Final ver.: 2016/2/15“ Mathematical Society of Japan
2016 Annual Meeting

Titles and Short Summaries of the Talks

March, 2016
at University of Tsukuba

Final ver.: 2016/2/15

2016 Mathematical Society of Japan
ANNUAL MEETING
Dates: March 16th (Wed)–19th (Sat), 2016
Venue: Area 1 and Area 3, University of Tsukuba
1–1–1 Tennodai, Tsukuba 305-8571
Contact to: University of Tsukuba
E-mail tsukuba16mar mathsoc jp
During session: Phone +81 (0) 90 1791 3483
Mathematical Society of Japan
Phone +81 (0) 3 3835 3483

I

II

III

IV

V

VI

VII

VIII

IX

Bldg. 3A
3A204

Bldg. 3A
3A402

Bldg. 3A
3A403

Bldg. 1C
1C310

Bldg. 1D
1D201

Bldg. 1D
1D204

Bldg. 1E
1E102

Bldg. 1E
1E203

Bldg. 1E
1E303

Statistics and Functional
Probability Equations

Found. of Math.
andHistory of Math.

Geometry

Topology

AppliedMathematics

ComplexAnalysis

Functional
Analysis

9:30–12:00
14:15–16:15

10:00–11:20
14:15–16:00

9:30–12:00
14:15–16:30

10:00–11:55
15:30–17:10

10:30–12:00
14:30–16:00

9:45–11:45
14:15–15:05

10:00–12:00

Algebra9:30–12:00

16th 14:15–16:50(Wed)

9:30–12:00

Featured Invited Talks
13:00–14:00
Invited Talks Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk
14:30–15:30
15:45–16:45

Algebra9:30–12:00

16:30–17:30

16:15–17:15

16:45–17:45

14:15–15:15

16:10–17:10

15:25–16:25
16:45–17:45

14:15–15:15

Statistics and Functional
Probability Equations

Found. of Math.
andHistory of Math.

Geometry

Topology

AppliedMathematics

ComplexAnalysis

Functional
Analysis

9:00–10:45

10:00–11:40

10:00–11:30
13:10–14:00

9:45–11:50
13:15–14:20

10:00–12:00

9:45–11:30

9:30–12:00

10:00–11:30
13:15–14:25

17th

Invited Talk

Invited Talk Invited Talk

Invited Talk

(Thu)

13:30–14:30

11:00–12:00

13:15–14:15

13:30–14:30

MSJ Prizes Presentation (Bldg. 1H, 1F 1H101) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15:00–15:20)
Plenary Talks(Bldg. 1H, 1F 1H101) MSJ Spring Prize Winner · · · · · · · · · · · · · (15:30–16:30)
Mikiya Masuda (Osaka City Univ.) · · · · · (16:40–17:40)
Oﬃcial Party(University Hall) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:00–20:00)
Algebra9:00–12:00

Statistics and Functional
Probability Equations
9:45–12:00

9:30–12:00
14:15–16:15

Real
Analysis

Geometry

Topology

9:30–12:00
14:15–16:10

9:30–11:50
14:15–16:00

10:00–11:45 14:30–16:00 10:00–12:00
14:15–15:30 Special Session 14:15–15:15
9:15–11:55

18th
(Fri)

AppliedMathematics

Infinite
Analysis

Functional
Analysis
9:30–12:00
14:15–15:00

Featured Invited Talks
13:00–14:00
Invited Talks Invited Talks Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk
14:30–15:30
15:40–16:40
16:50–17:50

Algebra9:30–12:00

14:15–15:15
15:30–16:30

16:30–17:30

Statistics and Functional
Probability Equations
9:50–12:00

9:30–12:00

16:30–17:30

16:15–17:15

Real
Analysis

Geometry

9:30–12:00

9:00–10:45

19th 14:15–15:45 14:15–16:10 14:15–15:45 14:15–15:00(Sat)

15:45–16:45

16:15–17:15

15:30–16:30

AppliedMathematics

Infinite
Analysis

10:00–12:00
14:15–15:45

9:30–12:00
14:15–15:15

Invited Talk

Featured Invited Talks
13:00–14:00
Invited Talk Invited Talk Invited Talk
Invited Talk Invited Talk

16:00–17:00

16:00–17:00

15:15–16:15

11:00–12:00

16:00–17:00

15:30–16:30

15:15–16:15

Final ver.: 2016/2/15
5

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

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

Foundation of Mathematics and History of Mathematics

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

4March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

9March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

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

20March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

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

29

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

Functional Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

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

45

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

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

51

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

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

57

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

Final ver.: 2016/2/15
6

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

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

67

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

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

76

March 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

March 17th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

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

83

March 18th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

March 19th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Final ver.: 2016/2/15
1

Plenary Talks

Plenary Talks
March 17th (Thu) Bldg. 1H, 1F 1H101
MSJ Spring Prize Winner····················································(15:30–16:30)

Mikiya Masuda (Osaka City Univ.)

Toric topology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(16:40–17:40)

Summary: Around 1970, a very beautiful and successful theory called toric geometry was established by
Demazure, Miyake-Oda, Mumford and others. Toric geometry connects two diﬀerent mathematical fields:
algebraic geometry (toric varieties) and combinatorics (fans and convex polytopes). It also provides new
insight and unexpected applications, e.g. an application by R. Stanley to a longstanding problem called
g-conjecture about characterization of face numbers of simplicial convex polytopes. Around 1980, equivariant
symplectic geometry was developed and its close relation to toric geometry was recognized, especially throughthe celebrated Atiyah-Guillemin-Sternberg convexity theorem.
Motivated by this success story, a new mathematical field called toric topology is emerging and rapidly
developing. Toric topology is a new topological discipline concerned with a class of problems on the borders
between the topology of torus actions, commutative and homological algebra, toric geometry, combinatorics
and equivariant symplectic geometry etc. In this talk I overview the development of toric topology.

Final ver.: 2016/2/15
2Featured Invited Talks

Featured Invited Talks
March 16th (Wed)Conference Room V
Qing-Ming Cheng (Fukuoka Univ.)

Geometry of λ-hypersurfaces of the weighted volume-preserving
mean curvature flow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: In this talk, we introduce mean curvature flow and mean curvature type flow, which is called theweighted volume-preserving mean curvature flow.
A self-shrinker of the mean curvature flow is a self-similar solution of the mean curvature flow. On the other
hand, it can be seen a critical point of the weighted area functional from the view point of variations. We
give a definition of a weighted volume, which is preserved by the weighted volume-preserving mean curvature
flow. Thus, we consider variations of the weighted area functional, which preserve the weighted volume.
A critical point of the weighted area functional for the weighted volume-preserving variations is defined a
λ-hypersurface of weighted volume-preserving mean curvature flow.
We study geometry of λ-hypersurfaces of weighted volume-preserving mean curvature flow. First of all,many examples of compact embedded λ-hypersurfaces of weighted volume-preserving mean curvature flow
are constructed. Secondly, complete λ-hypersurfaces are studied. The results on complete self-shrinkers ofmean curvature flow due to Huisken (J. Diﬀ. Geom., 1990) and Colding-Minicozzi (Ann. of Math., 2012) are
generalized to complete λ-hypersurfaces of weighted volume-preserving mean curvature flow. We also definea F-functional and study F-stability of λ-hypersurfaces. Furthermore, lower bound growth and upper boundgrowth of the area for complete and non-compact λ-hypersurfaces are also studied.
Conference Room VII
Guest Talk from the Japan Society for Industrial and Applied Mathematics
Tetsuya Sakurai (Tsukuba Univ.) Large-scale simulation and data analysis using quadraturetype eigensolver · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)
Conference Room VIII
Toshiyuki Sugawa (Tohoku Univ.)

Geometry and analysis of Schwarzian derivative · · · · · · · · · ·(13:00–14:00)

Summary: In this talk, we will survey the Schwarzian derivative from its birth to several recent extensions
in various contexts. The Schwarzian derivative of a nonconstant meromorphic function f (z) of a complex
variable is defined as f ′′′ (z)/f ′ (z) − 3(f ′′ (z)/f ′ (z))2 /2. This quantity looks a little complicated but has
unexpectedly many and deep applications in a wide variety of fields in Mathematics including Conformal
Geometry, Mathematical Physics, Teichmüller theory, Dynamical Systems as well as Function Theory.
We start the talk with a historical account of the Schwarzian derivative and then present a couple ofapplications as examples. Especially, we will explain how the Schwarzian derivative is used to construct theBers embedding of the Teichmüller space.
In the second half, we will mention possible generalizations or extensions of the Schwarzian derivative. In
particular, we will present our recent higher-order analogues of the Schwarzian derivative of holomorphic
maps between Riemann surfaces equipped with a conformal metric and projective structure.

Final ver.: 2016/2/15
3Featured Invited Talks

March 18th (Fri)
Conference Room II
Akio Suzukawa (Hokkaido Univ.)

Multivariate survival analysis based on shared frailty models· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: Multivariate survival data occur in many areas, including medicine, biology, engineering, andeconomics. Shared frailty models are random eﬀects models for analyzing multivariate survival data. They
are closely related to dependence modeling based on Archimedean copulas. In this paper, we discuss about
the shared frailty models and their extensions.
Conference Room IX♭
Jiro Sekiguchi
Free divisors and diﬀerential equations · · · · · · · · · · · · · · · · · ·(Tokyo Univ. of Agri. and Tech.)(13:00–14:00)

March 19th (Sat)
Conference Room I
Satoshi Wakatsuki (Kanazawa Univ.)

Dimension formulas of Siegel modular forms · · · · · · · · · · · · ·(13:00–14:00)

Summary: The purpose of this talk is to discuss dimension formulas for spaces of Siegel modular forms. In
particular, we give a dimension formula for spaces of Siegel cusp forms of general degree. The trace formulais one of the main tools to study the dimensions. In 1975, T. Shintani gave a formula which expresses asmall part of the geometric side of the trace formula by special values of Shintani zeta functions for spacesof symmetric matrices at non-positive integers. To be precise, it is the contribution of unipotent elements
corresponding to the partitions (2j , 12n−2j ), where n denotes the degree and 0 ≤ j ≤ n. After that, several
Japanese researchers conjectured that the other contributions will vanish and Shintani’s formula means thedimension itself. In this talk, we report that the conjecture was solved aﬃrmatively and the dimensions are
expressed by the special values. In 1995, T. Ibukiyama and H. Saito discovered an explicit formula of the
Shintani zeta functions. Their formula shows that the special values are described by the Bernoulli numbers,that is, they are rational numbers and computable. Therefore, our formula provides numerical values ofdimensions.
Conference Room III
Shigeaki Koike (Tohoku Univ.)

On ABP maximum principle · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: I will show a proof of the celebrated Aleksandrov-Bakelman-Pucci maximum principle and its
parabolic version by Krylov-Tso. This maximum principle is a nice tool to connect point-wise estimates withintegrations.
I start by the simplest case and arrive at the complete version. I hope to give some applications andextensions.

Final ver.: 2016/2/15
4Foundation of Mathematics and History of Mathematics

Foundation of Mathematics and History of Mathematics
March 16th (Wed)Conference Room IV

10:00–11:20
1 Toshio Harikae (Osaka Sangyo Univ.)

Solid figures in ancient China · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss the deference of several solid figures in the mathematical books written in
the Qin–Han period.
2 Makoto Tamura (Osaka Sangyo Univ.)

Chants in math books of the Qin and the Han Dynasties in China· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The book Shu of the Qin Dynasty housed at Yuelu Academy, the Suanshu slips of the Qin
Dynasty housed at Peking University, and the Zhangjiashan bamboo slips Suanshushu of the Han Dyansty aremathematical books in ancient China. They were textbooks for middle oﬃcers, and most of their problems
are on calculation of tax, area, and so on. However one of the Litian problems of the Suanshu housed at
Peking University was incomprehensible in such a way. In this talk, we show it is a type of chants formemorizing a conversion constant compared with the Litian problems of the Shu housed at Yuelu Academy
and Zhangjiashan Suanshushu.
3 Shunzi Horiguchi(Niigata Sangyo Univ.)

Handwriting analysis of Chinese characters in the picture scroll of kikugenpou betsuden ichimaki-hihachiji and 1000 characters of ten bodies
written by Koutaku Hosoi · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We do the handwriting analysis of Chinese characters in the picture scroll of kikugenpou betsuden
ichimaki-hihachiji and 1000 characters of ten bodies written by Koutaku Hosoi. As a result, we find thatthe handwritings of both are similar very much. Therefor, it is supposed that Hosoi wrote the picture scroll.
4 Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)

A modern transcription of the side writing method in the Taisei Sankei· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Taisei Sankei (1683–1711) is an encyclopedic work on mathematics by Seki Takakazu, Takebe
Kata’akira and Takebe Katahiro. To express algebraic equations they use the so-called side writing method.
In our enterprise to translate the work into English, we have encountered a problem of transcription of theside writing method, which is a generalization of the celestial element method developed in Song China.
The Taisei Sankei is written in Classical Chinese, which follows vertical lines, while English as well as othermodern languages are composed along horizontal lines. The side writing method is basically a verticalnotation, which is required to be transcribed horizontally in English translation.
5 Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)

On the last problem of Volume 19, the Taisei Sankei · · · · · · · · · · · · · · · · 15

Summary: Volume 19 of the Taisei Sankei contains 15 problems of algebraic equations of one or several
unknowns, which are treated thoroughly using notation of the side writing method. The last problem isconcerned with a system of eight algebraic equations with eight unknowns, which can be easily reduced toa system of four algebraic equations with four unknowns. The authors reduce this system to an equation of
one unknown by means of Seki Takakazu’s theory of elimination using, among others, the determinant of a
5 × 5 matrix.

Final ver.: 2016/2/15
5Foundation of Mathematics and History of Mathematics

11:20–11:50

Mathematics History Team Meeting

14:15–16:00
6 Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

Poisson’s paradigm in A Study of Mathematical Physics (Un Traité dePhysique Mathématique) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss Poisson’s paradigm which is consisted of the books in 1831, 1833 and 1835, namely,on the capillary action, on the mechanical problems and on the heat theory, which are his last works by thebook style in life, and within five years of Fourier’s death in 1830, in the rivalry to Fourier, Poisson works
his heavy theories including essential mathematical topics against Fourier in heat theory and Navier in fluid
dynamics, namely, in these book, Poisson mentiones the mathematical conclusions as the finishing strokes tocomplete his academic paradigm in the wave mechanics, the fluid mechanics and the heat theory. We think
his works finally rank with the Lagrange’s Méchanique analytique and the Laplace’s Méchanique céleste.
7 Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

The theories and equations of heat come from Fourier and Poisson· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss Fourier’s book and Poisson’s books on the heat problems. Poisson’s is one of his lastworks in life, and after five years of Fourier’s death, in the rivalry to Fourier, Poisson works his heat theory
including essential mathematical topics against Fourier in heat theory and Navier in fluid dynamics, namely,in these books, Poisson mentiones the mathematical conclusions as the finishing strokes of his academic
activities in the fluid dynamics and heat theory.
Why do we believe that Euler began algebraic analysis? · · · · · · · · · · · · · 15

8 Michiyo Nakane

Summary: In Japan, we have such a legend that Euler began algebraic analysis though he never named
his theory so. In Cauchy’s Cours d’Analyse: Analyse algébrique, Cauchy wrote an introductory courseof analysis was called as algebraic analysis noting Fourier’s analysis lectures. It is German translator’s
introduction of Cauchy’s book that Euler began algebraic analysis. Teizi Takagi accepted this description
and wrote his famous Kaiseki-gairon. It is an origin of the legend.
9 Ken Saito (Osaka Pref. Univ.)

Euclid’s Elements and the concept of prime factorization · · · · · · · · · · · · 15

Summary: The question is often asked whether Euclid proved the uniqueness of prime factorization. However,the question itself is wrong, for Euclid did not have the concept of prime factorization; at least he failed
to use this concept where it would have greatly simplified the proof. Through the examination of thearguments in the proposition concerning the perfect number (IX.36), I will show that this proposition isproved by preparing ad hoc lemmas, in the lack of general concept of prime factorization.
10 Koichiro Ikeda(Hosei Univ.)

A remark on non-saturated generic structures · · · · · · · · · · · · · · · · · · · · · 15

Summary: The generic construction is a new method that was invented by Hrushovski, and has given various
interesting structures. Many of them are saturated structures, but it is not well known what kind of
properties non-saturated generic structures have. In this talk, we focus on non-saturated generic structures
whose theories have finite closures, and want to explain their properties.
11 Hirotaka Kikyo(Kobe Univ.)

On constructions of countable projective planes · · · · · · · · · · · · · · · · · · · · 15

Summary: We present some observations on constructions of infinite projective planes. Projective planes are
incidence structures of points and lines. We can consider them as bipartite graphs. Any projective planeobtained as a generic structure of an ab initio type amalgamation class contains no finite projective planes
as its substructures except that of order 2 or 3. Any finite or countable bipartite graph with no 4 cycles
can be expanded to a countable projective plane. There is a countable projective plane which contains any
finite projective plane as a substructure. We also discuss problems relating to these results.

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6Foundation of Mathematics and History of Mathematics

16:15–17:15

Talk Invited by Section on Foundation and History of Mathematics

Byunghan Kim (Yonsei Univ.)

The Lascar groups and the 1st homology groups in model theory

Summary: Given a complete type p over an algebraically closed set in any complete theory T , one can define
the 1st homology group H1 (p) of p depending on the choice of an independence relation satisfying symmetry,transitivity, and extension.
(For example, if any two sets are assumed to be independent over any set, then this full independence
relation obviously satisfies the 3 axioms. Of course there is a non-trivial such relation for rosy theories too.)
We show that regardless of the choice of the independence relation, H1 (p) is always the same. More precisely,
there is the canonical epimorphism from the Lascar Galois group of p to H1 (p), and H1 (p) is G/K where G
is the group of automorphisms of p and K is the normal subgroup of G fixing each orbit of the realizationsof p under the action of the derived subgroup of G. This is a joint work with Jan Dobrowolski and Junguk
Lee.

March 17th (Thu)

Conference Room IV

10:00–11:30♭

12 Takashi Oyabu
Summary: (1)PhysicalDiﬀ(M): Physics, and other 5 talks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

laws

are

physics====DIFF(M)-physics:(2) Philosophy of mathematics:
sein:::==idea theory:

described

by

diﬀerential

equations===diﬀeomorphism:

We interprete aut(R)::epistemology in mathematical philosophy:∑(3) Entropy concept in mathematics is introduced :::2ND law of thermodynamics:: H=δdA (µi)Ui: theoryof H-theorems: dH/dt=<0====→0:(4) Galois theory and geometry: Gllois geometry: K(V),→=K(V): Galois group::□G:Γ):(5) A history of thermodynamics: Clausius::Boltzmann:Gibbs::Onsager::::Prigogine:::→Equibrium thermodynamics and non equibrium thermodynamics(6) Representation::induced representation:L2(M)=⊕dimπ(Γ)π M=ΓG:G/Γ:compact
13 Yasuhiko Omata (Tohoku Univ.)
Florian Pelupessy (Tohoku Univ.)

Dickson’s lemma and weak Ramsey theory · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Dickson’s lemma, originally used in algebra, in particular for showing Hilbert’s basis theorem, isnowadays commonly used in termination proofs in computer science. The weak Paris–Harrington theorem forpairs was originally used as an easy intermediate version in showing lower bounds for the Paris–Harrington
theorem for pairs. We provide simple constructions which show that witnesses of one of these statements
can be expressed explicitly as witnesses of the other. As a consequence these statements are equivalentover RCA∗0 . Additionally our construction provides an explicit formula for weak Ramsey numbers and tightupper bounds for the weak Paris–Harrington theorem derived from those for Dickson’s lemma.
14 Daisuke Ikegami (Tokyo Denki Univ.)

Boolean valued second order logic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the research of second order predicate logic, the following two semantics are mainly considered;full semantics (or Tarski semantics) and Henkin semantics. Full semantics can express much more things
than the standard semantics for first order logic, but it is very complicated and hard to analyze while Henkin
semantics for second order logic is essentially the same as the standard semantics for first order logic.
In this talk, we propose another semantics for second order logic which is called “Boolean valued semantics”.
We investigate the basic properties of this semantics and compare it with full semantics. This is joint workwith Jouko Väänänen.

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7Foundation of Mathematics and History of Mathematics

15 Sakaé Fuchino(Kobe Univ.)

On reflection numbers of some topological and combinatorial properties· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss about partial solutions of Galvin’s Conjecture and Hamburger’s Problem, and present
some results on the reflection numbers related to these problems.
16 Makoto Kikuchi (Kobe Univ.)
Joel David Hamkins (CUNY)

On the element-of relation and the inclusion relation in set theory · · · · 15

Summary: We proved that in the universe (V, ∈) of set theory, there is a definable relation ∈∗ , diﬀerent
from ∈, such that (V, ∈∗ ) is isomorphic to the original universe (V, ∈) and that the corresponding inclusion
relation ⊂∗ is identical to the usual inclusion relation ⊆. It follows from this fact that the element-of relation
cannot be defined in terms of the inclusion relation in set theory. We proved also that if (V, ∈∗ ) is a modelof set theory and ⊆∗ is identical to ⊆, then (V, ∈∗ ) is isomorphic to (V, ∈).
17 Masanao Ozawa (Nagoya Univ.)

Order of reals in quantum set theory: Diﬀerence of its operational
meaning for the diﬀerent choices of conditionals · · · · · · · · · · · · · · · · · · · · 15

Summary: In quantum logic there are three well-known candidates for conditional: the Sasaki conditional,
the contrapositive Sasaki conditional, and the relevance conditional. A fundamental problem is to show how
the choice aﬀects the probabilistic interpretation of quantum theory. Here, we attempt such an analysis
through quantum set theory. We construct models of quantum set theory based on the above conditionals
and consider equality and order between reals in those models. We show that the truth values of theequality are the same, whereas those of the order significantly depend on the underlying conditional. We
characterize their operational meanings by joint probability for successive projective measurements. Thosecharacterizations will play an important role in applications of quantum set theory to quantum physics.
11:30–12:00

Research Section Assembly

13:15–14:25
18 Takahiro Seki

(Niigata Univ.)

The decidability of some non-associative substructural logics · · · · · · · · 15

Summary: Associativity (of fusion) is regarded as one of the important structural rules. Recently, somestudies on non-associative substructural logics have been developed. In this talk, we show that some
non-associative substructural logics are decidable using a Gentzen-style formulation.
19 Yoshihito Tanaka(Kyushu Sangyo Univ.)

Axioms of S4.3 in EL and their algebraic models · · · · · · · · · · · · · · · · · · · 15

Summary: In this report, we introduce two sets AS4.3 and BS4.3 of concept inclusions of EL which axiomatize
modal logic S4.3, and discuss their algebraic models. The standard semantics for EL is equivalent tocomplete atomic completely additive Boolean algebras with operators (CA) model, but a natural algebraic
semantics defined from the logical connectives of EL is semilattices with operators (SLO) model. We showthat the sets of SLOs defined by AS4.3 and BS4.3 are not equal, while the sets of CAs defined by them
are equal. We also prove that SLO model and CA model are not equivalent when either AS4.3 or BS4.3 ofaxioms are assumed. This is a joint work with S. Kikot, A. Kurucz, F. Wolter and M. Zakharyaschev.
20 Kenshi Miyabe(Meiji Univ.)

Mass problem of randomness notions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study Muchnik degrees and Medvedev degrees of randomness notions, which can be seen as
subsets of the Cantor space. In order to separate the randomness notions, we need detailed information ofTuring degrees and uniformity.

Final ver.: 2016/2/15
8Foundation of Mathematics and History of Mathematics

21 Kohtaro Tadaki (Chubu Univ.)

An operational characterization of the notion of probability by algorithmic randomness II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of probability plays an important role in almost all areas of science and technology.
In modern mathematics, however, probability theory means nothing other than measure theory, and theoperational characterization of the notion of probability is not established yet. In our former work, basedon the toolkit of algorithmic randomness we presented an operational characterization of the notion ofprobability. Algorithmic randomness is a field of mathematics which enables us to consider the randomnessof an individual infinite sequence. We used the notion of Martin–Loef randomness with respect to Bernoulli
measure to present the operational characterization, in particular, to finite probability spaces. In this talk,we present an operational characterization of the notion of probability to an arbitrary discrete probability
space whose sample space is countably infinite.

Final ver.: 2016/2/15
9AlgebraAlgebraMarch 16th (Wed)Conference Room I

9:30–12:00
1 Toshio Sumi (Kyushu Univ.)
Mitsuhiro Miyazaki(Kyoto Univ. of Edu.)
Toshio Sakata (Kyushu Univ.)

On the real radical of determinantal ideals of matrices defined by certain
tensors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In studying tensor rank over the real number field, we used the theory of determinantal ideals
over a commutative ring. We developed a theory on the determinantal ideal of a matrix defined by a tensor
in order to pursue our study of tensor rank which is interesting in its own right. In this talk, we report our
result.
2 Takafumi Shibuta (Kyushu Univ.)
Shinichi Tajima (Univ. of Tsukuba)

Computation of the standard basis of modules based on Matlis duality· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let R be a ring of power series over a field. In this talk, we give an algorithm for computing thestandard basis of a module M which is a submodule of a free R-module F such that F/M has finite length.
The algorithm is based on Matlis duality.
3 Yusuke Suyama (Osaka City Univ.)

The Ehrhart polynomial of a 3-dimensional simple integral convex
polytope · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For a simple integral convex polytope P of dimension d, Pommersheim gave a method forcomputing the (d − 2)-th coeﬃcient of the Ehrhart polynomial of P by using toric geometry. In this talk,we give a formula for the Ehrhart polynomial of P of dimension 3 by applying this method.
4 Akiyoshi Tsuchiya (Osaka Univ.)
Takayuki Hibi (Osaka Univ.)
Kazunori Matsuda (Osaka Univ.)

Normal Gorenstein Fano polytopes arising from partially ordered sets
and the Ehrhart polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from afinite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ).
In this talk, we will introduce study on Ehrhart polynomials of three normal Gorenstein Fano polytopes
Γ(O(P ), −O(Q)), Γ(O(P ), −C(Q)) and Γ(C(P ), −C(Q)), where P and Q are partially ordered sets with
|P | = |Q|.
5 Kazuho Ozeki (Yamaguchi Univ.)
Maria Evelina Rossi (Genova Univ.)

The structure of the Sally module of integrally closed ideals · · · · · · · · · 15

Summary: The first two Hilbert coeﬃcients of a primary ideal play an important role in commutative
algebra and in algebraic geometry. In this paper we give a complete algebraic structure of the Sally
module of integrally closed ideals I in a Cohen–Macaulay local ring A satisfying the equality e1 (I) =e0 (I) − ℓA (A/I) + ℓA (I 2 /QI) + 1, where Q is a minimal reduction of I, and e0 (I) and e1 (I) denote the firsttwo Hilbert coeﬃcients of I.
6 Akihiro Higashitani(Kyoto Sangyo Univ.)

Almost Gorenstein standard graded rings and their h-vectors · · · · · · · · 15

Summary: Recently, for the study of a new class of local or graded rings which are Cohen–Macaulay but not
Gorenstein, almost Gorenstein local or graded rings were defined and have been studied. In this paper, forthe further study of almost Gorenstein rings, we concentrate on almost Gorenstein standard graded rings
and investigate the h-vectors of almost Gorenstein standard graded rings.

Final ver.: 2016/2/15
10

Algebra7 Satoshi Yamanaka (Okayama Univ.) ♭ Some remarks on the weakly separability in skew polynomial rings · · · 10
Summary: The notion of weakly separable extensions was introduced as a generalization of separable extensions. In this talk, we shall study the diﬀerence between the separability and the weakly separability inskew polynomial rings of derivation type B[X; D]. Moreover, we shall treat weakly separable polynomials
in the general case B[X; ρ, D].
8 Naoyuki Matsuoka (Meiji Univ.)(Meiji Univ.)
Shiro Goto
Naoki Taniguchi (Meiji Univ.)
Ken-ichi Yoshida (Nihon Univ.)

The almost Gorenstein Rees algebras of contracted ideals · · · · · · · · · · · 15

Summary: Let (A, m) be a two-dimensional regular local ring with infinite residue class field A/m. GotoMatsuoka–Taniguchi–Yoshida showed that the Rees algebras of integrally closed ideals are almost Gorenstein.
Then one can ask how about the case when I is contracted. The purpose of this talk is to give an answer
to this question.
9 Kei-ichi Watanabe (Nihon Univ.) ♭ A characterization of two-dimensional rational singularities via Core of
Tomohiro Okuma (Yamagata Univ.) ideals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Kenichi Yoshida (Nihon Univ.)
Summary: We give a concrete description of the core of pg -ideals in 2-dimensional normal sngularities andas consequences, we give a characterization of rational singularities and prove the existence of good ideals.
14:15–16:50
10 Shigeru Iitaka (Gakushuin Univ.⋆)

On ϕ perfect numbers with respect to Euler’s function · · · · · · · · · · · · · · 10

Summary: Let P be a prime and m a positive integer. If ϕ(P e ) + 1 + m is prime then a = P e q is said to be(ϕ, m) perfect number.
11 Aiichi Yamasaki (Kyoto Univ.)
Akinari Hoshi (Niigata Univ.)
Ming-chang Kang (Nat. Taiwan Univ.)

Degree three unramified cohomology groups · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let p be an odd prime number. Peyre shows that there is a group G of order p12 such that
3
Hnr
(C(G), Q/Z) is non-trivial. Using Peyre’s method, we are able to prove that the same conclusion is true
for some groups of order p9 .
12 Aiichi Yamasaki (Kyoto Univ.)
Akinari Hoshi (Niigata Univ.)

Bravais group of dimension n ≤ 6 and corresponding quadratic forms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We confirm that H 1 (G, F ) = 0 for any Bravais group G if dimension n ≤ 6 where F is the flabby
class of the corresponding G-lattice of rank n (Voskresenskii’s conjecture). By using the algorithm wedeveloped, one can obtain (positive definite) invariant quadratic forms f under the action of Bravais group
G ≤ GL(n, Z).
13 Akinari Hoshi (Niigata Univ.)

On Noether’s problem for cyclic groups of prime order · · · · · · · · · · · · · · 15

Summary: Let k be a field and G be a finite group acting on the rational function field k(xg | g ∈ G)
by k-automorphisms h(xg ) = xhg for any g, h ∈ G. Noether’s problem asks whether the invariant fieldk(G) = k(xg | g ∈ G)G is rational (i.e. purely transcendental) over k. In 1974, Lenstra gave a necessary andsuﬃcient condition to this problem for abelian groups G. However, even for the cyclic group Cp of prime
order p, it is unknown whether there exist infinitely many primes p such that Q(Cp ) is rational over Q.
Only known 17 primes p for which Q(Cp ) is rational over Q are p ≤ 43 and p = 61, 67, 71. We show that forprimes p < 20000, Q(Cp ) is not (stably) rational over Q except for aﬃrmative 17 primes and undetermined
46 primes. Under the GRH, the generalized Riemann hypothesis, we also confirm that Q(Cp ) is not (stably)
rational over Q for undetermined 28 primes p out of 46.

