Final: 2015/08/20“ Mathematical Society of Japan
2015 Autumn Meeting

Titles and Short Summaries of the Talks

September, 2015
at Kyoto Sangyo University

Final: 2015/08/20

2015 Mathematical Society of Japan
AUTUMN MEETING
Dates: September 13th (Sun)–16th (Wed), 2015
Venue: Kyoto Sangyo University
Motoyama, Kamikamo, Kita-ku, Kyoto 603-8555
Contact to: Kyoto Sangyo University, Faculty of ScienceE-mail kyoto-sangyo15sept 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

X

Bldg. 11
Rm. 11304

Bldg. 6Rm. 514

Bldg. 6Rm. 515

Bldg. 6Rm. 518

Bldg. 5Rm. 5405

Bldg. 5Rm. 5406

Bldg. 5Rm. 5407

Bldg. 5Rm. 5301

Bldg. 5Rm. 5302

Bldg. 5Rm. 5303

AlgebraAppliedMathematics

Infinite
Analysis

Topology

Functional Statistics and Functional
Equations Probability Analysis

ComplexAnalysis

Geometry

9:15–11:50 9:30–12:00
15:30–18:00 14:15–16:20

13th
(Sun)

9:30–12:00

9:50–12:00 9:00–12:00 9:30–12:00 14:30–16:30 9:30–12:00 9:50–12:00
14:15–16:15 14:15–16:45
15:30–17:15 14:15–16:15 14:15–14:45

Featured Invited Talks
13:00–14:00
Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk
14:15–15:15 16:40–17:40 14:15–15:15 14:15–15:15 16:30–17:30 15:00–16:00 17:00–18:00 16:30–17:30
16:15–17:15

14th

AlgebraAppliedMathematics

Infinite
Analysis

Functional Statistics and Functional
Equations Probability Analysis

Complex Geometry
Analysis &Topology

9:15–12:00

9:15–11:45

9:30–12:00

9:00–12:00

9:30–12:00

Invited Talk Invited Talk Invited Talk

Invited Talk

Invited Talk Invited Talk Invited Talks

13:10–14:10 13:15–14:15 13:00–14:00

13:15–14:15

13:30–14:30 13:15–14:15 13:15–14:15
10:50–11:50

9:30–11:30(Mon)

9:30–12:00

MSJ Prizes Presentation (Kamiyama Hall) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:50–15:20)
Plenary Talks(Kamiyama Hall) MSJ Autumn Prize Winner · · · · · · · · · · · · · · · (15:30–16:30)
Hisashi Okamoto (Kyoto Univ.) · · · · · · · · · · · · ·(16:45–17:45)
Oﬃcial Party(Kamiyama Hall, Lounge “Furusato”) · · · · · · · · · · · · · · · · · · · · · · · (18:00–20:00)
Found. of Math.
andHistory of Math.

Algebra9:55–11:25

9:30–11:25 14:15–17:25

AppliedMathematics

Real
Analysis

Topology

Functional Statistics and Functional
Equations Probability Analysis

ComplexAnalysis

9:30–12:00

9:50–12:00

9:00–12:00

9:15–12:00 10:00–12:00
14:15–16:25

9:30–12:00

9:00–12:00

15th 14:15–16:00 15:30–17:50 Special Session 14:15–16:25 14:15–15:45 14:15–16:15 14:15–15:15 14:15–16:45
9:30–11:55(Tue)Featured Invited Talks
13:00–14:00
Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk

Invited Talk Invited Talk
16:15–17:15 14:15–15:15

Found. of Math.
andHistory of Math.
16th
(Wed)

Geometry

9:30–11:20

Algebra16:40–17:40 16:15–17:15 16:30–17:30 15:30–16:30 17:00–18:00
16:40–17:40

AppliedMathematics

Real
Analysis

9:30–12:00 9:30–12:00 9:15–12:00
14:15–15:45 14:15–16:45 14:15–15:15

Functional Statistics andEquations Probability
9:00–12:00

9:30–12:00

Invited Talk
16:45–17:45

Geometry
10:00–12:00
14:15–16:15

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

Invited Talk

16:00–17:00 17:00–18:00 15:30–16:30

16:45–17:45

14:15–15:15

Final: 2015/08/20
5

目次
Plenary Talks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

Foundation of Mathematics and History of Mathematics

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

5

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

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

9September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

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

21

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

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

30

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

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

37

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

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

51

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

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

57

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

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

63

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

Final: 2015/08/20
6September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

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

73

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

September 16th (Wed) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

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

86

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

September 15th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

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

93

September 13th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

September 14th (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

Final: 2015/08/20
1

Plenary Talks

Plenary Talks
September 14th (Mon) Kamiyama HallMSJ Autumn Prize Winner····················································(15:30–16:30)

Hisashi Okamoto (Kyoto Univ.)

Diﬃculties arising in mathematical fluid mechanics · · · · · · ·(16:45–17:45)

Summary: The Euler and the Navier-Stokes equations for incompressible fluid motion have attracted a large
number of mathematicians. If we look back the challenges of mathematicians in the last fifty years, it
seems to me that the equations look dangerous rather than beautiful in the sense that very many talented
mathematicians were beaten or betrayed. Beautiful theories which work very well in other branches ofmathematics are often helpless in the Navier-Stokes equations or at least their values are marginal. I, too,
observed such scenes, and this talk is my personal recollections of the diﬃculties of the equations.

Final: 2015/08/20
2Featured Invited Talks

Featured Invited Talks
September 13th (Sun)
Conference Room III
Mariko Hagita (Ochanomizu Univ.)

Existence properties on error-correcting sequences · · · · · · · ·(13:00–14:00)

Summary: We define an (N, k, d) error-correcting sequence over X as a periodic sequence {ai }i=0,1,... (ai ∈ X)
with period N , such that its sub k-tuples {(ai , ai+1 , . . . , ai+k−1 )|i = 0, 1, . . . , N − 1} (multiset) are all
distinct for 0 ≤ i ≤ N − 1, and that they form an error-correcting code with minimum distance d :=∑k−1min0≤s<t≤N −1 { i=0 δ(ai+s , ai+t )}, where δ(x, y) = 1 for x ̸= y and = 0 for x = y. If d ≥ 2e + 1, then one
can correct up to e errors in a k-tuple, so the sequence is said to be e-error correcting.
An m-sequence over GF (q) of period q n − 1 is a (q n − 1, n, 1) error-correcting sequence. We shall consider
when an m-sequence will be an error-correcting sequence with minimum distance d = 3 or d = 5 and we gavesome new constructions of error-correcting sequences.
Conference Room IV
Toshiaki Maeno (Meijo Univ.) ∗ Schubert polynomials and Schur polynomials · · · · · · · · · · · ·(13:00–14:00)

Summary: In my talk, I will survey some basic properties of the Schubert polynomials in comparison with
the Schur polynomials. The Schubert polynomials were introduced by A. Lascoux and M.-P. Schutzenberger
around 1980 in the context of the Schubert calculus on the flag varieties. They form a natural linear basis of
the polynomial ring in the infinite variables, which includes the Schur polynomials as its subfamily. Hence,
the Schubert polynomials can be considered as a nonsymmetric generalization of the Schur polynomials.
They indeed retain combinatorial or algebraic properties of the Schur polynomials in the viewpoint of the
Schubert calculus. One of the interesting features of the Schubert polynomials is their combinatorial structure
controlled by some noncommutative algebras related to integrable systems. Nowadays the Schubert calculus
is widely developed, and a lot of corresponding variants of the Schubert polynomials have been constructed.
Conference Room VI
Guest Talk from Korean Mathematical Society
Dongho Chae (Chung-Ang Univ.) The incompressible Euler equations and the Liouville/uniquecontinuation theorems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Final: 2015/08/20
3Featured Invited Talks

September 15th (Tue)
Conference Room I
Makoto Kikuchi (Kobe Univ.)

The Incompleteness Theorems: The Bounds and Possibilities
of Formalized Mathematics · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: The incompleteness theorems proved by Gödel in 1931 are monumental achievements in mathematical logic in which the existence of an undecidable statement in arithmetic and the unprovability of theconsistency of a formal system of mathematics are shown. These theorems are among the most famous andimportant theorems in mathematics of the last century and, by bringing us novel insights on the concepts oftruth and proof in mathematics, they have had a great influence on philosophy, computer science, cognitive
science, and many other areas which are related to human reasoning and computation over many decades.
However, the proofs of the theorems require some subtle conditions concerning the validity of formalizationsof mathematics, and we need to be careful in the mathematical treatment of the conditions and in the understanding of the meanings of the theorems. In this talk, we introduce basic notions and facts in mathematical
logic such as the completeness theorem for predicate logic and the axioms of arithmetic and set theory, andwe show the outline of the proofs of the incompleteness theorems and some related theorems in mathematical
logic. Then, we discuss the mathematical significance and philosophical consequences of the incompletenesstheorems, and we argue the bounds and possibilities of formalizations of mathematics within the frameworkof predicate logic.
Conference Room V
Isao Nakai (Ochanomizu Univ.)

Some topics in Web geometry · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: A d-web of codimension one is a configuration W = (F1 , F2 , ..., Fd ) of foliations of codimension one.
Web structure is ubiquitous in the mathematical nature. For instance, the theta divisor Θ of the Jacobian
J(C) of a non-hyperelliptic compact Riemann surface C of genus g possesses naturally a 2g − 2-web structureof codimension one. The dual (Legendre transform) of a codimension one foliation of degree d of the projective
space is a d-web of codimension (and of degree one). An implicit ordinary diﬀerential equation f (x, y, p) = 0,p = dy/dx, of degree d in p defines a d-web on the xy-plane by the solutions. Two vector fields generate
2-webs of dimension one. All these webs are ”non commuting” on generic condition, and determined by their
topological (even set theoretical) structure. On one hand, ”commuting” webs with polyhedral symmetry etc
appear as in the special cases corresponding to the elliptic curve, Klein-Halphen singularities. In this talk I
will introduce the various webs and explain their structure.

September 16th (Wed)Conference Room II
Seidai Yasuda(Osaka Univ.)

Motivic multiple zeta values and finite multiple zeta values· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: I would like to talk about motivic and finite multiple zeta values and related topics. A main topic
of my talk is a relation between motivic and finite multiple zeta values. It is applied to give an upper boundof the dimension of the space of finite multiple zeta values of a fixed weight. Besides, I would also like toexplain some other aspects in my interest of the theory of multiple zeta values and some open questions.

Final: 2015/08/20
4Featured Invited Talks

Conference Room IV
Toyohiko Aiki (Japan Women’s Univ.)

On mathematical models for concrete carbonation · · · · · · · ·(13:00–14:00)

Summary: The concrete is important material constituting infrastructure supporting society. Recently, several
interesting mathematical models have been proposed for investigation of damage, carbonation, compositionand chemical reaction for concrete. In this talk we focus on two models describing a carbonation process.
The first model is given as a free boundary problem on an interval in the real line and proposed by Böhm
and Muntean in 2007. In this model the free boundary corresponds to the carbonation front so that thevalue of the free boundary indicates the depth of concrete carbonation. On the simplified model of their one
we could get the large time behavior result which guarantees the real experimental law for the depth of the
carbonation. The aim of second one is to describe the carbonation process in a domain of R3 and the model
is a system two nonlinear partial diﬀerential equations describing mass conservation laws for moisture andcarbon dioxide. The main diﬃculty is how to deal the hysteresis on the relationship between humidity andsaturation of degree. Here, we show the existence and uniqueness results for this system. Moreover, we havesupposed the other free boundary problem in order to overcome the diﬃculty. At the end of this talk we
introduce the two scale model consists of two partial diﬀerential equations and the free boundary problem for
macro and micro parameters, respectively.

Final: 2015/08/20
5Foundation of Mathematics and History of Mathematics

Foundation of Mathematics and History of Mathematics
September 15th (Tue)

Conference Room I

9:55–11:25
The fluid dynamics and the heat theory by Poisson · · · · · · · · · · · · · · · · · 15

1 Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

Summary: We discuss Poisson’s voluminous book on the heat problems, which is one of his last works inlife, 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 thisbook, Poisson mentiones the mathematical conclusions as the finishing strokes of his academic activities in
the fluid dynamics and heat theory.
2 Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

The historical derivatives of the particular value and the particularfunction in the wave and heat theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the trigonometric series and eigen values are derived from the particular value in theprocess of the study of heat and wave. Euler and Lagrange studied wave equation of the cords or strings.
Lagrange derives from this study the trigonometric series in the linear equation using the particular value.
Fourier and Poisson develope the series. Sturum and Liouvill specially derived the particular value from thesolving heat problem, which is also the same problem by Poisson. Hilbert solves the integral equation using
the eigenvalue and the eigenfunction, of which the former is hinted from the studies of linear heat problem
by Sturm and Liouville. These points here are our propositions.
3 Shotaro Tanaka∗

Method of finding values of approximate expressions and cosets of Suida
power series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Wada, old Japanese mathematician made six kinds of power series, i.e., Rokuyaku; He solved
thirty eight problems. But he did not solve the values of approximate expressions and cosets. We would
like to show the method finding them.
Point of the method: Example: Sk − xSk = d2 (1) + Σ(n = 2 → k)xn−1 − d2 (k)xk .
If Sk = Σ(n = 1 → k)d2 (n)xn−1 = 1 + 3x + 6x2 + 10x3 + 21x4 + · · · + d2 (k), d2 (n) = (1/2!)n(n + 1).
1. Sk = 1/(1 − x)3 − xk {d0 (k)/(1 − x)3 + d1 (k)/(1 − x)2 + d2 (k)/(1 − x)}.
2. S¯k = xk {d0 (k)/(1 − x)p+1 + d1 (k)/(1 − x)p + · · · + dp (k)/(1 − x)}.
4 Shunzi Horiguchi(Niigata Sangyo Univ.)

Handwriting analysis of Chinese characters in the picture scroll of
Kikugenpou Betsuden Ichimaki-Hihachiji and 1000 characters that are
written by Koutaku Hosoi · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Netherlands surveying surgery is transmitted to the Edo period of Japan. Sadanori Shimizu (1645–1717) established in the Netherlands survey surgery. Edo shogunate was using this survey surgery. Kikugenpou betsuden ichimaki-hihachiji is a secret picture scroll of the Netherlands surveying which Sadanori
Shimizu established. Koutaku Hosoi (1658–1735) and Sadanori Shimizu are both served in Inaba Tansyu
from 1702. At this time, we think that they had intimate exchanges. Therefore, it is supposed that Kotaku
Hosoi wrote the picture scroll. Therefore we asked for the handwriting analysis such as the title. We got
the result that there is a high possibility that Koutaku Hosoi wrote the picture scroll.

Final: 2015/08/20
6Foundation of Mathematics and History of Mathematics

5 Shunzi Horiguchi(Niigata Sangyo Univ.)

Comparison of the picture scroll of Kikugenpou Betsuden IchimakiHihachiji and the catalog of kikugenpou betsuden-catalog illustrationof hihachi · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Netherlands surveying surgery is transmitted to the Edo period of Japan. Sadanori Shimizu (1645–1717) established the Netherlands survey surgery. Kikugenpou betsuden ichimaki-hihachiji is a secret picture
scroll of the Netherlands surveying which Sadanori Shimizu established. But we don’t know the date of
manufacture with an author of this picture scroll. On the other hand, Yoshisato Yanada wrote the catalog
of kikugenpou betsuden-catalog illustration of hihachi in 1759. The contents of both are diﬀerent from thefirst four pages and genealogy. Surveying contents are the same. Therefore we compare both in the details.
We oﬀer a document to consider which was written earlier by this.
11:30–12:00

Mathematics History Team Meeting

14:15–16:00
6 Yoshihiro Abe (Kanagawa Univ.)

How to define isocoherence · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Tow ideals I and J on κ, regular uncountable, are isocoherent if there is a bijection f : κ → κ suchthat f∗ (I) = {X ⊂ κ : f −1 (X) ∈ I} and J have a comon proper extension. In this case f∗−1 (J) and I havea common proper extension.
Direct translation to Pκ λ might be unsuccessful. That is, f∗−1 (J) may not be an ideal even if f∗ (I) is an
ideal.
First choice is restricting f so that f∗−1 (J) is an ideal. Second, weaker one, is only assuming f to be abijection so that even f∗ (I) might not be an ideal.
7 Toshimichi Usuba (Kobe Univ.)

On elementary submodel topology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a topological space X = ⟨X, T ⟩ and an elementary submodel M ≺ ⟨Hθ , ∈⟩ with X ∈ M , let
XM be the space with the base set X ∩ M and the topology generated by {O ∩ M : O ∈ T ∩ M }. In thistalk, we give a partial answer of Tall’s irrational problem: Suppose 2ω > ω1 and 2<κ = κ for every regularcardinal κ with 2ω ≤ κ < |X|. If XM is completely metrizable, separable, and uncountable, then XM = X.
8 Makoto Takahashi (Kobe Univ.)

On frame systems of axiom A posets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Most of axiom A posets are not σ-short. We introduce frame systems of axiom A posets andprove non-σ-shortness of axiom A posets which have frame systems.
9 Kota Takeuchi (Univ. of Tsukuba)

Ramsey property of free amalgamation classes · · · · · · · · · · · · · · · · · · · · · 15

Summary: In model theory, Ramsey-type theorems are often used for constructing (generalized) indiscernible
sets. In this talk we give a complete proof of the Ramsey property of free amalgamation classes using finite
combinatorial methods, which have been discussed for a long period with many incomplete or wrong proofs.
10 Koichiro Ikeda(Hosei Univ.)

Generic structures with SOP3 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Evans–Wong proved that if an omega-categorical generic structure is not simple then it has SOP3 .
Our talk is about a generalization of their result.
11 Hirotaka Kikyo(Kobe Univ.)

Model completeness of generic graphs: irrational coeﬃcient case · · · · · 15

Summary: Let f be a log-like function and α a real number such that 0 < α < 1. Let Kf,α be a class ofbinary graphs defined as an amalgamation class of ab initio type with α a coeﬃcient for the predimension
function. Under some mild assumption on f , it has been shown that a generic graph for (Kf,α , <) has amodel complete theory if α is a rational number. One of the key facts is that there is a certain kind of
0-extensions. We will discuss that how this fact for the rational number cases can be applied to irrational
number cases.

Final: 2015/08/20
7Foundation of Mathematics and History of Mathematics

16:15–17:15

Talk Invited by Section on Foundation and History of Mathematics

Takako Nemoto(JAIST) ♭ Determinacy of infinite games in second order arithmetic

Summary: It is known that determinacies of infinite games characterize not only “Big Five Systems” butalso various other subsystems of second order arithmetic. In this talk, I will give an overview of these results
and talk about recent work on descriptive complexity of winning strategies.

September 16th (Wed)Conference Room I

9:30–11:20
12 Takashi Oyabu♭

World of phenomena: Aut(R), and other 5 talks · · · · · · · · · · · · · · · · · · · 5

Summary: (1) World of phenomena: Aut(R): Axiomatic set theory: Aut(R):−Mathematics: Philosophycal
arguments: R ===========> SPEC(R): R ===========> M(R): R ===========>
Aut(R)(2) Spectral problem: Spectral geometry: Main theorems;: Isomorphism of the Hilbert spaces(3) Fluctuation;: δxp: Fluctuation formulas: δxp: Some cases are studied(4) Algebraic construction: To constract mathematics by the algebraic methods: Algebraic: Abstract: The
possibilities:(5) Dynamical systemn: Finite dimensional:: Infinite dimensional dynamical systems: φt = exp(tX|p), φt =exp(tP ) general arguments/(6) Abelian diﬀerential: Automorphic functions:: Automorphic forms: Induced representation: Riemanniansurfaces;::: Abelian diﬀerentials: We seek the possibilities of representations of the Galois group of algebraic
functions: On Abelian diﬀerentials;;; Automorphic representation:
13 Hideto Ishihara (Kyoto Univ.)

Sorites paradox · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Introducing a new idea, CA-concept, of improved model theory, we solve Sorites paradox. Millionsof our intuitions will be wrong. As an example, we show that there exists no (concept of) excellent ethnic
group and hence no cause of ethnic identity.
14 Kyohei Yokomizo (Nihon Univ.)

A conservativity problem on fragments of intermadiate propositional
logics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let {→} ⊆ S ⊆ {→, ∧, ∨, ¬}. HS denotes the Hilbert-style intuitionistic propositional logic
H restricted axioms and substitution to S-formulas. Horn proved that HS is the S-fragment of H. We
determine the sets S with the following property : for any sets Σ of S-formulas, H + Σ is conservative overHS + Σ. We also consider this problem between HS and HS ′ (S ⊆ S ′ ).
15 Nobu-Yuki Suzuki (Shizuoka Univ.)

Axiom schemata preserving disjunction and existence properties of
intuitionistic predicate logic · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss axiom schemata preserving the disjunction and existence properties (DP and EP)
of intuitionistic predicate logic H∗ . The DP and EP are regarded as “hallmarks” of constructivity of
intuitionistic predicate logic. However, there are (uncountably) many intermediate predicate logics having
DP and EP. We consider axiom schema A such that H∗ with the axiom schema A (i.e., H∗ + A) still enjoys
DP and EP. A suﬃcient condition in terms of Kripke models is given. By making use of this condition, wegive some examples of axiom schemata preserving DP and EP, including the Gabbay–de Jongh axiom andthe axiom schema of Markov’s principle.

Final: 2015/08/20
8Foundation of Mathematics and History of Mathematics

16 Toshio Suzuki (Tokyo Metro. Univ.)

A solution to Yamakami’s problem on advised context-free languages· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Yamakami [2011, Theoret. Comput. Sci.] studies context-free languages with advice functions.
We consider the class of non-uniform contextfree languages where the lengths of advices are assumed tobe the same as those of inputs. CFL/n denotes the resulting class. We let CFL(2) denote the class ofintersections of two contextfree languages. Yamakami raised a problem whether there is a CFL-immune set
in CFL(2) - CFL/n. We present an aﬃrmative solution to the problem.
17 Kohtaro Tadaki (Chubu Univ.)

The principle of typicality: A refinement of the probabilistic interpretation of quantum mechanics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of probability plays a crucial role in quantum mechanics. It appears as the Born rule.
In modern mathematics which describes quantum mechanics, however, probability theory means nothingother than measure theory, and therefore any operational characterization of the notion of probability is
still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness,
we presented an alternative rule to the Born rule for specifying the property of results of measurements inan operational way. This rule is about pure states. In this talk, we present an alternative rule to the Bornrule for mixed states, and show that these two rules both for pure and mixed states can be derived from a
rule, called the principle of typicality, in a unified manner.
18 Kenshi Miyabe(Meiji Univ.)

Characterization of 3-randomness via complexity · · · · · · · · · · · · · · · · · · · 15

Summary: We give a characterization of 3-randomness via complexity, which is induced by a 2-randomness
version of Miller–Yu’s result.
11:30–12:00

Research Section AssemblyFinal: 2015/08/20
9

AlgebraAlgebraSeptember 13th (Sun)

Conference Room II

9:15–11:50
1 Katsuyoshi Ohara (Kanazawa Univ.)
Tajima Shinichi (Univ. of Tsukuba)
Akira Terui (Univ. of Tsukuba)

Computation of basis for generalized eigenspaces using minimal annihilating polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give eﬃcient algorithm for computing basis for generalized eigenspaces of matrices
with rational numbers. In well-known method, the computation uses the arithmetric of polynomials and it isslow. Our algorithm depends on minimal annihilating polynomials and uses the arithmetric of only rational
numbers. So it is faster and eﬃcient. Our program is implemented on Risa/Asir a computer algebra system.
2 Kazunori Matsuda (Osaka Univ.) ∗ Normality and Gorenstein Fano properties of twinned ordered polyTakayuki Hibi (Osaka Univ.) topes. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Let P and Q be finite partially ordered sets on [d] = {1, . . . , d}, and O(P ) ⊂ Rd and O(Q) ⊂ Rd
their order polytopes. The twinned order polytope of P and Q is the convex polytope ∆(P, −Q) ⊂ Rd whichis the convex hull of O(P ) ∪ (−O(Q)). It follows that the origin of Rd belongs to the interior of ∆(P, −Q)
if and only if P and Q possess a common linear extension. It will be proved that, when the origin of Rd
belongs to the interior of ∆(P, −Q), the toric ideal of ∆(P, −Q) possesses a quadratic Gröbner basis withrespect to a reverse lexicographic order for which the variable corresponding to the origin is smallest. Thusin particular if P and Q possess a common linear extension, then the twinned order polytope ∆(P, −Q) isa normal Gorenstein Fano polytope.
3 Akiyoshi Tsuchiya (Osaka Univ.)

Best possible lower bounds on the coeﬃcients of Ehrhart polynomials· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For an integral convex polytope P ⊂ Rd , we recall i(P, n) = |nP ∩ Zd | the Ehrhart polynomialof P. Let gr (P) be the r-th coeﬃcients of i(P, n) for r = 0, . . . , d. Martin Henk and Makoto Tagami gave
lower bounds on the coeﬃcients gr (P) in terms of the volume of P. They proved that these bounds are best
possible for r ∈ {1, 2, d − 2}. In this talk, we give a new and best possible lower bounds.
4 Akihito Wachi (Hokkaido Univ. of Edu.)

A volume formula for lattice polyhedra · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Macdonald (1963) proves a volume formula for lattice polyhedra of arbitrary dimension, which isa generalization of Pick’s formula (1899) for two-dimensional lattice polygons. In the proof of Macdonald
analysis of the Ehrhart polynomials is essential. In this talk we show a generalization of Nukaga’s volume
formula (1990) for two-dimensional lattice polygons by using polynomials which are similar to the Ehrhart
polynomials.
5 Ken-ichi Yoshida (Nihon Univ.)(Meiji Univ.)
Shiro Goto
Naoki Taniguchi (Meiji Univ.)

Almost Gorenstein property of Rees algebras of pg ideals in two-dimensional normal local rings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let A be a two-dimensional normal local ring with the unique maximal ideal m, and I be an
m-primary ideal of A. Then I is a pg ideal if and only if the Rees algebra R(I) is a Cohen–Macaulay normal
domain. If A has a resolution of singularities, there exists a pg ideal of A. Moreover, if A is a rational
singularity, then any integrally closed ideal is a pg ideal. As a main result, we prove the following theorem:
Theorem: Let A be a two-dimensional excellent Gorenstein normal local domain, and I a pg ideal of A.
Then R(I) is a graded almost Gorenstein ring in the sense of Goto–Takahashi–Taniguchi.

Final: 2015/08/20
10

Algebra(Meiji Univ.)
6 Shiro Goto
Naoyuki Matsuoka (Meiji Univ.)
Naoki Taniguchi (Meiji Univ.)
Ken-ichi Yoshida (Nihon Univ.)

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

Summary: The purpose of this talk is to give a characterization for the Rees algebras of socle ideals in a
regular local ring to be almost Gorenstein graded rings. This shows that almost Gorenstein Rees algebras
rather rarely exist for socle ideals, if the dimension of the base local ring is greater than two.
7 Takanori Nagamine (Niigata Univ.)

The kernels of derivations of R[x, y] · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let R be a UFD containing a rational number field and let d and D be R-derivations of R[x, y].
We have a necessary and suﬃcient condition for Kerd = KerD.
8 Ryota Okazaki (Fukuoka Univ. of Edu.)
Kohji Yanagawa (Kansai Univ.)

Cohen–Macaulay-ness of the bounded complex and the matroid idealof an aﬃne oriented matroid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An aﬃne oriented matroid is a generalization of an aﬃne hyperplane arrangement, and its
bounded complex corresponds to the CW-complex consisting of bounded regions cut by aﬃne hyperplanes.
In 2002, Novik et al. defined the matroid ideal of a bounded complex and showed that the matroid ideal
has a (cellular) graded minimal free resolution supported by the bounded complex. In this talk, we will give
characterization of Cohen–Macaulay-ness of a bounded complex and that of its matroid ideal, and showthat a bounded complex is Cohen–Macaulay if its matroid ideal is also.
9 Hiroki Matsui (Nagoya Univ.)

