Final: 2022/3/4“ The Mathematical Society of Japan
2022 Annual Meeting

Titles and Short Summaries of the Talks

March, 2022
at Saitama University2022 The Mathematical Society of Japan
ANNUAL MEETING
Dates: March 28th (Mon)–31st (Thu), 2022
Supported by: Saitama University
Venue: Saitama University
Shimo-Okubo 255, Sakura-ku, Saitama-shi
Contact to: Faculty of Science, Department of Mathematics,
Saitama University
Shimo-Okubo 255, Sakura-ku, Saitama-shi
mail saitama22mar mathsoc jp
The Mathematical Society of Japan

I

II

III

IV

V

VI

VII

VIII

IX

1-205,
1-206,
1-207,
1-301,
1-304,
1-401,
1-402,
1-403,
3-101,
1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 1st Lecture Hall 3rd Lecture Hall

Functional
Analysis

Functional Statistics andEquations Probability

10:00–11:30

9:00–12:00
14:15–16:15

28th

9:00–11:50
14:15–15:05(Mon)

AlgebraAppliedMathematics

Geometry

Topology

9:30–11:45
15:30–17:40

10:00–12:00
14:15–16:00

9:20–12:00
14:15–16:00

9:30–12:00
14:15–15:05

Featured Invited Talks

ComplexAnalysis

Found. of Math.
& Hist. of Math.

9:30–11:50

9:50–11:20
15:45–17:15

13:00–14:00

Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk
14:15–15:15

16:30–17:30

15:15–16:15
16:30–17:30

Functional
Analysis

Functional Statistics andEquations Probability

10:00–12:00

9:00–12:00

9:00–11:30

14:15–15:15

16:15–17:15

16:15–17:15

15:20–16:20

14:15–15:15

14:30–15:30

AlgebraAppliedMathematics

Geometry

Topology

ComplexAnalysis

Found. of Math.
& Hist. of Math.

9:00–12:00
13:00–14:00

10:00–11:45
13:15–14:15

9:45–11:45

9:30–11:50

9:30–11:30

9:45–11:25

29th Invited Talk Invited Talk
(Tue)

13:00–14:00

Invited Talk Invited Talk Invited Talk Invited Talk

13:00–14:00

13:15–14:15

13:15–14:15

13:15–14:15

13:00–14:00

MSJ Prizes Presentation (1-301, 1st Lecture Hall) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:45–15:15)
Plenary Talks(1-301, 1st Lecture Hall) Spring Prize Winner · · · · · · · · · · · · · · · · · · (15:30–16:30)
Yoshiko Ogata (Univ. of Tokyo) · · · · · · · · · (16:45–17:45)
Functional
Analysis

Functional Statistics andEquations Probability

10:00–11:30

9:00–12:00
14:15–16:15

9:50–11:40

30th

Algebra9:30–10:30

AppliedMathematics
9:00–10:45
14:15–17:00

Featured Invited Talks(Wed)

Geometry

Topology

RealAnalysis

InﬁniteAnalysis

9:10–11:45

9:30–12:00
14:15–15:15

9:30–11:45
14:30–16:00

10:00–12:00
14:15–14:50

13:00–14:00

Invited Talk Invited Talk Invited Talks Invited Talks Invited Talk Invited Talks Invited Talk Invited Talk Invited Talk
14:15–15:15

16:30–17:30

14:25–15:25
15:45–16:45

Functional Statistics andEquations Probability
31st

9:00–12:00
14:15–16:15(Thu)

9:50–11:40
14:20–16:25

14:15–15:15
15:25–16:25
16:35–17:35

Algebra9:30–12:00
14:15–16:00

11:00–12:00

14:15–15:15
15:30–16:30

AppliedMathematics

Geometry

9:00–10:45

9:15–12:00

Featured Invited Talks

15:30–16:30

16:15–17:15

15:00–16:00

Real
Analysis

InﬁniteAnalysis

9:30–12:00
14:15–15:15

10:00–12:00

13:00–14:00

Invited Talk

Invited Talk

Invited Talk Invited Talk

16:30–17:30

11:00–12:00

15:30–16:30

14:15–15:15

Final: 2022/3/4
3

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

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

Foundation of Mathematics and History of Mathematics

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

5March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

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

20March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

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

28

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

32

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

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

45

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

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

50

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

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

54

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

Final: 2022/3/4
4

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

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

65

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

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

76

March 28th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

March 29th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

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

82

March 30th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

March 31st (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

Final: 2022/3/4
1

Plenary Talks

Plenary Talks
March 29th (Tue) 1-301, 3F, 1st Lecture Hall
Award Lecture for the 2022 MSJ Spring Prize
Spring Prize Winner····················································(15:30–16:30)

Yoshiko Ogata (Univ. of Tokyo)

Classiﬁcation of gapped ground state phases in quantum spin
systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(16:45–17:45)

Summary: Recently, classiﬁcation problems of gapped ground state phases attract a lot of attention in quantum
statistical mechanics. We explain about our operator algebraic approach to these problems.

Final: 2022/3/4
Featured Invited Talks

2

Featured Invited Talks
March 28th (Mon)
Conference Room II
Yuichi Yoshida(Nat. Inst. of Informatics)

Spectral theory for directed graphs and hypergraphs · · · · · ·(13:00–14:00)

Summary: The usual spectral graph theory is a theory for undirected graphs that considers a matrix called
the Laplacian and uses its eigenvalues and eigenvectors to reveal the properties of the graph. In practicalapplications, however, directed graphs, which have orientated edges, and hypergraphs, which can containmore than three vertices in a single edge, are also very important objects. To ﬁll this gap, spectral theory
for directed graphs and hypergraphs has recently been developed, and various results such as clustering andsparsiﬁcation were obtained. Laplacians for directed graphs and hypergraphs are not matrices (i.e., linear
operators), but nonlinear (multivalued) operators, and key mathematical tools that help us to analyze those
Laplacians are the theories of submodular functions and monotone operators. In this talk, I will review these
progresses and discuss future outlook.
Conference Room III
Guest Talk from the Japan Society for Industrial and Applied Mathematics
Taiji Suzuki (Univ. of Tokyo) Mathematical theories of deep learning · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: In this talk, I present mathematical theories of deep learning, especially, I discuss how deeplearning can outperform shallow learning methods such as kernel methods and show its connection to classic
statistics/machine-learning theories such as “sparseness.” First, I will introduce some examples in which
deep learning can outperform the shallow methods, in which sparsity and non-convex geometry of the targetfunction space play the essential role. Next, I present a deep learning optimization theory based on anoisy gradient descent, and show how it can achieve the global optimal solution. Theoretical tools fromthe probability theory such as stochastic diﬀerential equations and Wasserstein geometry play the key role.
Throughout the talk, I also discuss the limitation of the current theory to explain the behavior of deeplearning.

Final: 2022/3/4
3Featured Invited Talks

Conference Room IV
Kenji Ueno
(Yokkaichi Univ. / Kyoto Univ.⋆)

Yang Hui suanfa and Seki Takakzu · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: This talk will focus mainly on the Yang Hui suanfa and discuss how it inﬂuenced the mathematics
of Seki Takakazu, such as the summation of inﬁnite geometric series, the numerical solution of algebraic
equations (Seki–Horner method), and equation theory. Yang Hui was a mathematician active in the Southern
Song dynasty in the second half of the 13th century. His three books, published in the 1270s, were compiledin the Ming dynasty and published in 1378 as the Yang Hui suanfa. In this book, counting rods was used as
the basis of calculation. However, as the abacus became popular in China, the counting rods was no longer
used and the Yang Hui suanfa was lost. The book was reprinted in Korea, and the edition published in 1433
was brought to Japan, where it can still be seen today. This book is considered by historians of mathematics
to be an elementary textbook, as it describes how to calculate with counting rods and how to solve equations
using counting rods. From a mathematical point of view, however, the ﬁrst chapter, in which the method of
rapid arithmetic is described, is very interesting because it describes how to calculate using various properties
of integers. In addition, the method for solving quadratic and degree 4 equations using counting rods inYang Hui suanfa contains instructions on how to move the rods, which may have helped Seki Takakazu tounderstand the Tianyuan shu.
Seki Takakazu studied and transcribed this Yang Hui snafu. This transcription is not a mere copy of theoriginal, but a kind of revised edition, in which he corrected errors in the solution, corrected textual errors in
the original, and changed the order of the chapters according to the year of publication. Although the original
manuscript by Seki Takakazu has been lost, two manuscripts have survived. There are subtle diﬀerences
between the two manuscripts, such as the diﬀerent dates of Seki’s transcriptions. By comparing the two
manuscripts, this talk will show that the two manuscripts may be copies of the same manuscript, and will
clarify the dating of Seki Takakazu’s manuscript.

March 30th (Wed)Conference Room II

Masahiro Kubo (Wakayama Univ.)

Time-dependent subdiﬀerential evolution equations and quasivariational evolution equations · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: We review the theory of time-dependent subdiﬀerential evolution equations and its application toquasi-variational evolution equations. The key concept is the energy inequality satisﬁed by the solution of
the evolution equation. We consider evolution equations of parabolic as well as elliptic-parabolic types.
Conference Room IV

Kimihiko Motegi (Nihon Univ.)

Twisting knots and twisting Dehn surgeries · · · · · · · · · · · · ·(13:00–14:00)

Summary: Let K be a knot in the 3-sphere S 3 . Take a trivial knot c disjoint from K. Cutting K along a disk
bounded by c, and connecting it again after n full twists, we obtain a new knot Kn in S 3 . We call Kn the
knot obtained from K by an n-twist about a twisting circle c. Twisting may be applied to a Dehn surgery(K, r) (“cut and paste” of a tubular neighborhood of K) by twisting K and the surgery slope r (describing
the “pasting”) simultaneously to obtain a new Dehn surgery (Kn , rn ).
In this talk we explain how we use twisting to construct the “Seifert Surgery Network” which gives us aperspective on the entirety of Dehn surgeries producing Seifert ﬁber spaces. This viewpoint naturally leads
us to a study of twist families of Heegaard Floer L-space knots. Then we illustrate relationships among an
asymptotic behavior of Kn as |n| → ∞, the position of twisting circles, and a pattern of occurrence of L-spaceknots—and more generally, tight ﬁbered knots—in twist families. We will also discuss a novel characterizationof braid axes in this context.

Final: 2022/3/4
Featured Invited Talks

4

March 31st (Thu)
Conference Room III

Akihiro Higashitani (Osaka Univ.)

Various commutative rings arising from combinatorial objects · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: One of the goals in the area of combinatorial commutative algebra is to construct commutative
rings from combinatorial objects (e.g., graphs, simplicial complexes, matroids, posets, and so on) and to
discuss their algebraic properties in terms of the original combinatorial objects. In this talk, we present
several typical commutative rings arising from combinatorial objects and some algebraic properties of thoserings. Moreover, we focus on a couple of them and discuss their relations.
Conference Room IV

Hiraku Nakajima (Univ. of Tokyo)

Towards geometric Satake correspondence for Kac–Moody
Lie algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: About 30 years ago, I gave a geometric construction of representations of a Kac–Moody Lie algebraby quiver varieties, motivated by earlier works by Ringel, Lusztig, Ginzburg. In a 2014 proposal ‘symplectic
duality’ by Braden–Licata–Proudfoot–Webster, this construction is regarded as ‘dual’ to geometric Satakecorrespondence. Geometric Satake correspondence is formulated by using the aﬃne Grassmannian of theLanglands dual group, hence was known only for ﬁnite dimensional Lie algebras. The symplectic dual to moregeneral quiver varieties are Coulomb branches introduced by my joint work with Braverman and Finkelberg
in 2016. Hence Braverman, Finkelberg and I hoped geometric Satake correspondence for Kac–Moody Lie
algebras using Coulomb branches as substitutes of aﬃne Grassmannian. It is still conjectural in general as
we do not have enough tools to analyze Coulomb branches. When the Kac–Moody Lie algebra is of aﬃne
type A, I have an alternative description of Coulomb branches as Cherkis bow varieties, as established byjoint work with Takayama. It enables me to check geometric Satake correspondence for type A.

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5Foundation of Mathematics and History of Mathematics

Foundation of Mathematics and History of Mathematics
March 28th (Mon)

Conference Room IX

9:50–11:20
1 Noriko Tanaka(Aichi Prefectural Asahigaoka High School)

The Experimental Class for Science Education in Kyoto in the near endof the World War II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Following a decision of the Ministry of Education, the Experimental Classes for Science Education
were formed in four cities of Japan in the near end of the World War II. The one of the Experimental classes
were established in the Kyoto-Prefectural Kyoto First Secondary School, one each in the 3rd, 2nd and 1st
year. The origins of the classes, entrance examinations, contents of the courses, teachers are described
together until the abolition. I will once again shed light on the Experimental Class for Science Education,and make use of a part of science and technology education in Japan in the future.
2 Makoto Tamura (Osaka Sangyo Univ.)

On the solution of cubic equations in China · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: “Jigu Suanjing (Continuation of Ancient Mathematics)” written in 626 deals with cubic equations,but does not explain how to solve them. However, the book shows solutions to many cubic equations, it
seems that the method was established before the book appeared. Here we consider a numeric solution
according to the text proposed by Qian Baocong.
3 Tsukane Ogawa (Yokkaichi Univ.)

Mathemacical thought of Oka Yukitada (1791–?) · · · · · · · · · · · · · · · · · · · 15

Summary: Oka Shichibei Yukitada (1791–?) of the Takuma School wrote the “Regular examples for the
methods of writing solution and clarifying the path,” whch summarized the basic techniques of the “Methodsof writing solution and clarifying the path.” It can be said to represent Oka’s mathematical thought. He
analyzed methods for solving problems in plane geometry, extracted the techniques, and organized theminto the book. He then illustrated the application of these techniques in the form of problems and theirsolutions. In this respect, Oka’s mathematics is diﬀerent from mere problem solving.
4 Hideyuki Majima (Ochanomizu Univ.⋆)

The year 2022, the memorial 314th year of Seki Takakazu and the 300th
anniversary of Tetsujjutsu-Sankei · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The author talked about the works of SEKI Takakazu (?–1708), and TAKEBE Katahiro (1664–1739) 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.
5 Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)

On the Sekisan Shidensho · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This is a survey talk on Toita Yasusuke’s Sekiryuu Shidensho, which is a collection of more than
500 wasan materials compiled by Toita Yasusuke (1708–1784). This collection contains the Taisei Sankei
and works of Seki Takakazu and mathematicians of the school Sekiryuu. The collection is composed of fourparts, each of which contain about hundred materials. As Seki Takakazu passed away in 1708, this collection
gives us interesting information about mathematical researches after Seki Takakazu’s years.

Final: 2022/3/4
Foundation of Mathematics and History of Mathematics

11:30–11:45

Mathematics History Team Meeting

14:30–15:30

Talk Invited by Section on Foundation and History of Mathematics

Naoki Osada(Tokyo Woman’s Christian Univ.⋆)

6

The works of Seki Takakazu and their propagation

Summary: In order to evaluate the mathematics of Seki Takakazu, it is necessary to determine his genuine
works. In this lecture, the lecturer ﬁrst discusses whether or not the works conventionally attributed to
Seki Takakazu are his genuine works, and if not, whose works they are, based on the previous study by
Tatsuhiko Kobayashi and my recent research. Next, the lecturer describes how Seki’s manuscripts weretranscribed at Seki Takakazu’s school and discusses which of Seki’s manuscripts were in the possession of
Araki Murahide, the ﬁrst descendant of the Seki school, and Matsunaga Yoshisuke, the second descendant.
Based on these considerations and the previous research of Ken’ichi Satō, the lecturer speculates on how
the Katsuyō Sampō (Essential Mathematics) which has been said to be ”Seki’s posthumous manuscripts
published by his disciple Araki Murahide and Araki’s disciple Ōtaka Yoshimasa,” was published, In addition,
the lecturer also speculates on how the manuscripts of Seki, especially his Kaikendai no Hō (Methods ofSolving Explicit Problems) and Kaiindai no Hō (Methods of Solving Hidden Problems), were propagated.
15:45–17:15
6 Takahiro Seki

(Niigata Univ.)

Commutativity of non-associative substructural logics with restricted
weakening and contraction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is well-known that the associative substructural logic FLcw , obtained from FL by adding bothcontraction and weakening rules, derives exchange rule. In this talk, we consider the commutativity resultin non-associative substructural logics with weakening, contraction, restricted weakening and restricted
contraction axioms.
7 Toshihiko Kurata (Hosei Univ.)
Ken-etsu Fujita (Gunma Univ.)

Spectral spaces for models of intuitionistic logic · · · · · · · · · · · · · · · · · · · · 15

Summary: In the ordinary framework of neighbourhood semantics, the propositions of intuitionistic logic
are interpreted as the compact open sets of Heyting spaces. In contrast, we attempt to give anotherinterpretation based on the open sets of spectral spaces.
8 Hisashi Aratake (Kyoto Univ.)

Limits, colimits, and spectra of modelled spaces · · · · · · · · · · · · · · · · · · · · 15

Summary: It is well-known that the construction of Zariski spectra of commutative rings yields an adjunction
between the category of rings and the category of locally ringed spaces. Many constructions of spectra ofalgebras can be considered as such an adjunction. Michel Coste uniﬁed them in the language of categorical
logic by showing that, for any triple (T,T’,A) such as (rings, local rings, local homomorphisms), each
T-model can be associated with a T’-modelled space (Coste spectrum) and that this construction yields
an adjunction between the category of T-models and the category of T’-modelled spaces. In this talk, we
extend Coste spectra to spectra of T-modelled spaces and then show existence of limits and colimits in
categories of modelled spaces.
9 Kenshi Miyabe(Meiji Univ.)

The rate of convergence of computable inductions · · · · · · · · · · · · · · · · · · 15

Summary: In the setting of inductive inference by Solomonoﬀ, we consider predicting the next bit when
we observe a ﬁnite binary sequence. For a sequence that is random with respect to a computable model
measure, any suﬃciently general conditional prediction will converge to the conditional model. Furthermore,
the sum of the errors between conditional prediction and model is a left-c.e. Martin–Löf random real whenthe error is measured by Kullback–Leibler. We show that this is also true for the case that the model
measure is a Bernoulli measure.

Final: 2022/3/4
7Foundation of Mathematics and History of Mathematics

10 Kohtaro Tadaki (Chubu Univ.)

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

Summary: The notion of probability plays a crucial role in quantum mechanics. It appears as the Born rule.
In modern mathematics which describes quantum mechanics, however, probability theory means nothingother than measure theory, and therefore any operational characterization of the notion of probability is
still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness,
we presented an operational reﬁnement of the Born rule, called the principle of typicality, for specifying
the property of the results of quantum measurements in an operational way. In this talk, we reﬁne andreformulate the Holevo–Schumacher–Westmoreland theorem based on the principle of typicality, in order todemonstrate how properly our framework works in practical problems in quantum mechanics.

March 29th (Tue)

Conference Room IX

9:45–11:25
11 Kenta Tsukuura (Univ. of Tsukuba)

The extent of saturation of induced ideals · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Kunen constructed a model in which ω1 carries a saturated ideal. We give a simpliﬁed construction
by using later improvements. Furthermore, we investigate the extent of saturation of the induced ideal interms of strong saturation, layeredness, and, centeredness.
12 Daisuke Ikegami(Shibaura Inst. of Tech.)I-regularity, determinacy, and Solovay models · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show under ZF+DC+ADR that every set of reals is I-regular for any σ-ideal I on the Bairespace ω ω such that PI is proper. This answers the question of Khomskii in his Ph.D. thesis. We also showthat the same conclusion holds under ZF+DC+AD+ if we additionally assume that the set of Borel codesfor I-positive sets is ∆21 .
13 Teruyuki Yorioka (Shizuoka Univ.)

σ-uniformizations of ladder system colorings and Todorcevic’s fragmentsof Martin’s Axiom · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Uniformization of ladder system colorings has been introduced by analysis of a proof of theShelah’s solution of Whitehead problem. Shelah’s proof can be separated into the following two theorems:MAℵ1 implies U({ω1 ∩ Lim}), and U({ω1 ∩ Lim}) implies the existence of a non-free Whitehead group. In
MSJ Autumn Meeting 2019, it is explained that the assertion K3 , which is one of Todorcevic’s fragments ofMartin’s Axiom, implies that U(stat) holds.
σ-uniformizations of ladder system colorings are introduced, and it is proved that K2 implies that every
ladder system colorings can be σ-uniformized. This implies that K2 implies U(stat). This improves theabove results.
14 Koichiro Ikeda(Hosei Univ.)

Imaginaries in generic structures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The theory of a generic structure is said to be normal, if ā ∈ acl(A) implies d(ā/A) = 0 for anyā, A ⊂ M. We show that any saturated normal generic structure has weak elimination of imaginaries but
does not have the ﬁnite set property.
15 Hirotaka Kikyo(Kobe Univ.)

On model completeness of certain generic structures · · · · · · · · · · · · · · · · 15

Summary: Let δ(A) = |A| − α · e(A) for any ﬁnite graphs A where |A| is the number of all vertices of A ande(A) the number of all edges of A. Let Kf be the class of graphs like amalgamation classes used to construct
Hrushovski’s pseudoplanes using a log-like control function f . Suppose Kf has the free amalgamation
property, and let M be the generic structure of (Kf , <) where < is deﬁned as in the Hrushovski’s case. If α
is rational then the theory of M is model complete. In the case that α is irrational, with some more mild
assumptions on f , the theory of M is also model complete.

Final: 2022/3/4
Foundation of Mathematics and History of Mathematics

16 Akito Tsuboi (Univ. of Tsukuba⋆)

8

Instability, CH and Keisler’s isomorphism theorem · · · · · · · · · · · · · · · · · 10

Summary: We give a talk on our results related to Keisler’s isomorphism theorem.
11:30–11:45

Research Section Assembly

13:00–14:00

Talk Invited by Section on Foundation and History of Mathematics

Ryoma Sin’ya(Akita Univ.)

Separation and measurability problems on an inﬁnite hierarchy of regular languages

Summary: A regular language is a set L of words described by a regular expression, but it has the following
alternative characterisation via logic: L is regular if and only if L is “deﬁnable” by a monadic second-orderformula.
This logical characterisation gives us an inﬁnite hierarchy in the class of all regular languages, e.g., the class
SF of “star-free” languages deﬁnable by ﬁrst-order logic FO and the classes of languages corresponding toseveral fragments of ﬁrst-order logic (e.g., quantiﬁer alternation hierarchy of FO, FO with restricted numberof variables or diﬀerent predicates, etc.).
The ﬁrst part of this talk introduces the well-known connection between languages, logics, and algebras (several subclasses of ﬁnite monoids). In this part, two important theorems are introduced: (1)Schützenberger’s theorem stating that the algebraic counterpart of SF is the class of aperiodic monoids. (2)Eilenberg’s variety theorem stating that there is a natural one-to-one correspondence between the subclassesof regular languages and ﬁnite monoids equipping certain rich closure properties, so-called “varieties” and“pseudovarieties”, respectively.
The second part is an invitation to recent developments on this inﬁnite hierarchy. In this part, two decision
problems are described: (1) Separation problem for subclasses of star-free languages. (2) Measurability
problem for subclasses of regular languages.

Final: 2022/3/4
9

AlgebraAlgebraMarch 28th (Mon)

Conference Room IV

9:30–11:45
1 Kana Ito(Tokyo Tech)(2)

The relation between level 2 standard modules of type Aodd and Zoperators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will discuss a representation of the vacuum spaces of level 2 standard modules of(2)

type A9 using Z-operators in accordance with Kanade–Russell’s conjecture of partition conditions. Rogers–
Ramanujan type identities are the identities represented in the form of (inﬁnite sum)=(inﬁnite product)with the Pochhammer symbols like Rogers–Ramanujan identities. Since the work by Lepowsky–Wilson,
there has been an expectation that by assigning a non-negative integer to each vertex of an aﬃne Dynkin
diagram, we can obtain Rogers–Ramanujan type identities and integer partition theorems. Related to this,we will propose a conjecture for the relations between the vacuum spaces of level 2 standard modules of(2)

type Aodd and Z-operators.
2 Yutaka Yoshii (Ibaraki Univ.)

Structure of certain modules for the hyperalgebra Dist((SL2 )r ) · · · · · · 10

Summary: In the ﬁnite-dimensional hyperalgebra Ur = Dist((SL2 )r ), certain elements B (ε) (a, j) have been
already constructed before. We report that each Ur -module Ur B (ε) (a, j) has a certain basis determined by
ε and (a, j) and that the Ur -module has simple head and simple socle, which are isomorphic.
3 Ryotaro Kawago (Waseda Univ.)
Takeshi Ikeda (Waseda Univ.)

Multiplicities of Schubert varieties in the ﬂag varieties of classical types· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider Schubert varieties in the ﬂag varieties of classical types. For singularities of Schubertvarieties, there is a combinatorial formula for the multiplicity in the case of Grassmannian of classical types.
We obtained results extending this formula to the case of Schubert varieties associated to vexillary signed
permutations of ﬂag varieties of classical types.
4 Tomohiro Itagaki(Takasaki City Univ. of Econ.)
Takeshi Torii (Okayama Univ.)
Kazunori Nakamoto(Univ. of Yamanashi)

Hochschild cohomology of Nm · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Nm (R) = {(aij ) ∈ Mm (R) | a11 = a22 = · · · = amm and aij = 0 for any i > j} for acommutative ring R. We calculate the Hochschild cohomology ring HH∗ (Nm (R), Nm (R)) as R-algebras. We
also calculate HH∗ (Nm (R), Mm (R)/Nm (R)) as R-modules.
5 Yuichiro Goto

(Osaka Univ.) ♭ Generalizations of the relationship between quasi-hereditary algebras
and directed bocses · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Quasi-hereditary algebras were introduced by Cline, Parshall and Scott to study the highest
weight categories in Lie theory. On the other hand, bocses were introduced in the context of Drozd’s tameand wild dichotomy theorem. Koenig, Külshammer and Ovsienko connected them by giving equivalences
between the module categories of ∆-ﬁltered modules over quasi-hereditary algebras and those over directedbocses. In this talk, we discuss some problems occurring when we prove a similar theorem for ∆-ﬁlteredalgebras and give two lemmas necessary for the proof. Here, a ∆-ﬁltered algebra is known to be one ofnatural generalizations of a quasi-hereditary algebra.

Final: 2022/3/4
Algebra6 Yasuaki Gyoda (Nagoya Univ.)

10

Generalization of Gabriel’s theorem in τ -tilting theory and its cluster
algebraic approach · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Gabriel’s theorem, shown in 1972, is a theorem that classiﬁes path algebras of ﬁnite representation
type using Dynkin diagrams, and is a very important theorem that suggests a connection between Lie theory
and the representation theory of algebras. In this talk, I will generalize Gabriel’s theorem by using cluster
algebra theory, which has been rapidly developed recently and is closely related to both Lie theory and therepresentation theory of algebras.
7 Toshiya Yurikusa (Tohoku Univ.)
Yasuaki Gyoda (Nagoya Univ.)

Bongartz completion via c-vectors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Bongartz completion is an important subject in representation theory of ﬁnite dimensional
algebras, in particular, τ -tilting theory. We characterize it using c-vectors. From this point of view,
we introduce the notion of Bongartz completion for cluster algebras using c-vectors, and we give someproperties. This is a joint work with Peigen Cao and Yasuaki Gyoda.
8 Ryotaro Koshio (Tokyo Univ. of Sci.)
Yuta Kozakai (Tokyo Univ. of Sci.)

Support τ -tilting modules and semibricks over blocks under vanisingconditions of Schur multipliers of factor groups · · · · · · · · · · · · · · · · · · · · 10

Summary: Let G be a ﬁnite group, k an algebraically closed ﬁeld of characteristic p > 0 and B a blockof group algebra kG. Support τ -tilting modules and semibricks over B are corresponding B-modules to
two-term tilting complexes and two-term simple minded collections over B, which are both special forms oftilting complexes and simple minded collections over B , respectively. Let G̃ be a ﬁnite group containing
G as a normal subgroup and B̃ a block of k G̃ covering B. In this talk, we will introduce the methods ofconstructions of support τ -tilting modules and semibricks over B̃ from the ones over B under the vanisingcondition of Schur multipliers of the factor group G̃/G over k.
(Kinki Univ.)
9 Fumihito Oda
Yugen Takegahara(Muroran Inst. of Tech.)

Crossed Burnside rings and cohomological Mackey 2-motives · · · · · · · · 10

Summary: Balmer and Dell’Ambrogio introduced the pseudo-functor P from the bicategory of k-linear
Mackey 2-motives to the bicategory of k-linear cohomological Mackey 2-motives over a commutative ring k.
They showed that P maps the general Mackey 2-motives to the cohomological Mackey 2-motives by using
the ring homomorphism from the crossed Burnside ring of a ﬁnite group G over k to the center ZkG ofgroup algebra kG. We study the behavior of motivic decomposition of cohomological Mackey 2-motives as
images by P of motivic decomposition of Mackey 2-motives.
10 Hirotake Kurihara (Yamaguchi Univ.)
Akihiro Higashitani (Osaka Univ.)

Homogeneous quandles arising from ﬁnite groups · · · · · · · · · · · · · · · · · · 15

Summary: Quandle is an algebraic system with one binary operation, but it is quite diﬀerent from a group.
In our talk, we investigate a special kind of quandles, called generalized Alexander quandles Q(G, ψ), which
is deﬁned by a group G together with its group automorphism ψ. We develop the quandle invariants forgeneralized Alexander quandles.

Final: 2022/3/4
11

Algebra14:15–15:15

Talk Invited by Algebra Section
Tatsuyuki Hikita (Kyoto Univ.) K-theoretic canonical bases and their elliptic analogues
Summary: Representation theory of semisimple Lie algebras are closely related to the geometry of Springer
resolutions.

In particular, Lusztig deﬁned certain canonical bases in equivariant K-theory of Springer

resolutions and conjectured that they describe modular representation theory of semisimple Lie algebras.
This conjecture was proved by Bezrukavnikov–Mirkovic for large enough characteristic by beautifully relating
coherent sheaves on Springer resolutions, representations of semisimple Lie algebras in positive characteristic,
and certain perverse sheaves on aﬃne ﬂag manifolds.
In this talk, I deﬁne canonical bases in equivariant K-theory of more general conical symplectic resolutions
and explain their expected properties. If time permits, I will explain an attempt to ﬁnd their elliptic
analogues which reveal new duality under symplectic duality.
15:30–17:40
11 Kohsuke Shibata (Nihon Univ.)

F -rationality of two-dimensional graded rings with a rational singularity· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: It is known that a two-dimensional F -rational ring has a rational singularity. However a twodimensional ring with a rational singularity is not F -rational in general.

In this talk, we investigate

F -rationality of a two-dimensional graded ring with a rational singularity in terms of the multiplicity.
Moreover, we determine when a two-dimensional graded ring with a rational singularity and a small
multiplicity is F -rational.
12 Shinnosuke Ishiro (Nihon Univ.)
Kazuma Shimomoto (Nihon Univ.)
Mohsen Asgharzadeh

Surjectivity of some scalar maps on local cohomology modules and an
application to the second vanishing thorem · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The second vanishing theorem has a long history in the theory of local cohomology modules overregular local rings and the case of ramiﬁed regular local rings is unsolved. We give a partial answer to it
using the surjectivity of scalar maps of local cohomology modules. In our talk, we introduce our results andsome examples of the vanishing of local cohomology modules to exhibit the non-triviality of our results.
13 Shinnosuke Ishiro (Nihon Univ.)
Kazuma Shimomoto (Nihon Univ.)
Kei Nakazato (Nagoya Univ.)