Final ver.: 2016/2/15
11

Algebra14 Akinari Hoshi (Niigata Univ.)
Hidetaka Kitayama (Wakayama Univ.)

Three-dimensional purely quasi-monomial actions · · · · · · · · · · · · · · · · · · 15

Summary: Let G be a finite subgroup of Autk (K(x1 , . . . , xn )) where K/k is a finite field extension andK(x1 , . . . , xn ) is the rational function field with n variables over K. The action of G on K(x1 , . . . , xn ) is
called quasi-monomial if it satisfies the following three conditions (i) σ(K) ⊂ K for any σ ∈ G; (ii) K G = k∏nawhere K G is the fixed field under the action of G; (iii) for any σ ∈ G and 1 ≤ j ≤ n, σ(xj ) = cj (σ) i=1 xi ij
where cj (σ) ∈ K × and [ai,j ]1≤i,j≤n ∈ GLn (Z). A quasi-monomial action is called purely quasi-monomial
if cj (σ) = 1 for any σ ∈ G, any 1 ≤ j ≤ n. When k = K, a quasi-monomial action is called monomial.
The main problem is that, under what situations, K(x1 , . . . , xn )G is rational over k. We determine therationality when n = 3 and the action is purely quasi-monomial except for few cases. As an application, we
will show the rationality of some 5-dimensional purely monomial actions which are decomposable.
15 Tetsuya Ando

(Chiba Univ.)

PSD cone on a semialgebraic set · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We define a semialgebraic set of a real algebraic variety. This notion is stable under regularmaps. We prove that an open set of a real algebraic variety with an algebraic boundary is semialgebraic.
For a given linear system H on the real algebraic variety X and a semialgebraic set A of X, the set of
all the functions in H which is positive semidefinite on A is called a PDS cone of H on A. This cone issemialgebraic. We study the structure of PSD cones.
16 Goo Ishikawa (Hokkaido Univ.)
Tatsuya Yamashita (Hokkaido Univ.)

Leibniz complexity of Nash functions on diﬀerentiations · · · · · · · · · · · · · 15

Summary: We show that, for any non-Nash analytic function, it is impossible to derive its derivatives
algebraically, i.e., by using linearity and Leibniz rule finite times. In fact we prove algebraically theimpossibility of algebraic computations, by using Kähler diﬀerentials. Then the notion of Leibniz complexityof a Nash function is introduced as the minimal number of usages of Leibniz rules to compute the total
diﬀerential algebraically. We provide general observations and upper estimates on Leibniz complexity ofNash functions.
17 Katsumi Akahori(Gifu Pharmaceutical Univ.)

Remarks on normal generation of special line bundles with deg(L) <2g − 1 − 4h1 (L) on algebraic curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let L be a special very ample line bundle with degree deg(L) on a smooth projective curve X oflarge enough genus g. One says that L is normally generated if X is projectively normal under the associatedprojective embedding. We show that L is normally generated if deg(L) ≥ 2g − 2s + 1 − 2(s + 1)h1 (L)(s ≥ 2)
and X is not a m(m ≤ s)-sheeted covering.
18 Shinya Kitagawa(Gifu Nat. Coll. of Tech.)An example of a genus two fibration with no section on a rational surface· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Every genus two fibration on a smooth projective surface whose geometric genus is zero has a notnecessarily eﬀective divisor whose intersection number with a general fibre equals one. However there exists
a genus two fibration with no section on a rational surface.

Final ver.: 2016/2/15
12

AlgebraMarch 17th (Thu)

Conference Room I

9:30–12:00♭
Further refinement of Shokurov’s projectivity criterion · · · · · · · · · · · · · · 15
19 Tomohiro Iwami(Kyushu Sangyo Univ.)

Summary: The author gave a certain refinement of Shokurov’s projectivity criterion, September 2012, basedon several theory of semi-log canonical (slc) pairs mainly developed by J. Kollar. On the other hand, after
then,projectivity criterion for moduli spaces are rapidly achieved with special regards to the compactificationof moduli of varieties of general type. In this talk,the author will report further refinement of Shokurov’s
projectivity criterion, as succeeding to the author’s previous refinement, based on global extendability
property associated to certain strata for slc pairs appearing in O. Fujino’s recent work.
20 Yoshiaki Fukuma (Kochi Univ.)

On polarized 4-folds (X, L) with h0 (KX + 3L) ≤ 1 · · · · · · · · · · · · · · · · · 15

Summary: Let (X, L) be a polarized manifold of dimension n. Then we want to study (X, L) with small
h0 (KX + (n − 1)L). This topic relates to a conjecture of Beltrametti and Sommese. It has been alreadystudied for n ≤ 3. So, in this talk, we will consider the case n = 4, and we will give a classification of (X, L)
with h0 (KX + 3L) ≤ 1.
21 Atsushi Noma (Yokohama Nat. Univ.)

Regularity of projected Roth varieties · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We work over an algebraically closed field of characteristic zero. The purpose here is to study theCastelnuovo–Mumford regularity of projected Roth varieties, which are divisors of rational scrolls of certain
types. These varieties appear, as an exceptional case, in the study of finding whether a projective variety isdefined by equations of the expected low degree.
22 Tomoo Matsumura(Okayama Univ. of Sci.)(Postech)Thomas Hudson

Segre classes in algebraic cobordism · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will explain a new result about the Segre classes of vector bundles in algebraic
cobordism introduced by Levine–Morel.
23 Yuki Kato (Ube Nat. Coll. of Tech.)

Loop stacks of the aﬃne motivic stack of K-theory · · · · · · · · · · · · · · · · · 15

Summary: We introduce the theory of motivic derived algebraic geometry which is obtained by combining
Lurie’s derived algebraic geometry and Voevodsky’s A1 -homotopy theory. By applying the theory of motivic
derived algebraic geometry to algebraic K-theory, we define the pointed P1 -loop stack of the aﬃne motivic
stack of the K-theory spectrum. By our main result, we obtain a relation between the pointed P1 -loop stackof the K-theory and the logarithmic diﬀerential form Bott element on the K-theory.
24 Yu Yasufuku(Nihon Univ.)

Vojta’s conjecture on surfaces, the abc conjecture, and Farey sequences· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We prove Vojta’s conjecture for certain rational surfaces. Moreover, for certain other rationalsurfaces, we prove that the Vojta’s conjecture implies a special case of the abc conjecture, whose proof
has been announced by Mochizuki. Conversely, we will also show that the abc conjecture implies Vojta’s
conjecture for these surfaces. For the proofs, we will use some properties of Farey sequences.
25 Hiroshi Tsunogai (Sophia Univ.)
Michihiko Sawa (Sophia Univ.)

Determination of Galois orbits of genus 1 dessins of degree up to 6
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We calculated the defining equations of all Belyi pairs of genus 1 of degree up to 6, and determined
the Galois orbits in these cases. As a result, we show that these Galois orbits can be separated by known
Galois invariants of dessins: valency lists, monodromy groups, Nielsen classes, cartographic groups andautomorphism groups.

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13

Algebra

The Riemann–Hilbert correspondence for unit F -crystals · · · · · · · · · · · · 15

26 Sachio Ohkawa (Univ. of Tokyo)

Summary: Let X be an algebraic variety defined over a perfect field k of characteristic p > 0 with anembedding X ,→ P into a proper smooth scheme P over the Witt ring Wn (k). We show that thetriangulated category of bounded complexes of DP/Wn (k) -modules with unit Frobenius structures supported
on X satisfying certain conditions does not depend on the choice of embeddings and this triangulated
category is anti-equivalent to the triangulated category of bounded complexes of étale sheaves of Z/pn Zmodules with constructible cohomology sheaves and of finite Tor dimension. Our results can be regarded asa generalization of some part of the Emerton–Kisin theory of the Riemann–Hilbert correspondence for unit
F -crystals to the case of embeddable algebraic varieties in characteristic p.
27 Yûsuke Okuyama (Kyoto Inst. Tech.)

A potential theoretic characterization of polynomials among rational
functions on the Berkovich projective line · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let K be an algebraically closed field that is complete with respect to a non-trivial and possibly
non-archimedean absolute value | · |. Let P1 = P1 (K) be the Berkovich projective line over K, which
is a compactification of P1 = P1 (K). A potential theory on P1 has been developed by Baker–Rumely,
Favre–Rivera-Letelier, and Thuillier.
We say a rational function f ∈ K(z) of degree > 1, which canonically acts on P1 , has a potentially good∪
reduction if there is a point S ∈ P1 \ P1 such that # n∈N f −n (S) < ∞, and otherwise, f has no potentiallygood reductions. In this talk, we will talk about a characterization of polynomials among rational functions,
up to rational functions having potentially good reductions as exceptions, in terms of potential theory anddynamics on P1 .

March 18th (Fri)

Conference Room I

9:00–12:00
28 Yasutoshi Nomura♭

On congruences of Apery-like numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let A(n), ..., G(n) denote Apery-like numbers in which A(n) and B(n) were introduced by R.
Apery. In this talk we state some conjectures about values mod p, p prime, of numbers: X(p-m) for odd p,
1<m<p, X((pp-1)/8) for odd p, X((ppp-e)/9) for p congruent to e mod 3, e=1 or -1, where X denote oneof A, B, ..., G.
29 Taka-aki Tanaka (Keio Univ.)
Miho Nakashima (Keio Univ.)

On the algebraically independent subsets of the ‘intersection’ of the real
numbers R and the finite number of the p-adic fields Qp · · · · · · · · · · · · 10

Summary: The main result of this talk asserts the algebraic independence of the limits of fixed sequences ofrational numbers with respect to the ordinary absolute value and to the finite number of the p-adic absolutevalues. We regard such limits, which are indeed the values at a rational point of Mahler functions over Q,
as numbers belonging to the ‘intersection’ of the rational numbers R and the finite number of the p-adic
fields Qp .
30 Takahisa Kawada(Nagoya Inst. of Tech.)
Masakazu Yamagishi(Nagoya Inst. of Tech.)On the unimodality of the coeﬃcients of Gegenbauer polynomials · · · · 15

Summary: In this talk, we will focus on the unimodal property of the sequence of the coeﬃcients ofGegenbauer polynomials Cnλ (x). We classify the Gegenbauer polynomials with 2 modes in the case λ ∈ Z.
This generalizes a result of Belbachir–Bencherif in which they treated (essentially) the cases λ → 0 and
λ = 1, i.e., the Chebyshev polynomials of the first and second kind. We also study asymptotic behavior of
the mode of Cnλ (x) as a function of n.

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14

Algebra31 Yoshio Tanigawa (Nagoya Univ.)
Jun Furuya(Hamamatsu Univ. School of Medicine)
Makoto Minamide (Yamaguchi Univ.)

On a restricted divisor problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We shall consider the function dα (n) which denotes the number of positive divisors k of a positive∑
integer n satisfying nα ≤ k ≤ n1−α (0 < α < 1/2). We deduce the asymptotic formula for n≤x dα (n),where α = 1/N (N is a positive integer ≥ 3). Moreover, we study the mean square of the error term of theformula.
32 Debika Banerjee(Harish-Chandra Res. Inst.)
Makoto Minamide (Yamaguchi Univ.)

On the first moment of ∆(1) (x) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We define an arithmetical function D(1) (n) by the coeﬃcients of the Dirichlet series (ζ ′ (s))(Re s > 1), where ζ ′ (s) is the derivative of the Riemann zeta function. We are studying the error term∑∆(1) (x) in the asymptotic formula forn≤x D(1) (n). In this talk, we show some formulas on the first2

moment of ∆(1) (x).
33 Yuta Suzuki(Nagoya Univ.)

On the sum of a prime and a prime power · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the additive problem of expressing positive integers as a sum of a prime
and a prime power. In particular, we study the exceptional set for the asymptotic formula of Hardy–
Littlewood type in short intervals. As for the asymptotic formula without any restriction, we succeeded in
improving the previous result of C. Bauer (1998).
34 Kaneaki Matsuoka (Nagoya Univ.) ♭ Mean values of higher derivatives of Hardy’s function · · · · · · · · · · · · · · · 10
Summary: I will talk about Mean values of higher derivatives of Hardy’s function
35 Tomoya Machide(Nat. Inst. of Information/JST ERATO)

On identities involving cyclic sums of regularized multiple zeta values
each of depth less than 5 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give identities involving cyclic sums of regularized multiple zeta values of depth
less than 5. As a corollary, we present an extension of Hoﬀman’s theorem for symmetric sums of multiple
zeta values for this case.
36 Tomohiro Ooto (Univ. of Tsukuba)

Properties of Diophantine exponents for formal Laurent series over afinite field · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study about Mahler’s exponent wn and Koksma’s exponent wn∗ for formal Laurent
series over a finite field. We give some results related to the spectrum of the function wn − wn∗ and that of
the function wn at algebraic points.
37 Fumihiro Sato (Rikkyo Univ.⋆)
Kazunari Sugiyama(Chiba Inst. of Tech.)
Takahiko Ueno
(St. Marianna Univ. School of Med.)Real analytic automorphic forms arising from certain prehomogeneous
zeta functions in two variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we explain that the zeta functions in two variables attached to a certain prehomogeneous vector space related to quadratic forms are essentially the Mellin transforms of real analytic
automorphic forms.

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Algebra38 Tadashi Okazaki (Nat. Taiwan Univ.)

Prime number and scaling dimension via Whittaker function · · · · · · · · 15

Summary: We show that the dilatation expectation values in conformal quantum mechanics lead to theasymptotic smoothed counting function of the Riemann zeros. We propose a conceivable implication
between fundamental building blocks in math and in physics as a prime number in number theory and ascaling dimension in quantum mechanics.
39 Koji Yamagata (Nagoya Inst. of Tech.)
Masakazu Yamagishi(Nagoya Inst. of Tech.)On the ring of integers of real cyclotomic fields · · · · · · · · · · · · · · · · · · · · 15

Summary: Let ζ be a primitive nth root of unity. As is well known, Z[ζ + ζ −1 ] is the ring of integersof Q(ζ + ζ −1 ). We give an alternative proof of this fact by using the resultants of modified cyclotomic
polynomials.
14:15–14:30

Presentation Ceremony for the 2016 MSJ Algebra Prize

14:30–15:30

Award Lecture for the 2016 MSJ Algebra Prize

Kazuhiko Kurano (Meiji Univ.)

Intersection theory over local rings and its application to the theory of
Cohen–Macaulay modules

Summary: P.Roberts applied the singular Riemann–Roch theory to commutative ring theory in the 1980s,
and aﬃrmatively solved Serre’s vanishing conjecture of intersection multiplicities in 1987. On the other
hand, Dutta, Hochster and McLauglhin gave a counterexample to the generalized vanishing conjecture in
1985. After that, by the research of Levine, Roberts, Srinivas, etc, we know that such an example are notabnormal. Therefore we should study why such examples exist. Using functions does not vanish like this,we define the notion of numerical equivalence on the K-group G0 (A) of finitely generated modules over a
Noetherian local rings A. We prove that G0 (A) (the K-group divided by the numerical equivalence) becomesa lattice. Maximal Cohen–Macaulay (MCM) modules play a role of positive elements in this situation. We
consider the cone spanned by MCM’s in the lattice tensored with the real number field R. Studying thiscone, we prove that, for each positive integer r, there exist only finitely many numerical types of MCM’s ofrank r. Furthermore, there exist only finitely many MCM’s of rank 1 over isolated hypersurface singularities
of dimension 3. For such rings, we prove that G0 (A) ≃ Z ⊕ Cl(A), in particular Cl(A) is torsion free. By
this formula, we know that, if such a ring is not UFD, there exists an example like Dutta, Hochster and
McLauglhin. (Isolated complete intersection singularities of dimension d are UFD if d ≥ 4. In the case ofd = 2, there exist examples that have infinitely many MCM ideals.) A part of these results are joint workwith Hailong Dao (University of Kansas).
15:40–16:40

Award Lecture for the 2016 MSJ Algebra Prize

Masa-Hiko Saito (Kobe Univ.)

Moduli spaces of connections and diﬀerential equations of Painlevé type

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Algebra16:50–17:50

Award Lecture for the 2016 MSJ Algebra Prize

Hidenori Katsurada(Muroran Inst. of Tech.)

Periods and congruences of automorphic forms and related topics

Summary: For a primitive form f for SL2 (Z), let fb be a certain lift of f to the space Sl (Γ ) of cusp forms
for some another modular group Γ , that is, let fb be a Hecke cuspidal eigenform whose certain L-function isexpressed in terms of certain L-functions of f . Then we ask the following question:⟨fb, fb⟩(A). Express the ratio
e of periods (Petersson products) in terms of special values of certain L-functions⟨f, f ⟩of f .
If the answer to (A) is aﬃrmative, the algebraic parts of such L-values are sometimes related with congruence
for fˆ, and in particular we ask the following question:(B). Characterize primes giving congruence between fb and another Hecke eigenform in Sl (Γ ) not comingfrom the lift in terms of the invariants in (A).
In this talk, we give an aﬃrmative answer to (A) in the case where fˆ is the Duke–Imamoglu–Ikeda lift or
the Hermitian Ikeda lift, and to (B) in the case where fˆ is the Duke–Imamoglu–Ikeda lift. We also discuss
some other related topics.

March 19th (Sat)

Conference Room I

9:30–12:00
40 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)
Hiroshi Michiwaki (NejiLaw Inc.)
Masato Yamada(Inst. of Reproducing Kernels)

Reality of the division by zero z/0 = 0 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We will give some clear evidences of the reality of the division by zero z/0 = 0 with a fundamental
algebraic theorem, and physical and geometrical examples; that is, A) a field structure containing thedivision by zero, B) by the gradient of the y axis on the (x, y) plane, C) by the reflection 1/z of z withrespect to the unit circle with center at the origin on the complex z plane, and D) by considering rotationof a right circle cone having some very interesting phenomenon from some practical and physical problem.
41 Saburou Saitoh(Gunma Univ.⋆/Inst. of Reproducing Kernels)
Masato Yamada(Inst. of Reproducing Kernels)

The concept of divisions (fractionals) in fields containing the divisionby zero · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We will introduce the concept of the divisions (fractions) in fields containing the division by zero
whoes concept is a natural extension of the division by zero z/0 = 0 on the complex field C.
42 Osamu Shimabukuro (Nagasaki Univ.)
Akihide Hanaki (Shinshu Univ.)

Modular adjacency algebras and standard representations of wreath
products of complete graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let λ be a given non-negative integer sequence (q1 , q2 , · · · , qn ) (qi ≥ 2, 1 ≤ i ≤ n). (X λ , S λ ) bean association scheme Kq1 ≀ Kq2 ≀ · · · ≀ Kqn defined by a repeated wreath product of complete graph Kqi withqi vertices for 1 ≤ i ≤ n and F be a field of characteristic p. We consider the structure of this scheme overF.

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Algebra43 Katsuhiko Kuribayashi (Shinshu Univ.)
Yasuhiro Momose (Shinshu Univ.)

On Mitchell’s embedding theorem for a quasi-schemoid · · · · · · · · · · · · · 15

Summary: A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial
data. In this talk, Mitchell’s embedding theorem for a tame schemoid is discussed. One of main theorems
allows us to give a cofibrantly generated model category structure to the category of chain complexes overa functor category with a schemoid as the domain.
44 Hideo Kamimura(Fukuoka Inst. of Tech.)Isao Kikumasa (Yamaguchi Univ.)
Yosuke Kuratomi (Yamaguchi Univ.)

On direct projective H-supplemented modules · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider a direct projective H-supplemented module which is a generalizationof a discrete module. We show that any direct projective H-supplemented module satisfies the exchange
property and also that if M1 and M2 are direct projective H-supplemented modules, then M = M1 ⊕ M2 isdirect projective H-supplemented if and only if Mi is radical Mj -projective (i ̸= j).
45 Ryo Tabata (Ariake Nat. Coll. of Tech.)Kazuya Aokage(Ariake Nat. Coll. of Tech.)

Congruences on irreducible spin characters of symmetric groups · · · · · · 10

Summary: There are congruences on the irreducible characters of ordinary representations of finite groups.
The similar type of relations for irreducible spin characters has not been found, although the spin analoguesof many properties to the ones of ordinary representations are expected to appear.
It is known that the row and column in the spin character table (ζρ (λ))ρ,λ of the symmetric group Sn areparametrized by strict partitions ρ and odd partitions λ of n, respectively. In terms of this, we will explainsome congruences of the spin characters with respect to Sn ; ζρ (λ) ≡ ±ζρ (µ) mod p, where the sign depends
on the prime number p and its multiplicity that compose diﬀerent parts in λ and µ. As the result of this, aconjecture will also be presented.
46 Kenichi Shimizu (Nagoya Univ.)

Remarks on non-semisimple modular tensor categories · · · · · · · · · · · · · · 15

Summary: We show that a ribbon finite tensor category is a modular tensor category in the sense of
Lyubashenko if and only if it is a factorizable braided tensor category in the sense of Etingof, Nikshych
and Ostrik. As a consequence, the monoidal center Z(C) of a finite tensor category C is a modular tensor
category provided that Z(C) is a ribbon category. Generalizing a result of Kauﬀman and Radford, we givea necessary and suﬃcient condition for Z(C) to be a ribbon category. As an application, we show that Z(C)is a modular tensor category if C is spherical in the sense of Douglas, Schommer–Preis and Snyder.
47 Tsunekazu Nishinaka (Univ. of Hyogo)

Uncountable locally free groups and their group rings · · · · · · · · · · · · · · · 10

Summary: A group is called locally free if all of its finitely generated subgroups are free. Clearly, a locally
free group G whose cardinality is countable has always a countably infinite subgroup which is free. In thistalk, we extend this fact to the result for the general cardinality case: If G is a locally free group, then G
has a free subgroup whose cardinality is the same as that of G itself.
48 Hiroki Shimakura (Tohoku Univ.)

On orbifold constructions of holomorphic vertex operator algebras ofcentral charge 24 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, I will explain orbifold constructions of holomorphic vertex operator algebras andrecent progress on the classification of holomorphic vertex operator algebras of central charge 24.

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Algebra49 Yusuke Arike (Univ. of Tsukuba)
Masanobu Kaneko (Kyushu Univ.)
Kiyokazu Nagatomo (Osaka Univ.)
Yuichi Sakai

Aﬃne vertex operator algebras and modular linear diﬀerential equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a C2 -cofinite and rational vertex operator algebra V , there is a modular linear diﬀerential
equation whose space of solutions contains the space of characters of simple V -modules. In general, thespace of solutions of this modular linear diﬀerential equation does not always coincide with the space ofcharacters of simple V -modules. In this talk we focus on aﬃne vertex operator algebras and show that the
spaces of characters of simple modules of aﬃne vertex operator algebras coincide with the spaces of solutionsof modular linear diﬀerential equations if the dimensions of the spaces of characters are at most 5.
50 Yusuke Arike (Univ. of Tsukuba)
Kiyokazu Nagatomo (Osaka Univ.)
Yuichi Sakai

Vertex operator algebras, minimal models, and modular linear diﬀerential equations of order 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we classify vertex operator algebras with two conditions which arise from Virasoro
minimal models. One is that the space of characters of simple modules is the space of solutions of amodular linear diﬀerential equation of order 4. The other restricts dimensions of spaces of lower weights ofa vertex operator algebra. It is shown that such vertex operator algebras have central charges c = −46/3,−3/5, −114/7, 4/5, and are isomorphic to minimal models for c = −46/3, −3/5 and their extensions forc = −114/7, 4/5.
14:15–15:45
51 Hiroshi Yamauchi(Tokyo Woman’s Christian Univ.)
Ching Hung Lam (Academia Sinica)

On types of Miyamoto involutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will use VOAs generated by 3-dimensional Griess algebras and determine types of Miyamoto
involutions associated to simple Virasoro vectors on the commutant subalgebras. We can apply this result
to Conway–Miyamoto correspondeces for Monster, Baby–Monster and Fischer 3-transposition groups.
52 Tomohiro Kamiyoshi(Matsue Coll. of Tech.)
Yoshiteru Kurosawa(Numazu Nat. Coll. of Tech.)
Hiroshi Nagase (Tokyo Gakugei Univ.)
Makoto Nagura(Nara Nat. Coll. of Tech.)

Counting hom-orthogonal partial tilting modules associated with valued
Dynkin graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We count the number of isomorphism classes of hom-orthogonal partial tilting modules over tensor
algebras of valued graph of Dynkin type; that is, of type Bn , Cn , F4 , and G2 . This number is independent
on the choice of an oriented modulation of the graph. In our presentation, we will give an explanation ontype Bn as an example, with combinatorial detail.
(Shizuoka Univ.)
53 Izuru Mori
Kenta Ueyama (Hirosaki Univ.)

Tilting theory for noncommutative quotient singularities · · · · · · · · · · · · 15

Summary: In the study of triangulated categories, tilting objects play a key role. They often enable us
to realize abstract triangulated categories as concrete derived categories of modules over algebras. In
this talk, we show that the derived category of the noncommutative projective scheme associated to a“noncommutative quotient isolated singularity” has a tilting object. Moreover, we also show that the stable
category of graded maximal Cohen–Macaulay modules over a “noncommutative Gorenstein quotient isolated
singularity” has a tilting object. As a consequence, these categories are triangle equivalent to the derived
categories of finite dimensional algebras.

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Algebra54 Kengo Miyamoto (Osaka Univ.)

A component of the stable AR quiver that contains Heller lattices:
the case of the Kronecker algebra over complete discrete valuation ring
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let A be the Kronecker algebra over a complete discrete valuation ring O, and we consider the
additive category consisting of A-lattices M with the property that M ⊗ K is projective as an A ⊗ K-module,
where K is the fraction field of O. We determine the shape of the component of the stable Auslander–Reiten
quiver, say C, that contains Heller lattices of vertical modules and horizontal modules of the Kronecker
algebra O[X, Y ]/(X 2 , Y 2 ). Consequently, we have C = ZA∞ .
55 Ayako Itaba (Shizuoka Univ.)
Gahee Kim (Shizuoka Univ.)

Frobenius Koszul algebras and superpotential · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let k be an algebraically closed field of characteristic 0, A a graded k-algebra finitely generated
in degree 1 and V a k-vector space. For a Frobenius Koszul algebra A satisfying (rad A)4 = 0, we consider
the following two conjectures: (I) for every A, there exist a superpotential w ∈ V ⊗3 and an automorphism τof V such that the Koszul dual A! of A and the derivation-quotient algebra D(wτ ) of wτ are isomorphic as
graded algebras; (II) for every A, there exists a symmetric algebra S such that A and S are graded Morita
equivalent. In this talk, we give partial results for the above two conjectures.
16:00–17:00

Talk Invited by Algebra Section

Pierre Baumann(Univ. de Strasbourg, CNRS)

Paths, polytopes and loops in representation theory

Summary: One word has been on purpose omitted from the title of this talk, and this word is crystal. As
is well-known nowadays, Kashiwara’s theory of crystals is a device that give combinatorial insight into
the representation theory of a semisimple Lie algebra. I will focus on two concrete models that incarnate
crystals: Littelmann’s path models and Anderson and Kamnizter’s MV polytopes. I will also focus on two
geometric devices that allow to construct the finite-dimensional representations of a semisimple Lie algebra:
the geometric Satake correspondence and Lusztig’s nilpotent varieties. MV polytopes naturally emerge inboth settings, but in two very diﬀerent fashions. Moreover, Littelmann’s path model is closely related to
the geometric Satake correspondence. (This connection somehow boils down to the observation that thegeometric Satake correspondence makes use of loop groups, and that loops are closed paths.) Through thegeometric Satake correspondence, there is thus an indirect connection between Littelmann’s paths and MV
polytopes. Unfortunately, one does not know yet how to extend this connection to the case of aﬃne Liealgebras, though Littelmann’s paths and MV polytopes both exist in this setting.

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Geometry

Geometry
March 16th (Wed)Conference Room V

9:30–12:00
1 Sampei Hirose (Shibaura Inst. of Tech.)Jun-ichi Inoguchi (Univ. of Tsukuba)
Kenji Kajiwara (Kyushu Univ.)
Nozomu Matsuura (Fukuoka Univ.)
Yasuhiro Ohta (Kobe Univ.)

Discretization of the vortex filament equation · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The local induction equation, or the binormal flow on space curves is a well-known model of
deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature isgoverned by the nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, amodel of deformation of discrete space curves by the discrete nonlinear Schrödinger equation.
(Chiba Univ.)
2 Jun O’Hara
Gil Solanes(Univ. Autònoma de Barcelona)

Regularization of Riesz energy of submanifolds · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the regularization of Riesz energy (which is the integration of the distance between
a pair of points to some power on the product space) of knots, closed surfaces, and convex bodies in the
Euclidean spaces. We study two types of geometric quantities, Hadamard’s finite part of the energy andresidues of the energy generalized by analytic continuation.
3 Takanari Saotome(Shibaura Inst. of Tech.)

The Olivier Rey’s inequality on the Heisenberg group · · · · · · · · · · · · · · · 15

Summary: We will study CR analogue of the Olivier Rey’s inequality on the Heisenberg group. In confromalsetting this inequality is used to prove the existence of the solution to the linearized Yamabe equation.
This inequality shows that the energy functional for perturbed Yamabe equation is bounded below, if theperturbation is small enough.
In this article, we identify the Heisenberg group and the standard sphere via the Cayley transformation,
and analyze the eigenvalues of the sub-Laplacian ∆b on S 2n+1 .
4 Atsufumi Honda(Miyakonojo Nat. Coll. of Tech.)

Isometric immersions with singularities between space forms of the same
positive curvature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give a definition of coherent tangent bundles of space form type, which is a
generalized notion of space forms. Then, we classify their realizations in the sphere as a wave front, which
is a generalization of a theorem of O’Neill and Stiel: any isometric immersion of the n-sphere into the(n + 1)-sphere of the same sectional curvature is totally geodesic.
5 Kotaro Kawai (Univ. of Tokyo)

Stabilities of aﬃne Legendrian submanifolds · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce the notion of aﬃne Legendrian submanifolds in Sasakian manifolds and define acanonical volume called the ϕ-volume as odd dimensional analogues of aﬃne Lagrangian (totally real or
purely real) geometry. Then we derive the second variation formula of the ϕ-volume to obtain the stability
result in some η-Einstein Sasakian manifolds. It also implies the convexity of the ϕ-volume functional on
the space of aﬃne Legendrian submanifolds.

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21

Geometry

6 Kazuyuki Hasegawa (Kanazawa Univ.)
Katsuhiro Moriya (Univ. of Tsukuba)

Twistor lifts and factorization for conformal maps of a surface I · · · · · · 15

Summary: We consider conformal maps from Riemann surfaces to the four-dimensional Euclidean space.
Such surfaces can be studied by twistor theory and quaternionic holomorphic geometry. The purpose of thistalk is to give the relation between these theories explicitly and show a factorization of the diﬀerential of aconformal map with respect to the multiplication of quaternions.
7 Katsuhiro Moriya (Univ. of Tsukuba)
Kazuyuki Hasegawa (Kanazawa Univ.)

