Kobe Univ.)

Hopf bifurcation in a delayed epidemic model with quarantine · · · · · · · 15

Summary: In this study, we construct a time-delayed epidemic model with quarantine and obtain sufficientconditions for a Hopf bifurcation, which represents the recurrent epidemic waves. We show that if the basic
reproduction number R0 is less than 1, then the disease-free equilibrium is globally asymptotically stable,
whereas if R0 > 1, then the unique endemic equilibrium exists and it can be destabilized and a nontrivial
periodic solution can arise in a Hopf bifurcation. Our numerical simulation suggests that the quarantine
and time delay play important roles in the occurrence of recurrent epidemic waves.

Final: 2023/2/8
Applied Mathematics

37 Yoshiki Takeguchi (Kyoto Univ.)
Kazuyuki Yagasaki (Kyoto Univ.)

74

Optimal control of the SEIR epidemic model using a dynamical systems
approach · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the susceptible-exposed-infected-removed (SEIR) epidemic model and apply optimal
control to it. Our approach is to reduce the computation of the optimal control input to that of the stablemanifold of an invariant manifold in a Hamiltonian system. Some numerical examples in which the computer
software AUTO is used to numerically compute the stable manifold are given to demonstrate the usefulnessof our approach for the optimal control in the SEIR model. Our study suggests how we can decrease thenumber of infected individuals quickly before a critical situation occurs while keeping social and economic
burdens small.
38 Sohei Tasaki (Hokkaido Univ.)
Hiroki Nagai(Univ. of Tokyo / Tohoku Univ.)
Luis Augusto Eijy Nagai(Univ. of Tokyo)
Ryuichiro Nakato (Univ. of Tokyo)
Masayuki Miura (Univ. of Tokyo)
Yu-ichiro Nakajima(Univ. of Tokyo / Tohoku Univ.)

Mathematical analysis of dedifferentiation in the intestinal epithelial
cell community · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The intestinal epithelium is a highly flexible and adaptive cell community that is formed andregulated by the proliferation and differentiation of intestinal stem cells (ISCs). We have quantitatively
analyzed the nutrient-dependent tissue expansion of the adult Drosophila intestinal epithelium just after
eclosion. We have shown that stem cell division alone cannot explain the increase in stem cell number,and have proposed a novel dedifferentiation phenomenon as a possible compensatory mechanism. We havedeveloped a mathematical model of intestinal epithelial cell society and established a simulation system thatenables quantitative prediction of cell population dynamics. The analysis is revealing that enteroendocrine
cell dedifferentiation is a good way to efficiently achieve intestinal enlargement while maintaining cell
diversity.
39 Kaname Matsue(Kyushu Univ. / Kyushu Univ.)
Hiroyuki Ochiai (Kyushu Univ.)
Hisatoshi Kodani (Kyushu Univ.)
Akitoshi Takayasu (Univ. of Tsukuba)

Correspondence between asymptotic expansions of blow-up solutions
for ODEs and dynamics at infinity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We provide a natural correspondence of eigenstructures of Jacobian matrices associated withequilibria for appropriately transformed two systems (describing asymptotic expansions and dynamics at
infinity) describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As acorollary, we see that asymptotic expansions of blow-ups themselves provide a criterion of the existence ofblow-ups with an intrinsic gap structure of stability information among two systems.
40 Yikan Liu(Hokkaido Univ.)

Initial-boundary value problems for coupled systems of time-fractional
diffusion equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is concerned with the initial-boundary value problem for a moderately coupled systemof time-fractional diffusion equations with Caputo derivatives of orders in (0, 1). Regarding the coupledpart of components as a source term, we define the mild solution by an integral equation. Then we
establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior of
the solution, which mostly inherit those of a single equation.

Final: 2023/2/8
75

Applied Mathematics

41 Tomoyuki Miyaji (Kyoto Univ.)
Robert Sinclair

A conjecture on the asymptotic reflection rule of a self-propelled particle· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a four-dimensional ODE model of a self-propelled particle that interacts repulsively
with the domain boundary. It is derived from certain planar reaction-diffusion systems. A previous study
proves that the particle governed by this model moves almost in a straight line and reflects from theboundary without collision. In addition, numerical simulations suggest that the angle of reflection is greaterthan that of incidence, which is proved under certain conditions. Recently, we have proposed a conjectureon the functional relationship between the angles. We will discuss how we arrived at the conjecture andbecame convinced.
42 Hiroshi Ishii(Kyoto Univ.)