Perfectoid towers and its small tilts · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Perfectoid theory has many applications to commutative ring theory and singularity theory. For
example, the direct summand conjecture, perfectoid multiplier/test ideals are such instances. However, rings
studied in the perfectoid theory are usually non-Noetherian, which are diﬃcult to study via the standard
commutative ring theory. For this reason, we build a new framework that can also treat Noetherian rings
via perfectoids, which are called perfectoid towers and small tilts. In this talk, we plan to explain deﬁnitions
and basic properties.
14 Jun Horiuchi (Nippon Inst. of Tech.)
Kazuma Shimomoto (Nihon Univ.)
Kazufumi Eto (Nippon Inst. of Tech.)

On integrality of rings and the monoidal map · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will derive some ring theoretic properties of the tilt of the ring. In this process, we make useof the monoidal structure of the tilt and so-called monoidal map. We explain the key discussion due to
Fontaine, and we will discuss further development and application.
15 Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)

On the non-Gorenstein locus of the Ehrhart ring of the stable set
polytope of an odd cycle graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G = (V, E) be an odd cycle graph. We describe the non-Gorenstein locus of the Ehrhart ringof the stable set polytope of G by showing the radical of the trace of the canonical module of that ring is
the intersection of prime ideals corresponding to certain faces of the stable set polytope of G.

Final: 2022/3/4
Algebra16 Yuki Ishihara (Tokyo Univ. of Sci.)

12

On double ideal quotient and primary decomposition · · · · · · · · · · · · · · · 15

Summary: It is known that “primary decomposition” is a basic notion in Commutative Algebra. In order toanalyze properties of primary decomposition, we introduce a special ideal “double ideal quotient”, which has
the form I : (I : J). By using double ideal quotient, we can obtain criteria for prime divisors and primary
components. Also, we can generate the particular primary component from a given ideal and its prime
divisor. We can apply these properties to compute the localization of an ideal at a prime ideal in themultivariable polynomial ring over a computable ﬁeld.
17 Shinya Kumashiro(Oyama Nat. Coll. of Tech.)

Graded ﬁltrations and ideals of reduction number two · · · · · · · · · · · · · · 15

Summary: We give a way to construct graded ﬁltrations of graded modules. We then apply the ﬁltration to
the Sally module, which describes a correction term of the Hilbert function of ideals. As a result, we obtain
the inequality of the Hilbert coeﬃcients for ideals of reduction number 2.
18 Kazuho Ozeki (Yamaguchi Univ.)

The ﬁrst Hilbert coeﬃcient of stretched ideals · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we explore the almost Cohen–Macaulayness of the associated graded ring of stretchedm-primary ideals with small ﬁrst Hilbert coeﬃcient in a Cohen–Macaulay local ring (A, m). In particular,
we explore the structure of stretched m-primary ideals satisfying the equality e1 (I) = e0 (I) − ℓA (A/I) + 4
where e0 (I) and e1 (I) denote the multiplicity and the ﬁrst Hilbert coeﬃcient respectively.

March 29th (Tue)

Conference Room IV

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

Topological chiral algebras and characteristic classes · · · · · · · · · · · · · · · · 15

Summary: The chiral-factorization algebra theory of Beilinson and Drinfeld is an algebraic system witha geometric nature inspired by the physics of holomorphic conformal ﬁeld theories. In this talk, I will
try to re-investigate the sigma-model interpretation of the chiral de Rham complex. This interpretation
was initiated by the works of Nekrasov and Witten, but my computation is after the toric diagrams andcomputational algebraic geometry. The assumption was the OPE preservation under the Nekrasov Ansatz
after the generalized complex structure of Hitchin school. The sigma-model interpretation was conﬁrmed
by Gorbounov, Gwilliam, and Williams in their Astérisque paper, but my work was earlier and has more
inclination toward Beilinson and Drinfeld.
20 Akio Nakagawa (Chiba Univ.)

Appell–Lauricella hypergeometric functions over ﬁnite ﬁelds · · · · · · · · · 15

Summary: We study ﬁnite ﬁelds analogues of integral representations of Appell–Lauricella hypergeometricfunctions FA , FB , FC and FD . Furthermore, as an application, we see relations between these functions andthe numbers of rational points of some algebraic varieties over ﬁnite ﬁelds.
21 So Yamagata (Hokkaido Univ.)
Simona Settepanella

On the non very genericy of hyperplane arrangements. · · · · · · · · · · · · · · 15

Summary: In 1989, Manin and Schechtman introduced a family of arrangements of hyperplanes generalizingclassical braid arrangements, which they called the discriminantal arrangements. It is well known that there
exists an open Zariski set Z in the space of central generic arrangements of n hyperplanes in Ck such thatthe intersection lattice of the discriminantal arrangements B(n, k, A) are independent from the choice of thearrangement A ∈ Z. In this talk we see a suﬃcient condition for A to be non very generic in terms ofvectors.

Final: 2022/3/4
13

Algebra22 Norihiro Nakashima(Nagoya Inst. of Tech.)
Shuhei Tsujie (Hokkaido Univ. of Edu.)

The conditions for the extended Shi and Catalan arrangements of type
A to be hereditarily free · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we prove that the cone of the extended Catalan arrangement of type A is always
hereditarily free, while we determine the dimension that the cone of the extended Shi arrangement of type
A is hereditarily free. For this purpose, we deﬁne a class of arrangements which contains the extended Shi
and Catalan arrangement of type A and which closed under restriction, using digraphs with vertex weights.
23 Tetsuya Ando

(Chiba Univ.)

Extremal positive semideﬁnite forms of cubic homogeneous polynomialsof three variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15+
Summary: Let P3,3
be the set of all the cubic homogeneous polynomials f (x, y, z) which satisfy f (x, y, z) ≥ 0+
for all x ≥ 0, y ≥ 0, z ≥ 0. We determine all the extremal elements of P3,3.

24 Tomohiro Iwami (Kyushu Inst. of Tech.)Intermediate Jacobian of an extended three-dimensional extremal neighborhood. Part I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For an semi-stable extremal neighborhood (X, C) ⊂ C4 with C is irreducible and reduced, thebounded terminality of 2-game between the invariants l(P ), q(P ), related to 0-dimensional supports of| − KX |, gives the existence of 3-dimensional ﬂips ([S. Mori, 1988]). Regarding to [S. Mori, 1988], the author
had studied: for (X, C) ⊂ C4 where C is not necessary irreducible nor reduced, denoted as (X, Cs ) ⊂ C4([I2019March]), i) to induce Miyaoka–Yau type inequality with c3 , as abbreviated (M Y )3,c3 , ii) to study(M Y )3,c3 by the associated Higgs sheaves, and iii) to more study (M Y )3,c3 by introducing diﬀrential
operators “of codimension 2 type” for ii), and so on. In this talk, based on these works i)–iii), the author
will report: a) to construct “period space” for (X, Cs ), and b) for a), to introduce intermediate Jacobianfor (X, Cs ), which gives “2-Albanese”, or “2-Picard” varieties. Here, the preﬁx “2-” mainly comes from iii),
probably relate to n(≥ 1)-motif. These varieties are expected to work to rationality of (X, Cs ) of type A. In
the sequel parts, the author will give studies regards to these points.
25 Makoto Miura(Kyoto Univ.)

Geometric transitions for Calabi–Yau hypersurfaces · · · · · · · · · · · · · · · · 15

Summary: Geometric transition is a process of connecting two smooth Calabi–Yau 3-folds by a birational
contraction followed by a complex smoothing. It has attracted the interest of both mathematicians andphysicists, since it may give the right notion to connect moduli spaces of Calabi–Yau 3-folds. For Calabi–Yau
hypersurfaces in toric varieties, a well-known idea of constructing geometric transitions is to use nested
reﬂexive polytopes. In this talk, I will introduce a reﬁnement of this idea and show recent progress.
26 Takeshi Usa(Univ. of Hyogo)

The adjacent concurrence on inﬁnitesimally unstable Betti syzygy
classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Even for an arithmetic D2 non-singular projective subvariety X ⊆ PN (C) = P , when we consider
a 1-st inﬁnitesimal embedded deformation of X in P , some classes in the q-th Betti syzygy space (or Koszul
(q)

(q)

1,q
homology) Tm= (ZX /S+ · ZX )(m) of X in (polynomial) degree m may suddenly disappear. When weonce ﬁnd such an inﬁnitesimally unstable q-th Betti syzygy class, we often ﬁnd a non-zero (q + 1)-th Betti
1,q+1
1,q−1
syzygy space Tm
or a non-zero (q − 1)-th Betti syzygy space Tmwith the same polynomial degree mat the same time, which has also an inﬁnitesimally unstable Betti syzygy class. Here, in a general situation,
we give a steady explanation of this phenomena.

Final: 2022/3/4
Algebra27 Ryo Ohashi (Yokohama Nat. Univ.)
Momonari Kudo (Univ. of Tokyo)
Shushi Harashita(Yokohama Nat. Univ.)

14

The a-numbers of non-hyperelliptic curves of genus three with large
cyclic automorphism group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the study of algebraic curves and their moduli spaces, it is important to determine the anumbers of curves over a ﬁeld of positive characteristic. It is known that non-hyperelliptic curves of genus 3
are classiﬁed by the structures of their automorphism groups as ﬁnite groups. In this paper, we determine
the a-numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6 or 9.
Moreover, we also ﬁnd the exact number of the isomorphism classes of such curves attaining the possible
maximal a-number.
28 Ryo Ohashi (Yokohama Nat. Univ.)

On the maximality or minimality of Howe curves of genus 3 · · · · · · · · · 15

Summary: A nonsingular curve C over Fq is called maximal (resp. minimal) if the number of Fq -rational
points of C attains the Hasse–Weil upper (resp. lower) bound. It is known that maximal or minimal curves
over Fp2 are superspecial, while superspecial curves over Fp2 are not neccesarily maximal nor minimal.
In this lecture, we talk about the maximality or minimality of Howe curves of genus 3. A Howe curve is thedesingularization of the ﬁber product over P1 of two elliptic curves. We show that if a Howe curve of genus
3 is superspecial, then its standard form is maximal or minimal over Fp2 without taking its Fp2 -form.
13:00–14:00
29 Kohei Sato (Oyama Nat. Coll. of Tech.)
Yusuke Sato (Univ. of Tokyo)

Hilb-desingularizations for three-dimensional canonical cyclic quotient
singularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: M. Ishida and N. Iwashita classiﬁed three-dimensional canonical cyclic quotient singularities.
By using this classiﬁcation, we proved that there exists an iterated Fujiki–Oka resolution which is a
Hilb-desingularization for any three-dimensional canonical cyclic quotient singularity.
30 Yuki Mizuno(Waseda Univ.)

An explicit construction of derived moduli stacks of Harder–Narasimhan
ﬁltrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Harder–Narasimhan(HN) ﬁltrations are ﬁltrations of sheaves obtained from semistable sheaves.
Any pure coherent sheaf has a unique HN ﬁltration. On the other hand, moduli spaces of HN ﬁltrations areconstructed as stacks (not as schemes) Moreover, Behrend, Ciocan–Fontanine, Hwang and Rose constructedderived moduli schemes of (semi) stable sheaves as diﬀerential graded (dg) schemes coming from bundlesof curved dg Lie algebras. Derived schemes and stacks are generalizations of schemes and stacks. Theirstructure sheaves are sheaves of dg algebras. By using their method, we construct derived moduli stacksof HN ﬁltrations as quotient dg-stacks explicitly. (So, they also become derived moduli stacks of unstablesheaves.)
31 Norihiko Minami(Nagoya Inst. of Tech.)

Two applications of the birational motive to the retract (−i)-rationality· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The birational motives of Kahn–Sujatha and Rost is applied to study the following two typesof implications of the retract (−i)-rationality of a smooth projective variety: (1) in terms of an arbitrary
P 1 -invariant Nisnevich sheaf with transfer. (2) in terms of the Bloch-Srinivas type decomposition of the
diagonal.

Final: 2022/3/4
15

AlgebraMarch 30th (Wed)Conference Room IV

9:30–10:30
32 Hiroki Matsui (Tokushima Univ.)
Olgur Celikbas (West Virginia Univ.)
Uyen Le (West Virginia Univ.)

Paraphrasing Huneke–Wiegand conjecture · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Huenke–Wiegand conjecture is the long-standing conjecture in commutative algebra. It says thatfor a one-dimensional local domain, the tensor product of non-free and torsion-free module and its algebraic
dual has torsion. This conjecture is quite open and only the known case is for hypersurface local domains.
In this talk, I will paraphrase Huneke–Wiegand conjecture over complete intersection local domains to a
conjecture over hypersurface local domains.
33 Kaito Kimura (Nagoya Univ.)(Nagoya Univ.)
Yuya Otake
Ryo Takahashi (Nagoya Univ.)

Auslander–Reiten conjecture over Cohen–Macaulay rings · · · · · · · · · · · · 15

Summary: Projectivity of modules in terms of Vanishing of Ext modules over a local ring is an actively
studied subject in commutative algebra. One of the most important problems is a celebrated long standing
conjecture called the Auslander–Reiten conjecture.

In this talk, we consider the above problems overCohen–Macaulay rings, which form one of the most important classes in commutative algebra.
34 Masahisa Sato
(Aichi Univ./Univ. of Yamanashi⋆)
Summary: Generalized

On generalized Nakayama(Azumaya)’s lemma · · · · · · · · · · · · · · · · · · · · · 10

Nakayama(Azumaya)’s

lemma

is

a

generalization

of

well

known

Nakayama(Azumaya)’s Lemma, i.e., the assertion that MJ(R)=M implies M=0 for a module M
which is a direct summand of a direct sum of ﬁnitely generated modules, where J(R) is the Jacobson radicalof a ring R. First we show this lemma is equivalent to the non-existence of a non-zero Nakayama–Azumaya
module. Next we show, in fact, that there is no non-zero (weak) Nakayama–Azumaya module. Also as
applications of this lemma, we show the existence of a maximal submodule for some kind modules.
35 Masaki Matsuno (Shizuoka Univ.)
Haigang Hu (Shizuoka Univ.)(Shizuoka Univ.)
Izuru Mori

Noncommutative smooth conics in Calabi–Yau quantum projective
planes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Throughout this talk, let k be an algebraically closed ﬁeld of characteristic 0.Let S be a 3dimensional Calabi–Yau quantum polynomial algebra, and f ∈ S2 a regular central element. We call
A = S/(f ) a noncommutative conic in a Calabi–Yau quantum P2 . Our goal is to classify the associatednoncommutative projective schemes Projnc A.

In this talk, we will show that there exist at least 9

isomorphism classes of Projnc A.
11:00–12:00

Presentation Ceremony for the 2021 & 2022 MSJ Algebra Prize

14:15–15:15

Award Lecture for the 2022 MSJ Algebra Prize

Osamu Fujino(Kyoto Univ.)

Generalization of the Kodaira vanishing theorem and its application tobirational geometry

Summary: The Kodaira vanishing theorem plays a crucial role for the study of complex projective varieties.
We have already known many important generalizations. One of the most famous generalizations is the
Kawamata–Viehweg vanishing theorem. It is the main ingredient of the theory of minimal models forhigher-dimensional complex projective varieties. We generalize the Kodaira vanishing theorem from the
Hodge theoretic viewpoint. By using the theory of mixed Hodge structures on cohomolgy with compact
support, we establish a useful package of vanishing theorems. It greatly generalizes the framework of theminimal model program.

Final: 2022/3/4
Algebra15:25–16:25

16Award Lecture for the 2022 MSJ Algebra Prize

Masaaki Furusawa (Osaka City Univ.)

On the Gross–Prasad conjecture with its reﬁnement for (SO(5), SO(2))
and the generalized Boecherer conjecture

Summary: In this talk, I will describe a joint work with Kazuki Morimoto at Kobe University, where we
prove the Gross–Prasad conjecture and its reﬁnement, i.e. the Ichino–Ikeda type formula for the Bessel
periods, in the case of (SO(5), SO(2)), by combining several theta correspondences. Our Ichino–Ikeda type
formula is valid for any irreducible tempered cuspidal automorphic representations. In the 1980’s, Boecherer
proclaimed a remarkable conjecture concerning the relationship betwee a certain sum of Fourier coeﬃcientsof Siegel cusp forms of degree two which are Hecek eigenforms and a central value of quadratic twists ofdegree four spinor L-functions, which we proved earlier. As a corollary of our Ichino–Ikeda type formula
above, we prove a natural gereralization of Boecherer’s conjecture to the not necessarily trivial troidal
character case.
16:35–17:35

Award Lecture for the 2022 MSJ Algebra Prize

Izuru Mori

(Shizuoka Univ.)

Classiﬁcation of noncommutative projective surfaces (focusing on ASregular algebras)

Summary: The classiﬁcation of 3-dimensional AS-regular algebras (introduced by Artin and Schelter) is a
starting point of noncommutative algebraic geometry. Noncommutative projective planes are deﬁned as thenoncommutative projective schemes (introduced by Artin and Zhang) associated to 3-dimensional quadratic
AS-regular algebras, and they are the most basic objects of study in noncommutative algebraic geometry.
On the other hand, it is interesting to study more general noncommutative projective surfaces. In fact,classiﬁcation of noncommutative projective surfaces is one of the major projects in noncommutative algebraic
geometry. In this talk, I will give some history of noncommutative algebraic geometry and classiﬁcation of
noncommutative projective surfaces, focusing on AS-regular algebras.

March 31st (Thu)

Conference Room IV

9:30–12:00
36 Shigeru Iitaka (Gakushuin Univ.⋆)

Ultra 2 perfect numbers of Mersenne type · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Given odd prime h and an integer m, natural numbers a, A deﬁned by A = σ(a) − m, and B
deﬁned by B = hσ(A) + 2h̃m + h̃(h − 2), (h̃ = h + 1),
are said to be Ultra 2 perfect numbers of Mersenne type whenever σ(B) = σ(2h̃)(a + 1).
Associated nnmbers A and B are called partner and shadow, repectively.
37 Shigeru Iitaka (Gakushuin Univ.⋆)
Hikaru Kajita(Crimson Global Academy)

Ultra perfect numbers of twin primes type · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Given an odd prime h and an integer m , if natural numbers a , A and B satisfy eualitiesa = 2hφ(A) + m + 1, hA = φ(B) − m + 2and B = φ(a) − 1 then they are said to be ultra perfect numbersof twin primes type.
38 Daniel Tsai

(Nagoya Univ.) ♭ The fundamental period of a periodic phenomenon pertaining to vpalindromes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In March 2021, I introduced the concept of v-palindromes and proved a theorem pertaining tov-palindromes and repeated concatenation of the decimal digits of a natural number, illustrating a periodic
phenomenon. In this talk, we show how to calculate the fundamental, i.e. smallest, period.

Final: 2022/3/4
17

Algebra39 Daniel Duverney(Baggio Engineering School)
Takeshi Kurosawa (Tokyo Univ. of Sci.)
Iekata Shiokawa (Keio Univ.)

Irrationality exponents of generalized Hone series · · · · · · · · · · · · · · · · · · 10

Summary: We compute the exact irrationality exponents of a generalized Hone series using a continued
fraction expansion.
40 Shin-ya Koyama (Toyo Univ.)

Chebyshev’s bias and the deep Riemann hypothesis · · · · · · · · · · · · · · · · 10

Summary: We unravel the mystery of Chebyshev’s bias in terms of zeta-parametrization of the counting
function of primes. As applications we obtain newly discovered biases. For example, we ﬁnd the biased
distributions of 1) non-principal prime ideals in number ﬁelds of class number two, 2) non-splitting primes
in certain abelian extensions, 3) Ramanujan’s τ -functions in positive values.
41 Kohei Takehira (Tohoku Univ.)

On the dynamical zeta function associated with a dynamical system on
the projective line · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A discrete dynamical system is deﬁned by regarding a rational function ϕ over a ﬁeld as aself-map on a projective line. In 1995, Hatjispyros and Vivaldi deﬁned the zeta function associated withthis dynamical system using a quantity called the multiplier of periodic points, which describes the local
behavior of the dynamical system. In this talk, we will give a cohomological interpretation of this zetafunction and use it to discuss the rationality of this zeta function, explicit computation of the zeta function,and other issues.
42 Hideto Iwata(Nagoya Univ.)

The consideration using by the Volterra integral equation for the remainder term in the asymptotic formula on the associated Euler totientfunction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: J. Kaczorowski deﬁned the analogue of the Euler totient function associated with the generalized
L-functions including the Riemann zeta function, Dirichlet L-functions and obtained an asymptotic formula.
We consider the Volterra integral equation of second type for the remainder term in the asymptotic formulafor the associated Euler totient function. Moreover, we split the remainder term in the asymptotic formulafor the associated Euler totient function into two summands called the arithmetic and the analytic partrespectively.
43 Yuichiro Toma (Nagoya Univ.)

The mean square values of the Apostol–Vu double zeta-function · · · · · 10

Summary: The mean square formulas for various multiple zeta-functions have been studied in recent years.
We give the asymptotic formula for the mean square values of the Apostol–Vu double zeta-function
ζAV,2 (s1 , s2 , s3 ) on the assumption that s1 and s2 are ﬁxed.
44 Wataru Takeda (Tokyo Univ. of Sci.)
Maki Nakasuji (Sophia Univ.)

Shuﬄe product formula for the Schur multiple zeta values of hook type
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the theory of the Euler–Zagier type multiple zeta functions, the product formula of two multiple
zeta values, called Shuﬄe product, is known. It is obtained by considering their integral expression. In thisstudy, we formulate the Shuﬄe product formula for the Schur multiple zeta values of hook type by using
their integral expression.
45 Maki Nakasuji (Sophia Univ.)(Tohoku Univ.)
Yasuo Ohno

Duality formula and its generalization for Schur multiple zeta values· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the study on multiple zeta values, the duality formula is one of the families of basic relations
and plays an important role in the investigation of algebraic structure of the space spanned by all multiple
zeta values along with the generalized duality formula, so-called Ohno’s relation. As a generalization ofthem, we obtain those for skew type Schur multiple zeta values by introducing the new standard piece ofindex, called “admissible piece”.

Final: 2022/3/4
Algebra(Sophia Univ.)
46 Yuna Baba
Maki Nakasuji (Sophia Univ.)

18

Schur type multi-poly-Bernoulli numbers · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The poly-Bernoulli numbers and its relative are deﬁned by the generating series using thepolylogarithm series, and we call them type B and C, respectively. As a generalization of these polyBernoulli numbers, we introduce Schur type multi-poly-Bernoulli numbers, which has relation with Schurmultiple zeta functions. We obtain the relation between Schur type multi-poly-Bernoulli numbers of type B
and that of type C. Furthermore, we deﬁne a generalization of Arakawa-Kaneko multiple zeta function to
Schur type, and obtain their expression using Schur type multi-poly-Bernoulli numbers.
14:15–16:00
47 Masato Kobayashi (Kanagawa Univ.)(Euler Circle)
Sarth Chavan

An integral representation of Apery number and its applications tomultiple values · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will talk on an integral representation of Apery number by arcsin function and its applications
to multiple values ζ(3, 2, ..., 2) and t(3, 2, ..., 2).
48 Ryojun Ito(Chiba Univ.)

Hypergeometric expressions of L-values for a Borweins theta productof weight 3 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 2012, by an analytic method, Rogers–Zudilin gave a hypergeometric expression of the L-value
at 2 for a cusp form of weight 2, which is a product of the Borweins theta series. In this talk, by theRogers–Zudilin method, we express some special values of the L-function of a Borweins theta product ofweight 3 in terms of special values of the Kampé de Fériet hypergeometric function, which is a two-variablegeneralization of generalized hypergeometric functions.
49 Yusuke Nemoto (Chiba Univ.)

On the K2 -regulator of the Hesse cubic curve and hypergeometricfunctions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we discuss the Hesse cubic curve which is deﬁned by x30 + y03 + z03 = 3tx0 y0 z0 . It
is known that its periods are written in terms of Gauss’s hypergeometric functions. We construct someelements in K2 -group of the Hesse cubic curve by using the tangent lines at the ﬂex points. We compute their
Beilinson regulators via the dlog map and express them in terms of generalized hypergeometric functions
3 F2 .

50 Ryosuke Shimada (Univ. of Tokyo)

Geometric structure of aﬃne Deligne–Lusztig varieties for GL3 · · · · · · 15

Summary: The Langlands correspondence, which contains class ﬁeld theory as a special case, is one of themost important topics in number theory. Shimura varieties have been used, with great success, towards
applications in the realm of the Langlands program. In this context, geometric and homological properties
of aﬃne Deligne–Lusztig varieties have been used to examine Shimura varieties and the local Langlands
correspondence. In this talk we study the geometric structure of aﬃne Deligne–Lusztig varieties Xλ (b) forGL3 and b basic. We completely determine the irreducible components of the aﬃne Deligne–Lusztig variety.
In particular, we classify the cases where all of the irreducible components are classical Deligne–Lusztig
varieties times ﬁnite-dimensional aﬃne spaces.
51 Yasushi Mizusawa(Nagoya Inst. of Tech.)

Metabelian 2-class ﬁeld towers over Z2 -extensions of real quadratic ﬁelds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a family of real quadratic ﬁelds such that the 2-class ﬁeld towers over their cyclotomic
Z2 -extensions have metabelian Galois groups of abelian invariants [2, 2, 2]. We also consider the boundednessof the Galois groups in relation to Greenberg’s conjecture with some explicit examples.

Final: 2022/3/4
19

Algebra52 Daisuke Shiomi (Yamagata Univ.)

The divisibility of class numbers of cyclotomic function ﬁelds · · · · · · · · 10+
Summary: Let h−
N (resp. hN ) be the minus (resp. plus) part of the class number of the N th cyclotomic

function ﬁeld. By using Goss’s criterion, Feng proved that there exist inﬁnitely many irreducible polynomials+
N with h−
N ≡ 0 (mod p) (resp. hN ≡ 0 (mod p)). In this talk, we study the N -divisibility of some Cartliz

zeta values, and improve Feng’s results.
53 Fumitake Hyodo(Kawasaki Univ. of Med. Welfare)

A note on a Hecke ring associated with the Heisenberg Lie algebra· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk focuses on the theory of the Hecke rings associated with the general linear groups
originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings
associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie
algebra, we show an analog of the classical theory.

Final: 2022/3/4
Geometry

20

Geometry
March 28th (Mon)

Conference Room VI

9:20–12:00
1 Yoshito Ishiki(RIKEN)On dense subsets of spaces of metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In spaces of metrics, we investigate topological distributions of the doubling property, the uniform
disconnectedness, and the uniform perfectness, which are quasi-symmetrically invariant properties appearing
in the David–Semmes theorem. We show that the set of all doubling metrics and the set of all uniformly
disconnected metrics are dense in spaces of metrics on ﬁnite-dimensional and zero-dimensional compact
metrizable spaces, respectively. Conversely, this denseness of the sets implies the ﬁnite-dimensionality, zerodimensionality, and the compactness of metrizable spaces. We also determine the topological distribution of
the set of all uniformly perfect metrics in the space of metrics on the Cantor set.
2 Yoshito Ishiki(RIKEN)

Branching geodesics of the Gromov–Hausdorﬀ distance · · · · · · · · · · · · · 15

Summary: We ﬁrst evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metricspaces equipped with the Gromov–Hausdorﬀ distance.

We then construct branching geodesics of theGromov–Hausdorﬀ distance continuously parameterized by the Hilbert cube, passing through or avoiding
sets of all spaces satisfying some of the three properties shown above, and passing through the sets of allinﬁnite-dimensional spaces and the set of all Cantor metric spaces.
3 Daisuke Kazukawa (Osaka Univ.)
Takumi Yokota (Tohoku Univ.)

Boundedness of precompact sets of metric measure spaces · · · · · · · · · · · 15

Summary: Gromov introduced a distance function, called the box distance, and a partial order, called the
Lipschitz order, on the set of isomorphism classes of metric measure spaces. These are fundamental tools
in his theory on the convergence of metric measure spaces. In this talk, we present and prove Gromov’s
statement comparing two boundedness with respect to the box distance and the Lipschitz order. He only
sketched the proof in his book.
4 Kenshiro Tashiro (Tohoku Univ.)

On the systolic inequality on compact quotients of Carnot groups · · · · 15

Summary: On a compact Riemannian manifold M n , the systole represents the ‘thickness’ of the manifold.
Namely it is deﬁned by the minimal length of closed non-null homologous curves. The systolic inequality
1

asserts that there is a constant C = C(n) such that systole ≤ C · (V ol(M )) n . It is shown for asphericalmanifolds and its technical generalization. We show a sub-Riemannian version of the systolic inequality forcompact quotient spaces of Carnot groups. There systole is deﬁned via the sub-Riemannian length structure,
the total measure is given by the Popp’s volume, and the constant can be chosen so that it depends only on
the Hausdorﬀ dimension.
5 Hiroki Nakajima (Tohoku Univ.)
Takashi Shioya (Tohoku Univ.)

A natural compactiﬁcation of the Gromov–Hausdorﬀ space · · · · · · · · · · 15

Summary: We introduce a pseudometric on the family of isometry classes of (extended) metric spaces. Usingit, we obtain a natural compactiﬁcation of the Gromov–Hausdorﬀ space, which is compatible with ultralimit.

Final: 2022/3/4
21

Geometry

6 Homare Tadano (Yamaguchi Univ.)

Radial m-Bakry–Émery Ricci curvatures, Riccati inequalities, andMyers-type theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: By using some line integrals in terms of the radial m-Bakry–Émery Ricci curvature, we givevarious compactness criteria for complete Riemannian manifolds when m is a positive constant, a negative
constant, or inﬁnity. Our results not only guarantee the compactness of complete Riemannian manifolds
allowing the presence of negative amounts of the radial m-Bakry–Émery Ricci curvature, but also give newMyers-type theorems via m-Bakry–Émery Ricci curvature even the line integrals are reduced to pointwise
positive lower bounds on the m-Bakry–Émery Ricci curvature. The key ingredients in proving our results
are Riccati inequalities obtained from Bochner–Weitzenböck formulas via m-Bakry–Émery Ricci curvature.
7 Homare Tadano (Yamaguchi Univ.)

Ambrose and Calabi type theorems via m-Bakry–Émery Ricci curvature· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We establish various new compactness criteria for complete Riemannian manifolds via m-Bakry–Émery Ricci curvature when m is a positive constant, a negative constant, or inﬁnity, which not only
generalize classical compactness criteria for complete Riemannian manifolds via Ricci curvature by W.
Ambrose and E. Calabi allowing some negative amounts of the m-Bakry–Émery Ricci curvature, but also
relax previous Myers and Cheeger–Gromov–Taylor type compactness criteria via m-Bakry–Émery Ricci
curvature obtained when m is a positive constant, a negative constant, or inﬁnity.
8 Homare Tadano (Yamaguchi Univ.)

New compactness criteria via m-Bakry–Émery Ricci curvature of exponential decay · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We establish some new compactness criteria for complete Riemannian manifolds by assuming some
exponential decay conditions on the m-Bakry–Émery Ricci curvature. Our results not only generalize Myers
type theorems via m-Bakry–Émery Ricci curvature obtained by M. Fernández-López and E. Garcı́a-Rı́o,M. Limoncu, Z. Qian, G. Wei and W. Wylie, J.-Y. Wu, but also relax quadratic decay conditions on the
m-Bakry–Émery Ricci curvature of the Cheeger–Gromov–Taylor type theorems obtained by Y. Soylu and
L.F. Wang. The key ingredients in proving our results are Bochner formulas and Laplacian comparison
theorems via m-Bakry–Émery Ricci curvature.
9 Homare Tadano (Yamaguchi Univ.)