Prethick subcategories of modules and characterizations of local rings· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we studies characterizing local rings in terms of homological dimensions. The key tool
is the notion of a prethick subcategory which we introduce in this talk. Our methods recover the theoremsof Salarian, Sather–Wagstaﬀ and Yassemi.
10 Daisuke Suyama (Hokkaido Univ.)

The supersolvability, inductive freeness, and freeness of the Ish arrangement · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Ish arrangement was introduced by Armstrong recently to give a new interpretation of theq, t-Catalan numbers of Garsia and Haiman. In this talk, I will show that the Ish arrangement is a freearrangement.
14:15–15:15

Talk Invited by Algebra Section

Hidefumi Ohsugi(Kwansei Gakuin Univ.)Gröbner bases of toric ideals and their application

Summary: The theory of Gröbner bases has a lot of application in many research areas, and is implemented
in various mathematical software. In this talk, we will focus on recent developments in the theory of Gröbner
bases of toric ideals and their application.
15:30–18:00
11 Ryo Kanda(Nagoya Univ.) ♭ Atom-molecule correspondence in Grothendieck categories · · · · · · · · · · 15

Summary: For a one-sided noetherian ring, Gabriel constructed two maps between the isomorphism classes
of indecomposable injective modules and the two-sided prime ideals. We generalize these maps as maps
between two spectra of a Grothendieck category with some property. The two spectra are called theatom spectrum and the molecule spectrum. This generalization provides a simple way to understand theconstruction of Gabriel’s maps, and it is shown that they induce a bijection between the minimal elementsof the atom spectrum and those of the molecule spectrum.

Final: 2015/08/20
11

Algebra12 Hideto Asashiba (Shizuoka Univ.)

Cohen–Montgomery duality for bimodules and its applications to equivalences given by bimodules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We fix a commutative ring k and a group G. For small k-categories R and S with G-actions
we define G-invariant S-R-bimodules and their category denoted by S-ModG -R, and denote by R/G theorbit category of R by G. For small G-graded k-categories A and B we define G-graded B-A-bimodules
and their category denoted by B-ModG -A, and denote by A#G the smash product of A and G. We thendefine functors (-)/G : S-ModG -R → (S/G)-ModG -(R/G) and (-)#G : A-ModG -B → (A#G)-ModG -(B#G),
and show that they are equivalences and quasi-inverses to each other having good properties with tensor
products and preserving projectivity of bimodules. We apply this to equivalences given by bimodules suchas Morita equivalences, stable equivalences of Morita type and standard derived equivalences.
13 Takeshi Usa(Univ. of Hyogo)

Universal families of homological shells, Koszul domains, and Koszul
graph maps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Homological shells of a given projective subvariety X ⊆ PN (C) whose arithmetic depth is greaterthan or equal to 2 always move in a finite union of connected algebraic families without fixing theirdimensions or their degrees in advance. To study their geometric behavior, we define three kinds offamilies of homological shells, and construct three kinds of the universal families depending on their kindsof the families of homological shells by stratifying the Hilbert schemes suitably. As byproducts of these
constructions, we obtain Koszul domains, and Koszul graph maps, which bring us geometric tools to study
the families of homological shells.
14 Ayako Itaba (Shizuoka Univ.)

Finite condition (Fg) for self-injective Koszul algebras · · · · · · · · · · · · · · 10

Summary: We consider a finite-dimensional algebra over an algebraically closed field k. For a relationshipbetween a cogeometric pair (E, σ) and the finite condition (Fg), the following conjecture is proposed by
Mori. Let A be a cogeometric self-injective Koszul algebra and the complexity of A/rad A finite. Then A
satisfies the condition (Fg) if and only if the order of σ is finite. In this talk, we show that if A is cogeometricand satisfies the condition (Fg), then the order of σ is finite. Also, if A satisfies (rad A)3 = 0, then we showthat this conjecture holds.
15 Satoshi Yamanaka (Okayama Univ.)

On weakly separable polynomials and weakly quasi-separable polynomials in skew polynomial rings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Recently, N. Hamaguchi and A. Nakajima introduced the notions of weakly separable extensions
and weakly quasi-separable extensions. In this talk, we show the diﬀerence between the separability andthe weakly separability in skew polynomial rings. Moreover, we give some results concerning weakly
quasi-separable polynomials in skew polynomial rings.
16 Mitsuo Hoshino (Univ. of Tsukuba)
Noritsugu Kameyama (Shinshu Univ.)
Hirotaka Koga (Tokyo Denki Univ.)

Crossed products for matrix rings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let R be a ring and n ≥ 2 an integer. We provide a systematic way to define new multiplications on
Mn (R), the ring of n×n full matrices with entries in R. The obtained new rings Λ are Auslander–Gorenstein
if and only if so is R.
17 Takahide Adachi (Nagoya Univ.)

Brauer star algebras and triangulations · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give a combinatorial description of two-term tilting complexes for a Brauer star
algebra. Namely, we establish a bijection between two-term tilting complexes and signed triangulations ofa polygon with a puncture.

Final: 2015/08/20
12

Algebra18 Yuya Mizuno(Nagoya Univ.)

Preprojective algebras of Dynkin type, tilting theory and Weyl group· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Preprojective algebras are one of the fundamental object in the representation theory of algebra.
In this talk, we explain a close relationship between representation theory of Preprojective algebras andWeyl group. In particular, we discuss a connection between tilting theory and Weyl group, braid group.

19 Tomohiro Itagaki (Tokyo Univ. of Sci.)

The Hochschild (co)homology of a class of algebras given by a cyclic
quiver and two paths · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For an algebra given by a cyclic quiver and one path relation, its Hochschild (co)homology iscomputed by Xu and Wang. In this talk, we describe the Hochschild (co)homology of algebras given by acyclic quiver and two paths.
20 Daiki Obara (Tokyo Univ. of Sci.)

On the Hochschild cohomology ring modulo nilpotence of the finite
dimensional quiver algebras with quantum-like relations · · · · · · · · · · · · · 15

Summary: We consider the finite dimensional quiver algebras defined by n cycles and quantum-like relations.
We determine the minimal projective resolutions and the Hochschild cohomology rings modulo nilpotenceof these algebras. We introduce the simple examples of these algebras.

September 14th (Mon)

Conference Room II

9:15–12:00∗
21 Tomohiro Iwami
Some remarks on Fano fibrations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Kyushu Sangyo Univ.)

Summary: Based on the author’s previous talk about certain Q-conic bundles of semi-stable type in the caseof (three-dimensional) polarized log pairs, I discuss on triviality of moduli-part of log adjunction or (local)
isotriviality of certain fibrations associated to such Q-conic bundles, with regards to several properties of
local triviality or conic bundles appearing in Fano fibrations studied by J. Kollar–Y. Miyaoka–S. Mori, and
E. Sato.
22 Katsuki Asa
Masahiro Watari(Okinawa Nat. Coll. of Tech.)

Plane curves with small polar degree · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let C be a projective plane curve defined by a reduced homogeneus polynomial F in C[x, y, z].
()
For this C, we consider the polar map φC : P2 (C) −→ P2 (C) defined by p 7−→ Fx (p), Fy (p), Fz (p) . We callthe degree of φC the polar degree of C. Dolgachev determined all curves whose polar degrees are equal to
1. After his work, we consider the plane curves whose polar degrees are 2, 3 and 4.
23 Katsumi Akahori(Gifu Pharmaceutical Univ.)

Remarks on normal generation of special line bundles on algebraic
curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let L be a very ample line bundle with h1 (L) ≥ 2 on a smooth projective curve of genus g. Onesays that L is normally generated if X is projectively normal under the associated projective embedding.
We show that L is normally generated if deg(L) ≥ 2g − 1 − 4h1 (L) for large enough genus g.
24 Takanori Ayano (Osaka City Univ.)

On Jacobi inversion problem for telescopic curves · · · · · · · · · · · · · · · · · · 15

Summary: For a compact Riemann surface X, it is well known that the divisor class group of X is isomorphic
to the Jacobian of X by the Abel–Jacobi map. Given an element u of Jacobian, one wants to express, interms of u, the element of the divisor class group corresponding to u. This problem is called Jacobi inversion
problem. For hyperelliptic curves, it is well known that one can solve the problem by the hyperelliptic sigma
functions. These results were extended to the more general plane algebraic curves defined by y r = f (x),which are special cases of (n, s) curves, by Matsutani and Previato. In this talk, we extended the results tothe telescopic curves proposed by Miura, which contain (n, s) curves as special cases.

Final: 2015/08/20
13

Algebra25 Yoshifumi Tsuchimoto (Kochi Univ.)

The Dolbeault complex of non commutative projective spaces · · · · · · · 15

Summary: We give Dolbeault complex of non commutative projective space of positive characteristics.
26 Tomoo Matsumura(Okayama Univ. of Sci.)
Takeshi Ikeda (Okayama Univ. of Sci.)
Hiroshi Naruse (Univ. of Yamanashi)(Postech)Thomas Hudson

K-theoretic Segre classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce K-theoretic Segre classes for a vector bundle and also for a virtual
bundle. The main results are the formula for the K-theoretic Segre classes in terms of the generating
function and the pushforward formula for the relative Segre classes.
27 Tomoo Matsumura(Okayama Univ. of Sci.)
Takeshi Ikeda (Okayama Univ. of Sci.)
Hiroshi Naruse (Univ. of Yamanashi)(Postech)Thomas Hudson

Determinant formula of the K-theory Schubert classes · · · · · · · · · · · · · · 15

Summary: In this talk, we will explain the formula that describes K-theory Schubert classes of Grassmannians. It is written as a determinant with entries given by the Segre classes of tautological vector bundles. The
proof is based on Kazarian’s method which uses the Kempf–Laksov resolutions of the Schubert varieties.
28 Narutaka Ozawa (Kyoto Univ.)

Noncommutative real algebraic geometry of Kazhdan’s property (T)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Noncommutative real algebraic geometry is an emerging subject which deals with equations andinequalities in noncommutative algebra over the reals, with the help of analytic tools such as representation
theory and operator algebras. After introducing this concept, I will present a simple characterization of agroup to have Kazhdan’s property (T) in terms of NCRAG. The result suggests the possibility of finding
new examples of property (T) groups by use of computers. In fact, Netzer and Thom recently obtained
a computer-based proof of property (T) for SL(3,Z) that yields a much better estimate of the Kazhdan
constant than the previously known.
29 Makoto Enokizono (Osaka Univ.)

Slopes of fibered surfaces with a finite cyclic automorphism · · · · · · · · · 15

Summary: In this talk, we study slopes of cyclic covering fibrations of a fibered surface. Firstly, we give thelower bound of the slope of these fibrations, which is a generalization of the double covering case. Secondly,
we define singularity indices for cyclic covering fibrations of a ruled surface and give the slope equality ofthese fibrations, which is a generalization of the hyperelliptic case. Finally, we give an upper bound of theslope of these fibrations by estimating these singularity indices.
30 Ryo Okawa(Kyoto Univ.) ♭ Wall-crossing between stable and co-stable ADHM data · · · · · · · · · · · · · 15

Summary: We prove formula between Nekrasov partition functions defined from stable and costable ADHM
data for the plane following method by Nakajima–Yoshioka based on the theory of wall-crossing formuladeveloped in Mochizuki. This formula is similar to the conjecture by Itoh–Maruyoshi–Okuda for A1
singularity.

Final: 2015/08/20
14

Algebra13:10–14:10

Talk Invited by Algebra Section

Sho Hei Ma(Tokyo Tech) ♭ On the Kodaira dimension of certain orthogonal modular varieties

Summary: I will report on my study of the birational type of modular varieties associated to orthogonal
grops of signature (2, n). For the full orthogonal groups of a certain class of quadratic forms, I prove that
there are only finitely many modular varieties that are not of general type. A similar finiteness is proved forthe stable orthogonal groups (a canonical congruence subgroup) in much wider generality. The study has anapplication to a conjecture of Gritsenko and Nikulin on reflective modular forms. In the course I calculatea certain generalization of classical Gauss sum that could be called orbital Gauss sum.

September 15th (Tue)

Conference Room II

9:30–11:25
31 Tatsuki Kuwagaki (Univ. of Tokyo)

The nonequivariant coherent-constructible correspondence for toric surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The nonequivariant coherent-constructible correspondence (NCCC) conjecture is a version ofhomological mirror symmetry for toric varieties. NCCC is first discovered by Bondal and formulated interms of microlocal sheaf theory by Fang–Liu–Treumann–Zaslow. In this talk, we give a proof of NCCC
conjecture in the case of toric surfaces.
32 Tomoaki Shirato (Nagoya Univ.)

Frobenius splitting for elliptic fibrations with wild fiber and applications· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A notion of Frobenius splitting was firstly introduced by Mehta and Ramanathan to investigate
the cohomology of Schubert varieties in positive characteristic field. Frobenius splitting is a global condition
on projective varieties in positive characteristic field and sometimes behave nicely in positive characteristic
filed. I will talk about the Frobenius splitting elliptic fibrations with wild fiber and their applications byusing the relative Frobenius morphism and classify the Frobenius splitting elliptic fibrations with wild fibers
by anti-Euler characteristic and the multiplicities of multiple fibers.
33 Masataka Tomari (Nihon Univ.) ∗ Normal two-dimensional singularities where the normalized tangent
cone is reduced · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We give a characterization of the normal two-dimensional singularities where the normalized
tangent cone is reduced as the Kodaira singularities with maximal degree in terms of Artin’s fundamental
cycle (Theorem 1). We show that every normal two-dimensional singularity can be embedded in the classof Theorem 1 as the 1st infinety near neighborhood by the normalized blowing-up. Further we also showthat suﬃciently negative exceptional divisor is blowing down to the singularity of Theorem 1.
34 Kiwamu Watanabe (Saitama Univ.) ∗ Uniform families of minimal rational curves on Fano manifolds · · · · · · · 15
Summary: It is a well known fact that families of minimal rational curves on rational homogeneous manifolds
of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting
type on each curve of the family. In this talk we prove that certain –stronger– uniformity conditions on afamily of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold
is homogeneous.
35 Hiroyuki Nakasora (Okayama Univ.) ∗ On the support t-designs of extremal binary doubly even self-dual codes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let C be an extremal binary doubly even self-dual code of length n and Dw be the support designof C for a weight w. We introduce the two numbers δ(C) and s(C): δ(C) is the largest integer t such that,for all weight, Dw is a t-design; s(C) denotes the largest integer t such that there exists a w such that Dw
is a t-design. We consider the possible values of δ(C) and s(C).

Final: 2015/08/20
15

Algebra36 Kazufumi Kimoto (Univ. of Ryukyus)
Masato Wakayama (Kyushu Univ.)

Analog of group determinants for group-subgroup pairs · · · · · · · · · · · · · 10

Summary: For a given pair (G, H) of finite group G and its subgroup H, we define an analog of the so-calledgroup determinant in terms of the wreath determinant, which is defined for rectangular matrices suchthat the number of rows divides the number of columns. We show a factorization formula of the wreath
determinant for a group-subgroup pair (G, H) when G is a finite abelian group and the variables are suitably
specialized.
37 Shuhei Kamioka (Kyoto Univ.)

Plane partitions and orthogonal polynomials · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A connection between plane partitions and orthogonal polynomials is revealed. It is shown thatthe trace generating function for plane partitions, originally found by Stanley and generalized by Gansner,can be naturally derived from determinant calculation based on the little q-Laguerre polynomials anda generalization of them. A generalization of the q-Chu–Vandermonde sum is also given to prove theorthogonality of the generalized little q-Laguerre polynomials.
11:30–12:00

Research Section Assembly

14:15–15:15

Talk Invited by Algebra Section

Shunsuke Tsuchioka (Univ. of Tokyo)

KOR conjecture and beyond

Summary: In their paper (Invent. Math. 151 (2003) 513–552), Külshammer–Olsson–Robinson initiateda study of modular character theory of finite groups over a positive integer which is not necessarily aprime. While the “main conjecture” in the paper (KOR conjecture) is settled aﬃrmatively by Anton Evseev
recently, I will talk on new directions including: (1) Graded refinement of the KOR conjecture, (2) Lie
theoretic analog of the KOR conjecture, (3) Rogers–Ramanujan type identities arising from super analog of
KOR theory.
15:30–17:50(Kinki Univ.)
38 Fumihito Oda
Yugen Takegahara(Muroran Inst. of Tech.)Tomoyuki Yoshida(Hokusei Gakuen Univ.)

The units of a partial Burnside ring relative to the Young subgroups ofa symmetric group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The unit group of a partial Burnside ring relative to the Young subgroups of the symmetric group
Sn on n letters is included in the image by the tom Dieck homomorphism. As a consequence of this fact, thealternating character νn of Sn is expressed explicitly in a Z-linear combinations of permutation characters
associated with finite left Sn -sets Sn /Y for the Young subgroups Y .
39 Shigeto Kawata (Osaka City Univ.) ∗ On height zero lattices and Auslander–Reiten components for blocks offinite groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let OG be the group ring of a finite group G over a complete discrete valuation ring O. Thenthe tree classes of the Auslander–Reiten components containing certain OG-lattices of height 0 are A∞ .
40 Taiki Shibata (Univ. of Tsukuba)

On irreducible representations of quasireductive supergroups · · · · · · · · 15

Summary: We work over an algebraically closed field k. An algebraic supergroup (scheme) G is the groupfunctor represented by a finitely generated commutative Hopf superalgebra. There is a largest algebraic
subgroup Gev of G. An algebraic supergroup G is quasireductive if Gev is split reductive. In 2011, V.
Serganova studied representations of quasireductive supergroups when k is characteristic zero. In this talk,we will construct irreducible representations of quasireductive supergroups when the characteristic of k is
not equal to 2. This is a generalization of Serganova’s results.

Final: 2015/08/20
16

Algebra41 Kenichi Shimizu (Nagoya Univ.)

Internal character theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a pivotal finite tensor category C over an algebraically closed field k, we define the adjoint
object A ∈ C, the algebra CF(C) = HomC (A, 1) of class functions, and the internal character ch(X) : A → 1
in C for an object X ∈ C. Let Grk (C) be the Grothendieck algebra of C defined over k. We show that themap ch : Grk (C) → CF(C) given by [X] 7→ ch(X) is a well-defined injective algebra map. As an application,
we show that Grk (C) is a semisimple algebra if C is a non-degenerate pivotal fusion category over k.
42 Maki Nakasuji (Sophia Univ.)
Hiroshi Naruse (Univ. of Yamanashi)

Casselman problem and duality · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Casselman(1980) defined a basis of the space of Iwahori fixed vectors of principal series representation of a p-adic group. The problem is to express Casselman’s basis in terms of another natural basis,and vice versa. In this talk, we show that Casselman’s problem results in the transition matrix of standard
basis and Yang–Baxter basis through Hecke algebra and prove a duality relation for the coeﬃcients in theexpression by generalizing the result of Lascoux–Leclert–Thibon(1997) of type A to general Lie type.
∗43 Kazutoshi Kariyama
A remark on Jacquet–Langlands correspondence and invariant s · · · · · 10
(Onomichi City Univ.)

Summary: Let F be a non-Archimedean local field, and let G be an inner form of GLN (F ) with N ≥ 1. Let
JL be the local Jacquet–Langlands correspondence between GLN (F ) and G. In this talk, we report that we
can compute the invariant s associated with the essentially square-integrable representation JL−1 (ρ) for a
cuspidal representation ρ of G by using the parametric degree due to Bushnell and Henniart, and we restate
the second part of a theorem given by Deligne, Kazhdan, and Vignéras in terms of the invariant s.
44 Kazuya Kawasetsu (Univ. of Tokyo)

W-algebras with non-admissible levels and the Deligne exceptional series· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The W-algebras are certain vertex operator algebras constructed by the so-called quantizedDrinfel’d-Sokolov reduction from the aﬃne vertex operator algebras. The W-algebras has been conjectured
to be C2 -cofinite and rational only if the level k is admissible. In this talk, structure of certain simple
W-algebras assocated with the Deligne exceptional Lie algebras and non-admissible levels are described as
the simple current extensions of certain vertex operator algebras. As an application, the C2 -cofiniteness andZ2 -rationality of the algebras are proved.
45 Kazuya Kawasetsu (Univ. of Tokyo)

The generalized principal subspaces and an intermediate vertex subalgebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce the notion of the generalized principal subspaces associated with
the non-necessarily integral lattices, generalizing the principal subspaces associated with integral lattices.
Combinatorial bases and the characters of the generalized principal subspaces are given. As an application,
we decompose the intermediate vertex subalgebra VE7+1/2 , which is the “level one aﬃne VOA” of theintermediate Lie algebra E7+1/2 , by using a generalized principal subspace. Then, we obtain modular
invariance of the n-point correlation function of VE7+1/2 .
46 Tomoyuki Arakawa (Kyoto Univ.)
Anne Moreau (Univ. Poitiers)

Joseph ideals and lisse minimal W-algebras · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a lifting of Joseph ideals for the minimal nilpotent orbit closure to the setting ofaﬃne Kac–Moody algebras and find new examples of aﬃne vertex algebras whose associated varieties areminimal nilpotent orbit closures. As an application we obtain a new family of lisse (C2-cofinite) W-algebrasthat are not coming from admissible representations of aﬃne Kac–Moody algebras.

Final: 2015/08/20
17

AlgebraSeptember 16th (Wed)Conference Room II

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

General Mersenne numbers and Wieferich prime with respect to P · · · 10

Summary: Let P be an odd prime.
A prime Q(̸= P ) is called Wieferich prime with respect to P , if P Q−1 − 1 has a squre factor Q2 .
If p = e + 1 is a prime and a general Mersenne number Np = P P−1 has squre factor Q2 ( Q : prime ), then
Q turns out to be a Wieferich prime with respect to P .
In the classical case (P = 2), no square factor is found in 2p − 1 where the p are primes. But in the generalpcase there are many square factors in Np = P P−1 .
p(Hirosaki Univ.)
48 Hiromi Ei
Florian Luca (Univ. of Witwatersrand)
Yohei Tachiya (Hirosaki Univ.)

Linear independence results for the reciprocal sums of Fibonacci numbers associated with Dirichlet characters · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let {Fn }n≥0 be the sequence of Fibonacci numbers. In this talk, we give linear independence∑∞
results over Q for the infinite series n=1 χj (n)/Fn with certain nonprincipal real Dirichlet characters χj .
We also deduce the irrationality results for the special principal Dirichlet characters and for anothermultiplicative functions.
49 Takao Komatsu (Wuhan Univ.)

Some explicit formulas of Bernoulli and Cauchy polynomials in termsof r-Stirling numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The integral values of Bernoulli polynomials are expressed in terms of r-Stirling numbers of thesecond kind. The integral values of Cauchy polynomials are expressed in terms of r-Stirling numbers of
the first kind. Several relations between the integral values of Bernoulli polynomials and those of Cauchy
polynomials are obtained in terms of r-Stirling numbers of both kinds. Also, we find a relation between the
Cauchy polynomials and hyperharmonic numbers.
(Nagoya Univ.) ∗ On the lcm-sum function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
50 Soichi Ikeda
Kaneaki Matsuoka (Nagoya Univ.)
Summary: We consider a generalization of the lcm-sum function, and we give two kinds of asymptotic
formulas for the sum of that function.
51 Tomohiro Ikkai (Nagoya Univ.)

On counting binomial coeﬃcients not divided by a prime along polynomial curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Picking binomial coeﬃcients which cannot be divided by a given prime from Pascal’s triangle,
we find that they form a set with self-similarity. Stein and Wilson proved that the points in the first rowsof Pascal’s triangle modulo a prime (the above set with self-similarity) multiply ‘randomly’. The speaker
talk about that certain ways to count the points in Pascal’s triangle modulo a prime provide their ‘random
multiplying’. The speaker will also mention the connection between such counting and Essouari’s zetafunctions associated to Pascal’s triangle modulo a prime.
52 Yuta Suzuki(Nagoya Univ.)

A mean value on the sum of two primes in arithmetic progressions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Some variants of the Goldbach problem have been studied by many researchers. In this talk,we consider such a variant with primes in arithmetic progressions, and study about the mean value of therepresentation function of this problem. We show a kind of explicit formula for this mean value under aweakened variant of GRH. This is an improvement of the result of Rüppel (2012) and a generalization of
the result of Languasco–Zaccagnini (2012).

Final: 2015/08/20
18

Algebra53 Ade Irma Suriajaya (Nagoya Univ.)
Junghun Lee (Nagoya Univ.)
Tomokazu Onozuka (Nagoya Univ.)

Some probabilistic value distributions of the Riemann zeta function andits derivatives · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We investigate a uniform distribution of ζ (k) and an application of Birkhoﬀ’s ergodic theorem toζ and ζ (k) under an aﬃne Boolean transformation.
54 Genki Shibukawa (Osaka Univ.)

New elliptic function identities and an elliptic analogue of reciprocity
laws of generalized Dedekind sums · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We obtain new elliptic function identities, which are product-to-sum type formulas for derivativeof some elliptic functions. Further, from specializations of our formulas, we derive not only various known
an elliptic analogue of reciprocity laws of generalized Dedekind sums by Egami, Fukuhara–Yui, but also newreciprocity laws of an elliptic analogue of generalized Dedekind sums.
55 Makoto Minamide (Yamaguchi Univ.) ∗ The truncated Voronoı̈ formula in a new circle problem · · · · · · · · · · · · · 10
Jun Furuya(Hamamatsu Univ. School of Medicine)
Yoshio Tanigawa (Nagoya Univ.)
Summary: We shall consider a new problem concerning the circle problem. In the classical problem, many∑
researchers study the error term of the asymptotic formula for n≤x r(n), where r(n) is the number of∑∞pairs of integers (k, l) satisfying k 2 + l2 = n. It is known that r(n) is given by 4ζ(s)L(s) = n=1 r(n)n−s(Re s > 1), where ζ(s) is the Riemann zeta function and L(s) is the Dirichlet L-function w.r.t. the non-trivial∑∞
character mod 4. In our problem we define R(1) (n) by ζ ′ (s)L′ (s) = n=1 R(1) (n)n−s (Re s > 1), and study∑
the error term of the asymptotic formula for n≤x R(1) (n).
∗56 Debika Banerjee
On nonsquare-free integers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Harish-Chandra Res. Inst.)
Makoto Minamide (Yamaguchi Univ.)

Summary: In the previous talk (at Meiji Univ. March 2015), we showed the asymptotic formula for thenumber of square-free integers ≤ x whose prime factors > y, where xε < y ≤ x. By this result we see thatthe number of nonsquare-free integers ≤ x whose prime factors > y is estimated ≪ x/ log2 y. In this talk,we will try to improve this result.
∗
57 Debika Banerjee
On nonk-free integers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Harish-Chandra Res. Inst.)
Makoto Minamide (Yamaguchi Univ.)

Summary: Let k be an integer ≥ 2. We will deduce the formula for the number of k-free integer ≤ x whose
prime factors > y, where xε < y ≤ x. Also we will see that the number of nonk-free integers ≤ x whose
prime factors > y is estimated ≪ x/ log2 y. We will improve this result in this talk.
58 Yoshio Tanigawa (Nagoya Univ.) ∗ Mean square estimate in short intervals · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let a(n) be an arithmetical function whose generating Dirichlet series belongs in a certain Selberg
class. Let E(x) be an arithmetical error term obtained by the sum of a(n). I am going to talk my recent
results with X. Cao and W. Zhai on the mean square estimate for E(x) in short intervals.

Final: 2015/08/20
19

Algebra14:15–15:45
59 Yuichi Sakai
Masanobu Kaneko (Kyushu Univ.)
Kiyokazu Nagatomo (Osaka Univ.)