Twistor lifts and factorization for conformal maps of a surface II · · · · · 15

Summary: In this talk, we take up two classes of conformal maps and apply the canonical factorization. One
is constrained Willmore surfaces and the other is minimal surfaces. A factor of a canonical factorization
for a conformal map provides a canonical lift of a conformal map. We characterize constrained Willmore
surfaces by canonical lifts. A factor of a canonical factorization for a conformal map provides the area
element of a conformal map. We give an upper bound of the area of a minimal surface around a branch
point.
8 Katsuhiro Moriya (Univ. of Tsukuba)

The Schwarz–Pick theorem for super-conformal maps · · · · · · · · · · · · · · · 15

Summary: We factorize a super-conformal map. This factorization connects a super-conformal map with aholomorphic map. Then we obtain the Schwarz–Pick theorem for super-conformal maps. Then we define a
distance on the image of a super-conformal map.
9 Hiroshi Iriyeh (Ibaraki Univ.) ♭ Hamiltonian non-displaceability of Gauss images of isoparametric hyper(Tsinghua Univ.) surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hui MaReiko Miyaoka (Tohoku Univ.)
Yoshihiro Ohnita (Osaka City Univ.)
Summary: We study the Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces inthe spheres as Lagrangian submanifolds embedded in complex hyperquadrics.
14:15–16:30
10 Mitsuhiro Imada(Ibaraki Nat. Coll. of Tech.)Complex contact metric structures on complex hypersurfaces in hyperkähler manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We showed that any complex hypersurface in hyperkähler manifolds admits complex almost
contact metric structures. In this talk, we show the condition that complex hypersurfaces in hyperkähler
manifolds admit complex contact metric structures.
11 Hiroshi Sawai(Numazu Nat. Coll. of Tech.)

Structure theorem for Vaisman completely solvmanifolds · · · · · · · · · · · · 15

Summary: Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallelwith respect to Riemannian metric. In this talk, we have the structure theorem for Vaisman completely
solvmanifolds.
12 Changhwa Woo(Kyungpook Nat. Univ.)
Young Jin Suh (Kyungpook Nat. Univ.)
Doo Hyun Hwang(Kyungpook Nat. Univ.)

Ricci semi-symmetric hypersurface in complex two-plane Grassmannians · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a new notion of Ricci semi-symmetric hypersurface in complex two-plane Grassmannians. Then we give a non-existence property for Ricci semi-symmetric Hopf hypersurfaces in complex
two-plane Grassmannians by using simultaneous diagonalization of commuting symmetric operators.

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Geometry

13 Isami Koga

(Kyushu Univ.)

Rigidity of a certain strongly projectively flat map into the complex
Grassmannian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, the author defines a strongly projectively flat map, which is a certain holomorphic
map of compact Kähler manifold into the complex Grassmannian manifold. And then, the author showthat if strongly projectively flat maps of compact simplly connected homogeneous Kähler manifolds into thecomplex Grassmannian is equivariant with respect to the identity component of isometry groups, then they
are rigid.
14 Toru Kajigaya (Osaka City Univ.)
Takahiro Hashinaga(Kitakyushu Nat. Coll. of Tech.)

Homogeneous Lagrangian submanifolds obtained by solvable Lie groups
in complex hyperbolic space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let M = CH n ≃ G/K = SU (1, n)/S(U (1) × U (n)) be the complex hyperbolic space and S thesolvable part of the Iwasawa decomposition of G. We classify homogeneous Lagrangian submanifolds in M
which are obtained by the actions of connected Lie subgroups of S.
15 Kazuhiro Suzuki (Nagoya Inst. of Tech.)
Misa Ohashi (Nagoya Inst. of Tech.)
Hideya Hashimoto (Meijo Univ.)

Caluculation methods of polynomial representations of non-flat totally
geodesic surfaces in symmetric spaces of type AI · · · · · · · · · · · · · · · · · · · 15

Summary: The famous Hopf fibration π : S 3 −→ S 2 over two dimensional sphere S 2 with S 1 fiber is related
to the primitive map of the Cartan imbedding of type AI. Taking the composition of this imbedding andnon-flat totally geodesic imbedding from S 2 to SU (n)/SO(n) of symmetric space of type AI, we give theexplicit representation of this totally geodesic imbedding from S 2 to SU (n).
16 Shinobu Fujii(Oshima Nat. Coll. of Maritime Tech.)

Quartic Cartan–Münzner polynomials and Casimir operators · · · · · · · · 10

Summary: We are interested in a relationship between quartic Cartan–Münzner polynomials and Casimir
operators of symplectic representations. In this talk, we consider the Cartan–Münzner polynomials obtained
from the isotropy representations of irreducible Hermitian symmetric spaces of rank two, of compact typeand of classical type.
17 Shinji Ohno (Tokyo Metro. Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Hajime Urakawa (Tohoku Univ.⋆)

Construction of biharmonic homogeneous submanifolds in compact symmetric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we obtain new examples of biharmonic homogeneous submanifolds in compact
symmetric spaces whose codimension is two or greater.
18 Makiko Tanaka (Tokyo Univ. of Sci.)
Hiroyuki Tasaki (Univ. of Tsukuba)

Maximal antipodal subgroups of compact Lie groups II · · · · · · · · · · · · · 15

Summary: In the previous MSJ meeting we gave a talk titled “Maximal antipodal subgroups of compact Liegroups” in which we gave the classifications of maximal antipodal subgroups of the quotient groups U (n)/Zµ
and SU (n)/Zµ . This talk is a sequel to that. We classify maximal antipodal subgroups of O(n)/{±1n },SO(n)/{±1n }, Sp(n)/{±1n } and G2 .

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23

Geometry

16:45–17:45

Talk Invited by Geometry Section♭
Jost-Hinrich Eschenburg
Extrinsic symmetric spaces(Univ. of Augsburg)

Summary: Compact submanifolds of euclidean space with parallel second fundamental form have many
astonishing properties. All their isometries extend to the ambient space. They are “extrinsic symmetric”,
that is invariant under reflection along all of their normal spaces. Thus they form an interesting subclassof symmetric spaces which are linked to other symmetric spaces in several ways. E.g. they form certain
isotropy orbits of symmetric spaces, real forms of hermitian symmetric spaces, and midpoint components
between center elements of symmetric spaces. Moreover, they are symmetric R-spaces: the action of theisometry group can be enlarged to a noncompact transformation group, like the conformal group on thesphere. They contain their noncompact dual space as an open subset, and the dual isometry group becomesa subgroup of this noncompact group. We try to link all these properties.

March 17th (Thu)

Conference Room V

9:00–10:45
19 Yuto Yamamoto (Univ. of Tokyo)

Geometric monodromy around the tropical limit · · · · · · · · · · · · · · · · · · · 15

Summary: The main subjects of study in tropical geometry are tropical varieties which are defined aspolyhedral complexes which have certain kinds of aﬃne structures. One can associate a tropical variety T toa one-parameter family of complex varieties {Xq }q by tropicalization. It is known that the tropical variety
T encodes the information of the behavior of {Xq }q in the limit q → ∞. In this talk, we give a concrete
description of the monodromy transformation of {Xq }q around q = ∞ in terms of the tropical variety T .
20 Kazushi Kobayashi (Chiba Univ.)

Structure of the mapping cone of a morphism between holomorphic line
bundles on T2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct the mapping cone of a morphism between holomorphic line bundles on T2 anddiscuss it’s structure geometrically via the homological mirror symmetry.
21 Satoshi Sugiyama (Univ. of Tokyo)

On an application of the Fukaya categories to the Koszul duality · · · · · 15

Summary: The Koszul duality is known as a duality between certain finite dimensional algebras, called
Koszul algebras, which are isomorphic to quotient algebras of path algebras divided by quadratic ideals. In
this talk, we construct the Koszul dual A! of a Koszul algebra A via Fukaya category of a Riemann surface
and prove the bounded derived equivalence of them. Finally, we generalize this construction to higher Koszul
algebras and obtain their Koszul duals as A∞ -algebras and prove their bounded derived equivalences.
22 Yosuke Morita (Univ. of Tokyo)

Obstructions to the existence of compact manifolds locally modelled on
homogeneous spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Extending the result of Kobayashi–Ono, we give necessary conditions, which are written in termsof relative Lie algebra cohomology, for the existence of a compact manifold locally modelled on a given
homogeneous space. Applications include both reductive and nonreductive cases.
23 Kenta Hayano (Hokkaido Univ.)
Noriyuki Hamada (Univ. of Tokyo)

Topology of holomorphic Lefschetz pencils on abelian surfaces · · · · · · · 15

Summary: In this talk, we will discuss smooth isomorphism classes of holomorphic Lefschetz pencils on
2-dimensional complex tori. Our main result states that the isomorphism class of such a pencil is uniquelydetermined by its genus and the divisibility of the homology class of its regular fiber. We will also show
some applications of this result to problems on topology of Lefschetz pencils.

Final ver.: 2016/2/15
24

Geometry

24 Yohsuke Imagi(Kavli IPMU) ♭ Construction of compact special Lagrangian T 2 -conifolds · · · · · · · · · · · · 15

Summary: Special Lagrangian submanifolds are volume-minimizing submanifolds of Calabi–Yau manifolds.
I have been studying singularity of them. Compact special Lagrangian T 2 -conifolds are theoretically wellstudied but their existence has been unproven so far as I know. I have recently proved it using an idea ofMark Haskins and Dominic Joyce. I explain it in the talk. I start with an explicit algebro-geoemtric data
and use a gluing technique in non-linear analysis, which goes back to Taubes’ result in Yang–Mills gauge
theory.
11:00–12:00

Talk Invited by Geometry Section

Hiraku Nozawa (Ritsumeikan Univ.)

On rigidity and characteristic classes of (G, X)-foliations

Summary: We will discuss some rigidity results on foliations with geometric structures. First we make abrief introduction to characteristic classes of foliations, and review some related rigidity results and open
problems. The first results of this talk, obtained in a collaboration with Jesús Antonio Álvarez López,
are Bott–Thurston–Heitsch type formulas to compute the Godbillon–Vey classes of certain foliated spherebundles, and a rigidity result on transversely conformally flat foliations on the unit tangent sphere bundlesof hyperbolic manifolds. The second results, obtained in a collaboration with Gaël Meigniez, is thatRiemannian foliations whose leaves are isometric to a locally symmetric space is diﬀeomorphic to somestandard foliations on double coset spaces of Lie groups.

March 18th (Fri)

Conference Room V

9:30–11:50
25 Takuya Tsuchiya (Waseda Univ.)(Kyoto Univ.)
Kei Yamada
Hideki Asada (Hirosaki Univ.)

Linear stability of the triangular solution for the three problems ingeneral relativity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, the three problems in general relativity are considered. The three problems arewell known that the general solution does not exists. Whereas the collinear solution and the triangularsolution exist. We examine the post-Newtonian eﬀects to the linear stability of the triangular solution in two
dimensional space using the Einstein–Infeld–Hoﬀmann equation which is the motion of equation included
the general relativistic eﬀects. Furthermore, we will discuss the stability of the triangular solution in three
dimensional space.
26 Stefan Andrew Horocholyn(Tokyo Metro. Univ.)

On the Stokes matrices of the tt∗ -Toda equations · · · · · · · · · · · · · · · · · · 15

Summary: We derive a formula for the signature of the symmetrized Stokes matrix S + S T for the tt∗ -Toda
equations. As a corollary, we verify a conjecture of Cecotti and Vafa regarding when S + S T is positive
definite, reminiscent of a formula of Beukers and Heckmann for the generalized hypergeometric equation.
The condition S + S T > 0 is prominent in the work of Cecotti and Vafa on the tt∗ equation; we show that
the Stokes matrices S satisfying this condition are parameterized by a convex polytope.
27 Yutaro Kabata (Hokkaido Univ.)

Recognition problem of plane-to-plane map-germs and its application
to projective diﬀerential geometry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show useful criteria to determine the types of given plane-to-plane map-germs, which gives a
new insight to the classification result given by J. H. Rieger from the viewpoint of recognition problem. We
also show the application of our criteria to generic projective diﬀerential geometry.

Final ver.: 2016/2/15
25

Geometry

28 Atsushi Yano (Hokkaido Univ.)

On the characterization of second order partial diﬀerential equations ofseveral unknown functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Diﬀerential systems may be regarded as systems of first order diﬀerential equations according toRealization Lemma. We characterize the geometric structure of systems of second order partial diﬀerential
equations of several unknown functions in terms of diﬀerential systems.
29 Goo Ishikawa (Hokkaido Univ.)
Tatsuya Yamashita (Hokkaido Univ.)

Aﬃne connections and singularities of tangent surfaces to space curves· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give the complete solution to the local diﬀeomorphism classification problem of genericsingularities which appear in tangent surfaces, in as wider situations as possible. We interpret geodesics aslines whenever a (semi-)Riemannian metric, or, more generally, an aﬃne connection is given in an ambient
space of arbitrary dimension. Then, given an immersed curve, or, more generally a directed curve which
has well-defined tangent directions along the curve, we define the tangent surface by the ruled surface bytangent geodesics to the curve. We give the generic classification of singularities of tangent surfaces andprovide the characterizations of singularities.
30 Kazuyoshi Watanabe (Tohoku Univ.) ♭ Zero-points of closed 1-form on topological spaces · · · · · · · · · · · · · · · · · · 10
Summary: A new Lusternik–Schnirelmann type theory for closed 1-forms on smooth manifolds is introducedby M. Farber. This theory aims at finding relations between topology of the zero set of a closed 1-form andhomotopical information, based on the cohomology class of the form. And more, it is related to a dynamics ofclosed 1-form, a homoclinic cycle. A continuous closed 1-form on topological spaces is defined in this theory.
I will talk the definition of zero-point of continuous closed 1-form and show that the Lusternik–Schnirelmann
type theory is constructed for CW-complexes used by continuous closed 1-form.
31 Tomoshige Yukita (Waseda Univ.)

On the growth rate of cofinite Coxeter groups in hyperbolic 3-space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Certain classes of real algebraic integers show up in the study of the growth rates of hyperbolic
Coxeter groups. We study the arithmetic property of growth rates of cofinite Coxeter groups in hyperbolic
3-space and prove that their growth rates are always Perron numbers.
32 Yoshifumi Matsuda(Aoyama Gakuin Univ.)

Uniform simplicity of Thompson’s group T · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show uniform simplicity of Thompson’s group T . As a corollary, it follows that Thompson’sgroup T does not admit any unbounded conjugation-invariant norms and any unbounded real-valued
quasimorphisms.
33 Takefumi Kondo (Kagoshima Univ.)
Shin Nayatani (Nagoya Univ.)(Keio Univ.)
Hiroyasu Izeki

Fixed point property for aﬃne actions on a Hilbert space · · · · · · · · · · · 15

Summary: We report that any aﬃne action of a random group in the Gromov graph model on a Hilbert
space, satisfying a certain mild-growth condition, has a fixed point.
14:15–16:00
34 Ryosuke Takahashi (Nagoya Univ.)

Asymptotic stability for Kähler–Ricci solitons · · · · · · · · · · · · · · · · · · · · · 10

Summary: Kähler–Ricci solitons arise from the geometric analysis, such as Hamilton’s Ricci flow, and havebeen studied extensively in recent years. It is expected that the existence of canonical metrics is closely
related to some GIT stability of manifolds. For instance, Donaldson showed that any cscK polarized
manifold with discrete automorphisms admits a sequence of balanced metrics and this sequence converges
to the cscK metric. In this talk, we explain that a similar result holds for Kähler–Ricci solitons. This
generalizes a previous work of Berman–Witt Nyström, and is an analogous result on asymptotic relative
Chow stability for extremal metrics obtained by Mabuchi.

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26

Geometry

35 Ryosuke Takahashi (Nagoya Univ.)
Shunsuke Saito (Univ. of Tokyo)

An obstruction to the existence of anti-canonically balanced metrics on
Fano manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Anti-canonically balanced metrics are approximations to Kähler–Einstein metrics obtained bymeans of holomorphic sections of high powers of the anti-canonical line bundle. In this talk, we use thejumping of complex struxtures to produce a new obstruction to the existence of anti-canonically balanced
metrics on Fano manifolds. We also discuss some relation to asymptotic Chow stability.
36 Kenta Tottori (Tohoku Univ.)

Calabi’s conjecture of the Kähler–Ricci soliton type · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss Calabi’s equation of the Kähler–Ricci soliton type on a compact Kähler
manifold. This equation was introduced by Zhu as a generalization of Calabi’s conjecture. We give necessary
and suﬃcient conditions for the unique existence of a solution for this equation on a compact Kähler manifoldwith a holomorphic vector field which has a zero point. We also consider the case of a nowhere vanishing
holomorphic vector field, and give suﬃcient conditions for the unique existence of a solution for this equation.
37 Masaya Kawamura(Tokyo Metro. Univ.)

C α -convergence of the Chern–Ricci flow on elliptic surfaces · · · · · · · · · · 15

Summary: We will study the Chern–Ricci flow on minimal non-Kähler properly elliptic surfaces. Thesesurfaces are compact complex surfaces whose first Betti number is odd, Kodaira dimension is equal to 1,
admitting an elliptic fibration π : M → S to a smooth compact curve S and no (−1)-curve in any fibersof π. We will show that a solution of the Chern–Ricci flow is uniformly bounded in the C 1 -topology andconverges in the C α -topology on these elliptic surfaces by choosing a special initial metric.
38 Hikaru Yamamoto (Univ. of Tokyo)

On self-similar solutions in gradient shrinking Ricci solitons · · · · · · · · · 10

Summary: There are many results about self-similar solutions in a Euclidean space. In this talk, I introduce
the notion of self-similar solutions in a gradient shrinking Ricci soliton, and I talk about some properties ofthese, which are some kind of generalizations of results of Futaki-Li-Li and Cao-Li established for self-similarsolutions in a Euclidean space.
39 Naoyuki Koike (Tokyo Univ. of Sci.)

On the preservability of the curvature-adaptedness along the mean
curvature flow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we state some results related to the preservability of the curvature-adaptedness along
the mean curvature flow starting from a compact curvature-adapted hypersurface in irreducible locallysymmetric spaces, where the curvature-adaptedness means that the shape operator and the normal Jacobi
operator of the hypersurface commute.
40 Yoshihiro Tonegawa (Tokyo Tech)(Tokyo Tech)
Lami Kim

Mean curvature flow of grain boundaries · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Suppose that Γ0 ⊂ Rn+1 is a closed countably n-rectifiable set whose complement Rn+1 \ Γ0consists of more than one connected component. Assume that the n-dimensional Hausdorﬀ measure of Γ0
is finite or grows at most exponentially near infinity. Under these assumptions, we prove a global-in-timeexistence of mean curvature flow in the sense of Brakke starting from Γ0 . There exists a finite family ofopen sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincidewith the space-time support of the mean curvature flow.

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27

Geometry

16:15–17:15

Talk Invited by Geometry Section

Eliot Fried(Okinawa Inst. of Sci. and Tech. Grad. Univ.)

Variational problems for soap films spanning flexible loops

Summary: We discuss recent results concerning the onset of instability for flat circular solutions to theequilibrium equations for a system in which a soap film spans a flexible loop. Adopting a variational
approach, we base our analysis on an energy functional which is the sum of a term proportional to themapping area of the surface representing the soap film and the shape energy of an elastic rod that models
the bounding loop. We also discuss a possible strategy for obtaining nontrivial equilibrium configurations bystudying a simple and yet physically motivated model for the dissipative evolution of the system, in whichinternal friction produces a viscoelastic behavior.

March 19th (Sat)

Conference Room V

9:00–10:45
41 Hirotaka Ebisui (Oval Research Center)4 points collinear theorem among two given circles (Ellipses) · · · · · · · · 15

Summary: In mathematics history,a lot of Collinear Theorem have apeared.For Example,Papus Therem,Pascal Theorem, Desargues Theorem,Simson Theorem apear in big year interval. Some of them are somekind of Projective Geometry Theorem,and,these are Basic on Geometry.This time ,We found another kindof Collinear Theorem.This theorem consist of Two circles(2 Ellipses) and 9 lines,and Among them 4points
Collinear line apear. We show this theorem composition by Figure 1,2. This figure is very simple,so,we cansee Importancy in geometry on it. Anyway, we report New THeorem,here.
42 Kenzi Satô (Tamagawa Univ.)

A definition of escribed and inscribed simplices of higher dimensional
Euclidean spaces and an expansion of Bevan point theorem · · · · · · · · · · 15

Summary: Escribed and inscribed triangles for a triangle on the plane is generalized to a simplex on the
n-dimensional Euclidean space with n ≧ 3. As an application, we can get Bevan point theorem for a simplex
on the n-dimensional Euclidean space.
43 Mitsuhiro Itoh (Univ. of Tsukuba)
Hiroyasu Satoh (Nippon Inst. of Tech.)Fisher information metric on the space of probability measures anddistance function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let P + (M ) be the space of probability measures on a compact, connected smooth manifold M. We
report that the distance between two probability measures of P + (M ) with respect to Fisher metric is exactly
the arc-length function of the uniquely defined geodesic segment between them. This result is verified by
the aid of three propositions, familiar in a finite dimensional Riemannian geometry; Gauss lemma, Existence
theorem of totally normal neighborhood and theorem of characterization of curve minimizing length.
44 Mitsuhiro Itoh (Univ. of Tsukuba)
Hiroyasu Satoh (Nippon Inst. of Tech.)

Generalized mean of probability measures and geodesics for Fisher
information metric · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The space of all probability measures having positive density function on a compact connected
C ∞ -manifold M , denoted by P + (M ), carries the Fisher information metric G. In this talk we consider
generalized means, called the α-power mean, of two probability measures and give characterizations ofgeodesics for G by the normalized geometric mean (0-power mean). Moreover, we also mention the
α-geodesics of dualistic structure (∇(α) , ∇(−α) ) on (P + (M ), G).
45 Ryunosuke Ozawa (Kyoto Univ.)

Stability of Talagrand’s inequality under the concentration topology· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Gromov introduced the observable distance between two metric measure spaces. The topology
generated by the observable distance function admits a convergence sequence of Riemannian manifolds ofunbounded dimension. We talk about the stability of Talagrand’s inequality under the topology generated
by the observable distance function.

Final ver.: 2016/2/15
28

Geometry

46 Nobuhiro Innami (Niigata Univ.)

Geodesics in a Finsler surface of revolution · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show the global behavior of geodesics in a Finsler surface of revolution. In particular, we
generalize Clairaut’s theorem for geodesics in a Riemannian torus of revolution.
47 Kei Kondo (Yamaguchi Univ.)
Minoru Tanaka (Tokai Univ.)

Diﬀerentiable exotic sphere theorem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We prove a diﬀerentiable sphere theorem for a pair of topological spheres, even for that of exotic
ones. Furthermore, we prove that for each exotic sphere Σn of dimension n > 4, there exists a bi-Lipschitz
homeomorphism between the n-dimensional unit standard sphere and Σn which is a diﬀeomorphism except
for a single point.
11:00–12:00

Talk Invited by Geometry Section

Asuka Takatsu (Tokyo Metro. Univ.) ♭ Wasserstein/Information geometry and its applications
Summary: Both Wasserstein geometry and the information geometry are geometry on the space of probability
measures. On the one hand the Wasserstein geometry is a metric geometry, where the metric heritages thenature of the underlying space; on the other hand, in the Information geometry, we regard the space of
probability measures as a Riemannian manifold, where the Riemannian metric with a pair of connection
play central roles. Although these two geometries are completely diﬀerent from each other, they are related
to each other.
By the combined use of two geometry, we develop the theory of Wasserstein geometry, Information geometry.
We moreover apply both geometry to the analysis of some evolution equations.

Final ver.: 2016/2/15
29

Complex Analysis

Complex Analysis
March 16th (Wed)Conference Room VIII

9:45–11:45
1 Rintaro Ohno (Tohoku Univ.)
Toshiyuki Sugawa (Tohoku Univ.)

On a Fekete–Szegö-type problem of concave functions · · · · · · · · · · · · · · 15

Summary: In the present talk we discuss coeﬃcients of bounded holomorphic functions with a fixed point
inside the unit disk as well as a maximum value problem for a quadratic polynomial. As an application, weare going to apply the results for the Fekete–Szegö-type problem of concave functions with simple pole atsome p ∈ (0, 1).
2 Rintaro Ohno (Tohoku Univ.) ♭ On the second Hankel determinant of concave functions · · · · · · · · · · · · · 10
Toshiyuki Sugawa (Tohoku Univ.)
Summary: First, we will characterize the coeﬃcient body of order 2 for the class of analytic functions φ(z)on |z| < 1 with |φ| < 1 and φ(p) = p where p ∈ (0, 1). Using the obtained results, we will consider the∑∞
Hankel determinants H(f ) = a2 a4 − a23 of order 2 for normalized concave functions f (z) = z + n=2 an z nwith a pole at p.
3 Masanori Amano (Tokyo Tech)

A global coordinate of the Teichmüller space related to asymptotic
Jenkins–Strebel rays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give a parametrization of asymptotic Jenkins–Strebel rays. It is a kind of
global coordinates of the Teichmüller space. For any admissible curve family of a surface, the subset ofthe boundary of the Teichmüller space which is constructed by pinching of the given curve family can be
determined. There exists a homeomorphism of the product of the boundary space and several parameter
spaces onto the Teichmüller space such that each family of asymptotic Jenkins–Strebel rays is represented
when varies only the parameters.
4 Masashi Kisaka (Kyoto Univ.)
Tomoki Kawahira (Tokyo Tech)

Julia sets appear quasi-conformally in the Mandelbrot set · · · · · · · · · · · 15

Summary: If we zoom in a certain part of the Mandelbrot set, we can see a figure J ′ which is very similar toa certain Julia set. Furthermore, as we zoom in the middle part of J’, we can see a certain nested structure
which is similar to the iterated preimages of J ′ by z 2 and finally a small Mandelbrot set M ′ appears. We
explain how to formulate this phenomena and show that this actually occurs. Also we show that this kindof nested structure exists in Jc for c ∈ M ′ .
5 Tomoki Kawahira (Tokyo Tech)

From Cantor to Misiurewicz along parameter rays · · · · · · · · · · · · · · · · · · 15

Summary: We consider degeneration process from a Cantor Julia set to a Misiurwicz Julia set in the familyof quadratic maps. We give an estimate of the speed of the holomorphic motion when the parameter moves
along a pre-periodic parameter ray of the Mandelbrot set. Then we will conclude that such a particularmotion dynamically converges. (joint with Yi-Chiuan Chen)
6 Tomoki Kawahira (Tokyo Tech)

The Riemann hypothesis and holomorphic index in complex dynamics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give an interpretation of the Riemann hypothesis in terms of complex and topological dynamics.
For example, the Riemann hypothesis is aﬃrmative and all zeros of the Riemann zeta are simple if and only
if a certain meromorphic function has no attracting fixed point. To obtain this, we use holomorphic index(residue fixed point index), which characterizes local properties of fixed points in complex dynamics.

Final ver.: 2016/2/15
30

Complex Analysis

7 Hiroki Sumi

(Osaka Univ.)

Hausdorﬀ dimension of the Julia sets of postcritically bounded polynomial semigroups and transversality condition · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the dynamics of 2-generator hyperbolic polynomial semigroups with bounded planar
postcritical set. We show that for the parameter f = (f1 , f2 ) in the boundary of connectedness locus, there
exists an open neighborhood V of f such that for a.e. g = (g1 , g2 ) ∈ V with respect to the Lebesgue measure
on V , the Hausdorﬀ dimension of the Julia set of the semigroup generated {g1 , g2 } is equal to the criticalexponent of the Poincare series of (g1 , g2 ). Note that we do not know whether for such a g ∈ V , the open
set condition is satisfied or not.
14:15–15:05
8 Kentarou Itou
Ryozi Sakai
Noriaki Suzuki(Meijo Univ.)(Meijo Univ.)(Meijo Univ.)

On weighted polynomial approximation by the de la Vallée Poussin
mean · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study polynomial approximation by the de la Vallée Poussin mean vn (f ) for exponential
weight w(x) = exp(−Q(x)) on whole real line. On a proof of this theorem, Lp boundedness of the de laVallée Poussin mean plays an important role. We also discuss estimates of derivatives of the de la Vallée
Poussin mean and approximation for absolutely continuous functions.
9 Yoŝuke Hishikawa (Gifu Univ.)
Masaharu Nishio (Osaka City Univ.)
Yamada Masahiro (Gifu Univ.)

L(α) -conjugates on parabolic Bloch spaces · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The parabolic Bloch space is the set of all solutions u of the parabolic operator L(α) with thefinite Bloch norm ∥u∥Bα (σ) . In this talk, we introduce a notion of L(α) -conjugates, and investigate several
properties of L(α) -conjugates on parabolic Bloch spaces.
10 Kiyoki Tanaka (Osaka City Univ.)

Biharmonic Bergman kernel of an external domain · · · · · · · · · · · · · · · · · 15

Summary: We consider the weighted biharmonic Bergman space on an external domain. The weighted
biharmonic Bergman space has the reproducing kernel, which is called the weighted biharmonic Bergman
kernel. In this talk, we introduce the form of the weighted biharmonic Bergman kernel of an external
domain.
15:25–16:25

Talk Invited by Complex Analysis Section

Johannes Jaerisch (Shimane Univ.)

Hausdorﬀ dimension of the Julia sets of non-hyperbolic polynomial
semigroups and the method of inducing

Summary: There is a rich interplay between the geometric and dynamical properties of Julia sets of semigroupsof holomorphic maps on the Riemann sphere Ĉ. In the 1970s, R. Bowen characterised the Hausdorﬀ
dimension of the limit sets of certain Fuchsian groups in terms of the dynamical notion of topologicalpressure. This formula, which is referred to as Bowen’s formula, has been generalized to Julia sets ofrational maps on Ĉ by D. Sullivan, and it is still an active area of research.
After a brief introduction of the necessary preliminaries on Bowen’s formula, we will formulate a new version
of Bowen’s formula for the Hausdorﬀ dimension of the Julia sets of certain non-hyperbolic postcriticallybounded polynomial semigroups satisfying the open set condition. The key to investigate these semigroups
is to develop a fractal theory for an associated infinitely generated hyperbolic subsemigroup and to use themethod of inducing. By using this method we have a strong tool to analyze the geometric and dynamical
properties of various non-hyperbolic semigroups of holomorphic maps on the Riemann sphere. We will
discuss the underlying ideas and concepts from ergodic theory and complex analysis. This is a joint workwith H. Sumi.

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31

Complex Analysis

16:45–17:45

Talk Invited by Complex Analysis Section
Yoshihiko Matsumoto (Tokyo Tech) Deformations of complete Einstein metrics on strictly pseudoconvex
domains
Summary: We discuss a certain construction of new complete Einstein metrics on a smoothly bounded strictly
pseudoconvex domain Ω of a Stein manifold. S. Y. Cheng and S. T. Yau showed in 1980 that one obtains acomplete Kähler–Einstein metric on Ω with negative scalar curvature by solving the complex Monge–Ampèreequation. The approach that we take here is to deform this Cheng–Yau metric by an application of theinverse mapping theorem, which generalizes the work of O. Biquard on the deformations of CH n (and thecorresponding work of R. Graham and J. Lee for the real case). Recasting the problem into the questionof vanishing of an L2 -cohomology and taking advantage of the “asymptotic complex hyperbolicity” of theCheng–Yau metric at the boundary, we establish the possibility of such a deformation when the dimensionof Ω is at least 3. I intend to make this talk so organized that it also works as an introduction to geometricanalysis on asymptotically complex hyperbolic manifolds.