Pattern dynamics depending on integral kernel shape in reactiondiffusion equations with sufficiently weak nonlocal effect · · · · · · · · · · · · 15

Summary: In this talk, we consider reaction-diffusion equations with nonlocal effects described by the
convolution with an appropriate integral kernel. Such a nonlocal effect is used to describe the diffusion
process of substances and cell-cell interactions, for example. This work is particularly concerned with the
behavior of the widths of phase-separated patterns. The equation of motion of the width is derived andapplied to several integral kernels as examples to explain how the pattern dynamics of the solution dependon the shape of the integral kernel.
14:15–15:05(Chuo Univ.)
43 Kota Ohno
Toshiyuki Ogawa (Meiji Univ.)

Stability of traveling wave in nonlocally coupled oscillator system · · · · 15

Summary: Coupled oscillator systems have been studied in various fields of physical and biological phenomena.
Among them, systems of nonlocally coupled oscillators can exhibit chimera states, which consist of spatiallycoherent and incoherent states. However, the stability and bifurcation origin of chimera states have notbeen understood. Stuart–Landau type nonlinearity enables us to formulate the stability problem of travelingwaves precisely through Floquet theory. We analyzed Floquet multiplier and confirmed the transition ofstability of traveling wave by changing the parameters of nonlocal coupling. In this study, we will state therelationship between the stability of traveling waves and chimera states.
44 Ayuki Sekisaka (Meiji Univ.)
Toshiyuki Ogawa (Meiji Univ.)

Stability problem of segmented pattern for oscillatory reaction-diffusion
systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In reaction-diffusion systems of oscillatory fields, especially those in which wave bifurcations occur,
it is known that traveling waves with periodic profiles appear. Even if the traveling waves are asymptoticallystable, starting from a random initial value, several segments are formed, each consisting of different periodic
traveling waves. Pattern dynamics is then observed in which the segments change from one to another.
The transition between different segments is considered to be the so-called defect solution. In this lecture,
we will discuss whether the defect solution can be regarded as a steady-state observation of the segment
pattern.
45 Toshiyuki Ogawa (Meiji Univ.)
Shunsuke Kobayashi(Univ. of Miyazaki)

Turing instability on compact metric graph · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Studies on the behavior of reaction-diffusion systems on a one-dimensional domain with junctions(metric graph) have been increasing recently. It is expected that joint research with cell physiology andecology will progress more and more in the future. So, we would like to clarify from the basics what kindof pattern formation occurs in compact metric graphs. First, by preparing 2 or 3 bounded intervals, let usclassify the metric graph that is created by connecting them, and consider the eigenvalue problem there.
Then, we describe the conditions under which Turing instability occurs for each modes, and discuss thedifferences in pattern formation by metric graphs.

Final: 2023/2/8
Applied Mathematics

15:20–16:20

76

Talk Invited by Applied Mathematics Section

Kei Nishi (Kyoto Sangyo Univ.)

Pulse dynamics in a three-component reaction-diffusion system

Summary: The pulse dynamics in a three-component FitzHugh–Nagumo system is considered both numerically and analytically. The system admits a pulse solution of bistable type, which exhibits a variety
of interface dynamics, not observed for the two-component FitzHugh–Nagumo systems. In this talk, we
focus on the parameter regime α > 0, β < 0, where there appear not only two types of pulse solutions,whose profiles are mutually inverted, but also multiple-pulse solutions which show collective motions suchas clustered traveling pulses and an array of oscillating pulses. In order to analytically investigate thesepulse behaviors, we apply the multiple scales method to the original reaction-diffusion system, and derive
finite-dimensional ordinary differential equations which describe the motions of the pulse interfaces. The
reduced ODEs enable us to reveal the global bifurcation structures of the pulse solutions, as well as theclustered multiple-pulse solutions, and to elucidate the mechanism for the rich variety of pulse dynamics ina clear, unified manner.

Final: 2023/2/8
77Topology

Topology
March 15th (Wed)Conference Room III

9:30–12:00
1 Shintaro Kuroki(Okayama Univ. of Sci.)

Orlik–Raymond type classification of simply connected 6-dimensional
torus manifolds with vanishing odd degree cohomology · · · · · · · · · · · · · 15

Summary: A torus manifold is defined as an even-dimensional compact manifold with a half-dimensional
torus action which has fixed points.