Integral radial m-Bakry–Émery Ricci curvatures and Myers–Ambrosetype theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Stimulated by a recent work due to J.-Y. Wu, we establish several new compactness criteria forcomplete Riemannian manifolds via integral radial m-Bakry–Émery Ricci curvatures when m is a positive
constant, a negative constant, or inﬁnity. Our results not only relax a compactness criterion via integral
radial Bakry–Émery Ricci curvature due to J.-Y. Wu by allowing some growth conditions on integral
radial m-Bakry–Émery Ricci curvatures, but also give new Myers-type theorems for complete Riemannian
manifolds even integral radial m-Bakry–Émery Ricci curvatures are reduced to pointwise lower bounds on
m-Bakry–Émery Ricci curvatures. Moreover, we generalize these Myers-type theorems in the spirit of theclassical compactness criterion via Ricci curvature due to W. Ambrose.
10 Homare Tadano (Yamaguchi Univ.)

Cheeger–Gromov–Taylor type compactness theorems via integral radial
m-Bakry–Émery Ricci curvatures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Inspired by a recent work due to J.-Y. Wu, we extend the classical compactness theorem
for complete Riemannian manifolds via Ricci curvature due to Cheeger–Gromov–Taylor by replacing apointwise lower bound on the Ricci curvature with integral radial m-Bakry–Émery Ricci curvatures when mis a positive constant, a negative constant, or inﬁnity. Our results generalize Cheeger–Gromov–Taylor typecompactness theorems for complete Riemannian manifolds via m-Bakry–Émery Ricci curvatures obtainedby Y. Soylu and the author in integral sense.

Final: 2022/3/4
Geometry22

14:15–16:00
11 Masaya Kawamura(Kagawa Nat. Coll. of Tech.)

On estimates for a function on almost Hermitian manifolds and its
application to the Monge–Ampère equation · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, there have been a lot of studies in almost Hermitian geometry. Especially, the Monge–
Ampère type equations have been investigated on almost Hermitian manifolds vigorously. For instance, J.
Chu, V. Tosatti and B. Weinkove have derived a priori estimates and have shown existence and uniqueness ofsolutions to the Monge–Ampère equation on compact almost Hermitian manifolds. In Hermitian geometry,¯ In almost Hermitian geometry, we do not have
it is well-known that we have ∂ 2 = ∂¯2 = 0 and ∂ ∂¯ = −∂∂.
¯ ∂∂
¯ ∂φ,
¯ ∂∂∂ ∂φ¯ and sothese appreciated relations, which leads that we have to deal with terms like ∂∂ ∂φ,on, where φ is a smooth real-valued function. In this regard, we need a new technique for dealing with these
¯ ∂∂
¯ ∂φ.
¯
terms. From this point of view, we establish a new estimate for ∂∂ ∂φ,
12 Satoshi Nakamura(Numazu Nat. Coll. of Tech.)Calabi type functionals for coupled Kähler–Einstein metrics · · · · · · · · · 15

Summary: The Calabi type functional, called the coupled Ricci–Calabi functional, for coupled Kähler–
Einstein metrics is introduced to obtain a moment weight inequality which relates this functional and an
algebro-geometric invariant.
13 Naoto Yotsutani (Kagawa Univ.)

Diﬀeomorphism classes of the doubling Calabi–Yau threefolds · · · · · · · 15

Summary: In our previous work (New York J. Math. 20 (2014) 1–33), we constructed Calabi–Yau threefolds
by a diﬀerential-geometric gluing method using Fano threefolds with their smooth anticanonical K3 divisors.
In this talk we further consider the diﬀeomorphic types of the resulting Calabi–Yau threefolds starting from
diﬀerent pairs of Fano threefolds of Picard number one.
14 Yuta Watanabe (Univ. of Tokyo)

Cohomology on neighborhoods of non-pluriharmonic loci in pseudoconvex Kähler manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The classical result, the Lefschetz hyperplane theorem on complex projective manifolds, hasrecently been extended by Prof. Tiba to an analogous result on Stein manifolds. This is a claim forcohomology on open neighborhoods in non-pluriharmonic loci of exhaustive plurisubharmonic functions. In
this talk, I will introduce a new result, which is an extension from Stein manifolds to pseudoconvex Kähler
manifolds with some kind of q-completeness. An example that does not ﬁt into the situation of Stein
manifolds is quasi-torus.
15 Takayuki Moriyama (Mie Univ.)(Mie Univ.)
Takashi Nitta

Graded algebra structure on the space of quaternionic k-vector ﬁelds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We provided the correspondence of a quaternionic k-vector ﬁeld on a quaternionic Kähler manifold
to a holomorphic (k, 0)-vector ﬁeld on the twistor space. The space of holomorphic multi vector ﬁelds admits
a graded algebra structure, naturally. In this talk, we introduce a graded algebra structure on the spaceof quaternionic multi vector ﬁelds and show that the correspondence induces an isomorphism of these twograded algebras.
(Meiji Univ.)
16 Isami Koga
Yasuyuki Nagatomo (Meiji Univ.)

Equivariant harmonic immersions of complex projective line into thecomplex Grassmannian manifolds of rank two · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct and classify equivariant harmonic immersions of complex projective line into thecomplex Grassmannian manifolds of rank two.

Final: 2022/3/4
23

Geometry

16:15–17:15

Talk Invited by Geometry Section

Yoshinori Hashimoto (Tokyo Tech) ♭ Recent progress on constant scalar curvature Kähler metrics with 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 29th (Tue)

Conference Room VI

9:45–11:45
17 Noriaki Ikeda (Ritsumeikan Univ.)(Azabu Univ.)
Yuji Hirota

Homotopy momentum sections on pre-multisymplectic manifold · · · · · · 15

Summary: We introduce a notion of a homotopy momentum section on a Lie algebroid over a premultisymplectic manifold.

A homotopy momentum section is a generalization of the momentum mapwith a Lie group action and the momentum section on a pre-symplectic manifold, and is also regarded asa generalization of the homotopy momentum map on a multisymplectic manifold. We show that a gauged
nonlinear sigma model with Wess-Zumino term with Lie algebroid gauging has the homotopy momentum
section structure.
18 Taika Okuda (Tokyo Univ. of Sci.)
Akifumi Sako (Tokyo Univ. of Sci.)

Deformation quantization with separation of variables for 2-complex
dimensional locally symmetric Kähler manifold · · · · · · · · · · · · · · · · · · · · 15

Summary: For a Kähler manifold, Karabegov found a method to construct a deformation quantization
called deformation quantization with separation of variables. Especially, the deformation quantizations
for locally symmetric Kähler manifolds have been studied by Sako–Suzuki–Umetsu, and Hara–Sako, andtheir constructions have been realized for any complex one-dimensional manifold, CN , CPN and CHN . In
this work, we obtained a formula that explicitly determines the deformation quantization for any complex
two-dimensional locally symmetric Kähler manifold.
19 Yuya Takahashi (Nagoya Univ.)

The moduli space of spatial polygons and geometric quantization · · · · 15

Summary: The moduli space of spatial polygons is known as a symplectic manifold equipped with bothKähler and real polarizations. In this talk, we will construct morphisms of operads fKäh and fre by using
the quantum Hilbert spaces HKäh and Hre associated to the Kähler and real polarizations respectively.
Moreover, we will relate the two morphisms fKäh and fre and prove the equality dim HKäh = dim Hre in
general setting. This operadic framework is regarded as a development of the recurrence relation methodby Kamiyama (2000) for proving dim HKäh = dim Hre in a special case.
20 Yuji Hirota
Tosiaki Kori

(Azabu Univ.)(Waseda Univ.)

On the existence of (twisted) Dirac structures over the space of connections on 3 and 4 dimensional manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We shall concretely construct (twisted) Dirac structures on the space of irreducible connections
on a trivial SU (n)-bundle over three and four dimensional manifolds via bundle morphisms to show theexistence of (twisted) Dirac structures over those spaces of connections. It turns out that the twist term isgiven by the Cartan 3-form on those spaces of connections. We ﬁnd that it vanishes over the subspace ofﬂat connections, and give a Dirac structure on the space of ﬂat connections with degree 0 over the boundary
three-manifold.

Final: 2022/3/4
Geometry

24

21 Takeru Asaka (Univ. of Tokyo) ♭ Earthquake maps and cluster algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Tsukasa Ishibashi (Kyoto Univ.)
Shunsuke Kano (Tohoku Univ.)
Summary: Eathquake maps give important ﬂows on the Teichmuller spaces. We calculate earthquake maps
in terms of shear coordinates, which are examples of cluster X-variables in the cluster algebra. In thistalk, we give a new relation between earthquake maps and the separation formula for cluster X-variables byidentifying the former one as a continuation of the latter. In addition, we deﬁne an analogue of earthquake
maps for any cluster algebras of ﬁnite type and prove a similar result to the Thurston’s earthquake theorem.
22 Takashi Otofuji (Nihon Univ.)
Martin Guest (Waseda Univ.)

Stokes matrices of tt∗ -Toda equations and positive energy representations of aﬃne Lie algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a construction which produces a positive energy representation of the aﬃne Lie algebra
b n+1 C from the Stokes data of a solution of the tt*-Toda equations.
sl
23 Masahiro Futaki (Chiba Univ.)
Fumihiko Sanda (Kyoto Univ.)

Equivariant homological mirror symmetry for CP1 · · · · · · · · · · · · · · · · · 15

Summary: We formulate an A-inﬁnity category consisting of equivariant Lagrangian branes for CP1 andprove an equivariant version of the homological mirror symmetry.
13:15–14:15

Talk Invited by Geometry Section

Daisuke Tarama (Ritsumeikan Univ.)

On integrable geodesic ﬂows of a semi-simple Lie group

Summary: This talk deals with the complete integrability and the dynamical property of relative equilibrium
points for the geodesic ﬂow of a semi-simple Lie group equipped with a left-invariant metric. After a shortreview over the geometric settings for general left-invariant Hamiltonian systems on the cotangent bundle toa Lie group, a class of left-invariant metrics is considered on a semi-simple Lie group, following Mishchenko
and Fomenko. It is known that these metrics give rise to completely integrable geodesic ﬂows since late1970’s. It is however rather recent that their equilibrium points are studied mostly on the basis of techniquesin symplectic/Poisson geometry. In the talk, a brief overview is given on these recent progresses. Then, as amain 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 arealso mentioned.

March 30th (Wed)Conference Room VI

9:10–11:45
24 Yuuki Sasaki (Tokyo Nat. Coll. of Tech.)

Maximal antipodal sets of E6 and some compact symmetric spaces · · · 15

Summary: We explicitly classify congruent classes of maximal antipodal sets of E6 and compact symmetricspaces of EI, EII, EIII, EIV type by using the complex exceptional Jordan algebra JC .Moreover, we realize
these compact symmetric spaces as Grassmaniann of JC . We describe each antipodal set in this realizationand observe some relations between antipodal sets and totally geodesic submanifolds.
25 Shoichi Fujimori (Hiroshima Univ.)
Shin Kaneda (Hiroshima Univ.)

Higher genus nonorientable maximal surfaces · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct higher genus nonorientable maximal surfaces in Lorentz–Minkowski 3-space.

Final: 2022/3/4
25

Geometry

26 Hiroshi Sawai(Numazu Nat. Coll. of Tech.)On the inverse of the structure theorem for Vaisman solvmanifolds · · · 15

Summary: In locally conformal Kähler geometry (for short LCK), it is said to be Vaisman structure if Lee
form is parallel with respect to Levi–Civita connection. The nilradical of a Vaisman solvmanifold is givenby H(n) × Rk , where H(n) is a (2n + 1)-dimensional Heisenberg Lie group. In the case of Inoue surface
S + with non-Vaisman LCK structure, its nilradical is given by H(1). In this talk, we prove that a LCK
solvmanifold such that the nilradical of the solvable Lie group is given by H(n) × Rk (n ≥ 1) is Vaisman
manifold or Inoue surface S + .
27 Kazuhiko Takano (Shinshu Univ.)

On trajectory of mass points inertially moving in the Minkowski space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Trajectory of mass points inertially moving on a surface is a geodesic. The simplest cosmic modelthat is uniform and isotropic is the Minkowski space. The Minkowski space is ﬂat because the Christoﬀel’s
symbols are all zero, and the timelike, spacelike and lightlike geodesics are all straight lines. We havedetermined a new connection to preserve the ﬂatness of the Minkowski space.
We discuss geodesics of inertially moving mass points in the Minkowski space with the new connection.

28 Rika Akiyama (Tokyo Metro. Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Yuichiro Sato
(Kogakuin Univ./Tokyo Metro. Univ.)

The ﬁrst variational formulae for integral invariants of the second fundamental form of a map between Riemannian manifolds · · · · · · · · · · · · 15

Summary: By using the idea of integral geometry, we deﬁne integral invariants of the second fundamental
form of a map between Riemannian manifolds and construct a family of energy functionals including thebienergy functional. In this talk, we focus on some energy functionals deﬁned by homogeneous polynomials ofdegree two among them and show their ﬁrst variational formulae. From these results, we obtain alternative
expression of the Euler–Lagrange equation of the bienergy functional and introduce the Chern–Federerenergy functional whose Euler–Lagrange equation is a second-order partial diﬀerential equation.
29 Yuya Kodama (Tokyo Metro. Univ.)

Generalizations of the Lodha–Moore group · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, I state the new groups obtained by generalizing the Lodha–Moore group. The
Lodha–Moore group is known as a nonamenable ﬁnitely presented group and is similar to the Thompson
group F . Since the Lodha–Moore group is deﬁned by using inﬁnite binary words, it can be generalized into
“n-ary”. After I give a short deﬁnition of the Lodha–Moore group, I will state the deﬁnitions of generalized
one and results of “expected” properties.
30 Taro Kimura(Nat. Inst. of Tech., Tsuruoka Coll.)
Katsuya Mashimo (Hosei Univ.)

Biharmonic Cartan embeddings deﬁned by inner automorphism · · · · · · 15

Summary: In this talk, we give the examples of proper biharmonic submanifolds in compact Lie groups which
are the image of Cartan embeddings deﬁned by inner automorphism.
31 Nobutaka Boumuki (Oita Univ.)

On the dimensions of linear spaces concerning holomorphic vector bundles over elliptic orbits · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, I deal with the complex linear space of holomorphic cross-sections of a homogeneous
holomorphic vector bundle over an elliptic adjoint orbit, and give a suﬃcient condition for the linear space
to be ﬁnite-dimensional.
32 Kazuhiro Okumura(Asahikawa Nat. Coll. of Tech.)

Real hypersurfaces in a nonﬂat complex space form whose star-Ricci
tensor is D-parallel · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give a classiﬁcation of real hypersurfaces in a nonﬂat complex space form whose
star-Ricci tensor is D-recurrent. By virtue of this result, we also know a classiﬁcation of real hypersurfaces
in a nonﬂat complex space form whose star-Ricci tensor is parallel.

Final: 2022/3/4
Geometry

14:15–15:15

26

Talk Invited by Geometry Section

Takefumi Kondo (Kagoshima Univ.)

Nonlinear spectral gaps of Coxeter groups with respect to CAT(0)spacesSummary: Nonlinear spectral gap is an invariant deﬁned for a pair of a ﬁnite graph and a metric space andplays important roles in geometric group theory and metric geometry. Pansu calculated the exact values ofnonlinear spectral gaps of cycles and generalized triangles with respect to CAT(0) spaces by applying the
Wirtinger inequalities for ﬁnite cyclic groups proved by Gromov. However, no example of exact calculation
was known other than Pansu’s results.
In this talk, we discuss variants of the Wirtinger inequalities for ﬁnite irreducible Coveter groups and its
application to calculations of nonlinear spectral gaps of Coxeter groups. This contains a nonlinear analogueof computations of spectral gaps of Coxeter groups by Kassabov and Ivrissimtzis–Peyerimhoﬀ.
This is a joint work with Tetsu Toyoda and Takato Uehara.
15:30–16:30

Talk Invited by Geometry Section

Masatoshi Kokubu (Tokyo Denki Univ.)

Flat fronts in hyperbolic three-space and related topics

Summary: Recent works about ﬂat fronts and related topics will be introduced after a brief overview. It is
known that a complete ﬂat surface immersed in hyperbolic 3-space is either a horosphere or a hyperbolic
circular cylinder. However, if the condition is weakened so that surfaces are not necessarily immersed, thenthere are many ‘complete ﬂat surfaces’, properly speaking, weakly complete ﬂat fronts. The word ‘front’comes from a wavefront which means a mapping which have a Legendrian lift to the projective cotangent
bundle of the target space. In early 2000s, M. Umehara, K. Yamada and I started to study ﬂat fronts.
After that, W. Rossman and K. Saji joined and our research was advanced. There are still some interesting
problems that I am working on.

March 31st (Thu)

Conference Room VI

9:15–12:00
33 Natsuo Miyatake (Osaka Univ.) ♭ Generalized Kazdan–Warner equations on foliated manifolds · · · · · · · · · 15
Summary: Generalized Kazdan–Warner equation is a second-order elliptic PDE which was introduced byspeaker as a generalization of the classical Kazdan–Warner equation. In this talk, we show that on acompact foliated Riemannian manifold, the unique solution of the generalized Kazdan–Warner equation isa basic function with respect to the foliation if the Laplacian preserves the space of basic functions and if
the functions which are given to deﬁne the equation are basic.
34 Keita Kunikawa (Utsunomiya Univ.)
Yohei Sakurai (Saitama Univ.)

Liouville type theorem for harmonic maps of controlled growth · · · · · · 15

Summary: We show a Liouville type result for harmonic maps from manifolds with nonnegative Ricci
curvature into positively curved target spaces under the condition that the maps have controlled growth.
35 Junya Takahashi (Tohoku Univ.)
Colette Anné (Univ. de Nantes)

Small eigenvalues of the rough and Hodge Laplacians under ﬁxed volume· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For each degree p and each natural number k ≥ 1, we construct on any closed manifold a familyof Riemannian metrics, with ﬁxed volume such that the k th positive eigenvalue of the rough or the Hodge
Laplacian acting on diﬀerential p-forms converge to zero. In particular, on the sphere, we can choose these
Riemannian metrics as those of non-negative sectional curvature. This is a generalization of the results by
Colbois and Maerten in 2010 to the case of higher degree forms.

Final: 2022/3/4
27

Geometry

36 Tomoya Nakamura (Kogakuin Univ.)
Naoki Kimura (Waseda Univ.)

The compatibility of Jacobi structures and pseudo-Riemannian cometrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Boucetta introduced the compatibility between a Poisson structure π and a pseudo-Riemannian
cometric g ∗ on a smooth manifold M using the Levi–Civita connection of g ∗ on (T ∗ M )π .

This is a

generalization of Kähler structures on M . This notion can be generalized on a Lie algebroid A over M . In
this talk, we generalize this notion more and deﬁne the compatibility between Jacobi structures and pseudoRiemannian cometrics on a Jacobi algebroid (A, ϕ0 ). The compatibility behaves well for the Poissonizationsof Jacobi structures. We show that this is a generalization of Sasakian structures on M .
37 Asuka Takatsu (Tokyo Metro. Univ.) ♭ Concavity preserved by heat ﬂow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Kazuhiro Ishige (Univ. of Tokyo)(Univ. Firenze)
Paolo Salani
Summary: We proved that the log-concavity is the only power concavity preserved by the Dirichlet heat ﬂow
in a convex domain of a Riemannian manifold.
38 Shin Nayatani (Nagoya Univ.)

Laplacian ﬁrst-eigenvalue maximization and embedding optimization· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will introduce an embedding optimization problem for a compact manifold equipped witha volume form and a Riemannian metric.

We also introduce a ﬁrst-eigenvalue maximization problem

concerning the Bakry–Émery Laplacian, as the dual problem of the former one. I will discuss an analogueof the Nadirashvili minimal surface theorem.
39 Takumi Gomyou (Nagoya Univ.)
Shin Nayatani (Nagoya Univ.)

Maximization of the ﬁrst eigenvalue and embedding of a ﬁnite graph· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A graph can be realized in a Euclidean space by using eigenfunctions of the ﬁrst nonzero
eigenvalue of the graph Laplacian. Göring–Helmberg–Wappler considered the maximization of the ﬁrst
nonzero eigenvalue of the weighted graph Laplacian over all edge weights under a certain normalization.
For an optimal edge weight of Göring–Helmberg–Wappler’s problem, we obtain a graph embedding having
a good geometrical property. We also consider a variant of their problem and establish a similar result.
40 Norihiko Minami(Nagoya Inst. of Tech.)

Cohomological characterization of the hierarchical structures interpolating the uniruledness and the rationally connectedness · · · · · · · · · · · · 15

Summary: For a complex projective manifold, Boucksom–Demailly–Păun–Peternell (J. Algebraic Geom.,2013) characterized its uniruledness by the non pseudoeﬀectivesness of its canocinal divisor. Furthermore,
Campana–Demailly–Peternell (London Math. Soc. Lecture Note Ser., 417, 2015) gave a cohomologicalcharacterization of rationally-connectedness. In this talk, I shall report these characterizations can beinterporated to give some chomological characterization of the hierarchical structures interpolating theuniruledness and the rationally connectedness.
41 Masayuki Aino

(RIKEN) ♭ Convergence of the Laplacian Eigenmaps and its rate for submanifolds
that are not necessarily smooth · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Laplacian Eigenmaps is a dimensionality reduction method using eigenvectors of the graphLaplacian which approximates the eigenfunctions of the Laplacian on a submanifold under appropriate
assumptions when random samples are obtained on the submanifold in Euclidean space. The convergence of
Laplacian Eigenmaps has been discussed assuming lower bound for a quantity called reach, which does notallow non-smooth submanifolds. In this talk, I will discuss the convergence of Laplacian Eigenmaps under
the weaker assumptions that non-smooth submanifolds can appear in the limit.

Final: 2022/3/4
Complex Analysis

28

Complex Analysis
March 28th (Mon)

Conference Room VIII

9:30–11:50
1 Shun Kumagai (Tohoku Univ.)

Family of ﬂat surfaces with a parallelogram decomposition · · · · · · · · · · 15

Summary: In this century, a square-tiled translation surface (an origami) is intensively studied as an object
with special properties of its translation structure and its SL(2, R)-orbit embedded in the moduli space. We
generalize this concept in the language of ﬂat surfaces appearing naturally in the Teichmüller theory. We
study the combinatorial structure of origamis and show that a certain system of linear equations realizes
the ﬂat surface in which rectangles of speciﬁed moduli replace squares of an origami. This construction
gives a parametrization of the family of ﬂat surfaces with two ﬁnite Jenkins–Strebel directions for eachcombinatorial structure of parallelogram decomposition.
2 Yûsuke Okuyama (Kyoto Inst. Tech.)

Uniform perfectness in non-archimedean dynamics · · · · · · · · · · · · · · · · · 15

Summary: The notion of uniform perfectness of subsets in C (or P1 ) plays an important role in complex
analysis, complex dynamics, and (complex) potential theory.

In this talk, we will introduce a non-archimedean counterpart to this important notion, and give a few applications of it in non-archimedan
dynamics and potential theory on the Berkovich projective line.
3 Katsuhiko Matsuzaki (Waseda Univ.)
Huaying Wei (Waseda Univ.)

BMO embeddings, chord-arc curves, and Riemann mapping parametrization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the space of chord-arc curves on the plane passing through the inﬁnity with theirparametrization γ on the real line, and embed it into the product of the BMO Teichmüller spaces. The fundamental theorem we prove on this representation is that log γ ′ also gives a biholomorphic homeomorphismof it into the complex Banach space of BMO functions. Using these two equivalent complex structures, wedevelop a clear exposition on the analytic dependence on involved parameters in this space. Especially, we
examine the parametrization of a chord-arc curve by using the Riemann mapping and its dependence on the
arc-length parametrization. As a consequence, we can solve a conjecture of Katznelson, Nag, and Sullivan
by showing that this dependence is not continuous.
4 Katsunori Shimomura (Ibaraki Univ.)

Real rational function and time transformation of caloric morphism on
semi-euclidean spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we show that any non-constant real rational function appears as a time transformationof a caloric morphism, mapping which preserves caloric functions, between semi-eucledean spaces.
5 Ryoya Fukasaku (Kyushu Univ.)
Shinichi Tajima (Niigata Univ.⋆)

Eﬃcient algorithms for computing univariate residues · · · · · · · · · · · · · · 10

Summary: We introduce a new algorithm for computing univariate residues, which is based on the theories
of local cohomology classes and diﬀerential operators. In addition, we compare the algorithm with existingalgorithms.
6 Yoshihiko Shinomiya (Shizuoka Univ.)

Period matrices of some hyperelliptic Riemann surfaces · · · · · · · · · · · · · 15

Summary: We give new examples of period matrices of Riemann surfaces. We construct Riemann surfaces
from polygons which are constructed from some rectangles and give their algebraic equations. The algebraic
equations are of the form w2 = z(z 2 − 1)(z 2 − a21 )(z 2 − a22 ) · · · (z 2 − a2g−1 ) (1 < a1 < a2 < · · · < ag−1 ). We
also see that all algebraic curves of these types of equations are constructed from our way. Period matrices
are calculated by ﬁnding symplectic bases.

Final: 2022/3/4
29

Complex Analysis

7 Sachiko Hamano (Osaka City Univ.)
Masakazu Shiba (Hiroshima Univ.⋆)

The period matrices of an open Riemann surface and its closings in the
Siegel upper half space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

R g
Summary: Let R be an open Riemann surface of genus g (1 ≤ g < ∞), and χR = {ARj , Bj }j=1 be a canonicalhomology basis of R modulo dividing cycles. We show that (R, χR ) determines a unique point in the Siegel

upper half space Sg of degree g, which deserves to be called the period matrix of the open Riemann surface(R, χR ). We also prove that the period matrices of the closings of (R, χR ) satisfy a set of inequalities in Sg .
8 Joe Kamimoto (Kyushu Univ.)

Resolution of singularities for C ∞ functions and meromorphy of local
zeta functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We attempt to resolve the singularities of the zero variety of a C ∞ function of two variables asmuch as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express
the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but
may include ﬂat functions. As an application, we investigate analytic continuation of local zeta functions
associated with C ∞ functions of two variables.
9 Rikio Yoneda (Kanazawa Univ.)

Weighted composition operators between H p and Lqa · · · · · · · · · · · · · · · 10

Summary: We study weighted composition operators between the Hardy space and the Bergman spaces.
14:15–15:15

Talk Invited by Complex Analysis Section
Kazuya Tohge (Kanazawa Univ.) Revisiting the Stothers–Mason theorem with Nevanlinna

Summary: By the Stothers–Mason theorem we mean the well-known abc inequality for complex polynomials
stating: Three relatively prime and non-constant polynomial a, b and c satisfy the relation a + b = c only
if each of them is of degree at most the number of distinct roots of the product abc minus one. It is wellknown that this estimate is sharp by examples and applies polynomial or rational solutions to Fermat’s
equation as well as the so-called Davenport inequality. One can bring Picard’s Little Theorem over to theobservation of a + b = c so that some of the known generalizations of the Stothers–Mason theorem arestated in Nevanlinna’s value distribution theory of meromorphic functions on the complex plane. Then it isobvious that Wronskian plays an essential role in order to count the number of distinct roots of abc. In thistalk, we change a way of counting roots for another abc inequality and give an aﬃrmative partial answer tothe strange question: Can diﬀerence operation substitute well for diﬀerentiation in function theory? The
way of judging a root to be multiple in a diﬀerent angle actually observes the multiplicity as the numberof the stepping-roots with a ﬁxed stride. Therefore, our operation is naturally a shift or diﬀerence operator
with the stride. We see an abc inequality in this setting and apply it to deduce the corresponding Fermat or
Davenport type estimates and reproduce several function-theoretic generalizations of the Stothers–Mason
theorem by using this operator. The discussions proceed in parallel to those in the usual diﬀerential setting
where, for example, Wronskian is simply replaced by Casoratian, and examples to examine the sharpness of
the inequalities can be found in a simple translation rule. These are all for entire functions not for integers
but a tiny and naive attempt at the very end. This is based on a joint work with K. Ishizaki, R. Korhonen,and N. Li.

March 29th (Tue)

Conference Room VIII

9:30–11:30
10 Satoshi Ogawa (Osaka City Univ.)

Linearization of transition functions along some Levi-ﬂat hypersurfaces
with the structure of S 1 -bundle · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce suspension construction and we can obtain a Levi-ﬂat hypersurface which has the
structure of the unit circle bundle. By focusing on Diophantine condition, we investigate the linearizationof transition function along this Levi-ﬂat.

Our linearization is based on Ueda’s result and primitive

KAM-theory for one-variable dynamical systems.

Final: 2022/3/4
Complex Analysis

11 Shota Kikuchi (Nagoya Univ.)30

On sharper estimates of Ohsawa–Takegoshi L2 -extension theorem inhigher dimensional case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Hosono obtained sharper estimates of the Ohsawa–Takegoshi L2 -extension theorem by allowing
the constant depending on the weight function for a domain in C. In this talk, I explain the higher
dimensional case of sharper estimates of the Ohsawa–Takegoshi L2 -extension theorem. In order to provethis, we establish an analogue of Berndtsson–Lempert type L2 -extension theorem by using the pluricomplex
Green function with poles along subvarieties.
12 Takeo Ohsawa (Nagoya Univ.⋆) ♭ On the cohomology vanishing with polynomial growth on complex
manifolds with pseudoconvex boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · 15r,swill be studied. It will be shown that, given a
Summary: ∂ cohomology groups with polynomial growth Hp.g.

complex manifold M , a locally pseudoconvex bounded domain Ω ⋐ M satisfying certain geometric boundaryr,scondition and a holomorphic vector bundle E → M , Hp.g.
(Ω, E) = 0 holds for all s ≥ 1 if E is Nakanor,spositive and r = dim M . It will be also shown that Hp.g.
(Ω, E) = 0 for all r and s with r + s > dim M if

moreover rankE = 1.
13 Takanori Ayano (Osaka City Univ.)
Victor M. Buchstaber(Steklov Inst. of Math.)

Reduction of hyperelliptic functions of genus 2 to elliptic functions · · · 15

Summary: When solutions of diﬀerential equations in terms of hyperelliptic functions of genus 2 are given,
under conditions when a reduction of these functions to elliptic functions is possible, it is important to ﬁnd
an explicit form of these solutions in terms of elliptic functions. In this talk, we consider a hyperelliptic curve
V of genus 2 which admits a morphism of degree 2 to an elliptic curve. Then there exist two elliptic curves
Ei , i = 1, 2, and morphisms of degree 2 from V to Ei . We express the hyperelliptic functions associatedwith V on C2 in terms of the Weierstrass elliptic functions associated with Ei . As a corollary, a solution of
the KdV-hierarchy in terms of the Weierstrass elliptic functions is given.
14 Takayuki Koike (Osaka City Univ.)

Holomorphic foliation associated with a semi-positive class of numericaldimension one · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Let X be a compact Kähler manifold and α be a class in the Dolbeault cohomology class ofbidegree (1, 1) on X. When the numerical dimension of α is one and α admits at least two smoothsemi-positive representatives, we show the existence of a family of real analytic Levi-ﬂat hypersurfaces in X
and a holomorphic foliation on a suitable domain of X along whose leaves any semi-positive representativeof α is zero. As an application, we give the aﬃrmative answer to our conjecture on the relation between
the semi-positivity of the line bundle [Y ] and the analytic structure of a neighborhood of Y for a smoothconnected hypersurface Y of X.
15 Yoshihiko Matsumoto (Osaka Univ.)