March 17th (Thu)

Conference Room VIII

9:45–11:50
11 Kouichi Kimura

Homogeneous pseudoconvex Reinhardt domains in C3 · · · · · · · · · · · · · · 15

Summary: A homogeneous Reinhardt domain in C∗ coinsides with C∗ . Generalizing this fact, we showed thata homogeneous pseudoconvex Reinhardt domain in (C∗ )n coinsides with (C∗ )n . Conversely, we investigate
pseudoconvex Reinhardt domains containing the origin in C3 this time, and we decide Liouville foliations
which can be defined on them. From this, when the preceeding domains are homogeneous, we classify these
domains by means of algebraic equivalence and determine thier canonical forms.
12 Atsushi Yamamori (Nagoya Univ.)

Yet another proof of Poincaré’s theorem on the inequivalence of theunit ball and the polydisk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This talk gives a concise proof of a classical Poincaré’s theorem which asserts that the unit ball
Bn and the polydisk Dn are not biholomorphic equivalent for any n > 1.
13 Tatsuhiro Honda(Hiroshima Inst. of Tech.)
Ian Graham (Univ. of Toronto)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)
Kwang Ho Shon (Pusan Nat. Univ.)

Radius of univalence and related problems in complex Hilbert spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: There are various results related to radius of univalence, parametric representation, starlikenessor convexity for holomorphic mappings on the Euclidean unit ball in Cn . In this talk, we are concernedwith certain radius problems for holomorphic mappings on the unit ball in a complex Hilbert space.
14 Filippo Bracci(Univ. di Roma“Tor Vergata”)
Ian Graham (Univ. of Toronto)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Variation of Loewner chains, extreme and support points in the class
S 0 in several complex variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce a family of normalized Loewner chains in Bn , which we call “geräumig”—
spacious—which allow to construct, by means of suitable variations, other normalized Loewner chains whichcoincide with the given ones from a certain time on. We apply our construction to the study of support
points, extreme points in the class S 0 of mappings admitting parametric representation.

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32

Complex Analysis

15 Yukitaka Abe (Univ. of Toyama)

Cohomology groups of sections of homogeneous line bundles over a
toroidal group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We completely determine cohomology groups of sections of homogeneous line bundles over a
toroidal group.
16 Atsushi Atsuji(Keio Univ.)

Nevanlinna type theorems for meromorphic functions on negatively
curved Kähler manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a second main theorem of Nevanlinna theory on complete negatively curved Kähler
manifolds. It’s remainder term depends only on Ricci curvature of the manifolds.
17 Masanori Adachi (Tokyo Univ. of Sci.)
Judith Brinkschulte (Univ. Leipzig)

Curvature restrictions for Levi-flat real hypersrufaces in complex projective planes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study curvature restrictions of Levi-flat real hypersurfaces in complex projective planes,
whose existence is in question. We focus on its totally real Ricci curvature, the Ricci curvature of the real
hypersurface in the direction of the Reeb vector field, and show that it cannot be greater than −4 along a
Levi-flat real hypersurface. We rely on a finiteness theorem for the space of square integrable holomorphic
2-forms on the complement of the Levi-flat real hypersurface, where the curvature plays the role of the sizeof the infinitesimal holonomy of its Levi foliation.
18 Takeo Ohsawa (Nagoya Univ.) ♭ An optimal L2 extension theorem on Cn · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In view of the proofs of optimal L2 extension theorems due to Blocki and Guan–Zhou, I could finda straightforward proof of their optimal L2 extension theorem (to appear in Nagoya Math. J.). Applying
this method, an optimal L2 extension theorem will be shown on Cn .
13:15–14:20
19 Shinichi Tajima (Univ. of Tsukuba) ♭ Limiting tangent spaces and local cohomology · · · · · · · · · · · · · · · · · · · · · 15
Katsusuke Nabeshima(Univ. of Tokushima)
Summary: Limiting tangent spaces associated with hypersurface isolated singularities are considered. A neweﬀective method for computing limiting tangent spaces is described. The key is the use of the concept ofparametric local cohomology system.
20 Masataka Tomari (Nihon Univ.) ♭ On maximal ideal cycle of normal two-dimensional graded singularity
Tadashi Tomaru (Gunma Univ.) whose centeral curve is a nonsingular rational curve · · · · · · · · · · · · · · · · 15
Summary: We study the maximal ideal cycle and the fundamental cycle for normal two-dimensional singularities with star-shaped resolution where the central curve is a nonsingular rational curve. Our interestis the identification of these, when the cordinated ring of singularity do not have a homogeneous reduced
element in the minimal degree.
21 Katsusuke Nabeshima(Univ. of Tokushima)
Shinichi Tajima (Univ. of Tsukuba)

A computation method of Bruce–Roberts’ Milnor numbers with parameters · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Logarithmic vector field of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this talk, logarithmic
vector field associated with hypersurface isolated singularities are considered in the context of symbolic computation. As an application, an algorithm for computing Bruce–Roberts’ Milnor numbers with parametersis introduced, too.

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33

Complex Analysis

22 Katsusuke Nabeshima(Univ. of Tokushima)
Katsuyoshi Ohara (Kanazawa Univ.)
Shinichi Tajima (Univ. of Tsukuba)

Computing holonomic D-modules and b-functions with parameters · · · 15

Summary: Let f be a polynomial with n variables. In this talk an annihilater ideal Ann(f s ) is considered in
DX [s]. A computation method of Ann(f s ) is introduced by using Poincaré–Birkhoﬀ–Witt algebra. As anapplication, an algorithm for computing b-fucntions with parameters, is given, too.

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34

Functional Equations

Functional Equations
March 16th (Wed)Conference Room III

9:30–12:00
1 Katsumi Matsuda (Tokai Univ.)

On the exact figure eight solution of the eqal-mass planar 3-bodyproblem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: I describe a new constructon method of planar choreographic three bodies, whose center of massis the original point and whose angular momentum is constantly zero. Moreover, I explain a trial toward
the exact figure eight solution of the equal-mass planar 3-body problem.
2 Takuya Yamashiro (Kumamoto Univ.) ♭ Holonomic system singular along quartic curve with three cusps · · · · · 12
Yoshishige Haraoka (Kumamoto Univ.)
Summary: We consider the problem to construct the regular holonomic system singular along a prescribedcurve. As a curve, we choose a irreducible quartic curve with three cusps. We classified the irreducible
representations of the fundamental group of the complement of the curve. The irreducible representations
exist only in the case dimension two. Then we construct a corresponding rank two regular holonomic system
explicitly. It turns out that we need an appearent singular locus.
3 Masafumi Yoshino (Hiroshima Univ.)

Application of Borel summability to small denominator problem · · · · · 12

Summary: Convergence of formal series solution of some semilinear partial diﬀerential equation in the caseof small denominators is shown without assuming the Diophantine condition. Instead of the Diophantine
condition we make use of Borel summability with respect to a certain parameter introduced in the equationin order to show the convergence.
4 Hikaru Igarashi (Chuo Univ.)(Hosei Univ.)
Shin Isojima
Kouichi Takemura (Chuo Univ.)

New Airy-type solutions of the ultradiscrete Painlevé II equation withparity variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The q-diﬀerence Painlevé II equation admits special solutions written in terms of determinant
whose entries are the general solution of the q-Airy equation. An ultradiscrete limit of the special solutions
is studied by the procedure of ultradiscretization with parity varialbes. Then we obtain new Airy-type
solutions of the ultradiscrete Painlevé II equation with parity variables, and the solutions have richer
structure than the known solutions.
5 Mika Tanda(Kwansei Gakuin Univ./Kinki Univ.)
Toshinori Takahashi (Kinki Univ.)(Kinki Univ.)
Takashi Aoki

The Voros coeﬃcients of the Gauss hypergeometric diﬀerential equation
with a large parameter · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Gauss hypergeometric diﬀerential equation with a large parameter from theviewpoint of the exact WKB analysis. We introduce a large parameter η in the parameters of thehypergeometric equation as general linear forms of η. We define the Voros coeﬃcient of the Gausshypergeometric diﬀerential equation with a large parameter for the origin. Explicit form of the Voros
coeﬃcient is given. Moreover, we compute the Borel sums of the Voros coeﬃcient in each Stokes region.
6 Toshinori Takahashi (Kinki Univ.)
Mika Tanda(Kwansei Gakuin Univ./Kinki Univ.)(Kinki Univ.)
Takashi Aoki

The hypergeometric function with a large parameter and WKB solutions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Gauss hypergeometric diﬀerential equation and its WKB solutions. These solutions are Borel summable under suitable conditions. We investigate the relation between the hypergeometricfunction and the Borel resummed WKB solutions.

Final ver.: 2016/2/15
35Functional Equations

7 Patrick van Meurs (Kanazawa Univ.)

Discrete-to-continuum convergence of interacting particle systems · · · · 12

Summary: We study the many-particle limit of an interacting particle system. The velocities of the particles
are described by a non-linear function which depends on all particle positions. The resulting system offirst-order ODEs has a gradient flow structure with respect to an energy functional En , where n is thenumber of particles. Our first main result states Γ-converge of the energy functionals En as n → ∞ to theΓ-limit E. The functional E is defined on the space of measures, equipped with the 2-Wasserstein topology.
These measures represent the particle density. Our second result guarantees the convergence of the related
gradient flows.
8 Masakazu Onitsuka(Okayama Univ. of Sci.)
Satoshi Tanaka (Okayama Univ. of Sci.)

Attractivity, rectifiability and non-rectifiability of solutions for twodimensional linear diﬀerential systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider a nonautonomous linear diﬀerential system x′ = y, y ′ = −x − h(t)y, where h ∈C[t0 , ∞). The aim of this talk is to establish a necessary and suﬃcient condition for every nontrivial
solution to be rectifiable. Moreover, a necessary and suﬃcient condition for the zero solution to be
attractive is also presented.
9 Masashi Toyoda (Tamagawa Univ.)
Toshiharu Kawasaki (Tamagawa Univ.)

Note on Knežević–Miljanović’s theorem in a class of fractional diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we show the existence and uniqueness of solutions of the Cauchy problem in a classof singluar fractional diﬀerential equations.
10 Hiroyuki Usami(Gifu Univ.) ♭ Asymptotic forms of slowly decaying solutions of a kind of Lanchestertype system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: It is shown that some class of Lanchester type systems have slowly decaying solutions. In thistalk, we give the asymptotic forms of such solutions near the infinity.
14:15–16:15
11 Tomoyuki Tanigawa (Kumamoto Univ.)

Asymptotic behavior of positive solutions of second order half-linear
functional diﬀerential equations with deviating arguments of mixed
type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: It is well known that there is the qualitative similarity between linear diﬀerential equations andhalf-linear diﬀerential equations. Therefore, in our previous paper we proved how useful the regularly varing
functions were for the study of nonoscillation and asymptotic analysis of the half-linear functional diﬀerential
equation with both retarded and advanced arguments. Aim of this talk is to establish a sharp condition of
the existence of generalized regularly varying solutions of diﬀerential equations with deviating arguments of
mixed type.
12 Hideaki Matsunaga (Osaka Pref. Univ.)
Satoru Murakami
Yutaka Nagabuchi(Okayama Univ. of Sci.)
Nguyen Van Minh (Univ. of Arkansas)

Center manifold theorem and stability for integral equations with infinite delay · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: For autonomous integral equations with infinite delay, we establish existence, local exponential
attractivity and other properties of center manifold by means of the variation-of-constants formula in thephase space. And then we investigate stability properties of the zero solution of certain nonlinear scalarintegral equation in the critical case.

Final ver.: 2016/2/15
36Functional Equations

13 Tetsutaro Shibata (Hiroshima Univ.)

Inverse bifurcation problems for the equation of population model · · · · 12

Summary: We consider the bifurcation curves for the equation which is related to the population model. Let
λ > 0 be a bifurcation parameter, and m, k > 0 be the unknown constants which control the growth of
the number of population. We determine the unknown constants m, k from the asymptotic behavior of thebifurcation curves λ(α), where α = ∥uλ ∥∞ > 0.
14 Shingo Takeuchi(Shibaura Inst. of Tech.)Multiple-angle formula of generalized trigonometric functions and its
applications to the p-Laplacian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Generalized trigonometric functions with two parameters were introduced by Drábek andManásevich in 1999 to study an inhomogeneous eigenvalue problem of p-Laplacian. Concerning thesefunctions, no multiple-angle formula has been known except for the classical case and a special case discovered by Edmunds–Gurka–Lang in 2012, not to mention addition theorems. In this talk, we will present a
new multiple-angle formula which is established between two kinds of generalized trigonometric functions,and apply the formula to some problems for p-Laplacian.
15 Masato Hashizume (Osaka City Univ.)

Minimization problem on the Hardy–Sobolev inequality · · · · · · · · · · · · · 12

Summary: We consider a minimization problem related to the Hardy–Sobolev inequality on a boundeddomain. The attainability of the best constant of the inequality is aﬀected by the position of the singularity.
In this talk, we consider the interior singularity case and we prove that the attainability of the best constantchanges depending on the scale of the domain.
16 Megumi Sano (Osaka City Univ.)
Futoshi Takahashi (Osaka City Univ.)

Scale invariance structures of the critical and the subcritical Hardy
inequalities and their improvements · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: First we establish an improved subcritical Hardy inequality on the whole space.

This alsoenables us to improve the sharp version of the critical Hardy inequality on a ball. A key ingredient is
a new transformation connecting the Hardy inequalities in critical and subcritical cases. By using thetransformation, we reveal a relationship between the scale invariance structures of those Hardy inequalities.
17 Megumi Sano (Osaka City Univ.)

Scaling invariant Hardy type inequalities with non-standard remainder
terms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the Rellich inequality on the whole space and the critical Hardy inequality on a ball.
These two Hardy type inequalities can be refined by adding remainder terms. Our remainder terms are
expressed by a distance from the families of the “virtual” extremals. A key ingredient is the critical Hardy
inequality on the whole space which was proved by Machihara, Ozawa, and Wadade in 2015.

16:30–17:30

Talk Invited by Functional Equations Section
Mitsuru Shibayama (Kyoto Univ.) A variational approach to periodic orbits in the n-body problem

Summary: In recent years variational methods have been successfully applied to the N -body problem toprove the existence of periodic solutions. In this talk we outline ideas and proofs for some recent progresses,
and show our results.

March 17th (Thu)

Conference Room III

9:30–12:00
18 Atsushi Kosaka (Osaka City Univ.)

Singular perturbation of semilinear Neumann problems on non-smoothdomains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: In this talk we consider singular perturbation of semilinear Neumann problems, and investigate
the asymptotic behavior of least-energy solutions. On domains with smooth boundary, it is known that aleast-energy solution concentrates at the point where the mean curvature is attained. We consider similar
problems on cone-like domains. Then a least-energy solution concentrates at the vertex which has the least
angle.

Final ver.: 2016/2/15
37Functional Equations

19 Daisuke Naimen (Tokyo Tech)
Masataka Shibata (Tokyo Tech)Two solutions for the Kirchhoﬀ type elliptic problem with criticalnonlinearity in high dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Kirchhoﬀ type elliptic problem involving the critical Sobolev exponent in highdimension. We show the existence of two positive solutions of the problem. A typical diﬃculty occurs
because of the lack of the compactness of the associated Sobolev embedding. In addition, the Kirchhoﬀ
type nonlocal coeﬃcient induces the multiplicity of solutions of the limiting problem. This causes a serious
diﬃculty in the concentration compactness argument. We overcome this by new techniques utilizing thefibering map method combined with the description of Palais–Smale sequences.
20 Norihisa Ikoma (Kanazawa Univ.)
Patricio Felmer (Univ. de Chile)

Existence of positive solutions for nonlinear elliptic equations involving
the Pucci operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk concerns with the existence of positive solutions for nonlinear elliptic equations involving
the Pucci operators and potential functions. Under suitable conditions on the potential functions, we shallgive the existence or the nonexistence result of positive solutions which decay at infinity.
21 Kotaro Watanabe(Nat. Defense Acad. of Japan)
Naoki Sioji (Yokohama Nat. Univ.)

Uniqueness of positive solutions of Brezis–Nirenberg problems on Hn· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the uniqueness of positive solutions of ∆Hn φ + λφ + φp = 0 on the n-dimensional
hyperbolic space Hn , where n ∈ N with n ≥ 2, λ ≤ (n − 1)2 /4, and p is subcritical or critical. In particular,
in the case n = 2, we improve Mancini and Sandeep’s uniqueness result.
22 Ryuji Kajikiya(Saga Univ.)

Nonradial positive solutions of the p-Laplace Emden–Fowler equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the p-Laplace Emden–Fowler equation with a radial and sign-changing weight in the unit
ball under the Dirichlet boundary condition. We show that no least energy solution is radially symmetric.
Moreover, we prove in the one dimensional case that a positive solution is unique under a suitable assumptionof the weight function.
23 Satoshi Tanaka (Okayama Univ. of Sci.)

Morse index and symmetry-breaking bifurcation for the one-dimensional
Liouville type equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The one-dimensional Liouville type equation is considered. The Morse indexes of even solutions
are studied, and the existence of at least one symmetry-breaking bifurcation is shown.
24 Tomohiko Sato (Nihon Univ.)
Takashi Suzuki (Osaka Univ.)

Morse indices of the solutions to the Liouville–Gel’fand problem withvariable coeﬃcients · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider a sequence of blow-up solutions to the Liouville–Gel’fand problem with variable
coeﬃcients, and their linearized eigenvalue problems. We show the precise coincides of the Morse indicesof the solution and the critical point of the Hamiltonian of the singular limit. The results are naturalextensions of those for constant coeﬃcients.
25 Masaaki Mizukami(Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Boundedness in a two-species chemotaxis system with any chemical
diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk is concerned with boundedness of solutions to a two-species chemotaxis system. Negreanu
and Tello studied the system with “non”-diﬀusive chemoattractant in 2015 and dealt with “slow” chemical
diﬀusion in 2014. The main result asserts existence of bounded global-in-time solutions to the system with“any” chemical diﬀusion.

Final ver.: 2016/2/15
38

Functional Equations

26 Tatsuki Mori (Ryukoku Univ.)
Kousuke Kuto
(Univ. of Electro-Comm.)
Tohru Tsujikawa (Univ. of Miyazaki)
Shoji Yotsutani (Ryukoku Univ.)

All global bifurcation curves for a cell polarization model · · · · · · · · · · · 12

Summary: We have investigated a stationary limiting problem for a cell polarization model proposed by Y.
Mori, A. Jilkine and L. Edelstein-Keshet (SIAM J.Appl Math, 2011). We give answers to the existence,
nonexistence, direction, connection of all global bifurcation curves including the unique existence of thesecondary bifurcation point. We also clarify all limiting profiles of solutions as a diﬀusion coeﬃcient tends
to 0.
13:30–14:30

Award Lecture for the 2015 MSJ Analysis Prize

Kazunaga Tanaka (Waseda Univ.)

Singular perturbation problems for nonlinear elliptic equations —variational
methods for degenerate setting—

Summary: We consider the existence of solutions for nonlinear elliptic problems. Especially we are interested
in peaked (or bump) soluitons. In this talk, we introduce a variational approach together with applications.
Our approach can be applicable to a wide class of nonlinear elliptic problems.

March 18th (Fri)

Conference Room III

9:30–12:00(Tokyo Tech)
27 Tsubasa Itoh
Hideyuki Miura (Tokyo Tech)
Tsuyoshi Yoneda (Tokyo Tech)

The growth of the vorticity gradient for the two-dimensional Euler flow
on domains with a corner · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the two-dimentional Euler equation on domains with a coner. We areconcerned with the question how fast the maximum of the gradient of the vorticity can grow as t → ∞. It
is shown that the growth of the vorticity gradient is depending on the angle of the sector.
28 Naoki Tsuge(Gifu Univ.)

Cauchy problem for the compressible Euler equation with an outer force· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the compressible Euler equation with an outer force. The global existence theorem
has been proved in many papers, provided that the outer force is bounded. However, the stability of theirsolutions has not yet been obtained until now. Our goal in this paper is to prove the existence of a global
solution without such an assumption as boundedness. Moreover, we deduce a uniformly bounded estimate
with respect to the time. This yields the stability of the solution. When we prove the global existence,
the most diﬃcult point is to obtain the bounded estimate for approximate solutions. To overcome this, weemploy an invariant region, which depends on both space and time variables. To use the invariant region, we
introduce a modified diﬀerence scheme. To prove their convergence, we apply the compensated compactness
framework.
(NTT)
29 Hirotada Honda(Keio Univ.⋆)
Atusi Tani

On maximal attractor and inertial set for Kuramoto–Sakaguchi equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We show the existence of the maximal attractor and inertial set of the Kuramoto– Sakaguchi
equation.

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39

Functional Equations

30 Masatoshi Okita(Kurume Nat. Coll. of Tech.)
Yoshiyuki Kagei (Kyushu Univ.)

Asymptotic profiles for the compressible Navier–Stokes equations in thewhole space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We will consider the large time behavior of the strong solutions of the compressible Navier–Stokes
equation in whole space. We show asymptotic profiles of nonlinear term. Kawashima–Matsumura–Nishida(’79) and Hoﬀ–Zumbrun (’95) proved that the solution is time-asymptotic to the one of the linearized
problem. In this talk we will show the second-order asymptotics of strong solution.
31 Kazuyuki Tsuda (Kyushu Univ.)

Time periodic problem for the compressible Navier–Stokes equation on
R2 with antisymmetry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the existence of a time periodic solution to the compressible Navier–Stokes equationon the whole space. We show the existence when the space dimension is equal to 2 for suﬃciently small time
periodic external force with antisymmetry. The proof is based on the spectral properties of the time-T -map
associated with the linearized problem around the motionless state with constant density in some weighted
L∞ and Sobolev spaces. We also obtain the existence of a stationary solution for the stationary problem on
R2 for small external force with the antisymmetry.
32 Yuko Enomoto (Shibaura Inst. of Tech.) ♭ Some global well-posedness results for the compressible barotropic visYoshihiro Shibata (Waseda Univ.) cous fluid flow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: I would like to talk about some asymptotic behaviors of Matsumura–Nishida solutions in the
study of compressible barotropic viscous fluid flow.
33 Yoshiyuki Kagei (Kyushu Univ.)
Takaaki Nishida (Kyoto Univ.)

On Chorin’s method for stationary solutions of the Oberbeck–Boussinesq
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: A. Chorin proposed an artificial compressible system to find stationary solutions of the Oberbeck–
Boussinesq equation. The proposed system is obtained by adding the time derivative of the pressure ϵ∂t pto the continuity equation of the Oberbeck–Boussinesq equation, where ϵ > 0 is a small parameter. If thesolution of the artificial compressible system converges to a stationary solution, then the stationary solutionis also a stationary solution of the Oberbeck–Boussinesq equation. In this talk a mathematical justificationof Chorin’s method is considered. It will be shown that if a stationary solution of the Oberbeck–Boussinesq
equation is asymptotically stable and the velocity field of the stationary solution satisfies some smallness
condition, then it is also asymptotically stable as a stationary solution of the artificial compressible system
for suﬃciently small ϵ.
34 Hajime Koba

(Waseda Univ.)

On compressible fluid flow on an evolving hypersurface · · · · · · · · · · · · · 10

Summary: We consider compressible fluid flow on an evolving hypersurface. We focus on kinetic, dissipation,and thermal energies to derive governing equations for the motion of compressible viscous flow on an evolving
hypersurface.
35 Hajime Koba

(Waseda Univ.)

On incompressible fluid flow on an evolving hypersurface · · · · · · · · · · · · 10

Summary: We consider incompressible fluid flow on an evolving hypersurface. We focus on kinetic, dissipation,and thermal energies to derive governing equations for the motion of incompressible viscous flow on an
evolving hypersurface.
36 Erika Ushikoshi (Tamagawa Univ.)
Shuichi Jimbo (Hokkaido Univ.)
Hideo Kozono (Waseda Univ.)
Yoshiaki Teramoto (Setsunan Univ.)

Hadamard variational formula for the eigenvalues of the Stokes equations and its application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: By means of the Hadamard variational formula for the multiple eigenvalues of the Stokes equations,
we shall analyze the geometry of the domain.

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40Functional Equations

37 Teppei Kobayasi (Meiji Univ.) ♭ A steady flow of an incompressible viscous fluid in a generalized aperture
domain for a plane · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: In this talk, we introduce a generalized aperture domain in a plane. Furthermore we consider
the steady Navier–Stokes equations approaching Jeﬀery–Hamel’s flow at infinity in a generalized aperture
domain in a plane.
14:15–16:15
38 Ana Silvestre (Tech. Univ. of Lisbon) ♭ A boundary control problem for the steady self-propelled motion of a
Takéo Takahashi (Univ. of Lorraine) rigid body in a Navier–Stokes fluid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Toshiaki Hishida (Nagoya Univ.)
Summary: A boundary control problem for the steady self-propelled motion of a rigid body in a viscousincompressible fluid is studied. We provide a physically relevant control, which vanishes outside a prescribed
portion of the boundary but leads to a given rigid motion. It is also shown that the self-propelled condition
implies better summability of the fluid flow at infinity.
39 Hideo Kozono (Waseda Univ.)
Yutaka Terasawa (Nagoya Univ.)
Yuta Wakasugi (Nagoya Univ.)

A remark on Liouville-type theorems for the stationary Navier–Stokes
equations in three space dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Consider the 3D homogeneous stationary Navier–Stokes equations in the whole space R3 . We deal
with solutions vanishing at infinity in the class of the finite Dirichlet integral. By means of quantities having
the same scaling property as the Dirichlet integral, we establish new a priori estimates. As an application,
we prove the Liouville theorem in the marginal case of scaling invariance.
40 Takahiro Okabe (Hirosaki Univ.)

Time periodic strong solution to the Navier–Stokes equations with large
data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the incompressive Navier–Stokes equation in a three dimensional bounded smoothdomain. For any large periodic external force, we construct a periodic strong solution, provided the period
is short enough. Moreover, for a long period and a large external force, we construct a unique and stable
time periodic strong solution of the Navier–Stokes equations introducing the highly oscillating data in thesense of eigenfunctions of the Stokes operator.
41 Mitsuo Higaki (Tohoku Univ.)

Navier wall law for nonstationary viscous incompressible flows · · · · · · · 12

Summary: The Navier wall law is an eﬀective boundary condition to describe the viscous incompressible flows
near the rough boundary, which is formally derived from the boundary layer analysis. In this talk we study
the Navier wall law for the two-dimensional initial boundary value problem of the Navier–Stokes system.
The Navier wall law is verified for the initial data in C 1 class under the natural compatibility condition.
Our proof relies on the boundary layer analysis and the L∞ theory of the Navier–Stokes equations in thehalf space.
42 Noboru Chikami (Tohoku Univ.)
Raphaël Danchin (Univ. Paris-Est)

Global solution for the Navier–Stokes–Poisson system in two and higher
dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We obtain a new a priori estimate for solutions of the Navier–Stokes–Poisson system. As acorollary, we establish the unique global solvability in critical spaces for that system in any dimension n ≥ 2.
43 Hirokazu Saito (Waseda Univ.)(Waseda Univ.)
Sri Maryani

On the R-boundedness of solution operator families for two-phase
Stokes resolvent equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we show the R-boundedness of solution operator families for two-phase Stokes
N
resolvent equations on a general domain. Such a domain covers e.g. ṘN = RN
+ ∪ R− (N ≥ 2), perturbed
NṘN , layers, perturbed layers, bounded domains, and exterior domains, where RN+ and R− are the open
upper and lower half spaces, respectively. The essential assumption is the unique solvability of the weak

Dirichlet–Neumann problem, which will be introduced in the talk.

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41Functional Equations(Kyoto Univ.)

44 Ken Abe

On regularity of axisymmetric Navier–Stokes flows in an exterior domain· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial-boundary value problem of the Navier–Stokes equations for axisymmetricinitial data with swirl in the exterior of an infinite cylinder Πε = {x ∈ R3 ||xtan | > ε, x3 ∈ R}, subject
to the slip boundary condition. We prove global well-posedness of the problem and study spatial profilesof potential singularities as ε → 0. We establish an upper blow-up estimate in terms of energy for theazimuthal component of vorticity, and prove that a blow-up rate of the energy is at most O(ε−2 ) as ε → 0.
The proof is based on the Boussinesq system. It is shown that the system is globally well-posed in theexterior domain for axisymmetric initial data without swirl.
45 Takashi Suzuki (Osaka Univ.)

2D Smoluchowski–Poisson equation: criteria on collision of sub-collapses······························································ 8

Summary: We study the blowup in finite time in the 2D Smoluchowski–Poisson equation. Any blowup point
is simple if and only if it has type II blowup rate and the total free energy is bounded.
46 Takayoshi Ogawa (Tohoku Univ.) ♭ Non-uniform bound and finite time blow up for solutions to a driftHiroshi Wakui (Tohoku Univ.) diﬀusion equation in higher dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We show the non-uniform bound for a solution to the Cauchy problem of a drift-diﬀusion equationof a parabolic-elliptic type in higher space dimensions. If an initial data satisfies a certain condition involving
the entropy functional, then the corresponding solution to the equation does not remains uniformly bounded
in a scaling critical space.
16:30–17:30

Talk Invited by Functional Equations Section♭
Masaki Kurokiba
Finite time blow up for a solution to system of the drift-diﬀusion(Muroran Inst. of Tech.) equations in higher dimensions

Summary: We discuss the existence of the blow-up solution for multi-component parabolic-elliptic drift
diﬀusion model in higher space dimensions. We show that the local existence, uniqueness and well-posednessof a solution in the weighted L2 spaces. Moreover we prove that if the initial data satisfies a certain
condition, then the corresponding solution blows up in a finite time. This is a system case for the blow
up result of the chemotactic and drift-diﬀusion equation proved by Nagai (2001) and Nagai–Senba–Suzuki(2000) and gravitational interaction of particles by Biler (1995), Biler–Nadzieja (1994, 1998). We generalize
the result in Kurokiba–Ogawa (2003,2015) and Kurokiba (2014) for multi-component problem and give a
suﬃcient condition for the finite time blow up of the solution.

March 19th (Sat)

Conference Room III

9:30–12:00
47 Yuki Kimura(Tohoku Univ.)

Asymptotic profile of a solution to thermoelastic equations · · · · · · · · · · 12

Summary: We consider the asymptotic behavior of a solution to a linear thermoelastic equation in 2dimension. Decomposing the elastic wave into irrotational and rotational components via the Helmholtz
decomposition, we obtain that the solution converges to the solution of heat equations and the diﬀusive
wave by eliminating the certain wave parts.