This notion was introduced by Hattori–Masuda in 2003 as thegeneralization of the toric and the quasitoric manifolds. The aim of this talk is to classify simply connected6-dimensional torus manifolds with vanishing odd-degree cohomology. It is shown that there is a one-toone correspondence between equivariant diffeomorphism types of such manifolds and 3-valent torus graphs
introduced by Maeda–Masuda–Panov. Using this correspondence and combinatorial arguments, we provethat such a manifold is equivariantly diffeomorphic to the 6-dimensional sphere or an equivariant connected
sum of copies of 6-dimensional quasitoric manifolds or 4-dimensional sphere bundles over the 2-dimensional
sphere.
2 Masakazu Nasu

The limits of resolving directions of automorphisms of sofic systems· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present the results that an automorphism of a sofic system has the same limits of resolving
directions as those of its canonical support by way of the Krieger cover and that a similar result to this holds
for an automorphism of a transitive sofic system and its canonical support by way of the Fischer cover. Oneof the corollaries to these proves that no automorphism of a transitive sofic system has an irrational unique
non-expansive direction.
3 Taketo Shirane (Tokushima Univ.)
Meirav Amram (Shamoon Coll. of Eng.)
Shinzo Bannai (Okayama Univ. of Sci.)
Uriel Sinichkin (Tel Aviv Univ.)
Hiro-o Tokunaga (Tokyo Metro. Univ.)

Splitting invariants and a π1 -equivalent Zariski pair of conic-line arrangements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the embedded topology of plane curves on the complex projective plane
P2 . It is known that there are π1 -equivalent Zariski pairs (C1 , C2 ) of plane curves C1 , C2 ⊂ P2 , i.e., C1 and C2
have the same embedded topology in their tubular neighborhoods but different embedded topology in P2 ,and π1 (P2 \ C1 ) ∼= π1 (P2 \ C2 ). Known examples of π1 -equivalent Zariski pairs consist of curves containing acomponent with either singularities or genus g ≥ 1. The aim of this talk is to give a π1 -equivalent Zariski
pair of conic-line arrangements, i.e., a pair of curves consisting of smooth rational curves.
4 Kaori Yamazaki(Takasaki City Univ. of Econ.)

Extensions of continuous increasing functions · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we study extensions of continuous increasing functions, and provide an increasing
version of Gillman–Jerison theorem.
5 Naoki Fukasawa (Tokyo Metro. Univ.)

Persistent cohomology and computation of cup length function · · · · · · 15

Summary: We introduce the structure theorem of the persistent cohomology to describe the representative
cocycles in detail. Then, taking cup products of representative cocycles, we can compute the cup length
function of a finite metric space.

Final: 2023/2/8
Topology

6 Yu Tajima (Hokkaido Univ.)
Masahiko Yoshinaga (Osaka Univ.)

78

Magnitude homotopy type of graphs and Mayer–Vietoris type theorem· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Magnitude homology is defined by Hepworth and Willerton as a categorification of the magnitude(an invariant for metric spaces). They proved the Kunneth formula and Mayer–Vietoris type theorem for
magnitude homology of graphs. Recently, Asao–Izumihara introduced the pair of simplicial complexes (K,K’) whose homology groups are isomorphic to direct summands of graph magnitude homology groups. We
call the CW complex K/K’ magnitude homotopy type. In this talk, we give a new proof of Mayer–Vietoris
type theorem using Discrete Morse theory on magnitude homotopy types. If time permits, we also talkabout generalizatios to metric spaces.
7 Shuichi Harako (Univ. of Tokyo)

The modular class of an orientable ρ-Q-manifold · · · · · · · · · · · · · · · · · · · 15

Summary: As one generalization of Lie algebras and commutative algebras, we have ρ-Lie algebras andρ-commutative algebras, respectively. We will introduce a concept of a ρ-manifold, whose functional algebra
is locally isomorphic to a ρ-commutative algebra, and discuss its modular class where the ρ-manifold isorientable and equipped with a Q-structure.
8 Shun Wakatsuki (Nagoya Univ.) ♭ Independence complexes of grid graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Takahiro Matsushita(Univ. of Ryukyus)
Summary: We determine the homotopy types of the independence complexes of (n × 4), (n × 5) and (n × 6)square grid graphs. In fact, they are homotopy equivalent to wedges of spheres.
14:20–15:20

Talk Invited by Topology Section

Noboru Ogawa(Tokai Univ.)