The CR Killing operator and the Bernstein–Gelfand–Gelfand construction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: What we call the CR Killing operator D on a contact manifold (M, H) equipped with a compatible
almost CR structure J (also known as a strictly pseudoconvex partially integrable almost CR manifold) is
the linear diﬀerential operator describing trivial deformations of J. We report our recent ﬁnding that D canalso be found as the ﬁrst operator in the so-called Bernstein–Gelfand–Gelfand sequence. More precisely, D
is the ﬁrst BGG operator induced by a modiﬁed tractor connection introduced by Čap, not by the normal
tractor connection, of the adjoint tractor bundle.

16 Yusaku Tiba (Ochanomizu Univ.)

Asymptotic estimates of holomorphic sections on Bohr–Sommerfeld
Lagrangian submanifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let M be a projective manifold and L be an ample line bundle over M with a Hermitian metrich whose Chern form is a Kähler form ω. Let X ⊂ M be a Lagrangian submanifold of (M, ω). WhenX satisﬁes the Bohr–Sommerfeld condition, we give an asymptotic estimate of the norm |f |hk on X forf ∈ H 0 (M, Lk ).

Final: 2022/3/4
31

Complex Analysis

13:15–14:15

Talk Invited by Complex Analysis Section

Shinichi Tajima (Niigata Univ.⋆)

Complex analysis, algebraic analysis and algorithms in singularity thoery

Summary: In this talk, we consider singularities of varieties in the context of computational complex analysis
and algebraic analysis. Based on the concept of local cohomology and Grothendieck local duality, we
introduce a new approach for studying complex analytic properties of singularities. As applications of the
proposed approach, eﬀective methods for computing, for instance, logarithmic vector ﬁelds, limiting tangent
spaces, integral dependence relations, micro-local b-functions are shown.
We introduce a new method for computing holonomic D-modules associated to non-isolated hypersurface
singularities.

Main ingredient of the approach are Poincaré-Birkhoﬀ-Witt algebra and the theory ofcomprehensive Gröbner systems. As applications, we present a method for computing vertical monodromyof vanishing cycles sheaves and micro-local b-functions. We discuss some relations between characteristic
varieties of relevant holonomic D-modules and Lê cycles introduced by D. Massey.

Final: 2022/3/4
Functional Equations

32

Functional Equations
March 28th (Mon)

Conference Room II

9:00–12:00
1 Daichi Komori (Hokkaido Univ.)

The equivalence of the sheaf of pseudodiﬀerential operator and its
symbol class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The study of pseudodiﬀerential operators was developed by Aoki and Kataoka with symbol
theory. Locally they constructed the morphism between the stalks of two sheaves by the aid of the Radontransformation. However their method cannot be extended to the global case. In this talk we introduce theconstruction of the sheaf morphism from the sheaf of pseudodiﬀerential operators to the sheaf of its symbol
class via Čech–Dolbeault cohomology. The theory of Čech–Dolbeault cohomology was originated by Suwa,
and it allows us to manipulate the sheaf cohomology without some conditions such as Steinness of coverings.
We also show that two morphisms are compatible with each other.
2 Shunya Adachi (Kumamoto Univ.)

Monodromy invariant Hermitian forms for second order Fuchsian differential equations with four singularities · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Gauss hypergeometric diﬀerential equation (GHE) is the second order Fuchsian diﬀerential equation with three singularities. Under some suitable condition, GHE has a monodromy invariant Hermitianform, which is useful for the study of geometric nature of solutions. More generally, it is known that for
the Fuchsian diﬀerential equation having an integral representation of solutions, there exists an invariant
Hermitian form. In this talk we consider second order Fuchsian diﬀerential equations with four singularities,
which seems to have no integral representation of solutions in general. As a main result, without assuming
the existence of integral representation of solutions, we give suﬃcient and necessary condition for the
existence of monodromy invariant Hermitian form.
3 Genki Shibukawa (Kobe Univ.)

Artin-style characterizations for multiple gamma and sine functions · · 10

Summary: We give multiple analogues of Artin’s characterizations for the gamma function. As applicationsof our results, we characterize the multiple gamma and (Kurokawa’s) sine functions.
4 Hiroshi Ogawara (Kumamoto Univ.)

Diﬀerential transcendence of solutions for q-diﬀerence equation of Ramanujan function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we show any non-trivial solution for the second order linear q-diﬀerence equationof the Ramanujan function, one of the q-analogue of the Airy function, satisﬁes no non-trivial algebraic
diﬀerential equation over the rational function ﬁeld. Our proof is based on the criterion for diﬀerential
transcendence of solutions for diﬀerence Riccati equations, which is constructed by Nishioka.
5 Takashi Aoki
Takao Suzuki
Shofu Uchida(Kinki Univ.⋆)(Kinki Univ.)(Kinki Univ.)

Exact WKB analysis for the Pearcey system with a large parameter· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The Pearcey system is an extension of the Airy equation for multi variables. In this talk, we showthat the Borel transform of WKB solutions for the Pearcey system can be written as linear combinations ofalgebraic functions.
6 Kazuki Ishibashi(Hiroshima Nat. Coll. of Maritime Tech.)

Nonoscillation theorems for half-linear dynamic equations with mixed
derivatives on a time scale · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk deals with half-linear dynamic equations on a time scale that have two types ofderivatives, and obtains suﬃcient conditions to be nonoscillatory. Note that if the time scale is selectedfrom the set of all real numbers or the set of all natural numbers, then these equations will be half-linear
diﬀerential equations and half-linear diﬀerence equations.

Final: 2022/3/4
33

Functional Equations

7 Hiroyuki Usami (Gifu Univ.)
Manabu Naito (Ehime Univ.⋆)

On the existence and asymptotic behavior of solutions of perturbed
half-linear ordinary diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The existence and asymptotic behavior of solutions of half-linear ordinary diﬀerential equations
with perturbed terms are investigated. The proofs of the results are based on the analysis of generalized
Riccati equations associated with this half-linear equation.
8 Tetsutaro Shibata (Hiroshima Univ.)

Asymptotic behavior of solution to semilinear eigenvalue problem · · · · 12

Summary: We consider the asymptotic behavior of the solution curve of nonlinear ODEs with logarithmic
nonlinear term. It is known that the bifurcation curve λ is a continuous function of the maximum norm
α = ∥uλ ∥∞ of the solution uλ associated with λ, and is written as λ = λ(α). We establish the asymptotic
formulas for uα (t) and ∥uα ∥1 as α → ∞.
9 Marius Ghergu (Univ. College Dublin)
Yasuhito Miyamoto (Univ. of Tokyo)
Vitaly Moroz (Swansea Univ.)

Polyharmonic inequalities with nonlocal terms · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the existence and non-existence of classical solutions for inequalities of type±∆m u ≥ Ψ(|x|) ∗ up uq

in RN (N ≥ 1).

Here, ∆m (m ≥ 1) is the polyharmonic operator, p, q > 0 and ∗ denotes the convolution operator, whereΨ > 0 is a continuous non-increasing function. We devise new methods to deduce that solutions of the above
inequalities satisfy the poly-superharmonic property. This further allows us to obtain various Liouville type
results. Our study is also extended to the case of systems of simultaneous inequalities.
10 Takeyuki Nagasawa (Saitama Univ.)
Aya Ishizeki (Saitama Univ.)

The Möbius energies of knots and links: Decomposition, the cosine
formula, and their Möbius invariance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Möbius energy of knots is one of O’Hara’s energies, named after the invariance under Möbiustransformations. A similar energy is deﬁned for links. In this talk, we unify the treatment of these energies,
and give a Möbius invariant decomposition in a way simpler than before. For this, we use a map which iscalled the Gauss map in the case of links. Using it, we ﬁnd that the decomposition of energy density isderived from the parallelogram theorem. Also, the cosine formula holds for the decomposed energies, which
is known as an alternative expression for the original energy.
11 Takeyuki Nagasawa (Saitama Univ.)
Aya Ishizeki (Saitama Univ.)

The Möbius energy of knots as a limit of the Möbius energy of links· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Analyzing the Möbius energy of knots, we always encounter diﬃculties of singularity of integrandat the diagonal part. As a simple way to avoid them, we regularize the denominator in the integrand. The
regularized energy, however, loses the Möbius invariant property. Introducing the Möbius energy of links,
we attempt a way to avoid singularity preserving this geometrically interesting property. Precisely saying,
we show that the energy of links with a compensated term convergences to the Möbius energy of a knot as
two components of links approaches to one closed curve which represents the knot. The link energy diverges
without a compensated term. Our compensated term, which is constructed from the Gauss map, vanishes
for any knots.

Final: 2022/3/4
Functional Equations

34

14:15–16:15
12 Toshio Horiuchi (Ibaraki Univ.)

The CKN type inequalities involving non-doubling weights · · · · · · · · · · 12

Summary: We discuss validity of CKN type inequalities involving non-doubling weights, after a quick reviewof the classical CKN type inequalities. In one-dimensional case, a function w(t) on (0, ∞) is said to be adoubling weight if there exists a positive number C such that we haveC −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 bea non-doubling weight in the present talk. In one-dimensional case we typically treat e−1/t and e1/t . In
such cases the limit of ratio w(t)/w(2t) as t → +0 may become 0 or +∞, and hence they are regarded as
non-doubling weights according to our notion.
13 Hiroshi Ando (Ibaraki Univ.)
Toshio Horiuchi (Ibaraki Univ.⋆)

Variational problems relating the generalized weighted Hardy’s inequalities with compact perturbations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Let Ω be a bounded domain of RN with boundary of class C 2 . We consider the variational
problems relating the generalized weighted Hardy’s inequalities with compact perturbations. As weights wetreat the functions of distance to the boundary of Ω. We study the inﬁmum of the variational problem
and it’s achievability. Then we use the generalized weighted Hardy’s inequalities with remainder terms on
a tubular neighborhood of the boundary of Ω.
14 Naoki Hamamoto (Osaka Pref. Univ.)

Sharp Rellich–Hardy inequality for constrained vector ﬁelds · · · · · · · · · 10

Summary: We report on sharp constant in the Rellich–Hardy inequality for constrained vector ﬁelds, especially for solenoidal ﬁelds. This inequality serves as an intermediate between the weighted Hardy and
Rellich inequalities for solenoidal ﬁelds, which we established in our previous work as a development of
Costin–Maz’ya’s work on sharp Hardy inequality for axisymmetric solenoidal ﬁelds.
15 Yoshinori Kametaka (Osaka Univ.⋆)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)(Tsuda Coll.)
Atsushi Nagai(
Kazuo Takemura Nihon Univ.)
Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)

Positivity and hierarchical structure of Green functions and the best
constant of Sobolev inequality corresponding to a bending problem ofa beam on a half line · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the boundary value problem for 4-th order linear ordinary diﬀerential equation in a
half line (0, ∞), which represents bending of a beam on an elastic foundation under a tension. A tension
is relatively stronger than a spring constant of elastic foundation. We here treat 4 self-adjoint boundary
conditions, clamped, Dirichlet, Neumann and free edges, at x = 0.

We show the positivity and thehierarchical structure of 4 Green functions and the best constants of the corresponding Sobolev inequalities.
16 Tatsuki Mori (Musashino Univ.)
Sohei Tasaki (Hokkaido Univ.)
Tohru Tsujikawa (Univ. of Miyazaki⋆)
Shoji Yotsutani (Ryukoku Univ.⋆)

Global structure of stationary solutions for the 1-dimension Fix–Caginalp
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We are interested in stationary solutions of the Fix–Caginalp equation, which is proposed by Fix(1983) and Caginalp (1986) to understand phenomena of the non-isothermal solid-liquid phase transition.
Elliott–Zheng (1990) and Suzuki–Tasaki (2009) obtained some partial results concerning the existence andnon-existence of stationary solutions under restricted conditions. In this talk, we show the global structureof all stationary solutions of the 1-dimensional Fix–Caginalp equation with Neumann boundary conditions.

Final: 2022/3/4
35

Functional Equations

17 Kengo Terai (Univ. of Tokyo)
Hiroyoshi Mitake (Univ. of Tokyo)

On weak solutions to ﬁrst-order discount mean ﬁeld games · · · · · · · · · · 10

Summary: In this talk, we establish the existence and uniqueness of weak solutions to ﬁrst-order discountmean ﬁeld games and a stability result to give the existence for the ergodic problem. We show an example
to illustrate the multiplicity of weak solutions to the ergodic problem. With this motivation, we address aselection condition, which is a necessary condition that any limit of solutions under subsequence satisﬁes.
As an application, we show a nontrivial example to get the convergence of weak solutions.
18 Ryunosuke Mori (Meiji Univ.)
Eita Tomimatsu (Tokyo Tech)
Yoshihiro Tonegawa (Tokyo Tech)

On a strong solution to a generalized mean curvature ﬂow with atransport term in the sense of Brakke’s formulation · · · · · · · · · · · · · · · · 12

Summary: Suppose that a family of k-dimensional surfaces in Rn evolves by the generalized mean curvature
ﬂow with a given transport vector in the sense of Brakke’s formulation of velocity. When the ﬂow is locallyclose to a time-dependent k-dimensional plane in a weak sense of measure in space-time, it is represented
as a graph of a C 1,α function over the plane. On the other hand, it is not known if the graph satisﬁes thecorresponding PDE pointwise in general. For this problem, when k = n − 1 and the distributional time
derivative of the graph is a signed Radon measure, it is proved that the graph satisﬁes the PDE pointwise.
An application to a short-time existence theorem for a surface evolution problem is given.
16:30–17:30

Award Lecture for the 2021 MSJ Analysis Prize

Futoshi Takahashi (Osaka City Univ.) ♭ Mathematical analysis related with Hardy inequalities
Summary: In this talk, I will concern several topics on Hardy inequalities in subcritical or critical regime,
Hardy–Leray inequalities for vector ﬁelds, and related functional inequalities. This talk is based on several
works with Megumi Sano, and Naoki Hamamoto.

March 29th (Tue)

Conference Room II

9:00–12:00
19 Tomoyuki Oka (Tohoku Univ.)(Tohoku Univ.)
Goro Akagi

Space-time periodic homogenization for the porous medium equation
with nonnegative initial data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we shall discuss a space-time periodic homogenization problem for the porous medium
equation with periodically oscillating (in space and time) coeﬃcients and nonnegative initial data.
20 Ryuichi Sato (Fukuoka Univ.)
Takahiro Kosugi(Tottori Univ. of Environ. Stud.)On existence of solutions to a system of fully nonlinear parabolic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this talkwe shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global
existence is speciﬁc to the fully nonlinear parabolic system.
(Kyoto Univ.)
21 Yu Yoshimi
Takayoshi Ogawa (Tohoku Univ.)
Senjo Shimizu (Kyoto Univ.)

Maximal L1 -regularity of the heat equation under the oblique boundary
condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For the inhomogeneous oblique boundary data, maximal L1 -regularity of the heat equation issobtained in time end-point case upon the homogeneous Besov space Ḃp,1(Rn+ ) with 1 < p < ∞. We use

the method of Ogawa–Shimizu (arXiv:2110.10442 to be published in JEE) in which they utilized the almost
orthogonal properties between the boundary potential and the Littlewood–Paley dyadic decomposition ofunity in the Besov and the Lizorkin–Triebel spaces.

Final: 2022/3/4
Functional Equations

22 Hiroshi Wakui (Tokyo Univ. of Sci.)
Szymon Cygan (Univ. of Wroclaw)
Grzegorz Karch (Univ. of Wroclaw)
Krzysztof Krawczyk (Univ. of Wroclaw)

36

Stability of constant steady states of a drift-diﬀusion equation · · · · · · · 12

Summary: We study stability of constant steady states of a drift-diﬀusion equation on n-dimensional Euclidean spaces. Our problem has its constant steady states which can be chosen as arbitrary real number.
We have proved that stability of each constant steady states depend on the value of itself.
23 Yekaterina Epshteyn (Univ. of Utah)
Chun Liu (Illinois Inst. of Tech.)
Masashi Mizuno (Nihon Univ.)

Long-time asymptotic behavior for solutions to the Fokker–Planck equation related to the evolution of grain boundaries · · · · · · · · · · · · · · · · · · · 12

Summary: We consider long-time asymptotic behavior for solutions to the Fokker–Planck equation, whichis related to the mathematical model of the evolution of grain boundaries with two state variables, thelattice misorientation and the triple junction. Since the Fokker–Planck equation satisﬁes the energy law, thelong-time asymptotics of the solutions seems the Boltzmann distribution of the state variables. We show
the exponential stability of the Boltzmann distribution in a weighted L2 space. Furthermore, we explain
the relationship between the Boltzmann distribution and the marginal distribution.
24 Yuki Tsukamoto (Meiji Univ.)

Convergence of the Allen–Cahn equation with transport term in abounded domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we explane the Allen–Cahn equation with transport term in a bounded domain.
We prove that the limit interface is mean curvature ﬂow with transport term under the condition that theenergy is uniformly bounded with respect to time. Using this result, we can show the existence of mean
curvature ﬂow with a gradient vector ﬁeld as transport term.
25 Tsukasa Iwabuchi (Tohoku Univ.)

A spectral localization applied to the critical surface quasi-geostrophic
equation on a ball · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the Cauchy problem for the quasi-geostrophic equations in a ball of the two dimensional
space under the homogeneous Dirichlet boundary condition. We show the existence, the uniqueness of thestrong solution in the framework of Besov spaces. In the proof, we establish a spectral localization techniqueand commutator estimates.
26 Dáithı́ Ó hAodha (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

The optimal decay estimate of solutions to the surface quasi-geostrophic
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We construct a linear approximation of the solution to the Surface Quasi-Geostrophic Equationin two-dimensional Euclidean space, and obtain a convergence rate, in the Lebesgue norm, between thesolution and this approximation with respect to time. We also demonstrate that the nonlinear term of thesolution is bounded sharply by the same function of time.
27 Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)

A Liouville type theorem of reaction diﬀusion system and its application
to spreading problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We establish a Liouville type theorem for entire solutions of these reaction-diﬀusion systems.
Based on this theorem, we derive the stabilization of the solutions of the reaction-diﬀusion system to theunique positive constant state, under the condition that this positive constant state is globally stable in thecorresponding kinetic systems. An example about spreading phenomena from epidemiology are given toillustrate the applications of this theory.

Final: 2022/3/4
37Functional Equations

28 Masahiko Shimojo(Tokyo Metro. Univ.)
Jong-Shenq Guo (Tamkang Univ.)
Yu-Shuo Chen (Tamkang Univ.)

Spreading problem and traveling wave of a singular predator-prey system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We concern the dynamical behaviors of a singular predator-prey model. We compute the spreading
speed of the predator and asymptotic behavior of the spreading solution beyond and behind the front. Someexistence theorems of traveling wave on a line is also discussed.
29 Kousuke Kuto (Waseda Univ.)

Global bifurcation structure of segregated steady-states for a crossdiﬀusion limit in the Shigesada–Kawasaki–Teramoto model · · · · · · · · · · 12

Summary: Recently, the author obtained a limiting (shadow) system of the stationary Shigesada–Kawasaki–
Teramoto model as both cross-diﬀusion terms tend to inﬁnity with the same order. This talk is concernedwith the bifurcation structure of nonconstant solutions of the limiting system. In the one-dimensional case,this result gives inﬁnitely many branches that connect the positive constant solution with a singular limit.
13:00–14:00

Talk Invited by Functional Equations Section

Hiroshi Matsuzawa (Kanagawa Univ.)

A free boundary problem of reaction-diﬀusion equation with a multistable type nonlinearity in high space dimensions

Summary: In this talk, I will treat propagation phenomena in a free boundary problem of reaction diﬀusion
equation of the form : ut = ∆u+f (u) (t > 0, x ∈ Ω(t)) with free boundary Γ(t) = ∂Ω(t) which is determinedby the Stefan condition of the form ut = µ|∇u|2 on Γ(t). In the work of Du and Lin (2010), this type ofproblem was introduced when N = 1 as a model which describes the spreading of new or invasive species.
From this work, propagating phenomena in the free boundary problems attract more and more attention ofmathematicians. In this talk, I will present some recent study on propagation proﬁles of solutions for thefree boundary problem of reaction-diﬀusion equation with some class of multi-stable nonlinearity in highspace dimensions. I will give ﬁrst the result about radially symmetric case. I will also present the general(non-symmetric) case. This talk is based on some joint works with Dr. Yuki Kaneko (Japan Women’s
University) and Professor Yoshio Yamada (Waseda University).

March 30th (Wed)Conference Room II

9:00–12:00
30 Takeshi Suguro (Tohoku Univ.) ♭ Well-posedness of the Cauchy problem of the parabolic-elliptic Keller–
Segel system in uniformly local spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the Cauchy problem of the parabolic-elliptic Keller–Segel system. This system is oneof the diﬀusion equations involving a nonlocal term. It is interesting whether this problem is well-posed infunction spaces containing non-decaying functions. We show that the Cauchy problem of the Keller–Segelsystem is well-posed in uniformly local Lebesgue spaces.
31 Tatsuya Hosono (Tohoku Univ.) ♭ Finite time blow-up of solutions to an attraction–repulsion chemotaxis
system in four dimensional case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: This talk deals with the solution of the Cauchy problem for an attraction-repulsion chemotaxis
system in Rn with the positive parameters β1 , β2 , λ1 , λ2 . According to previous results in R2 , it has shownthat for the initial mass ∥u0 ∥L1 , the value 8π/(β1 − β2 ) is the threshold whether the solution exists globallyin time or not under the attractive dominant case β1 > β2 . In this talk, for the 4-dimensional case, weshow that the solution with ∥u0 ∥L1 > (8π)2 /χ may blow up in ﬁnite time, where χ is a positive constant
explicitly determined by β1 , β2 , λ1 , λ2 . The constant (8π)2 can be regarded as the 4-dimensional thresholdvalue for the global existence corresponding to the system which has 8π-dichotomy in R2 .

Final: 2022/3/4
Functional Equations

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

38

Blow-up in a degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk deals with a degenerate parabolic-elliptic chemotaxis system with logistic source andnonlinear production. In a nondegenerate case, a condition such that solutions blow up in ﬁnite time wasobtained in our previous work (J. Math. Anal. Appl.; 2022; 506; 29). The purpose of this talk is to showthat solutions blow up in ﬁnite time in a degenerate case.
33 Yutaka Kamimura♭ Soliton solutions of the Boussinesq system · · · · · · · · · · · · · · · · · · · · · · · · · 12
(Tokyo Univ. of Marine Sci. and Tech.)
Summary: Based upon a reﬂectionless inverse scattering theory we establish an inverse scattering method bywhich N-soliton solutions of a nonlinear evolution system (the Boussinesq system) are constructed.
34 Masafumi Yoneda (Chiba Univ.)

Asymptotic stability of soliton for discrete nonlinear Schrödinger equation on one-dimensional lattice · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Discrete nonlinear Schrödinger equation (DNLS) is a partial diﬀerential equation which appear invarious region of physics. We will explain the behavior of the solution of DNLS. In particular, we focus on
the stability of soliton. The stability is that the solution of DNLS converge to standing wave solutions insome sense for a long time. The standing wave solution is a special solution of DNLS.We will explain proofof the stability which consists of spectrum theory, linear estimates and boot strap argument.
35 Masafumi Yoshino (Hiroshima Univ.)

Movable singular point of non autonomous Hamiltonian system of degree of freedom one · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk we study the movable singular point of a Hamiltonian system with Hamiltonian
H := H0 + H1 . Here H0 is integrable and has a singular solution v while H1 is a perturbation. A singularsolution for H has the form F (v) for some transformation F deﬁned on a domain of the phase space whichcontains the orbit of v tending to inﬁnity.
36 Noriyoshi Fukaya (Tokyo Univ. of Sci.)
Vladimir Georgiev (Pisa Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)

On stability and instability of standing waves for 2d-nonlinear Schrödinger
equations with point interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study existence and stability properties of ground-state standing waves for two-dimensional
nonlinear Schrödinger equation with a point interaction and a focusing power nonlinearity. The Schrödinger
operator with a point interaction (−∆α )α∈R describes a one-parameter family of self-adjoint realizationsof the Laplacian with delta-like perturbation. The operator −∆α always has a unique simple negative
eigenvalue eα . We prove that if the frequency of the standing wave is close to −eα , it is stable. Moreover,
if the frequency is suﬃciently large, we have the stability in the L2 -subcritical or critical case, while theinstability in the L2 -supercritical case.
37 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.

Final: 2022/3/4
39

Functional Equations

38 Masaru Hamano (Saitama Univ.)
Masahiro Ikeda (RIKEN/Keio Univ.)
Shuji Machihara (Saitama Univ.)

Blow-up solutions to nonlinear Schrödinger equation with an inverse
power potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we treat nonlinear Schrödinger equation with a mass-critical nonlinear term and an
inverse power potential in one dimension. We note that the equation is not scale invariant. We consider thetime behavior of solutions for initial data with negative energy. In particular, we prove that the solutions
blow up. Ogawa–Tsutsumi proved the similar result for an equation without a potential. They used scale
invariance of the equation without the potential. Since our equation has not scale invariance, we cannot
apply directly Ogawa–Tsutsumi’s argument. Therefore, we change scale of weighted function in a localized
virial identity and prove our result.
39 Takuya Sato

(Tohoku Univ.) ♭ Lower bound estimates of solutions to the dissipative nonlinear Schrödinger
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem for the nonlinear Schrödinger equation with a power typenonlinearity λ|u|p−1 u. The condition Im λ < 0 yields a dissipative property for the solution to the nonlinear
Schrödinger equation. We show that p = 1 + 2/n is the critical exponent to exhibit the L2 -decay of
dissipative solutions, namely we show the L2 -lower bound of the solution when p > 1 + 2/n.
40 Sonae Hadama (Kyoto Univ.)

Well-posedness of the Hartree equation for inﬁnitely many particles
with the Riesz potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the Hartree equation describing the time evolution of the wave functions of N fermionsinteracting with each other. From a physics perspective, the case where N is inﬁnite is also important. In
this case, the well-posedness and scattering was ﬁrst studied by Lewin–Sabin. It has been advanced recently
by Chen–Hong–Pavlović and Collot–de Suzzoni. However, these studies only deal with the cases where theinteraction is weak, and therefore, there were no results for the cases with strong interaction, for example,
the Riesz potential. In this talk, we report the results on the local and global well-posedness of the Hartree
equation with the Riesz potential, which is important from a physics perspective.
14:15–16:15
41 Shunya Hashimoto (Saitama Univ.)
Isamu Dôku (Saitama Univ.⋆)
Shuji Machihara (Saitama Univ.)

The local well-posedness of the stochastic nonlinear Schrödinger equations in H 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Cauchy problem for the stochastic nonlinear Schrödinger equation with a multiplicable noise
is considered where the nonlinear term is of a power type and its coeﬃcients are complex numbers. In
particular, it is important to consider the complex coeﬃcients in the noise which cover non-conservative
cases, because they include measurement eﬀects in quantum physics. The main purpose of this work is toconstruct classical solutions in H 2 (Rd ) for the problem in question.
42 Isao Kato

(Kyoto Univ.)

Ill-posedness for the half wave Schrödinger equation · · · · · · · · · · · · · · · · 10

Summary: We study ill-posedness for the half wave Schrödinger equation introduced by Xu (2017). Illposedness is obtained in the super-critical or at the critical space. The proof for the super-critical space isbased on the argument established by Christ, Colliander and Tao (2003). For the critical space, we use thestanding wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi (2021).

Final: 2022/3/4
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 a classiﬁcation result of systems with two unknowns and cubic polynomial
nonlinearities. We deﬁne an equivalence relation between two systems by the linear transformation of
unknowns. The goal is to understand a quotient set with respect to the equivalence relation. To this end, we
introduce a matrix representation of a system. The representation not only gives us an explicit formula ofthe equivalence relation and but also describes characteristic properties of the system such as conservation
laws. The classiﬁcation result is based on the study of nonlinear dispersive equations but it is applicable toa wide class of systems of PDEs and ODEs.
44 Satoshi Masaki (Osaka Univ.)
Jun-ichi Segata (Kyushu Univ.)
Kota Uriya (Okayama Univ. of Sci.)

On asymptotic behavior of solutions to a nonlinear Klein–Gordon system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we study the asymptotic behavior of solutions to a speciﬁc system of the cubic
Klein–Gordon equations in one dimension. The cubic nonlinearity is critical in one dimension with respect
to the large-time behavior of (small) solutions. It turns out that the system, which is obtained systematicallyby our classiﬁcation result, admits a solution with a new type of asymptotic behavior.
45 Shunsuke Kitamura (Tohoku Univ.) ♭ The lifespan estimates of classical solutions of one dimensional semilinHiroyuki Takamura (Tohoku Univ.) ear wave equations with characteristic weights · · · · · · · · · · · · · · · · · · · · · 12
Kyouhei Wakasa(Kushiro Nat. Coll. of Tech.)
Summary: In this talk, we report on the lifespan estimates of classical solutions of semilinear wave equations
with characteristic weights and compactly supported data in one space dimension. The results includes
those for weights by time-variable, but excludes those for weights by space-variable in some cases. We haveinteractions of two characteristic directions.
46 Hiroyuki Takamura (Tohoku Univ.) ♭ Semilinear wave equations of derivative type with spatial weights in one
Shunsuke Kitamura (Tohoku Univ.) space dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Katsuaki Morisawa (Tohoku Univ.)
Summary: In this talk, we discuss about the initial value problems for semilinear wave equations of derivative
type with spatial weights in one space dimension. The lifespan estimates of classical solutions are quite
diﬀerent from those for nonlinearity of unknown functions itself as the global-in-time existence can beestablished by spatial decay.
47 Hiroyuki Takamura (Tohoku Univ.) ♭ The combined eﬀect in one space dimension beyond the general theory
Takiko Sasaki
for nonlinear wave equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
(Musashino Univ./Tohoku Univ.)
Katsuaki Morisawa (Tohoku Univ.)
Summary: In this talk, we introduce lifespan estimates for a special class of semi-linear wave equations in one
space dimension for which the so-called combined eﬀect is observed. It is remarkable that we have better
results than those in the general theory which was established in 1992.

Final: 2022/3/4
41

Functional Equations

16:30–17:30

Talk Invited by Functional Equations Section

Motohiro Sobajima(Tokyo Univ. of Sci.)

Weighted energy estimates for wave equations with space-dependent
damping

Summary: In this talk we summarize recent progress on weighted energy estimates of polynomial type forthe wave equation with space-dependent damping ∂t2 u − ∆u + a(x)∂t u = 0, where the damping coeﬃcient a
decays like a polynomial |x|−α (α ∈ [0, 1)) at spatial inﬁnity. When we consider weighted energy estimatesto such problems, usually the exponential function of the form eψ(x,t) appears as a weight function in theenergy functional. However, this choice excludes a class of initial data with polynomial decay. In contrast,
we introduce another class of weight functions involving the conﬂuent hypergeometic functions to provide
corresponding weighted energy estimates which have weight functions with polynomial order. Next, we deal
with global existence for the semilinear problem with a power type nonlinearity as an application of such
estimates.

March 31st (Thu)

Conference Room II

9:00–12:00
48 Takahito Kashiwabara (Univ. of Tokyo)
Hiromichi Itou (Tokyo Univ. of Sci.)