The 3rd order modular linear diﬀerential equations · · · · · · · · · · · · · · · · · 15

Summary: We propose a 3rd order generalization of the Kaneko–Zagier modular diﬀerential equation, which
has essentially two parameters. We describe modular and quasimodular solutions of integral weight in thecase where one of the exponents at infinity is a multiple root of the indicial equation. We also classify
solutions of character type, that is, solutions which are expected to relate to characters of simple modulesof some vertex operator algebras.
60 Seiichi Hanamoto (Kyushu Univ.)

Zeros of weakly holomorphic modular forms of level 5 · · · · · · · · · · · · · · · 10

Summary: Let Mk# (5) be the space of weakly holomorphic modular forms of weight k for Γ0 (5) that are
holomorphic at all cusps except possibly at ∞. We define a canonical basis for Mk# (5) and prove that foralmost all of the basis elements, the majority of their zeros in a fundamental domain for Γ0 (5) lie on thelower boundary of the fundamental domain.
61 Kazuki Utsumi (Ritsumeikan Univ.)
Masato Kuwata (Chuo Univ.)

Mordell–Weil generators of a certain elliptic K3 surface · · · · · · · · · · · · · 10

Summary: A complex singular K3 surface has a Jacobian fibration with two II∗ fibers. In this talk, we givethe explicit Mordell–Weil generators of the fibration on the singular K3 surface whose transcendental latticeis isometric to ⟨6⟩2 .
62 Kazuto Ota(Tohoku Univ.)

On the Mazur–Tate refined conjecture of BSD type · · · · · · · · · · · · · · · · 10

Summary: For an elliptic curve, the p-adic L-fucntion interpolates special values of the twists of the Hasse–
Weil L-function by the Dirichlet characters with conductor a power of p. As its refinement, for each positive
integer S, Mazur and Tate constructed the Mazur–Tate element, which interpolates the twists by thecharacters with conductor S, and proposed conjectures connecting the element with arithmetic invariants.
One of our main results shows that the “order of vanishing” of Mazur–Tate elements is greater than or equal
to the algebraic rank in many cases. Our main method is to study some divisibility of Kato’s Euler system
by extending Darmon’s argument on Heegner points.
63 Fumio Sairaiji (Hiroshima Int. Univ.) ♭ On the class numbers of the fields of the pn -torsion points of elliptic
Takuya Yamauchi (Kagoshima Univ.) curves over Q with conductor p · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk, we give a lower bound of the order of the p-Sylow group of the ideal class group of
the field Kn of pn -torsion points of an elliptic curve over Q with conductor p. Our bound depends on n and
the Z-rank of E(Q). We also give an example such that p2n divides the class number of the field Kn in thecase of p = 5077 for each positive integer n.
∗
64 Yasushi Mizusawa
On the Galois group of a certain real tamely ramified 2-extension · · · · 10
(Nagoya Inst. of Tech.)

Summary: We give a family of triples of odd prime numbers such that the maximal totally real 2-extensionof Q unramified outside the three prime numbers has the Galois group of order 512 and derived length 3.
The Galois group is presented explicitly by generators and relations.
∗
65 Yasushi Mizusawa
On tame pro-2 Galois groups over the basic Z2 -extension · · · · · · · · · · · · 10
(Nagoya Inst. of Tech.)

Summary: We classify all finite sets S of primes of Q except 2 such that the Galois groups of the maximal
pro-2-extensions of Qcyc unramified outside S are pro-metacyclic, where Qcyc denotes the Z2 -extension of
Q. We also consider an application to Greenberg’s conjecture.

Final: 2015/08/20
20

Algebra16:00–17:00

Talk Invited by Algebra Section

Tomoki Mihara(Univ. of Tokyo / Keio Univ.)

Characterisation of the Berkovich spectrum of the Banach algebra of
p-adic continuous functions

Summary: Let k be a complete valuation field, and X a topological space. We study the Berkovich
spectrum M (X) of the Banach k-algebra of k-valued bounded continuous functions on X. The evaluation
gives a continuous map ιX : X → M (X), which is a homeomorphism onto the image if and only if X
is zero-dimensional and Hausdorﬀ. We verify that ιX satisfies the universality of a totally disconnectedcompactification, and hence is independent of k.

Final: 2015/08/20
21

Geometry

Geometry
September 13th (Sun)

Conference Room X

9:50–12:00
1 Hirotaka Ebisui (Oval Research Center)

Ebisui-Papus-Papus theorem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: Papus theorem is famous in geometry history. But, the application is few. This Time, we foundconcurent theorem in two papus theorem composition by combining them in 3 paralell lines. We show thisfigure and oﬀer this theorem as the matter of its proof. Of course, we confirm the reliability by CAD zoomtool.
2 Hiroaki Izumi

The SYNC · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I creative “the Branch Equations” that describe phase transition and the SYNC. Indeed, myequations describe in-phase synchronization and anti-phase synchronization. Their critical points at phaselocking move from original critical points.
3 Hiromasa Tanabe(Matsue Coll. of Tech.)
Maeda Sadahiro (Saga Univ.)

Geometry of ruled real hypersurfaces in a nonflat complex space form
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Ruled real hypersurfaces are typical examples of non-Hopf hypersurfaces in a nonflat complex
space form. These examples are constructed by the same method in a complex projective space and acomplex hyperbolic space. In this talk, we make a survey of geometric properties of ruled real hypersurfaces
which depend on the sign of the sectional curvature of those ambient spaces.
4 Makoto Sakaki (Hirosaki Univ.) ∗ Lorentzian stationary surfaces in 4-dimensional space forms of index 2(II) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We discuss a curvature property of Lorentzian stationary surfaces in 4-dimensional space forms
of index 2, which is related to a property of null curves via a characteristic initial value problem.
5 Shintaro Akamine (Kyushu Univ.)

Causal characters of zero mean curvature surfaces of Riemann-type in
the Lorentz–Minkowski 3-space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A zero mean curvature surface in the Lorentz–Minkowski 3-space is said to be of Riemann-type
if it is foliated by circles in parallel planes. We classify all zero mean curvature surfaces of Riemann-type
according to their causal characters, and as a corollary, we prove that if a zero mean curvature surface ofRiemann-type has exactly two causal characters, then the lightlike part of the surface is a part of a straightline.
6 Kosuke Naokawa (Kobe Univ.)
Masaaki Umehara (Tokyo Tech)
Kotaro Yamada (Tokyo Tech)

Isometric deformations of cuspidal edges · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A C ∞ -map germ which is right-left equivalent to (u, v) 7→ (u, v 2 , v 3 ) at the origin is called acuspidal edge. A cuspidal edge is said to be generic if the limitting normal curvature κν which is definedalong the singular curve does not vanish. In this talk, we show that any real-analytic generic cuspidal edge
admits an isometric deformation (i.e. a deformation of preserving the first fundamental form).
7 Kosuke Naokawa (Kobe Univ.)

The topology of developable closed strips on given knots in spaces of
constant curvature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In the speaker’s previous work, the isotopy types of developable closed strips along a given realanalytic knot in 3-dimensional spaceforms were determined. In this talk, we show that it can be generalized
to the case of the ambient space being a 3-space of constant curvature which might be non-simply-connected
or non-orientable.

Final: 2015/08/20
22

Geometry

8 Naoya Ando (Kumamoto Univ.)
Masaaki Umehara (Tokyo Tech)
Toshifumi Fujiyama (Univ. of Tokyo)

C 1 -umbilics with arbitrarily high indices · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, the existence of C 1 -umbilics with arbitrarily high indices is shown. This implies
that more than C 1 -regularity is required to prove Loewner’s conjecture.
9 Shoichi Fujimori (Okayama Univ.)
Yu Kawakami (Kanazawa Univ.)
Masatoshi Kokubu (Tokyo Denki Univ.)
Wayne Rossman (Kobe Univ.)
Masaaki Umehara (Tokyo Tech)
Kotaro Yamada (Tokyo Tech)

Analytic extension of Jorge–Meeks type maximal surfaces · · · · · · · · · · · 15

Summary: The Jorge–Meeks n-noid (n ≥ 2) is a complete minimal surface of genus zero with n-catenoidal
ends in the Euclidean 3-space, which has (2π/n)-rotation symmetry with respect to its axis. In this talk,we show that the corresponding maximal surface in Lorentz–Minkowski 3-space has an analytic extension
as a properly immersed zero mean curvature surface. The extension changes type into a time-like surface.
14:15–16:45
10 Takahiro Hashinaga (Hiroshima Univ.)
Yoshio Agaoka (Hiroshima Univ.)

Local isometric embeddings of three-dimensional Lie groups · · · · · · · · · 10

Summary: It is known that any three-dimensional Riemannian manifold can be locally isometrically embedded
into the six-dimensional Euclidean space. On the other hand, the least dimensional Euclidean space into
which the given Riemannian manifold can be locally isometrically embedded is not so well understood,
even for the left-invariant Riemannian metrics on Lie groups. In this talk, we report the classificationof left-invariant Riemannian metrics on three-dimensional Lie groups which can be locally isometricallyembedded into the four-dimensional Euclidean space.
11 Kurando Baba
(Fukushima Nat. Coll. of Tech.)

Examples of austere orbits of the isotropy representations for semisimple
pseudo-Riemannian symmetric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We investigate semisimple orbits of the isotropy representations for semisimple pseudo-Riemanniansymmetric spaces. By using restricted root system we give the Jordan–Chevalley decomposition for the
shape operators of the orbits. As applications, we give examples of austere orbits.
12 Shinji Ohno (Tokyo Metro. Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Hajime Urakawa (Tohoku Univ.⋆)

Biharmonic homogeneous hypersurfaces in compact symmetric spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all
the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits ofcommutative Hermann actions of cohomogeneity one.
13 Shinji Ohno (Tokyo Metro. Univ.)

Weakly reflective submanifolds in compact symmetric spaces · · · · · · · · 15

Summary: In this talk, we give suﬃcient conditions for orbits of Hermann actions to be weakly reflective interms of symmetric triads, that is a generalization of irreducible root system.
14 Makiko Tanaka (Tokyo Univ. of Sci.) ∗ Maximal antipodal subgroups of compact Lie groups · · · · · · · · · · · · · · · 15
Hiroyuki Tasaki (Univ. of Tsukuba)
Summary: Compact Lie groups are compact Riemannian symmetric spaces with respect to their bi-invariant
Riemannian metrics. So we can consider antipodal sets of them, defined by Chen and Nagano. We classify
maximal antipodal subgroups of the quotient groups U (n)/Zµ and SU (n)/Zµ .

Final: 2015/08/20
23

Geometry

15 Makiko Tanaka (Tokyo Univ. of Sci.) ∗ Isometries of extrinsic symmetric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Jost-Hinrich Eschenburg(Univ. of Augsburg)Peter Quast (Univ. of Augsburg)
Summary: We show that every isometry of an extrinsic symmetric space extends to an isometry of its ambient
Euclidean space. As a consequence, any isometry of a real form of a Hermitian symmetric space extends toa holomorphic isometry of the ambient Hermitian symmetric space. Moreover, every fixed point componentof an isometry of a symmetric R-space is a symmetric R-space itself.
16 Kotaro Kawai (Univ. of Tokyo)

Cohomogeneity one coassociative submanifolds · · · · · · · · · · · · · · · · · · · · 15

Summary: Coassociative submanifolds are 4-dimensonal calibrated submanifolds in G2 -manifolds. We construct explicit examples of coassociative submanifolds in Λ2− S 4 , which is the complete G2 -manifold constructed by Bryant and Salamon. Classifying the Lie groups which have 3- or 4-dimensional orbits, we showthat the only homogeneous coassociative submanifold is the zero section of Λ2− S 4 up to the automorphisms
and construct many cohomogeneity one examples explicitly.
17 Naoyuki Koike (Tokyo Univ. of Sci.)

Volume-preserving mean curvature flow for tubes in a symmetric space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We investigated the volume-preserving mean curvature flow starting from a tube (of non-constantradius) over a compact closed domain of a certain kind of reflective submanifold in a symmetric space andproved that the tubeness is preserved along the flow under certain conditions.
18 Hajime Ono (Saitama Univ.)
Hiroshi Iriyeh (Ibaraki Univ.)

Almost all Lagrangian torus orbits in CP n are not Hamiltonian volume
minimizing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove that most of Lagrangian torus orbits in CP n are not Hamiltonian volume minimizing
when n ≥ 3.

September 14th (Mon)

Conference Room X

10:30–10:45

Presentation Ceremony for the 2015 MSJ Geometry Prize

10:50–11:50

Award Lecture for the 2015 MSJ Geometry Prize

Hiroshi Iritani(Kyoto Univ.)

Mirror symmetry for toric varities

Summary: I will explain a mirror construction for the big equivariant quantum cohomology of toric varieties
via shift operators of equivariant parameters. Shift operators in equivariant quantum cohomology havebeen introduced in the work of Braverman, Okounkov, Maulik and Pandharipande and can be regarded as
equivariant lifts of the Seidel representation. These operators naturally define a mirror Landau–Ginzburg
potential and a primitive form. I will also explain that shift operators are closely related to the Gamma
structure in quantum cohomology.
13:15–14:15

Award Lecture for the 2015 MSJ Geometry Prize

Osamu Saeki(Kyushu Univ.)

Stable maps and topology of manifolds

Summary: In this talk, we consider generic smooth maps, called stable maps, between manifolds that are
singular in general, and see how their topology and their singularities are related to the diﬀerential topologyof the manifolds over which the maps are defined. When the singularities are relatively mild, we will seethat the existence of such maps gives strong restrictions to the topology of the manifolds. We also review
the theory of singular fibers of stable maps and present its applications to the cobordism theory of maps
and manifolds together with applications to the visualization of scientific data.

Final: 2015/08/20
24

Geometry

September 15th (Tue)

Conference Room X

10:00–12:00
19 Takashi Komatsu (Tohoku Univ.)

Limiting distributions of discrete-time quantum walks on the squarelattice · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of quantum walks was introduced by Aharonov as a quantum counterpart of theclassical random walks. It is one of the problem to determine limiting distribution of quantum walks. In
this talk, we will propose a model of discrete-time quantum walks on the square lattice without localizationand give its limiting distribution. Furthermore, we discuss the relationship between our quantum walk andone-dimensional quantum walk.
20 Masaru Hasegawa (Univ. de São Paulo)

Parabolic, ridge and sub-parabolic curves of implicit surfaces withsingularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we discuss parabolic, ridge and sub-parabolic curves of implicit surfaces defined bysmooth functions having Morse singularities of index 1 or 2.
21 Takeyuki Nagasawa (Saitama Univ.) ∗ The Möbius invariance of decomposed Möbius energies · · · · · · · · · · · · · 15
Aya Ishizeki (Saitama Univ.)
Summary: It is well known that one of O’Hara’s knot energies is called the Möbius energy because of its
invariance under Möbius transformations. We gave in a previous talk that the Möbius energy can be
decomposed into three parts that retain invariance except for under an inversion with respect to a spherecentered on a knot. Here, we consider the exception by assuming the knots have an extra regularity. The
result holds not only for knots but also for closed curves in Rn .
22 Yasushi Homma (Waseda Univ.)

The Rarita–Schwinger operator on Einstein spin manifolds · · · · · · · · · · 10

Summary: The Rarita–Schwinger operator is an elliptic first order diﬀerential operator on the spin 3/2
fields. We show that the operator on Einstein spin manifolds satisfies an algebraic relation, which gives
an interesting feature of its spectrum. In particular, we have a method of calculating the spectrum on
irreducible compact symmetric spaces.
23 Kaoru Ikeda(Keio Univ.) ♭ The principal series of GLn (R) parameterized by the energy of the Toda
lattice and geometrical quantizations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk I introduce the geometrical constructions of the unitary representations of GLn (R)along the recipe of the geometrical quantization given by Kostant. The unitary representations are classified
by the connections defied by the iso-energy surfaces of the Toda lattice
24 Satoshi Nakamura (Tohoku Univ.)

K-stability with a divisor and Log-Futaki invariant · · · · · · · · · · · · · · · · · 10

Summary: Szekelyhidi introduced the notion of K-stability with a divisor in his Ph. D. thesis. By studying
his K-stability condition, we got an numerical obstruction to existence of constant scalar curvature Kähler
metric which has cusp singularity along a divisor.
25 Genki Hosono (Univ. of Tokyo) ∗ Approximations and examples of singular Hermitian metrics on vector
bundles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We study singular Hermitian metrics on vector bundles on complex manifolds. In this talk, wegive two results and examples. Our first result shows coherence of the higher rank analogue of multiplierideals when metrics are defined by global sections. Related to this result, we construct an example of asingular Hermitian metric whose Nakano-curvature is not bounded below. Our second result can be used todetermine all negatively curved singular Hermitian metrics on certain rank 2 bundles on elliptic curves.

Final: 2015/08/20
25

Geometry

26 Masao Jinzenji (Hokkaido Univ.)

Toward direct proof of mirror theorem of projective hypersurfaces · · · · 15

Summary: We discuss direct computational proof of mirror theorem (especially generalized mirror transformation ) of genus 0 Gromov–Witten invariants of projective hypersurfaces. The main diﬃculty lies in taking
non-equivariant limit of residue integral representation of Gromov–Witten invariants. We have constructed
a way to take this limit up to d = 8 rationnal curves. If this construction is completed, the proof is reduced
to combinatorial identities of rational functions associated with tree graphs.
14:15–16:25
27 Keita Kunikawa (Tohoku Univ.)

Splitting theorem for translating solitons in arbitrary codimension · · · 15

Summary: We study the translating solitons of the mean curvature flow. Although many authors study
the translating solitons in codimension one, there are few examples for higher codimensional cases except
for Lagrangian translating solitons. First we give non-trivial examples of translating solitons in arbitrarycodimension. We will see that they have the property called parallel principal normal (PPN). Inspired bythis fact and the work of Smoczyk for self-shrinkers in 2005, we then show the splitting theorem for complete
translating solitons with PPN.
28 Homare Tadano (Osaka Univ.)

An upper diameter bound for compact Ricci solitons with applications
to the Hitchin–Thorpe inequality · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall give an upper diameter bound for compact shrinking gradient Ricci solitons
in terms of the range of the scalar curvature. As an application, we shall provide a suﬃcient condition forfour-dimensional compact shrinking gradient Ricci solitons to satisfy the Hitchin–Thorpe inequality.
29 Ryosuke Takahashi (Nagoya Univ.)

Asymptotic stability for Kähler–Ricci solitons · · · · · · · · · · · · · · · · · · · · · 15

Summary: Kähler–Ricci solitons arise from the geometric analysis, such as Kähler–Ricci flow, and havebeen studied extensively in recent years. As is the case of Kähler–Einstein metrics, it is expected thatthe existence of Kähler–Ricci solitons is closely related to some GIT stability of manifolds. For instance,
Donaldson showed that any cscK manifolds with discrete automorphism group admit the sequence ofbalanced metrics. In this talk, we explain that an analogue of this result also holds for Kähler–Ricci solitons.
We introduce a certain kind of balanced metric, called quantized Kähler–Ricci solitons, and show that thestrong analytic K-polystability leads to the existence of quantized Kähler–Ricci solitons, and this sequence
converges to the Kähler–Ricci soliton in the L1 -topology.
30 Tomoya Nakamura (Waseda Univ.)

The deformation of symplectic structures by a moment mapping · · · · · 15

Summary: Presentation of the subject is that deforming a symplectic structure on a manifold by applying
the theory of a quasi-Poisson action with a moment mapping to a symplectic manifold with a Hamilton
action. In particular, we fully describe the deformation of the symplectic structure of the canonical Kähler
form on CP 1 .
31 Suguru Ishikawa (Kyoto Univ.)

Spectral invariants of distance functions · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Calculating the spectral invariants of Floer homology of distance-like functions, we recently foundsome kind of superheavy subsets in symplectic manifolds. We showed if convex open subsets in Euclidian
space with the standard symplectic form are disjointly embedded in a spherically negative monotone closed
symplectic manifold, their compliment is superheavy. The key of the proof is the estimate of the Conley–
Zhender index of the periodic orbits of the special Hamiltonian. This method can also be applied tospherically monotone symplectic manifolds, by which we can show an analogous property of sphericallymonotone symplectic manifolds.

Final: 2015/08/20
26

Geometry

32 Yoshihiro Sugimoto (Kyoto Univ.) ♭ Energy-capacity inequality of Hofer’s pseudo metric of Lagrangian submanifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We will talk about Hofer’s pseudo matric on the space of Lagrangian submanifolds. We will
explain an inequality which is the Lagrangian version of the inequality of Gromov width and displacement
energy which is called energy-capacity inequality.
33 Yoshihiro Sugimoto (Kyoto Univ.) ♭ A construction of a partial symplectic quasi-state via symplectic homology and its application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We use symplectic homology to construct partial symplectic quasi-states on symplectic manifolds
with contact type boundaries. We apply this partial symplectic quasi-states to the study of symplectic
homology itself. We prove that our symplectic homology of a symplectic manifold with a contact typeboundary vanishes if it is displaceable in its symplectic completion.
16:45–17:45

Talk Invited by Geometry Section
Masato Mimura (Tohoku Univ.) ∗ Strong algebraization of fixed point properties
Summary: Purely algebraic criteria of fixed point properties with respect to superreflexive Banach spaces,
under relative fixed point property, inspired from Shalom’s one in ICM 2006, are established. No bounded
generation is imposed. One application is that Steinberg groups St(n, A) over any finitely generated, unital,
commutative, and associative ring A, possibly noncommutative, enjoy the fixed point property with respect
to any noncommutative Lp -space, provided that n at least 4, and that p in (1, ∞).

September 16th (Wed)Conference Room X

10:00–12:00
34 Jin-ichi Itoh (Kumamoto Univ.)
Yutaro Yamashita(Mimata Junior High School)

Quadratic surfaces as the surfaces generated by circles or rectangular
hyperbolas · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: D. Hilbert and S. Cohn-Vossen wrote in their book “Anschauliche Geometrie” that ellipsoids
and other quadratic surfaces are generated by parallel circles. Here we show how ellipsoids, one-sheeted
hyperboloids, two-sheeted hyperboloids, and elliptic paraboloids are explicitly represented by two familiesof parallel circles (as circular surfaces) using coordinates. As circles are important objects in ellipsoids,
rectangular hyperbolas (whose two asymptotes are orthogonal) are important objects in general hyperbolas.
We found that many one-sheeted hyperbolas and two sheeted hyperbolas are represented by parallel circles(how they are constructed by rectangular hyperbola), and there are infinitely many families of parallel
rectangular hyperbola instead of only two as in circular cases. Also all hyperbolic paraboloids are generated
by rectangular hyperbolas.
35 Jin-ichi Itoh (Kumamoto Univ.)Joël Rouyer (IMRA, Bucharest)
Costin Vı̂lcu (IMRA, Bucharest)

Moderate smoothness of most Alexandrov surfaces · · · · · · · · · · · · · · · · · 10

Summary: We show that, in the sense of Baire categories, a typical Alexandrov surface with curvaturebounded below by κ has no conical points. We use this result to prove that, on such a surface (unless it isflat), at a typical point, the lower and the upper Gaussian curvatures are equal to κ and ∞ respectively.
36 Nobuhiro Innami (Niigata Univ.)

Voronoi diagrams and cut loci in a surface · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let P be a finite set of points in a compact surface M . The Voronoi edges are contained in the
cut locus of P . We study a relation of the Voronoi edges and the cut locus of P . In particular, we show theEuler characteristic of M by the numbers of the minimum points, saddle points and maximum points of the
distance function to P .

Final: 2015/08/20
27

Geometry

37 Youhei Sakurai (Univ. of Tsukuba)

Rigidity of manifolds with boundary under a lower weighted Ricci
curvature bound · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound.
We prove several rigidity theorems for such manifolds with boundary. We have a rigidity theorem for the
inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundaries, and a
splitting theorem. We also obtain rigidity results for the smallest Dirichlet eigenvalues for the weighted
p-Laplacians.
38 Yu Kitabeppu(Kyoto Univ.)

A finite diameter theorem on RCD spaces · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give an equivalent relation between the finiteness of the diameter of a metric measure spacewith Riemannian curvature-dimension condition and a behavior of the heat distributions on such space. Asan application, we also give a dimeter bound, which is asymptotically sharp estimate. The result had notbeen known even in the case of Riemannian manifolds.
39 Kota Hattori(Keio Univ.) ∗ The nonuniqueness of the tangent cone at infinity of Ricci-flat manifolds· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is shown by Colding and Minicozzi the uniqueness of the tangent cone at infinity of Ricci-flat
manifolds with Euclidean volume growth which has at least one tangent cone at infinity with a smooth crosssection. In this article we raise an example of the Ricci-flat manifold implying that the assumption for thevolume growth in the above result is essential. More precisely, we construct a complete Ricci-flat manifoldof dimension 4 with non-Euclidean volume growth who has at least two distinct tangent cones at infinity
and one of them has a smooth cross section.
40 Asuka Takatsu (Tokyo Metro. Univ.) ♭ High-dimensional metric-measure limit of Stiefel manifolds · · · · · · · · · · 15
Takashi Shioya (Tohoku Univ.)
Summary: We study and specify the high-dimensional limit of Stiefel manifolds as metric measure spaces in
Gromov’s topology. The limit is the infinite-dimensional Gaussian space, which is drastically diﬀerent fromthe manifolds.
41 Asuka Takatsu (Tokyo Metro. Univ.) ♭ Riemannian Wasserstein geometry on the space of Gaussian measures
Hiroshi Kawabi (Okayama Univ.) over the Wiener space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: The space of Gaussian measures on an abstract Wiener space being equivalent to the Wiener
measure becomes a Hilbert manifold, and the manifold admits a non-positive Riemannian metric derived
from the information geometry. We consider another geometric structure on the manifold, so-called theWasserstein geometry, which is a metric geometry on the space of probability measures. We first show
the convexity of the manifold with respect to the Wasserstein geometry, which enables us to restrict the
Wasserstein geometry to the manifold naturally. We then construct a Riemannian metric on the manifold,which induces the Wasserstein distance function. The Riemannian manifold has a non-negative sectional
curvature, which provdies the diﬀerence from the information geometry.

Final: 2015/08/20
28

Geometry

14:15–16:15
42 Nobuhiko Otoba (Keio Univ.) ∗ Metrics of constant scalar curvature on sphere bundles · · · · · · · · · · · · · · 15
(CIMAT)
Jimmy Petean
Summary: We construct Riemannian metrics of constant scalar curvature on twisted sphere bundles anddraw a similar picture as in the following situation studied previously by O. Kobayashi (1985, 1987), Schoen(1989), Petean (2010) et al. Let r > 0 be a real number and g(r) the Riemannian metric of S m (1) × S k (r),the direct product of two round spheres (m ≥ 1, k ≥ 1, n := m + k ≥ 3). The number of solutions to thecorresponding Yamabe equationn+2n−2−4 n−1n−2 ∆g(r) u + Rg(r) u = Rg(r) u(u > 0)on S m × S k diverges to infinity as r → ∞ (resp. r → 0) unless m = 1 (resp. k = 1). On the other hand, if
k−1
k
2
m
k
m ≤ r ≤ m−1 , there is no nonconstant solution depending only on one of the S - and S -variables.
43 Yoshihiro Umehara (Tohoku Univ.)