Liouville and Weinstein structures on convex symplectic manifolds

Summary: In symplectic geometry, there are two important classes on convexity: Liouville structures andWeinstein structures. The former is a symplectic manifold equipped with a conformally expanding symplectic
vector field which is pointing outward. The latter is imposed so that the vector field is gradient-like. Suchstructures have played a significant role in the study of symplectic and contact topology. For example, theconvexity provides a constraint on the behavior of pseudo-holomorphic curves by the maximum principle.
By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff
gave the first example which is a Liouville manifold without any Weinstein structures. The purpose ofthis talk is to present recent advances on the difference between the two structures, up to homotopy. In
particular, I will show that the stabilization of McDuff’s example admits a flexible Weinstein structure.
The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu(Kyoto University of Education). If time permits, I would like to discuss some open questions, progress andperspective.
15:40–17:30
9 Naotsugu Chinen(Nat. Defense Acad. of Japan)

Isometry groups of symmetric products of (Rk )qp · · · · · · · · · · · · · · · · · · · 15

Summary: By Fn (X), n ≥ 1, we denote the n-th symmetric product of a metric space (X, d) as the spaceof the nonempty finite subsets of X with at most n elements endowed with the Hausdorff metric dH . By
Iso(X) we denote the topological group of all isometries from X onto itself with the topology of pointwise
convergence. We are interested in what topological group Iso(Fn (X)) is.The aim is to decide a topologicalgroup structure of Iso(Fn ((Rk )qp )) for any (n, k, p, q) ∈ N × N × (N ∪ {∞}) × (N ∪ {∞}).

Final: 2023/2/8
79Topology

10 Atsuhide Mori (Osaka Dent. Univ.)

Mutual Bayesian learning for manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In previous work, the author described the geometry of Bayesian learning on a manifold. In thistalk, we take the square of any manifold and a positive function which takes the maximum 1 on the diagonal
set. Then we define the mutual Bayesian learning between the factors of the square. Particularly, we
consider mutual learning between two copies of the parameter space of a statiscal model, and associate theabove function with the relative entropy. Although the mutual learning forgets all about the model except
the relative entropy, it still substitutes for the usual Bayesian estimation of the parameter in a certain case.
11 Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Tohoku Univ.)

Unbounded sl3 -laminations and their shear coordinates · · · · · · · · · · · · · 15

Summary: Generalizing the work of Fock–Goncharov on rational unbounded laminations, we give a geometricmodel of the tropical points of the moduli space XP GL3 ,Σ of framed P GL3 -local systems on a marked surface
Σ based on the Kuperberg’s sl3 -webs. We introduce their tropical cluster coordinates as an sl3 -analogue of
the Thurston’s shear coordinates associated with any ideal triangulation. We also describe tropical points
of Goncharov–Shen’s moduli space PP GL3 ,Σ . Then we give a tropical anologue of gluing morphisms among
the moduli spaces as a geometric gluing procedure of sl3 -laminations with “shearings”. We also investigate
a relation to the graphical basis of the sl3 -skein algebra by Ishibashi–Yuasa, which conjecturally leads to aquantum duality map.
12 Katsuhisa Koshino (Kanagawa Univ.)

A characterization of compact sets in Lp -spaces and its application· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give a characterization of compact sets in Lp -spaces on metric measure spaces.
As its application, we investigate the topological types of the subspace consisting of lipschitz functions withbounded supports.
13 Masanori Adachi (Shizuoka Univ.)
Yoshifumi Matsuda(Aoyama Gakuin Univ.)
Hiraku Nozawa (Ritsumeikan Univ.)

Harmonic measures and rigidity for surface group actions on the circle· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study rigidity properties of surface group actions on the circle via foliated harmonic measureson the suspension bundles. We show a curvature estimate and a Gauss–Bonnet formula for an S 1 -connection
obtained by taking the average of the flat connection on the suspension bundle with respect to a harmonicmeasure. As consequences, we give a precise description of the harmonic measure on suspension foliations
with maximal Euler number and an alternative proof of rigidity theorems of Matsumoto and Burger–Iozzi–
Wienhard.

March 16th (Thu)

Conference Room III

9:30–12:00
14 Takahiro Yamamoto(Tokyo Gakugei Univ.)

Fiber singularities of continuous maps · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of fiber-singularities of continuous maps between topological manifolds are introduced.
Then, we investigate some examples of fiber-singularities and, study fiber-singularities of simplicial maps of
PL maps of surfaces.

Final: 2023/2/8
Topology(KLab Inc.)
15 Naoki Hamada(Keio Univ.)
Kenta Hayano
Hiroshi Teramoto (Kansai Univ.)

80

Classification and recognition of constraint function-germs and feasible
set-germs in multiobjective optimization · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For functions g1 , . . . , gq and h1 , . . . , hr on the Euclidian space, we consider the minimizing
problems of some given functions on the set M (g, h) = {x | ∀i, gi (x) ≤ 0, ∀j, hj (x) = 0}. The functions gi ’s,
hj ’s and the set M (g, h) are respectively called the constraint functions and the feasible set for the problem.
In this talk, we will explain the results on classification and recognition of constraint function-germs undersuitable equivalence for them (called K[G]-equivalence). If time permits, we will also discuss how the results
are related with classification of feasible set-germs.
16 Erika Kuno

(Osaka Univ.)