Unique solvability of a crack problem with Signorini-type and Tresca
friction conditions in a linearized elastodynamic body · · · · · · · · · · · · · · 12

Summary: We consider a time-dependent linear elasticity equation including a crack, which is a thin surface
embedded in a bulk domain. On the crack we impose a non-penetrating (a.k.a. Signorini) condition anda given friction (a.k.a. Tresca) condition for the normal and tangential directions, respectively. Sincean original Signorini condition involving only displacement leads to a severe mathematical diﬃculty, we
modiﬁed it in such a way that it includes velocity. For this problem we are able to prove existence anduniqueness of a strong solution, which is our main result.
49 Ikki Fukuda (Shinshu Univ.)
Kenta Itasaka

Higher-order asymptotic proﬁles of the solutions to the viscous Fornberg–
Whitham equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for the viscous Fornberg–Whitham equation which is one of thenonlinear and nonlocal dispersive-dissipative equations. In this talk, we establish the global existence ofthe solutions and study its asymptotic behavior. We show that the solution to this problem converges tothe self-similar solution to the Burgers equation called the nonlinear diﬀusion wave, due to the dissipationeﬀect by the viscosity term. Moreover, we analyze the optimal asymptotic rate to the nonlinear diﬀusion
wave and the detailed structure of the solution by constructing higher-order asymptotic proﬁles. Also, weinvestigate how the nonlocal dispersion term aﬀects the asymptotic behavior of the solutions and compare
the results with the ones of the KdV–Burgers equation.
50 Souhei Sugizaki (Tokyo Tech)
Shinya Nishibata (Tokyo Tech)
Itsuko Hashimoto (Kanazawa Univ.)

Asymptotic stability of a radially symmetric stationary solution for thecompressible Navier–Stokes equation with an inﬂow boundary condition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study a radially symmetric stationary solution for the compressible Navier–Stokes equation
with an inﬂow boundary condition.

Precisely, we obtain the decay rates of the solution and its ﬁrst

derivatives. Moreover, we show an asympotic stability of the stationary solution.
51 Motofumi Aoki (Tohoku Univ.)
Tsukasa Iwabuchi (Tohoku Univ.)

On the energy conservation law for the full system of compressible
Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study a suﬃcient condition such that a weak solution of the full system of compressible
Navier–Stokes equations satisﬁes the energy conservation law. We focus on two and three space dimensions
and especially consider the case that the pressure is written by the ideal gas law.

Final: 2022/3/4
Functional Equations

52 Masashi Ohnawa(Tokyo Univ. of Marine Sci. and Tech.)
Masahiro Suzuki (Nagoya Inst. of Tech.)

42

Asymptotic stability of air ﬂow over mountains with wave breaking· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider stationary shock waves appearing in air ﬂow over mountains modeled by onedimensional shallow water equation. The shock wave connects an upstream supercritical state to adownstream subcritical state discontinuously. If the discontinuity is located in a lee side of the mountain,
we claim the asymptotic stability of the stationary shock wave whatever large the strength of the shock or
the gradient of the mountain height may be.
53 Kota Ikeda(Meiji Univ.)

Stability analysis of a uniform ﬂow in a mathematical model of camphor
boats · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Various collective motions of camphor boats, called jamming, clustering, and swarming state
observed in a one-dimensional circuit, have been studied. It is expected that the center manifold theories
proposed in previous works are useful for the analysis of the collective motion of camphor boats. In my
previous work, we have developed a new theory for a system with Dirac’s delta functions in L2 -framework.
In this talk, we will examine the stability analysis in the reduced system and numerically show that theuniform ﬂow can be destabilized even if the length of the circuit is large.
(RIKEN)
54 Ken Furukawa(
Takahito Kashiwabara Univ. of Tokyo)

Singular limit problems on the primitive equations and Navier–Stokes
equations in anisotropic spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we introduce the mathematical relationship between the Navier–Stokes equations andthe primitive equations. Then we show that the solution of the scaled Navier–Stokes equations converges tothe solution of the primitive equations in anisotropic Lebesgue spaces under less regularity assumptions.
55 Takeshi Gotoda (Tokyo Tech)

Energy conservation in 2D incompressible inviscid ﬂows · · · · · · · · · · · · · 10

Summary: We consider energy conservation in 2D incompressible inviscid ﬂows through weak solutions of theﬁltered-Euler equations, which describe a regularized Euler equations. We show that the energy dissipation
rate for the ﬁltered weak solution with vorticity in Lp , p > 3/2 converges to zero in the limit of the ﬁlter
parameter. Although the energy deﬁned in the whole space is not ﬁnite in general, we formally extract atime-dependent part from the energy and deﬁne the energy dissipation rate as its time-derivative. Moreover,the limit of the ﬁltered weak solution is a weak solution of the Euler equations and it satisﬁes a local energybalance in the sense of distributions.
56 Hiroyuki Tsurumi (Kyoto Univ.)
Yasunori Maekawa (Kyoto Univ.)

Existence of the 2D stationary Navier–Stokes ﬂow on the whole planearound a radial ﬂow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the stationary Navier–Stokes equations on the whole plane R2 . We show that for agiven small and smooth external force around a radial ﬂow, there exists a classical solution decaying like|x|−1 . In our result, it is not necessary to impose any symmetric conditions on external forces.
14:15–16:15
57 Hideo Kozono(Waseda Univ. / Tohoku Univ.)
Yutaka Terasawa (Nagoya Univ.)
Yuta Wakasugi (Hiroshima Univ.)

Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier–Stokes equations outside of an inﬁnite cylinder with aperiodic boundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the asymptotic behavior of solutions to the steady Navier–Stokes equations outside of
an inﬁnite cylinder in R3 . We assume that the ﬂow is periodic in x3 -direction and has no swirl. This
problem is closely related with two-dimensional exterior problem. Under a condition on the generalizedﬁnite Dirichlet integral, we give a pointwise decay estimate of the vorticity at the spatial inﬁnity. Moreover,
we prove a Liouville-type theorem only from the condition of the generalized ﬁnite Dirichlet integral.

Final: 2022/3/4
43Functional Equations

58 Lorenzo Brandolese (Univ. Lyon 1)
Takahiro Okabe (Osaka Univ.)

Control of weak solutions of the Navier–Stokes equation by external
forcing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the incompressible Navier–Stokes equations in the whole space Rn , n = 2, 3, 4. The
aim of this talk is to control of the energy decay of weak solutions by external force. For this purpose, wegive a reﬁnement of the method in our previous result and derive weighted L1 -estimate of weak solutions of
the Navier–Stokes equations which satisﬁes the strong energy inequality.
59 Keiichi Watanabe (Waseda Univ.)

Stability of stationary solutions to a free boundary problem of theNavier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the stability of equilibrium ﬁgures of uniformly rotating viscous incompressible ﬂuid
in R3 with surface tension, where the equilibrium ﬁgures are rotationally symmetric about a certain axis.
It is proved that this stability result can be obtained by the positivity of the second variation of the energyfunctional associated with the equation that determines equilibrium ﬁgures, provided that initial data areclose to an equilibria state. The solution converges exponentially to an equilibrium. The proof is inspiredby a series of papers due to Shibata, but a new orthogonal condition is introduced in order to show the
exponential stability of an associated analytic C0 -semigroup. If a value of initial angular momentum issmall, the steady-state is determined uniquely.
60 Miho Murata (Shizuoka Univ.)
Yoshihiro Shibata (Waseda Univ.)

Global well posedness for a Q-tensor model of nematic liquid crystals· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the global well posedness and the decay estimates for a Q-tensor model of nematic
liquid crystals in RN , N ≥ 3. This system is coupled system by the Navier–Stokes equations with aparabolic-type equation describing the evolution of the director ﬁelds Q. The proof is based on the maximal
Lp -Lq regularity and the Lp -Lq decay estimates to the linearized problem.
61 Mikihiro Fujii (Kyushu Univ.)

Large time behavior of solutions to the 3D anisotropic Navier–Stokes
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the large time behavior of the solution to the 3D Navier–Stokes equation withhorizontal viscosity and show that the Lp decay rate of the horizontal components of the velocity ﬁeld
coincides to that of the 2D heat kernel, while the vertical component decays like the 3D heat kernel.
Moreover, we consider the asymptotic expansion of the solution and ﬁnd that a portion of the nonlinear
term aﬀect the leading term of the horizontal components of the velocity ﬁeld, whereas the leading term of
the vertical component is given by only the linear solution.
62 Yoshihiro Shibata (Waseda Univ.)

Global solution of the 3D compressible Navier–Stokes equations withfree surface in the maximal regularity class · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this paper concerns the global wellposedness issue of the barotropic compressible Navier–Stokes
equations (CNS) with free surface in the smooth exterior domain in 3D Euclidean space. By using the decay
estimate in the semigroup theory, we construct the global-in-time solution in the time weighted maximal
Lp -Lq regularity class for some p > 2 and q > 3. Namely, the solution is bounded as Lp in time and Lq
in space. Compared with the previous results of the free boundary value problem of (CNS) in unboundeddomains, we relax the regularity assumption on the initial states, which is the advantage by using the
maximal Lp -Lq regularity framework.
63 Yoshihiro Shibata (Waseda Univ.)

The Lp -Lq decay estimate for the multidimensional compressible ﬂow
with free surface in the exterior domain · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The aim of this talk is to develop the general Lp theory for the barotropic compressible Navier–Stokes equations with the free boundary condition in the exterior domain in the N dimensional Euclidean
space (N ≥ 3). By the spectral analysis, we obtain the classical Lp -Lq decay estimate for the linearized
model problem in view of the partial Lagrangian transformation.

Final: 2022/3/4
Functional Equations

16:30–17:30

44

Talk Invited by Functional Equations Section

Yoshihiro Ueda

(Kobe Univ.)

Mathematical analysis of the dissipative structure for the symmetric
hyperbolic system with relaxation

Summary: In this talk, we consider the dissipative structure for the linear symmetric hyperbolic systemwith non-symmetric relaxation. If the relaxation matrix of the system has symmetric property, Shizuta
and Kawashima in 1985 introduced the suitable stability condition, and Umeda, Kawashima and Shizuta in
1984 analyzed the dissipative structure. On the other hand, Ueda, Duan and Kawashima in 2012 and 2018
focused on the system with non-symmetric relaxation, and got the partial results. Furthermore, they argued
the new dissipative structure called the regularity-loss type. In this situation, our purpose of this talk is
to extend the stability theory introduced by Shizuta and Kawashima in 1985 and Umeda, Kawashima and
Shizuta in 1984 for our general system.

Final: 2022/3/4
45

Real Analysis

Real Analysis
March 30th (Wed)Conference Room VIII

9:30–11:45
1 Yukino Tomizawa(Niigata Inst. of Tech.)

Geometric properties of complete geodesic space · · · · · · · · · · · · · · · · · · · 15

Summary: In general, geodesic spaces is not linear, but they have generalization of properties in linear spaces.
The purpose of this study is to elucidate the geometrical characteristics of geodesic spaces. We report somegeometric properties such as uniform convexity in complete Busemann spaces.
2 Shin-ya Matsushita (Akita Pref. Univ.)

On the Douglas–Rachford algorithm · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Douglas–Rachford algorithm is an important and powerful algorithm that can be applied tosolving problems, such as minimizing the sum of two proper closed convex functions, or, more generally,ﬁnding a zero point of the sum of two monotone operators. In this talk, we study a modiﬁed version of the
Douglas–Rachford algorithm for convex minimization problem in a real Hilbert space.
3 Sachiko Atsushiba(Tokyo Woman’s Christian Univ.)

Convergence theorems for monotone nonexpansive mappings · · · · · · · · 15

Summary: In this talk, we prove nonlinear ergodic theorems for a family of monotone nonexpansive mappingsin ordered uniformly convex Banach spaces. We also weak and strong convergence theorems for the mappings.
4 Koji Aoyama(Chiba Univ.)

A quasinonexpansive extension of a mapping with an attractive point· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show that, under appropriate conditions, there exists a quasinonexpansive extension of a
mapping with an attractive point in the sense of Takahashi and Takeuchi (2011) such that the ﬁxed point
set of the extension equals the attractive point set of the given mapping. Then using the quasinonexpansive
extension, we establish some convergence theorems for approximating attractive points of a generalized
hybrid mapping in the sense of Kocourek, Takahashi, and Yao (2010).
5 Ryotaro Tanaka (Tokyo Univ. of Sci.)

Nonlinear classiﬁcation of Banach spaces based on Birkhoﬀ–James orthogonality · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For Banach spaces X, Y , we say that X is isomorphic to Y with respect to the structure of
Birkhoﬀ–James orthogonality, denoted by X ∼BJ Y , if there exists a bijection T : X → Y that preserves
Birkhoﬀ–James orthogonality in both directions. It is shown that the ﬁnite dimension of a Banach space
is preserved under “∼BJ ”, reﬂexive smooth Banach spaces are isomorphically classiﬁed from the viewpointof Birkhoﬀ–James orthogonality, and three or more dimensional Hilbert spaces are characterized by theirstructure of Birkhoﬀ–James orthogonality.
6 Kenichi Mitani (Okayama Pref. Univ.)
Kichi-Suke Saito (Niigata Univ.⋆)

Some recent results on skewness of Banach spaces · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we present some recent results on the skewness of Banach spaces, especially inconnection with James constant and characteristic of convexity.
7 Toshiharu Kawasaki (Tamagawa Univ.)

Notes on the extended indeﬁnite integral · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will describe the points to note regarding the family of indeﬁnite integral withrespect to the extended integral.

Final: 2022/3/4
Real Analysis

46

14:30–16:00
8 Jun Kawabe(Shinshu Univ.)

A topology on the space of measurable functions on a nonadditive
measure space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, given a nonadditive measure µ, a topology, which is compatible with convergence inµ-measure, is deﬁned on the real linear space of all measurable functions by using the distance introduced by
Dunford and Schwartz. Some properties of the topology, such as the open sphere condition, completeness,
the Hausdorﬀ separation axiom, separability, linearlization, and pseudo-metrizability, are related to thecharacteristics of nonadditive measures.
(Oita Univ.)
9 Ryoji Fukuda
Aoi Honda (Kyushu Inst. of Tech.)
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

Completion of a monotone measure space and completeness of a measure
algebra and L0 space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let (X, B, µ) be a monotone measure space. We discuss the µ-completion of the σ-algebra B andcompleteness of the measure algebra and the L0 topology. We consider these problems under the conditionof weak zero additivity, quasi subadditivity, and some other assumptions for the monotone measure µ. To
prove the completeness, we deﬁne power transform of a monotone measure or a pseudo metric. This concept
is very useful for our proof. Using this concept, we also prove the metrizability of these topologies.
10 Satoshi Yamaguchi (Ibaraki Univ.)(Ibaraki Univ.)
Eiichi Nakai

Generalized fractional integral operators on Campanato spaces andtheir bi-preduals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we prove the boundedness of the generalized fractional integral operator Iρ on
generalized Campanato spaces with variable growth condition, which is a generalization and improvementof previous results, and then, we establish the boundedness of Iρ on their bi-preduals. We also prove theboundedness of Iρ on their preduals by the duality.
Pointwise multipliers on weak Orlicz–Morrey spaces · · · · · · · · · · · · · · · · 15

11 Ryota Kawasumi

Summary: In this talk we give the characterization of pointwise multipliers on weak Orlicz–Morrey spaces.
To do this we ﬁrst prove a generalized Hölder’s inequality for the weak Orlicz–Morrey spaces. Next, tocharacterize the pointwise multipliers, we use the fact that all pointwise multipliers from a weak Orlicz–
Morrey space to another weak Orlicz–Morrey space are bounded operators. Weak Orlicz–Morrey spaces
contain weak Lp , weak Orlicz and generalized weak Morrey spaces. Then our results contain several previous
results as corollaries.
12 Naoya Hatano(Chuo Univ.)

Weak-type boundedness of commutators with respect to singular integral operators on Orlicz–Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we give the weak-type boundedness of its commutators on Orlicz–Morrey spaces.

Final: 2022/3/4
47

Real Analysis

16:15–17:15

Talk Invited by Real Analysis Section

Yasunori Kimura (Toho Univ.)

Resolvent operators on complete geodesic spaces

Summary: The convex minimization problem is one of the central topics in convex analysis, and many
researchers have investigated this problem in various ways. The notion of resolvent operators is an essential
and powerful tool for studying this topic because it connects convex analysis to ﬁxed point theory fornonexpansive and other nonlinear mappings.
This talk focuses on the convex functions deﬁned on complete geodesic spaces with their curvature bounded
above. According to the geometric structures of the underlying space, we need to change the deﬁnition of theresolvent operator. We ﬁrst survey the variety of known deﬁnitions and their fundamental properties. Then,
we consider minimization problems for such functions. To generate an approximating sequence converging
to a solution to this problem, we use a resolvent operator. Finally, we obtain some convergence theorems ofthe generated iterative sequence.
We can extend the notion of resolvent operators for convex functions to that for bifunctions for equilibrium
problems. We will also discuss this topic and recent developments.

March 31st (Thu)

Conference Room VIII

9:30–12:00
13 Shodai Kubota (Chiba Univ.)
Ken Shirakawa (Chiba Univ.)

Optimal controls in 1D-time-discrete Warren–Kobayashi–Lobkovsky–
Carter system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider optimal control problems for time-discrete state problems of one-dimensional systems.
Each state problem is denoted by (S)ε , with ε ≥ 0, and is based on the non-isothermal model of grainboundary motion.In this regard, each optimal control problem is denoted by (OP) ε , with ε ≥ 0, and it isprescribed as a minimization problem of a cost function. Additionally, the problems (S) ε and (OP)ε aresupposed to admit limiting proﬁles as ε ↓ 0, and then, the limiting problems are supposed to contain nolittle singularities. The main mathematical results concerned with: (A) the solvability to the problems (S) ε ;(B) the existence of the optimal control; (C) the necessary condition for the optimal control when ε > 0;(D) limiting observation as ε ↓ 0; will be reported as the main theorems of this talk.
14 Yutaro Chiyo (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

A simpliﬁed quasilinear attraction-repulsion chemotaxis system: boundedness · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system.
When there is no repulsion term, global existence and boundedness were obtained by the eﬀect of thediﬀusion term by Tao–Winkler (J. Diﬀerential Equations; 2012; 252; 692–715). The purpose of this talk is
to establish global existence and boundedness in a quasilinear attraction-repulsion chemotaxis system byusing the repulsion term instead of the diﬀusion term.
15 Yutaro Chiyo (Tokyo Univ. of Sci.)

A simpliﬁed quasilinear attraction-repulsion chemotaxis system: stabilization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with stabilization in a quasilinear parabolic-elliptic-elliptic attraction-repulsion
chemotaxis system. As to a quasilinear parabolic-parabolic Keller–Segel system, it was shown by Cieślak–
Winkler (Nonlinear Anal.; 2017; 159; 129–144) that solutions converge to the mean value of the initial data.
The purpose of this talk is to conﬁrm that their method is also eﬀective for a quasilinear parabolic-ellipticelliptic attraction-repulsion chemotaxis system.

Final: 2022/3/4
Real Analysis

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

48

Existence of strong solutions for the model representing motions ofcompressible elastic materials on the plane · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We talk about existence of strong solutions to the initial and boundary value problem for beam
equations with the viscosity term. For this model, we have already shown the existence and uniqueness of
weak solutions. On our problem we suppose that the stress function has a singularity such that the value
tends to inﬁnity as the strain goes to −1. By applying this singularity, we obtain an estimate for the strain
from below, and from the estimate and the time discretization method, we can prove existence of a strong
solution. The uniqueness is guaranteed by the uniqueness of the weak solution. We would like to consider
the large time behavior of solutions as future work.
17 Kota Kumazaki (Nagasaki Univ.)
Toyohiko Aiki (Japan Women’s Univ.)
Adrian Muntean (Karlstad Univ.)

A one-dimensional free boundary problem describing migration into
rubber with a non-monotone boundary condition · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a one-dimensional free boundary problem describing the migration ofdiﬀusants into rubber. In this problem, the free boundary represents the front of the diﬀusant region and its
growth rate is given by an ordinary diﬀerential equation including the eﬀect of breaking the growth of thediﬀusant region. Due to the breaking eﬀect, it is diﬃcult to prove the existence of a solution because theboundary condition imposed on the moving boundary becomes non-monotone. In this talk, we establish theexistence and uniqueness of a solution to the problem and give the maximum value of the free boundary.
18 Takeshi Fukao (Kyoto Univ. of Edu.)

A quasi ill-posed problem on the boundary · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a quasi ill-posed problem on the boundary on some two or three
dimensional bounded domain. In order to discuss the solvability of the quasi ill-posed problem on theboundary, we consider a transmission problem with the Cahn–Hilliard equations as an auxiliary condition in
the bulk. In a previous study, we characterize the second-order nonlinear diﬀusion equation as an asymptotic
limit from the fourth-order Cahn–Hilliard equations. Following this idea, we apply the vanishing viscosity
method to LW model, that is, the equation and dynamic boundary condition of Cahn–Hilliard type.
19 Noriaki Yamazaki (Kanagawa Univ.)
Nobuyuki Kenmochi (Chiba Univ.⋆)
Ken Shirakawa (Chiba Univ.)

Singular optimal control problems for doubly nonlinear evolution inclusions with quasi-variational structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider singular optimal control problems for abstract doubly quasi-variational
evolution inclusions governed by time-dependent subdiﬀerentials with the unknown-dependent constraints.
Then, we show the existence of optimal control for our problems. Also, we apply our abstract results toquasi-variational inequalities with time-dependent gradient constraints.
14:15–15:15
20 Shunsuke Kurima (Tokyo Univ. of Sci.)

A nonlocal Penrose–Fife type phase ﬁeld system with inertial term · · · 15

Summary: This talk deals with a nonlocal Penrose–Fife type phase ﬁeld system with inertial term. Colli–
Grasselli–Ito (2002) have proved existence of solutions to a parabolic-hyperbolic Penrose–Fife phase ﬁeld
system. However, nonlocal Penrose–Fife type phase ﬁeld systems with inertial term seem to be not studied
yet. The present work asserts that we can establish existence of solutions to a nonlocal Penrose–Fife typephase ﬁeld system with inertial term.
21 Hiroshi Watanabe (Oita Univ.)

Oleinik type estimates for entropy solutions to scalar parabolic-hyperbolic
conservation laws and their applications · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation
laws. The equation has both properties of hyperbolic equations and those of parabolic equations. Accordingly, it is diﬃcult to investigate the regularity and the behavior of solutions to (CP). In this talk, we prove
Oleinik type estimates for entropy solutions to (CP). Moreover, we also discuss their applications.

Final: 2022/3/4
49

Real Analysis(Tohoku Univ.)
22 Goro Akagi
Naoki Tanaka (Shizuoka Univ.)

Gradient ﬂow theory for time-dependent energies and applications tononlinear PDEs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall present an abstract theory for (generalized) gradient ﬂows and applications
to nonlinear PDEs.
15:30–16:30

Talk Invited by Real Analysis Section

Shuji Yoshikawa(Oita Univ.)

Mathematical analysis for the problems related to dynamic deformationof CRFP

Summary: CFRP (Carbon-Fiber-Reinforced Plastics) are well-known materials that are layered plastic plates
strengthened by ﬁbered carbons like plywoods. My interest is directed to consider the dynamical behavior
of CFRP. To give a mathematical analysis for CFRP, we ﬁrst decompose the problem into four components:
thermo-elastic, plastic, anisotropic, and composite materials. Each problem has interesting open problems
from the mathematical viewpoint. I will ﬁrst introduce some results related to these problems, especiallythrough the perspective of the energy method and structure-preserving discretization technique.

Final: 2022/3/4
Functional Analysis

50

Functional Analysis
March 28th (Mon)

Conference Room I

10:00–11:30
1 Shunji Sasaki(Kamiaoki Junior High School)

Homage of Riemann zeta function “Zeta one function” · · · · · · · · · · · · · · 15

Summary: In researching the “Riemann zeta function”, we created a new function “zeta-one function” which
is obtained by adding 1 to the denominator of the function and derives the relation equation between
this new function and the “Riemann zeta function” It was also found to be represented by the “digammafunction.” It would be greatly appreciated if it could help research future zeta functions.
2 Michio Seto
(Nat. Defense Acad. of Japan)
Shuhei Kuwahara(Sapporoseishu High School)

On construction of strictly positive deﬁnite kernels · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give new examples of strictly positive deﬁnite kernels with the theory of the Hardy
space over the unit disk.
3 Kazuki Kannaka(RIKEN) ♭ Multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A pseudo-Riemannian locally symmetric space is the quotient manifold Γ\G/H of a semisimple
symmetric space G/H by a discontinuous group Γ. Toshiyuki Kobayashi initiated the study of spectral
analysis of intrinsic diﬀerential operators (such as the Laplacian) of a pseudo-Riemannian locally symmetricspace. For instance, Kassel–Kobayashi studied the behavior of eigenvalues of intrinsic diﬀerential operatorsof Γ\G/H when deforming a discontinuous group Γ. As a special case, they found inﬁnitely many stableeigenvalues of the (hyperbolic) Laplacian of a compact anti-de Sitter 3-manifold Γ\SO(2, 2)/SO(2, 1) ([Adv.
Math. 2016]). In this talk, I would like to explain recent results about multiplicities of stable eigenvalues in
the anti-de Sitter setting.
4 Toshimitsu Takaesu (Gunma Univ.)

On the ﬁrst order expansion of a ground state energy of the ϕ4 modelwith cutoﬀs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the ϕ4 model with a spatial cutoﬀ and momentum cutoﬀ. The total Hamiltonian isa self-adjoint operator on a boson Fock space. Suppose regularity conditions of the momentum cutoﬀ. Then
we obtain the ﬁrst order expansion of a non-degenerate ground state energy of the total Hamiltonian.
5 Yoritaka Iwata (Kansai Univ.)

Generation of nolinear semigroup by the logarithm of operators · · · · · · 15

Summary: Logarithmic representation of inﬁnitesimal generators are directly associated with the higher
order evolution equations, as well as some nonlinear evolution equations. In particular nonlinear transforms
such as the Cole–Hopf transform and the Miura transform are the transform to the nonlinear diﬀerential
equations. Meanwhile the recurrence formula generalizing the Cole–Hopf transform and the Miura transform
clariﬁes the unknown relation between the 1st order and higher order evolution equations. In this talk,nonlinear abstract evolution equation in a Banach space is studied by the logarithmic representation ofoperators. In conclusion a representation for the nonlinear semigroup is obtained.

Final: 2022/3/4
51

Functional Analysis

14:15–15:15

Talk Invited by Functional Analysis Section

Megumi Sano (Hiroshima Univ.)

Harmonic transplantation and its application to functional inequalities

Summary: First, we will introduce harmonic transplantation proposed by Hersch in 1969. Also, we will
explain the diﬀerence between harmonic transplantation and Mobius transformation. We will point out thatvarious transformations can be understood as a special case or a general case of harmonic transplantation. As
an application, we will derive several improvements and several limiting forms of the Hardy and the Sobolev
inequalities via harmonic transplantation. In the half-space, we cannot apply harmonic transplantation tothese inequalities directly due to the lack of the explicit form of the p-Green function. Therefore, we willconsider a modiﬁcation of the original harmonic transplantation. By using that, we derive the improved
Hardy inequality in the half-space and the critical Hardy inequality as the limiting form.

March 29th (Tue)

Conference Room I

10:00–12:00
6 Nobukazu Shimeno(Kwansei Gakuin Univ.)
Yamato Taniguchi(Kwansei Gakuin Univ.)
Mugiho Nakamura(Kwansei Gakuin Univ.)

Zonal spherical function on a real symplectic group · · · · · · · · · · · · · · · · · 15

Summary: We give explicit expressions of the zonal spherical functions on some weakly symmetric spacesthat are close to a rank one symmetric space for a real symplectic group by using the Jacobi function andelementary functions.
7 Junko Inoue
Ali Baklouti(Tottori Univ.)(Univ. of Sfax)

The norm of the Lp -Fourier transform on compact extensions of locallycompact groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the norm of the Lp -Fourier transform on locally compact groups. Let G be a separable
unimodular locally compact group of type I, and let N be a unimodular closed normal subgroup of type I suchthat G/N is compact. For all exponents p such that 1 < p ≤ 2, we show the inequality ∥F p (G)∥ ≤ ∥F p (N )∥,where ∥F p (G)∥ and ∥F p (N )∥ are the norms of Lp -Fourier transforms on G and N respectively.
8 Vı́ctor Pérez Valdés (Univ. of Tokyo)

Construction of vector-valued diﬀerential symmetry breaking operators
for the group SO(4, 1) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we construct and give a complete classiﬁcation of all the symmetry breaking operators
D : C ∞ (S 3 , Vλ3 ) → C ∞ (S 2 , Lν,m ) that can be written as diﬀerential operators, between the spaces of smoothsections of a 3-rank vector bundle Vλ3 → S 3 over the 3-sphere, and a line bundle Lν,m → S 2 over the
2-sphere. In particular, we give the necessary and suﬃcient condition on the tuple of parameters (λ, ν, m)
for which these diﬀerential symmetry breaking operators exist.
9 Ryosuke Nakahama (Kyushu Univ.)

Computation of weighted Bergman norms on block diagonal matrices
in bounded symmetric domains for Sp(r, R) · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G/K ≃ D ⊂ p+ be a Hermitian symmetric space realized as a bounded symmetric domain, andwe consider the weighted Bergman space Hλ (D) on D. Then the norm on each K-type in Hλ (D) is explicitly
computed by Faraut–Korányi (1990). In this talk, we consider the case G = Sp(r, R), p+ = Sym(r, C), ﬁxr = r′ + r′′ , and decompose p+ into 2 × 2 block matrices. Then the speaker presents the results on explicit
computation of the norm of Hλ (D) on each K ′ -type in the space of polynomials on the block diagonal+
matrices p+
11 ⊕ p22 . Also, as an application, the speaker presents the results on Plancherel-type formulas on
the branching laws for the symmetric pair (Sp(r, R), U (r′ , r′′ )).

Final: 2022/3/4
Functional Analysis

10 Hideyuki Ishi (Osaka City Univ.)
Kazuhide Oshiro (HOSEI Inc.)

52

Continuous wavelet transforms for vector-valued functions · · · · · · · · · · · 15

Summary: We give a suﬃcient condition for the existence of admissible vectors for a unitary representation of
the semidirect product group of a linear Lie group with the vector group, where the unitary representation
is naturally deﬁned on the space of square-integrable vector-valued functions. Moreover, we give a concrete
admissible vector explicitly for the unitary representation of the 3-dimensional similitude group realized on
the space of square-integrable complex vector ﬁelds.
11 Atsumu Sasaki(Tokai Univ.)

A realization of the restriction of quasi-regular representations of the
Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk gives a realization of the restriction of quasi-regular representations of the Heisenberg
group to a certain closed subgroup in the continuous representation on the space of holomorphic functions
on the complex Heisenberg homogeneous space. Our realization is based on the heat kernels and the heat
kernel transforms on Rk and the Heisenberg group.
12 Koichi Arashi (Nagoya Univ.)

Coherent state representation and multiplicity-free representation of ageneralized Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We classify holomorphic multipliers of a generalized Heisenberg group over a (not necessarily
homogeneous) Siegel domain of the second kind, and show that the natural representations of the groupdeﬁned by the multipliers are multiplicity-free.
13:00–14:00

Talk Invited by Functional Analysis Section
Takeshi Ikeda (Waseda Univ.) ♭ K-theoretic Schubert calculus
Summary: During the last decade, there were signiﬁcant progress in K-theoretic (quantum) Schubert calculus.
First of all, I will try to give an overview on these works. The spaces we consider are the generalized ﬂag
varieties of semisimple linear algebraic group G. We are interested in the basis of the cohomology ring ofthese varieties associated to Schubert subvarieties. Main question is to determine the coeﬃcients when
we multiply two elements from the Schubert basis. Similar questions exist for a reasonable cohomology
theory. In this talk, we consider the ordinary cohomology and the algebraic K-theory, and their quantum(equivariant) versions. Even in type A, i.e. G is the special linear group, and for the ordinary cohomology,
we do not know an explicit formula for the Schubert structure constants of the full ﬂag variety. On theother hand, the structure constants for the Grassmannian variety is also (well) known as the Littlewood–
Richardson rule. I will explain the corresponding results for some typical Grassmannians in other classicaltypes.
In the second part, we will discuss a remarkable new aspects in Schubert calculus stemming from the study
on the aﬃne Grassmannian variety. The cohomology groups of the aﬃne Grassmannian has a natural ring
structure. D. Peterson discovered a connection between the quantum cohomology ring of ﬂag variety andthe homology ring of the aﬃne Grassmannian. The topics were further studied by many authors including
Lam, Shimozono, Lapointe, Morse, Schilling. I will report on recent progress on the topics mainly fromcombinatorial point of view.