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42Functional Equations

48 Hiromichi Itou (Tokyo Univ. of Sci.)
Victor A. Kovtunenko (Univ. of Graz)
Kumbakonam R. Rajagopal(Texas A & M Univ.)

On a crack problem for nonlinear elasticity · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Within the framework of nonlinear elasticity with limiting small strains introduced by Rajagopal,
the nonlinear crack problem subject to non-penetration conditions is considered. In this talk, we introduce
a solution of generalized variational inequalities, which coincides with the weak solution if the solution
possesses extra regularity. The wellposedness is provided by the construction of an approximation problem
using elliptic regularization and penalization techniques.
49 Hideo Soga

(Ibaraki Univ.)

Generalization of the Maxwell equation and relation to elastic equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk is on generalization of the Maxwell equation. A real-symmetric system of partial
diﬀerential equations is proposed as the generalized Maxwell equation. It is explained that this equation
can be transformed each other into a generalized elastic equation and that the equation can be decomposed
into two parts associated with waves of the transversal type and ones of the longitudinal type. Expression
by the potential is also described.
50 Hironari Miyoshi (Waseda Univ.)
Masayoshi Tsutsumi (Waseda Univ.)

Convergence of hydrodynamical limits for generalized Carleman models
with nonhomogeneous boundary condition · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial boundary value problem for a 2-speed system of first order semi-linear
hyperbolic equations with inhomogeneous boundary data. We establish the existence of global weak solutionsin L1 by the theory of nonlinear evolution operators in a non reflexive Banach space. Using the monotone
method and the div-curl lemma, we investigate the hydrodynamical limits of solutions of the hyperbolic
systems and show that the limits verify the doubly nonlinear parabolic equations.
51 Hironobu Sasaki (Chiba Univ.)

Small analytic solutions to the Hartree equation · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for the Hartree equation in space dimension d ≥ 3. We assume
that the interaction potential V belongs to the weak Ld/2 space. We prove that if the initial data ϕ issuﬃciently small in the L2 -sense and the Fourier transform Fϕ satisfies a real-analytic condition, then thesolution u(t) is also real-analytic for any t ̸= 0. We also prove that if ϕ and V satisfy some strong condition,then u(t) can be extended to an entire function on Cd for any t ̸= 0. We remark that no L2 smallness
condition is imposed on first and higher order partial derivatives of ϕ and Fϕ.
52 Sojiro Murai (Univ. of Electro-Comm.)
Kiyoshi Mochizuki(Tokyo Metro. Univ.⋆ /Chuo Univ.)

Smoothing and scattering for Klein–Gordon equations in exterior domain with time dependent perturbations · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This paper deals with the existence, smoothing properties and scattering of solutions to magnetic
Klein–Gordon equations in exterior domain with time dependent small perturbations. Smoothing properties
based on the resolvent estimates will reinforce the abstract scattering theory developed in our previous
paper, and our concrete problems are treated in this framework.
53 Mamoru Okamoto (Shinshu Univ.)
Shuji Machihara (Saitama Univ.)
Hyungjin Huh (Chung-Ang Univ.)

Well-posedness and ill-posedness of the Cauchy problem for the one
dimensional nonlinear Dirac equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for the nonlinear Dirac equations (∂t ± ∂x )U± =i|U± |k |U∓ |m−k U± in one spatial dimension which was introduced by Huh (2013). Several results on
well-posedness and ill-posedness have been btained. Since the nonlinearity is not smooth if k or m is odd,
an upper bound of s to be well-posed appears. We prove that the upper bound is essential. More precisely,
we show ill-posedness in H s (R) for suﬃciently large s.

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43Functional Equations

54 Takiko Sasaki (Univ. of Tokyo)

Blow-up curve for a derivative nonlinear wave equation · · · · · · · · · · · · · 10

Summary: We study one dimensional wave equation ∂t2 u − ∂x2 u = (∂t u)p . The solution of this equation blows
up in finite time, under the appropriate initial condition. We are concerned with the shape of the blow-up
curve which is defined by Γ = ∂ {(x, t) ∈ R × (0, ∞) | |∂t u| < +∞} . The purpose of this paper is to showthat Γ is a C 1 space-like surface if the initial values are large and smooth enough. Our proof is based on
the proof Caﬀarelli and Friedman (1986).
55 Hiroyuki Takamura(Future Univ.-Hakodate)

Improved Kato’s lemma and a new conjecture on the lifespan of solutionsof semilinear wave equations in two space dimensions · · · · · · · · · · · · · · · 12

Summary: We introduce improved Kato’s lemma for ordinary diﬀerential inequality to have a new conjectureon the lifespan of solutions of semilinear wave equations in two space dimensions. Our result is the upperbound of the lifespan only, but it is shorter than the one from the analogy to higher space dimensions when
the integral of the initial speed does not vanish.
56 Masaru Ikehata (Hiroshima Univ.)

On finding an obstacle embedded in the rough background medium via
the enclosure method in the time domain · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: A mathematical method for through-wall imaging via wave phenomena in the time domain is
introduced. The method makes use of a single reflected wave over a finite time interval and gives us acriterion whether a penetrable obstacle exists or not in a general rough background medium. Moreover, if
the obstacle exists, the lower and upper estimates of the distance between the obstacle and the center pointof the support of the initial data are given.
57 Yuta Wakasugi (Nagoya Univ.)

Scaling variables and asymptotic profiles of solutions to the semilinear
damped wave equation with variable coeﬃcients · · · · · · · · · · · · · · · · · · · 10

Summary: We study the asymptotic behavior of solutions for the semilinear damped wave equation withvariable coeﬃcients. We prove that if the damping is eﬀective, and the nonlinearity can be regarded
as perturbations, then the solution is approximated by the scaled Gaussian of the corresponding linear
parabolic problem. The proof is based on the scaling variables and energy estimates.
14:15–15:45
58 Sohei Ashida(Kyoto Univ.)

Propagation estimates for the scattering channels with 2 clusters ofN-body Schrödinger operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the propagation estimates for the scattering channels with two clusters. When there
are bounded clusters, the clusters are accelerated by the gain of the kinetic energy from the bound stateenergy. To obtain the minimal velocity estimates positivity of the commutator of the generator of thedilations and the Hamiltonian restricted to small energy interval is used. We use the operator which consistsof the generator of the dilations of external coordinates, the projection to the bound state and the cutoﬀ
function restricting the channel instead.
59 Masayuki Hayashi (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

Global solutions for a generalized nonlinear derivative Schrödinger equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the Cauchy problem for a generalized nonlinear derivative Schrödinger equationi∂t u + ∂x2 u + i|u|2σ ∂x u = 0, with the Dirichlet boundary condition. We prove small data global in time
well-posedness in H01 if σ ≥ 1, and large data global existence of solutions in H01 if 1/2 ≤ σ < 1.
60 Ryosuke Hyakuna (Waseda Univ.)

On global solutions to the nonlinear Schrödinger equations with large
Lp -initial data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We investigate the Cauchy problem for the nonlinear Schrödinger equation with the pure power
nonlinearity |u|α−1 u. It is shown that a local solution of the initial value problem exists in Lq[−T,T ] (Lr )-space
if p < 2 and p is close to 2. Moreover, we show that the local solution can be extended globally if p is
suﬃciently close to 2.

Final ver.: 2016/2/15
44Functional Equations(Kyoto Univ.)
61 Takahisa Inui
Masahiro Ikeda (Kyoto Univ.)

Global Dynamics for a nonlinear Schrödinger equation with a repulsive
Dirac delta potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider a focusing L2 -supercritical nonlinear Schrödinger equation with a repulsive Dirac deltapotential (δNLS). It is well known that δNLS is locally well-posed in H 1 (R) and there exist standing wave
solutions eiωt Qω (x) when ω > γ 2 /2 where Qω is a unique radial positive solution to − 21 ∂x2 Q + ωQ − γδ0 Q =|Q|p−1 Q. Our aim is to find a necessary and suﬃcient condition to determine the behavior of solutions
below the standing waves.
62 Kota Uriya(Tohoku Univ.)

Final state problem for systems of cubic nonlinear Schrödinger equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We are concerned with the asymptotic behavior of the solution to systems of cubic nonlinear
Schrödinger equations in one dimension. It is known that mass transition phenomenon occur for a systemof quadratic nonlinear Schrödinger equations in two dimensions under the mass resonance condition. We
show that mass transition phenomenon also occurs for cubic nonlinearities under the corresponding mass
resonance conditions.
(Osaka Univ.)
63 Yuji Sagawa
Hideaki Sunagawa (Osaka Univ.)

The lifespan of small solutions to cubic derivative nonlinear Schrödinger
equations in one space dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Consider the initial value problem for cubic derivative nonlinear Schrödinger equations in one
space dimension. We provide a detailed lower bound estimate for the lifespan of the solution, which can becomputed explicitly from the initial data and the nonlinear term. This is an extension and a refinement of
the previous work (H. Sunagawa; Osaka J. Math. 43 (2006), 771–789) where the gauge-invariant nonlinearity
was treated.
16:00–17:00

Award Lecture for the 2015 MSJ Analysis Prize

Mitsuru Sugimoto (Nagoya Univ.)

Smoothing eﬀect of Schrödinger equations in the angular direction

Summary: In 1997, Hoshiro discovered a smoothing eﬀect of Schrödinger equations in the angular direction.
We will discuss how this result has been developed in the last two decades.

Final ver.: 2016/2/15
45

Real Analysis

Real Analysis
March 18th (Fri)

Conference Room IV

9:30–12:00
1 Yoshifumi Ito (Univ. of Tokushima⋆) ♭ New proof of Plancherel’s theorem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this paper, we give the new proof of Plancherel’s theorem by using the method of orthogonalmeasure.
2 Yōhei Yamasaki (Yamato Univ.)

Around a Jordan curve of positive measure in R3 · · · · · · · · · · · · · · · · · · 15

Summary: We construct a Jordan curve of positive measure in the eucledean space of dimension 3 and ameasure preserving homeomorphism between the closed simplex and a ball with an additional measure on
the center pole.
3 Yōhei Yamasaki (Yamato Univ.)

On the “directed measure” not in the C1 class · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk shows that the absolute continuity does not suﬃce to develope the theory of directed
measure not in the C1 class.
4 Kiyohisa Tokunaga (Yamaguchi Univ.)

The antisymmetric total double integral · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Our new kind of antisymmetric total double integral and the conventional double partial integrals
as the iterated anti-derivatives figure out same values for an integrand of various kinds of monomials, andfor a domain of a segment and three types of conic section. Moreover, our integral has advantage over theconventional one for approximate values calculated as finite double sums. However, the relationship between
the definition of our integral and that of the conventional one is not known. If it is possible to derive one
kind of definition from the other between these two kinds of double integrals, it is conjectured that our
integral may be reduced to be the conventional one as its special case.
5 Toshiharu Kawasaki (Nihon Univ.)

Some examples between the Lebesgue and Denjoy integrals · · · · · · · · · · 15

Summary: In this talk, we give new integrals between the Lebesgue integral and the restricted Denjoy
integral. Moreover we give some examples of these integrable functions.
6 Yukino Tomizawa (Chuo Univ.)

Fixed point property with respect to the Bregman distance · · · · · · · · · · 10

Summary: The purpose is to consider the fixed point property of firmly nonexpansive mappings with respect
to the Bregman distance.
7 M. Ali Khan (Johns Hopkins Univ.)
Nobusumi Sagara (Hosei Univ.)

Maharam-types and Lyapunov’s theorem for vector measures on locallyconvex spaces without control measures · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We formulate the saturation property for vector measures in locally convex Hausdorﬀ spaces asa nonseparability condition on the derived Boolean σ-algebras by drawing on the topological structure ofvector measure algebras. We exploit a Pettis-like notion of vector integration in locally convex Hausdorﬀ
spaces, the Bourbaki–Kluvánek–Lewis integral, to derive an exact version of the Lyapunov convexity theorem
in locally convex Hausdorﬀ spaces without the Bartle–Dunford–Schwartz property. We apply our Lyapunov
convexity theorem to the bang-bang principle in Lyapunov control systems in locally convex Hausdorﬀ
spaces to provide a further characterization of the saturation property.

Final ver.: 2016/2/15
46

Real Analysis

8 Ryotaro Tanaka (Niigata Univ.)
Naoto Komuro(Hokkaido Univ. of Edu.)
Kichi-Suke Saito (Niigata Univ.)

On the duality of James constant of rotation invariant norms · · · · · · · · 15

Summary: In this talk, we show that the James constant of the space R2 endowed with a π/2-rotation
invariant norm coincides with that of its dual space. In particular, we have the same statement on thesymmetric absolute norms on R2 as a corollary.
9 Hiroyasu Mizuguchi (Niigata Univ.)

On the duality of a new constant related to Isosceles orthogonality· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider Isosceles orthogonality and Birkhoﬀ orthogonality, which are the most used notionsof generalized orthogonality. In 2006, Ji and Wu introduced a geometric constant D(X) to measure thediﬀerence between these two orthogonality types. From their results, we have that D(X) = D(X ∗ ) holds
for any symmetric Minkowski plane. On the other hand, for the James constant J(X), Saito, Sato andTanaka recently showed that if the norm of a two-dimensional space X is absolute and symmetric then
J(X) = J(X ∗ ) holds. We consider a new constant D(X, λ) such that D(X) = inf λ∈R D(X, λ) and obtainthat in the same situation D(X, λ) = D(X ∗ , λ) holds for any λ ∈ (0, 1).
14:15–16:10
10 Hiroko Manaka (Yokohama Nat. Univ.)

Fixed point theorems for an elastic nonlinear mapping in Banach spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let E be a smooth Banach space with a norm || · ||. Let V (x, y) = ||x||2 + ||y||2 − 2 < x, Jy >for any x, y ∈ E, where < ·, · > stands for the duality pair and J is the normalized duality mapping. We
defined a V -strongly nonexpansive mapping with respect to this bifunction V (·, ·). This nonlinear mapping
is nonexpansive in a Hilbert space. However, we could show that this mapping is not nonexpansive in some
Banach spaces. In this talk, we shall introduce convergence theorems and existence theorems for fixed pointsof this elastic nonlinear mapping.
11 Fumiaki Kohsaka (Tokai Univ.)

Strong convergence of an implicitly defined iterative sequence for maximal monotone operators in Banach spaces · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study the strong convergence of an iterative sequence which is implicitly definedby using the resolvent of maximal monotone operators in Banach spaces.
12 Koji Aoyama(Chiba Univ.)

Strongly quasi-nonexpansive mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we focus on strongly quasinonexpansive mappings in a metric space or a Banach
space. In particular, we present some properties and characterizations of such mappings.
13 Tomonari Suzuki(Kyushu Inst. of Tech.)Topology on ν-generalized metric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about topology on ν-generalized metric spaces.
14 Aoi Honda (Kyushu Inst. of Tech.)
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

Fractional Shepp sequence space and fractional diﬀerence operators on
Lp · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We have introduced the Shepp sequence space which is determined by an Lp function. In this talk,we generalize the Shepp sequence space to the fractional Shepp sequence space and discuss its topologicalstructure and linearity.

Final ver.: 2016/2/15
47

Real Analysis

15 Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)
Aoi Honda (Kyushu Inst. of Tech.)Lp space for a subadditive monotone measure and its dual L†p · · · · · · · 15

Summary: We introduce the Lp -space for a sub-additive monotone measure based on the Choquet integral
and its dual space L†p . The basic properties of Lp and L†p are studied. Lp is a quasi-metric space and L†p is
a complete metric space by the dual metric.
16 Naohito Tomita (Osaka Univ.)
Loukas Grafakos (Univ. of Missouri)
Akihiko Miyachi(Tokyo Woman’s Christian Univ.)
Hanh Van Nguyen (Univ. of Missouri)

Multilinear Fourier multipliers with minimal Sobolev regularity · · · · · · 15

Summary: The problem to find the smoothness conditions for multilinear Fourier multipliers that are as
small as possible to ensure the boundedness of the corresponding operators from products of Hardy spaces
H p1 × · · · × H pm to Lp , 1/p1 + · · · + 1/pm = 1/p, is considered.
16:30–17:30

Talk Invited by Real Analysis Section

Enji Sato(Yamagata Univ.⋆)

The operators related to Fourier multipliers on some function spaces

Summary: We talk about the operators related to Fourier multipliers on some function spaces which are Lp
spaces, Morrey spaces and etc.

March 19th (Sat)

Conference Room IV

9:30–12:00
17 Yutaka Tsuzuki (Tokyo Univ. of Sci.)
Alexander Leonidovich Skubachevskii(Peoples’ Friendship Univ. of Russia)

Existence of solutions to Vlasov–Poisson systems in a half-space · · · · · 15

Summary: This talk is concerned with solvability of Vlasov–Poisson systems in a half-space. In 2013, an
existence result on a time interval (0, T ) was obtained by Skubachevskii. However largeness of initial
function f0β is too strong. The purpose of this talk is to weaken the condition of largeness of f0β .
18 Akio Ito
Yusuke Murase(Meijo Univ.)

Existence of solutions for brewing model of Japanese Sake with stirringeﬀect. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss the existence of solution for brewing model of Japanese Sake with stirringeﬀect. This model is formulated by using partial diﬀerential equations with constraint condition. The
constraint set in the model is fixed if temperature is given. In other words, the solution of this model
depends upon the solution self. It shows that the model is a problem of quasi-variational inequality type.
19 Dai Noboriguchi (Waseda Univ.)
Kazuo Kobayasi (Waseda Univ.)

The existence theorem of solutions for degenerate parabolic equations
with stochastic forcing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial value problem for degenerate parabolic partial diﬀerential equations withmultiplicative noise on a d-dimensional torus Td :du + div(B(u)) dt = div(A(u)∇u) dt + Φ(u) dW (t)in Td × (0, T )We focus on the existence of a solution. Using nondegenerate smooth approximations, Debussche, Hofmanová
and Vovelle proved the existence of a kinetic solution. On the other hand, we propose to construct a sequenceof approximations by applying a time splitting method. This method will somewhat give us not only asimpler and more clear discussion but an improvement over the existence result.

Final ver.: 2016/2/15
48

Real Analysis

20 Hiroshi Watanabe (Salesian Polytech.)Continuous dependence of BV -entropy solutions to strongly degenerate
parabolic equations with variable coeﬃcients · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial value problem (CP) for strongly degenerate parabolic equations withvariable coeﬃcients. Strongly degenerate parabolic equations are regarded as a linear combination of thetime-dependent conservation laws (quasilinear hyperbolic equations) and the porous medium type equations(nonlinear degenerate parabolic equations). Thus, this equation has both properties of hyperbolic equationand those of parabolic equations and describes various nonlinear convective diﬀusion phenomena such as
filtration problems, Stefan problems and so on.
In this talk, we consider BV-entropy solutions to (CP). Our purpose is to prove the continuous dependenceof the BV-entropy solutions.
21 Ken Shirakawa (Chiba Univ.)
Hiroshi Watanabe (Salesian Polytech.)
Salvador Moll (Univ. of Valencia)

Energy-dissipation for phase field model of grain boundary motion withanisotropy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, a system of parabolic variational inequalities is considered. The system is a modified
version of the Kobayashi–Warren–Carter system of grain boundary motion such that the governing freeenergy includes some anisotropic eﬀects of grains. Additionally, we note that our mathematical model enables
to reproduce the dynamic changes of structural units, caused by the rotations of crystalline orientations. In
the last MSJ meeting (in Kyoto Sangyo Univ.), we reported the solvability result for our system. Based on
the previous work, we set the subject of this talk to discuss about the continuing topics, that are concernedwith energy-dissipation and large-time behavior for our system.
(Kochi Univ.)
22 Risei Kano
Takesi Fukao (Kyoto Univ. of Edu.)

The convergence of solutions for the perfect plasticity models · · · · · · · · 15

Summary: In this talk, in the variational inequalities related to the perfect plasticity models, we discuss theconvergence of the solution at the diﬀusion parameter to 0.
23 Takeshi Fukao (Kyoto Univ. of Edu.)

Degenerate parabolic equations with dynamic boundary conditions · · · 15

Summary: In this talk, an asymptotic limit of Cahn–Hilliard systems to a degenerate parabolic equation
with dynamic boundary condition is focused. The target diﬀusion equation is an abstract form of the Stefan
problem, porous media equation, Hele-Shaw profile, nonlinear diﬀusion of singular logarithmic potential,
nonlinear diﬀusion of Penrose–Fife type, fast diﬀusion equation and so on. By setting the suitable potentialof the Cahn–Hilliard systems all of these problems are characterized by the limit of the Cahn–Hilliard
systems.
24 Noriaki Yamazaki (Kanagawa Univ.)
Takeshi Fukao (Kyoto Univ. of Edu.)
Mohammad Hassan Farshbaf-Shaker(WIAS, Germany)

Lagrange multiplier and singular limit of double obstacle problems forAllen–Cahn equation with constraint · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we study the properties of the Lagrange multiplier to an Allen–Cahn equation withdouble obstacle potential. Here, dynamic boundary condition, including the Laplace–Beltrami operator on
the boundary, is investigated. Then, we establish the singular limit of our system and clarify the limit of
the solution and the Lagrange multiplier to our problem.

Final ver.: 2016/2/15
49

Real Analysis

25 Toyohiko Aiki (Japan Women’s Univ.)
Sato Naoki(Nagaoka Nat. Coll. of Tech.)
Murase Yusuke (Meijo Univ.)

Hysteresis behavior of a solution to the free boundary problem describing an adsorption phenomena · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider a free boundary problem which is proposed as a mathematical model for
adsorption phenomena in a porous media. The existence, uniqueness and large time behavior of solutions
were already discussed. Also, we pointed out that the relationship between the humidity and the degree ofsaturation observed in experiments are represented by our model through some numerical simulations. In
this talk we investigate the asymptotic behavior of a free boundary as the density of water in air tends to0, and hysteresis behavior of a solution to the limit problem.
14:15–15:00
26 Kentarou Fujie (Tokyo Univ. of Sci.)
Sachiko Ishida (Tokyo Univ. of Sci.)
Akio Ito
Tomomi Yokota (Tokyo Univ. of Sci.)

Existence and large time behavior of a global-in-time solution to achemotaxis tumor invasion model with degenerate diﬀusion · · · · · · · · · · 15

Summary: In this talk, we consider an initial-boundary problem of a chemotaxis, not haptotaxis, tumor
invasion system with a degenerate diﬀusion. Actually, first of all we can show that our problem has at least
one global-in-time solution by considering appropriate approximate systems with non-degenerate diﬀusions
and deriving some uniform estimates, which are independent of approximate parameters and enable us to
use the limit procedure. Moreover, we succeed investing a large-time behavior of this global-in-time solution.
27 Noriaki Yoshino (Tokyo Univ. of Sci.)

An operator theoretic approach to parabolic-parabolic chemotaxis systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider existence of solutions to parabolic-parabolic chemotaxis systems of generalform. In the case of parabolic-ellipic chemotaixis systems, existence of local solutions was already shown via
nonlinear m-accretive operator theory. However, in the case of parabolic-parabolic chemotaxs systems there
is no existence result by this approach. In this talk existence of solutions is obtained by applying nonlinear
m-accretive operator theory.
28 Toshitaka Matsumoto (Shizuoka Univ.)
Naoki Tanaka (Shizuoka Univ.)

Quasilinear theoretical approach to size-structured models · · · · · · · · · · 15

Summary: The well-posedness for abstract quasilinear evolution equations in Banach spaces is discussed. We
do not assume the denseness of the domain of quasilinear operators. Global well-posedness of C 1 -solutions
is obtained and the abstract result is applied to size-structured models.

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50

Real Analysis

15:15–16:15

Talk Invited by Real Analysis Section

Motohiro Sobajima(Tokyo Univ. of Sci.)

On an Lp -theory for second-order elliptic operators with unbounded
coeﬃcients

Summary: This talk is concerned with an Lp -theory for second-order elliptic operators of the form Au =−div (a∇u) + F · ∇u + V u in RN , where N ∈ N,1 < p < ∞ and all coeﬃcients a = (ajk )jk , F = (Fj )j andV are allowed to be unbounded at infinity. The essential m-accretivity and m-sectoriality in Lp -spaces havebeen investigated in recent years. In this talk we deal with the m-accretivity and m-sectoriality in Lp -spacesof minimal realization of A from the view-point of the decomposition formula
(
) ]
∫
∫ [
divF
(Au)v dx =a∇u · ∇v + V −
uv dx
p
RN
RN
(
)
∫
v∇u u∇v
F·
+
− ′
dx
p
p
RN
which may be regarded as a generalization of the formula decomposing sesqui-linear forms in L2 into
symmetric and skew-symmetric parts. Particularly, the L2 -theory for Schrödinger operators has been widely
considered since it plays an important role in the field of quantum mechanics. Despite of this, the problem
for selfadointness of operators having rapidly growing diﬀusion and potential, posed by T. Kato in 1981,
has been remained open until 2010. As a byproduct of the Lp -theory in this talk, the answer seems to bevery close.

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Functional Analysis

Functional Analysis
March 16th (Wed)Conference Room IX

10:00–12:00
1 Hisashi Morioka(Shibaura Inst. of Tech.)
Kazunori Ando (Ehime Univ.)
Hiroshi Isozaki (Univ. of Tsukuba)

Spectral properties of Schrödinger operators on perturbed lattices · · · · 15

Summary: We show the absence of eigenvalues embedded in the continuous spectrum of discrete Schrödinger
operators on perturbed lattices, and we construct its scattering theory. Our theory covers the square,
triangular, diamond, Kagome lattices, as well as the ladder, the graphite and the subdivision of squarelattice.
2 Kazunori Ando (Ehime Univ.)
Hyeonbae Kang (Inha Univ.)

Spectral properties of the Neumann–Poincaré operator and anomalous
localized resonance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the spectral properties of the Neumann–Poincaré operator on bounded simply connecteddomains in two and three dimensions with C 1,α -boundaries. Then, using the quasi-static approximation, weshow that anomalous localized resonance (ALR) occurs on ellipses in two dimensions; on the other hand,
ALR does not occur on balls in three dimensions.
3 Toshimitsu Takaesu (Gunma Univ.)

Essential spectrum of a fermionic quantum field model and its application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider an interaction system of a fermionic quantum field. The state space is defined bya tensor product of a fermion Fock space and a Hilbert space, and the total Hamiltonian is a self-adjoint
operator on the Hilbert space. Then it is proven that a subset of real numbers is the essential spectrum. Itsapplication to the Yukawa model is also considered, and the HVZ theorem is obtained.
4 Atsuhide Ishida (Otemon Gakuin Univ.)

A propagation property for the fractional power of negative Laplacian· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Enss (1983) obtained one of the propagation estimates for the free Schrödinger operator and it
turned out that this estimate was very useful for the inverse scattering problem by Enss–Weder (1995).
Since then, this method has been called the Enss–Weder method. We study the same type of propagation
estimate for the fractional power of negative Laplacian. In the same way of Enss–Weder, we try to apply
our estimate to the inverse scattering problem.
5 Michiyuki Watanabe (Niigata Univ.)
Hiroshi Isozaki (Univ. of Tsukuba)
Mitsuteru Kadowaki(Univ. of Shiga Pref.)Asymptotic behavior of stationary solutions to elastic wave equationsin half-spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the stationary scattering problem for the elastic operator in a perturbed half-space.
In this talk, we present(1) Construction of the generalized Fourier transform.
(2) Characterization of solutions in terms of the generalized Fourier transform.
(3) Asymptotic expansion of solutions and the S-matrix.

Final ver.: 2016/2/15
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Functional Analysis

6 Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)
Yoshinori Kametaka (Osaka Univ.⋆)

The best constant of discrete Sobolev inequalities on the regular polyhedra including double bond · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We have obtained the best constant of discrete Sobolev inequalities on the regular polyhedra
including double bond. By giving appropriate indices on vertices of polyhedra and by introducing discrete
Laplacians, we have obtained Green matrices and pseudo Green matrices. (Pseudo) Green matrices are
the reproducing kernels by setting appropriate vector spaces and inner products. By applying Schwarz
inequality to the reproducing relations, the discrete Sobolev inequalities are obtained.The maximum of the
diagonal values of pseudo Green matrices is the best constants of inequalities.
7 Toshinao Kagawa (Tokyo City Univ.)
Kunio Yoshino (Tokyo City Univ.)

The Hermite expansion of the characteristic functions · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to show the examples of the Hermite function expansion. We determine
the coeﬃcients of the Hermite expansion of the characteristic function of [−a, a] and [0, a], explicitly. As
applications, we determine the coeﬃcients of the Hermite expansion of the sinc function, the Heavisidefunction
14:15–15:15

Talk Invited by Functional Analysis Section

Hiroaki Niikuni(Maebashi Inst. of Tech.)

Band-gap spectral structure of carbon nanotubes

Summary: Carbon has possibilities of forming a lot of types of allotropes: diamonds, fullerenes, graphite andgraphene. Allotropes of carbons located on lattices with cylindrical structures are called carbon nanotubes
and have been playing important roles in the field of mechanical engineering due to their outstanding
properties such as electrical conduction and hardness. In this talk, we study the spectrum of carbon
nanotubes from the point of view of quantum graphs. Namely, we examine the spectral properties of
periodic Schrödinger operators on metric graphs corresponding to carbon nanotubes. Especially, we deal
with one of the simplest models of periodically broken carbon nanotubes and examine its spectral properties.
By utilizing the Floquet–Bloch theory, we show that its spectrum has the band-gap structure. Namely,
we notice that its spectrum consists of the absolutely continuous spectrum and the set of eigenvalues with
infinite multiplicities. Furthermore, we prove that the absolutely continuous spectrum is characterized
by the corresponding discriminants and consists of infinitely many closed intervals. We note that our
spectral discriminants are generally not entire functions but meromorphic functions, whereas the spectral
discriminants for the standard Hill operators are entire.

March 17th (Thu)

Conference Room IX

10:00–12:00
8 Hideyuki Ishi

(Nagoya Univ.)

Harmonic analysis on Bergman–Hartogs domains · · · · · · · · · · · · · · · · · · 15

Summary: The Bergman–Hartogs domain is a Hartogs domain defined by a negative power of the Bergman
kernel function over a bounded homogeneous domain. This domain has a relatively large holomorphic
automorphism group, though the domain is not homogeneous in general. We discuss unitary representationsof the group realized on Hilbert spaces of holomorphic functions on the Bergman–Hartogs domain. The
multiplicity free decomposition of the representation is described in terms of harmonic analysis on thebounded homogeneous domain.
9 Ryosuke Nakahama (Univ. of Tokyo)

Explicit embeddings of holomorphic discrete series representations · · · 15

Summary: In this talk the speaker presents the result on the explicit construction of embedding maps
between two holomorphic discrete series representations. Today we mainly deal with the embedding of theholomorphic discrete series representation of Sp(r, R) × Sp(r, R) into that of Sp(2r, R).

Final ver.: 2016/2/15
53

Functional Analysis

10 Masatoshi Kitagawa (Univ. of Tokyo)
Summary:

The BGG category O and the category of generalized Harish-Chandra
modules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Using Zuckerman’s derived functor, Enright gave a functor from the BGG category to thecategory of Harish-Chandra modules of a connected semisimple complex Lie group. He proved that thefunctor is exact and preserve irreducibility. In this talk, the speaker generalizes the functor defined by
Enright to a functor from the BGG category to the category of generalized Harish-Chandra modules. The
main purpose of this talk is to introduce that the functor is exact fully faithful, and preserve irreducibility.
As an application, we can see that Enright’s functor gives an category equivalence.
11 Narufumi Nakagaki(Nara Univ. of Edu.)
Tatsuya Tsurii (Osaka Pref. Univ.)