Distribution of the pair of two conformal invariant on a 3-dimensional
closed manifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a smooth closed manifold X of dimension three, the author study the distribution of the pairof two conformal invariant, which are the Yamabe constant and the L1 -norm of the Cotton tensor.
44 Yoshihiko Matsumoto (Tokyo Tech)
Kazuo Akutagawa (Tokyo Tech)

Harmonic maps between asymptotically hyperbolic manifolds · · · · · · · · 15

Summary: We consider the asymptotic Dirichlet problem for harmonic maps between noncompact manifolds.
When the domain and the target manifolds are both hyperbolic spaces, existence and uniqueness were studied
by Akutagawa and Li–Tam in the 1990s. Here we generalize their results to the case of asymptotically
hyperbolic manifolds. Analogously to the classical theorems of Eells–Sampson and Hamilton, the uniqueexistence in each relative homotopy class is shown under some assumption.
45 Yoshihiko Matsumoto (Tokyo Tech)
Kengo Hirachi (Univ. of Tokyo)
Christian Lübbe(Birkbeck, Univ. of London)

Q-curvature of Weyl connections and asymptotically hyperbolic Einstein manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We extend the notion of Branson’s Q-curvature to Weyl connections on even-dimensional conformal manifolds. This is related to an asymptotic Dirichlet problem for Weyl structures on asymptotically
hyperbolic manifolds that are approximately Einstein.
46 Jun Nonaka(Waseda Univ. Senior High School)

The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space · · · 15

Summary: Kellerhals and Perren conjectured that the growth rates of the reflection groups given by hyperbolic
Coxeter polyhedra are always Perron numbers. We prove that this conjecture is always true for the case ofideal Coxeter polyhedra in H3 . We also detect the ideal Coxeter polyhedron in H3 with the minimal growthrate. In addition, we show that there are correlations between the volumes and the growth rates of ideal
Coxeter polyhedra in H3 in many cases.
47 Ryokichi Tanaka (Tohoku Univ.)

Vershik’s question on Gromov hyperbolic groups · · · · · · · · · · · · · · · · · · · 10

Summary: I will discuss about the entropy, the speed and the volume growth associated with a random walkon a hyperbolic group.

Final: 2015/08/20
29

Geometry(Niigata Univ.)
48 Hiroki Sako
Masato Mimura (Tohoku Univ.)
Narutaka Ozawa (Kyoto Univ.)
Yuhei Suzuki (Univ. of Tokyo)

Group approximation in Cayley topology and coarse geometry, Part III:
Geometric property (T) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study correspondence between the following: (1) large scale structure of the metric spaceconsisting of Cayley graphs of finite groups with k generators; (2) structure of groups which appear in
the boundary in the space of k-marked groups. We show the correspondence among the metric properties‘geometric property (T)’, ‘cohomological property (T),’ and the group property ‘Kazhdan’s property (T)’.
Geometric property (T) of Willett–Yu is stronger than being expander graphs. Cohomological property (T)is stronger than geometric property (T) for general coarse spaces.
16:45–17:45

Talk Invited by Geometry Section

Tomohiro Fukaya (Tohoku Univ.)

Boundary of relatively hyperbolic group and the coarse geometry

Summary: Let G be a hyperbolic group. The Gromov boundary of G contains coarse geometric properties
of G. For example, it can be used to show the injectivity of the coarse assembly map and thus, the Novikov
conjecture of G. It is also used to study the group cohomology of G.
Higson and Roe constructed “coarse algebraic topology”. By using this, they verified the coarse Baum–
Connes conjecture for CAT(0)-groups and hyperbolic groups. Boundaries play an important rule in their
theory. Fukaya–Oguni verified the coarse Baum–Connes conjecture for the product of hyperbolic groups,
CAT(0)-groups, polycyclic groups, and, some relatively hyperbolic groups. In our theory it is essential toconstruct an appropriate boundary of the product of metric spaces.
Relatively hyperbolic group H is characterized by the action on the compact metric space M . This space H
can be regarded as a boundary of H, and thus is called the Bowditch boundary. However, M is not enoughto study the coarse geometric properties of H. We constructed an appropriate boundary of H by blowing-up
all parabolic points of the Bowditch boundary. In the construction, we use the “coarse structure”, which
is not neccesary induced by a metric. We will explain how we can use this boundary to study the coarse
geometric properties of H, for example, to compute the K-theory of the Roe algebra of H, via the coarse
assembly map.

Final: 2015/08/20
30

Complex Analysis

Complex Analysis
September 13th (Sun)

Conference Room IX

9:30–12:00∗
1 Katsuyuki Nishimoto
The solutions to the Laplace’s non-homogeneous ordinary diﬀerential(Descartes Press Co.) equations by means of the N-fractional calculus · · · · · · · · · · · · · · · · · · · · 15

Summary: In this article, the solutions to the non-homogeneous ordinary diﬀerential equations with linear
coeﬃcients, φ2 · (az + b) + φ1 · (gz + h) + φ · (pz + q) = f , (φν = dν φ/dz ν for ν > 0, φ0 = φ = φ(z),a, b, g, h, p, q: constants, agp ̸= 0, f = f (z) ̸= 0) which are called as “the Laplace’s ordinary diﬀerential
equations”, are discussed by means of the N (Nishimoto’s)-fractional calculus (NFC-method) (The calculus
in the 21st century).
2 Shigeyoshi Owa (Yamato Univ.) ∗ Notes on some conditions for univalency · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let A be the class of functions f (z) in the open unit disk U with f (0) = f ′ (0) − 1 = 0. Let S
and S ∗ be subclasses of A consisting of f (z) which are univalent in U and starlike in U, respectively. The
object of the present talk is to discuss some conditions for f (z) to be in the classes S and S ∗ .
3 Kazuo Kuroki(Osaka Univ. of Health and Sport Sci.)

Some starlikeness conditions concerned with the second coeﬃcient · · · · 15

Summary: Let A be the class of analytic functions f (z) = z +∞∑ak z k in the open unit disk U = {z ∈ C :k=2|z| < 1}. Some starlikeness conditions for f (z) ∈ A missing the second coeﬃcient a2 were discussed. In thepresent talk, by considering starlikeness of order α for f (z) ∈ A with a2 ̸= 0, we discuss some starlikenessconditions concerned with the second coeﬃcient a2 .
4 Toshio Hayami (Setsunan Univ.)

Notes on the convex combinations of harmonic univalent functions · · · 15

Summary: Let H be the class of all functions f (z) = h(z) + g(z) which are harmonic and sense-preserving
in the open unit disk U = {z : z ∈ C and |z| < 1} and normalized by f (0) = h′ (0) − 1 = 0, and let SH be
the subclass of H consisting of all univalent functions in U. This class is preserved under some elementarytransformations. But we note that even if f1 (z) and f2 (z) are in SH , the convex combination f3 (z) of f1 (z)and f2 (z) defined as f3 (z) = tf1 (z) + (1 − t)f2 (z) (0 < t < 1) is not necessarily a member of SH . In thepresent talk, we discuss some conditions for f3 (z) to belong to SH .
5 Rintaro Ohno (Tohoku Univ.)

Conditions and properties of concave functions · · · · · · · · · · · · · · · · · · · · 15

Summary: Similar to starlike or convex functions, concave functions define a special class in the geometricfunction theory. Meromorphic functions with a simple pole inside the unit disk are said to be concave,
if they map the unit disk conformally onto the complement of a convex set. In this presentation we will
introduce some analytic characterizations of concave functions as well as extensions to the necessary andsuﬃcient conditions. We will also take a closer look at the coeﬃcients using these properties and discuss
their bounds.
6 Narufumi Tsuboi (Tokyo Tech) ∗ The defects of power series in the unit disk with Hadamard gaps · · · · · 15
Summary: Letf (z) = c0 +∞∑ck z nkk=1

be a power series with Hadamard gaps, i.e. nk+1 /nk ≥ q > 1 (k ≥ 1), convergent in the unit disk
D = {|z| < 1}. It is known that if lim supk→∞ |ck | > 0, then f (z) has no finite defective value. We shall∑∞discuss the defects of f (z) in the case where limk→∞ ck = 0 and k=0 |ck |2 = +∞.

Final: 2015/08/20
31

Complex Analysis(Oita Univ.) ∗ Trudinger’s inequality for Riesz potentials of functions in Musielak–
7 Takao Ohno
Tetsu Shimomura (Hiroshima Univ.) Orlicz spaces on metric measure spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk we are concerned with Trudinger’s inequality for Riesz potentials of functions inMusielak–Orlicz spaces on metric measure spaces.
8 Masaharu Nishio (Osaka City Univ.) ♭ Reproducing kernel for iterated parabolic operators on the upper half
space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider parabolic operators of fractional order and their iterates on the upper half space on
the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall discuss,in this talk, the existence of reproducing kernels and give an explicit form by using their fundamental
solutions.
9 Kiyoki Tanaka (Osaka City Univ.)

Polyharmonic Bergman space and its reproducing kernel · · · · · · · · · · · · 10

Summary: We consider the polyharmonic Bergman space on the unit ball. We give the form of the
reproducing kernel of biharmonic Bergman space and the estimates for the reproducing kernel.
14:15–16:15
10 Masashi Kisaka (Kyoto Univ.)
Tomoki Kawahira (Tokyo Tech)

A mechanism of appearing small copies of the Mandelbrot set · · · · · · · 15

Summary: We explain a new phenomenon which concern about small copies of the Mandelbrot set.
11 Junghun Lee(Nagoya Univ.)

J-stability of immediately expanding rational maps in non-Archimedean
dynamics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We will see J-stability theorem of immediately expanding rational maps in non-Archimedean
dynamics as an analogue of R. Manñè, P. Sad, and D. Sullivan’s J-stability theorem in complex dynamics.
12 Yûsuke Okuyama (Kyoto Inst. Tech.)

Equidistribution of rational functions having a superattracting periodic
point · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about an approximation of the activity current Tc in the parameter space Λ (aconnected complex manifold) of a holomorphic family f : Λ × P1 → P1 of rational functions fλ = f (λ, ·) ofdegree d > 1 having a marked critical point c : Λ → P1 by parameters λ for which c(λ) is periodic under fλ ,i.e., is a superattracting periodic point.
This gives an aﬃrmative answer, in the superattracting case, to a question on the removability of aseemingly technical assumption on the parameter space Λ posed by Dujardin–Favre for rational functions
having preperiodic critical points, and refines Bassanelli–Berteloot on a similar approximation of thebifurcation current Tf of the holomorphic family f , simplifying the original proofs of those results.
13 Hiroki Sumi

(Osaka Univ.)

Complex analogues of the Takagi function in random complex dynamics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Regarding the i.i.d. random dynamical system on the extended real line such that at every step
we choose f1 (x) = 2x with probability p and we choose f2 (x) = 2x − 1 with probability 1 − p, let Ap (x) be
the probability of tending to +∞ regarding the random orbits starting with the initial value x. Then thefunction Ap (x) on [0, 1] is equal to Lebegue’s singular function with respect to parameter p. Also, the partial∂Ap (x)|p=1/2 with respect to p at p = 1/2 is equal to 2B(x), where B(x) is the Takagi function.
derivative ∂p
We consider complex analogues of the above story in random complex dynamical systems.

Final: 2015/08/20
32

Complex Analysis

14 Johannes Jaerisch (Shimane Univ.)(Osaka Univ.)
Hiroki Sumi

Hölder regularity of the complex analogues of the Takagi function · · · · 15

Summary: Recently, H. Sumi introduced complex analogues of the Takagi function, which play a rolein the iteration of rational maps on the Riemann sphere Ĉ and random complex dynamical systems. We
investigate the Hölder regularity of a complex analogue C of the Takagi function. Under certain assumptions,by employing methods from ergodic theory, we obtain new results about the set of points in which C satisfies
a local Hölder condition with a prescribed Hölder exponent. In particular, we determine the set of pointsz ∈ Ĉ for which C is not locally constant in a neighbourhood of z. This is a joint work with H. Sumi.
15 Shizuo Nakane(Tokyo Polytechnic Univ.)

Stretching rays for complex cubic polynomials · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will extend the results on the non-landing of stretching rays for real cubic polynomials to
non-real cubic polynomials. For a given critical portrait, there exists a surface which consists of cubic
polynomials with that critical portrait. In this surface, stretching rays are level curves of the Boettcher
vector map. We will show that, if the Boettcher vector is not an integer, the ray does not land, that is, its
accumulation set is non-trivial.
16 Naotaka Kajino (Kobe Univ.)

The Laplacian on the Apollonian gasket and its Weyl type eigenvalue
asymptotics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Apollonian gasket is a fractal subset of R2 obtained by repeating indefinitely the process ofremoving the interior of the inner tangent circles of the ideal triangles starting from an ideal triangle. (Theclosed region in R2 enclosed by three circles each of which is tangent to the other two is called an ideal
triangle.) It has been observed by Teplyaev that the notion of a canonical energy form can be introduced
for functions on the Apollonian gasket but no analysis of this form has been done. The purpose of this talkis to present the author’s recent results on a concrete description of this energy form, its closedness in an
appropriate L2 -space, and the Weyl type eigenvalue asymptotics of the associated Laplacian saying that thegrowth order of the large eigenvalues is given by the Hausdorﬀ dimension d of the Apollonian gasket andthat the limit in the asymptotics is comparable to the d-dimensional Hausdorﬀ measure of the gasket.
16:30–17:30

Talk Invited by Complex Analysis Section

Noriaki Suzuki(Meijo Univ.) ∗ Polynomial approximation and potential theory

Summary: We study polynomial approximation on real line R with exponential weights of the form w(x) =exp(−Q(x)). We assume that w belong to a relevent class F(C 2 +). Let Pn be the set of all polynomialsof degree not more than n ∈ N. Put En,p (f, w) = inf P ∈Pn ∥(f − P )w∥Lp (R) for f w ∈ Lp (R), 1 ≤ p < ∞and f w ∈ C0 (R) when p = ∞. A question is that when limn→∞ Ep,n (f, w) = 0 holds, which is known
as the Bernstein approximation problem. In the 1970’s, G. Freud investigates systematically for a weightQ(x) = |x|α , α > 1. In his theory, infinite-finite range inequalities play an important role, which means∥P W ∥Lp (R) ≤ C∥P W ∥Lp (In ) for all P ∈ Pn , where In = [−cn1/α , cn1/α ]. In 1984, potential theory gave a
big breakthrough on approximation theory. Rakhmanov and Mhasker–Saﬀ independently defined a number√∫1
an by a solution of 2 0 an tQ′ (an t)/ 1 − t2 dt = nπ, which is called the MRS number. By using weighted
potential theory, they proved ∥P W ∥Lp (R) ≤ 2∥P W ∥Lp (Jn ) for all P ∈ Pn , where Jn = [−an , an ]. Notethat a weight w in F(C 2 +) has a positive answer to the Bernstein problem. For w ∈ F(C 2 +), we set
T (x) = xQ′ (x)/Q(x). If T is bounded, then w ia called a Freud-type weight. Otherwise, w is called an
Erdös-type weight. There are many study for Freud-type weights, for, example, Ep,n (f, w) ≤ CEp,n−1 (f ′ , w)
(Favard inequality) and ∥P ′ w∥Lp (R) ≤ C(n/an )∥P w∥Lp (Jn ) holds for every P ∈ Pn (Markov–Bernsten
inequality). The main purpose of my talk is to give extensions of the above results to Erdöd-type weights.
Then powers of T appear in those inequalities.

Final: 2015/08/20
33

Complex Analysis

September 14th (Mon)

Conference Room IX

9:30–12:00
17 Yohei Komori (Waseda Univ.)
Tomoshige Yukita (Waseda Univ.)

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

Summary: We study the set S of growth rates of of ideal Coxeter groups in hyperbolic 3-space which consistsof real algebraic integers greater than 1. We show that (1) S is unbounded while it has the minimum, (2)any element of S is a Perron number, and (3) growth rates of of ideal Coxeter groups with n generators arelocated in the closed interval [n − 3, n − 1].
18 Katsuhiko Matsuzaki (Waseda Univ.)

Barycentric extension of circle diﬀeomorphisms · · · · · · · · · · · · · · · · · · · · 15

Summary: The barycentric extension due to Douady and Earle gives a conformally natural extension of aquasisymmetric automorphism of the circle to a quasiconformal automorphism of the unit disk. We consider
such extensions for circle diﬀeomorphisms of Hoelder continuous derivatives and show that this operation iscontinuous with respect to an appropriate topology for the space of corresponding Beltrami coeﬃcients.
19 Hiroshige Shiga (Tokyo Tech)

On the number of Teichmüller curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let M (g, n) be the moduli space of Riemann surfaces of type (g, n) with 2g − 2 + n > 0. A
Teichmüller curve is a pair (C, f ) of a hyperbolic Riemann surface C of finite analytic type and a locallyisometric holomorphic map f : C → M (g, n) with respect to the hyperbolic distance on C and theTeichmüller distance on M (g, n). In this talk, we discuss a bound of the number of Teichmüller curves when
the topological type of C is fixed.
20 Masanori Amano (Tokyo Tech)

On families of asymptotic Jenkins–Strebel rays · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give a parametrization of asymptotic Jenkins–Strebel rays. For any admissible
curve family of a surface, the subset of the boundary of the Teichmüller space which is constructed bypinching of the given curve family can be determined. There exists a homeomorphism of the product ofparameter spaces and the boundary space onto the Teichmüller space such that each family of asymptotic
Jenkins–Strebel rays is represented when varies only the parameters.
21 Hideki Miyachi (Osaka Univ.)

Extremal length functions are log-plurisubharmonic · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall show that the extremal length functions on Teichmüller space are logplurisubharmonic. As a corollary, we obtain an alternative proof of S. Krushkal’s result that a function defined by the Teichmüller distance from a reference point is plurisubharmonic. To show the logplurisubharmonicity, we obtain explicit formulae of the Levi forms of the extremal length functions.
22 Toshihiro Nakanishi (Shimane Univ.) ∗ Parametrization of Teichmüller spaces by trace functions and mapping
Gou Nakamura (Aichi Inst. of Tech.) class group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We give a set of trace functions which give a global parametrization of the Teichmüller space
T (g, n) such that the action of the mapping class group on T (g, n) can be represented by rational transformations in the parameters.
23 Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

The Schwarz lemma and the Schwarz–Pick lemma in several complex
variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We generalize the harmonic Schwarz lemma to pluriharmonic mappings of the unit ball BX of
a complex Banach space X into the unit ball B n of Cn with respect to an arbitrary norm. Also, we
obtain a generalization of the harmonic Schwarz–Pick lemma to the case of pluriharmonic mappings of thehomogeneous unit ball BX of a complex Banach space X into the unit ball B n . Further, we will generalize
the Schwarz–Pick lemma to holomorphic mappings of the homogeneous unit ball BX of a complex Banach
space X into the unit ball BY of an arbitrary complex Banach space Y .

Final: 2015/08/20
34

Complex Analysis

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

The Landau theorem in several complex variables · · · · · · · · · · · · · · · · · · 10

Summary: As an application of the Schwarz lemma and Schwarz–Pick lemma, we will generalize the Landau
theorem by Chen and Gauthier to mappings of finite dimensional homogeneous unit balls into the Euclidean
space. By using similar arguments, we can also generalize the pluriharmonic Landau theorem by Chen and
Gauthier to mappings of finite dimensional homogeneous unit balls into the Euclidean space.
25 Hidetaka Hamada(Kyushu Sangyo Univ.)

Bonk’s distortion theorem and the Bloch constant for Bloch mappingsin Cn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let BX be a homogeneous unit ball in X = Cn . In this talk, we generalize Bonk’s distortion
theorem to Bloch mappings on BX . As an application, we give a lower bound of the Bloch constant.
13:15–14:15

Talk Invited by Complex Analysis Section

Takeo Ohsawa (Nagoya Univ.) ♭ L2 extension theorems and Suita conjecture
Summary: In the theory of functions of complex variables, Riemann (1857) first tried to introduce acoordinate system in the set of algebraic functions of one variable. Periods of integrals of Riemann surfaces
are components of such a coordinate. By generalizing this notion of periods, Griﬃths established a theoryof period mappings for families of compact Kaehler manifolds. Based on the theory of Griﬃths, T. Fujita
discovered a convexity property of this generalized period mapping in terms of the curvature of the direct
image of relative canonical bundles. This is in the context of Hodge theory where the L2 harmonic forms areanalyzed. On the other hand, after the foundation of several complex variables was established by K. Oka
and H. Cartan, the L2 method was developed to obtain eﬀective results in complex analysis and geometry.
An extension theorem with L2 growth condition was obtained in this context. It was applied to study
singularities of plurisubharmonic functions, to prove the invariance of plurigenera for families of projective
varieties, and to study the multiplier ideal sheaves. Recently, J. Cao proved in a general context that an L2
extension theorem implies the semipositivity of the direct image of relative canonical bundles. Vice versa,
B. Berndtsson and L. Lempert showed that such a curvature property implies an L2 extension theorem inan optimal form. Since this progress is closely related to the solution of a long-standing conjecture of N.
Suita, it might be a good occasion to give an overview of this development going back to the origin of theideas of deformation and extension.

September 15th (Tue)

Conference Room IX

9:15–12:00
26 Shinichi Tajima (Univ. of Tsukuba) ∗ A method for computing Bruce–Roberts’ Milnor numbers via local
Katsusuke Nabeshimacohomology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Univ. of Tokushima)
Summary: A new eﬀective method is proposed for computing Bruce–Roberts’ Milnor numbers.

A key

ingredient of the proposed method is the concept of local cohomology.
27 Shinichi Tajima (Univ. of Tsukuba) ∗ Algorithms for computing holonomic D-modules associated with a hyKatsusuke Nabeshima
persurface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Univ. of Tokushima)
Summary: Algorithms are obtaind for computing holonomic D-modules associated with hypersurface singularities.

Final: 2015/08/20
35

Complex Analysis

28 Shinichi Tajima (Univ. of Tsukuba) ∗ Algorithms for computing holonomic D-modules associated with a hyKatsusuke Nabeshima
persurface II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Univ. of Tokushima)
Summary: The structure of holonomic D-modules associated with non-isolated hypersurface singularities is
considered. Eﬀectivity of the resulting algorithms is described by using examples.
29 Yûsuke Okuyama (Kyoto Inst. Tech.)

Lehto–Virtanen, Marty, and Zalcman-type theorems and their applications to Kobayashi hyperbolic geometry · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will talk about a Lehto–Virtanen-type theorem and a rescaling principle for an isolated
essential singularity of a holomorphic curve in a complex space, as well as a Marty-type theorem and a
Zalcman-type one for a family of holomorphic curves in a complex space, which are useful for establishing a
big Picard-type theorem and a big Brody-type one for holomorphic curves.
30 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.)

Growth, distortion and coeﬃcient bounds on complex Banach spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider growth, distortion theorems and coeﬃcient bounds for holomorphic
mappings on the unit ball of on a complex Banach space, including some sharp improvements of existing
results.
31 Takayuki Koike (Univ. of Tokyo) ∗ Toward a higher codimensional Ueda theory · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Ueda’s theory is a theory on a flatness criterion around a smooth hypersurface of a certain typeof topologically trivial holomorphic line bundles. We propose a codimension two analogue of Ueda’s theory.
As an application, we give a suﬃcient condition for the anti-canonical bundle of the blow-up of the three
dimensional projective space at 8 points to be non semi-ample however admit a smooth Hermitian metricwith semi-positive curvature.
32 Sachiko Hamano (Fukushima Univ.)

Variational formula for Ls -canonical semi-exact diﬀerential and application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We establish the variational formula of Ls -canonical semi-exact diﬀerential (−1 < s ≤ 1) for the
deforming open torus R(t) with complex parameter t ∈ ∆ = {|t| < r}. This formula implies the intimate
relation between the Euclidean radius of the moduli disk for R(t) and the pseudoconvexity.
33 Satoru Shimizu (Tohoku Univ.) ∗ Structure and equivalence of a class of tube domains with solvablegroups of automorphisms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In the study of the holomorphic equivalence problem for tube domains, it is fundamental toinvestigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to theholomorphic equivalence problem for such tube domains TΩ , investigating certain solvable subalgebras ofg(TΩ ) plays an important role, where g(TΩ ) is the Lie algebra of all complete polynomial vector fields onTΩ . Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvablegroups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism groupis solvable and contains nonaﬃne automorphisms.
34 Takeo Ohsawa (Nagoya Univ.) ♭ Application and simplified proof of a sharp L2 extension theorem · · · · 15
Summary: As an application of a sharp L2 extension theorem for holomorphic functions due to Guan–Zhou,
a stability theorem for the boundary asymptotics of the Bergman kernel is proved. An alternate proof ofthis extension theorem is given, too. It is a simplified proof in the sense that it is free from ODE.

Final: 2015/08/20
36

Complex Analysis

35 Junjiro Noguchi (Univ. of Tokyo⋆) ♭ On convergnece radius of the inverse of Abelian integrals and Levi’s
problem for ramified domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We introduce a positive scalar function ρ(a, Ω) for a domain Ω of a complex manifold X with a
global holomorphic frame of the cotangent bundle by closed Abelian diﬀerentials, which is an analogue ofHartogs’ radius. We prove an estimate of Cartan–Thullen type with ρ(a, Ω) for holomorphically convex hullsof compact subsets. In one dimensional case, we apply the obtained estimate of ρ(a, Ω) to give a new proofof Behnke-Stein’s Theorem for the Steiness of open Riemann surfaces. We then extend the idea to deal withthe problem to generalize Oka’s Theorem (IX) for ramified Riemann domains over Cn . We obtain somegeometric conditions in terms of ρ(a, X) which imply the validity of the Levi problem (Hartogs’ inverse
problem) for a finitely sheeted ramified Riemann domain over Cn .

Final: 2015/08/20
37

Functional Equations

Functional Equations
September 13th (Sun)

Conference Room VI

9:00–12:00
1 Saburou Saitoh (Gunma Univ.⋆) ∗ Aveiro discretization method in mathematics: A new discretization
L. P. Castro (Univ. of Aveiro) principle (I: Principle) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8(Kyoto Univ.)
H. Fujiwara
M. M. Rodrigues (Univ. of Aveiro)
Vu Kim Tuan (Univ. of West Georgia)
Summary: We found a very general discretization method for solving wide classes of mathematical problems
by applying the theory of reproducing kernels. An illustration of the generality of the method is here
performed by considering several distinct classes of problems to which the method is applied. In fact, one of
the advantages of the present method —in comparison to other well-known and well established methods—
is its global nature and no need of special or very particular data conditions. Numerical experiments havebeen made, and consequent results are here exhibited.
2 Saburou Saitoh (Gunma Univ.⋆) ∗ Aveiro discretization method in mathematics: A new discretization
L. P. Castro (Univ. of Aveiro) principle (II: Applications) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8(Kyoto Univ.)
H. Fujiwara
M. M. Rodrigues (Univ. of Aveiro)
Vu Kim Tuan (Univ. of West Georgia)
Summary: Due to the powerful results which arise from the application of the present method, we consider
that this method has everything to become one of the next generation methods of solving general analyticalproblems by using computers. In particular, we would like to point out that we will be able to solve very
global linear partial diﬀerential equations satisfying very general boundary conditions or initial values (andin a somehow independent way of the boundary and domain). Furthermore, we will be able to give anultimate sampling theory and an ultimate realization of the consequent general reproducing kernel Hilbert
spaces. The general theory is here presented in a constructive way, and containing some related historicaland concrete examples.
3 Ichiro Tsukamoto (Toyo Univ.) ∗ A nonliear diﬀerential equation with an irregular singular point andslowly varying solutions of x′′ = t−2 x1+α with α < 0 · · · · · · · · · · · · · · · · 10
Summary: We have a slowly varying solution of the diﬀerential equation denoted in the title from a nonlinear
diﬀerential equation with an irregular singular point. So, we state new theorems on the asymptoticity andthe convergence of the formal power series solutions of this diﬀeretial equation in the general form, and get
an analytical expression of that slowly varying solution from these theorems.
4 Sunao Ōuchi(Sophia Univ.) ∗ A functional equation with solutions of irregular singular type. · · · · · · 10∑mmm
i=1 ai (z)u(φi (z)) = f (z) is considered, where {ai (z)}i=1 , {φi (z)}i=1 are′holomorphic at z = 0 and φi (0) = 0, φi (0) = 1 and f (z) is holomorphic in a sector or a formal power series.

Summary: A Functional equation

We show under certain conditions that the equation has a solution of formal power series and for f (z) ≡ 0
it has a formal solution of the form ṽ(z) = eψ(1/z) z α w̃(z), where ψ(t) is a polynomial of t and w̃(z) is aformal power series. These shows that the equation has formal solutions of irregular singular type in thetheory of ordinary equations.