March 30th (Wed)Conference Room I

10:00–11:30
13 Yuki Seo (Osaka Kyoiku Univ.)

Matrix trace inequalities related to the Tsallis relative entropies of real
order · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we show matrix trace inequalities related to Tsallis relative entropies. Hiai and Petzshow the Hiai–Petz inequality related to Umegaki relative entropy and Fujii–Kamei relative entropy and a
1-parameter extension of it. We extend it by virtue of the Tsallis relative entropies.

Final: 2022/3/4
53

Functional Analysis

14 Mitsuru Uchiyama(Shimane Univ.⋆ /Ritsumeikan Univ.)

Operator means and matrix quadratic equations · · · · · · · · · · · · · · · · · · · 15

Summary: Let A, B be Hermitian matrices satisfying A ≥ B ≥ 0. Then we determine X ≥ 0 and Y ≥ 0 suchthat the arithmetic mean and the geometric mean of X and Y are respectively A and B. Further, we referto a quadratic equation which these X and Y are solutions of.
15 Masaru Nagisa(Chiba Univ./Ritsumeikan Univ.)
Yasuo Watatani (Kyushu Univ.)

Non-linear positive maps on C*-algebras · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study non-linear positive maps on C*-algebras, which are not necessary completely positive.
We give several examples of such non-linear positive maps. We characterize the class of compositions of*-multiplicative maps and positive linear maps as the class of non-linear maps of boundedly positive typeabstractly.
16 Hiroyuki Osaka (Ritsumeikan Univ.)
Masaru Nagisa (Chiba Univ.⋆)
Raisei Tomita(Atsugi-Commercial Senior High School)

Stable rank for inclusions of Banach algebras · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present a formula for the stable rank of inclusions of unital Banach algebras in the sense ofﬁnite Watatani index. As an application we show that the stable rank of ℓ1 -algebras of Disk algebras byany action of ﬁnite groups is 2.
17 Takuya Hosokawa (Ibaraki Univ.)

Weighted composition operators from the Lipschitz space to the spaceof bounded functions on a tree · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the weighted composition operators between the Lipschitz space and the space ofbounded functions on the set of vertices of an inﬁnite tree.

We characterized the boundedness, thecompactness, and the boundedness from below, the isometricity of weighted composition operators.
14:15–15:15

Talk Invited by Functional Analysis Section

Shûichi Ohno

Weighted composition operators and their diﬀerences

Summary: (Weighted)composition operators have been extensively investigated on various analytic function
spaces, especially the Hardy and Bergman spaces, during recent decades. Then the main theme is tocharacterize the operator-theoretic behavior of weighted composition operators in terms of the functiontheoretic properties of their weight and analytic self-map. We here list problems on weighted composition
operators and their diﬀerences on the Hardy and Bergman spaces.

Final: 2022/3/4
Statistics and Probability

54

Statistics and Probability
March 28th (Mon)

Conference Room III

9:00–11:50
1 Takaaki Toyoshima (Tokyo Tech)

Fractional stochastic Navier–Stokes equation driven by space-time white
noise · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the stochastic Navier–Stokes equation driven by space-time white noise, where theLaplacian is replaced by a fractional one. In this equation, the nonlinearity has no meaning as a product ofthe distributions due to the poor regularity of the space-time white noise. To handle this type of singularstochastic partial diﬀerential equations, we use the renormalization method. In addition, the lower fractional
index reduces the order of regularity expected in the Schauder estimate, and as a result, the number of
elements to be renormalized increases. To deal with this situation, we use the theory of regularity structure
for the construction. In particular, we will solve the equation without changing the form although we need
the renormalization procedure.
2 Yu Ito(Kyoto Sangyo Univ.)

Backward representation of rough integral: an approach via fractional
calculus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Using fractional calculus, M. Zähle (1998) introduced an approach to the Stieltjes integrals. As
an extension of the (forward) integral by Zähle (1998), Y. Hu and D. Nualart (2009) and the speaker (2019)
introduced an approach to the rough integral of controlled paths along Hölder rough paths of orderβ ∈ (1/3, 1/2]. In this talk, we extend the backward integral by Zähle (1998) to the rough integral, anddescribe a backward representation of the rough integral. Our deﬁnitions of the rough integral are given
explicitly in terms of Lebesgue integrals for fractional derivatives, without using any arguments from discrete
approximation.
(Osaka Univ.)
3 Ryoji Takano
Masaaki Fukasawa (Osaka Univ.)

A partial rough path space for rough volatility · · · · · · · · · · · · · · · · · · · · · 15

Summary: A rough volatility model is a stochastic volatility model for an asset price process with volatility
being rough, meaning that the Holder regularity of the volatility path is less than half. Unfortunately, thismodel does not fall into the framework of the existing rough path theory because the integrand is not acontrolled path of the integrator. In this talk, we will discuss about a new variant of rough path theory
to analyze such a rough volatility model. Our ﬁrst step is to construct an integration of an uncontrolled
path and to prove its continuity. Second step is then to show the continuity of the solution of RDE which
is driven by such an integral.
(Osaka Univ.)
4 Takuto Ugai
Masaaki Fukasawa (Osaka Univ.)

Limit distributions for the discretization error of stochastic Volterra
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Our study aims to specify the asymptotic error distribution in the discretization of a stochastic
Volterra equation with a fractional kernel. It is well-known that for a standard stochastic diﬀerential√
equation, the discretization error, normalized with its rate of convergence 1/ n, converges in law to thesolution of a certain linear equation. Similarly to this, we ﬁrst consider the rate of convergence to normalize
the error. Then we show that the normalized discretization error of the Volterra equation converges in law
to the solution of a certain linear Volterra equation.

Final: 2022/3/4
55

Statistics and Probability

5 Yushi Hamaguchi (Osaka Univ.)

On general solutions of linear stochastic Volterra integral equations · · 15

Summary: We provide a general solution to a linear stochastic Volterra integral equation, which includes aclass of fractional stochastic diﬀerential equations. By means of the chaos expansion technique, we introduce
a notion of the product generalizing the stochastic convolutions and show that the class of stochastic Volterra
kernels becomes a Banach algebra. Then, we give a variation of constant formula for a general class of linear
stochastic Volterra integral equations.
6 Yuji Shinozaki(Bank of Japan / Tokyo Tech)
Syoiti Ninomiya (Tokyo Tech)

Application of high-order recombination to weak approximations of
stochastic diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this presentation, the error evaluation formula for the high-order recombination method given
by Litterer–Lyons is improved and some partitioning algorithms based on this improved estimation are
also presented. Speciﬁcally, it is proved that the error depends not only on the radiuses of the partitioned
patches but also the weights of them. The algorithms are applied to some known higher-order discretization
methods. Some numerical examples of practical ﬁnancial problems are also discussed.
7 Isamu Dôku(Saitama Univ.)

On a solution for random equations with Lévy noise · · · · · · · · · · · · · · · · 10

Summary: We consider the random equations driven by a Lévy noise. Actually we treat the Cauchy problem
for random equations with compensated Poisson random measure. The principal operator part is describedin an abstract manner in the sense of functional analysis.

Other coeﬃcient parts are given by somemeasurability and slight regularity assumptions. With an appropriate additional assumption we show thatthe random equation in question possesses a unique local mild solution.
8 Shigeyoshi Ogawa (Ritsumeikan Univ.)

Noncausal integrals and mean value theorems · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The mean value theorem for the integral is well known. But we are now concerned with thevalidity of a statement like the mean value theorem for the stochastic integral. The aim of the talk is toshow that we can establish mean value theorems as exact formula when limitted to the noncausal stochastic
Rb
integral(also called ogawa integral) of the form a f (Xt )d∗ Wt , where Wt is Brownain motion and Xt an ItôRbprocess, causal or not. We also discsuss the case of Itô integral a f (Xt )d0 Wt , moreover such a genuin
noncausal case where the process Xt is noncausal. Whole discussions are developed in the framework of
the noncausal stochastic calculus. hence for the related materials and basic facts we would refer to themonograph “Noncausal Stochastic Calculus” by Ogawa,S.,(2017, Springer).
9 Kensuke Ishitani (Tokyo Metro. Univ.)

On the construction of Brownian house-moving and its properties · · · · 15

Summary: The purpose of this presentation is to construct a new stochastic process “Brownian housemoving,” which is a Brownian bridge that stays between its starting point and its terminal point. To
construct this process, statements are prepared on the weak convergence of conditioned Brownian bridgeand conditioned three-dimensional Bessel bridge. Also studied are the sample path properties of Brownian
house-moving and the decomposition formula for its distribution.
10 Shun Yanashima (Tokyo Metro. Univ.)
Kensuke Ishitani (Tokyo Metro. Univ.)

On the construction of Bessel house-moving and its properties · · · · · · · 15

Summary: The purpose of this presentation is to introduce the construction of a new stochastic process “δdimensional Bessel house-moving” and its properties. δ-dimensional Bessel house-moving is a δ-dimensional
Bessel process hitting a ﬁxed point at t = 1 ﬁrstly. We have two methods of the construction of this process,which are to characterize it using the ﬁrst hitting time of a Bessel process, and to obtain it as the weaklimit of conditioned Bessel bridges. We also study sample path properties of this process, and give thedecomposition formula for its distribution.

Final: 2022/3/4
Statistics and Probability

56

14:15–15:05
11 Tetsuo Kurosawa (Tokyo Metro. Univ.)
Shunsuke Nishijima(Tokyo Metro. Univ.)
Kumiko Hattori (Tokyo Metro. Univ.)

Loop erased random walk on a random branched Koch curve · · · · · · · · 15

Summary: A loop erased random walk is a random walk obtained by removing the loop from a simple random
walk. It is a non-Markovian process that has been studied on Zd and on fractals. In this talk, we deal witha loop erased random walk under random environments. I will discuss the existence of a continuous limit
on a random branching Koch curve and the asymptotic properties of the sample function around time 0.
12 Koĥei Sasaya(Kyoto Univ.)

Some relation between spectral dimension and Ahlfors regular conformal
dimension of resistance metrics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The spectral dimension dS of a metric space is an exponent associated with the asymptotic
behavior of the heat kernel of the standard Dirichlet form and Brownian motion on the space. The Ahlfors
regular conformal dimension dimAR of the metric space is a quasisymmetric invariant, where quasisymmetry
is a well-studied property of homeomorphisms between metric spaces. For (generalized) Sierpiński carpets
or Sierpiński gaskets, Kigami showed that dimAR ≤ dS < 2 or dimAR ≥ dS ≥ 2 holds, in 2020. In thislecture, we give an appropriate extension of these results to the framework of resistance forms. We also
show that another simple extension, which is to be expected, does not hold in the framework in general.
13 Naotaka Kajino (Kyoto Univ.)

On singularity of energy measures for symmetric diﬀusions with fulloﬀ-diagonal heat kernel estimates II: Some borderline examples · · · · · · 15

Summary: We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular
Sierpiński gaskets and each of which is equipped with a canonical strongly local regular symmetric Dirichletform. We prove that any fractal K in this family satisﬁes the full oﬀ-diagonal heat kernel estimates withsome space-time scale function ΨK and the singularity of the associated energy measures with respect tothe canonical volume measure (uniform distribution) on K, and also that the decay rate of r−2 ΨK (r) to 0
as r ↓ 0 can be made arbitrarily slow by suitable choices of K. These results together support [Ann. Probab.
48 (2020), no. 6, 2920–2951, Conjecture 2.15] stating that the full oﬀ-diagonal heat kernel estimates withspace-time scale function Ψ satisfying limr↓0 r−2 Ψ(r) = 0 imply the singularity of the energy measures.

Final: 2022/3/4
57

Statistics and Probability

15:15–16:15

Award Lecture for the 2021 MSJ Analysis Prize

Makoto Katori(Chuo Univ.)

Multiple Schramm–Loewner evolution and Dyson’s Brownian motion
model

Summary: Schramm–Loewner evolution (SLE) is a stochastic extension of the classical Loewner theory incomplex analysis on a simply connected proper domain of C such that the driving function of the Loewner
chain of conformal maps is given by a one-dimensional stochastic process. Here we assume that the domain
is the upper-half complex-plane H and the driving process runs on R. It was proved that the SLE driven bya time changed Brownian motion on R, (Bκt )t≥0 , κ > 0, determines a one-parameter family of probability
laws of a random continuous curve in H connecting 0 and ∞, and that this family, denoted by SLEκ ,κ > 0, covers all probability laws of such curves having the conformal invariance and the domain Markov
property. In probability theory and statistical physics, the SLE κ has been playing a central role in studying
critical phenomena associated with continuous phase transitions and fractal geometries in two dimensions.
Therefore, it is natural to generalize the SLE theory to describe random multiple curves in H driven by aninteracting particle system on R. The problem is that the requirement of the conformal invariance and thedomain Markov property is not suﬃcient to determine a ‘canonical’ family of multiple SLEs. Motivated by
the recent work by Sheﬃeld on the quantum gravity zipper and a series of papers by Miller and Sheﬃeld
on the imaginary geometry, we employ the coupling of Gaussian free ﬁelds (GFFs) and multiple SLEs. We
show that a multiple SLE is correctly coupled with a certain GFF if and only if the driving particle system
is given by Dyson’s Brownian motion model studied in random matrix theory. Dyson’s Brownian motion
model is also a one-parameter (β > 0) family of one-dimensional log-gases. The coupling is achieved if
and only if β = 8/κ. The present study on the GFF/multiple SLE coupling enables us to clarify the basic
properties of the constructed multiple SLE (e.g., continuity of multiple SLE curves, ‘phase transitions’ atκ = 4 and 8). Moreover, we expect that a notion of conformal invariance of SLE will enrich the study ofrandom matrix theory via the present results on the trinity of the GFF, the multiple SLE, and Dyson’s
Brownian motion model. The present talk is based on a joint work with Shinji Koshida (Aalto University).
16:30–17:30

Talk Invited by Statistics and Probability Section

Takahiro Hasebe (Hokkaido Univ.)

Loewner chains, Markov processes and non-commutative stochastic
processes

Summary: Loewner chains had been a key tool for proving the Bieberbach conjecture, which was ﬁnallysettled by de Branges in 1985. The second main application of Loewner chains was discovered in theﬁeld of SLE around 2000, where a randomized Loewner chain is used to describe certain scaling limits ofprobabilistic models. It was realized more recently that Loewner chains also appear in connection witha certain class of non-commutative stochastic processes, which are further in correspondent with Markov
processes. In this talk I will summarize the work on the interplay between those objects (Loewner chains,
Markov processes and non-commutative stochastic processes). The talk is based on joint works with Uwe
Franz, Sebastian Schleissinger and Ikkei Hotta.

Final: 2022/3/4
Statistics and Probability

March 29th (Tue)58

Conference Room III

9:00–11:30
14 Katsunori Fujie (Hokkaido Univ.)
Takahiro Hasebe (Hokkaido Univ.)

The spectra of principal submatrices in unitarily invariant randommatrices · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we observe a concentration phenomenon on the empirical eigenvalue distribution(EED) of the principal submatrix in a random hermitian matrix whose distribution is invariant under unitaryconjugacy; for example, this class includes GUE (Gaussian Unitary Ensemble) and Wishart matrices. Moreprecisely, if the EED of the whole matrix converges to some deterministic probability measure m, then thediﬀerence of rescaled EEDs of the whole matrix and of its principal submatrix concentrates at the Rayleighmeasure (in general, a Schwartz distribution) associated with m by the Markov–Krein correspondence. For
the proof, we use the moment method with Weingarten calculus and free probability. This talk is based on
joint works with Takahiro Hasebe in Hokkaido university.
15 Makoto Maejima (Keio Univ.⋆)
Noriyoshi Sakuma (Nagoya City Univ.)

On free selfsimilar additive processes and free selfdecomposable distributions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we shall introduce new deﬁnition of selfsimilarity in free probability theory andconstruct free analogue of the theorem by Sato, which connects H-selfsimilar free additive processes andselfdecomposable distributions. In addition, we give stochastic integration with respect to free additive
processes and give a stochastic integral representation to construct back driving Lévy process for free
selfdecomposable distributions.
16 Kei Noba (Inst. of Stat. Math.)
Noriyoshi Sakuma (Nagoya City Univ.)
Yuki Ueda (Hokkaido Univ. of Edu.)

On Boolean selfdecomposability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we will introduce Boolean selfdecomposable distributions. In the case of classicaland free case, there are distributional similarities. In Boolean case, they are broken. We will show it with
explicit examples.
(Keio Univ.)
17 Ryoichi Suzuki
Noriyoshi Sakuma (Nagoya City Univ.)

A modiﬁed Φ-Sobolev inequality for canonical Lévy processes and its
applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we derive a new modiﬁed Φ-Sobolev inequality for canonical L2 -Lévy processes. Thisis a generalization of Φ-Sobolev inequality for the Poisson space and it for the Wiener space. Moreover,as an application of main theorem, we also get a concentration inequality for canonical Lévy processes andderive several examples.
18 Kei Noba (Inst. of Stat. Math.)

On the optimality of the refraction–reﬂection strategies for Lévy processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we think about de Finetti’s optimal dividend problem with capital injection under
the assumption that the dividend strategies are absolutely continuous. In many previous studies, the process
before being controlled was assumed to be a spectrally one-sided Lévy process, however in this paper weuse a Lévy process that may have both positive and negative jumps. In the main theorem, we show that a
refraction–reﬂection strategy is an optimal strategy.
19 Toshihiro Uemura (Kansai Univ.)
Masayoshi Takeda (Kansai Univ.)

On symmetric stable-type processes with singular Lévy densities · · · · · 15

Summary: We are concerned with symmetric stable-type processes with singular Lévy densities. We ﬁrst
introduce a class of test functions of the inﬁnitesimal generators of the symmetric Dirichlet forms associatedwith the processes as a “core” and then show some estimates of the processes in the talk.

Final: 2022/3/4
59

Statistics and Probability

20 Nobuaki Naganuma (Kumamoto Univ.)

On generalization of the fourth moment theorem · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider generalization of the fourth moment theorem shown by Nualart andPeccati (2005) and provide new criterion on central convergence of Wiener functionals belonging to a ﬁxed
Wiener chaos. We show the assertion by borrowing idea developed by Azmoodeh et al. (2016).
21 Masafumi Hayashi (Univ. of Ryukyus)
So Oshiro (Univ. of Ryukyus)
Masato Takei (Yokohama Nat. Univ.)

Rate of moment convergence in the central limit theorem for elephantrandom walks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The one-dimensional elephant random walk is a typical model of discrete-time random walk withstep-reinforcement, and is introduced by Schütz and Trimper (2004). The walk admits a phase transition
from the diﬀusive behavior to the superdiﬀusive behavior. We study the rate of the moment convergence inthe central limit theorem for the position of the walker in the diﬀusive regime.
22 Hiroki Takahashi (Keio Univ.)
Shintaro Suzuki (Keio Univ.)

Almost-sure weighted equidistibution of cycles for the random Gauss
map · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider an i.i.d. random dynamical system generated by the Gauss map and an alternating
Gauss map with a neutral ﬁxed point. We show that cycles of this random system weighted with theirrandom Lyapunov exponents equidistribute with respect to the unique stationary measure that is absolutely
continuous with respect to the Lebesgue measure. Our main tool is a level-2 large deviations for topological
Markov shifts over countably inﬁnite alphabet.
23 Johannes Jaerisch (Nagoya Univ.)
Hiroki Takahasi (Keio Univ.)

Multifractal analysis of homological growth rates for hyperbolic surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We perform a multifractal analysis of homological growth rates of oriented geodesics on a
hyperbolic surface.

Our main result provides a formula for the Hausdorﬀ dimension of level sets ofprescribed growth rate in terms of a generalized Poincare exponent of the Fuchsian group. Using methodsof ergodic theory and thermodynamic formalism we prove the analyticity of the dimension spectrum.
11:30–12:00

Research Section Assembly

March 30th (Wed)Conference Room III

9:50–11:40
24 Teruo Tanaka (Hiroshima City Univ.)

Markov decision processes with fractional rewards · · · · · · · · · · · · · · · · · · 10

Summary: We consider a Markov decision process with Borel state and action spaces under a discounted
fractional criterion. At ﬁrst, the fractional discounted Markov decision process is transformed to a discounted
Markov decision process by using the parametric method.

Next, assuming suitable conditions on thecomponents of the corresponding Markov decision process, a standard approach is used. Applying theseprocedures and the dynamic programming approach, we obtain the optimal value function and policy forour problem.
25 Toshiharu Fujita(Kyushu Inst. of Tech.)

Decision process model with feedforward loop system · · · · · · · · · · · · · · · 15

Summary: In this study, we consider a deterministic decision process model with a feedforward loop system
which is one of the nonserial transition systems.
programming technique.

We introduce recursive equations by using dynamic

Final: 2022/3/4
Statistics and Probability

26 Shoko Chisaki (Osaka Inst. of Tech.)Shinji Kuriki (Osaka Pref. Univ.⋆)
Ryoh Fuji-Hara (Univ. of Tsukuba⋆)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

60

Optimality of spanning bipartite block designs · · · · · · · · · · · · · · · · · · · · · 10

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 discuss the optimality of how small
the variance of the estimator was. And we prove that the variances of all estimators are equal (variancebalanced). We also show the goodness of SBBD by the simulation.
27 Satoru Kadowaki(Matsue Coll. of Tech.)
Sanpei Kageyama (Hiroshima Univ.⋆)

Two existence results between an aﬃne resolvable SRGD design and adiﬀerence scheme · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The existence of aﬃne resolvable block designs has been discussed since 1942 in the literature(cf. Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2010, 2012) obtained
a number of results on combinatorics for the existence of an aﬃne resolvable SRGD design. In this paper,a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama(2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and alsoa generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2010).
28 Masatake Hirao (Aichi Pref. Univ.)

On p-frame potential of the Beltrán and Etayo point processes on thesphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We address the expectation of the p-frame potential of two types of point processes on the sphere
introduced by Beltrán and Etayo (2018, 2019). In particular, we show that the expectation of the p-frame
potential of the process on the odd dimensional sphere has low potential among those of other well-studied
random conﬁgurations on the sphere. As a by-product, we show that the random conﬁgurations of points
coming from the process converge more rapidly towards ﬁnite unit norm tight frames than those comingfrom i.i.d. random points according to uniform measure on the sphere.
29 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.
30 Kengo Fujisawa (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)

Asymmetry plus association model for square contingency tables withordinal categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For the analysis of contingency tables, we are interested in considering a statistical model insteadof independence when the independence between row and column variable does not hold. Many association
models which indicate the structure of odds ratios have been proposed. Also, symmetry and asymmetry
models which indicate the symmetric or asymmetric structure for cell probabilities have been proposed forthe analysis of square contingency tables. We propose an asymmetry plus association model for squarecontingency tables with ordinal categories and provide its characteristics.

Final: 2022/3/4
61

Statistics and Probability

12:15–12:45

Presentation Ceremony for the 2021 MSJ Analysis Prize

14:25–15:25

Talk Invited by Statistics and Probability Section

Masayo Hirose (Kyushu Univ.)

Small area inference under area level model and its application

Summary: An empirical best linear unbiased predictor (EBLUP) can contribute in terms of the eﬃciency
especially when the sample size within each area is not large enough to make reliable direct estimates.
Moreover, it is of importance to assess its mean squared prediction error in small area inference. In thisconference, I will brieﬂy introduce to small area inference under area level model and then explain some ofour recent results for EBLUP having further desired properties. Some data analysis results will be shown inconclusion.
15:45–16:45

Talk Invited by Statistics and Probability Section

Takeshi Emura (Kurume Univ.)

Estimating the diﬀerence of survival distributions; a copula-based approach to dependent censoring

Summary: Traditional estimators for survival distributions can handle censored data under the independent
censoring assumption. When the assumption of independent censoring fails to hold, the traditional Kaplan–
Meier estimator is biased. Accordingly, any two-sample comparison based on two Kaplan–Meier estimators
leads to biased results, in particular, the Mann–Whitney eﬀect estimator derived from two Kaplan–Meierestimators. We derive the asymptotic bias of this naive estimator of the Mann–Whitney eﬀect under
dependent censoring. We also propose a copula-based estimator of the Mann–Whitney eﬀect, which canadjust for the bias due to dependent censoring. We derive the consistency and asymptotic normality of the
proposed estimator under a misspeciﬁed copula. Simulations are conducted to check the performance of the
proposed method. We apply our proposed method to a real dataset.

March 31st (Thu)

Conference Room III

9:50–11:40
31 Kou Fujimori (Shinshu Univ.)(Waseda Univ.)
Yuichi Goto(
Waseda Univ.)
Yan Liu
Masanobu Taniguchi (Waseda Univ.)Sparse principal component analysis for high-dimensional stationary
time series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss the sparse principal component analysis for high-dimensional stationary
processes. The standard principal component analysis performs poorly when the dimension of the process
is large. We establish the oracle inequalities for penalized principal component estimators for the processes
including heavy-tailed time series. The rate of convergence of the estimators is established. We also elucidate
the theoretical rate for choosing the tuning parameter in penalized estimators. The performance of thesparse principal component analysis is demonstrated by numerical simulations.
(Waseda Univ.)
32 Yujie Xue
Masanobu Taniguchi (Waseda Univ.)

Hellinger distance estimation for non-regular spectra · · · · · · · · · · · · · · · 15

Summary: For a Gaussian stationary process, in this talk, we will derive a time series Hellinger distancepp
R
for spectra f and g: T (f, g) = log{ 12 f (λ)/g(λ) + 12 g(λ)/f (λ)}dλ. By evaluating T (fθ , fθ+h ) of
the form O(hα ), we elucidate the 1/α-consistent asymptotics of the maximum likelihood estimator ofθ for non-regular spectra. For regular spectra, we introduce the minimum Hellinger distance estimatorθT (ĝn ) = arg minθ T (fθ , ĝn ), where ĝn is a nonparametric spectral density estimator, and as a benchmark,we introduce the Whittle divergence estimator θW (ĝn ). It can be shown that both θT (ĝn ) and θW (ĝn ) are
asymptotically eﬃcient, and that the former is more robust than the latter. Small numerical studies will be
provided.

Final: 2022/3/4
Statistics and Probability

62(Waseda Univ.) ♭ Comparison between the exact likelihood and Whittle likelihood for
33 Xiaofei Xu(Waseda Univ.) moving average processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Zhengze Li
Masanobu Taniguchi (Waseda Univ.)
Summary: In this talk, we investigate the diﬀerence between the exact likelihood and Whittle likelihood withﬁnite sample size for moving average processes of order one. We elucidate the theoretical expressions of
two likelihood functions and their expectations and evaluate the performance between exact likelihood andWhittle likelihood numerically. We ﬁnd that the exact likelihood and Whittle likelihood perform similarly
when the true value of parameter is close to zero, while the diﬀerence becomes large and Whittle estimator
performs poorly when parameter is close to one. This is an important warning when we use the Whittle
likelihood and estimator if the moving average process has near unit root.
34 Yan Liu(Waseda Univ.)

On the model selection of symmetric α-stable processes · · · · · · · · · · · · · 15

Summary: In this talk, we consider the model selection problem of symmetric α-stable processes. The
symmetric α-stable processes are known as a model with inﬁnite variance. This is a distinct feature fromthe model with ﬁnite variance considered in the usual time series analysis. We consider the GAIC, an
extended information criterion of AIC, to choose the correct model. It is shown that the selected order ofthe model is consistent with the true order of the model. This is a remarkable diﬀerence from the original
property of AIC for a regular model with ﬁnite variance. The proof and numerical results will be shown in
the presentation.
(Waseda Univ.)
35 Yuichi Goto
Kotone Suzuki (Waseda Univ.)(Waseda Univ.)
Xiaofei Xu
Masanobu Taniguchi (Waseda Univ.)

Tests for the existence of group eﬀects and interactions for two-way
models with dependent error · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we propose tests for the existence of group eﬀects and interactions for two-way models
with dependent errors. Our framework allows us to deal with correlated groups, although many existing
papers assume the independence of groups. Our test statistics are in the form of the natural extension of
the classical F-statistic. We show the asymptotic null distribution of the proposed test statistic and theconsistency of the test. Moreover, the nontrivial power of our test under the alternative is derived. A
simulation study illustrates the ﬁnite-sample performance of the test. In the empirical study, we apply our
test to the daily log-returns of 24 stock prices from six countries and four sectors.
36 Jin Hatomoto(Tokyo Nat. Coll. of Tech.)

Poisson limit distributions for diﬀeomorphisms with weak hyperbolic
product structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider a diﬀeomorphism which admits a weak hyperbolic product structure region, whichis the intersection of two transversal families of weak stable and weak unstable disks, with countably manybranches and integrable return times. We introduce that for such maps the distribution of the number ofvisits to balls converges to the Poisson distribution as the radius decays to 0.
37 Takao Namiki (Hokkaido Univ.)
Satoru Tadokoro (Hokkaido Univ.)
Shunsuke Kajikawa (Kyoto Univ.)
Masao Matsuhashi (Kyoto Univ.)(Kyoto Univ.)
Akio Ikeda
Ichiro Tsuda(Chubu Univ. / Chubu Univ.)

Evaluation of permutation entropy by time-series transition graph analysis and its application to epilepsy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We proposed a method called time series transition graph for nonlinear time series analysis, which
improves the evaluation of permutation entropy. We also applied this method to ECoG recorded brain wave
data of epilepsy patients to characterize seizures in the epileptic focus.

Final: 2022/3/4
63

Statistics and Probability

14:20–16:25
38 Eri Kurita (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

A sample measure of Mardia’s multivariate kurtosis with three-stepmonotone missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a sample measure of Mardia’s multivariate kurtosis with three-stepmonotone missing data. In the case of complete data, Mardia (1970) has deﬁned the sample measure ofmultivariate kurtosis and given its exact mean and exact variance under multivariate normal population.
In this talk, we deﬁne a new sample measure of multivariate kurtosis for three-step monotone missing
data. Furthermore, we derive its expectation and variance using perturbation method. From this result,
we obtain a multivariate normality test statistic in the case of three-step monotone missing data. Finally,some simulation results for three-step monotone missing data are presented to investigate the accuracy ofthe normal approximation of the test statistic proposed in this talk.
39 Nobuhiro Taneichi(Hokkaido Univ. of Edu.)
Yuri Sekiya (Hokkaido Univ. of Edu.)
Jun Toyama(Inst. for Pract. Appl. of Math.)