Fusion rule algebras associated with inductions and restrictions of irreducible representations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a compact group G, the fusion rule algebra F(Ĝ) is obtained associated with the dual Ĝ of G.
c0 )Let G0 be a closed subgroup of G such that the index [G : G0 ] is finite. Then Frobenius diagram D(Ĝ ∪ Gc0 ) related with
is obtained by Frobenius’ reciprocity theorem. We discuss the fusion rule algebra F(Ĝ ∪ G
cFrobenius diagram D(Ĝ ∪ G0 ).
12 Shohei Oyanoki (Nara Univ. of Edu.)
Tatsuya Tsurii (Osaka Pref. Univ.)

Hypergroup duals and geometric duals · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Associated with many symmetric graphs (diagrams) we obtain finite commutative hypergroups
by considering random walks. Conversely, associated with faithful irreducible ∗-actions of many finite
commutative hypergroups we obtain symmetric graphs.
hypergroups and graphs and discuss their duals.
13 Taiki Okamoto (Nara Univ. of Edu.)
Tatsuya Tsurii (Osaka Pref. Univ.)

We make clear the correspondence between

Polynomial representations of hypergroups · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce polynomial representations π (of one-variable and two-variable) of certain finite
commutative hypergroups K. Moreover we make clear the relation between hypergroup structure of thedual K̂ of K and the roots of the determinant equations of π(K).
14 Tatsuya Tsurii (Osaka Pref. Univ.)
Hiromichi Ohno (Shinshu Univ.)
Akito Suzuki (Shinshu Univ.)
Yasumichi Matsuzawa (Shinshu Univ.)
Satoe Yamanaka (Nara Women’s Univ.)

Non-commutative hypergroup of order five · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss a commutativity of finite hypergroups. For a group, the minimum order of noncommutative groups is six. But in the case of a hypergroup there exists a non-commutative hypergroup oforder five.
13:15–14:15

Talk Invited by Functional Analysis Section

Atsumu Sasaki(Tokai Univ.)

Admissible representations, multiplicity-free representations and visible
actions on non-tube type Hermitian symmetric spaces

Summary: In this talk, we give a new characterization for a non-compact Hermitian symmetric space to beof tube type (or non-tube type) by multiplicities in some branching laws and visible actions. Further, we
provide an example of a kind of the Cartan decomposition for non-symmetric homogeneous spaces.

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Functional Analysis

March 18th (Fri)

Conference Room IX

9:30–12:00
15 Yukiko Iwata (Meteorological Coll.)

Constrictive Markov operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Consider a Markov operator T : L1 (X, Σ, µ) → L1 (X, Σ, µ) defined on a finite measure space(X, Σ, µ). In this talk, we shall give a necessary and suﬃcient condition for a constrictive Markov operator
T which is an integral operator with stochastic kernel satisfying T 1X = 1X .
16 Kazuya Okamura (Nagoya Univ.)
Masanao Ozawa (Nagoya Univ.)

Measurement theory in local quantum physics · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we aim to establish foundations of measurement theory in local quantum physics. We
introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence
between completely positive (CP) instruments with the NEP and statistical equivalence classes of measuring
processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP and thatevery CP instrument on an injective von Neumann algebra is approximated by those with the NEP. Two
examples of CP instruments without the NEP are obtained. It is thus concluded that in local quantum
physics not every CP instrument represents a measuring process, but in most of physically relevant cases
every CP instrument can be realized by a measuring process within arbitrary error limits.
17 Shûichi Ohno (Nippon Inst. of Tech.) ♭ Weighted composition operators on H ∞ ∩ Bo · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We here characterize the boundedness and compactness of weighted composition operators on
H ∞ ∩ Bo . Moreover we will consider the domain of weighted composition operators as H ∞ bigger thanH ∞ ∩ Bo . We present some examples concerning with our results. As a corollary, we have that theboundedness of Cφ : H ∞ → H ∞ ∩ Bo is equivalent to the compactness of Cφ : Bo → Bo .
18 Sin-Ei Takahasi(Yamagata Univ.⋆ / Toho Univ.)
Yuji Kobayashi (Toho Univ.)
Makoto Tsukada (Toho Univ.)

A complete classification of continuous fraction-like operations on thecomplex field · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This is a research report about the classification problem of continuous fraction-like binary
operations on the complex field C. We show that non-trivial continuous fraction-like binary operations on C
can be completely classified by the ratio of two complex numbers whose pair determines such an operation.
Furthermore, we mention that the set of all the equivalence classes of such operations is equipped with anatural topology and it is homeomorphic to the unit disk {z ∈ C : |z| ≤ 1}.
19 Toshikazu Abe (Niigata Univ.)

A generalization of normed space based on gyrogroup · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a generalization of normed space, which addition is not necessarily acommutative group but a gyrocommutative gyrogroup.
20 Benoit Collins (Kyoto Univ.)
Takahiro Hasebe (Hokkaido Univ.)
Noriyoshi Sakuma (Aichi Univ. of Edu.)

Free probabilistic analysis of random matrices converging to compact
operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In a recent preprint in 2015, Shlyakhtenko found a free probabilistic method to analyze theeigenvalues of perturbed GUEs (Gaussian Unitary Ensemble). We will strengthen Shlyakhtenko’s result andthen we analyze polynomials of random matrices whose eigenvalues converge to eigenvalues of a compact
operator.

Final ver.: 2016/2/15
55

Functional Analysis

21 Hiroaki Tohyama(Maebashi Inst. of Tech.)
Hiroshi Isa (Maebashi Inst. of Tech.)
Masatoshi Ito (Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)

Expanded forms of operator valued α-divergence and Petz–Bregman
divergence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, we have defined new operator divergences as the diﬀerences of relative operator entropies
and have represented them by using Petz–Bregman divergence D0 (A|B) ≡ B − A − S(A|B). In addition,
we have discussed Ψ-Bregman divergence for several functions Ψ which relate to divergences defined by
the diﬀerences of entropies. In this talk, we define expanded Petz–Bregman divergence D0,r (A|B) ≡B − A − Tr (A|B) and show similar results to our former ones. Moreover, we make a report of results
obtained on Ψ-Bregman divergence for several functions Ψ which relate to expanded forms of divergences
defined by the diﬀerences of entropies.
22 Masaru Nagisa (Chiba Univ.)
Albania Nugraha Imam (Chiba Univ.)

Matrix monotone function and Operator monotone function · · · · · · · · · 15

−1
Summary: We consider functions with some special forms as follows: for real numbers a, b, let h(t) = ab ttb −1at ∈ (0, ∞). We decide values of a, b if and only if h(t) becomes operator monotone on (0, ∞). We also showthat h(t) is operator monotone if and only if h(t) is 2-matrix monotone.
2
We consider the similar result for functions with the form h(t) = (taab(t−1)
t ∈ (0, ∞). When b = 1 − a−1)(tb −1)

and −1 ≤ a ≤ 2, this function is called Petz–Hasegawa’s function and is known the operator monotonicityof this function.

14:15–15:00
23 Yuki Seo (Osaka Kyoiku Univ.)

Matrix inequalities via positive multilinear maps · · · · · · · · · · · · · · · · · · · 10

Summary: Utilizing the notion of positive multilinear mappings, we present some matrix inequalities. In
particular, Choi–Davis–Jensen and Kantorovich type inequalities including positive multilinear mappings
are presented.
24 Tsuyoshi Kajiwara (Okayama Univ.)
Yasuo Watatani (Kyushu Univ.)

C*-algebras associated with two dimensional self-similar maps · · · · · · · 15

Summary: In this talk, we present analysis of the C*-algebras associated with two dimensional self-similar
maps. We mainly consider the case of the product of the one dimensional tent map. Contrast to theone dimensional cases, there exist chains of branched points. The corresponding Pimsner C*-algebra issimple and purely infinite. By the calculation of K-groups, it coincide with Cuntz algebra Ø∞ . We do acomplete classification of finite traces on the gauge invariant subalgebra (the core), and present the matrix
representation of the finite cores.
25 Hajime Moriya (Shibaura Inst. of Tech.)

Hidden supersymmetries in some fermion lattice models · · · · · · · · · · · · 15

Summary: We study hidden supersymmetries in fermion lattice models. We consider high degeneracy of
SUSY ground states for some concrete SUSY models due to H. Nicolai and by P. Fendley et al. In terms offunctional analysis, we formulate these SUSY models as supersymmetric C*-dynamics on the CAR algebra
avoiding known obstacles. Some part of this work is collaboration with H. Katsura and Y. Nakayama.

Final ver.: 2016/2/15
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Functional Analysis

15:15–16:15

Talk Invited by Functional Analysis Section

Hiroshi Ando

(Chiba Univ.)

Ultraproducts of operator algebras

Summary: In this talk I report on some recent works on ultraproducts of von Neumann algebras and its
connection to QWEP problem and C*-algebras. The talks are divided in 3 parts.
In part 1, I recall basic notions of the following notiosn: ultralimits, von Neumann algebras and tracial
central sequences.
In part 2, I explain various generalizations of tracial ultraproducts and how they are related to each other,and also that how their relationships give structural results on Ocneanu ultraproduct of type III factors.
In part 3, I explain some applications of ultraproducts to (a) Kirchberg’s QWEP problem, or equivalently
Connes’ embedding problem (b) noncommutativity of C*-central sequence algebras for a large class of
separable C*-algebras.
The above works are combinations of works with Uﬀe Haagerup, Carl Winslow and Eberhard Kirchberg.

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Statistics and Probability

Statistics and Probability
March 16th (Wed)Conference Room II

9:30–12:00
1 Isamu Dôku(Saitama Univ.)

Cox–Perkins type limit theorem for EDMs · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider an environment-dependent model, namely, a kind of stochastic interacting system.
Under suitable conditions, if the model is rescaled, then the rescaled process converges to a superprocess,i.e., a Dawson–Watanabe superprocess with spatially dependent branching rate. The result is an extensionof the work done by Cox–Perkins (2005).
2 Toshio Nakata (Fukuoka Univ. of Edu.)

Weak laws of large numbers for weighted independent random variables
with infinite mean · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study weak laws of large numbers for weighted independent random variables with infinite
mean. In particular, this paper explores the case that the decay order of the tail probability is −1. Moreover,
we extend a result concerning the Pareto–Zipf distributions given by A. Adler.
3 Koji Tsukuda (Kurume Univ.)

On L2 (0, 1) functional central limit theorems for logarithmic assemblies· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Functional central limit theorems in L2 (0, 1) for logarithmic assemblies are presented.

The

results in the literature proved the weak convergences of random processes associated with logarithmic
assemblies to a standard Borwnian motion (B(u))u∈[0,1] in the Skorokhod space. On the other hand, in thispresentation, weak convergences in L2 (0, 1) of random processes with the standardization varying with u to√(B(u)/ u)u∈(0,1) are proved.
4 Yong Moo Chung (Hiroshima Univ.)
Hiroki Takahasi (Keio Univ.)
Juan Rivera-Letelier(Univ. of Rochester)On the large deviation principle in one-dimensional dynamics · · · · · · · · 15

Summary: We study a topologically exact smooth interval map with non-flat critical points. Assuming themap has only hyperbolic repelling periodic points and no critical relation, we establish the large deviation
principle for empirical means.
5 Haruyoshi Tanaka(Wakayama Med. Univ.)

Asymptotic perturbation of graph iterated function systems · · · · · · · · · 15

Summary: In this talk, we study an asymptotic perturbation of the limit set generated from a finitely
family of conformal contraction maps endowed with a directed graph. We show that if those maps haveasymptotic expansions under certain weak conditions, then the Hausdorﬀ dimension of the limit set behaves
asymptotically by the same order. We also prove that the Gibbs measure of a suitable potential andthe measure theoretic entropy of this measure have asymptotic expansions under an additional condition.
Finally, we demonstrate degeneration of graph iterated function systems.
6 Takahiro Hasebe (Hokkaido Univ.)
Noriyoshi Sakuma (Aichi Univ. of Edu.)

On unimodality for free Lévy processes · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We will prove that a symmetric free Lévy process is unimodal if and only if its free Lévy
measure is unimodal and that Every free Lévy process with boundedly supported Lévy measure is unimodal
in suﬃciently large time. For the proof we will (almost) characterize the existence of atoms and theexistence of continuous probability densities of marginal distributions of a free Lévy process in terms ofLévy Khintchine representation.

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Statistics and Probability

7 Kazuhiro Yoshikawa(Ritsumeikan Univ.)

Some identities of characters of infinitely divisible multidimensional
Shintani zeta distributions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In recent years, Aoyama and Nakamura introduced multidimensional Shintani zeta functions,where a class of multidimensional discrete distributions associated with these zeta functions was definable([2]). By applying Euler products, they showed that the class contained compound Poisson distributions
enough ([1]). In this talk, we consider some conditions for multidimensional Shintani zeta distributions to
be infinitely divisible. Some of the conditions have relations to identities of multiple zeta values. Our aim is
to calculate probabilities for multidimensional Shintani zeta distributions by making use of their identities.
8 Kiyoiki Hoshino (Osaka Pref. Univ.)
Tetsuya Kazumi (Osaka Pref. Univ.)

On the integrability of Ogawa integrals of noncausal Wiener functionals· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In the framework of Wiener chaos, in case a noncausal function is represented by a Skorokhod
integral, we are to give a suﬃcient condition the function is Ogawa-integrable,and to represent the Ogawa
integral by Skorokhod integrals under the condition.
9 Takafumi Otsuka (Tokyo Metro. Univ.)
Kumiko Hattori (Tokyo Metro. Univ.)
Noriaki Ogo (Tokyo Metro. Univ.)

A family of self-avoiding random walks interpolating the loop-erased
random walk and a self-avoiding walk on the Sierpinski gasket · · · · · · · 15

Summary: We show that the ‘erasing-larger-loops-first’ (ELLF) method, which was first introduced forerasing loops from the simple random walk on the Sierpinski gasket, does work also for non-Markov random
walks, in particular, self-repelling walks to construct a new family of self-avoiding walks on the Sierpinski
gasket. The one-parameter family constructed in this method continuously connects the loop-erased random
walk and a self-avoiding walk which has the same asymptotic behavior as the ‘standard’ self-avoiding walk.
We prove the existence of the scaling limit and study some path properties: The exponent ν governing
the short-time behavior of the scaling limit varies continuously in u. The limit process is almost surely
self-avoiding, while it path Hausdorﬀ dimension 1/ν, which is strictly greater than 1.
10 Shin Harase (Ritsumeikan Univ.)
Tomooki Yuasa (Ritsumeikan Univ.)

A comparison study of Sobol’ sequences in option pricing · · · · · · · · · · · 15

Summary: We consider multivariate numerical integration in financial engineering by quasi-Monte Carlo
methods. Sobol’ sequences are typical quasi-Monte Carlo sequences with small discrepancy based on the(t, m, s)-nets. Here, there are several Sobol’ sequences with distinct parameter sets. In this talk, we compare
Sobol’ sequences in terms of examples of option pricing.
14:30–15:30

Talk Invited by Statistics and Probability Section

Kazutoshi Yamazaki (Kansai Univ.)

Refracted-reflected Lévy processes

Summary: We study a combination of the refracted and reflected Lévy processes. Given a spectrally onesided Lévy process and two boundaries, it is reflected at the lower boundary while, whenever it is above theupper boundary, a linear drift at a constant rate is subtracted from the increments of the process. Using
the scale functions, we compute the resolvent measure, the Laplace transform of the occupation times aswell as other fluctuation identities that will be useful in applied probability including insurance, queues, andinventory management. This talk is based on a joint work with José Luis Pérez (CIMAT).

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Statistics and Probability

15:45–16:45

Talk Invited by Statistics and Probability Section

Seiichiro Kusuoka (Okayama Univ.)

An approach to the solutions and the fundamental solutions to nondivergence form parabolic equations by stochastic analysis

Summary: We consider the solutions and the fundamental solutions to time-inhomogeneous non-divergenceform parabolic partial diﬀerential equations with low-regular coeﬃcients by stochastic analysis. If thecoeﬃcients are Hölder continuous, there is a well-known result by the parametrix method. In this talk, we
consider the case of less regular coeﬃcients. Precisely speaking, we treat the case that the coeﬃcient of
the second-order derivative is continuous in the spacial component uniformly in time and the coeﬃcients ofthe first-order derivative and of the multiplication are bounded measurable, and obtain the modulus of thecontinuity of the solutions and the fundamental solutions. We also consider the probabilistic aspect of theperturbation of equations, and obtain the existence and the two-sided bounds of the fundamental solution
to the perturbed equations. As an application of the probabilistic representation of the perturbation weconcern stochastic diﬀerential equations with path-dependent drift terms.

March 17th (Thu)

Conference Room II

9:45–11:30
11 Fumio Nakajima (Iwate Univ.)

Statistical approach to the form of Mt. Fuji through its contour map· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We shall investigate the form of Mt. Fuji through its contour map from mean value and standard
deviation of their data.
12 Yoshihiko Maesono (Kyushu Univ.)
Taku Moriyama (Kyushu Univ.)

Direct kernel type estimator of a hazard ratio and its asymptotic properties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we propose a direct kernel type estimator of a hazard ratio and discuss asymptotic
properties of them. We obtain asymptotic mean squared errors and compare them with a natural estimator,
which is constituted of two kernel type estimators of density and distribution functions. Mean squared
errors of the natural estimator are already obtained. Comparing these mean squared errors, we show thatthe direct estimator is superior than the in-direct estimator in many cases.
13 Gaku Igarashi (Univ. of Tsukuba)

Boundary-bias-free density estimation using multivariate log-normal
kernel · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the recent fifteen years, in order to avoid the boundary bias problem, several univariate
asymmetric kernel (AK) estimators of a density with support [0, ∞) or [0, 1] have been suggested. Also, a
few multivariate AK estimators were discussed. The log-normal kernel estimator is one of the univariate
AK estimators. In this talk, we report the asymptotic properties of the multivariate AK estimator using
multivariate log-normal kernel.
(Kansai Univ.)
14 Sigeo Aki
Katuomi Hirano (Josai Univ.)

On monotonicity of expected values of some run-related distributions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show that the expectation of the binomial distribution of order k with success probability p
is monotonically increasing with respect to p for all n and k. The result is extended to the problems on
exchangeable random sequences and expectations of distributions of mixtures of binomial distributions oforder k are studied. If the mixing measure is stochastically increasing with respect to its parameter, theexpectation of the mixture of binomial distributions of order k becomes nondecreasing. As examples of
mixing measures submodels of beta distributions are examined and the resulting expectation of the mixture
distribution is monotonically strictly increasing. Further, we show some properties on the expectation of
the ℓ-overlapping 1-runs.

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Statistics and Probability

15 Nobuki Takayama (Kobe Univ.)(Kobe Univ.)
Yoshiaki Goto
Yoshihito Tachibana (Kobe Univ.)

Numerical evaluation of conditional probability for two way contingency
table · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a complexity analysis of the holonomic gradient method (HGM) to evaluate numericallyand exactly the conditional probability of a given two way contingency table. A modular method is applied
to evaluate eﬃciently the probability.
16 Tamio Koyama (Univ. of Tokyo)

Numerical calculation of simplex probability by holonomic gradientmethod · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We utilize the holonomic gradient method for the numerical calculation of the probability content
of a simplex with a multivariate normal distribution. For this purpose, we calculate the derivatives of thefunction associated with the probability content of a polyhedron in general position. And we show thatthese derivatives can be written as integrals on the faces of the polyhedron.
17 Katusi Fukuyama (Kobe Univ.)
Mai Yamashita(Osaka Toin Junior and Senior High School)

Metric discrepancy results for geometric progressions with large ratios······························································ 5

Summary: For geometric progressions with common ratios greater than 4, the law of the iterated logarithm
for discrepancies is proved and the speed of convergence to the uniform distribution is determined for almost
all initial values.
18 Yasuki Isozaki (Kyoto Inst. Tech.)Density of the first hitting time of the integer lattice by symmetric Lévy
processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For one-dimensional Brownian motion, the exit time from an interval has finite exponential
moments and its probability density is expanded in exponential terms. In this note we establish its
counterpart for certain symmetric Lévy processes. We obtain the partial fraction expansion for the Laplacetransform of the first hitting time of the integer lattice and by inversion the expansion of the density inexponential terms. Intermediate results such as finite exponential moments are also obtained for a class of
nonsymmetric Lévy processes.
11:30–12:00

March 18th (Fri)

Conference Room II

9:45–12:00
19 Seiichi Iwamoto (Kyushu Univ.⋆)

Dual least squares method —some variants— · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk presents some variants of dual least squares method. Four models – (1) linear perturbation, (2) quadratic-convexity, (3) x-quadratic y-linearity, and (4) y-quadratic x-linearity – are introducedwith its closed form of primal and dual optimal solutions. The linear perturbation model is completely
solved. The others also have the same structure in optimal solution. The dual (maximization) problem isderived from the primal (minimization) problem through three – (a) dynamic, (b) plus-minus, (c) inequality– approaches.
20 Yutaka Kimura (Akita Pref. Univ.)
Seiichi Iwamoto (Kyushu Univ.⋆)

Is Golden path optimal? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is shown that Golden path is optimal for two quadratic programming problems (maximizationand minimization) under semi-Fibonacci constraints. Some relations to reversed problem and dual problem
are discussed. It turns out that both the problems are dual to each other and have an identical optimal
solution (point and value). The optimal solution is characterized by the Golden number.

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Statistics and Probability

21 Akio Tanikawa (Osaka Inst. of Tech.)

A generalized class of pseudomeasurements for identifying unknown
parameters of linear stochastic systems · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A new class of pseudomeasurements for discrete-time stochastic systems are derived fromcontinuous-time linear stochastic systems with unknown parameters by applying time-discretization andTaylor expansion. Utilizing these pseudomeasurements, we propose new iterative methods which estimate
the states of the discrete-time stochastic systems and identify the unknown parameters simultaneously.
22 Masayuki Horiguchi (Kanagawa Univ.)
A. B. Piunovskiy (Univ. of Liverpool)

Optimal stopping problem in uncertain Markov decision processes · · · · 15

Summary: This note is concerned with the optimal stopping problem under Markov decision processes withthe total expected cost criterion. The state of the system is observable, but the transition matrices are
unknown. Under the general formulation, the problem is solved by combining dynamic programming andBayesian approach and the optimal stopping rule of a threshold type is derived.
23 Masahiko Sakaguchi (Kochi Univ.)

A minimal imbedding for maximization the S. W. Golomb exponentialfunction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We maximize the the exponential function by S. W. Golomb (Amer. Math. Monthly 75, 1968).
The original problems are equivalent to the maximizing problem with a multiplicative reward function withreal numbers. Therefore we give a minimal imbedding for the maximizing multiplicative reward problem
and the optimal recursive equation.
24 Kazuki Matsubara (ChuoGakuin Univ.)
Sanpei Kageyama (Tokyo Univ. of Sci.)

Some existence of cyclic splitting BIB designs · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The concept of splitting balanced incomplete block (BIB) designs B(v, u × k, λ) has been definedwith some applications for authentication codes in Ogata et al. (2004). In this talk, some fundamental
combinatorial properties of splitting BIB designs with cyclic automorphism are given and some direct
methods of constructing such designs are provided. Finally, the complete existence of a cyclic splitting
B(v, 2 × 2, λ) for any v and λ, and non-existence of a cyclic splitting B(k 2 t + 1, 2 × k, 1) for any odd integersk ≥ 3 and t ≥ 1 are shown.
25 Xiao-Nan Lu (Nagoya Univ.)
Masakazu Jimbo (Chubu Univ.)

A construction of cyclic 3 × 3 grid-block designs and its application· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of grid-block designs originated from the experimental designs for DNA library
screening as follows: For a v-set V , let B be a collection of r × k arrays with rk diﬀerent entries in V . A
pair (V, B) is called an r × k grid-block design if every pair of distinct points in V occurs exactly once in thesame row or in the same column of a grid-block of B. Moreover, (V, B) is cyclic, if B admits a cyclic groupof order v as its automorphism. In this talk, by utilizing cyclotomic methods, we investigate a constructionof cyclic 3 × 3 grid-block designs and apply the resultant designs to construct resolvable 3 × 3 grid-block
designs.

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Statistics and Probability

26 Hiromu Yumiba (Int. Inst. for Nat. Sci.)
Yoshifumi Hyodo(Okayama Univ. of Sci./Int. Inst. for Nat. Sci.)
Masahide Kuwada(Int. Inst. for Nat. Sci.)

Characteristics of balanced fractional 3m factorial designs of resolutionR∗ ({10, 01}|{00, 10, 01, 20, 11}) with N < ν(m) · · · · · · · · · · · · · · · · · · · · 15

Summary: Consider a fractional 3m factorial design with m factors each at three levels, which is derived froma simple array (SA) of three symbols, where m ≥ 4, and the non-negligible factorial eﬀects are the generalmean, the linear components and the quadratic ones of the main eﬀect, and the linear by linear ones andthe linear by quadratic ones of the two-factor interaction. Under these situations, if all the main eﬀects are
estimable, and the remaining non-negligible factorial eﬀects may or may not be estimable, then a design issaid to be of resolution R∗ ({10, 01}|Ω), where Ω = {00, 10, 01, 20, 11}. Then by using the properties of somealgebra, we give the existence conditions of a 3m -BFF design of resolution R∗ ({10, 01}|Ω) derived from an
SA, where the number of assemblies is less than the number of non-negligible factorial eﬀects.
27 Masanori Sawa (Kobe Univ.)
Masatake Hirao (Aichi Pref. Univ.)
Hirotaka Yamamoto (Kobe Univ.)

A generalization of the corner-vector method for constructing D-optimal
designs on the hyperballs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Many publications have been devoted to the constructions of D-optimal designs on the hyperballs,
most of which are however for regression models for polynomials of degree at most 3. In this talk we
propose a geometric construction of D-optimal designs and thereby find such designs of degree at least
4. The proposed method is not only of statistical interest but also a natural generalization of a classicalconstruction of Euclidean designs using the corner vectors for the hyperoctahedoral group in algebraic
combinatorics.
14:15–15:15

Talk Invited by Statistics and Probability Section

Nobuhiro Taneichi (Kagoshima Univ.)

An approximation for the distribution of the multinomial goodness-of-fit
statistic and its application to discrete statistical model

Summary: On the goodness-of-fit test for the multinomial distribution, an approximation based on an
asymptotic expansion for the distribution of a test statistic under simple null hypothesis has been developed(Ranga Rao (1961), Yarnold (1972), Siotani & Fujikoshi (1984), Read (1984)). First, we summarize
the theory of the approximation and show a diﬃculty to extend the theory. Second, we consider theapproximation for the distribution of a test statistic under alternative hypotheses. Third, we apply theapproximation to some discrete statistical models (e.g., contingency table, generalized linear model withbinary response).
15:30–16:30

Award Lecture for the 2015 MSJ Analysis Prize

Akimichi Takemura (Univ. of Tokyo)

Studies on holonomic gradient method

Summary: We give a review talk on holonomic gradient method, from its origin to recent developments.
The holonomic gradient method combines algebraic algorithms for the module of diﬀerential operators andnumerical solvers for ordinary diﬀerential equations. The method is found to be very useful for evaluationof the normalizing constants of many probability distributions in statistics and the computation of the
maximum likelihood estimators.

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Statistics and Probability

March 19th (Sat)

Conference Room II

9:50–12:00
28 Fumiya Akashi (Waseda Univ.)
Xiaofeng Shao
(Univ. of Illinois at Urbana-Champaign)

LAD-based empirical likelihood method for linear hypothesis and its
local asymptotic power · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we construct the least absolute deviation (LAD)-based empirical likelihood (EL) test
statistic for a linear hypothesis on unknown parameters of linear regression models. As a noteworthy result,
LAD-based EL test statistic is shown to converge to the standard chi-square distribution. Since the limit
distribution is pivotal, we can construct a testing procedure without estimating any unknown quantitiesof the model. In addition, the limit distribution of LAD-based EL test statistic under local contiguousalternatives is elucidated, and the asymptotic local power of the proposed test is derived. Finally, weinvestigate finite sample performance of the proposed test by simulation experiments, and it is shown that
our approach has advantages in many senses compared with classical one.
29 Fumiya Akashi (Waseda Univ.)

Self-weighted empirical likelihood method for hypothesis testing of stable ARMA models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk applies the empirical likelihood method to the testing problem for a linear hypothesis ofstable ARMA models, which is one of infinite variance processes. In particular, by using the method called
self-weighting, we construct self-weighted least absolute deviation-based empirical likelihood (SWLAD-EL)
test statistic. Remarkably, it is shown that the limit distribution of the proposed test statistic becomesa standard chi-square distribution, and hence we can carry out hypothesis testing without estimating any
unknown quantities of the underlying model. We also compare the finite sample performance of the proposed
test with that of classical LAD-based test by simulation experiments. It is also reported that the proposed
test is applicable to the real data analysis such as variable selection or testing serial correlations.
30 Yan Liu(Waseda Univ.)

Box–Cox transformation for variance stabilization of dependent observations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Box–Cox transformation is one of the most famous transformations to stabilize the varianceof estimators. In this talk, we focus on the dependent random variables with the multivariate Tweedie
distributions to derive the optimal power coeﬃcient in Box–Cox transformation for stabilizing variance ofdependent random variables. Under a new condition between dispersion parameters, we show the formulafor power parameter in the Box–Cox transformation for variance stabilization of dependent observations.
The result shows that even in the dependent case, the same formula as that in the case of identically andindependent distributed random variables holds. The proof and numerical simulation will also be given.
(Waseda Univ.)
31 Yujie Xue(Waseda Univ.)
Yan Liu
Masanobu Taniguchi (Waseda Univ.)

Minimax extrapolation error of predictors · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In characterizing time series,an important representation is of frequency domain because of theperiodic nature of the trigonometric functions. As we know, for a weakly stationary process {Xt : t ∈ Z}
with mean 0 and spectral distribution function F (λ), the linear prediction problem can be transferred into aminimization problem of the distance from 1 to a subspace of L2 ( dF ). In this paper, we give the structureof optimal predictor of l-step prediction problem when L2 (·) is extended to the cases of p > 1 i.e., Lp (·),
and the minimax extrapolation error of predictors is discussed.

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Statistics and Probability

32 Hideaki Nagahata (Waseda Univ.)
Masanobu Taniguchi (Waseda Univ.)

Analysis of variance for multivariate time series · · · · · · · · · · · · · · · · · · · · 10

Summary: An asymptotic distribution about three test statistics (likelihood ratio, Lawely–Hotelling,
Bartlett–Nanda–Pillai) under MANOVA model with an independently and identically distributed innovation term is well-known. In practice, we often need to analyze multivariate time series data (for example
real financial data). For this, under MANOVA model with dependent error processes we drive the asymptotic distribution about the three test statistics. We give a suﬃcient condition for the tests to have theχ2 -asymptotic distribution. It is shown that the CHARN models satisfy this condition, which leads to a lotof applications in financial analysis. Also some interesting numerical studies will be given.
33 Yoshihiro Suto (Waseda Univ.)