Uniform hyperbolicity of nonseparating curve graphs of nonorientablesurface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let N be a connected nonorientable surface with or without boundary components and punctures.
We prove that the graph consists of the isotopy classes of nonseparating curves of N is connected and Gromov
hyperbolic with a constant which does not depend on the topological type of the surface by using the bicorn
curves introduced by Przytycki and Sisto. The proof is based on the argument by Rasmussen on the uniform
hyperbolicity for the graphs consists of the isotopy classes of nonseparating curves for orientable surfaces.
(Osaka Univ.)
17 Erika Kuno
Mitsuaki Kimura (Kyoto Univ.)

Uniform hyperbolicity of fine curve graphs of nonorientable surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A fine curve graph defined by Bowden, Hensel, and Webb (J. Amer. Math. Soc. (2021)) is a new
curve graph consists of all essential simple closed curves on a surface. They proved that the fine curve graphof any closed orientable surface of genus g ≥ 1 is uniformly hyperbolic in the sense of Gromov. We provedthat the fine curve graph of any closed nonorientable surface of genus g ≥ 2 is also uniformly hyperbolic.
18 Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)
Nao Imoto

Action on non-separating simple closed curves by the level 2 mappingclass group of a non-orientable closed surface · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The level 2 mapping class group M2 (N ) of a non-orientable closed surface N is the subgroupof the mapping class group of N consisting of elements acting trivially on H1 (N ; Z/2Z). In our work, we
proved that for any non-separating simple closed curves α and β of N , there is φ ∈ M2 (N ) such thatφ(α) = β if and only if α and β are equal as elements in H1 (N ; Z/2Z).
19 Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)
Nao ImotoThe group generated by squares of Dehn twists about non-separating
simple closed curves of a non-orientable closed surface · · · · · · · · · · · · · · 15

Summary: The level 2 mapping class group of an orientable closed surface is equal to the group generated
by squares of Dehn twists about non-separating simple closed curves. In our work, we proved that the twist
subgroup of the level 2 mapping class group of a non-orientable closed surface is not equal to the group
generated by squares of Dehn twists about non-separating simple closed curves and Dehn twists about
separating simple closed curves. As an application, we gave a finite generating set for this group.
20 Genki Omori (Tokyo Univ. of Sci.)

A finite presentation for the balanced superelliptic handlebody group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The balanced superelliptic handlebody group is the normalizer of the transformation group of
the balanced superelliptic covering space in the handlebody group of the total space. We give a finite
presentation for the balanced superelliptic handlebody group. To give this presentation, we construct afinite presentation for the liftable Hilden group.

Final: 2023/2/8
81Topology

21 Genki Omori (Tokyo Univ. of Sci.)

A small generating set for the balanced superelliptic handlebogy group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The balanced superelliptic handlebody group is the normalizer of the transformation group of
the balanced superelliptic covering space in the handlebody group of the total space. We prove that thebalanced superelliptic mapping class group is generated by four elements. To prove this, we also proved thatthe liftable Hilden group is generated by three elements. This generating set for the liftable Hilden group is
minimal except for some hyperelliptic cases and the generating set for the balanced superelliptic mappingclass group above is also minimal for several cases.
13:00–14:00
22 Teruaki Kitano (Soka Univ.)
Tatsuro Shimizu (Tokyo Denki Univ.)

On the torus sum formula of Reidemeister torsion defined by Morse–
Smale flows · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider Reidemeister torsion for a 3-manifold. It can defined by several ways. For a 3manifold with a torus decomposition, the torus sum formula of Reidemeister torsion is well known. In thistalk we give a proof of the torus sum formula by using Morse–Smale flows.
23 Masakazu Teragaito (Hiroshima Univ.)

Hyperbolic L-space knots and their Upsilon invariants · · · · · · · · · · · · · · 10

Summary: For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on theinterval [0, 2]. It is known that for an L-space knot, the Upsilon invariant is determined only by theAlexander polynomial. We exhibit infinitely many pairs of hyperbolic L-space knots such that two knotsof each pair have distinct Alexander polynomials, so they are not concordant, but share the same non-zero
Upsilon invariant. Conversely, we examine the restorability of the Alexander polynomial of an L-space knot
from the Upsilon invariant through the Legendre–Fenchel transformation.
24 Teruhisa Kadokami (Kanazawa Univ.)