On an approximation of the distribution of test statistics for conditional
independence of 3-way contingency tables. · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Tests of the hypothesis of conditional independence in J x K x L contingency tables are considered.
Class of statistics based on fai-divergence for testing the hypothesis are also considered. All members of thestatistics have the same chi-square limiting distribution under the hypothesis. We show derivation of an
expression of approximation for the distributions of the class of statistics based on an asymptotic expansion.
Using the expression, transformed statistics are obtained which converge to a chi-square limiting distribution
faster than the original ones.
40 Takuma Bando (Univ. of Tokyo)
Tomonari Sei (Univ. of Tokyo)
Kazuyoshi Yata (Univ. of Tsukuba)

Consistency of the objective general index in high-dimensional settings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The objective general index is a scale-invariant weighting method for ranking of multivariate data.
We show that the sample objective general index is a consistent estimator of the population counterpart in
high-dimensional settings together with a set of conditions, where the ratio of the dimension to the sample
size is assumed to tend to zero. The proof is based on a recent result on random matrix theory. Numericalexperiments are conducted to support the theoretical result. An example of real data analysis suggests anapplication of the weight to variable selection.
41 Yoshihiko Maesono (Chuo Univ.)
Spiridon Penev(Univ. of New South Wales)

Improved conﬁdence intervals for expectiles in risk management · · · · · 15

Summary: In this presentation, we will study asymptotic properties of the expectile estimator. We obtain
asymptotic representations of the estimator and Edgeworth expansion of the estimator.
42 Hiroki Masuda (Kyushu Univ.)
Shoichi Eguchi (Osaka Inst. of Tech.)

On model selection of Lévy driven SDE models · · · · · · · · · · · · · · · · · · · · 15

Summary: We develop information criteria for the parametric coeﬃcients of a semiparametric ergodicLévy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage
Gaussian quasi-likelihood function of the Euler-approximation type. For model selections of the scale anddrift coeﬃcients, we propose explicit Gaussian quasi-information criteria through the stepwise inference
procedure.

Final: 2022/3/4
Statistics and Probability

43 Yuta Koike(Univ. of Tokyo)

64

Asymptotic mixed normality of realized covariance in high-dimensions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The asymptotic mixed normality of the realized covariance matrix of a multi-dimensional continuous semimartingale observed at a high-frequency is established, where the dimension may be muchlarger than the sample size. More precisely, a mixed-normal approximation of the error distribution interms of the Kolmogorov distance is shown in such a setting. The proof is based on a variant of theChernozhukov–Chetverikov–Kato theory on high-dimensional central limit theorems for sums of independent random vectors, where the theory is accommodated to random asymptotic covariance matrices withthe help of Malliavin calculus.
44 Yugo Nakayama (Kyoto Univ.)
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Outlier detection based on high-dimensional principal component scores· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider outlier detection based on the principal component analysis (PCA)
for high-dimensional low-sample-size data. The classical method of outlier detection uses the Mahalanobis
distance. However, if the dimension is large, inverting the sample covariance matrix used in the Mahalanobis
distance may result in substantial numerical instability, so that the alternative is needed. On the other
hand, one example of the methods for the univariate data is the Smirnov–Grubbs test. We propose a test
procedure by applying the ﬁrst PC scores to the Smirnov–Grubbs test. By using asymptotic properties of
the PCA, we evaluate its size and power. Finally, we check the performance of the test procedure boththeoretically and numerically.

Final: 2022/3/4
65

Applied Mathematics

Applied Mathematics
March 28th (Mon)

Conference Room V

10:00–12:00
1 Xiao-Nan Lu (Univ. of Yamanashi)
Shota Kawaguchi(Nippon-Engineer Co. Ltd.)
Miwako Mishima (Gifu Univ.)

Almost external diﬀerence families via cyclotomy · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will introduce a new type of combinatorial designs, called almost external diﬀerence
families (AEDFs). The notion of AEDFs is a generalization of external diﬀerence families, and AEDFs also
have natural relationship with well-studied combinatorial designs such as almost diﬀerence sets, disjoint
diﬀerence families, and diﬀerence systems of sets. AEDFs can be used as a combinatorial characterization
for special types of optimal weak algebraic manipulation detection codes, which are employed as coding
schemes for linear secret sharing. Furthermore, a construction of AEDFs via cyclotomy in ﬁnite ﬁelds will
be proposed.
2 Norifumi Ojiro (Toyota Tech. Inst.)
Hajime Matsui (Toyota Tech. Inst.)

Reversible error-correcting codes over rational integer residue rings · · · 15

Summary: Codes over the ring of rational integers modulo ideal are called integer codes. We formulate atheorem on reversibility of the prime factorization for generator matrices of integer codes. To show that thistheorem brings an eﬀective construction of reversible integer codes of large modulus, we exhibit searching
results for reversible and self-dual integer codes of various modulus at code lengths 3 and 4.
3 Tomohiro Kamiyoshi(Matsue Coll. of Tech.)
Makoto Nagura(Osaka Electro-Comm. Univ.)
Shinichi Otani (Kanto Gakuin Univ.)

On exponential extended Riordan array and uniﬁed Stirling numbers· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We propose the notion of extended Riordan array, permitted negative indices, of exponential typeby using the Roman factorial. In this context, we will establish a fundamental theory of the uniﬁed Stirlingnumbers that were introduced by Hsu and Shiue. As a consequence, we give a luminous explanation for thereciprocity law among those numbers that was discovered by Choi, et al. and Maltenfort. Moreover, ourmethods reveal that some interesting numbers appear in a certain part of the exponential extended array,
although the numbers in the area had been regarded as zero until now.
4 Kazuhide Hirohata(Ibaraki Nat. Coll. of Tech.)
Bradley Elliott (Univ. of Kentucky)
Ronald J. Gould (Emory Univ.)

Degree sum conditions for the existence of vertex-disjoint chorded cycles
in a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let k be a positive integer. In 2008, Finkel proved that if G is a graph of order at least 4k andthe minimum degree of G is at least 3k, then G contains k vertex-disjoint chorded cycles. Chiba et al. and
Gould et al. improved Finkel’s result. In this talk, we consider a generalization of these results.

Final: 2022/3/4
Applied Mathematics

5 Kiyoshi Ando (Nat. Inst. of Informatics)

66

Properly 3-contractible edges in a minimally 3-connected graph · · · · · · 15

Summary: A 3-contractible edge is said to be “properly 3-contractible” if it is contained in no triangle. Let
E ∗ (G) denote the set of edges of G which are contained in no triangle and let Ec∗ (G) denote the set ofproperly 3-contractible edges of G. Let U (i) (G) denote the set of degree 3 vertices x of G such that the
subgraph of G induced by the neighborhood of x has i edges.
We prove that, “For a minimally 3-connected graph G, the following (1), (2) and (3) are equivalent. (1) G
is a wheel, (2) E ∗ (G) = ∅ and (3) U (0) (G) = U (1) (G) = ∅.” and (I) |Ec∗ (G)| ≥ 21 |U (1) (G)| + |U (0) (G)| and(II) |Ec∗ (G)| > 21 |E ∗ (G)|.” We also show the sharpness of the inequalities.
6 Shinya Fujita (Yokohama City Univ.)

Extremal problems on rainbow connectivity in edge-colored graphs · · · 10

Summary: Some recent results on rainbow connectivity in edge-colored graphs will be reviewed.
7 Naoki Matsumoto (Keio Univ.)

Chromatic number of triangle-free and broom-free graphs in terms of
their order · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Gyárfás–Sumner conjecture asks whether for every tree T , the class of (induced) T -free graphsis χ-bounded. The conjecture is solved for several special trees, but it is still open in general. Motivated by
the conjecture, the chromatic number of triangle-free and broom-free graphs is well studied, since a broomis one of the generalizations of a star, where a broom B(m, n) is the graph obtained from a star K1,n andan m-vertex path Pm by identifying the center of K1,n and a leaf of Pm . Gyárfás, Szemeredi and Tuza
proved that for every triangle-free and B(m, n)-free graph G, χ(G) ≤ m + n − 1. This upper bound has
been improved by Wang and Wu to m + n − 2 for m ≥ 2, n ≥ 1. In this talk, we introduce the result thatany triangle-free and B(4, 2)-free graph G is 3-colorable if the number of vertices of G is at least 17. The
sharpness of the bound of the order is attained by the Clebsch graph.
14:15–16:00
8 Kazuki Matsubara (Saitama Univ.)(Meiji Univ.)
Chie Nara

Continuous ﬂattening of multi-layered pyramids with rigid radial edges· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: There are many ways to continuously ﬂatten polyhedra. In this talk, under the assumptionthat every radial edge is rigid, we prove that a continuous ﬂattening motion exists for any multi-layered
pyramid having a common convex base, with each apex having a common perpendicular foot. Furthermore,
we illustrate an example of a multi-layered pyramid with a non-convex base that cannot be continuously
ﬂattened while maintaining the rigidity of the radial edges.
9 Masashi Shinohara (Shiga Univ.)
Sho Suda (Nat. Defense Acad. of Japan)
Hiroshi Nozaki (Aichi Univ. of Edu.)

Uniqueness of optimal two-distance sets in R8 · · · · · · · · · · · · · · · · · · · · · 15

Summary: A ﬁnite subsets X in the d-dimensional Euclidean space Rd is called a two-distance set if there are
only two diﬀerent values of distances between two distinct points in X. A two-distance set X in Rd is said
to be optimal if |X ′ | ≤ |X| for any two-distance set X ′ in Rd . It is known that |X| ≤ (d + 1)(d + 2)/2 for
two-distance set X in Rd . Lisoněk construct a two-distance set L in R8 with 45 points. By the inequality,
L is optimal two-distance set in R8 . In this talk, we prove a uniqueness of optimal two-distance sets in R8
up to isomorphism.

Final: 2022/3/4
67

Applied Mathematics

10 Sho Kubota (Yokohama Nat. Univ.)
Etsuo Segawa (Yokohama Nat. Univ.)

Perfect state transfer in Grover walks between states associated tovertices of a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study perfect state transfer in Grover walks, which are typical discrete-time quantum walkmodels. In particular, we focus on states associated to vertices of a graph. We call such states vertex typestates. Perfect state transfer between vertex type states can be studied via Chebyshev polynomials. We
derive a necessary condition on eigenvalues of a graph for perfect state transfer between vertex type states
to occur. In addition, we perfectly determine the complete multipartite graphs whose partite sets are thesame size on which perfect state transfer occurs between vertex type states, together with the time.
11 Hiromichi Ohno (Shinshu Univ.)
Akihiro Narimatsu(Yokohama Nat. Univ.)
Md Sams Aﬁf Nirjhor (Tokyo Tech)
Kazuyuki Wada(Nat. Inst. of Tech., Hachinohe Coll.)

Unitary equivalence classes of quantum walks on cycles and split-step
quantum walks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We investigate unitary equivalence classes of quantum walks on cycles and split-step quantum
walks (SSQWs). Unitary equivalence classes of quantum walks on a cycle with N vertices are parameterized
by 2N real parameters. Moreover, the ranges of two of the parameters are restricted depending on the parity
of N. SSQWs are introduced by Kitagawa and generalized by Suzuki. We deﬁne a new class of quantum
walks which includes the above SSQWs, and clarify their unitary equivalence classes.
12 Chusei Kiumi (Yokohama Nat. Univ.)

Eigenvalues of multi-state quantum walks · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Localization is a characteristic property of multi-state quantum walks. It is well known that theexistence of eigenvalues of time evolution operator is a necessary and suﬃcient condition of the occurrence of
localization. The localization of space-homogeneous (i.e., the time evolution is consistent for every position.)
multi-state quantum walks is studied by various previous research. However, the mathematical analysisof the space-inhomogeneous case is not studied yet. Therefore, in this paper, we focus on the eigenvalue
problem on two-phase three and four-state quantum walks with one defect, which is very important forvarious applications. We use the transfer matrix to construct a generalized eigenfunction, then we derive thenecessary and suﬃcient condition for the existence of eigenvalue and its concrete solution for some examples.
13 Ken’ichi Yoshida (Saitama Univ.)
Hiroki Kodama (Tohoku Univ.)

A mathematical model of network elastoplasticity · · · · · · · · · · · · · · · · · · 15

Summary: A thermoplastic elastomer (TPE) is a polymeric material with rubber elasticity and is removable
at high temperatures. In this talk, we present results of modeling the elastoplastic deformation of a TPE byusing a network represented as a periodic graph. A TPE consists of a soft domain, which exhibits rubber
elasticity, and hard domains, which act as cross-links. This structure can be represented as a graph. We
introduce the tension tensor for a periodically realized graph, which induces the stress and the elasticity.
The hard domains of a TPE are less robust than the cross-links of vulcanized rubber. We express this as
local moves of a graph, which induce the plasticity in elongation.

Final: 2022/3/4
Applied Mathematics

16:15–17:15

68

Talk Invited by Applied Mathematics Section

Tetsuji Taniguchi(Hiroshima Inst. of Tech.)

A smallest eigenvalues of graphs and a generalization of line graphs

Summary: There is a previous study that uses the root system to classify graphs with smallest eigenvalue≥ −2.
It follows that such graphs are classiﬁed by the A, D, E-root systems. The A, D-integral lattice is a sublatticeof the standard lattice, but the E-integral lattice is not a sublattice of the standard lattice. However, Eintegral lattice is 2-integrable. The integrability of integral lattices constructed from graphs with smallest
eigenvalue≥ λ is a subject of interest.
It is also well known that the smallest eigenvalue of a line graph is greater than or equal to −2. Thisnaturally raises the question of knowing the hierarchical structure of graphs with smallest eigenvalues, but
the (well-known) method of constructing line graphs cannot construct graphs with smallest eigenvalues< −2.
Therefore, R. Woo and A. Neumaier formulated a method for constructing graphs with smallest eigenvalue<−2 by highly generalizing the method of constructing line graphs, which is a simple task of replacing ”edges”√
by ” vertices”. They studied graphs with smallest eigenvalue≥ −1 − 2 (1995). They introduce a graphcalled a Hoﬀman graph, and give a generalization of line graphs by the sum of Hoﬀman graphs. Then comesa relation between graphs and root systems, along with an irreducibility of Hoﬀman graphs.

March 29th (Tue)

Conference Room V

10:00–11:45
14 Norio Konno (Yokohama Nat. Univ.)
Yuki Oshima (Yokohama Nat. Univ.)

IPS/Zeta Correspondence for the Domany–Kinzel model · · · · · · · · · · · · 10

Summary: Our previous works presented zeta functions by the Konno–Sato theorem or the Fourier analysis
for one-particle models including random walks, correlated random walks, quantum walks, and open quantum
random walks. Moreover, we gave zeta functions for multi-particle models with probabilistic or quantum
interactions, called the interacting particle system (IPS). In this talk, we consider the zeta function for the
Domany–Kinzel model, as a special case of the IPS.
15 Norio Konno (Yokohama Nat. Univ.)
Shunya Tamura (Yokohama Nat. Univ.)

Walk/Zeta Correspondence for quantum and correlated random walks· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We compute the zeta function for the three- and four-state quantum walk, correlated random
walk, and multi-state random walk on the one-dimensional torus using the Fourier analysis. We deal withalso the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we
introduce a new class of models determined by the generalized Grover matrix bridging the gap between theGrover matrix and the positive support of the Grover matrix. Finally, we give a generalized version of theKonno–Sato theorem for the new class. We calculate the zeta function for the generalized Grover matrix onthe d-dimensional torus as a result.
16 Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Takashi Komatsu(Math. Res. Inst. Calc for Industry/Hiroshima Univ.)

Vertex-face/Zeta correspondence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present the characteristic polynomial for the transition matrix of a vertex-face walk on agraph, and obtain its spectra. Furthermore, we express the characteristic polynomial for the transition
matrix of a vertex-face walk on the 2-dimensional torus by using its adjacency matrix, and obtain its
spectra. As an application, we deﬁne a new walk-type zeta function with respect to the transition matrix
of a vertex-face walk on the 2-dimensional torus, and present its explicit formula.

Final: 2022/3/4
69

Applied Mathematics

17 Ayaka Ishikawa (Yokohama Nat. Univ.)

A family of quantum walks on a ﬁnite graph corresponding to thegeneralized weighted zeta function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We obtain a condition that associates the generalized weighted zeta function with a quantum
walks on a ﬁnite graph. The spectrum of the transition matrix of the quantum walk is given by thezeta function. This result gives a family of quantum walks that follow from the generalized weighted zetafunction.
18 Hideaki Morita (Muroran Inst. of Tech.)

On an alternating graph zeta function · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a zeta function deﬁned for alternating paths on a ﬁnite digraph, and provide thethree expressions; the exponential expression, the Euler expression, and the Hashimoto expression, in theframework of the combinatorial zeta function.
19 Osamu Kada

(Hosei Univ.)

Characteristic polynomials and zeta functions of equitably partitioned
graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is well known that for an equitable partition of the vertex set of a directed graph (digraph)
X, the characteristic polynomial of a quotient graph divides that of X, but the remainder part is notwell investigated. In this paper, we deﬁne a deletion graph which is a signed directed graph deﬁned for aﬁxed set of deleting vertices, and give a similarity transformation exchanging the adjacency matrix A(X)
which is compatible with the equitable partition for a block triangular matrix whose diagonal blocks are theadjacency matrix of the quotient graph and the deletion graph. In fact, we show the result for more generalmatrices, and as a corollary, we show a decomposition formula of the reciprocal of the Ihara–Bartholdi zetafunction over an equitably partitioned undirected graph into the quotient graph part and the deletion graphpart.
20 Seiken Saito (Kogakuin Univ.)

The distribution of the error terms of the number of non-backtracking
cycles for a regular graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For the number Nm of non-backtracking cycles of length m in a (q + 1)-regular graph, we consider
the error term tm of Nm . The sequence tm can be expressed by the adjacency eigenvalues whose absolute√values are less than 2 q. In this study, we investigate the distribution of the data tm (m = 1, 2, ...) and give√its moment generating function. We also applied this to show that the limit distribution of tm / n (where√
n is the number of eigenvalues whose absolute value is less than 2 q) becomes a normal distribution whena sequence of growing regular graphs satisﬁes certain conditions.
11:50–12:10

Presentation Ceremony for the 2021 MSJ Prize for Excellent Young Applied Mathematicians

13:15–14:15
21 Tomoya Machide(Nat. Inst. of Informatics)

An application of systems of Boolean polynomial equations to list color
problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give an application of systems of Boolean polynomial equations to list color problems to
obtain a computational complexity result having the bandwidth parameter. To symmetrize the result, we
also discuss a generalization of list color problem.

Final: 2022/3/4
Applied Mathematics

22 Yumiko Ohno (Yokohama Nat. Univ.)
Naoki Matsumoto (Keio Univ.)

70

The achromatic number and the pseudoachromatic number of caterpillars · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A pseudocomplete k-coloring of a graph is a (not necessarily proper) k-coloring such that eachpair of colors appears on at least one edge. A complete k-coloring is a pseudocomplete k-coloring which isalso a proper k-coloring. The pseudoachromatic number of a graph G is the largest number k such that G
has a pseudocomplete k-coloring and the achromatic number of G is the largest number k such that G has
a complete k-coloring.
In this talk, we deal with caterpillars, where a caterpillar is a tree such that the set of vertices of degree atleast two induces a path, and we shall show that pseudoachromatic number and achromatic number are thesame for a caterpillar satisfying certain conditions.
(Seikei Univ.)
23 Kengo Enami
Kenta Ozeki (Yokohama Nat. Univ.)
Tomoki Yamaguchi

Proper colorings of plane quadrangulations without rainbow faces · · · · 15

Summary: We consider a proper coloring of a plane graph such that no face is rainbow, where a face israinbow if any two vertices on its boundary have distinct colors. Such a coloring is said to be properanti-rainbow. A plane quadrangulation G is a plane graph in which all faces are bounded by a cycle oflength 4. In this paper, we show that the number of colors in a proper anti-rainbow coloring of a plane
quadrangulation G does not exceed 3α(G)/2, where α(G) is the independence number of G. Moreover,
if the minimum degree of G is 3 or if G is 3-connected, then this bound can be improved to 5α(G)/4 or
7α(G)/6 + 1/3, respectively. All of these bounds are tight.
24 Atsuhiro Nakamoto(Yokohama Nat. Univ.)
Kenta Ozeki (Yokohama Nat. Univ.)

Chromatic number of quadrangulations of the projective space · · · · · · · 15

Summary: Youngs proved that every quadrangulation on the 2-dimensional projective plane is 4-chromatic,
if it is non bipartite. In our talk, we deﬁne a quadrangulation of a 3-dimensional space, and consider
chromatic number of quadrangulations of the 3-dimensional projective space. We can ﬁnd a similar resulton the topic, but we can ﬁnd an essential diﬀerence between this and ours.

March 30th (Wed)Conference Room V

9:00–10:45
25 Yoshiki Jikumaru (Kyushu Univ.)
Yohei Yokosuka (Kagoshima Univ.)

On the diﬀerential geometric formulation of hanging membranes · · · · · 15

Summary: Antoni Gaudi, famous for his design of the Sagrada Familia, proposed a mechanically eﬃcient
structure obtained by a hanging chain to be upside-down. A hanging chain, often referred as catenary, isin equilibrium only with the tension for its own weight, therefore the upside-down object is in equilibrium
only with the compression. Due to the complexity of the treatment of membranes compared to curves,
previous research of hanging membranes in the architectural ﬁeld are based on many experiments ornumerical analysis. In this talk, we give a mathematically rigorous formulation of hanging membranes fromthe equilibrium equations of membranes and variational principles and show that our formulation is alsoeﬃcient for the numerical analysis.
26 Tomoharu Suda

(Keio Univ.)

Equivalence of topological dynamics without well-posedness · · · · · · · · · 15

Summary: The problem of topological classiﬁcation is fundamental in the study of dynamical systems.
However, when we consider systems without well-posedness, it is unclear how to generalize the notion ofequivalence. In this study, we formulate a notion of “topological equivalence” using the axiomatic theory of
topological dynamics proposed by Yorke, which we also generalize here to the action of topological groups.

Final: 2022/3/4
71

Applied Mathematics

27 Itsuki Watanabe (Waseda Univ.)

Deterministic limit of the stochastic model of nonlocal cross-diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The deterministic limit of the stochastic model of nonlocal cross-diﬀusion is considered. The
stochastic model is given by system with types of particle which the diﬀusion rate depends on the densityof another particle system. In this talk, we consider the deterministic limit of this model, and show theexistence of solution to some nonlocal cross-diﬀusion equation by Markov chain approximation method.
28 Satoru Iwasaki (Osaka Univ.)
Shuichi Jimbo (Hokkaido Univ.)
Yoshihisa Morita (Ryukoku Univ.)

Standing unimodal waves of reaction-diﬀusion equations on an unbounded graph with two vertices · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study standing unimodal waves of reaction-diﬀusion equations on an unbounded metric graphwith two vertices. In particular, we reveal a relation between a number of standing unimodal waves anda length of the bridge. Furthermore, stability of one of the standing unimodal waves is also studied byspectral analysis of linearized operators.
29 Satoru Iwasaki (Osaka Univ.)
Yutaro Yamaguchi (Osaka Univ.)

Number of stationary solutions of the Allen–Cahn equation in compact
metric graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, we deal with the Allen–Cahn equation in compact metric graphs. Particularly, thisstudy aims to reveal numbers of all stable stationary solutions of the problem. In this talk, we explain an
idea of an algorithm counting up numbers of stable stationary solutions based on analysis about the stargraph cases.
30 Toshikazu Kuniya (Kobe Univ.)
Tarik Mohammed Touaoula(Univ. Aboubekr Belkaı̈d)Global dynamics of a class of bistable reaction-diﬀusion equations withtime delay · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, we are concerned with a class of bistable reaction-diﬀusion equations with distributed
time delay. We investigate the global attractivity of each steady state and show that there can exist thebasins of attraction of the trivial steady state and a positive steady state, which is larger than anotherunstable positive steady state. We apply our analytical results to a delayed diﬀusive blowﬂies model with
Allee eﬀect.
11:00–12:00

Talk Invited by Applied Mathematics Section

Yusuke Imoto(Kyoto Univ.)

Invitation to single-cell data science

Summary: Single-cell data science is a new research ﬁeld of applied mathematics in this century. Recent developments of experimental techniques like next-generation sequencing (NGS) enable us to acquire molecular
data such as RNA, protein, and epigenome in single-cell resolutions. However, the single-cell data have thefollowing characteristics: high-dimensional, low-sample size, sparsity (low detection rate), non-time series,
and lack of 3D connectivity; these properties arose new data science challenges. In this talk, we would liketo introduce the mathematical problems in single-cell data science in detail. Moreover, the latest researchof the speaker and collaborators, which is a study of noise reduction based on high-dimensional statistics,
will be explained.

Final: 2022/3/4
Applied Mathematics

72

14:15–17:00
31 Jumpei Nagase (Shibaura Inst. of Tech.)Aoi Honda (Kyushu Inst. of Tech.)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Representation of the Choquet integral by deep neural networks · · · · · 15

Summary: The inclusion-exclusion integral is a generalized integral on non-additive measures, and theapplication to neural network models has been proposed as a data analysis method because it deals with
the interaction of each input. The Choquet integral, a fuzzy integral, is known as an example of inclusionexclusion integral. In this research, we consider the relationship between deep neural network models, whichhave been developing in wide range of ﬁelds in recent years, and Möbius-type Choquet integrals. In otherwords, the calculation of Choquet integrals can be explained as one of the functions that the perceptron
model can represent.
32 Kengo Nakai(Tokyo Univ. of Marine Sci. and Tech.)
Miki U. Kobayashi (Rissho Univ.)
Yoshitaka Saiki (Hitotsubashi Univ.)
Natsuki Tsutsumi (Hitotsubashi Univ.)

Reconstruction of invariant sets of dynamical systems by machine learning models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This study evaluates data-driven models obtained by machine-learning approach from a dynamicalsystem perspective, such as unstable ﬁxed points, periodic orbits and chaotic attractors. In addition, we ﬁndthat hetero-chaotic dynamics with diﬀerent unstable dimensions can be modeled by a data-driven model. A
part of this talk is based on Kobayashi, Nakai, Saiki, Tsutsumi, Phys. Rev. E 104, 044215 (2021).
33 Qiwen Sun (Nagoya Univ./RIKEN)
Takemasa Miyoshi (RIKEN)
Serge Richard (Nagoya Univ./RIKEN)

Control simulation experiments of extreme events with the Lorenz-96
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, we investigate the controllability of a chaotic dynamical system by adding small
perturbations to generate ampliﬁed eﬀects and to prevent extreme events. The high sensitivity to initialconditions would ultimately lead to modiﬁcations of extreme events with inﬁnitesimal perturbations. Basedon this idea, we design the control simulation experiment (CSE) for the Lorenz-96 model, a widely-used toy
system in data assimilation studies. We also study the sensitivity of the control to the amplitude of theperturbation, the forecast length, and the localized perturbation. The CSE would be applicable to otherchaotic dynamical systems including realistic numerical weather prediction models.
34 Naoto Yamaoka (Osaka Pref. Univ.)

Asymptotic behavior of solutions of discrete replicator equations withthe core-periphery model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the asymptotic behavior of solutions of the diﬀerence equation corresponding to a replicator equation with the core-periphery model ∆h λi (tn ) = {ωi (tn ) − ω̄(tn )}λi (tn ) (i = 1, 2).
We obtain a suﬃcient condition for solutions (λ1 (tn ), λ2 (tn )) of the diﬀerence equation to tend to theequilibrium (0, 1) as n → ∞.

Final: 2022/3/4
73

Applied Mathematics

35 Kaname Matsue(Kyushu Univ. / Kyushu Univ.)
Hiroyuki Ochiai (Kyushu Univ.)
Hisatoshi Kodani (Tohoku Univ.)
Takiko Sasaki(Musashino Univ./Tohoku Univ.)(Waseda Univ.)
Taisei Asai

Multiple-order asymptotic expansion of blow-up solutions for ODEs · · 15

Summary: Multiple-order asymptotic expansions of blow-up solutions near blow-up for ordinary diﬀerential
equations are considered. Under a mild assumption of vector ﬁelds involving the scale invariance, we develop
a general strategy for obtaining asymptotic expansion of blow-up solutions under the knowledge of blow-up
rates, which can be obtained through dynamics at inﬁnity. We show that, if the blow-up is type-I, allpossible terms appearing the expansion of a blow-up solution are determined by “eigenvalues” of the matrix
associated with vector ﬁelds near the principal term of the blow-up and lower order terms of vector ﬁelds.
The “eigenvalues” provide some algebraic aspects of blow-ups.
36 Takaaki Nishida (Kyoto Univ.⋆)

An example of heat convection in the horizontal layer with non-uniform
heat source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Stommel (1950) considered a model of thermal convection in horizontally long liquid layer withgravity. He obtained approximate solutions by asymptotic expansion of the equations with respect to adimension-less parameter and showed its picture of contour line of the stream function and isothermal line.
It may be considered as a simplest model of thermal eﬀect to the ocean current. (cf. Sverdrup 1942). Here
we show the existence of stationary solutions under some assumptions including h << 1/l and under stressfree boundary conditions on the velocity. Also we show a picture of the isothermal line and the contour
lines of the solution.
37 Koya Sakakibara(Okayama Univ. of Sci.)
Masaharu Nagayama (Hokkaido Univ.)
Harunori Monobe (Okayama Univ.)

Numerical computation of an interface model for deformable selfpropelled systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we deal with an interface model for deformable self-propelled systems in which thesurface tension diﬀerence is the driving force. Numerical results will be presented as a ﬁrst step to elucidate
the mathematical mechanism.
38 Kei Nishi (Kyoto Sangyo Univ.)
Yasumasa Nishiura (Hokkaido Univ.)

Transient behaviors of traveling multiple-pulse solutions in a threecomponent FitzHugh–Nagumo system · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The dynamics of traveling multiple-pulse solutions arising in a three-component FitzHugh–
Nagumo system is considered. It is numerically found that two traveling multiple-pulses weakly attract witheach other to become one larger multiple-pulse solution, and that, by parameter variations, such multiplepulse solutions are destabilized via a Hopf bifurcation and split up into smaller multiple-pulse solutions. In
order to elucidate the dynamics in more detail, we derive ordinary diﬀerential equations for the interface
motions of the multiple-pulses. The reduced ODEs allow us to reveal the global bifurcation structures ofmultiple-pulse solutions, especially traveling 2-pulse and 3-pulse solutions, and clarify the mechanism forthe numerically observed behaviors from a view point of the bifurcation theory.

Final: 2022/3/4
Applied Mathematics

74

39 Masaharu Nagayama (Hokkaido Univ.) ♭ On a numerical bifurcation analysis of a particle reaction-diﬀusion
Yusuke Yasugahira (Hokkaido Univ.) model for a motion of two self-propelled disks · · · · · · · · · · · · · · · · · · · · · 15
Summary: Theoretical analysis using mathematical models is often used to understand a mechanism ofcollective motion in a self-propelled system. In the experimental system using camphor disks, several kindsof characteristic motions have been observed due to the interaction of two camphor disks. In this paper, weunderstand the emergence mechanism of the motions caused by the interaction of two self-propelled material
by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematicalmodel. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, ischaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due totorus bifurcation.

March 31st (Thu)

Conference Room V

9:00–10:45
40 Fuminori Sakaguchi (Univ. of Fukui)

A reverse application of ‘ill-posedness’ —an advantage of multiple precision in a integer-type algorithm for solving ODEs— · · · · · · · · · · · · · · · 15

Summary: Usually, in numerical analysis, ‘ill-posedness’ and ‘ill-conditionedness’ are unwelcome. However,they aﬀect nothing, in the algorithms based only on four arithmetical operation among integers without
round-oﬀ errors. There, their ‘reverse applications’ for simplifying algorithms and reducing computational
quantities may be possible. An integer-type algorithm for solving higher-order linear ODEs, proposed by theauthor and M. Hayashi about ten years ago, turned out to have been a kind of such a ‘reverse applicationof ill-posedness’, in the sense that it utilizes simple integer operations among integer basis vectors which are
numerically almost linearly dependent (almost parallel). In this study, we investigate to what extent theadvantage of its ‘reverse application’ is enlarged by the use of multiple-precision integer operations. The
results are successful in reducing computational quantities considerably.
41 Takuya Tsuchiya(Hachinohe Inst. of Tech.)
Ryosuke Urakawa(Waseda Univ.)
Gen Yoneda

Numerical integration of Einstein equations in gravitational collapse
spacetime considering mass conservation · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We perform numerical simulations of the Einstein equations in the gravitational collapse spacetime.
We set the mass density in spherical symmetry as the initial condition, and integrate the Einstein equations
and the conservation equations of energy momentum tensor. We reported the simulations with the Crank–
Nicolson scheme and the centered space discretization at the MSJ Spring Meeting 2021. Then, the resultsof the mass density were the partially negative. Therefore, we improve the discretization by using theforth-order Runge–Kutta scheme and the upwind scheme. In addition, we will present some hi-precision
numerical simulations by the dynamical equations with the constraint terms.
42 Hirotada Honda (Toyo Univ.)