Shrinkage estimation for the misspecified pseudo interpotator of a stationary process · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a misspecified interpolation problem, and propose a shrinkage estimator of the usual
pseudo interpolator. We evaluate the mean squared interpolation error (MSIE) of the pseudo shrinkage
interpolator. Then we provide a condition when the pseudo shrinkage interpolator improves the usual
pseudo interpolator. Next we propose the practical shrinkage interpolator, and evaluate MSIE. Under theappropriate conditions, we see that the practical shrinkage estimator improves the usual pseudo interpolator
asymptotically. We also give some numerical examples which show an interesting feature of the pseudoshrinkage interpolator.
34 Yoshihide Kakizawa (Hokkaido Univ.)

Generalized Birnbaum–Saunders kernel density estimator · · · · · · · · · · · 15

Summary: We consider estimation of the probability density for nonnegative data. In that case, the standard
kernel density estimator is, in general, inconsistent near the boundary, due to the so-called boundary bias.
Many authors have suggested some remedies, on the basis of renormalization, reflection, and generalized
jackknifing (see Jones (1993)). On the other hand, over the last decade, there has been growing interest in
the use of asymmetric kernel (AK), whose support matches the support of the density to be estimated. We
propose AK density estimator using a generalized BS kernel.
35 Yoshihide Kakizawa (Hokkaido Univ.)

Some integrals involving multivariate Hermite polynomials · · · · · · · · · · 10

Summary: We present the formula for a certain integral with respect to multivariate Hermite polynomials.
Such integrals are used for deriving higher-order local power functions of asymptotically chi-squared tests.
Our argument for the proof of main theorem is very simple, except for the use of an unfamiliar derivativeof composite function f (g(t)), where f is a scalar-valued function of a real variable and g is a scalar-valued
function of a vector variable t = (t1 , . . . , tp )′ .
36 Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Estimation of a signal matrix for high-dimensional data · · · · · · · · · · · · · 15

Summary: In this talk, we consider the problem of recovering a signal (low-rank) matrix in high-dimension,
low-sample-size (HDLSS) situations. We first consider the conventional PCA to recover the signal matrix
and show that the estimation of the signal matrix holds consistency properties under severe conditions. The
conventional PCA is heavily subjected to a noise. In order to reduce the noise, we apply the noise-reduction(NR) methodology and propose a new estimation of the signal matrix. We show that the proposed estimationby the NR method holds the consistency properties under mild conditions and improves the error rate of
the conventional PCA eﬀectively.

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Statistics and Probability

14:15–16:10
37 Aki Ishii(Univ. of Tsukuba)

Note on two-sample tests for high-dimension, low-sample-size data · · · 15

Summary: A common feature of high-dimensional data is the data dimension is high, however, the sample
size is relatively low. We call such data HDLSS data. Ishii et al. (2015) gave asymptotic properties ofthe first principal component by using the noise-reduction (NR) methodology that was created by Yataand Aoshima (2012). In this talk, we consider two-sample tests for high-dimensional data when the data
dimension goes to infinity while the sample-size is fixed. We propose a new test statistic by applying the
NR estimator of the largest eigenvalue.
38 Ayaka Yagi (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)
Muni Srivastava (Univ. of Toronto)

On likelihood ratio test statistic for test of mean vector with monotone
missing data · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the likelihood ratio test (LRT) for testing of mean vector when the data have amonotone pattern of missing observations. In order to obtain the modified LRT statistic, we express the
LRT statistic as the combining independent LRT statistics, and we derive an asymptotic expansion for the
distribution of each independent LRT statistic. As a result, we propose a new modified LRT statistic using
the correction factors of the LRT statistics. Finally, we investigate the asymptotic behavior of these LRT
statistics for chi-squared distribution and the numerical powers using Monte Carlo simulation.
39 Mana Aizawa (Tokyo Univ. of Sci.)
Kouji Yamamoto (Osaka Univ.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Measure of departure from sum-symmetry model for square contingency
tables having ordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For the analysis of square contingency tables, Yamamoto et al. (2013, 2015) considered thesum-symmetry (SS) model. We propose a measure to represent the degree of departure from the SS model,
which is expressed by using Cressie and Read’s (1984) power-divergence.
40 Yusuke Saigusa (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

A measure of departure from second-order marginal symmetry for multiway contingency tables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For multi-way contingency tables, Bhapkar and Darroch (1990) considered the second-ordermarginal homogeneity model. We shall propose the measure to represent degree of departure from secondorder marginal homogeneity.
measure.

Also we shall give the approximate confidence interval of the proposed

41 Akira Shibuya (Tokyo Univ. of Sci.)
Kiyotaka Iki (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Diagonal exponent conditional symmetry model for square contingency
tables with ordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For square contingency tables with ordered categories, Tomizawa (1992) proposed the diagonal
exponent symmetry (DES) model which indicates that in addition to the structure of symmetry of theprobabilities with respect to the main diagonal of the table, the expected frequency has an exponential
form along every subdiagonal of the table. In this paper, we propose new model which indicate that inaddition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table,
the expected frequency has an exponential form along every subdiagonal of the table. Also this paper gives
the three kinds of decompositions of the DES model.
42 Ryotaro Maeda (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Extended double linear diagonals-parameter symmetry model and decomposition of double symmetry for square tables with ordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For square contingency tables with ordered categories, we consider the extended double linear
diagonals-parameter symmetry model, and show that the double symmetry model is separated into the
proposed model and the moment equality model. Also, the relationship between test statistics is given.

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43 Jo Suzuki(Osaka Univ.)Eﬃcient computation of model selection under n << p · · · · · · · · · · · · · · 15

Summary: We consider the problem of finding the parent set of variables on which a variable depends using
the MDL principle. It is known that the parent set can be eﬃciently found using branch and bound (Suzuki
1996). In this paper, we show that the optimal parent set has at most L = O(log n) variables and the total
computation is at most O(pL ) for the method.
44 Yoshikazu Takada (Kumamoto Univ.)

Improving on the best equivariant predictor under restricted parameters· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a prediction problem regarding the location and scale families with restrictedparameters. It is shown that the best equivariant predictors, which are constructed under unrestrictedparameters, are minimax, but are improved. Unlike the location and scale families, it seems diﬃcult
to generally show that there exists a predictor which dominates the best equivariant predictor in thelocation-scale family. Instead, we shall give an example in which the best equivariant predictor is improved.

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Applied Mathematics
March 16th (Wed)Conference Room VII

10:30–12:00
1 Kazuhiko Ushio

Balanced C9 -foil designs and related designs · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In graph theory, the decomposition problem of graphs is a very important topic. Various typeof decomposition of many graphs can be seen in the literature of graph theory. This paper gives balanced
C9 -foil designs and related designs.
2 Shoichi Tsuchiya (Senshu Univ.)
Michitaka Furuya (Tokyo Univ. of Sci.)

On maximum HIT in P6 -free graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that every 3-connected P5 -free graph of order at least 8 has a HIST. On the other
hand, we found an infinite family of k-connected P6 -free graphs without HISTs. In this talk, we introduce
a result on maximum HIT in a P6 -free graph.
3 Kenta Noguchi (Tokyo Denki Univ.)

Colorings of a medial graph of plane quadrangulations · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss colorings of a medial graph of plane quadrangulaions. The main theorem
is the following: every medial graph of a plane quadrangulation G has a proper vertex-3-coloring if the dualof G is C-simple.
4 Naoki Matsumoto (Seikei Univ.)

Graph-grabbing game on bipartite graphs · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A graph-grabbing game is a two-players game on weighted connected graphs. In the game, theyalternately remove a non-cut vertex from the graph and get the weight assigned to the vertex. Both players’
aim is to maximize their outcomes, when all vertices have been taken. Seacrest and seacrest proved that
Alice can obtain at least half of the total weight of every weighted tree with even order, and conjectured
that the same statement holds for connected bipartite graphs with even order. In this talk, we prove that
Alice can obtain at least 14 of the total weight of every weighted connected bipartite graph with even order.
5 Shohei Satake (Nagoya Univ.)
Masanori Sawa (Kobe Univ.)
Masakazu Jimbo (Chubu Univ.)

Asymmetry of oriented graphs and some related results · · · · · · · · · · · · · 15

Summary: In this talk, we deal with oriented graphs and hereafter, “graph” means oriented graph. First, we
define the asymmetry number of graphs with n vertices and show an upper bound. And we also introduce
the result which shows this bound is asymptotically best possible by using probabilistic methods. Moreover
we show some results about the symmetry of the random oriented graph RO. Next, we consider finite
graphs with n vertices and N edges and show an upper bound of the asymmetry number for such graphs
and we will also discuss the asymptotically best possibility.
14:30–16:00
6 Tadashi Takahashi (Konan Univ.)

The Inference Process using Automated Theorem Prover · · · · · · · · · · · · 10

Summary: Theorema system allows you to organize mathematical knowledge as hierarchies of interdependent
theories. We present a case study using the theorema system to explore for inference process.

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7 Masataka Kaneko (Toho Univ.)
Toshio Oshima (Josai Univ.)(Toho Univ.)
Setsuo Takato

Eﬀective linkage between TeX drawing and handling of graphical data
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this presentation, we introduce the KETCindy system which is a plug-in of dynamic geometry
software to convert its graphical data into TeX graphics code. Throgh the example of drawing Bezier curves
and its application to the calculation of the areas surrounded by those curves, it will be demonstrated
that the eﬀective linkage between TeX drawing and the handling of its graphical data can be realized by
KETCindy system. It is expected that these features of KETCindy system might serve a powerful tool inwide range of mathematical science.
8 Ryohei Miyadera(Kwansei Gakuin High School)
Yushi Nakaya(Kwansei Gakuin High School)

A Variant of Nim —A necessary and suﬃcient condition for the Grundy
number of this game to be the Nim-sum— · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Chocolate bar games are variants of Nim (or CHOMP) in which the goal is to leave your opponent
with the single bitter part of the chocolate. Here, we investigate step chocolate bars whose widths are
determined by a fixed function of the horizontal distance from the bitter square. We present a necessary
and suﬃcient condition for a chocolate bar to have Grundy number G({y, z}) = y ⊕ z. We also present anecessary and suﬃcient condition for a chocolate bar to have Grundy number G({y, z}) = (y ⊕ (z + s)) − s.
9 Akihiro Higashitani(Kyoto Sangyo Univ.)

Classification of lattice simplices and binary simplex codes · · · · · · · · · · 15

Summary: It was proven that for a lattice simplex of dimension d with degree k which is not a lattice pyramid
over a lower-dimensional simplex, the inequality d ≤ 4k − 2 holds. In this talk, we classify all the latticesimplices of dimension 4k − 2 with degree k which are not lattice pyramids up to unimodular equivalence.
Actually, such a lattice simplex is uniquely determined by its degree and arises from a binary simplex code.
10 Masahiro Hachimori(Univ. of Tsukuba)

Partitionability of simplicial complexes, h-triangles and hereditary properties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Shellability of simplicial complexes implies sequential Cohen–Macaulayness and partitionability. While sequentail Cohen–Macaulayness implies the nonnegativity of h-triangles, h-triangles of partitionable simplicial complexes can have negative entries. We, however, observe that partitionability
implies somewhat weaker nonnegativity property of h-triangles (i.e., property SNNDH). We then proced
to show that hereditary-shellability, hereditary-sequential Cohen–Macaulayness, hereditary-partitionability
and hereditary-SNNDH are all equivalent for dimensions upto 2.
16:10–17:10

Talk Invited by Applied Mathematics Section

Tadashi Sakuma (Yamagata Univ.)

Similarities and dissimilarities between the blocking and anti-blocking
polyhedra

Summary: The study of similarities and dissimilarities between the blocking and anti-blocking polyhedra
began with a series of celebrated papers by Fulkerson (1970, 1971, 1972), and it has grown up a mature
theory by significant contributions of Lehman, Lovász, Padberg, and others in 1970s and 1980s. Even today,
this theory still shows a big progression such as the perfect graph theorem of Seymour et al. (2006). In
this paper, we survey the current status of this research field with a focus on the conjecture of Conforti &Cornuéjols and the conjecuture of Grinstead.

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March 17th (Thu)

Conference Room VII

10:00–11:30
11 Iwao Sato (Oyama Nat. Coll. of Tech.)
Etsuo Segawa (Tohoku Univ.)
Kaname Matsue (Inst. of Stat. Math.)

Zeta function of a simplicial complex · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We define a zeta function for a 2-dimensional simplicial complex of a maximal planar graph,and present its determinant expression. Furthermore, we generalize it to a 2-dimensional cell complex of aplanar graph. Next, we define a zeta function for a skeleton of the clique complex of a graph, and give its
determinant expression. Finally, we give a determinant expression for the zeta function of the 2-dimensionalskeleton of the clique complex of a complete graph.
12 Hideo Mitsuhashi (Utsunomiya Univ.)
Norio Konno (Yokohama Nat. Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)

Quaternionic weighted zeta functions of finite graphs · · · · · · · · · · · · · · · 15

Summary: We establish the quaternionic weighted zeta function of a graph and its study determinant
expressions. For a graph with quaternionic weights on arcs, we define a zeta function by using an infinite
product which is regarded as the Euler product. This is a quaternionic extension of the square of the Ihara
zeta function. We show that the new zeta function can be expressed as the exponential of a generating
function and that it has two study determinant expressions, which are important for the theory of zetafunctions of graphs.
13 Akito Suzuki(Shinshu Univ.)

Asymptotic behavior of a quantum walker and the weak limit theorem· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the discrete time quantum walk on the line with a position dependent coin. We
construct the asymptotic velocity operator of the quantum walk. As a consequence, we obtain the weaklimit theorem.
14 Takuya Tsuchiya (Waseda Univ.)(Waseda Univ.)
Gen Yoneda

Numerical simulations of Maxwell’s equations by discrete variational
derivative method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, the discretized Maxwell’s equations using the discrete variational derivative method(DVDM) are considered. It is well known the discretized equations are not unique and that the results ofsimulations depend on the discretized equations used. However, this is diﬃcult because the discretization
scheme depends on the continuous equations. Using the DVDM, the discretized equations are derived
appropriately. We derive the discretized evolution equation of the constraint equation using the DVDM andthe iterated Crank–Nicolson scheme (ICNS), show the equation by the DVDM is superior to that by the
ICNS in analytical. Then we perform some simulations using the discretized equations using the DVDM
and the ICNS, confirm that the numerical results are consistent with analytical ones.
15 Fumihiko Nakamura (Hokkaido Univ.)

Asymptotic periodicity of non-expanding piecewise linear maps withrandom small noises · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The non-expanding piecewise linear map Sα,β (x) = αx + β (mod 1) for (α, β) ∈ (0, 1)2 is known
as the Nagumo–Sato model which describes simplified dynamics of a single neuron. We first consider
parameter regions of (α, β) in which Sα,β has a periodic point with period n for an arbitrary integer n. We
then describe these regions explicitly and show these complicated structure associated with the Farey series.
Next we consider the random dynamical system of NS model with random small noises. We discuss that
the Markov operator of this system is either asymptotically periodic or asymptotically stable depending ona noise level.

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13:10–14:00
16 Shinya Fujita (Yokohama City Univ.)

Some results on properly colored cycles in edge-colored graphs · · · · · · · 10

Summary: Some recent results on properly colored cycles in edge-colored graphs will be reviewed. We present
a new result on this topic.
(Nihon Univ.)
17 Akira Saito
kiyoshi Yoshimoto (Nihon Univ.)

The Chvátal–Erdős condition and a 2-factor with two components in agraph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A graph G is said to satisfy the Chvátal–Erdős condition if α(G) ≤ κ(G) holds, where α(G) andκ(G) are the independence number and the connectivity of G, respectively. Chen et al. (2007) have provedthat a graph G of order at least 128 satisfying the Chvátal–Erdős condition contains a 2-factor with twocomponents. Their proof uses the Ramsey theorem. By a diﬀerent approach which does not use the Ramsey
theorem, we have proved that a graph of order at least 31 satisfying the Chvátal–Erdős condition contains
a 2-factor with two components.
18 Kiyoshi Ando(Nat. Inst. of Information/JST ERATO)

A condition on G[V5 (G)] for a 5-connected graph G to have a contractible edge · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An edge of a 5-connected graph is said to be contractible if the contraction of it results in a5-connected graph. Let K4− stand for the graph obtained from K4 by deleting one edge. Let G be a
5-connected graph. Let V5 (G) denote the set of degree 5 vertices of G. We show that if G[V5 (G)] has acomponent H such that |H| ≤ 4 and H ̸∼
= K4− , then G has a contractible edge.
14:00–14:15

Presentation Ceremony for the 2015 MSJ Prize for Excellent Young Applied Mathematicians

March 18th (Fri)

Conference Room VII

9:15–11:55

Special Session “Topological data analysis and persistent homology”
Yasuaki Hiraoka (Tohoku Univ.) Topological data analysis and persistent homology · · · · · · · · · · · · · · · · · 35
Summary: In this talk, I survey recent progresses on topological data analysis, especially persistent homology,
and applications to materials science. On mathematical side, after a brief introduction, several connections toquiver representations are explained in detail. I show that Gabriel’s theorem, the Auslander–Reiten theory,and matrix problems studied in quiver representations are useful for generalizing persistent homology. Then,these generalizations are applied to geometric analysis on soft-matters such as amorphous structures andpolymers. I show that persistent homology is a powerful language for describing order in disorder.

Ippei Obayashi (Tohoku Univ.)

Inverse problem from persistence diagrams to point clouds · · · · · · · · · · 35

Summary: Persistent homology is the main tool of Topological data analysis (TDA), a mathematical framework to analyze data from the viewpoint of topology. In this talk, our data is a point cloud, a finite setof point in euclidean space. A persistence diagram is a visualization tool for persistence homology and it
encodes the ℓ-dimensional topological features of given data.
We already know the eﬃcient way to compute a persistence diagram from a point cloud and there aremany applications of persistence diagrams. In this talk, we consider the inverse problem from a persistence
diagram to a point cloud. In other words, we study how to find the point cloud whose persistence diagram isa given target diagram. Since the solution of this problem is not unique, we need an additional constraints.
In our method, for a given point cloud (called an initial point cloud), we try to find the point cloud closest
to the initial point cloud and whose persistence diagram is the given target diagram. The Newton–Raphson
method with pseudo inverse matrices is used to compute the solution. The key is the diﬀerentiability of thepersistence map, the map from the space of point clouds to the space of persistence diagrams.
In this talk, I will show the mathematical framework of the method and some numerical examples.
This study is a joint work with Marcio Gameiro (Universidade de São Paulo) and Yasuaki Hiraoka (Tohoku
University).

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Tomoyuki Shirai (Kyushu Univ.)

Random complex and persistent homology · · · · · · · · · · · · · · · · · · · · · · · · 35

Summary: In the beginning of this century persistent homology theory appears as a tool of topological data
analysis for point cloud data, protein data, image data, material sciences, and so on. It describes birthand death of homology classes as persistence diagram by providing an increasing sequence of simplicial
complexes. We are interested in the topological feasture of random object, in particular, random persistence
diagram obtained from random input. The Erdős–Renyi graph process is such a typical example of increasing
stochastic process and we can see its random persistence diagram as an output. In this talk, we focus on
simplicial complex versions of the Erdős–Renyi graph process and discuss the mean lifetime of its homology
classes by emphasizing the relationship between mean lifetime of persistent homology and minimum spanning
acycle.
Genki Kusano (Tohoku Univ.)

Kernel methods for persistent homology and topological data analysis· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 35

Summary: In this talk, we will establish a kernel based framework of statistics for “shapes of data”. In
topological data analysis, shapes of data are algebraically encoded and expressed as a persistence diagram(PD). It gives us novel applications in a wide variety of fields, such as biology, information technology,
material science, and image analysis, and these scientific rapid developments create new industrial movements
in data analysis. The statistical discussions for PDs, however, have not been developed until recently, and arestrongly desired by many researchers. Our results answer to this demand. The main theoretical contribution
is to ensure that perturbation of data does not drastically aﬀect the results of kernel methods. Moreover,the numerical experiments show the eﬀectiveness of our presented method in physics and material science.
14:30–16:00
19 Masaji Watanabe (Okayama Univ.)
Fusako Kawai (Kyoto Inst. Tech.)Study on inverse problems from modeling of exogenous type microbial
depolymerization processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A mathematical model for exogenous type depolymerization processes is described.

Inverseproblems are formulated for a time factor and a molecular factor of degradation rate. Techniques for inverse
problems are illustrated.
20 Fumio Nakajima (Iwate Univ.)

A mathematical approach to the economy of atomic power generation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We shall construct a mathematical model for the economy of the atomic power generation, andshow its ultimate state, which means the abolition of this generation.
21 Kaname Matsue (Inst. of Stat. Math.)

Covering-exchange for fast-slow systems with multi-dimensional slow
variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We provide a methodology of validating rigorous trajectories of the fast-slow system with multidimensional slow variables
x′ = f (x, y, ϵ),y ′ = ϵg(x, y, ϵ),which are near slow manifolds for the time interval O(1/ϵ) within an explicit scale parameter range (0, ϵ0 ],which will be applicable to rigorous numerics. Main tools of our procedure are a topological tool called
covering relation and the rigorous estimate of normal hyperbolicity for invariant manifolds via cone estimates.
The local product structure of covering relation and normal hyperbolicity of invariant manifolds enable us toconstruct trajectories which shadow slow manifolds even for systems with multi-dimensional slow variables.

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Applied Mathematics

22 Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Blow-up sets and rates for Type II blow-up solutions to a quasi-linear
parabolic partial diﬀerential equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a quasi-linear parabolic partial diﬀerential equations that solutions blow
up regionally and has blow-up rates of Type II. Our purpose is to specify their blow-up sets and blow-up
rates.
23 Toshikazu Kuniya (Kobe Univ.)

Global dynamics of a mathematical model for the spread of information· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, a mathematical model for the spread of information is formulated as a system ofpartial diﬀerential equations. The basic reproduction number Ro is obtained in the sense of reproduction of
new information spreaders by an information spreader invading into the information-free population. It is
proven that the information-free equilibrium is globally asymptotically stable if Ro is less than or equal to1, and the information-endemic equilibrium is so if Ro is greater than 1. In the numerical simulation, theoccurrence of traveling waves is observed.
16:15–17:15

Talk Invited by Applied Mathematics Section

Miyuki Koiso (Kyushu Univ.)

Geometry of anisotropic surface energy

Summary: An anisotropic surface energy is one that depends on the direction of a surface at each point. It
was introduced by Josiah Willard Gibbs (1839–1903) to model the equilibrium shape of a crystal. Whereas
the surface energy of a liquid drop is isotropic, the ordered arrangement of molecules in a crystal meansthat its interfacial energy depends on the surface direction. This causes that, while the closed surface withthe minimum area (isotropic surface energy) among closed surfaces enclosing a given volume is a sphere,
the closed surface with the minimum anisotropic surface energy is in general non-spherical. In this talk, we
discuss existence, stability, and uniqueness of equilibrium surfaces for anisotropic surface energy and theirgeometric properties.

March 19th (Sat)

Conference Room VII

10:00–12:00
24 Shunzi Horiguchi(Niigata Sangyo Univ.)

Experiments to compare the convergences of third extended Halley
method with Halley method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We can not obtain the degree of convergence of third extended Halley method. So, we do theexperiments to compare the convergences of third extended Halley method with Halley method.
25 Hidenori Ogata(Univ. of Electro-Comm.)
Hiroshi Hirayama(Kanagawa Inst. of Tech.)

Numerical integration method based on the hyperfunction theory · · · · 15

Summary: In this speech, we propose a numerical integration method based on Sato’s hyperfunction theory.
In our method, we transform a desired integral into a complex loop integral and approximate it by thetrapezoidal rule. A theoretical error estimate shows exponential convergence of this method if the integrandis a real analytic function, and numerical examples show that this method works very well especially for
integrals with strong endpoint singularities. We also remark that this method is closely related to thehyperfunction theory in the sense that, in this method, we approximate the complex integral which defines
the desired integral as a hyperfunction integral.

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26 Takaharu Yaguchi (Kobe Univ.)(Kobe Univ.)
Ai Ishikawa

Application to a learning algorithm for multilayer perceptrons of dissipative structure-preserving numerical methods · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is about application to a learning algorithm for multilayer perceptrons of structurepreserving numerical methods for the diﬀerential equations that stem from the Caldirolla–Kanai variational
principle. This principle is a variation of Hamilton’s principle of least action. Whereas Hamilton’s principle
considers an extremum of the integral of a given Lagrangian in the Caldirolla–Kanai variational principlethat of the weighted integral is considered. The diﬀerential equations that are derived from this principle
always have the energy-dissipation property. In this talk, some numerical schemes that preserve the propertyof the diﬀerential equation are derived and then applied to a learning algorithm for multilayer perceptrons.
27 Naoharu Ito (Nara Univ. of Edu.)

A study on self-inversive operator polynomials with spectrum on theunit circle · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Self-inversive operator polynomials with spectrum on the unit circle are studied. If the innernumerical radius of an associated polynomial is not less than one, the spectrum lies on the unit circle andconsists of normal approximate characteristic values.
28 Patrick van Meurs (Kanazawa Univ.)

Discrete-to-continuum limits of interacting dislocations · · · · · · · · · · · · · 15

Summary: Plasticity of metals is facilitated by the collective behaviour of many dislocations, which are
represented by point particles if we consider a two dimensional scenario. Currently, there exist several
diﬀerent models in the engineering literature for the dislocation density by means of a PDE. We aim
ultimately to quantify the accuracy of these models by establishing a precise connection between the‘continuum’ description (i.e. a continuity equation for the density) and the ‘discrete’ description (i.e. themovement of the particles described by a non-linearly coupled system of ODEs). To connect these two
descriptions, we establish the many-particle limit by relying on variational techniques such as Γ-convergence.
29 Fuminori Sakaguchi (Univ. of Fukui)

Implementation of an integer-type algorithm for linear partial diﬀerential equations using quasi-orthogonalization · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, a practical method is proposed for implementing an integer-type algorithm forsolving linear higher-order partial diﬀerential equations which utilizes quasi-orthogonalization of integer
vectors. This algorithm is a direct extension of an integer-type algorithm for linear ordinary diﬀerential
equations proposed by the author and M. Hayashi several years ago. However, this extension requires somecomplicated techniques based on discrete mathematics. In this presentation, the details of these techniques
are explained.
14:15–15:45
30 Hirofumi Notsu (Waseda Univ.)
Masahisa Tabata (Waseda Univ.)Mária Lukáčová-Medvid’ová(Univ. of Mainz)
Hana Mizerová (Univ. of Mainz)

Error estimates of a stabilized Lagrange–Galerkin scheme for an Oseentype diﬀusive Peterlin model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A stabilized Lagrange–Galerkin scheme for an Oseen-type diﬀusive Peterlin model is presented. It
employs a semi-implicit approximation for the time integration, which yields a nonlinear scheme. Existence,uniqueness, (essentially) unconditional stability and error estimates are proved for the scheme. Numericalresults are shown in order to see the theoretical convergence order.

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Applied Mathematics

31 Nobuyuki Higashimori (Kyoto Univ.)
Hiroshi Fujiwara (Kyoto Univ.)(Kyoto Univ.)
Yuusuke Iso

Convergence of an abstract finite diﬀerence scheme for the Cauchy
problem on a Banach scale · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show a suﬃcient condition for convergence of an abstract finite diﬀerence scheme to solve theCauchy problem on a Banach scale. As an application we obtain a result of convergence of a finite diﬀerence
scheme to solve the Cauchy problem for a partial diﬀerence equation of normal form whose coeﬃcients are
assumed to be real analytic in space variables but not so in the time variable. Moreover we do not requirethat the equation is hyperbolic or that the Courant–Friedrichs–Lewy condition (CFL condition) is satisfied
for the case of hyperbolic equation.
32 Yoshitaka Watanabe (Kyushu Univ.)
Takehiko Kinoshita (Kyoto Univ.)
Mitsuhiro T. Nakao(Sasebo Nat. Coll. of Tech.)

Computer-assisted instability proof with high accuracy for plane Poiseuilleflow · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk shows a numerical verification method for computing eigenpair enclosures of the Orr–
Sommerfeld equation describing hydrodynamic stability of Poiseuille flow. By using spectral Galerkinapproximate solutions bounding its small defect and the Banach fixed-point theorem, an eigenpair is
enclosed with guaranteed accurate error and locally unique bounds in computer. Some verification results
confirm the eﬀectiveness of the method, and, to the best of the authors’ knowledge, they give the best upperbound of the critical Reynolds number.
33 Akitoshi Takayasu (Waseda Univ.)
Makoto Mizuguchi (Waseda Univ.)
Kubo Takayuki (Univ. of Tsukuba)
Shin’ichi Oishi (Waseda Univ.)

Verified computations for solutions to nonlinear heat equations basedon fractional powers of a positive operator and the evolution operator· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider a numerical method for verifying existence and local uniqueness of asolution for an initial-boundary value problem of nonlinear heat equations. This method is based on a
fixed-point formulation using the evolution operator introduced by Tanabe–Sobolevskii. Using fractional
powers of a positive operator, we derive a suﬃcient condition for enclosing the solution in a neighborhoodof an approximate solution.
34 Makoto Mizuguchi (Waseda Univ.)
Akitoshi Takayasu (Waseda Univ.)
Takayuki Kubo (Univ. of Tsukuba)
Shin’ichi Oishi (Waseda Univ.)

On a computable Sobolev embedding constant for fractional powers ofa weighted Laplace operator · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is concerned with a computable Sobolev embedding constant for fractional powers of aweighted Laplace operator on a domain Ω ⊆ RN . The constant is explicitly described using the analytic
semigroup over L2 (Ω) and the infimum value of spectrum of the weighted Laplace operator. Each value ofthe constants for some domains will be presented.

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Applied Mathematics

16:00–17:00
Kota Ikeda

Talk Invited by Applied Mathematics Section(Meiji Univ.)

Congestion flow of pulses in an excitable reaction-diﬀusion system

Summary: Self-driven motion is observed in several fields, e.g., biology, chemistry, and nonlinear physics.
Organisms move spontaneously to aggregate and form self-organized structures. As a spatiotemporalcollective motion, congestion flow is observed in a system with animal and in animal organisms. For example,
camphor boats constitute a system for changing the number of particles and with simple interaction andgenerate congestion flow as reported by Suematsu et al in 2010. The mechanism of the congestion dynamics
of camphor boats has been investigated theoretically. As stated in our previous works, a traveling wave
solution in a model with an inhomogeneity plays an important role. Recently it was reported that travelingwave solutions with a pulse shape, simply called traveling pulses, could generate congestion flow in areaction-diﬀusion system with excitability. It is well-known that a traveling pulse is formed spontaneously inan excitable system like the FitzHugh–Nagumo model. This fact seems to imply that the same mechanism
as in a system with camphor boats works in the congestion flow of an excitable system. However, it is nottrue because the reaction-diﬀusion system has no inhomogeneity. In this talk, we focus on studying thetraveling pulse and consider what is diﬀerent between the congestion flow in the model of camphor boats
and the excitable system.