Final: 2015/08/20
38

Functional Equations

5 Shingo Takeuchi(Shibaura Inst. of Tech.)Complete (p, q)-elliptic integral and its application to Bhatia–Li’s mean
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We introduce a generalization of the elliptic integral of the first kind by using the (p, q)-sinefunction. Applying the generalized elliptic integral to a new mean, which was defined by Bhatia and Li in2012, we give another proof for their theorem on the mean.
6 Nobuki Takayama (Kobe Univ.)
Katsuyoshi Ohara (Kanazawa Univ.)

Evaluation of A-hypergeometric polynomials by diﬀerence equations · · 12

Summary: We give an method to evaluate A-hypergeometric polynomials numerically. The method utilizes
a system of diﬀerence equations satisfied by the polynomial. A-hypergeometric polynomials are normalizing
constants of A-distributions in statistics.
7 Yoshiaki Goto

(Kobe Univ.)

Contiguity relations and intersection matrices for hypergeometric functions of type (k, n) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the contiguity relations for hypergeometric functions of type (k, n), in terms of thetwisted cohomology groups and the intersection forms. To write the contiguity relations explicitly, we useintersection matrices and their inverse. In this talk, I would like to give expressions of the inverses of someintersection matrices.
This study will be applied to the numerical evaluation of the normalizing constant of the hypergeometric
distribution on the r1 × r2 contingency tables with fixed marginal sums.
∗
8 Kunihiko Taniguchi
Permanence for a nonautonomous Lotka–Volterra competition system(Kobe City Coll. of Tech.) with finite delays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider nonautonomous N -dimensional generalized Lotka–Volterra competition systems withdelays. Under certain conditions we show that such systems are permanent. Our result gives an extension
as well as an improvement of previous results.
9 Masakazu Onitsuka(Okayama Univ. of Sci.)

Uniform asymptotic stability and global exponential stability for twodimensional half-linear diﬀerential systems · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a half-linear diﬀerential system:x′ = a11 (t)x + a12 (t)ϕp∗(y),y ′ = a21 (t)ϕp (x) + a22 (t)y,where all time-varying coeﬃcients are continuous; p and p∗ are positive numbers satisfying 1/p + 1/p∗ = 1;
and ϕq (z) = |z|q−2 z for q = p or q = p∗ . The aim of this talk is to clarify that uniform asymptotic stability,
exponential stability, global uniform asymptotic stability, and global exponential stability are equivalent for
the half-linear diﬀerential system.
♭
Local uniqueness of solution to an inverse blow-up problem · · · · · · · · · · 12
10 Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.)
Hiroyuki Usami (Gifu Univ.)

Summary: We study an inverse problem to determine a nonlinearity of an autonomous equation from a
blow-up time of solutions of the equation, focusing on the local uniqueness of the nonlinearity.
11 Kazuki Himoto (Osaka Pref. Univ.)
Hideaki Matsunaga (Osaka Pref. Univ.)

The limits of the solutions of a linear integral delay system · · · · · · · · · · 12

Summary: In this talk we will classify the limits of the solutions of a linear integral delay system. In
particular, if the solution tends to a point or a periodic orbit, we will give the explicit expressions in termsof the coeﬃcient matrix, the delay parameter and the initial conditions.

Final: 2015/08/20
39

Functional Equations

12 Taisuke Yoneyama (Tokyo Univ. of Sci.)
Keiichi Kato (Tokyo Univ. of Sci.)

Characterization of the range of wave operators via wave packet transform · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we characterize the range of the wave operators for Schrödinger equations with timedependent short range potentials by way of wave packet transform.
13 Hajime Koba (Waseda Univ.) ∗ Generalized quasi-reversibility method for a backward heat equation
Hideki Matsuoka (Univ. of Tokyo) with a fractional Laplacian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7
Summary: We considers a backward problem on a heat equation with a fractional Laplacian. It is not easy
to solve a backward heat equation directly. To consider a backward heat equation, we apply the N -th
power of the Dirichlet–Laplacian and small parameters to regularize the equation. This method is called aquasi-reversibility method. We use the generalized quasi-reversibility method to study the backward heat
system.
14:15–16:15
14 Toshio Horiuchi (Ibaraki Univ.)
Naoki Chiba

Radial symmetry and its breaking in the Caﬀarelli–Kohn–Nirenberg
type inequalities for p = 1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The main purpose of this talk is to study the Caﬀarelli–Kohn–Nirenberg type inequalities with
p = 1. We show that symmetry breaking of the best constants occurs provided that a parameter |γ| is large
enough. In the argument we eﬀectively employ equivalence between the Caﬀarelli–Kohn–Nirenberg type
inequalities with p = 1 and isoperimetric inequalities with weights.
15 Motohiro Sobajima(Tokyo Univ. of Sci.)

Remarks on higher-order weighted Rellich inequalities in Lp · · · · · · · · · 12

Summary: The validity of higher-order weighted Rellich inequalities with respect to Lp -norm in RN(∥|x|α−2m u∥Lp ≤ C∥|x|α ∆u∥Lp ) for N ∈ N, 1 ≤ p ≤ ∞, m ∈ N and α ∈ R is investigated. The result generalizes the validity of weighted Rellich inequalities obtained in the previous work Metafune–Sobajima–Spina(2014).
16 Masaru Ikehata (Hiroshima Univ.) ∗ The enclosure method for the evaluation of the spot welding area using
Hiromichi Itou (Tokyo Univ. of Sci.) a solution of the Laplace equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Akira Sasamoto(Nat. Inst. of Adv. Industrial Sci. and Tech.)
Summary: We consider an inverse boundary value problem for the Laplace equation in two dimensions which
is a mathematical formulation of a nondestructive evaluation to know the location and shape of the weldedparts. Using the Enclosure Method, we give an explicit solution to the problem.
17 Shigeru Sakaguchi (Tohoku Univ.) ∗ Neutrally coated inclusions in three dimensions · · · · · · · · · · · · · · · · · · · · 12
Hyeonbae Kang (Inha Univ.)(Inha Univ.)
Hyundae Lee
Summary: Among coated inclusions each of which consists of a core and a shell with diﬀerent constantconductivities in three dimensions, we want to determine the neutrally coated inclusions, that is, thosewhich are neutral to all uniform fields in the isotropic medium. We first derive an over-determined boundary
value problem in the shell of the inclusion provided that the conductivity of the core is larger than that of
the shell. Then we prove that if the over-determined problem admits a solution, then the inclusion must be
spherical.
18 Ryuji Kajikiya(Saga Univ.)

A priori estimate for the first eigenvalue of the p-Laplacian · · · · · · · · · · 12

Summary: For a convex domain, we give an a priori estimate for the first eigenvalue of the p-Laplacian interms of the radius d of the maximum ball contained in the domain. As a consequence, we prove that thefirst eigenvalue diverges to infinity as p → ∞ if the domain is convex and d ≤ 1. We show that in theannulus a < |x| < b, the first eigenvalue diverges to infinity if b − a ≤ 2 and converges to zero if b − a > 2.

Final: 2015/08/20
40

Functional Equations(Ibaraki Univ.)
19 Xiaojing Liu
Toshio Horiuchi (Ibaraki Univ.)

Remarks on the strong maximum principle involving p-Laplacian · · · · · 10

Summary: The main purpose of this talk is to study the strong maximum principle involving p-Laplacianwith p ̸= 2. Let N ≥ 1, 1 < p < ∞ and p∗ = max(1, p − 1). Let Ω be a bounded domain of RN . We
shall study the strong maximum principle for the operator; −∆p + a(x)Q(·). Here a ≥ 0 a.e. in Ω, ∆p is∗1,p(Ω) if p ̸= 2. We
a p-Laplacian and Q(·) is a nonlinear term. Let u ∈ L1loc (Ω) if p = 2 and let u ∈ Wloc
1
assume that u ≥ 0 a.e. in Ω, Q(u) ∈ Lloc (Ω) and ∆p u is a Radon measure on Ω. When p ̸= 2, we assume

that u is admissible. Moreover, we assume that −∆p u + a(x)Q(u) ≥ 0 in Ω in the measure sense. Then we
prove that if ũ = 0 on a set of positive p−capacity in Ω, then u = 0 a.e. in Ω. Here ũ is a quasicontinuous
representative of u.
20 Kunihiro Usuba (Tokyo Univ. of Sci.)

Partial regularity of minimizers of p(x)-growth functionals with 1 <p(x) < 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we deal with the problem of regularity of the map which minimizes the functional of
the type called p(x)-growth.
We prove partial regularity of minimizers u for p(x)-energy functionals of the following type∫i
j p(x)/2
E(u) = (Aαβdx,ij (x, u)Dα u Dβ u )Ωassuming that Aαβij (x, u) and p(x) are suﬃciently smooth and that p(x) is subquadratic.
We prove that u ∈ C 0,α (Ω0 ) for some α ∈ (0, 1) and an open set Ω0 ⊂ Ω with Hm−γ1 (Ω − Ω0 ) = 0, where
Hs denotes the s-dimensional Hausdorﬀ measure and γ1 = inf Ω p(x).
16:30–17:30

Talk Invited by Functional Equations Section

Toshiyuki Mano (Univ. of Ryukyus)

A generalization of diﬀerential equations of Okubo type to several
variables case and flat structure

Summary: The aim of this talk is to give a generalization of diﬀerential equations of Okubo type to several
variables case and to show that the spaces of their independent variables admit a geometric structure called“flat structure”. This construction gives a generalization of B. Dubrovin’s theory on Frobenius manifolds.
As a consequence of our construction, it is shown that the isomonodromic deformations of generic Okubo
type diﬀerential equations are equivalent to solutions to a system of nonlinear diﬀerential equations called“generalized WDVV equation”. Besides, we show the existence of a special generator system called “flatgenerator system” for the ring of invariant polynomials of a complex reflection group. This is a generalizationof K. Saito’s result for finite Coxeter groups.

September 14th (Mon)

Conference Room VI

9:00–12:00
21 Satoshi Tanaka (Okayama Univ. of Sci.)

Uniqueness of sign-changing radial solutions for the scalar field equation
in some ball and annulus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The following Dirichlet problem is considered: ∆u − u + |u|p−1 u = 0, x ∈ Ω; u = 0, x ∈ ∂Ω. Here,Ω is either an annulus or a ball in RN and p > 1. The uniqueness of radial solutions having exactly k − 1
nodes is shown for the following cases: Ω is a suﬃciently thin annulus; Ω is a certain small ball, N ≥ 4 and1 < p < N/(N − 2); Ω is the unit ball, N = 3 and 1 < p ≤ 3; Ω is any annulus or any ball, but p > 1 issuﬃciently close to 1 and N = 3, 5 or 7.

Final: 2015/08/20
41

Functional Equations

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

Profiles of solutions to a stationary limiting problem for a cell polarization model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We investigate profiles and limiting profiles of solutions to a stationary limiting problem for a cell
polarization model proposed by Y. Mori, A. Jilkine and L. Edelstein-Keshet in SIAM J. Appl Math (2011).
Especially, we are interested in limiting profiles with an internal layer which appear due to mass constrain.
We study them by using exact representation of solutions which we have obtained. This is a joint workwith Professors K. Kuto (Univ. of Electro-Comm.), T. Tsujikawa (Univ. of Miyazaki) and Shoji Yotsutani(Ryukoku Univ.).
23 Tetu Makino (Yamaguchi Univ.⋆) ∗ On spherically symmetric solutions to the Einstein–Euler equations(Supplement) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We consider the exterior metric to time dependent spherically symmetric solutions to the Einstein–
Euler equations using the Schwartzschild metric under the Birkhoﬀ’s theorem.
24 Erika Ushikoshi (Tamagawa Univ.) ∗ Hadamard variational formula for the higher variation of the Greenfunction of the Laplace equation with the Dirichlet boundary condition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We establish the Hadamard variatinal formula for the higher variation of the Green function for
the Laplace equation with the Dirichlet boundary condition under the smoothly domain perturbation.
25 Keisuke Takasao (Univ. of Tokyo) ∗ Existence of weak solution for volume preserving mean curvature flow
via phase field method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we consider the phase field method for the volume preserving mean curvature flow.
In 1997 Golovaty studied the Allen–Cahn equation with non-local term. We show the convergence of thesolution to the weak solution for the volume preserving mean curvature flow. The weak solution is called
L2 -flow and is similar to the formulation of Brakke’s mean curvature flow.
26 Keisuke Takasao (Univ. of Tokyo) ∗ Gradient estimates for mean curvature flow with transport term andMasashi Mizuno (Nihon Univ.) Neumann boundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we consider a mean curvature flow with transport terms and Neumann boundary
conditions. We give the boundary gradient estimates for the mean curvature flow with the transport terms
via the weighted monotonicity formula. The estimates depend on the Wx1,p Lqt -norm with respect to thetransport terms, where p, q > 1 satisfy 1 − np − 2q > 0. Our assumption of regularity for the transport terms
is reasonable from the point of scaling arguments.
27 Masahiko Shimojyou(Okayama Univ. of Sci.)
Hiroshi Matano (Univ. of Tokyo)
Jong-Shenq Guo (Tamkang Univ.)
Chang Hong Wu (Nat. Univ. of Tainan)Classification of the behavior on a free boundary problem for thecurvature flow with driving force · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study a free boundary problem associated with the curvature dependent motion of planar
curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixedcontact angles. The main result concerns the classification of solutions; every solution falls into one of thethree categories, namely, area expanding, area bounded and area shrinking types.

Final: 2015/08/20
42

Functional Equations

28 Masahiko Shimojyou(Okayama Univ. of Sci.)
Hiroshi Matano (Univ. of Tokyo)
Jong-Shenq Guo (Tamkang Univ.)
Chang Hong Wu (Nat. Univ. of Tainan)

Asymptotic behavior on a free boundary problem for the curvature flow
with driving force · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study in detail the asymptotic behavior of solutions on a free boundary problem associatedwith the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide
along the horizontal axis with prescribed fixed contact angles. We show that solutions are asymptotically
self-similar both in the area expanding and the area shrinking cases, while solutions converge to either astationary solution or a traveling wave in the area bounded case. We also explain results on the concavity
properties of solutions.
29 Takashi Kagaya (Tokyo Tech)
Masahiko Shimojyou(Okayama Univ. of Sci.)

Exponential stability of a traveling wave for an area preserving curvature
motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The asymptotic behavior of solutions to an area-preserving curvature flow of planar curves in theupper half plane is investigated. Two endpoints of the curve slide along the horizontal axis with prescribed
fixed contact angles. First, by establishing an isoperimetric inequality, we prove the global existence of thesolution. We then study the asymptotic behavior of solutions with concave initial data near a travelingwave.
30 Motohiko Sato (Wakhok Univ.)

Dynamic boundary conditions for the singular degenerate parabolic
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I am concerned with geometric evolution of interface under the dynamic boundary conditions.
Using the level set approach the evolution of interface is described by the degenerate parabolic equations
including mean curvature flow equation on dynamic boundary conditions. I introduce the notions of viscosity
super-and subsolutions suitable for the singular degenerate parabolic equations on the dynamic boundary
conditions. I establish comparison and existence theorems of initial value problem for the singular degenerate
parabolic equations including mean curvature flow equation on the dynamic boundary conditions.
31 Jin Takahashi
Toru Kan(Tokyo Tech)(Tokyo Tech)

Solutions with time-dependent singularities in semilinear heat equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For semilinear parabolic equations with a power nonlinearity, we consider the existence and the
behavior of solutions with time-dependent singularities. Here, by time-dependent singularity, we mean asingularity with respect to the space variable whose position depends on the time variable. Under somecondition for the nonlinearity, we construct solutions with a time-dependent singularity. This is a joint workwith Toru Kan (Tokyo Institute of Technology).
32 Hirotada Honda (Keio Univ.)(Keio Univ.⋆)
Atusi Tani

On the vanishing diﬀusion limit of Sakaguchi–Kuramoto equation · · · · 12

Summary: The Kuramoto–Sakaguchi equation is a partial integro-diﬀerential equation of the physical theoryof coupled oscillators. It describes the temporal evolution of the phase distribution of coupled oscillators in
the presence of some additive perturbation. In this talk, we summarize the recent arguments concerning themathematical analysis of the Kuramoto–Sakaguchi equation, including the current status of our investigation.

Final: 2015/08/20
43

Functional Equations

33 Norisuke Ioku (Ehime Univ.)
Kazuhiro Ishige (Tohoku Univ.)(Tokyo Tech)
Eiji Yanagida

Sharp decay estimates in Lebesgue spaces for nonnegative Schrödinger
heat semigroups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: Let H := −∆ + V be a nonnegative Schrödinger operator on L2 (RN ), where N ≥ 2 and V isa radially symmetric function decaying quadratically at the space infinity. In this talk we consider the
Schrödinger heat semigroup e−tH and make a complete table of the decay rates of the operator norms of
e−tH in the Lebesgue spaces as t → ∞.
34 Masahiro Suzuki (Tokyo Tech)(Tokyo Tech)
Toru Kan

Time-periodic solutions to the drift-diﬀusion model for semiconductors· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We study the existence and the asymptotic stability of time-periodic solutions to the driftdiﬀusion model for semiconductors. If alternating-current voltage is applied to PN-junction diodes, a timeperiodic current flow is observed. The main purpose of this talk is mathematical analysis on this periodic
flow.
13:15–14:15

Talk Invited by Functional Equations Section

Fumihiko Hirosawa (Yamaguchi Univ.)

Linear wave equations with time dependent coeﬃcients and its applications

Summary: In this talk we consider linear wave equations with time dependent coeﬃcients and its application
to a nonlinear wave equation. Some equations with variable coeﬃcients can be handled by the same way
for the constant coeﬃcients if the coeﬃcients are “approximate constants”. However, some properties ofvariable coeﬃcients, for instance, oscillation, degeneration and less regularity, bring crucial problems if we
directly apply some kind of standard method for constant coeﬃcients equations. Actually, the behavior ofsome solutions of the equations with variable coeﬃcients are quite diﬀerent from the equations with constantcoeﬃcients. The aim of our research is to make clear the influence of some properties of variable coeﬃcientsto the solutions by using a precise analysis of the solution in Fourier space. Moreover, we try to apply the
result for the global solvability of a non-linear wave equation of Kirchhoﬀ type with non-analytic large data.

September 15th (Tue)

Conference Room VI

9:00–12:00
35 Kentarou Fujie (Tokyo Univ. of Sci.)
Takasi Senba (Kyushu Inst. of Tech.)Global existence and boundedness of radial solutions to a parabolicparabolic Keller–Segel system with general sensitivity · · · · · · · · · · · · · · 12

Summary: In this talk, global existence and boundedness of radial solutions to a fully parabolic Keller–Segelsystem will be established for general sensitivity.
36 Noriko Mizoguchi(Tokyo Gakugei Univ.)

Nonexistence of type I blowup solutions to parabolic-parabolic Keller–
Segel system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: This talk is concerned with the parabolic-parabolic Keller–Segel system in two dimensions. Whena solution (u, v) blows up at t = T < +∞, the blowup is called type I if ∥u(t)∥∞ ≤ C(T − t)−1 for t ∈ [0, T )with some constant C > 0, and type II otherwise. The speaker showed that each blowup is of type II underassumption of radial symmetry. It is given in this talk that the conclusion holds true in general case withno extra condition. The radial symmetry was essentially used in the proof of the previous result. A method
in Navier–Stokes equations is useful in the proof in the general case.

Final: 2015/08/20
44

Functional Equations

37 Yūki Naito(Ehime Univ.)

Global attractivity in the weighted norm for a supercritical semilinear
heat equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider the behavior of solutions to the Cauchy problem for a semilinear heat equation withsupercritical nonlinearity. We study the convergence of solutions to steady states in a weighted norm, andshow the global attractivity property of steady states. We also give its convergence rate for a class of initialdata.
38 Kimie Nakashima(Tokyo Univ. of Marine Sci. and Tech.)Wei-Ming Ni (Univ. of Minnesota)

Uniqueness and stability of multi-layered steady-state in a spatiallyinhomogeneous reaction diﬀusion equation · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk we will consider a miglation selection model for the evolution of gene frequencie which
is described as a reaction diﬀusin equation. We will show the existence of multi layered steady-state. We
will also prove that the steady-state is linearly stable and unique.
39 Hiroshi Matsuzawa(Numazu Nat. Coll. of Tech.)
Yihong Du (Univ. of New England)
Maolin Zhou (Univ. of New England)

Spreading speed and sharp asymptotic profiles of solutions in freeboundary problems for nonlinear diﬀusion equations in high dimensions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we consider nonlinear diﬀusion problems of the form ut = ∆u + f (u) with Stefan
type free boundary conditions, where the nonlinear term f (u) is monostable, bistable or combustion type.
Such problems may be used to describe the spreading of a biological or chemical species. In this talk, wewill focus on the radially symmetric solutions and their spreading phenomena, that is, the free boundary|x| = h(t) goes to infinity and u(t, x) → 1 as t → ∞. We will give a sharp estimate of h(t) and asymptotic
profile of solution u for large t. In particular, we will give a diﬀerence between one dimensional case andradially symmetric case in high dimensions.
40 Hiroko Yamamoto (Meiji Univ.)
Izumi Takagi (Tohoku Univ.)

Concentration points in stationary solutions of a singularly perturbed
reaction-diﬀusion equation with variable coeﬃcients · · · · · · · · · · · · · · · · 10

Summary: We consider a point-condensation phenomenon in solutions of a semilinear elliptic equation withvariable coeﬃcients. This means that distribution of a solution concentrates in very narrow regions arounda finitely many points. In order to know where the concentration points are, we introduce a locator function
composed of the coeﬃcients involved in the equation, and prove that any concentration point must be a
critical point of the locator function. Moreover, we construct a solution concentrating near a nondegeneratecritical point of the locator function.
41 Takashi Suzuki (Osaka Univ.)

2D Smoluchowski–Poisson equation: quantization of blowup in infinite
time · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8

Summary: We consider 2D Smoluchowski–Poisson equation. In this model, blowup in infinite time arises
only if the total mass is quantized.
42 Masaru Ikehata (Hiroshima Univ.) ∗ The enclosure method for inverse obstacle scattering using a solution of
the Maxwell system in the time domain · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: In this talk, a time domain enclosure method for an inverse obstacle scattering problem using
a single electromagnetic wave is introduced. The wave is observed at the same place as the support of thesource over a finite time interval and the governing equation is given by the Maxwell system outside the
obstacle. It is assumed that the obstacle is a perfect conductor placed in the whole space. Two types ofanalytical formulae which contain information about the geometry of the obstacle are given.

Final: 2015/08/20
45

Functional Equations

43 Eiji Onodera(Kochi Univ.)

Uniqueness of a fourth-order dispersive flow for closed curves on compact Riemann surfaces with constant sectional curvature · · · · · · · · · · · · 10

Summary: We consider the initial value problem for a fourth-order dispersive flow equation for maps fromthe one-dimensional flat torus into compact Riemann surfaces with constant sectional curvature, as a
generalization of two-sphere-valued physical models. We show the uniqueness of a time-local solution to theinitial value problem.
44 Tokio Matsuyama (Chuo Univ.) ∗ Gevrey class solutions of the Kirchhoﬀ equation · · · · · · · · · · · · · · · · · · · · 12
Michael Ruzhansky(Imperial Coll. London)
Summary: This talk is devoted to find Gevrey class solutions for the Cauchy problem to the Kirchhoﬀ
equation. Similar results are obtained for the initial-boundary value problems in bounded domains andexterior domains with compact boundary.
45 Yusuke Sugiyama (Tokyo Univ. of Sci.)

Degeneracy in finite time of some quasilinear wave equation · · · · · · · · · 12

Summary: We consider the large time behavior of solutions of the Cauchy problem of the quasilinear wave
equation: ∂t2 u = ∂x ((1 + u)2a ∂x u), which has richly physical backgrounds. If 1 + u(0, x) is bounded awayfrom a positive constant, we can construct a local solution for smooth initial data. When 1 + u(t, x) is goingto 0 in finite time, the equation degenerates. We give a suﬃcient condition that the equation degenerates in∫finite time. A known result on global existence and our main theorem determine a threshold of R u1 (x)dx
separating the global existence of solutions and the occurrence of the degeneracy.
46 Kyouhei Wakasa (Hokkaido Univ.) ∗ The lifespan of solutions to semilinear damped wave equations in one
space dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk, we consider the initial value problem for semilinear damped wave equations in one
space dimension. Wakasugi (2014) have obtained an upper bound of the lifespan for the problem in thesubcritical case. Also, M. D’Abbicco & S. Lucente & M. Reissig (2014) showed the blow-up result in thecritical case. The aim of this talk is to give an estimate of the upper bound of the lifespan in the criticalcase, and show the optimality of the upper bound. Also, we derive an estimate of the lower bound of thelifespan in the subcritical case which shows the optimality of the upper bound in Wakasugi. Moreover, weshow that the critical exponent changes when the initial data satisfies some symmetric assumption.
∗
47 Kazuyoshi Yokoyama
Life span of small solutions to a system of wave equations · · · · · · · · · · · 10
(Hokkaido Univ. of Sci.)(Mie Univ.)
Kunio Hidano

Summary: We study the Cauchy problem with small initial data for a system of semilinear wave equations□u = |v|p , □v = |∂t u|p in n-dimensional space. When n ≥ 2, we prove that blow-up can occur for arbitrarily
small data if (p, q) lies below a curve in p-q plane. On the other hand, we show a global existence result forn = 3 which asserts that a portion of the curve is in fact the borderline between global-in-time existence
and finite time blow-up. We also estimate the maximal existence time and get an upper bound, which is
sharp at least for (n, p, q) = (2, 2, 2) and (3, 2, 2).
48 Kunio Hidano(Mie Univ.) ∗ A note on the method for proving global existence of small solutions
to systems of 2D quasi-linear wave equations in the multi-speed setting· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: The Cauchy problem is studied for systems of quasi-linear wave equations with multiple speeds in
two space dimensions. Using the method of Klainerman and Sideris together with the localized energy estimate, we give an alternative proof of a beautiful result of Hoshiga and Kubo (Global small amplitude solutionsof nonlinear hyperbolic systems with a critical exponent under the null condition, SIAM J. Math. Anal. 31(2000), 486–513).

Final: 2015/08/20
46

Functional Equations

12:10–12:30

Presentation Ceremony for the 2015 MSJ Analysis Prize

14:15–16:15
Global behavior of mass subcritical generalized KdV equation · · · · · · · 1249 Satoshi Masaki (Hiroshima Univ.)
Jun-ichi Segata (Tohoku Univ.)

Summary: We consider global behavior of solutions to generalized KdV equation in mass subcritical setting.
The data is taken from a scale critical L̂p space. It turns out that under a physical assumption on relation
between nonlinear Schrodinger equation, there exists a threshold solution which has the smallest size in asuitable sense among all non-scattering soluitons.
50 Jun-ichi Segata (Tohoku Univ.) ∗ Small data global existence and scattering for the generalized Korteweg–
Satoshi Masaki (Hiroshima Univ.) de Vries equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: We study global existence and scattering for generalized Korteweg–de Vries (gKdV) equation insome scale critical space.
Virial identity for Hartree equations with an inverse-square potential of
critical case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

51 Toshiyuki Suzuki(Kanagawa Univ./Kogakuin Univ.)

Summary: We consider Hartree equations with inverse-square potentials (HE)a :
i

a )
∂u (
= −∆ + 2 u + λu (|x|−γ ∗ |u|2 ).
∂t|x|

If a > −(N − 2)2 /4, then we see blow-up in finite time (λ < 0, γ > 2) and scattering theory (λ > 0,
1 < γ < 2) by virtue of virial identity. Now we have proved the virial identity for (HE)a with critical casea = −(N − 2)2 /4; nevertheless the energy class does not coincide with H 1 (RN ).
52 Hideaki Sunagawa (Osaka Univ.)
Chunhua Li (Yanbian Univ.)