Revisiting the stability of GAN · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this article, we discuss the stability of min-max GAN originally proposed by Goodfellow et al.
We will make use of the theory of iterated function system.

Final: 2022/3/4
75

Applied Mathematics

43 Shinya Uchiumi (Gakushuin Univ.)

A pressure error estimate for a projection Lagrange–Galerkin schemeof Guermond–Minev type for the Oseen problem · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a ﬁnite element scheme for the transient Oseen problem, which is a linearizationof the Navier–Stokes (NS) problem. We focus on two numerical methods. One is the Lagrange–Galerkin(LG) method, which combines the method of the characteristics and Galerkin method. We also focus on
the projection method. The main advantage is the computational eﬃciency that decouples the velocity andpressure. Guermond and Minev have developed an LG/projection scheme for the NS problem, and derived
an error estimate for the velocity. The estimate for the pressure, however, is not known to the best of theauthor’s knowledge. Here, we derive an error estimate for the pressure in the Oseen problem.
44 Yoshitaka Watanabe (Kyushu Univ.)
Kaori Nagatou(Karlsruhe Inst. of Tech.)Michael Plum (Karlsruhe Inst. of Tech.)
Takehiko Kinoshita (Saga Univ.)
Mitsuhiro T. Nakao (Waseda Univ.)

A computer-assisted proof of critical Reynolds number for Orr–Sommerfeld
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk presents a computer-assisted proofs of the critical Reynolds number for the Orr–
Sommerfeld equation describing the hydrodynamic stability of Poiseuille ﬂow. Using spectral Galerkinapproximate solutions bounding its small defect and a ﬁxed-point theorem, an enclosure of a strong
candidate of the critical Reynolds number is shown.
45 Makoto Okumura (Hokkaido Univ.)
Yasuaki Kobayashi (Hokkaido Univ.)
Masaharu Nagayama (Hokkaido Univ.)
Hironobu Fujiwara (RIKEN)
Yasugahira Yusuke (Hokkaido Univ.)

A mathematical study of the mechanism of hair follicle formation using
a mathematical model for large deformation of basement membrane· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The skin is the boundary between the body and the outside world. All living things, including
humans, interact with the outside world through the skin. The skin is composed of epidermis, dermis, andsubcutaneous tissue. Besides, as an appendage of the skin, a hair follicle is the source of the hair. The hairfollicle is crucial for maintaining the epidermis and hair tissue homeostasis and for repairing damaged tissue.
In this study, we have attempted to examine the mechanism of hair follicle formation from a mathematicalpoint of view by applying a mathematical model, which enables the description of the concave deformationof the basement membrane. In this talk, we show the results obtained from this attempt.
11:00–12:00
Keita Iida

Talk Invited by Applied Mathematics Section(Osaka Univ.)

Single-cell gene expression data analysis

Summary: Gene expression is a biochemical process producing RNA and proteins that can regulates cellular
processes such as homeostasis, adaptation, and diﬀerentiation, however its dysregulation can induce cell
death or cancer formation. In recent years, experimental technologies to quantify gene expression such as
ﬂuorescence in situ hybridization and single-cell RNA sequencing have been developed and some of thesedata are available publicly. Furthermore, mathematical and bioinformatics studies oﬀer techniques to model
stochastic gene expressions, quantify biochemical parameters, and infer cell states. Here, we introduce ourmodel- and data-driven approaches to analyze such single-cell data to understand gene expression regulations
leading to cellular diﬀerentiation and dysregulation.

Final: 2022/3/4
Topology

76

Topology
March 28th (Mon)

Conference Room VII

9:30–12:00
1 Shunsuke Kano (Tohoku Univ.)
Tsukasa Ishibashi (Kyoto Univ.)

A characterization of pseudo-Anosov mapping classes by tropical clustertransformations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a mapping class on a punctured surface, we prove that the kind of pseudo-Anosov property
is equivalent to the combinatorial property of mutation loops. In particular, we conclude that the algebraic
entropies of the cluster A- and X-transformations induced by the mutation loop given by a pseudo-Anosov
mapping class both coincide with its topological entropy.
2 Ramón Barral Lijó (Ritsumeikan Univ.)
Jesús Antonio Álvarez López(Univ. of Santiago de Compostela)

Realization of manifolds as leaves of foliated spaces · · · · · · · · · · · · · · · · · 15

Summary: We will present our results about the geometric realization of Riemannian manifolds as leaves ofcompact foliated spaces with a leafwise Riemannian metric.
3 Hiroki Kodama(Tohoku Univ. / RIKEN)
Naohiko Kasuya (Hokkaido Univ.)
Yoshihiko Mitsumatsu (Chuo Univ.)
Atsuhide Mori (Osaka Dent. Univ.)

Torus ﬁbrations from S 5 to S 3 found from Milnor ﬁbrations of certain
complex surface singularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We explain Tpqr cusp singularities and Milnor ﬁbers Fθ of them. We construct a complex map g
on a Milnor ﬁber Fθ so that it has p + q + r critical points and the inverse images of regular values are tori
T 2 . We also construct a deformation of the Milnor ﬁber so that all critical points become Lefschetz type.
4 Yoshihiko Mitsumatsu (Chuo Univ.)
Naohiko Kasuya (Hokkaido Univ.)
Hiroki Kodama(Tohoku Univ. / RIKEN)
Atsuhide Mori (Osaka Dent. Univ.)

Lefschetz ﬁbration on Milnor ﬁbers of cusp singularities and topologicaldecomposition of K3 surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We explain that the K3 surface admits a smooth topological decomposition into the two Milnor
ﬁbers of Tpqr cusp singularities which are dual in the sense of the extended strange duality. Among such 10
decompositions, the pair T237 -T237 gives a particularly good decomposition.
5 Yasushi Hirata (Kanagawa Univ.)
Yukinobu Yajima(Kanagawa Univ.⋆ /Math Art Laboratory)

Undecidability for the extent of products of monotonically normal
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We say that a space is almost discrete if it has at most one non-isolated point. In this talk,we discuss the extent of product spaces. We show: it is consistent with and independent of ZFC that
there are a monotonically normal space X and an almost discrete space Y such that X × Y is normal ande(X × Y ) > ω = e(X) · e(Y ).
6 Hirokazu Nishinobu(Nagano Nat. Coll. of Tech.)Toshihiro Yamaguchi (Kochi Univ.)

An example of non-coformal classifying space with rational H(2)structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let Baut1 X be the Dold–Lashof classifying spaces of a space X. In this talk, we give an example
that there exists a space X such that Baut1 X are not coformal and are rational H(2)-spaces.

Final: 2022/3/4
77

Topology

7 Kaori Yamazaki(Takasaki City Univ. of Econ.)

Exchange economy from viewpoints of general topology · · · · · · · · · · · · · 15

Summary: In this talk, we study exchange economy from viewpoints of general topology.
8 Sachiko Saito (Hokkaido Univ. of Edu.)
Kosei Takashimizu(Seiryo Junior High School)

Newton non-degeneracy and strongly Newton non-degeneracy of mixed
weighted homogeneous polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A mixed polynomial f is called a mixed weighted homogeneous polynomial if it is both radiallyand polar weighted homogeneous. Let f be a mixed weighted homogeneous polynomial with respect toa strictly positive radial weight vector P and a polar weight vector Q. If f is Newton non-degenerateover the face ∆(P ) and f is polar weighted homogeneous of non-zero polar degree with respect to Q, thenf : C∗ n → C has no mixed critical points. Moreover, if f −1 (0) ∩ C∗ n ̸= ∅, then f : C∗ n → C is surjective.
In this talk, we give such an example of a mixed weighted homogeneous polynomial f which is Newton
non-degenerate over the face ∆(P ) and for which f −1 (0) ∩ C∗ n = ∅.
9 Yusuke Mizota (Kyushu Sangyo Univ.)
Shunsuke Ichiki (Tokyo Tech)(KLab Inc.)
Naoki Hamada

All unconstrained strongly convex problems are weakly simplicial · · · · 15

Summary: A multi-objective optimization problem is C 0 weakly simplicial if there exists a continuous
surjection from a simplex onto the Pareto set such that the image of each subsimplex is the Pareto set of a
subproblem. In this talk, we show that all unconstrained strongly convex problems are C 0 weakly simplicial.
(Joint work with Naoki Hamada and Shunsuke Ichiki)
14:15–15:05
10 Kazuhiro Ichihara (Nihon Univ.)(Kinki Univ.)
In Dae Jong

Purely cosmetic surgeries on alternating Montesinos knots · · · · · · · · · · 10

Summary: We show that alternating Montesinos knots admit no purely cosmetic surgeries. Precisely, it isshown that no pair of distinct Dehn surgeries on alternating Montesinos knots yield 3-manifolds that are
homeomorphic as oriented manifolds.
11 Masaki Ogawa (Saitama Univ.)

A characterization of a 3-manifold with a multibranched handlebody
decompsition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A decomposition of a 3-manifold by some handlebodies is called a handlebody decomposition.
The intersection of handlebodies in handlebody decomposition is called a partition of it. We say handlebody
decomposition is multibranched if the partition of a handlebody decomposition is a multibrahced surface.
Recently we showed that multibranched handlebody decomposition is stable equivalent if the number ofhandlebodies is four. In this talk, we consider the 3-manifolds which have a multibranched handlebody
decomposition with four handlebodies with genera at most one.
12 Teruaki Kitano (Soka Univ.)
Yuta Nozaki (Hiroshima Univ.)

Algebraic integrality of Reidemeister torsion · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For a 3-manifold M and an acyclic SL(2, C)-representation ρ of its fundamental group, theReidemeister torsion τρ (M ) ∈ C is deﬁned. If there are ﬁnitely many conjugacy classes of irreducible
representations, then the Reidemeister torsions are known to be algebraic numbers. In this talk we reportthat any value of them is an algebraic integer for a Seifert ﬁbered space under mild conditions, even though
there are iniﬁnite conjugacy classes.

Final: 2022/3/4
Topology

15:20–16:20

78

Talk Invited by Topology Section

Yuya Koda (Hiroshima Univ.)

Mapping class groups of Heegaard splittings

Summary: The mapping class group, or the Goeritz group, of a Heegaard splitting for a closed orientable
3-manifold is deﬁned to be the subgroup of the mapping class group of the Heegaard surface consisting ofmapping classes that extend to both of the handlebodies of the splitting. Simple problems on the structureof this group such as ﬁniteness, ﬁnite generation, ﬁnite presentability of the group are already highly
non-trivial and still open in general. In this talk, we give a short historical overview of these problems andintroduce its recent progress together with some applications.

March 29th (Tue)

Conference Room VII

9:30–11:50
13 Akihito Mori (Tohoku Univ.)
Yuya Murakami (Tohoku Univ.)

The Witten–Reshetikhin–Turaev invariant for plumbed manifolds · · · · 15

Summary: Gukov–Pei–Putrov–Vafa constructed q-series invariants called homological blocks in a physicalway in order to categorify Witten–Reshetikhin–Turaev (WRT) invariants and conjectured that radial limitsof homological blocks are WRT invariants. In this talk, we prove their conjecture for unimodular H-graphs.
As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth
two and of weight one with the quantum set Q. In the course of the proof of our main theorem, we ﬁrst
wrie the invariants as ﬁnite sums of rational functions. We second carry out a systematic study of weighted
Gauss sums in order to give new vanishing results for them. Combining these results, we ﬁnally prove thatthe above conjecture holds for H-graphs.
14 Yuta Taniguchi (Osaka Univ.)

A knot invariant obtained from an f -twisted Alexander matrix · · · · · · 15

Summary: Recently, A. Ishii and K. Oshiro introduced a new notion, which is called an f -twisted Alexander
matrix. An f -twisted Alexander matrix is a quandle version of an Alexander matrix of knot groups. In thistalk, we show that a certain knot invariant obtained from a f -twisted Alexander matrix is a stronger knot
invariant than the Alexander invariant.
15 Akihiro Takano (Univ. of Tokyo)

The Long–Moody construction and twisted Alexander invariants · · · · · 15

Summary: The Long–Moody construction is a method of constructing a new representation of the braid
group from a representation of the semidirect product of the braid group and the free group. In this talk,we show that its matrix presentation is described by the Fox derivation, and also a relation with twisted
Alexander invariants.
16 Shuichi Harako (Univ. of Tokyo)

Computational results for the symplectic derivation Lie algebras · · · · · 15

Summary: The Lie algebras consisting of symplectic derivations on certain algebras are called the symplectic
derivation Lie algebras.

We determined the second homology group of the certain Lie ideal of “thecommutative world” of the symplectic Lie algebras in terms of symplectic modules.
17 Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii(Hiroshima Univ. / RIKEN)

A classiﬁcation of 5-component link-homotopy classes through theclasper theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The link-homotopy classes of links are obtained from the link-homotopy classes of string links
modulo the partial conjugations. Yasuhara and Meilhan gave a standard form of the link-homotopy classesof string links by using the claspers. In this talk, we calculate the actions of the partial conjugations for the
5-component link-homotopy classes of string links by using the clasper theory and give a new presentationof the link-homotopy classes of 5-component links.

Final: 2022/3/4
79Topology

18 Takefumi Nosaka (Tokyo Tech)Fox pairings of Poincaré duality groups · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We develop the study of Fox pairings of a group G from viewpoints of group cohomology. We
compute some cohomology groups of Fox pairings of G, where G admits a Poincaré duality group pair. We
also suggest fundamental Fox pairings and higher Fox pairings.
19 Kentaro Yonemura (Kyushu Univ.)

Quandles over a one-sheet hyperboloid and longitudinal map · · · · · · · · 15

Summary: We deﬁne quandles over a one-sheet hyperboloid and compute longitudinal map, which is a knot
invariant deﬁned by Clark–Saito in 2019.
20 Tsukasa Ishibashi (Kyoto Univ.)
Wataru Yuasa (Kyoto Univ.)Stated and marked skein algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For a marked surface Σ and a Lie algebra g = sl2 , sl3 or sp4 , we construct an explicit isomorphism
between the reduced stated g-skein algebra and the boundary-localization of the (“Muller type”) marked
g-skein algebra.
12:15–12:25

Presentation Ceremony for the 2021 MSJ Geometry Prize

13:15–14:15

Talk Invited by Topology Section

Takefumi Nosaka (Tokyo Tech)

Nilpotent knot-invariants and Johnson homomorphisms of the mappingclass group

Summary: While there are many studies of knots in the 3-sphere, this study suggests a knot theory from theviewpoints of (nilpotently) rational homotopy theory or Johnson homomorphisms. More precisely, I deﬁned
a nilpotent monodoromy from a knot, which should be regarded as an element of an outer automorphismgroup. Fortunately, the outer automorphism group has been studied in terms from Johnson homomorphisms
and the mapping class groups, with a relation to Goldman Lie algebras. In this talk, I explain the deﬁnitionof the monodoromy, and an interaction between knot theory and studies of the mapping class group; I also
take about some approaches to the outer automorphism group in order to give some computations of themonodoromies.

March 30th (Wed)Conference Room VII

9:30–12:00
21 Erika Kuno

(Osaka Univ.)

Uniform hyperbolicity of nonseparating curve graphs of nonorientablesurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let N be a connected nonorientable surface with or without boundary components and punctures.
We prove that the graph of nonseparating curves of N is connected and Gromov hyperbolic with a constantwhich does not depend on the topological type of surface by using the bicorn curves introduced by Przytycki
and Sisto. The proof is based on the argument by Rasmussen on the uniform hyperbolicity of graphs ofnonseparating curves for orientable ﬁnite type surfaces.
(Osaka Univ.)
22 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 ≥ 3 is also uniformly hyperbolic.

Final: 2022/3/4
Topology

23 Hirotaka Akiyoshi (Osaka City Univ.)

80

Dirichlet domains for some one-cone torus bundles · · · · · · · · · · · · · · · · · 10

Summary: Two families of one-cone torus bundles parametrized by cone angles are studied. When thecone angles are suﬃciently small, the combinatorial structures of the Dirichlet domains with respect to thebasepoints in the singular locus are characterized.
24 Naoki Kimura (Waseda Univ.)

Bi-Legendrian rack coloring numbers of Legendrian knots · · · · · · · · · · · 10

Summary: Kulkarni and Prathamesh introduced an invariant of Legendrian knots by using rack colorings.
Ceniceros, Elhamdadi and Nelson deﬁned a Legendrian rack and generalized the invariant. In this talk,we deﬁne a bi-Legendrian rack and consider a further generalization of the invariant. We show that biLegendrian rack coloring numbers can distinguish all Legendrian unknots with the same Thurston–Bennequinnumber. We also consider pairs of Legendrian knots which cannot be distinguished by bi-Legendrian rackcoloring numbers.
25 Jumpei Yasuda (Osaka Univ.)

A plat form presentation for surface-links · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that every orientable surface-link can be described as a closed 2-dimensional braid.
In this talk, we introduce a new method of describing a surface-link using a braided surface, which we call aplat form. We prove that every surface-link, which is not necessarily orientable, can be described in a platform. We show how to obtain the surface-link group from the braided surface group by adding some simple
relations.
26 Takahiro Oba(Osaka Univ.)

A four-dimensional mapping class relation · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Relations between Dehn twists on mapping class groups of surfaces play an important role inthe study of symplectic manifolds via Lefschetz ﬁbrations. In higher dimensions, as little is known about
symplectic mapping class groups, ﬁbration-like structures are not so powerful yet. In this talk, I will givea relation between 4-dimensional Dehn twists on a Weinstein domain. One of the key ingredients in the2

construction is a solution to the symplectic isotopy problem for symplectic surfaces in CP2 #3CP .
27 Tatsumasa Suzuki (Tokyo Tech)
Motoo Tange (Univ. of Tsukuba)

Pochette surgery on S 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The boundary sum of the product of a circle with a 3-ball and the product of a disk with a2-sphere is called a pochette. For a pochette P embedded in a 4-manifold M , a pochette surgery on M
is the operation of removing the interior of P and gluing in P by a diﬀeomorphism of the boundary of
P . In this talk, we give a necessary condition for the operation of surgery on the 4-sphere to generate ahomotopy 4-sphere in a more precise manner. Furthermore, we show that any pochette surgery using thetrivial 2-knot, which becomes a homotopy 4-sphere, is diﬀeomorphic to the 4-sphere.
28 Sakumi Sugawara (Hokkaido Univ.)

Link diagrams of divides with cusps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A divide with cusps is the image of a generic, relative immersion allowing ﬁnite cusps of intervals
and curves into the unit disk. A divide with cusps is the generalization of the notion of the divide whichis introduced by A’Campo. We can associate the link L(P )in S 3 to a divide P . There are several ways todraw the diagram of the link L(P ) from a divide P . In this talk we introduce the algorithm to draw thediagram of the link L(P ) of a divide with cusps P , which is the application of Couture–Perron’s method.
29 Yu Tajima (Hokkaido Univ.)
Masahiko Yoshinaga (Hokkaido Univ.)

Magnitude homology of graphs and discrete Morse theory on Asao–
Izumihara complexes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Magnitude is an invariant for metric spaces introduced by Leinster, which measures the number
of eﬃcient points. As a categoriﬁcation of the magnitude, Hepworth and Willerton deﬁned magnitude
homology for graphs. Recently, Asao and Izumihara introduced CW-complexes whose homology groups are
isomorphic to direct summands of the graph magnitude homology group. We prove that the Asao–Izumihara
complex is homotopy equivalent to a wedge of spheres for pawful graphs introduced by Y. Gu.

Final: 2022/3/4
81

Topology

14:15–15:15
30 Koji Yamazaki(Tokyo Tech)

Sheaf theoretic characterization of étale groupoids · · · · · · · · · · · · · · · · · · 15

Summary: The study of Haeﬂier suggests that it is natural to regard a pseudogroup as an étale groupoid. We
show that any étale groupoid corresponds to a pseudogroup sheaf, a new generalization of a pseudogroup.
This correspondence is an analog of the equivalence of the two deﬁnitions of a sheaf: as an étale space andas a contravariant functor.
31 Shuhei Maruyama (Nagoya Univ.)

The Dixmier–Douady class, the action homomorphism, and cocycles on
the group of symplectomorphisms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a closed, one-connected, and integral symplectic manifold, there exist three kinds of cohomology classes; the Dixmier–Douady class of symplectic ﬁbrations, Weinstein’s action homomorphism, anda cohomology class of Ismagilov–Losik–Michor type. In this talk, we explain a relation between thesecohomology classes in terms of the Hochschild–Serre spectral sequence.
32 Hitoshi Moriyoshi (Nagoya Univ.)
Toshikazu Natsume(Nagoya Inst. of Tech.)

Quantum walk on the integer lattice and the Nöther index theorem· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A formulation of the index theorem for Quantum walk will be discussed. The framework of
K-theory provides a novel viewpoint that connects the classical index theorem by Fritz Noether in 1920 with
the new index theorem discovered by Suzuki–Tanaka and Matsuzawa.
15:30–16:30

Talk Invited by Topology Section

Takahiro Matsushita(Univ. of Ryukyus)

Invariant quasimorphisms and mixed commutator lengths

Summary: A quasimorphism on a group G is a real-valued function f on G such that the function f (xy) −f (x) − f (y) on G × G is uniformly bounded. A quasimorphism f on G is said to be homogeneous iff (xn ) = n · f (x) for every element x in G and for every integer n. Homogeneous quasimorphisms areclosely related to the second bounded cohomology and the stable commutator length, and they have been
extensively studied in geometric group theory, symplectic geometry, and theory of diﬀeomorphism groups.
Let N be a normal subgroup of a group G. A homogeneous quasimorphism f on N is said to be G-invariant
if f (gxg −1 ) = f (x) for every element g in G and for every element x in N . In this talk, we discuss several
relations among invariant quasimorphisms, the stabilizations of mixed commutator lengths, and the second(bounded) cohomology groups.
This talk is based on joint work with Morimichi Kawasaki (Aoyama Gakuin University), Mitsuaki Kimura(Kyoto University), Shuhei Maruyama (Nagoya University), and Masato Mimura (Tohoku University).

Final: 2022/3/4
Inﬁnite Analysis

82

Inﬁnite Analysis
March 30th (Wed)Conference Room IX

10:00–12:00
1 Kohei Motegi(Tokyo Univ. of Marine Sci. and Tech.)An extension of an identity for Grothendieck polynomials to skew
version using Yang–Baxter algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, Guo and Sun derived an identity for factorial Grothendieck polynomials which generalizes the one for Schur polynomials by Fehér–Némethi–Rimányi. We give an extension of the identity using
skew Grothendieck polynomials by using integrable model and associated Yang–Baxter algebra.
2 Yusuke Ohkubo(Daiichi Univ. of Pharm.)
Ayumu Hoshino(Hiroshima Inst. of Tech.)
Jun’ichi Shiraishi (Univ. of Tokyo)

Deformed Koornwinder operators and Macdonald polynomials of type
C I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A certain deformation of the Calogero–Moser–Sutherland operator and the Macdonald operator
was given by Sergeev and Veselov, which is related to the Lie superalgebras. In this talk, we present a Fockrepresentation of the Sergeev–Veselov type deformation of the Koornwinder operator. This representation
gives another proof of the kernel function identity for the deformed Koornwinder operator which was
originally proved by Atai.
3 Ayumu Hoshino(Hiroshima Inst. of Tech.)
Yusuke Ohkubo(Daiichi Univ. of Pharm.)
Jun’ichi Shiraishi (Univ. of Tokyo)

Deformed Koornwinder operators and Macdonald polynomials of typeC II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give explicit forms for the Macdonald polynomials of type C with hook diagrams. Moreover,
we give the Pieri formulas for the Macdonald polynomials of type C with hook diagrams and give a conjectureof the Pieri formulas for the type C degenerations of the Koornwinder polynomials with hook diagrams.
4 Toshiki Nakashima (Sophia Univ.)
Manal I. Alshuqayr (Sophia Univ.)

Decomposition theorem for product of fundamental crystals in monomial realization of type Cn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We shall describe the monomial realizations of the fundamental crystals of type Cn and show that
their product holds a crystal structure. Finally, we shall give the decomposition theorem of their products
explicitly and compare with the decomposition of their tensor product.
5 Yuki Kanakubo (Univ. of Tsukuba)(IITP RAS)
Gleb Koshevoy(
SophiaUniv.)
Toshiki Nakashima

An algorithm for Berenstein–Kazhdan decoration functions for minuscule representations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We can deﬁne a geometric crystal structure on a variety related to a simply connected connected
simple algebraic group, which is a geometric analog of Kashiwara crystals. Deﬁning a rational function‘Berenstein–Kazhdan decoration’, one can obtain a crystal in a polyhedral cone isomorphic to the crystal
base of negative part of quantum group. In this talk, we give an algorithm to partially compute the BK
decoration. In particular, if the algebraic group is special linear group, we can completely calculate BK
decoration, which induces an explicit form of the polyhedral cone.

Final: 2022/3/4
83

Inﬁnite Analysis

6 Travis Scrimshaw (Osaka City Univ.)

Quasi-solvable colored lattice models for types B and C · · · · · · · · · · · · · 15

Summary: We describe a colored vertex model whose partition function computes the Demazure atoms andcharacters for types B and C. A novel feature of this model is that it is not fully solvable (in the sensethat the exists a solution to each possible Yang–Baxter equation), but it still retains enough solutions of
the Yang–Baxter equations to compute the partition function. This is based on joint work with Valentin
Buciumas (arXiv:2101.08907)
14:15–14:50
7 Ryo Takenaka (Osaka City Univ.)
Masato Okado (Osaka City Univ.)

Vertex operator algebras and fermionic character formulas of aﬃne Liealgebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Using a vertex algebraic construction, we construct bases of principal subspaces, highest weight
modules of highest weight kΛ0 and parafermionic spaces for twisted aﬃne Lie algebras. As a consequence,
we obtain the fermionic character formula conjectured by Hatayama, Kuniba, Okado, Takagi and Tsuboi.
8 Hiromu Nakano (Tohoku Univ.)

On logarithmic modules of the N = 1 triplet vertex operator superalgebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The N = 1 triplet vertex operator superalgebra SW (m) was introduced by Adamović and Milasin 2009. We construct logarithmic SW (m)-modules and prove that the projective covers of every irreducible
SW (m)-modules are given by these logarithmic modules.
15:00–16:00

Talk Invited by Inﬁnite Analysis Special Session
Takeo Kojima (Yamagata Univ.) Quadratic relations of the deformed W -algebra Wq,t (g)Summary: Deformed W -algebra Wq,t (g) associated with Lie algebra g is a two parameter deformation of
the classical W -algebra W(g), including the W -algebra Wβ (g) and the q-Poisson W -algebra as special
cases. Using the free ﬁeld construction of the basic W -current T1 (z) of Wq,t (g), we introduce the higher
W -currents Ti (z) (i = 2, 3, 4, . . .) and obtain a closed set of quadratic relations among them. This allows us

to deﬁne Wq,t (g) by generators and relations. In this talk, we ﬁrst review the case of the aﬃne Lie algebra
(1)

(2)

g = AN , and then study the extensions to the cases of the twisted Lie algebra A2N and the super Lie
algebra A(M, N )(1) .

March 31st (Thu)

Conference Room IX

10:00–12:00
9 Kazuhiko Aomoto (Nagoya Univ.)
Masahiko Ito (Univ. of Ryukyus)

Product of Hessians on critical points of level function F attached to
hypergeometric integral associated with sphere arrangement · · · · · · · · · 15

Summary: We will talk about product formulae of values of a level function at critical points involvedin asymptotic behaviors of hypergeometric integrals associated with a symmetric arrangement of three
dimensional spheres. We show in an explicit way how the product of Hessians of the level function at all
critical points is related to the behavior of its critical points. We also state two conjectures concerning thesame problem associated with general hypersphere arrangements.
10 Taichiro Takagi(Nat. Defense Acad. of Japan)

Lax equations using the loop elementary symmetric functions · · · · · · · · 15

Summary: We consider a set of ordinary diﬀerential equations that is a sort of Bogoyavlensky lattices with Ln
dependent variables, where L and n are any pair of coprime natural numbers. We show a Lax representation
for the system where the elements of the Lax matrix are given by the so-called loop elementary symmetricfunctions of the dependent variables. The Lax equation is viewed as a continuous limit of the discrete
time analog of the Lax equation for the geometric lifting of the integrable cellular automata studied by theauthor.

Final: 2022/3/4
Inﬁnite Analysis

11 Shota Shigetomi (Kyushu Univ.)
Kenji Kajiwara (Kyushu Univ.)

84

Explicit formula of isoperimetric deformation of discrete space curvewith constant torsion angle in terms of elliptic theta function · · · · · · · · 15

Summary: We construct an explicit formula of isoperimetric deformation of discrete space curve with constanttorsion angle in terms of elliptic theta function. This formula represents a deformation of Kaleidocycle.
12 Tomoki Nakanishi (Nagoya Univ.)

Cluster scattering diagrams, dilogarithm elements, and pentagon relation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The cluster scattering diagrams (CSDs) was introduced by Gross, Hacking, Keel, and Kontsevich
to prove several important conjectures on cluster algebras. In this talk we show that every consistency
relation in any CSD can be reduced to a trivial one by the pentagon relation among dilogarithm elements
in its structure group (possibly applying inﬁnitely many times). The proof is based on a modiﬁcation of theconstruction of CSDs by Gross et al.
13 Kodai Matsushita (Nagoya Univ.)

Consistency relation of rank 2 cluster scattering diagrams of aﬃne type
and pentagon relation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Cluster scattering diagrams are important tools for studying cluster algebra. In rank 2 case, thediagrams are characterized by the consistency relation. In this talk, we prove that the consistency relation ofrank 2 cluster scattering diagram of aﬃne type is reduced to the trivial relation by using pentagon relations
inﬁnite times.
14 Yuma Mizuno(Chiba Univ.)

Mutations of blowups of toric surfaces and q-Painlevé systems · · · · · · · 15

Summary: We provide a relation between the geometric framework for q-Painlevé equations and cluster
Poisson varieties by using toric models of rational surfaces associated with q-Painlevé equations.

We

introduce the notion of seeds of q-Painlevé type by the negative semi-deﬁniteness of symmetric bilinear
forms associated with seeds, and classify the mutation equivalence classes of these seeds. This classiﬁcation
coincides with the classiﬁcation of q-Painlevé equations given by Sakai.
14:15–15:15

Talk Invited by Inﬁnite Analysis Special Session

Tomohiro Sasamoto (Tokyo Tech)

Skew RSK, aﬃne crystal and KPZ

Summary: We explain various properties and applications of the skew RSK dynamics, which we introduced
recently as a time evolution for a pair of skew Young tableaux (P,Q). The dynamics exhibits solitonic
behaviors similar to box ball systems (BBS). Associated aﬃne crystal structure allows to give a bijective
proof of the Cauchy identity for the q-Whittaker polynomials. Its reﬁnement provides a connection between
Kardar–Parisi–Zhang (KPZ) models and free fermions at ﬁnite temperature.