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76Topology

Topology
March 16th (Wed)Conference Room VI

10:00–11:55
1 Yusuke Takimura(Gakushuin Boys’ Junior High School)(Waseda Univ.)
Noboru Ito

Thirty-two equivalence relations on knot projections · · · · · · · · · · · · · · · · 10

Summary: For the set of the knot projections, we define 32 homotopy equivalence relations, each of which is
generated by some of the five types of Reidemeister moves. We show that 32 cases correspond to 8 trivial
cases and 20 non-trivial cases reduced from 24 cases. The 20 non-trivial cases are mutually diﬀerent. To
show the statement, we introduce new invariants of knot projections.
(Waseda Univ.)
2 Noboru Ito
Yusuke Takimura(Gakushuin Boys’ Junior High School)

Triply-graded knot projections under (1, 3) homotopy · · · · · · · · · · · · · · 15

Summary: In 2001, Oestlund conjectured that Reidemeister moves RI and RIII are suﬃcient to describe ahomotopy from any generic immersion of a circle into the plane to the simple closed curve. In 2014, Hagge
and Yazinski obtained a counterexample (having at least 16 double points) of this conjecture. In this study,
we obtain a counterexample of Oestlund conjecture where the minimum number of double points is 15. Weshow that for any integer k more than 14, there exists a knot projection where the minimum number ofdouble points is k. We also discuss the minimum number of Type RII Reidemeister moves required to obtainthe simple closed curve under the equivalence relation generated by Reidemeister moves RI and RIII.
3 Shosaku Matsuzaki (Waseda Univ.)
Makoto Ozawa (Komazawa Univ.)

Minors of multibranched surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We say that a 2-dimensional CW complex is a multibranched surface if we remove all points
whose open neighborhoods are homeomorphic to R2 , then we obtain a 1-dimensional complex which is
homeomorphic to a disjoint union of some S 1 ’s. A multibranched surface is a generalization of graphs. So
we can define “minors” of multibranchd surfaces analogously. We study various properties of the minors ofmultibranched surfaces.
4 Makoto Ozawa (Komazawa Univ.)
Shosaku Matsuzaki (Waseda Univ.)

Genera of multibranched surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We say that a 2-dimensional CW complex is a multibranched surface if we remove all points
whose open neighborhoods are homeomorphic to R2 , then we obtain a 1-dimensional complex which is
homeomorphic to a disjoint union of some S 1 ’s. We define the (minimal) genus of a multibranched surface
X as the minimal number of genera of 3-manifold into which X can be embedded. In this talk, we statesome inequalities which give an upper bound for the genus of a multibranched surface.
5 Shinya Okazaki (Osaka City Univ.)

An invariant comes from the Alexander polynomial of a handlebodyknot · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A handlebody-knot is a handlebody embedded in the 3-sphere. In this talk, we introduce aninvariant of a handlebody-knot which is represented by a vertex-weighted graph. This invariant comes fromthe Alexander polynomial of a handlebody-knot.

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Topology

6 Atsuhiko Mizusawa (Waseda Univ.)
Yuka Kotorii (Univ. of Tokyo)

On invariants of HBL-homotopy classes of 3-component handlebodylinks with vanishing linking numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A handlebody-link is an embedding of handlebodys into the 3-sphere. A handlebody-link isrepresented by its spine (a spatial graph). Two spatial graphs which represent the same handlebody-link aretransformed to each other by a sequence of contraction moves. Two handlebody-links are HBL-homotopic
if their representing spatial graphs are transformed to each other by a sequence of contraction moves andself-crossing changes. In this talk, we give a bijection between HBL-homotopy classes of 3-component
handlebody-links with vanishing linking numbers and 3-dimensional hyper matrices up to elementarytransformations. Through this map, we give some invariants of the HBL-homotopy classes.
7 Kodai Wada (Waseda Univ.)
Akira Yasuhara (Tokyo Gakugei Univ.)

Milnor invariants of clover links · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: J. P. Levine introduced a clover link to investigate the indeterminacy of Milnor invariants of alink. It is shown that for a clover link, Milnor numbers of length at most 2k + 1 are well-defined if thoseof length at most k vanish, and that Milnor numbers of length at least 2k + 2 are not well-defined if thoseof length k + 1 survive. For a clover link c with Milnor numbers of length at most k vanishing, we showthat the Milnor number µc (I) for a sequence I is well-defined up to the greatest common devisor of µc (J)′ s,
where J is a subsequence of I obtained by removing at least k + 1 indices. Moreover, if I is a non-repeatedsequence with length 2k + 2, the possible range of µc (I) is given explicitly. As an application, we give anedge-homotopy classification of 4-clover links.
8 Kazuhiro Ichihara (Nihon Univ.)
Toshio Saito (Joetsu Univ. of Edu.)(Kinki Univ.)
In Dae Jong

On cosmetic surgery conjecture on knots · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The cosmetic surgery conjecture saids that no pair of Dehn surgeries along inequivalent slopes
yield orientation preservingly homeomorphic 3-manifolds. First I will tlak about a recent result on thisconjecture for certain two-bridge knots. Next I will present a new example of a hyperbolic knot admitting
a pair of of Dehn surgeries along inequivalent slopes yield orientation reversingly homeomorphic hyperbolic
3-manifolds.
9 Kazuhiro Ichihara (Nihon Univ.)(Fudan Univ.)
Jiming Ma
Ken-ichi Yoshida (Nihon Univ.)

Hyperbolicity and the number of components for random link · · · · · · · 15

Summary: From a probabilistic point of view, Jiming Ma introduced and studied two models of random
links. One model is given as the closure of a braid obtained from a random walk on the braid group. For
such a random link, the expected value for the number of components was calculated by Jiming Ma. We
first report on the most expected number of components for a random link, and further, the most expectedpartition of the number of strings for a random braid. Another model is given by considering random bridge
decomposition for links. We next show that a random link via random bridge position is hyperbolic withasymptotic probability 1.
14:15–15:15

Talk Invited by Topology Section

Yukio Matsumoto(Gakushuin Univ./Chuo Univ./Univ. of Tokyo⋆)

On the compactification of moduli spaces and crystallographic groups

Summary: The purpose of this talk is to give a natural orbifold-chart system on the Deligne–Mumford
compactification of moduli space of Riemann surfaces of genus g ≧ 3. The charts are indexed by simplicesof the curve complex associated with the underlying topological surface. We will point out that certain
crystallographic group on E3g−3 arises from the orbifold-chart around each maximally degenerated ideal
point.

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Topology

15:30–17:10
10 Masakazu Teragaito (Hiroshima Univ.)

Generalized torsion elements in the knot groups of twist knots · · · · · · · 10

Summary: It is well known that any knot group is torsion-free, but it may admit a generalized torsion
element. We show that the knot group of any negative twist knot admits a generalized torsion element. Thisis a generalization of the same claim for the knot 52 , which is the (−2)-twist knot, by Naylor and Rolfsen.
11 Yuta Nozaki (Univ. of Tokyo)

The preimage of a knot under the covering map from S 3 to RP 3 · · · · · 15

Summary: When a knot K in S 3 is the preimage of a knot K ′ in RP 3 , we describe the fundamental group
π1 (S 3 \ K) in terms of π1 (RP 3 \ K ′ ). Using this description, we give a necessary condition for K being thepreimage of a knot K ′ in RP 3 .
12 Akiko Shima
Teruo Nagase(Tokai Univ.)(Tokai Univ.⋆)

Properties of CS-minimal charts · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Two charts are said to be CS-equivalent if one deforms to the other by a finite sequence ofC-moves, conjugations, stabilizations and destabilizations. Let Γ be an n-chart, w(Γ) the number of whitevertices in Γ, and f (Γ) the number of free edges in Γ. The pair (w(Γ), n − f (Γ)) is called the CS-complexityof Γ. A chart Γ is CS-minimal if its CS-complexity is minimal among the set of charts CS-equivalent toΓ with respect to the lexicographical order of the pair of integers. In this talk, we prove that if Γ is a
CS-minimal chart with w(Γ) = 6, then Γ is CS-equivalent to the product of a ribbon chart and a ‘chart’representing a 2-twist spun trefoil.
13 Noriyuki Hamada (Univ. of Tokyo)
Kenta Hayano (Hokkaido Univ.)

Finite covers of Lefschetz fibrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about the simple fact that taking an unbranched finite cover of a Lefschetz fibrationor pencil gives a new Lefschetz fibration/pencil. We will give a general recipe to imply the monodromy
factorization of such a fibration and then show several examples with (very) neat monodromies. Other
associated new fibrations will also be presented.
14 Erika Kuno

(Tokyo Tech)

Disk graphs and right-angled Artin subgroups in handlebody groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Koberda proved that if a graph Γ is a full subgraph of a curve graph C(S) of an orientable surface
S, then the right-angled Artin group A(Γ) on Γ is a subgroup of the mapping class group Mod(S) of S.
On the other hand, for a suﬃciently complicated surface S, Kim–Koberda gave a graph Γ which is notcontained in C(S), but A(Γ) is a subgroup of Mod(S). In this talk, we prove that if Γ is a full subgraph ofa disk graph D(H) of a handlebody H, then A(Γ) is a subgroup of the handlebody group Mod(H) of H.
Further, we show that there is a graph Γ which is not contained in some disk graphs, but A(Γ) is a subgroupof the corresponding handlebody groups.
15 Genki Omori(Tokyo Tech)

A simple infinite presentation for the mapping class group of a nonorientable surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We obtain a simple infinite presentation for the mapping class group of a non-orientable surface.
The generating set consists of Dehn twists and crosscap pushing maps. We use the Stukow’s finite
presentation for the mapping class group of a non-orientable surface and apply the Gervais’s discuccion in
the orientable case to obtain the presentation.

16 Genki Omori(Tokyo Tech)

Simple closed curves on a non-orientable surface and the twist subgroupof the mapping class group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The twist subgroup T (N ) of the mapping class group M(N ) of a non-orientable surface N is the
subgroup of M(N ) generated by all Dehn twists. M(N ) is not generated by Dehn twists and when N is
compact, T (N ) is an index 2 subgroup of M(N ). We consider the following problem: for simple closed
curves c1 , c2 on N whose complements are diﬀeomorphic, what is a condition to satisfy that there exists anelement f of T (N ) such that f (c1 ) = c2 . We answer the problem partially.

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Topology

March 17th (Thu)

Conference Room VI

10:00–11:40
17 Chieko Komoda(Kurume Nat. Coll. of Tech.)Open mapping theorems with finite fibers for C-spaces and finite Cspaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This is a joint work with Takashi Kimura. We assume that all spaces are normal and all mappings
are continuous.
In this talk we study open mapping theorems with finite fibers for C-spaces and finite C-spaces.
18 Katsuhisa Koshino (Kanagawa Univ.)

Topological types of hyperspaces of finite sets in metrizable spaces · · · 10

Summary: Let Fin(X) be the hyperspace consisting of non-empty finite subsets of a space X with the Vietoris
topology. In this talk, we characterize a metrizable space X whose hyperspace Fin(X) is homeomorphic toa pre-Hilbert space spanned by the canonical orthonormal basis of a non-separable Hilbert space.
19 Tomohiko Ishida (Kyoto Univ.)

Quasi-isometry type of the metric space derived from the kernel of theCalabi homomorphism · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove that the set of symmetrized conjugacy classes of the kernel of the Calabi homomorphismon the group of area-preserving diﬀeomorphisms of the 2-disk is not quasi-isometric to the half line.
20 Huhe Han (Yokohama Nat. Univ.)
Takashi Nishimura(Yokohama Nat. Univ.)

Strictly convex Wulﬀ shapes and C 1 convex integrands · · · · · · · · · · · · · 15

Summary: In this talk, it is shown that a Wulﬀ shape is strictly convex if and only if its convex integrand isof class C 1 . Moreover, applications of this result are given.
21 Takahiro Yamamoto(Kyushu Sangyo Univ.)

Elimination of B2 -singularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a stable map f : N → P of a 3-manifold with one boundary component into a surface withoutboundary, we show that f is homotopic to a stable map which have no B2 points.
22 Kenichirou Shinkai (Shinshu Univ.)
Yasuhiro Momose (Shinshu Univ.)

On the matrix Toda brackets and 3-rd cohomology groups of small
categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Hardie–Kamps–Marcum have given a categorical treatment of matrix Toda brackets introduced
Barratt in the category of topological spaces. Baues–Dreckmann shawed that there exists a class in Baues–
Wirsching cohomology of a small category which represents all classical Toda brackets. Our aim is togeneralize such a relationship to that between the cohomology of a 2-category and matrix Toda brackets.
23 Miho Hatanaka (Osaka City Univ.)

Cohomology representations of toric manifolds associated to some simple graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We can construct toric manifolds from simple graphs. The automorphism group of a simple
graph induces a representation on the cohomology ring of the toric manifold associated to the simple graph.
The automorphism group of a complete graph is a symmetric group. Procesi described the cohomology
representation when the simple graph is a complete graph. In this talk we take a graph obtained by removing
an edge from a complete graph and describe the associated cohomology representation.

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80Topology

13:30–14:30
Kei Irie

Talk Invited by Topology Section(Kyoto Univ.)

A C ∞ closing lemma for three-dimensional Reeb flows via embedded
contact homology

Summary: We prove a C ∞ closing lemma for three-dimensional Reeb flows, and deduce that for any closed
contact three-manifold with a C ∞ generic contact form the union of all periodic Reeb orbits is dense. The
proof uses recent developments in quantitative aspects of embedded contact homology, which is an invariantof contact three-manifolds defined by holomorphic curve techniques in symplectic geometry. Applications
to closed geodesics and area-preserving diﬀeomorphisms on surfaces will be also presented.

March 18th (Fri)

Conference Room VI

10:00–11:45
24 Hokuto Konno (Univ. of Tokyo)

Bounds on genus and configurations of embedded surfaces in 4-manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For finitely many surfaces with zero self-intersection number embedded in a 4-manifold with
b1 = 0, we show a lower bound on genus for at least one of the surfaces under some conditions on thesurfaces. As an application we derive a constraint for a pair of genera of two embedded surfaces and we
also give an alternative proof of the adjunction-type inequality by Strle for configurations of surfaces withpositive self-intersection numbers.
25 Antonio J. Di Scala(Politecnico di Torino)
Naohiko Kasuya(Aoyama Gakuin Univ.)(KIAS)
Daniele Zuddas

Non-Kähler complex structures on R4 II · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We already constructed uncountably many non-Kähler complex manifolds diﬀeomorphic to R4 ,and I talked about the construction at the last meeting of MSJ. This time, I will talk about various propertiesof our complex manifolds. For example, they have nontrivial Picard groups and cannot be holomorphicallyembedded in any compact complex surface. This is a joint work with Antonio J. Di Scala and Daniele
Zuddas.
26 Yoshihiko Mitsumatsu (Chuo Univ.)
Elmar Vogt (Freie Univ. Berlin)

Turbulization of 2-dimensional foliations on 4-manifolds · · · · · · · · · · · · · 15

Summary: The notion of turbulization is formulated for higher codimensional foliations. It has been wellknown for foliations of codimension one since long ago but in higher codimension case, it is not only
not-trivial to formulate but also complicated to a certain degree to realize it geometrically. In the case of
2-dimensional foliations on 4-manifolds it is done, where 3-dimensional geodesic Ansov foliations play animportant role.
Under this dimension setting, some other modifications which are similar to turbulization are also introduced.
The motivation from and the relation with the h-principle due to Thurston are also explained.
27 Yoshihiko Mitsumatsu (Chuo Univ.)

Convexity of symplectic ends, leafwise symplectic foliations on 5-sphere,
and strange symplectic 4-manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The construction of leafwise symplectic foliations of codimension one on the 5-sphere from thesimple elliptic singularities and cusp singuralities of complex three variables is reviewed, with an emphasison the topological flexibility of convexity of the end of open symplectic manifolds.
The method enables us to construct some b-symplectic structures on closed 4-manifolds and some strange
closed symplectic 4-manifolds as well.

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Topology

28 Takahiro Oba
Burak Ozbagci(Tokyo Tech)(Koç Univ.)

Open book decompositions of unit cotangent bundles of orientableclosed surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Thanks to a result of Giroux, we can make use of open book decompositions to study contact
structures. The unit cotangent bundle ST ∗ Σg of an orientable closed surface Σg admits the canonicalcontact structure ξcan . For g = 0, 1, an explicit description of a supporting open book decomposition of ξcanis known. For g ≥ 2, J. Johns gave an abstract description of a Lefschetz fibration on the unit disk bundle
DT ∗ Σg . It follows one of a supporting open book decomposition of ξcan . In this talk, we will present an
explicit description of a supporting open book decomposition of ξcan for any g. As a corollary of this result,
we will also give one of a Lefschetz fibration on DT ∗ Σg .
29 Kouichi Yasui (Hiroshima Univ.)

Nonexistence of Stein structures on 4-manifolds and maximal Thurston–
Bennequin numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For a 4-manifold represented by a framed knot in S 3 , it has been well known that the 4-manifold
admits a Stein structure if the framing is less than the maximal Thurston–Bennequin number of the knot.
In this paper, we prove either the converse of this fact is false or there exists a compact contractible oriented
smooth 4-manifold (with Stein fillable boundary) admitting no Stein structure. Note that an exotic smooth
structure on S 4 exists if and only if there exists a compact contractible oriented smooth 4-manifold with S 3boundary admitting no Stein structure.
30 Kouichi Yasui (Hiroshima Univ.)

Maximal Thurston–Bennequin number and reducible Legendrian surgery· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a method for constructing a Legendrian representative of a knot in S 3 which realizes
its maximal Thurston–Bennequin number under a certain condition. The method utilizes Stein handle
decompositions of D4 , and the resulting Legendrian representative is often very complicated. As anapplication, we construct infinitely many knots in S 3 each of which yields a reducible 3-manifold by a
Legendrian surgery in the standard tight contact structure. This disproves a conjecture of Lidman andSivek.
14:15–15:30
31 Motoo Tange (Univ. of Tsukuba)

On finite order corks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct examples of finite order cork. The point is to prove that the contractible 4-manifold
admits Stein structure. We realize it by describing some Legendrian link on #n S 2 × S 1 .
32 Motoo Tange (Univ. of Tsukuba)

Branched double covers and rational homology 4-balls · · · · · · · · · · · · · · 15

Summary: We give examples of non-slice knot whose branched cover bounds rational homology 4-ball. The
knots are Whitehead double of a torus knot. To find the examples, Heegaard Floer d-invariant is useful.
Further, we consider a way to compute CF K ∞ (#2 Tp,q ).
33 Kouki Sato

(Tokyo Tech)

1-connected rational filling of rational homology 3-spheres · · · · · · · · · · · 15

Summary: For a rational homology 3-sphere Y , a 1-connected rational filling W for Y is a rational homology
4-ball with boundary Y such that the induced map from the inclusion i∗ : π1 (Y ) → π1 (W ) is surjective.
In this talk, we consider which rational homology 3-spheres have 1-connected rational filings. In particular,
we give characterizations of such rational homology 3-spheres from diﬀerent two view points; cyclic branchedcovers of S 3 branched over knots, and Dehn surgeries on links in S 3 .
(OCAMI)
34 Tetsuya Abe
(
Univ.
of
Tsukuba)
Motoo Tange

Ribbon disks via handle decompositions of B 4 · · · · · · · · · · · · · · · · · · · · · 15

Summary: We recall Hudson–Sumners’ construction of ribbon disks. Using this construction, we give ribbon
disks with the same exterior.

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Topology

35 Tatsuro Shimizu (Kyoto Univ.)

Chern–Simons perturbation theory around a non-tirvial flat connection
and Morse homotopy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a Morse homotopy theoretic description of the degree 1 part of the Chern–Simons
perturbation theory around a non-trivial flat connection.
15:45–16:45

Talk Invited by Topology Section

Dai Tamaki(Shinshu Univ.)

Configuration spaces and homotopy theory

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Infinite Analysis

Infinite Analysis
March 18th (Fri)

Conference Room VIII

10:00–12:00
1 Masahiko Ito (Tokyo Denki Univ.)
Masatoshi Noumi (Kobe Univ.)

The Jackson integral of A type and a generalization of Ramanujan’s
1 ψ1 summation and Slater’s r ψr transformation · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about a connection formula for the Jackson integrals of A type. The connection
formula gives a generalization of Slater’s transformation formula for a basic hypergeometric series r ψr . As anapplication of the connection formula, we obtain a determinant formula as the Wronskian of the q-diﬀerence
system for the Jackson integrals of A type. The determinant formula includes Ramanujan’s summation
formula for a basic hypergeometric series 1 ψ1 .
2 Masahiko Ito (Tokyo Denki Univ.)
Masatoshi Noumi (Kobe Univ.)

A construction of the elliptic Lagrange interpolation functions of type A· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the connection formula for the Jackson integral of A type, the elliptic Lagrange interpolation
functions appear naturally as the connection coeﬃcients. We will explain a construction of the elliptic
Lagrange interpolation functions of type A. As a consequence, we will show the explicit expression of theelliptic Lagrange interpolation functions.
3 Shuhei Kamioka (Kyoto Univ.)

A generalization of the q-Chu–Vandermonde sum for basic hypergeometric series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A generalization of a q-Chu–Vandermonde sum for basic hypergeometric series, which involves
multiple parameters substituting for the base q, is exhibited. Generalizations of the little q-Laguerre(Wall) polynomials, that are classical orthogonal polynomials in the Askey scheme, are also shown. The
orthogonality of the generalized little q-Laguerre polynomials is proven by means of the generalized q-Chu–
Vandermonde sum.
4 Genki Shibukawa (Osaka Univ.)

Pseudo Wilson polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: By considering the image of the Jacobi transformation of a finite type orthogonal system constructed by the Jacobi polynomials, we obtain new finite type orthogonal polynomials, which we call “pseudo
Wilson polynomials”, and their properties.
5 Hidehito Nagao (Akashi Coll. of Tech.)
Yasuhiko Yamada (Kobe Univ.)Padé method and the q-Garnier system · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study some Padé problem of the diﬀerential grid, related to the q-Garnier system. Solving
the problem, we derive the evolution equation, the scalar Lax pair and the determinant formulae of special
solutions for the corresponding q-Garnier system.
6 Takao Suzuki(Kinki Univ.)

Fourth order q-Painlevé system containing q-hypergeometric function
3 ϕ2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We proposed the hyper order q-Painlevé system containing q-hypergeometric function n ϕn−1 inMarch 2012. In this talk, we give a new expression of that q-diﬀerence system.
14:15–15:15
7 Shotaro Konnai (Kobe Univ.)

Analysis of the Katz operations stabilizing the class of Okubo systems· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we investigate certain Katz operations (additions and middle convolutions) which
stabilize the class of Okubo systems of ordinary diﬀerential equations. We also dicuss some applications tothe connection problem for the fundamental solution matrices of Okubo systems.

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84

Infinite Analysis

8 Kazuki Hiroe(Josai Univ.)

Stokes structure and links · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Some similarities between ramified irregular singularities of linear ordinary diﬀerential equations
and singularities of plane curve germs are found, for instance in transformations: local Fourier transformand blowing up, in invariants: Komatsu–Malgrange irregularity and Milnor number, and so on. In this talkwe shall define links from linear ODEs with ramified irregular singularities as an analogy of links of singularplane curve germs. Some relations between link invariants and invariants of ODEs shall be explained.
Furthermore, it shall be discussed that isomonodromic deformation of ODEs induces link isotopy of thecorresponding links as an analogy of the fact that equisingularity of plane curve singularities induces link
isotopy.
9 Kimio Ueno

(Waseda Univ.)

Monodromy preserving deformation associated to KZ equation · · · · · · · 15

Summary: We consder the monodromy preserving deformation associated to the KZ equation of threevariables and holomorphic solutions to the deformation equations.
10 Yoshishige Haraoka (Kumamoto Univ.) ♭ On representations of braid groups associated with complex reflectiongroups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We classify three dimensional irreducible representations of braid groups associated with primitive
finite irreducible complex reflection groups in GL(3, C). Spectral types of the local monodromies play asubstantial role. The representations give monodromy representations for some uniformization equations.
15:30–16:30

Talk Invited by Infinite Analysis Special Session
Daisuke Yamakawa (Tokyo Tech) Twisted wild character varieties

Summary: This is joint work with Philip Boalch. The wild character varieties are Poisson algebraic varieties
related to the moduli spaces of unramified meromorphic connections on compact Riemann surfaces with
fixed irregular type at each singularity under the Riemann–Hilbert–Birkhoﬀ correspondence. We will extend
the construction of the wild character varieties to the case of ramified connections. In the unramified case,the formal monodromy of meromorphic connections can be interpreted as a group-valued moment map inthe sense of Alekseev–Malkin–Meinrenken. In order to extend that interpretation to the ramified case, we
introduce the moment maps taking values in “twisted groups”.

March 19th (Sat)

Conference Room VIII

9:30–12:00
11 Yoshihiro Takeyama(Univ. of Tsukuba)

Algebraic construction of multi-species q-Boson system · · · · · · · · · · · · · 15

Summary: We construct a stochastic particle system which is a multi-species version of the q-Boson system
due to Sasamoto and Wadati. Its transition rate matrix is obtained from a representation of a deformationof the aﬃne Hecke algebra of type GL.
12 Masato Okado (Osaka City Univ.)
Atsuo Kuniba (Univ. of Tokyo)
Shouya Maruyama (Univ. of Tokyo)

Multispecies TAZRP · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce an n-species asymmetric zero range process (n-TAZRP) on the periodic chain of
L sites. It is a continuous time Markov process, and obtained as the image of a projection from anotherb L ),
stochastic system called n-line process. By using a combinatorial R of the quantum aﬃne algebra Uq (slwe establish a matrix product formula of the steady state probability of the n-TAZRP in terms of cornertransfer matrices of a q = 0-oscillator valued vertex model. It is also derived from the commutativityof a layer-to-layer transfer matrix of a 3D lattice model constructed from a distinguished solution to thetetrahedron equation.

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Infinite Analysis

13 Saburo Kakei (Rikkyo Univ.)
Jonathan J. C. Nimmo(Univ. of Glasgow)
Satoshi Tsujimoto (Kyoto Univ.)
Ralph Willox (Univ. of Tokyo)

Linearization of the box-ball system: an elementary approach · · · · · · · · 15

Summary: Kuniba, Okado, Takagi, and Yamada found that the time-evolution of the Takahashi–Satsuma
box-ball system (BBS) can be linearized by considering rigged configurations associated with states of the(1)
BBS. We introduce a simple way to understand the rigged configuration of A1 -type, and give an elementary
proof of the linearization property.
14 Yasuhiro Ohta (Kobe Univ.)
Sampei Hirose (Shibaura Inst. of Tech.)Jun-ichi Inoguchi (Univ. of Tsukuba)
Kenji Kajiwara (Kyushu Univ.)
Nozomu Matsuura (Fukuoka Univ.)

Determinant and Pfaﬃan solutions for motion of discrete space curve· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Determinant and Pfaﬃan solutions for motion of discrete space curve are given.
15 Yoko Shigyo(Tsuda Coll.)

Expansion coeﬃcients of a solution of the BKP hierarchy · · · · · · · · · · · 15

Summary: In this talk we study the degenerate Giambelli type formulae in the BKP hierarchy. It is known
that a formal power series τ (x) expanded as Schur’s Q-function is a solution of the BKP hierarchy if andonly if the coeﬃcients of this expansion satisfy Giambelli type formulae. We proved this statement with acondition τ (0) ̸= 0. Here we prove this result with a condition τ (0) = 0.
16 Takanori Ayano (Osaka City Univ.)

A generalization of Jacobi inversion formulae to telescopic curves on all
the strata · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a hyperelliptic curve, it is well-known that an element of the k-th symmetric product isexpressed in terms of its Abel–Jacobi image by the hyperelliptic sigma functions on all the strata (Jacobi
inversion formulae). Matsutani and Previato extended the Jacobi inversion formulae to the more generalplane algebraic curves defined by y r = f (x), which are special cases of the (n, s) curves, and derived aproperty of the vanishing of the sigma functions as a corollary. In this talk, we extend the formulae totelescopic curves proposed by Miura, which contain the (n, s) curves as special cases, and remark that thevanishing property of the sigma functions is also satisfied for the telescopic curves.
17 Yosuke Saito (Osaka City Univ.)

Eigenfunctions of Ruijsenaars operator arising from the functional equation of the dual Cauchy type kernel function · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show that eigenfunctions of Ruijsenaars operator are obtained from the functional equationof the dual Cauchy type kernel function in a special case.
18 Diogo Kendy Matsumoto(Waseda Univ.)

Yang–Baxter maps on the Generalized pre-semiring · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce a generalized pre-semiring as a generalization of ring, and consider
Yang–Baxter maps on the generalized pre-semiring. These Yang–Baxter maps including many well-known
examples of the Yang–Baxter maps.
14:15–15:15
19 Takeshi Ikeda (Okayama Univ. of Sci.)

Littlewood-Richardson rule for factorial P -functions · · · · · · · · · · · · · · · · 15

Summary: We give a combinatorial description for the multiplicative structure constants of the factorial
P -functions.

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Infinite Analysis

20 Yuki Kanakubo (Sophia Univ.)
Toshiki Nakashima (Sophia Univ.)

Cluster variables on double Bruhat cell of classical group and cystal
base · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Coordinate rings of certain subgroups or cells of algebraic group G have the structures of cluster
algebra, and generalized minors are their cluster variables. In the case G = SLr+1 (C), generalized minors
are coincide with ordinary minors. Last year, we had shown a relation between minors on double Bruhat
cell of SLr+1 (C) and crystal bases. Using coordinate transformation, the minors become polynomials whoseterms are equal to the monomial realization of some crystal bases. In this talk, we will extend these results
to other classical groups.
21 Yoshiyuki Kimura (Kobe Univ.)

Remarks on quantum unipotent subgroup and dual canonical basis · · · 15

Summary: In this talk, we show the tensor product decomposition of the half of quantized universal enveloping
algebra associated with a Weyl group element that was conjectured by Berenstein and Greenstein using thetheory of the dual canonical basis.
22 Shunsuke Tsuchioka (Univ. of Tokyo)
Masaki Watanabe (Univ. of Tokyo)

Pattern avoidance seen in multiplicities of maximal weights of aﬃne Liealgebra representations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(1)

Summary: We prove that the multiplicities of certain maximal weights of g(An )-modules are counted bypattern avoidance on words. This proves and generalizes a conjecture of Misra–Rebecca. We also prove(2)(2)
similar phenomena in types A2n and Dn+1 . Both proofs are applications of Kashiwara’s crystal theory.
15:30–16:30

Talk Invited by Infinite Analysis Special Session

Hiroyuki Yamane (Univ. of Toyama)

Weyl groupoids and representation theory of generalized quantum
groupsSummary: In this talk, I introduce Weyl groupoids, and Matsumoto–Tits type theorem of them, and explain
how they can be used to study representation theory of generalized quantum groups U. We have got a
Shapovalov determinant formula for U and classification of finite dimensional simple U-modules.