The Ma–Qiu index and the Nakanishi index for a fibered knot are equal,and ω-solvability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a knot K, let G(K) be the knot group of K, a(K) the Ma–Qiu index, which is the minimal
number of normal generators of the commutator subgroup of G(K), and m(K) the Nakanishi index of K,
which is the minimal number of generators of the Alexander module of K. We generalize the notions fora pair of a group G and its normal sugroup N , and we denote them by a(G, N ) and m(G, N ) respectively.
Then it is easy to see m(G, N ) ≤ a(G, N ) in general. We also introduce a notion “ω-solvability” for a group.
Our main theorem is that if N is ω-solvable, then we have m(G, N ) = a(G, N ). As corollaries, for a fiberedknot K, we have m(K) = a(K), and we could determine the MQ indices of prime knots up to 9 crossingscompletely.

March 17th (Fri)

Conference Room III

9:30–12:00(Nihon Univ.)
25 Eri Matsudo(
Kanako Oshiro Sophia Univ.)
Gaishi Yamagishi (Sophia Univ.)

Minimum numbers of Dehn colors and R-palette graphs · · · · · · · · · · · · 10

Summary: We consider the number of colors for Dehn-colorings, and we define a R-palette graphs. In thistalk, for any Dehn p-colorable knot, we give a lower bound of the minimum number of colors on diagrams.

Final: 2023/2/8
Topology

26 Kazuhiro Ichihara (Nihon Univ.)
Katsumi Ishikawa (Kyoto Univ.)
Masaaki Suzuki (Meiji Univ.)(Nihon Univ.)
Eri Matsudo

82

Two-tone colorings and surjective dihedral representations for links · · · 10

Summary: It is well-known that a knot group admits a surjective homomorphism to the dihedral group ofdegree n if and only if the knot is Fox n-colorable. However, it is not true for links with two or morecomponents. In this talk, I will introduce a two-tone coloring on a link diagram, and give a condition forlinks that the link groups admit surjective representations to dihedral groups.
27 Takefumi Nosaka (Tokyo Tech)

Symmetric rack cocycle invariants of closed 3-manifolds · · · · · · · · · · · · · 10

Summary: We establish a new approach to obtain 3-manifold invariants via Dehn surgery.

For this,

we introduce racks with good involution and Property FR, and define cocycle invariants as 3-manifold
invariants.
28 Shosaku Matsuzaki(Int. Aﬀairs Ashikaga Univ.)
Tomo Murao (Waseda Univ.)

Spatial surfaces and multiple group rack cocycle invariants · · · · · · · · · · 10

Summary: A spatial surface is a compact surface embedded in the 3-sphere. A multiple group rack is analgebraic structure motivated from Reidemeister moves of oriented spatial surfaces. In this talk, we introduce
a multiple group rack cocycle invariant for oriented spatial surfaces and give some calculation examples.
29 Yuta Taniguchi (Osaka Univ.)
Kokoro Tanaka (Tokyo Gakugei Univ.)

A central extension of the n-quandle of a knot · · · · · · · · · · · · · · · · · · · · · 15

Summary: The fundamental quandle is a powerful invariant for knots. However, it is difficult to compare
them. Then, we often use a certain quotient of the fundamental quandle of a knot, which is called ann-quandle of a knot. In this talk, we show that the fundamental quandle of the n-twist spun knot, which is
a 2-knot introduced by Zeeman, is a central extension of the n-quandle. As a corollary, we determine thesecond quandle homology group of n-quandles.
30 Kokoro Tanaka (Tokyo Gakugei Univ.)
Yuta Taniguchi (Osaka Univ.)

Knot quandles and knot groups for 2-knots · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give examples of 2-knots with the same knot group but different knot quandles by analyzing
the knot quandles of twist-spun knots. As a byproduct of our method, we give a classification of all
twist-spun knots with finite knot quandles.
31 Kodai Wada

(Kobe Univ.)

Finite type invariants of ribbon 2-dimensional string links with generalized Brunnian properties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Gusarov and Habiro independently gave a topological interpretation of finite type invariants for
1-dimensional knots in terms of Ck -equivalence. As a 4-dimensional analogue, Watanabe introduced thenotion of RCk -equivalence on ribbon knotted surfaces and proved that two ribbon 2-dimensional knots are
RCk -equivalent if and only if they cannot be distinguished by any finite type invariant of degree less than k.
In this talk, we provide an extension of the above result of Watanabe to ribbon 2-dimensional string links
with generalized Brunnian properties.
14:20–15:20

Talk Invited by Topology Section

Atsushi Ishii (Univ. of Tsukuba)

Alexander type invariants of groups, quandles and MCQs

Summary: Groups, quandles and MCQs are algebraic objects appeared in low-dimensional topology. In
particular, the notions of quandles and multiple conjugation quandles (MCQs) were introduced via theaxioms corresponding to the Reidemeister moves for oriented knots and handlebody-knots, respectively. In
this talk, we discuss Alexander type invariants of groups, quandles and MCQs, which include the Alexander
ideal and the (twisted) Alexander polynomial.