On Schrödinger systems with dissipative nonlinearities of derivative
type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Consider the initial value problem for systems of cubic derivative nonlinear Schrödinger equations
in one space dimension with the masses satisfying a suitable resonance relation. We give structural conditions
on the nonlinearity under which the small data solution gains an additional logarithmic decay as t → +∞compared with the corresponding free evolution.
53 Gaku Hoshino (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

Space-time analytic smoothing eﬀect for a system of Schrödinger equations under mass resonance condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for a system of Schrödinger equations. We prove the existence
and uniqueness of solutions in analytic function space characterized by the pseudo-conformal generators fordata such as suﬃciently small and exponential decay at infinity.
54 Kazumasa Fujiwara (Waseda Univ.)

On the local solvability of semirelativistic equations · · · · · · · · · · · · · · · · 10

Summary: Nonexistence of local solutions to the Cauchy problem of semirelativistic equations with powertype nonlinearity is shown in scale subcritical and one space dimension case. The nonexistence result isobtained by a transformation of semirelativistic equations and a test function method with test functions
which cancel the highest order derivatives.
55 Hiroyuki Hirayama (Nagoya Univ.)
Mamoru Okamoto (Shinshu Univ.)

Almost sure well-posedness of the Cauchy problem for the fourth ordernonlinear Schrödinger equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for the fourth order nonlinear Schrödinger equation with
derivative nonlinearity (i∂t + ∆2 )u = ±|∇|(|u|2 u) on Rd , d ≥ 3, with random initial data. We prove that
almost sure local in time well-posedness, small data global in time well-posedness and scattering hold in
d−5d−3
H s (Rd ) with max( d−5
2 , 6 ) < s, whose lower bound is below the scale critical regularity sc = 2 .

Final: 2015/08/20
47

Functional Equations

56 Hiroyuki Hirayama (Nagoya Univ.)
Mamoru Okamoto (Shinshu Univ.)

Well-posedness and scattering for fourth order nonlinear Schrödinger
type equations at the scaling critical regularity · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the Cauchy problem of the fourth order nonlinear Schrödinger typeequation with derivative nonlinearity. In one dimensional case, we prove that the fourth order nonlinear
Schrödinger equation with the derivative quartic nonlinearity ∂x (u4 ) is the small data global in time wellposed and scattering to a free solution. Furthermore, we show that the same result holds for the dimensiond ≥ 2 and derivative polynomial type nonlinearity, for example |∇|(um ) with (m − 1)d ≥ 4.
57 Ryosuke Hyakuna (Waseda Univ.) ∗ On the local well-posedness for the pure power NLS in one spacedimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10s,p ,dSummary: We consider the Cauchy problem for the 1D pure power NLS with the initial data u0 ∈ H′ss,p = {ϕ ∈ S ′ (R) : (1 + ξ 2 ) 2 ϕ̂ ∈ Lp }. It is shown that the initial value problem is locally well-poseddwhere Hif 0 < s < 1/2 and p is near 2.
16:30–17:30

Talk Invited by Functional Equations Section

Kazuhiro Takimoto (Hiroshima Univ.)

Entire solutions to some types of parabolic Hessian equations

Summary: In this talk, we shall obtain our recent results on the characterization of entire solutions to
so-called parabolic Hessian equations which are fully nonlinear PDEs in general. This talk is based on joint
works with Saori Nakamori.

September 16th (Wed)Conference Room VI

9:00–12:00
58 Masayuki Hayashi (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

Local well-posedness for the derivative nonlinear Schrödinger equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study Cauchy problem for Schrödinger equations in one space dimension with power nonlinearity involving derivative. Ambrose and Simpson established the local existence of solutions on a periodic
domain in the energy space. We proved local well-posedness in the energy space by improving their method.
Our proof is based on the compactness argument, the gauge transformation and the Strichartz estimates.
(Tohoku Univ.) ∗ On the ill-posedness for a system of quadratic nonlinear Schrödinger
59 Kota Uriya
Takayoshi Ogawa (Tohoku Univ.) equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Tsukasa Iwabuchi (Osaka City Univ.)
Summary: We are concerned with the ill-posedness issue for a system of quadratic nonlinear Schrödinger
equations in two dimensions. From previous studies for the large time behavior of the solution to the system,
one may expect that the critical regularity to show the well-posedness depends on the dispersion coeﬃcients.
To prove the ill-posedness, we show the failure of the uniform continuity of the data-solution map for themass resonance case and show the norm inflation for other cases.
60 Shintaro Kondo (Meiji Univ.)

Almost-periodic solution of Hasegawa–Wakatani equations with vanishing resistivity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: In this talk, we consider the zero-resistivity limit for Hasegawa–Wakatani equations in a cylindrical
domain when the initial data are Stepanov-almost-periodic in the axial direction. Hasegawa–Wakatani
equations are nonlinear partial diﬀerential equations which describe nuclear fusion plasma. When thetemperature of the plasma is very high, the resistivity of the plasma approaches zero; therefore, it isimportant for nuclear fusion plasma research to consider the case of zero resistivity.

Final: 2015/08/20
48

Functional Equations(Tokyo Tech)
61 Penyuan Hsu
Hirofumi Notsu (Waseda Univ.)
Tsuyoshi Yoneda (Tokyo Tech)

A local analysis of the axi-symmetric Navier–Stokes flow near a saddle
point and no-slip flat boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We do numerical computations on axi-symmetric Navier–Stokes flows with no-slip flat boundary.
We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons
occur only in the swirl case: The distance between the maximum point of the velocity and the z-axis
is drastically changing around some time (turning point). An “increasing velocity phenomenon” occurs
near the boundary and the maximum value of the velocity is obtained near the point of symmetry at theboundary when time is close to the turning point.
62 Takahiro Okabe (Hirosaki Univ.) ∗ Navier–Stokes flow in the weighted Hardy space with applications to
Yohei Tsutsui (Shinshu Univ.) time decay problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
Summary: The asymptotic expansions of the Navier–Stokes flow in Rn and the rates of decay are studied
with aid of weighted Hardy spaces. Fujigaki and Miyakawa (’01), Miyakawa (’00) proved the nth order
asymptotic expansion of the Navier–Stokes flow if initial data decays like (1 + |x|)−n−1 and if nth momentof initial data is finite. In the presentation, it is clarified that the moment condition for initial data isessential in order to obtain higher order asymptotic expansion of the flow and to consider the rapid time
decay problem.
63 Hideo Kozono (Waseda Univ.)
Senjo Shimizu (Kyoto Univ.)

Navier–Stokes equations with external forces in Lorentz spaces and its
application to self-similar solutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We show existence theorem of global mild solutions with small initial data and external forcesin Lorentz spaces with scaling invariant norms. If the initial data have more regularity in another scaling
invariant class, then our mild solution is actually the strong solution. The result on local existence ofsolutions for large data is also discussed. Our method is based on the maximal regularity theorem on the
Stokes equations in Lorentz spaces. Then we apply our theorem to prove existence of self-similar solutions
provided both initial data and external forces are homogeneous functions.
64 Takahito Kashiwabara (Tokyo Tech)
Matthias Hieber (TU Darmstadt)

Global well-posedness of the primitive equations in Lp -spaces · · · · · · · · 10

Summary: We consider the primitive equations which describe the large-scale motion of atmosphere andocean in geophysics. Cao and Titi (Ann. Math., 2007) proved, in the L2 -setting, that they admit a uniqueglobal-in-time solution for arbitrarily large initial data. We extend their result to the Lp -setting by adopting
an analytic semigroup approach. Namely, we introduce the hydrostatic Stokes operator to rewrite theprimitive equations as a semi-linear parabolic equation. The local well-posedness is established by applying
Fujita–Kato’s method. It is then combined with an H 2 -a priori estimate to deduce the global well-posedness
as well as an exponential decay estimate as time goes to infinity.
65 Masahiro Sawada (Osaka Univ.)
Yoshitaka Yamamoto (Osaka Univ.)

Unboundedness of some solutions to isentropic model equations forthe one dimensional periodic motions of a compressible self-gravitating
viscous fluid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial value problem for the one dimensional system of equations of a compressible
viscous fluid driven by a bounded periodic self-gravitation of the fluid. We focus on the structure of stationary
solutions to the isentropic self-gravitational system and prove that a certain bounded stationary solution islost when the average of the specific volume reaches a critical value. We then show that there does exist
an unbounded solution for the initial value problem when the average exceeds the critical value. We alsopresent a suﬃcient condition for the unboundedness in terms of the initial values of an energy form.

Final: 2015/08/20
49

Functional Equations

66 Itsuko Hashimoto(Toyama Nat. Coll. of Tech.)

Decay rate of Radially symmetric solutions for Burgers equation · · · · · 10

Summary: We investigate the decay rate of the radially symmetric solution for Burgers equation on theexterior of a small ball in multi-dimensional space, where the boundary data and the data at the far field
are prescribed. In a previous paper, we showed that, for the case in which the boundary data is equal to
0 or negative, the asymptotic stability is the same as that for the viscous conservation law. This time, itis proved that if both boundary data is positive, the asymptotic state is a superposition of the stationary
wave and the rarefaction wave, which is a new wave phenomenon. The proof is given using a standard L2and L1 energy method.
67 Yoshiyuki Kagei (Kyushu Univ.)
Takaaki Nishida (Kyoto Univ.)

Traveling waves bifurcating from Poiseuille flow in viscous compressible
fluid · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: It is known that Poiseuille flow in compressible fluid becomes unstable when Reynolds and Mach
numbers are so large that they satisfy some condition. We show that traveling waves bifurcate from Poiseuilleflow for some values of Reynolds and Mach numbers in a range where the instability condition is satisfied.
68 Shouta Enomoto (Kyushu Univ.)
Yoshiyuki Kagei (Kyushu Univ.)

Stability of spatially periodic stationary solutions to the compressible
Navier–Stokes equation in periodic layer · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider large time behavior of solution to compressible Navier–Stokes equation around thespatially periodic stationary solutions in a periodic layer of Rn (n = 2, 3). There exists a spatially periodic
stationary solution if the external force is spatially periodic and is suﬃciently small in some Sobolev space.
n−1
We show that the L2 norm of perturbation decays in the order t− 4 as t → ∞ if the initial perturbation
is suﬃciently; in fact, the perturbation behaves diﬀusively in large time.
69 Jan Prüss
Senjo Shimizu(Univ. Halle)(Kyoto Univ.)

Local existence of compressible two-phase flows with phase transitions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12

Summary: We consider models for compressible two-phase flows with phase transitions. These are derived
by first principles, i.e., balance of mass, momentum, and energy. As a first step, we analyze a simplified
model, where the temperature is assumed to be constant. Performing a Hanzawa transform, the problem
is transformed to a quasilinear parabolic two-phase problem with complicated transmission conditions on
the interface in a fixed domain. Then the density can be considered as a function of the velocity andof the height function, applying the method of characteristics. We prove maximal Lp-regularity of a thecorresponding linearized problem, and then by a fixed point argument in a suitable space, we obtain local
existence of the isothermal model.
70 Takayuki Kubo (Univ. of Tsukuba) ∗ Local well-posedness of the compressible-compressible two phase probYoshihiro Shibata (Waseda Univ.) lem without surface tension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
(Keio Univ.)
Kohei Soga
Summary: We consider the two phase problem for compressible and comressible case without surface tension.
In this talk, we shall describe that local well-posedness of our problem.
71 Takayuki Kubo (Univ. of Tsukuba) ∗ Global well-posedness for some two phase problem: compressible-comYoshihiro Shibata (Waseda Univ.) pressible case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
(Keio Univ.)
Kohei Soga
Summary: We consider the two phase problem for compressible and compressible case. In this talk, we shalldescribe the global well-posedness for our problem when the initial data is suﬃcient small.

Final: 2015/08/20
50

Functional Equations

14:15–15:15

Talk Invited by Functional Equations Section

Nobu Kishimoto (Kyoto Univ.)

Unconditional uniqueness of solutions for nonlinear dispersive equations

Summary: When the solution to a nonlinear evolution equation is obtained by the iteration argument using
an auxiliary function space, uniqueness of solutions in a natural space (e.g. space of continuous functions
with values in the Banach space of initial data), which we call unconditional uniqueness, becomes a nontrivial property, and to show that often requires some additional work. Recently, unconditional uniquenessfor some nonlinear dispersive equations (such as the Korteweg–de Vries equation and nonlinear Schrödinger
equations) in the periodic setting has been shown by a simple integration by parts argument, which can be
regarded as a variant of the Poincaré–Dulac normal form reduction. In this talk, we review some resultsin this direction and introduce an abstract framework, which is applicable to a wide variety of nonlinear
dispersive equations. We also give a remark on the applicability of this method in the non-periodic case.

Final: 2015/08/20
51

Real Analysis

Real Analysis
September 15th (Tue)

Conference Room IV

9:30–12:00
1 Yoshifumi Ito (Univ. of Tokushima⋆)

On the relativity of motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we study the relativity of motion. Thereby, we remake Einstein’s theory of relativity.
Here it is important that the practical physical space is the 3-dimensional Euclidean space. Therefore, wehave to use the orthogonal coordinate system in order to express Newton’s equation of motion. The relativityof motion means that we study the meaning of the diﬀerence of observed motions when we observe themotion of one point of mass by using two diﬀerent orthogonal coordinate systems. This result is very new.
(2015.5.11)
2 Yoshifumi Ito (Univ. of Tokushima⋆)

Fourier transformation of L2loc -functions. Revisited · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we study the Fourier transformation of L2loc -functions on Rd . We prove Paley–
Wiener type theorem for L2 -functions on Rd . By using this result, we prove the structure theorems for the
Fourier images of L2c and L2loc . (2015.5.21)
3 Kiyohisa Tokunaga (Yamaguchi Univ.)

A triangular double integral by the arithmetic sequence · · · · · · · · · · · · · 15

Summary: The conventional double integral is usually calculated as a repeated integral, which is inverse
diﬀerentials for respective variables, but the general procedure to directly calculate by the formula of double
limits of independent double sums for a concrete example is not known. Meanwhile, we showed the generalprocedure of double Riemann integral based on a triangular element method as a single limit at infinity of
dependent double sums to directly calculate the correct value for a concrete example. The authenticity ofthe definition formula of integral calculus is determined by the possibility of the direct calculation without
using inverse diﬀerential in the single integral for 1-variable functions. We also apply this criterion to the
double integral for 2-variable functions.
4 Shigehiro Sakata (Waseda Univ.)

Power concavity of Poisson’s integral for the upper half space · · · · · · · · 15

Summary: We study the shape of Poisson’s integral for the upper half space. In particular, we investigate
its power concavity. The aim is to give a suﬃcient condition for the uniqueness of a maximizer of Poisson’s
integral.
5 Yukio Kasahara (Hokkaido Univ.)
Akihiko Inoue (Hiroshima Univ.)
Mohsen Pourahmadi(Texas A&M Univ.)

Rigidity for matrix-valued Hardy functions · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We present a matricial generalization of the concept of rigid functions in the Hardy space H 1 ,and a spectral characterization of complete nondeterminacy for multivariate stationary processes.
6 Shin-ya Matsushita (Akita Pref. Univ.)(Akita Pref. Univ.)
Li Xu

On the best approximation problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let H be a real Hilbert space, let x ∈ H and let C, D ⊂ H be subsets. We consider the problemof finding the closest point from x to C ∩ D. This problem is called the best approximation problem and iswell known in optimization theory. When C and D are closed and convex sets, many methods for solving
this problem have been studied in [1]. In this talk, we study the best approximation problem when the set
C is an open and convex cone.

Final: 2015/08/20
52

Real Analysis

7 Toshikazu Watanabe (Nihon Univ.)
Masashi Toyoda (Tamagawa Univ.)

Some applied results of a fixed point theorem in partially ordered sets
to boundary value problems for a fractional order diﬀerential equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we apply a fixed point theorem in partial ordered sets to boundary value problems
for fractional order diﬀerential equations. We prove the existence and uniqueness of nonnegative solutionsof boundary value problems for α order diﬀerential equations where 3 < α ≤ 4. To prove our main theorem,
we use a fixed point theorem in partially ordered sets.
8 Takeshi Iida
(Fukushima Nat. Coll. of Tech.)

The Adams inequality on weighted Morrey spaces of higher order commutators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In 2013, Izumi Komori-Furuya and Sato proves the Adams type inequality on weighted Morrey
spaces for the fracional integrals under the condition Ap,q . We aim to show the similar inequality of higher
order commutators generated by BMO-functions and the fractional integral operator.
9 Hiroki Saito (Kogakuin Univ.)
Hitoshi Tanaka (Univ. of Tokyo)

Some remarks on the Kakeya maximal operator and A∗∞ weights · · · · · 15

Summary: In this talk, we shall verify the weighted Kakeya (Nikodým) maximal operator KN,w is boundedon the weighted Lebesgue space L2 (w), whenever the radial weight w satisfies the doubling and supremum
conditions. To do this, we show that all such weights w belong to A∗∞ which is slightly modified Muckenhouptweight class.
14:15–16:25
10 Denny Ivanal Hakim(Tokyo Metro. Univ.)
Yoshihiro Sawano (Tokyo Metro. Univ.)

Interpolation of closed subspaces of Morrey spaces · · · · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to consider the diﬀerence between two complex interpolation functors. As
starting spaces, we consider the closure of essentially bounded and compactly supported functions in Morrey
spaces. We shall show that two functors result in diﬀerent function spaces.
11 Denny Ivanal Hakim(Tokyo Metro. Univ.)(Ibaraki Univ.)
Eiichi Nakai
Yoshihiro Sawano (Tokyo Metro. Univ.)

Linear operators on generalized Morrey spaces · · · · · · · · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to discuss why we need to postulate various conditions on generalized
Morrey spaces when we discuss the boundedness of operators.
12 Saburou Saitoh (Gunma Univ.⋆) ♭ Generalized delta functions as generalized reproducing kernels · · · · · · · 15
Yoshihiro Sawano (Tokyo Metro. Univ.)
Summary: In this talk, we will discuss what happens when we are given an increasing sequence of reproducing
kernel Hilbert spaces. We do not assume that the increasing sequence converges. As application, we considera realization of the Dirac delta.
13 Naohito Tomita (Osaka Univ.)
Akihiko Miyachi(Tokyo Woman’s Christian Univ.)

Flag paraproducts on Hardy spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the boundedness of multilinear Fourier multiplier operators which arecalled flag paraproducts.

Final: 2015/08/20
53

Real Analysis

14 Sachiko Atsushiba(Univ. of Yamanashi)

Fixed points, attractive points and convergence theorems for nonlinear
mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study the concept of acute points of a nonlinear mapping. We also study someproperties of acute points, attractive points and fixed points. Then, we prove some weak and strong
convergence theorems for nonlinear mappings.
15 Jun Kawabe(Shinshu Univ.)

Nonadditive portmanteau theorem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We formulate a general portmanteau theorem for nonadditive measures. As its direct consequence,
it turns out that Lévy convergence of nonadditive measures coincides with every one of Choquet, Šipoš,Sugeno, and Shilkret integral functional convergence. This result is applied when discussing the metrizabilityof the Lévy topology on the space of nonadditive measures and defining the Fortet–Mourier type metrics ona uniformly equi-autocontinuous set of nonadditive measures.
16 Ryotaro Tanaka (Niigata Univ.)

A new extremal structure in Banach spaces and its application · · · · · · 15

Summary: In this talk, we introduce the notion of the frame of the unit ball of a Banach space as a
new extremal structure. Some basic properties of frames of unit balls are given. Moreover, we consider
application of frames of unit balls to Tingley’s problem.
17 Hiroyasu Mizuguchi (Niigata Univ.)
Kichi-Suke Saito (Niigata Univ.)

On the upper bound of geometric constants in absolute normalized
normed spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the space R2 with a absolute normalized norm ∥ · ∥ψ . We treat the von Neumann–
Jordan constant, the modified von Neumann–Jordan constant and the Zbăganu constant. For each absolutenormalized norm, the upper bound of the von Neumann–Jordan constant in the space (R2 , ∥ · ∥ψ ) had beenobtained. We consider the conditions in which these constant coincide with the upper bound.
16:40–17:40

Talk Invited by Real Analysis Section

Kichi-Suke Saito (Niigata Univ.) ∗ Recent development on geometric structure of Banach spaces
Summary: Since 2000, we have a series of papers about geometrical structure of Banach spaces using thenotion of absolute norms. In particular, we characterized geometric properties of Banach spaces, for example,
strict convexity, uniform convexity and so on. Further, we presented new notions of geometric propertiesof Banach spaces using ψ-direct sums of Banach spaces. On the other hand, we have several geometricconstants of Banach spaces which are important to study the theory of Banach spaces. For example, we try
to calculate von Neumann–Jordan constant, James constant and so on. Our aim in this talk is to present
the recent development of our works.

September 16th (Wed)Conference Room IV

9:15–12:00
18 Noriaki Yoshino (Tokyo Univ. of Sci.)

An operator-theoretic approach using the Yosida approximation to aquasilinear degenerate chemotaxis system of parabolic-elliptic type · · · 15

Summary: This talk is concerned with existence of weak solutions to a quasilinear degenerate chemotaxis
system of parabolic-elliptic type. In the previous meeting we reported an existence result via a linear
approximation in the diﬀusion term.
approximation.

In this talk we will propose a new approach from the Yosida

Final: 2015/08/20
54

Real Analysis

19 Kentarou Fujie (Tokyo Univ. of Sci.)
Sachiko Ishida (Tokyo Univ. of Sci.)
Akio Ito
Tomomi Yokota (Tokyo Univ. of Sci.)

Global solvability and asymptotic behavior of solutions to a chemotaxis
model for tumor invasion with nonlinear diﬀusion · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with a chemotaxis model for tumor invasion with nonlinear diﬀusion. It is shownthat a solution of the system exists globally in time and remains bounded. Moreover it is established thatthe solution approaches a certain spatially homogeneous equilibrium.
20 Alexander Leonidovich Skubachevskii(Peoples’ Friendship Univ. of Russia)
Yutaka Tsuzuki (Tokyo Univ. of Sci.)

Solvability of 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, the time T > 0 should
be extremely small and, in view of physics, this assumption is quite unnatural. The purpose of this talk is
to remove or weaken the unnatural assumption.
21 Shun Uchida (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

Periodic problem for double-diﬀusive convection system in RN with
N = 3, 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the existence of periodic solutions for some system which describes double-diﬀusive
convection phenomena in the whole space. As for the periodic problem in unbounded domains, there exist
some results for the solvability of, e.g., Navier–Stokes equations. In their arguments, it seems that thesmallness of data is nessesary to construct solutions so that fixed point theorem can be applied. On theother hand, we can find some results for the solvability of periodic problem with large data in boundeddomain. However, it is diﬃcult to remove the assumption for boundedness of domain since some properties
for compactness are used in their arguments.
In this talk, we consider the solvability of periodic problem in the whole space, especially with large data.
22 Takeshi Fukao (Kyoto Univ. of Edu.)

Convergence of Cahn–Hilliard systems to the Stefan problem with dynamic boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The well-posedness of the Stefan problem with a dynamic boundary condition is treated. To
show the existence of the weak solution, the original problem is approximated by a limit of an equationand dynamic boundary condition of Cahn–Hilliard type. By using this Cahn–Hilliard approach, it becomes
clear that the state of the mushy region of the Stefan problem is characterized by an asymptotic limit of the
fourth-order system, which has a double-well structure. This fact also raises the possibility of the numericalapplication of the Cahn–Hilliard system to the degenerate parabolic equation, of which the Stefan problem
is one.
23 Motohiro Sobajima(Tokyo Univ. of Sci.)

On the threshold for Kato’s selfadjointness problem and its Lp -generalization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk the selfadjointness problem for Schrödinger operators Au = −div(a∇u) + V u in
RN (N ∈ N) posed by Kato in 1981 and its Lp -generalization (1 < p < ∞) are dealt with. Under|a(x)| ≤ k(1 + |x|)ℓ+2 and V (x) ≥ c|x|ℓ , the precise lower bounds of c for (essential) selfadjointness in L2
and m-sectoriality in Lp of minimal and maximal realizations of A are given.

Final: 2015/08/20
55

Real Analysis

24 Kentarou Yoshii (Tokyo Univ. of Sci.)
Luisa Malaguti(Univ. of Modena and Reggio Emilia)

Nonlocal solutions of hyperbolic type equations · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider existence and uniqueness of (classical) solutions to abstract nonlocal
Cauchy problems for nonlinear evolution equations(d/dt)u(t) + A(t)u(t) = f (t) + C(t, K(t)u)g(t), t ∈ I := [0, T ];
u(0) = u + M u.
0

Here {A(t); t ∈ I} is a family of closed linear operators in the complex Hilbert space X, K(t) : C(I; Y ) → C
is linear and bounded for all t ∈ I, K(·) is continuous on I and M : C(I; Y ) → Y is a bounded linear
operator, where Y is a subspace of X.
25 Hiroshi Watanabe (Salesian Polytech.)
Ken Shirakawa (Chiba Univ.)

Asymptotic behavior of solutions to non-isothermal mathematical models of grain boundary motions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider coupled systems of heat equations and PDE models of grain boundary motions. In
this light, these systems can be regarded as interactive mathematical models of a grain boundary motions
under non-isothermal setting. In this talk, we discuss the asymptotic behavior of solutions to our systems.
26 Ken Shirakawa (Chiba Univ.)
Hiroshi Watanabe (Salesian Polytech.)
Salvador Moll (Univ. of Valencia)

Kobayashi–Warren–Carter type models with anisotropic eﬀects · · · · · · 15

Summary: In this talk, an original nonlinear system of parabolic PDEs is proposed and studied. The system isa modified version of the Kobayashi–Warren–Carter model of grain boundary motion such that the governing
free-energy includes some anisotropic eﬀects of grains. Additionally, we note that our mathematical model
enables to reproduce the dynamic changes of structural units (stable structures), caused by the rotationsof crystalline orientations. After organizing the mathematical notations and assumptions, the modelling
method of our system and the results of mathematical analysis will be presented in the conclusion part ofthis talk.
27 Noriaki Yamazaki (Kanagawa Univ.)
Tomoyuki Suzuki (Kanagawa Univ.)
Keisuke Takasao (Univ. of Tokyo)

Remarks on numerical experiments of Allen–Cahn equations with constraint via Yosida approximation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a one-dimensional Allen–Cahn equation with constraint from the view-point of
numerical analysis. Our constraint is the subdiﬀerential of the indicator function on the closed interval,
which is the multivalued function. Therefore, it is very diﬃcult to make numerical experiments of ourequation. In this talk we approximate our constraint by Yosida approximation. Then, we study theapproximating system of our original model numerically. In particular, we give the criteria for the standard
forward Euler method to give stable numerical experiments of our approximating equation. Moreover, wegive some numerical experiments of approximating equation.
14:15–15:15(Kochi Univ.)
28 Risei Kano(
Kyoto
Univ. of Edu.)
Takesi Fukao

The existence of solutions for the weak-variational inequalities by theperfect plasticity model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss that the existence of solutions for the weak-variational inequalities by theperfect plasticity model. In order to weaken the conditions of the function in constraints, we consider thevariational inequalities for weak formulation.

Final: 2015/08/20
56

Real Analysis

29 Akio Ito
Nobuyuki Kenmochi
Yusuke Murase (Meijo Univ.)

Mathematical model for brewing Japanese Sake with stirring process
and its approximated problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss a certain model for brewing process of Japanese Sake with stirring
processes. This model is the system of diﬀerential equations with stirring terms and a constraint condition.
We analyze with putting homogeneous Neumann boundary conditions and Robin boundary condition forheat equation. we will show you some mathematical results for our model and its approximated problems.
30 Kota Kumazaki(Tomakomai Nat. Coll. of Tech.)

Solvability of a mathematical model for concrete carbonation process
consisting of moisture and carbon dioxide transport · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a mathematical model describing concrete carbonation process. Thismodel consists of moisture transport and carbon dioxide transport. Moisture transport is described asa quasilinear parabolic equation with a hysteresis eﬀect between the relative humidity and the degree ofsaturation. Carbon dioxide transport is a parabolic equation considered the concentration of carbon in air
and in water. In this talk, we discuss the existence and uniqueness of a solution of our model.
31 Naoki Sato
(Nagaoka Nat. Coll. of Tech.)
Toyohiko Aiki (Japan Women’s Univ.)

Existence theorems of periodic solutions for one dimensional free boundary problems for adsorption phenomena · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study one dimensional free-boundary problem for adsorption phenomenon in wet-dry process
on the surface of porous medium like paper. We consider a pore in the porous medium. Water-drop
will be generated in the pore if humidity becomes high. The boundary of the domain of water-drop
is a free boundary in time. We make mathematical model of this phenomenon as one dimensional freeboundary problem.Our main aim is to investigate the relation between a degree of saturation and humidity,
numerically. Because there is no quantitive result. In this talk, we introduce some results with respect to theexistence of a periodic solution in time for our problem. At first, we show solvability of Cauchy problems.
Next, using Schauder’s fixed point theorem, we get solvability of our periodic problem.
15:30–16:30

Talk Invited by Real Analysis Section

Sachiko Ishida (Tokyo Univ. of Sci.)

Mathematical analysis of chemotaxis-Navier–Stokes systems and related
modelsSummary: We would like to deal with chemotaxis-Navier–Stokes systems and fully parabolic Keller–Segelsystems. It is well known that Keller–Segel systems describe a part of the life cycle of cellular slime
molds with the chemotaxis. In more detail, slime molds move towards higher concentration of the chemical
substance when they plunge into hunger. The magnitude relation between the diﬀusion term and theaggregation term divides the solutions exist globally or blow up. We will introduce this result on thesystems with degenerate diﬀusion. We recently considered the chemotaxis-Navier–Stokes systems withposition dependent sensitivity which see that the bacteria cells swim in an incompressible fluid. We obtain
the results about global existence and boundedness on both degenerate and linear diﬀusion case, andmoreover, we try to have the stabilization of a solution.

Final: 2015/08/20
57

Functional Analysis

Functional Analysis
September 13th (Sun)

Conference Room VIII

14:30–16:30
1 Toshinao Kagawa (Tokyo City Univ.)

The Hermite function expansions of the Heaviside function · · · · · · · · · · 15

Summary: The aim of this talk is to give the examples of the Hermite function expansions of the tempered
disributions. We calculate the coeﬃcients of the Hermite function expansions of the Heaviside function,11x±i0 , the signum sgn(x) and the principal value p.v. x .

2 Toshinao Kagawa (Tokyo City Univ.)
Yasuyuki Oka(Kushiro Nat. Coll. of Tech.)

A characterization of the generalized functions via the special Hermite
expansions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to give the correspondence between the dual space of the Gel’fand–Shilov
space (S type) and the sequence with the exponential decreasing decay, and the dual space of the Gel’fand–Shilov space and the sequence space with the exponential increasing decay by means of the special Hermite
functions.
3 Kiyoomi Kataoka (Univ. of Tokyo) ∗ Micro local energy forms of Sobolev type for hyperfunctions with real
Kaito Yamasaki (Tokyo Shuppan Co.) analytic parameters and some applications · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We introduce some bilinear forms for hyperfunctions with real analytic parameters, which permit
energy estimates including 0-th order analytic pseudo-diﬀerential operators. We give some applications tomicro local analytic hypo-ellipticities of pseudo-diﬀerential equations.
4 Koichi Taniguchi (Chuo Univ.) ∗ Lp -boundedness of functions of Schrödinger operators · · · · · · · · · · · · · · 15
Tsukasa Iwabuchi (Osaka City Univ.)
Tokio Matsuyama (Chuo Univ.)
Summary: Let H = −∆ + V be a Schrödinger operator on an arbitrary open set Ω ⊂ Rd (d ≥ 3), where ∆is the Dirichlet Laplacian and the potential V belongs to the Kato class on Ω. The purpose of this paper is
to show Lp –boundedness of an operator φ(H) for any rapidly decreasing function φ on R. φ(H) is definedby the spectral resolution theorem. As a by-product, Lp –Lq –estimates for φ(H) are also obtained.
5 Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)
Yoshinori Kametaka (Osaka Univ.)
Atsushi Nagai (Nihon Univ.)

The best constant of Sobolev inequality corresponding to a bending
problem of a beam with periodic boundary condition · · · · · · · · · · · · · · · 15

Summary: We consider 2-point boundary value problem for 4-th order linear ordinary diﬀerential equation
which represents bending of a beam on an elastic foundation under a tension. We here treat the periodic
boundary condition. Green function is the reproducing kernel for suitable set of Hilbert space and innerproduct. As an application, the best constants of the corresponding Sobolev inequalities are expressed as
the maximum of the diagonal values of Green function.
6 Hiroaki Niikuni(Maebashi Inst. of Tech.)

Spectral structure of periodic Schrödinger operators with two potentials
on the degenerate zigzag nanotubes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study the spectra of periodic Schrödinger operators with two potentials on aquantum graph, which is related to a carbon nanotube. We show that the spectrum has the band structure.
Furthermore, we deal with a coexistence problem and see the diﬀerence between one-potential case andtwo-potentials case.

Final: 2015/08/20
58

Functional Analysis

7 Takeru Hidaka (Kyushu Univ.)
Fumio Hiroshima (Kyushu Univ.)

Self-adjointness and existence of the ground state for the semi-relativistic
Pauli–Fierz model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The spinless semi-relativistic Pauli–Fierz HamiltonianH=√(p ⊗ 1 − A)2 + M 2 + V ⊗ 1 + 1 ⊗ Hf ,M ≥ 0,

in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation
field, M a rest mass of a particle, V an external potential, Hf the free hamiltonian of a Boson Fock space.
The self-adjointness and existence of the ground state of H are shown. It is emphasized that it includes thecase of M = 0.
17:00–18:00

Talk Invited by Functional Analysis Section

Mitsuteru Kadowaki(Univ. of Shiga Pref.)Spectral analysis for wave propagation in two-layered media

Summary: In this talk, we illustrate about spectral analysis for wave propagation in two-layered media. This
wave propagation is the simplest model of one which has the refracted (transmitted) waves. Our motivationis the application to scattering theory. First of all, we investigate the limit absorption principle by Mourre
method and asymptotic completeness by Lax-Phillps-Enss method. Moreover, as recent result, we report
asymptotic behavior in far field of the resolvent. This is joint work with H. Isozaki and M. Watanabe.

September 14th (Mon)

Conference Room VIII

9:30–12:00
8 Masatoshi Kitagawa (Univ. of Tokyo)

Classification of multiplicity-free holomorphic discrete series representations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, I will explain a classication of multiplicity-free restrictions of holomorphic discrete
series representations with respect to symmetric subgroups. Using the theory of visible actions, T. Kobayashi
gave a suﬃcient condition for multiplicity-freeness of holomorphic discrete series representations. For theclassification, I use this condition and the well-known technique called the analytic continuation. By the
analytic continuation, we can reduce the multiplicity-freeness of holomorphic discrete series representations
to the multiplicity-freeness of finite-dimensional irreducible representations.
9 Ryosuke Nakahama (Univ. of Tokyo)

Laguerre semigroups for functions on symmetric cones and the Bessel
functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently the speaker got a new integral expression of the generalized I-Bessel function on a Jordan
algebra, which was introduced by Dib, and got an upper estimate of it. In this talk the speaker presents
this result, and its application on the estimate of some 1-dimensional holomorphic semigroup, called theLaguerre semigroup.
10 Toshihisa Kubo (Univ. of Tokyo)(BICMR)
Haian He(
OklahomaState
Univ.)
Roger Zierau

On the reducible points for the generalized Verma modules · · · · · · · · · · 15

Summary: In 1980’s Enright–Howe–Wallach and Jakobsen individually classified the reducible points for
scalar generalized Verma modules induced from parabolic subalgebras with abelian nilpotent radicals, forwhich the generalized Verma modules are unitarizable. Recently, Haian He classified all the reducible points
for such scalar generalized Verma modules. In this talk we will discuss about classifying reducible points
for scalar generalized Verma modules induced from maximal parabolic subalgebras with two-step nilpotent
radicals. This is a joint work in progress with Haian He and Roger Zierau.

Final: 2015/08/20
59

Functional Analysis

11 Atsumu Sasaki(Tokai Univ.)

Remarks on visible actions on spherical nilpotent orbits · · · · · · · · · · · · · 15

Summary: In this talk, we study a choice of a slice for a compact group action on a spherical nilpotent orbit
in a complex simple Lie algebra. The main result of this talk is that one can take a slice such that its
dimension equals the rank of the spherical nilpotent orbit.
12 Hideyuki Ishi

(Nagoya Univ.) ∗ The Laplace transforms and the Legendre transforms of functions on aconvex cone · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a good situation that the Laplace transforms of powers of a positive function on aregular convex cone are equal to the negative powers of a polynomial up to constant multiple. One of ourresults gives a method to produce examples of such a cone with required functions recurrently. Based on an
observation of the recurrent relation, we conjecture that the logarithm of the Laplace transform equals thelogarithm of the reciprocal of the positive function on the cone up to constant diﬀerence.
13 Takashi Yamasaki (Kyushu Univ.) ∗ Realizing homogeneous convex cones through oriented graphs · · · · · · · · 15
Takaaki Nomura (Kyushu Univ.)
Summary: In this talk, we realize any homogeneous cone by assembling uniquely determined subcones. These
subcones are realized in the cones of positive-definite real symmetric matrices of minimal possible sizes. The
subcones are found through the oriented graphs drawn by using the data of the given homogeneous cones.
14 Tatsuya Tsurii (Osaka Pref. Univ.)
Satoe Yamanaka (Nara Women’s Univ.)
Satoshi Kawakami (Nara Univ. of Edu.)

A hypergroup arising from characters of a compact hypergroup and its
subhypergroup · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We investigate a hypergroup arising from irreducible characters of a compact hypergroup H anda subhypergroup H0 of H with |H/H0 | < ∞. The convolution of this hypergroup is introduced by inducing
irreducible representations of H0 to H and by restricting irreducible representations of H to H0 .
15 Satoe Yamanaka (Nara Women’s Univ.)
Tatsuya Tsurii (Osaka Pref. Univ.)
Satoshi Kawakami (Nara Univ. of Edu.)

A commutative hypergroup associated with a hyperfield · · · · · · · · · · · · 15

Summary: Let H be a compact commutative hypergroup of strong type and L a discrete commutative
hypergroup of strong type. We introduce a commutative hypergroup K(H, φ, L) associated with a hyperfield
φ of H based on L. Moreover for the hyperfield φ we introduce the dual hyperfield φ̂ of L̂ based on Ĥ andbshow that K(H,φ, L) ∼= K(L̂, φ̂, Ĥ).
13:30–14:30

Talk Invited by Functional Analysis Section

Sho Matsumoto (Kagoshima Univ.)

Weingarten calculus and harmonic analysis on symmetric groups

Summary: Weingarten calculus is a systematic method for computing integrals of polynomials with respect
to the Haar measures over classical compact Lie groups. The integrals are expressed as sums of so-called
Weingarten functions over permutations. The Weingarten function for the unitary group is invariant overconjugacy classes of the symmetric group, whereas the Weingarten function for the orthogonal group isinvariant over double cosets of the hyperoctahedral group. We give a connection between these Weingarten
functions and Jucys–Murphy elements, and study an asymptotic behavior of Weingarten functions by using
an enumeration of monotone factorizations of a permutation. Furthermore, we introduce a variety ofWeingarten functions associated with classical compact symmetric spaces.

Final: 2015/08/20
60

Functional Analysis

September 15th (Tue)

Conference Room VIII

9:00–12:00
16 Hiroshi Isa (Maebashi Inst. of Tech.)
Masatoshi Ito (Maebashi Inst. of Tech.)Hiroaki Tohyama(Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)

Divergences on the paths A ♮x B and A ♯x,r B · · · · · · · · · · · · · · · · · · · · · 15

Summary: Amari introduced the α-divergence and Fujii reformed it to an operator valued one. Petz gave
a divergence by DF K ≡ B − A − S(A|B), where S(A|B) is relative operator entropy and we call it Petz–
Bregman divergence. In this report, we will consider diﬀerences between two relative operator entropies as
operator valued divergences and we represent the divergences by using Petz–Bregman divergence. Moreover,
we generalize these results for expanded relative entropies and expanded operator valued divergence on thepath on power mean.
17 Yoichi Udagawa (Tokyo Univ. of Sci.)
Takeaki Yamazaki (Toyo Univ.)
Masahiro Yanagida(Tokyo Univ. of Sci.)

Some properties of weighted operator means due to Pálfia and Petz
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We shall give the dual and orthogonal of general weighted operator means due to Pálfia and Petz.
We shall also give characterizations of numerical and operator interpolational means due to J. I. Fujii.
18 Yuki Seo (Osaka Kyoiku Univ.)

On the generalized Tsallis relative operator entropy · · · · · · · · · · · · · · · · 10

Summary: In this talk, some operator inequalities related to the solidarity and the generalized Tsallis relative
operator entropy are shown. As an application, we show the Shannon type operator inequalities and its
reverse in terms of the generalized Tsallis relative operator entropy.
19 Masatoshi Fujii (Osaka Kyoiku Univ.)
Shigeru Furuichi (Nihon Univ.)
Ritsuo Nakamoto

Inequalities associated with Heron mean for positive operators · · · · · · · 15

Summary: One of authors previously gave the inequalities among arithmetic mean, geometric mean andharmonic mean for positive operators. In this talk, we give a generalized result and an improved result forthe previous result. In addition, we give a refinement of the arithmetic-geometric mean inequality under theassumption of the strict order.
20 Junichi Fujii (Osaka Kyoiku Univ.)

From Fibonacci matrix to a matrix representation for anyons · · · · · · · · 15

Summary: Considering the Fibonacci matrix, we see why the Fibonacci anyon is named after him, which isa rare observation. Moreover it leads a commutative matrix representation for general anyon in TQC via
the fusion coeﬃcient matrices, which is however not an original result.
21 Hiroyuki Osaka (Ritsumeikan Univ.)
Shuhei Wada
(Kisarazu Nat. Coll. of Tech.)
Yukihiro Tsurumi (Ritsumeikan Univ.)

Symmetric operator monotone functions and operator means · · · · · · · · 15

Summary: We give some characterizations of self-adjointness and symmetrisity of operator monotone meanst+fand show that there are many non-symmetric operator means
by using the Barbour transform f 7→ 1+f
between the harmonic mean ! and the arithmetic mean ∇. Indeed, we show that there is a non-symmetric
operator mean between any two symmetric operator means. As an application, we characterize the harmonicmean and the arithmetic mean by operator inequalities. Moreover, we characterize the parameterizedharmonic mean !λ and the prametarized arithmetic mean ∇λ .

Final: 2015/08/20
61

Functional Analysis

22 Yasuo Watatani (Kyushu Univ.) ∗ Relative position of three subspaces in a Hilbert space containig a
Masatoshi Enomoto
pentagon as a direct summand · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We study the relative position of three subspaces in a separable infinite dimensional Hilbert space.
In the finite-dimensional case, Brenner described the general position of three subspaces completely. We
extend it to a certain class of three subspaces in an infinite dimensional Hilbert space. We give a partial
result which gives a condition on a system to have a (dense) decomposition containing a pentagon.
∗
23 Kengo Matsumoto
Strongly continuous orbit equivalence of topological Markov shifts and(Joetsu Univ. of Edu.) Cuntz–Krieger algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will introduce a notion of strongly continuous orbit equivalence in one-sided topological Markov
shifts. Strongly continuous orbit equivalence yields a topological conjugacy between their two-sided topological Markov shifts (X̄A , σ̄A ) and (X̄B , σ̄B ). We prove that one-sided topological Markov shifts (XA , σA )and (XB , σB ) are strongly continuous orbit equivalent if and only if there exists an isomorphism bewteen
the Cuntz–Krieger algebras OA and OB preserving their maximal commutative C ∗ -subalgebras C(XA ) andC(XB ) and giving cocycle conjugate gauge actions. An example of one-sided topological Markov shifts
which are strongly continuous orbit equivalent but not one-sided topologically conjugate is presented.
24 Narutaka Ozawa (Kyoto Univ.)

The Furstenberg boundary and C*-simplicity · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A (discrete) group G is said to be C*-simple if the reduced group C*-algebra of it is simple. I will
first explain Kalantar and Kennedy’s characterization of C*-simplicity for a group G in terms of its action
on the maximal Furstenberg boundary. Then I will talk about my result with Breuillard, Kalantar, andKennedy about examples and stable properties of C*-simple groups.
25 Kei Hasegawa (Kyushu Univ.)

K-nuclearity of amalgamated free product C∗ -algebras · · · · · · · · · · · · · · 15

Summary: We will introduce (strong) relative nuclearity for inclusions of C∗ -algebras with conditional
expectation. We will show that full and reduced amalgamated free products of unital separable nuclearC∗ -algebras are K-nuclear when the inclusions are strong relative nuclear.
26 Rui Okayasu (Osaka Kyoiku Univ.)
Narutaka Ozawa (Kyoto Univ.)
Reiji Tomatsu (Hokkaido Univ.)

Haagerup approximation property via bimodules · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a characterization of the Haagerup approximation property for a von Neumann
algebra in terms of bimodules.
14:15–16:45
27 Yusuke Isono(Kyoto Univ.)

Unique prime factorization and bicentralizer problem for a class of typeIII factors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce the class C(AO) of von Neumann algebras that particularly contains free (quantum)
group factors and free Araki–Woods factors. We show that any tensor product factor, which consists offinitely many factors in C(AO) , retains each tensor component (up to stable isomorphism). This generalizes
Ozawa–Popa’s pioneering work for free group factors and provides a new result for free Araki–Woods factors.
In order to obtain this, we show that Connes’s bicentralizer problem has a positive solution for all type III1
factors in the class C(AO) . This is joint work with C. Houdayer.
28 Reiji Tomatsu (Hokkaido Univ.)
Yoshimichi Ueda (Kyushu Univ.)

A characterization of fullness of continuous cores of free product factors· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We sketch out the proof of our recent result concerning the fullness of the continuous core of anarbitrary type III1 free product factor.

Final: 2015/08/20
62

Functional Analysis

29 Toshihiko Masuda (Kyushu Univ.)

Classification of outer actions of discrete amenable groups (G-kernels)
on injectice factors · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, I will explain an approach to classification of G-kernels on injective factors without
use of resolution groups, which is diﬀerent from Katayama–Takesaki’s approach on this problem.
30 Satoshi Goto

(Sophia Univ.)

Remarks on the flat part commuting squares · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We make two remarks on the flat part commuting squares. Some applications of the remarks are
given.
31 Kenjiro Yanagi (Yamaguchi Univ.)

On some generalized inequalities related to fidelity and trace distance· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In quantum information theory the diﬀerence between two density matrices is measured by fidelity
or trace distance.In the case of general positive matrices, we are interested in the inequalities related to
fidelity or trace distance. In this talk we give new inequality diﬀerent from the results given by Audenaert
etc.

32 Sin-Ei Takahasi(Toho Univ.)

A characterization of multipliers of a Lau algebra constructed bysemisimple commutative Banach algebras · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This is a research report about a multipliers of a Lau commutative Banach algebra. We firstly
give a necessary and suﬃcient condition for a Lau type binary operation defined by two mappings to
be an algebra-operation. Finally we give a characterization of multipliers of a Lau algebra constructedby semisimple commutative Banach algebras. This extends a characterization obtained recently by P. A.
Dabhi.
33 Toshikazu Abe (Niigata Univ.)

Algebraic structures on metric spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider metric spaces which satisfies some conditions. We introduce a binary
operation which is induced by the metric. It has a gyrocommutative gyrogroup structure which is compatible
with the metric structure.
∗
34 Keiji Izuchi
Path connected components in weighted composition operators on the(Niigata Univ. / Niigata Univ.) disk algebra with the essential operator norm. · · · · · · · · · · · · · · · · · · · · · 15
Yuko Izuchi

Summary: It is studied the structure of path connected components in the space of weighted composition
operators on the disk algebra with the essential operator norm topology. It is shown that the structures ofpath connected components with the operator norm and the essential operator norm topologies are diﬀerent.
35 Takuya Hosokawa (Ibaraki Univ.)
Kei Ji Izuchi (Niigata Univ.)
Shûichi Ohno (Nippon Inst. of Tech.)

Weighted composition operators between Hilbert spaces of analytic
functions in Hilbert–Schmidt norm topologies · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider weighted composition operators boundedly acting between two Hilbert spaces ofanalytic functions on the open unit disk, satisfying some natural hypotheses. We investigate the topologicalstructure of the space of weighted composition operators with the Hilbert–Schmidt norm topology. These
results will be involved in the investigation for the explicit cases of the classical Hardy–Hilbert space, theweighted Bergman spaces and the Dirichlet space.
17:00–18:00

Talk Invited by Functional Analysis Section
Osamu Hatori (Niigata Univ.) Isometries on substructures of function algebras and operator algebras
Summary: We discuss linear and non-linear isometries not only on Banach algebras themselves but on certain
substructures of them. In particular, we consider in the cases of spaces of functions and algebras of matrices
and operators: 1. A brief history of linear isometries including the Banach-Stone theorem; 2. Linear
isometries on function algerbas and C ∗ -algebras; 3. Isometries on general linear groups of function algebras
and unital C ∗ -algebras and their substructures. Related topics are also discussed.

Final: 2015/08/20
63

Statistics and Probability

Statistics and Probability
September 13th (Sun)

Conference Room VII

9:30–12:00
1 Naoki Kubota(Nihon Univ.)

Lower Gaussian concentration for the crossing random walk in random
potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the crossing random walk in i.i.d. nonnegative potentials on the multidimensional
cubic lattice. The travel cost from the origin to a remote point is, roughly speaking, an average over
all random walk paths connecting those points weighted by potentials. I will talk about lower Gaussianconcentration for the travel cost.
2 Masato Takei (Yokohama Nat. Univ.)

On linearly edge-reinforced random walks on the half-line · · · · · · · · · · · 10

Summary: We investigate the speed of linearly edge-reinforced random walks on the half-line. In the recurrent
case, the movement of the random walk is quite slow. On the other hand, in the transient case, the limiting
speed of the random walk is, in a sense, not aﬀected by the reinforcement parameter.
3 Yoshihiro Abe(Kyoto Univ.)

Maximum and minimum of local times for two-dimensional random
walk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, I will describe results about the maximum and the minimum of local times for thesimple random walk on the two-dimensional torus at time comparable to the cover time. These are analogues
of estimates on the two-dimensional Gaussian free fields by Bolthausen, Deuschel, and Giacomin (2001) and
Daviaud (2006), but I have diﬀerent exponents from the case of the Gaussian free field.
4 Katusi Fukuyama (Kobe Univ.) ∗ Metric discrepancy results for complex geometric progressions · · · · · · · 5
Noriyuki Kuri
(Daido Life Insurance Co.)
Summary: The law of the iterated logarithm for discrepancies of complex geometric progressions is proved.
5 Takayoshi Setokuchi(Setokuchi Roof Tile Factory Co. Ltd.)
Keizo Takashima(Okayama Univ. of Sci.)

Long-term behavior of discrepancies of irrational rotations based on
numbers having single isolated large partial quotient · · · · · · · · · · · · · · · · 15

Summary: Setokuchi and Takashima give general mathematical explanations for the occurrence of several
parabola-like hills in the behavior of discrepancies of irrational rotations having single isolated large partial
quotient, in somewhat short range of N . We extend their estimates and give some general conditions for
repetitions of hills of discrepancies. We apply our results on much larger N ’s and explain repetitions of hills
in much more longer ranges of N .
6 Yuji Hamana (Kumamoto Univ.)
Hiroyuki Matsumoto(Aoyama Gakuin Univ.)

The hitting time and the Wiener sausage of Brownian motion withconstant drift · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a fomula for the density of the first hitting time of Brownian motion with constant drift
and the asymptotic behavior of its tail probability. Moreover we obtain the explicit form of the expectedvolume of the Wiener sausage on time interval [0, t] of the Brownian motion and its large time asymptotics.
7 Yuki Suzuki(Keio Univ.) ∗ A diﬀusion process with a random potential consisting of two contracted
self-similar processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A diﬀusion process with a random potential consisting of two independent contracted self-similar
processes with diﬀerent indices for the right and the left hand sides of the origin is studied. The maximum
process and the minimum process of the process are also investigated.

Final: 2015/08/20
64

Statistics and Probability

8 Takashi Imamura (Chiba Univ.)
Tomohiro Sasamoto (Tokyo Tech)

Determinantal structures in the O’Connell–Yor directed random polymer model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the semi-discrete directed random polymer model introduced by O’Connell and Yor.
We obtain a representation for the moment generating function of the polymer partition function in termsof a determinantal measure. This measure is an extension of the probability measure of the eigenvalues for
the Gaussian Unitary Ensemble (GUE) in random matrix theory. To establish the relation, we introduce
another determinantal measure on larger degrees of freedom and consider its few properties, from which therepresentation above follows immediately.
9 Hirofumi Osada (Kyushu Univ.)
Hideki Tanemura (Chiba Univ.)

Cores of Dirichlet forms related to infinite particle systems · · · · · · · · · · 10

Summary: We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms describing
infinite systems of interacting Brownian motions. Our result includes the case that interaction among
particles is given by a pair potential of Ruelle’s class and a logarithmic pair potential treated in randommatrix theory.
10 Yu Ito

(Osaka Univ.)

Diﬀerential equations driven by rough paths: an approach via fractional
calculus · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This study is an alternative approach to the fundamental theory of rough paths on the basis of
fractional calculus. In this talk, using fractional derivatives, we formulate rough diﬀerential equations drivenby β-Hölder rough paths with β ∈ (1/3, 1/2]. As the main results of this talk, we report existence anduniqueness results of solutions to rough diﬀerential equations driven by geometric β-Hölder rough paths.
14:15–14:45
11 Hiroaki Hata (Shizuoka Univ.)

Risk-sensitive asset management with general factor models · · · · · · · · · 15

Summary: We consider risk-sensitive asset management on finite time horizon. In particular, we treat therisk seeking case. The returns and volatilities of the assets are random and aﬀected by some economic
factors, modeled as diﬀusion process. The problems become standard risk-sensitive control problems. We
derive the Hamilton–Jacobi–Bellman (HJB) equations and study these solutions. And, using solutions, weconstruct optimal strategies and optimal values.
12 Kazutoshi Yamazaki (Kansai Univ.)

Optimal double stopping of a Brownian bridge · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study optimal double stopping problems driven by a Brownian bridge. The objective is tomaximize the expected spread between the payoﬀs achieved at the two stopping times. We study several
cases where the solutions can be solved explicitly by strategies of threshold type.
15:00–16:00

Talk Invited by Statistics and Probability Section

Yuichi Shiozawa (Okayama Univ.)

Global properties of symmetric Markov processes and Dirichlet forms

Summary: We are concerned with the global path properties of symmetric Markov processes generated byregular Dirichlet forms. In particular, we characterize conservativeness and transience quantitatively bystudying the upper and lower rate functions: the upper rate function describes how far particles can gofor all suﬃciently large time, and the lower one expresses the speed of particles escaping to infinity. Ourcharacterizations relate these functions with the volume and coeﬃcient growth rates.

Final: 2015/08/20
65

Statistics and Probability

16:15–17:15

Talk Invited by Statistics and Probability Section

Fumio Hiroshima (Kyushu Univ.)