Final: 2023/2/8
83

Topology

15:40–17:00
32 Yohei Wakamaki (Osaka Univ.)

Corks of some rational surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Corks of 4-manifolds are one of the most important objects in the study of exotic 4-manifolds.
Nevertheless, we only have a few explicit examples of corks of standard simply-connected closed 4-manifolds
with small second Betti numbers b2 . In this talk, we give the first example of a cork of CP2 #8CP2 . This
achieves the smallest b2 where a cork of standard simply-connected closed 4-manifold has been found. We
also talk about new examples of corks of CP2 #9CP2 .
33 Nobutaka Asano(Tsuyama Nat. Coll. of Tech.)
Hironobu Naoe (Chuo Univ.)
Masaki Ogawa (Saitama Univ.)

Some lower bounds for the Kirby–Thompson invariant of 4-manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A trisection is a decomposition of a 4-manifold into three 1-handlebodies. This decomposition ischaracterized by a diagram called a trisection diagram. A trisection diagram is a 4-tuple consisting of aclosed surface and three cut systems. Kirby and Thompson introduced an invariant of a 4-manifold thatis a kind of complexity defined by its trisection diagrams. This invariant is called the Kirby–Thompson
invariant. In this talk, we give some lower bounds for the Kirby–Thompson invariant of certain 4-manifolds.
As an application, we find the first example of a 4-manifold with non-trivial Kirby–Thompson invariant.
34 Tsukasa Isoshima (Tokyo Tech)
Masaki Ogawa (Saitama Univ.)

Trisections of the 4-sphere obtained by Gluck twisting · · · · · · · · · · · · · · 15

Summary: A trisection of a 4-manifold, introduced by Gay and Kirby in 2012, is a decomposition of the
4-manifold into three 4-dimensional 1-handlebodies. A trisection can be described by a trisection diagramthat is similar to a Heegaard diagram. In this talk, we construct infinitely many trisection diagrams of the
4-sphere obtained by Gluck twisting along some spun torus knots. We also study the standardness of thetrisection diagrams.
35 Takahiro Oba(Osaka Univ.)

Symplectic submanifolds in dimension 6 from Lefschetz fibrations · · · · 15

Summary: Thanks to the affirmative answer to the symplectic Thom conjecture, all connected symplectic
surfaces representing the same homology class in a closed symplectic 4-manifold are diffeomorphic. In
higher dimension, for example, take CP3 with the Fubini–Study form. Then, it is known that its connected
symplectic submanifolds representing the class d[CP2 ] are mutually diffeomorphic as long as 1 ≤ d ≤ 3. In
this talk, I will present arbitrarily (finitely) many codimension 2 connected symplectic submanifolds in aclosed symplectic 6-manifold which are mutually homotopy inequivalent but homologous. A key ingredientof the construction is hyperelliptic Lefschetz fibrations.

Final: 2023/2/8
Inﬁnite Analysis

84

Inﬁnite Analysis
March 17th (Fri)

Conference Room IX

9:45–10:45
1 Yuichi Ueno
(Kogakkan Univ. / Kobe Univ.)

Polynomial Hamiltonians for quantum Garnier system in two variables· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Garnier system is the extension of Painlevé equations and is given as Frobenius integrable
multi-time Hamiltonian systems. In this talk, we construct and characterize the quantum Gariner system
by certain holomorphic properties. The characterization of the classical Garnier system by holomorphic
properties has been given by Sasano, and our result is a quantization of that work. In other words, we
introduce quantum canonical transformations such that the Hamiltonian system of the Garnier system isagain transformed into a polynomial Hamiltonian system, and show that the Hamiltonian can be uniquely
characterized by this holomorphic properties.
2 Nobutaka Nakazono(Tokyo Univ. of Agri. and Tech.)Consistency around a cube property of Hirota’s discrete KdV equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It has been unknown whether Hirota’s discrete analogue of the Korteweg-de Vries (KdV) equation
have the consistency around a cube (CAC) property, which is known as an integrability of 2-dimensional
difference equation. In this talk, we show that Hirota’s discrete KdV equation has the CAC property.
3 Takao Suzuki(Kindai Univ.)

An affine Weyl group action on the basic hypergeometric series arisingfrom the q-Garnier system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, we formulated the q-Garnier system and its variations as translations of an extended
(1)

(1)

(1)

affine Weyl group of type A2n+1 × A1 × A1 . On the other hand, those systems admit particular solutionsin terms of the basic hypergeometric series n+1 ϕn . In this talk, we investigate an action of the extended
affine Weyl group on n+1 ϕn . This talk is based on a joint work with Taiki Idomoto of Kindai University.
4 Yousuke Ohyama (Tokushima Univ.)(1)

Boundary behavior of q-Painlevé equation of type A4 · · · · · · · · · · · · · · 15

Summary: We study asymptotic analysis on the q-Painleve V equation around the origin. We solve theq-Riemann–Hilbert problem for any asymptotic series of q-Painleve V functions. We show the Mano-type
decomposition for q-Painleve V.
11:00–12:00
Rei Inoue

Talk Invited by Inﬁnite Analysis Special Session(Chiba Univ.)

Cluster realization of Weyl groups and its applications to representation
theorySummary: The cluster algebra is a commutative algebra introduced by Fomin and Zelevinsky around 2000.
The characteristic operation in the algebra called ‘mutation’ is related to various notions in mathematics
and mathematical physics.
In this talk we introduce a realization of Weyl groups in terms of cluster mutations, for finite dimensional
semisimple Lie algebras. We discuss its applications to (1) the geometric R-matrix of symmetric power
representations for the affine quantum algebra of A-type, and to (2) the q-characters of quantum non-twisted
affine algebras introduced by Frenkel and Reshetikhin, when q is a root of unity. If time permits we alsomention the application to higher Teichmüller theory.
This talk is based on joint works with Thomas Lam, Pavlo Pylyavskyy, Tsukasa Ishibashi, Hironori Oya,and Takao Yamazaki.

Final: 2023/2/8
85

Inﬁnite Analysis

March 18th (Sat)

Conference Room IX

10:00–10:45
5 Nao Komiyama (Nagoya Univ.)

Associators and the Grothendieck–Teichmüller group in mould theory· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we explain the mould theory introduced by Jean Ecalle, and we introduce mould
theoretic formulations of Drinfeld’s notion of the associator set and that of the Grothendieck–Teichmüllergroup. This talk is based on the joint work with Hidekazu Furusho and Minoru Hirose.
6 Atsuo Kuniba (Univ. of Tokyo)
Shuichiro Matsuike (Univ. of Tokyo)
Akihito Yoneyama (Univ. of Tokyo)

New solutions to the tetrahedron equation associated with quantizedsix-vertex models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we present a family of new solutions to the tetrahedron equation of the form
RLLL = LLLR, where L operator may be regarded as a quantized six-vertex model whose Boltzmann
weights are specific representations of the q-oscillator or q-Weyl algebras. When the three L’s are associatedwith the q-oscillator algebra, R coincides with the known intertwiner of the quantized coordinate ring
Aq (sl3 ). On the other hand, L’s based on the q-Weyl algebra lead to new R’s whose elements are either
factorized or expressed as a terminating q-hypergeometric type series.
7 Toshiki Nakashima (Sophia Univ.)

Geometric crystal on unipotent variety and crystal of modified quantum
algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We shall define a geometric crystal structure on the unipotent variety of a simple, simply connectedcomplex algebraic group. In SL(2)-case, certain relation to crystal base of a modified quantum algebra will
be presented.
11:00–12:00

Talk Invited by Inﬁnite Analysis Special Session

Travis Scrimshaw (Hokkaido Univ.) ♭ Krystal theory
Summary: Kashiwara’s theory of crystal bases has been applied to many different problems in representation
theory, physics, and geometry. In this talk, we will focus on their appearance in the K-theoretic Schubert
calculus of the Grassmannian. Specifically, we look at the symmetric function representatives of K-theory
classes that arise from Schubert varieties called (symmetric) Grothendieck polynomials {Gλ }λ and three otherrelated bases: the dual basis and their “weak” analogs. We construct a gln -crystal using the combinatorialdescriptions of Buch and Lam–Pylyavskyy to describe the decomposition of these bases into Schur functions
and describe their multiplicties. We will then discuss extensions to the (refined) canonical Grothendieckpolynomials introduced by Hwang et al. and Yeliussizov. This suggest an extension of Kashiwara’s theory
which we call K-crystals, or Krystals for short. We conclude with some open problems. This is based on
joint works with Graham Hawkes, Cara Monical, Oliver Pechenik.