Application of Feynman–Kac type formula to quantum field theory

Summary: It is proven that Feynman–Kac type formula is useful to study quantum field theory (QFT). In thistalk we represent Feynman–Kac type formulae of the semigroups generated by various kinds of Schrödinger
operators, which include semi-relativistic Schrödinger operators with spin 1/2 and its generalizations, andwe move on discussing an application of Feynman–Kac type formula to the spectral analysis of models in
QFT. We study the so called Nelson model in this talk, which is a typical model in QFT and has beenstudied since Nelson introduced it at 1964 from mathematical point of view. The Nelson model can berealized as a self-adjoint operator in some Hilbert space. The vector associated with the bottom of thespectrum of the Nelson model is called the ground state. In this talk (1) the existence and absence of groundstate of the Nelson model on a static Lorenzian manifold, (2) the existence of a Gibbs measure associatedwith the Nelson model, (3) properties of ground state, and (4) renormalization of UV cutoﬀ are shown. It
is emphasized that the results derived by Feynman–Kac type formula are non-perturbative. Finally we also
show applications to other models in QFT, e.g., Pauli–Fierz model, semi-relativistic Pauli–Fierz model andspin-boson model.

September 14th (Mon)

Conference Room VII

9:30–11:30(Niigata Univ.)
13 Hiroki Sako
Hayato Saigo(Nagahama Inst. of Bio-Sci. and Tech.)

The arcsine law, quantum classical correspondence, and orthogonal
polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Interacting Fock space connects the study of quantum probability theory, classical randomvariables, and orthogonal polynomials. It is a pre-Hilbert space associated with creation, preservation, andannihilation processes. We prove that if three processes are asymptotically commutative, the arcsine law
arises as the “large quantum number limits.” As a corollary, it is shown that for many probability measures,asymptotic behavior of orthogonal polynomials is described by the arcsine function. A weaker form ofasymptotic commutativity provides us a discretized arcsine law.
14 Kohei Tanaka (Shinshu Univ.)
Hitoshi Motoyama(Aoyama Gakuin Univ.)

Quantum probability theory from the categorical viewpoint · · · · · · · · · 15

Summary: We introduce a concept of conditional measures in quantum measure spaces from a view pointof Gelfand duality between classical measure spaces and quantum measure spaces. We also give categoricalstructures on classical and quantum measure spaces based on Bayes’ rule, respectively.
15 Ayako Hasegawa (Ochanomizu Univ.)
Noriyoshi Sakuma (Aichi Univ. of Edu.)
Hiroaki Yoshida (Ochanomizu Univ.)

On limit spectral measures of Marchenko–Pastur limit of random matrices with dependent entries and an application of fluctuations · · · · · · 15

Summary: We shall investigate the limit of the empirical spectral measure of the sample covariance matrix
with dependent entries. The dependence that we will discuss comes from a kind of two dimensional moving
average model and is correlated across rows and columns. In this case, we will see that the empirical
spectral measure converges to a compound free Poisson law. In addition, we will discuss the fluctuation ofthis convergence from free probability, and suggest an application to statistical data analysis of time series.

Final: 2015/08/20
66

Statistics and Probability

16 Tomonori Nakatsu (Ritsumeikan Univ.)

Integration by parts formulas concerning maxima of some one-dimensional SDEs with applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall consider a one-dimensional srochastic diﬀerential equation (SDE) and deal
with discrete and continuous time maximum of the solution to the SDE. Our goal is to prove integration
by parts formulas for the discrete and continuous time maximum. In addition, the expressions and upperbounds of their probability density functions will be obtained by means of the IBP formulas.
17 Dai Taguchi (Ritsumeikan Univ.)
Hoang-Long Ngo(Hanoi Nat. Univ. of Edu.)

Approximation for non-smooth functionals of SDEs with irregular drift· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the Euler–Maruyama scheme for SDEs with irregular drift and constantdiﬀusion coeﬃcient. We establish the rate of convergence for the Euler–Maruyama scheme in order tocompute the expectation of non-smooth functionals of SDEs. We also apply our method to the study of
the weak approximation of reflected stochastic diﬀerential equations whose drift is Hölder continuous. Our
approach of proof are change of measures and the Girsanov theorem.
18 Takafumi Amaba (Ritsumeikan Univ.)
Gô Yûki (Ritsumeikan Univ.)
Dai Taguchi (Ritsumeikan Univ.)

Convergence implications via dual flow method · · · · · · · · · · · · · · · · · · · · 15n
Summary: Given a sequence of discrete time stochastic flow {Xk,l}k≤l , n ∈ N as an approximation of astochastic flow {Xs,t }s≤t on [0, +∞), we will see how the rate of convergence for their dual flows is impliednfrom the rate of convergence of {Xk,l}k≤l → {Xs,t }s≤t .
19 Kazuhiro Yoshikawa(Ritsumeikan Univ.)
Takafumi Amaba (Ritsumeikan Univ.)

SLK martingales and representations of the Virasoro algebra · · · · · · · · 10

Summary: The Loewner diﬀerential equation whose driving function is a Brownian motion is called theSchramm Loewner evolution (SLE). The random coeﬃcients of the expansion of the SLE have a hierarchyof stochastic diﬀerential equations, which induces some class of polynomials characterized by martingales.
It is known that those polynomials connect the SLE to representations of the Virasoro algebra. In this talk,
we introduce random coeﬃcients based on Loewner–Kufarev equations and martingales related with the
Kirillov–Neretin polynomials.
20 Shigeyoshi Ogawa (Ritsumeikan Univ.)
Hideaki Uemura (Aichi Univ. of Edu.)

On the derivation of noncausal function from its Haar-SFCs · · · · · · · · · 10

Summary: Let f (t, ω) be a noncausal random function. We consider the stochastic Fourier coeﬃcient with(n)respect to the orthonormal basis of Haar functions {Hk (t)} (Haar-SFC in abbr.) of f (t, ω) defined by∫1∫(n)f (t, ω)Hk (t)dWt , where dWt stands for some stochastic integral. The question whether we can0
identify the original function f (t, ω) by its Haar-SFCs arises spontaneously. We study this problem under∫
the condition that dWt is the Ogawa integral, and give an aﬃrmative answer.

Final: 2015/08/20
67

Statistics and Probability

11:30–12:00

Research Section Assembly

September 15th (Tue)

Conference Room VII

9:30–12:00
21 Tamio Koyama (Univ. of Tokyo)

Diﬀerential systems for the normalizing constant of Fisher distribution
on the special orthogonal group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss a system of diﬀerential equations for the normalizing constant of Fisher distribution
on the special orthogonal group. Especially, we explicitly give a set of linear diﬀerential operators which
generates the annihilating ideal of the normalizing constant. For applications in statistics, diﬀerential
operators annihilating the normalizing constant for the diagonal matrix are more important. We also givea new approach which obtains these operators.
22 Takahiro Suto (Tokyo Univ. of Sci.)
Kiyotaka Iki (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

An asymmetry model with m-additional parameters for square contingency tables with ordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For square contingency tables with ordered categories, this lecture proposes an asymmetry
model with m-additional parameters, which indicates (1) the generalized marginal homogeneity and (2)the structure of quasi-symmetry for cumulative probabilities.The proposed model includes a modified
palindromic symmetry model by Iki, Oda and Tomizawa (2014). Also the lecture gives the decompositionof the symmetry model using the proposed model.
23 Akira Shibuya (Tokyo Univ. of Sci.)
Kiyotaka Iki (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Generalized diagonal exponent symmetry model and its orthogonal
decomposition in square contingency tables with ordered categories · · · 15

Summary: For square contingency tables with ordered categories, we propose a generalized Tomizawa’s(1992) diagonal exponent symmetry model. Also we give the orthogonal decomposition of proposed model.
24 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 for contingency table · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For the analysis of square contingency tables with ordered categories, Tahata and Tomizawa(2010) considered the double linear diagonals-parameter symmetry model which implies the structure ofboth asymmetry with represent to the main diagonal and with respect to the reverse diagonal in the table.
The present paper proposes extended double linear diagonals-parameter symmetry model.
25 Ayaka Yagi (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

On the likelihood ratio test for mean vectors with monotone missing
data in two-sample problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the problem of testing equality of two mean vectors with k-step monotone missing
data where two data sets have the same missing pattern. The maximum likelihood estimators (MLEs)of the mean vector and the covariance matrix under the null hypothesis are derived for the two-sample
problem. Using the above results and the MLEs by Yagi and Seo (2015), we give the likelihood ratio test
statistic. Further, as with the one-sample problem by Yagi and Seo (2015), we propose the approximate
upper percentiles using linear interpolation based on complete data sets. Finally, we investigate the accuracy
and asymptotic behavior of the approximation for χ2 distribution by Monte Carlo simulation.
26 Shoichi Sasabuchi (Kyushu Univ.)

On the distributions of test statistics fot homogeneity of mean vectors
under order restrictions when the covariance matrices are unknown · · · 10
Summary: We consider the problem of testing homogeneity of multivariate normal mean vectors under order
restrictions when the covariance matrices are common but unknown. Sasabuchi, Tanaka, and Tsukamoto(2003, A.S.) and Sasabuchi (2007, Sankhya) proposed some test statistics for this problem. In thispresentation, we show some properties of the distributions of these test statistics.

Final: 2015/08/20
68

Statistics and Probability

27 Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)Two-sample tests for high-dimensional data and their optimality · · · · · 15

Summary: In this talk, we consider two-sample tests for high-dimensional data. We first give a general
high-dimensional test statistics including the Mahalanobis distance type test statistics. We give suﬃcientconditions for the test statistics to hold a consistency property and asymptotic normality. With the help of
the properties, we discuss an optimality of the test statistics for high-dimensional data. Then, we show that
the Mahalanobis distance does not always give a preferable performance for high-dimensional data.
28 Yoshihiro Suto (Waseda Univ.)

Shrinkage estimation for the autocovariance matrix of vector-valued
Gaussian stationary processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We discuss the problem of shrinkage estimation for the autocovariance matrix of a Gaussianstationary vector-valued process to improve on the usual sample autocovariance matrix with respect to themean squares error. We propose a kind of empirical Bayes estimators when the mean of the stochastic
process is zero and non-zero. We show that the shrinkage estimators dominate the usual estimators, andthe asymptotic risk diﬀerences are similar to that of scalar-valued Gaussian stationary processes.
29 Hideaki Nagahata (Waseda Univ.)(Waseda Univ.)
Yan Liu
Hirotaka Uchiyama (Waseda Univ.)
Masanobu Taniguchi (Waseda Univ.)

Discriminant and cluster analysis of high-dimensional time series data
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a class of disparities for discriminant and cluster analysis of high-dimensional timeseries analysis. Although a scale adjusted disparity function was proposed for high-dimensional i.i.d. data,
the method may not be preferable in the case when the observations are dependent. The disparity givenin this paper is based on the Mahalanobis distance with the jackknife type adjustment. We compared theerror rate of several classifier by numerical experiments. Then, the proposed disparity provides smaller
error rates. The performance is also verified by real data of companies listed with the first and second of
the Tokyo Stock Exchange. We conclude that our adjustment method of jackknife type is suitable for thediscriminant and cluster analysis of high-dimensional dependent data.
30 Yoshihiko Maesono (Kyushu Univ.)
Taku Moriyama (Kyushu Univ.)

On asymptotic representation of kernel type estimator of density ratio· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we will discuss asymptotic properties of a kernel type estimator of a density ratio. We
obtain an asymptotic representation of the estimator, which enable us to obtain an Edgeworth expansion
with remainder term o(n−1/2 ).
14:15–15:15
31 Hiroshi Takahashi (Nihon Univ.)
Ken-ichi Yoshihara(Yokohama Nat. Univ.⋆)

A note on the Bahadur representation of sample quantiles for M-dependent random variables · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In the case of independent random variables, Bahadur introduced a representation for a sample
quantile and the empirical distribution function. Following his pioneer work, many studies have been
extended the Bahadur representation. For dependence random variables, Sen obtained the first extended
result to the case of m-dependent random variables. Recently, Berkes et al. introduced the notion of weakly
M-dependent random variables, which is an extension of m-dependence. In this talk, we show that the
Bahadur representation holds for some weakly M-dependent random variables.

Final: 2015/08/20
69

Statistics and Probability

32 Teppei Ogihara (Inst. of Stat. Math.)

Maximum-likelihood-type estimation for high-frequency financial data
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study maximum-likelihood-type estimation for a parametric model of diﬀusion
processes with high-frequency observations. In particular, we focus on two problems on high-frequency
financial data analysis, which complicate the statistical analysis. The first one is observation noise. When
we model financial market by stochastic processes, some empirical facts suggest the existence of additional
noise. This observation noise is called ‘market microstructure noise’. The second one is nonsynchronous
observations. We observe security prices when transactions occur. So observation times must be diﬀerent
for diﬀerent securities. We show asymptotic properties of our estimator under these problems.
33 Koji Tsukuda (Kurume Univ.)

Estimating the large mutation parameter of the Ewens sampling formula· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In order to model partitions, the Ewens sampling formula (ESF) is sometimes used. ESF has
the parameter θ called mutation parameter. To estimate θ, the maximum likelihood estimator (MLE) isfrequently used. On the other hand, there is a simple consistent estimator Kn / log n of θ, where Kn is
the number of distinct components of the Ewens partition. If Kn is large, two estimators get dramaticallydiﬀerent values. In sush a case, it is considered that MLE still work whreas the other does not. So, let us
assume the parameter is a power function of n and show some asymptotic behaviors of Kn . Based on the
results, some simple estimators of large θ are proposed.
34 Shintaro Hashimoto (Univ. of Tsukuba)
Ken-ichi Koike (Univ. of Tsukuba)

Reference prior via α-divergence in a non-regular multi-parametric case
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In Bayesian inference, the selection of priors has been an important and much-discussed problem.
When we have little prior information, we need to consider ‘non-informative’ or ‘reference’ prior. In thistalk, we present reference prior based on α-divergence for a non-regular multi-parametric model in thepresence of nuisance parameter. As examples, we show reference priors in the case of location-scale andone-sided truncated exponential families.
15:30–16:30

Talk Invited by Statistics and Probability Section

Toshihiro Abe (Nanzan Univ.)

On some cylindrical distributions and their related topics

Summary: We propose cylindrical distributions obtained by combining the sine-skewed von Mises distribution(circular part) with the Weibull distribution (linear part). This new model, the WeiSSVM, enjoys numerous
advantages: simple normalizing constant and hence very tractable density, parameter-parsimony andinterpretability, good circular-linear dependence structure, easy random number generation thanks to
known marginal/conditional distributions, and flexibility illustrated via excellent fitting abilities. Inferential
issues, such as independence testing, can easily be tackled with our model, which we apply on a distinct
data set. We also introduce other new circular-linear models, based on the same idea, and compare theWeiSSVM with well-known densities from the literature. We conclude the talk by showing a straightforward
extension to directional-linear cylindrical distributions and by discussing future applications of our model.

Final: 2015/08/20
70

Statistics and Probability

16:40–17:40

Talk Invited by Statistics and Probability Section

Kengo Kamatani (Osaka Univ.)

Asymptotic theory of Markov chain Monte Carlo method in high-dimension

Summary: In this talk, it is demonstrated how the high-dimensional asymptotic theory (d → ∞) of Markov
chain Monte Carlo (MCMC) methods can be applied to practical Bayesian inference problems. The theory
was initially studied in quantum physics community in the late 1980s, and developed in Roberts, Gelman
and Gilks Ann. Appl. Probab. 1997. They proved that when the proposal variance of the random-walkMetropolis algorithm is O(1/d), the Markov chain has a limiting diﬀusion process. By using this, they
constructed a criterion for constructing a good MCMC methods.
This approach has been further developed in this twenty years by generalizing the target probability
distribution and by studying other MCMC/SMC algorithms. We will review some results, including eﬃcient
MCMC strategy for heavy-tailed target distributions.

September 16th (Wed)Conference Room VII

9:30–12:00
35 Yutaka Saito (Niigata Univ.)
Tamaki Tanaka (Niigata Univ.)
Syuuji Yamada (Niigata Univ.)

A generalization of some minimax inequality theorem into set-valued
maps via scalarizaion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we propose Ricceri’s theorem on Fan–Takahashi minimax inequality for set-valued
maps by using the scalarization method proposed by Kuwano, Tanaka and Yamada.
36 Satoshi Suzuki (Shimane Univ.)
Daishi Kuroiwa (Shimane Univ.)

Characterizations of the solution set for quasiconvex programming · · · 15

Summary: In convex programming, characterizations of the solution set in terms of the subdiﬀerential havebeen investigated by Mangasarian. Motivated by these results, various characterizations of the solution set
for mathematical programming have been studied extensively. In this talk, we study characterizations of thesolution set for quasiconvex programming in terms of quasi-subdiﬀerential. To the purpose, we introduce
a necessary and suﬃcient optimality condition for quasiconvex programming by quasi-subdiﬀerential. Also,
we compare our results with previous ones. Especially, we prove some of Mangasarian’s characterizations ascorollaries of our results.
37 Xiao-Nan Lu (Nagoya Univ.)
Masakazu Jimbo (Chubu Univ.)

Applications of diﬀerence families to graceful labeling of digraphs · · · · 15

Summary: Let G denote an additively written group of order v. Let A be a collection of k-subsets (base∪blocks) of G, such that each non-identity element of G appears exactly λ times in the multiset A∈A ∆A,
where ∆A = {a − a′ | a, a′ ∈ A, a ̸= a′ }. Then A is called a (v, k, λ) diﬀerence family in G. Furthermore, if
all the base blocks of A are mutually disjoint, then A is said to be a disjoint diﬀerence family. In this talk,we discuss some relations between disjoint diﬀerence families and graceful labeling of digraphs.

Final: 2015/08/20
71

Statistics and Probability

38 Shohei Satake (Nagoya Univ.)
Masanori Sawa (Kobe Univ.)
Masakazu Jimbo (Chubu Univ.)

Some results on the asymmetry of digraphs and probabilistic methods· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A graph G is asymmetric if it does not admit any nontrivial automorphism. In a paper, Erdős
and Rényi defined the asymmetry of a given graph G to be the number A(G) of deleted/added edges suchthat the resulting graph is no longer asymmetric. They showed that
A(G) ≤ [n−1](∀G ∈ Gn )2

where Gn denotes the set of all simple graphs with n vertices, and the bound is asymptotically best by using
probabilistic methods. In this talk, we propose a measure of asymmetry of directed graphs, and discuss
what an Erdős–Rényi type bound should be and whether our bound could be best asymptotically.
This is joint work with Masanori Sawa (Kobe University) and Masakazu Jimbo (Nagoya University).

39 Masanori Sawa

(Kobe Univ.)

Developing design theory for measure spaces III —Sobolev’s theorem
and its generalization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A famous theorem due to S. L. Sobolev (1962) states that, for a finite subgroup G of the orthogonalgroup O(Rd ), a G-invariant cubature formula on the unit sphere S d is exact for all polynomials of degree at
most n if and only if it is exact for all G-invariant polynomials of degree at most n. In this talk, Sobolev’s
theorem is generalized for G-invariant cubature formulas for general functional spaces, together with some
applications.
40 Masahide Kuwada(Int. Inst. for Nat. Sci.)
Yoshifumi Hyodo(Okayama Univ. of Sci./Int. Inst. for Nat. Sci.)
Hiromu Yumiba (Int. Inst. for Nat. Sci.)

Existence conditions for balanced fractional 2m factorial designs ofresolution R∗ ({1}|Ω4 ) with N < ν4 (m) · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Consider a fractional 2m factorial design with m factors each at two levels, which is derived
from a simple array (SA) of 2 symbols, where m ≥ 8, and the five-factor and higher-order interactions are
assumed to be negligible. Under these situations, if the main eﬀect is estimable, and furthermore some of
the remaining non-negligible factorial eﬀects may or may not be estimable, then a design is said to be ofresolution R∗ ({1}|Ω4 ). Using the algebraic structure of the TMDPB association scheme, we give a necessary
and suﬃcient condition for an SA to be a 2m -BFF design of resolution R∗ ({1}|Ω4 ), where the number ofassemblies is less than the number of non-negligible factorial eﬀects.
41 Kazuki Matsubara (ChuoGakuin Univ.)
Sanpei Kageyama (Tokyo Univ. of Sci.)

Pairwise additive 1-rotational BIB designs · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The existence of pairwise additive balanced incomplete block (BIB) designs has been discussedwith direct and recursive constructions in Sawa et al. (2007) and Matsubara et al. (2013). In this talk,pairwise additive 1-rotational BIB designs are proposed and some recursive methods of constructing suchdesigns are provided. It is finally shown that no ℓ PARB(v, 3, 1) exist for any ℓ ≥ 2 and v ≥ 6, and that 2
PARB(v, 2, 1) can be constructed for any v ≥ 4.

Final: 2015/08/20
72

Statistics and Probability(Kobe Univ.)
42 Satoshi Aoki
Takayuki Hibi (Osaka Univ.)
Hidefumi Ohsugi(Kwansei Gakuin Univ.)

Markov chain Monte Carlo methods for the Box–Behnken designs andcentrally symmetric configurations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider Markov chain Monte Carlo methods for calculating conditional p values of statisticalmodels for count data arising in Box–Behnken designs. The statistical model we consider is a discrete
version of the first-order model in the response surface methodology. For our models, the Markov basis, a
key notion to construct a connected Markov chain on a given sample space, is characterized as generatorsof the toric ideals for the centrally symmetric configurations of root system Dn . We show the structure of
the Gröbner bases for these cases.
43 Masatake Hirao (Aichi Pref. Univ.)

QMC design sequences generated by determinantal point processes on
the sphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The concept of QMC design is introduced by Brauchart et al. (2014). In this talk we consider aprobabilistic generation of a sequence of QMC design by using determinatal point processes (DPPs). For
example, spherical ensembles generate QMC design sequence for Sobolev space Hs (S2 ) with 1 < s < 2.
Moreover, we deal with DPPs constructed by reproducing kernel for polynomial spaces Pt (Sd ).

Final: 2015/08/20
73

Applied Mathematics

Applied Mathematics
September 13th (Sun)

Conference Room III

9:30–12:00
1 Minoru Fujimoto (Seika Science Lab.)
Kunihiko Uehara (Tezukayama Univ.)

On the Goldbach conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give an estimation of the existence density for the 2d diﬀerent primes by using a new andsimple algorithm for getting the 2d diﬀerent primes. The algorithm is a kind of the sieve method, but
the remainders are the central numbers between the 2d diﬀerent primes. We apply this algorithm to the
Goldbach conjecture and conclude that the number of cases for the Goldbach conjecture is consistent with
the Hardy–Littlewood paper.
2 Minoru Fujimoto (Seika Science Lab.)
Kunihiko Uehara (Tezukayama Univ.)

On the relation of the limit for the calculation period between the prime
factorization and the NP complete problem · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the quadratic residue problem known as an NP complete problem by way of the prime
number and show that the prime factorization for large numbers does not belong to the class P because ofa random distribution of solutions for the quadratic residue problem.
3 Nobuo Shindo

3-colors solution of the edges of all maximum plane graphs · · · · · · · · · · 10

Summary: In this paper, I prove that the edges of any maximum plane graph G are 3-colors soluble. First ofall, I prove that if graph G without any one face is 3-colors soluble, graph G is 3-colors soluble, too. Next,
we solve any one face into 3 colors. And, thirdly, we can pick up half of (f − 2) faces of graph G, whichenable the number of cases of 3-colors solution become more than doubles about each face of half of (f − 2)
faces of graph G. Lastly, at least one case remains when we consider along each face another half of (f − 2)
faces of graph G. So we can prove the main theorem of this paper.
4 Kazuhiko Ushio (Kinki Univ.)

Balanced C8 -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
C8 -foil designs and related designs.
5 Iwao Sato (Oyama Nat. Coll. of Tech.)
Hideo Mitsuhashi (Utsunomiya Univ.)
Hideaki Morita (Muroran Inst. of Tech.)

A new determinant expression for the weighted Bartholdi zeta functionof a digraph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the weighted Bartholdi zeta function of a digraph D, and give a new determinant
expression of it. Furthermore, we give a new decomposition formula for the the weighted Bartholdi zetafunction of a group covering of D. Finally, we treat a weighted L-function of D, and give a new determinant
expression of it.
6 Hiroshi Nozaki (Aichi Univ. of Edu.)

Maximizing the order of a regular graph of given valency and second
eigenvalue · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: From Alon and Boppana, and Serre, we know that for any given integer k ≥ 3 and real number√
λ < 2 k − 1, there are only finitely many k-regular graphs whose second largest eigenvalue is at most λ. In
this talk, we give the largest number of vertices of such graphs for several (k, λ).

Final: 2015/08/20
74

Applied Mathematics

7 Suh-Ryung Kim (Seoul Nat. Univ.)
Jung Yeun Lee (Seoul Nat. Univ.)(Asia Univ.)
Boram Park
Yoshio Sano (Univ. of Tsukuba)

On the competition numbers of diamond-free graphs · · · · · · · · · · · · · · · 10

Summary: In this talk, we show a new upper bound for the competition numbers of diamond-free graphs.
(Kinki Univ.)
8 Kumi Kobata
Shinsei Tazawa (Kinki Univ.⋆)
Tomoki Yamashita (Kinki Univ.)

On graphs such that both of the graph and its complement are 2connected · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is well known that the complement of a disconnected graph is connected. By this fact, it iseasy to count graphs such that both of the graph and its complement are connected. In this talk, we will
investigate the structure of graphs such that both of the graph and its complement have connectivity 1.
This result is a generalization of results due to Akiyama and Harary (1979) and Kawarabayashi, Nakamoto,Oda, Ota, Tazawa and Watanabe (2002). By examining the structure, we can count the number of suchgraphs and also the number of graphs such that both itself and its complement are 2-connected.
9 Kenta Noguchi(Keio Univ.)

Embeddings of complete graphs with every face k-gonal · · · · · · · · · · · · · 10

Summary: In this talk, we show that for any odd k, there exist infinitely many integers n such that thecomplete graph on n vertices can be embedded on some surface with every face k-gonal.
10 Jun Fujisawa(Keio Univ.)

Matching extendability of triangulations of the projective plane · · · · · · 15

Summary: A matching M of G is said to be extendable in G if M is a subset of a perfect matching of G, anda graph with at least 2m + 2 vertices in which every matching of size m is extendable is called m-extendable.
Moreover, a graph with at least 2m + 2 vertices is said to be distance d m-extendable if any matching M
with |M | = m in which the edges lie pair-wise distance at least d is extendable. In this talk we introduce
the following result: Every 5-connected triangulation of the projective plane with an even order is distance
4 m-extendable for any m.
14:15–16:20
11 Shinya Fujita (Yokohama City Univ.)
Michitaka Furuya (Tokyo Univ. of Sci.)
Reza Naserasr (Univ. Paris-Sud 11)
Kenta Ozeki(Nat. Inst. of Information/JST ERATO)

A new approach towards a conjecture on intersecting three longest paths· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 1966, T. Gallai asked whether every connected graph has a vertex that appears in all longest
paths. Since then this question has attracted much attention and many work has been done in this topic.
One important open question in this area is to ask whether any three longest paths contains a common
vertex in a connected graph. It was conjectured that the answer to this question is positive. In this paper,
we propose a new approach in view of distances among longest paths in a connected graph, and give asubstantial progress towards the conjecture along the idea.
(Nihon Univ.)
12 Akira Saito
Nawarat Ananchuen (Silpakorn Univ.)
Watcharaphong Ananchuen(Sukhothai Thammathirat Open Univ.)

Extendability of the complementary prism of a bipartite graph · · · · · · 15

Summary: The complementary prism of a graph G is the graph defined by G and its complement constructed
on a set of vertices disjoint from G by joining each corresponding vertices by an edge. Janseana andAnanchuen (2014) gave a lower bound of the extendability of the complementary prism in terms of theextendabilities of G and its complement in the case that neither G nor its complement is a bipartite graph.
In this talk, we discuss the case that G is a bipartite graph and give a sharp lower bound to the extendabilityof the complementary prism of G.

Final: 2015/08/20
75

Applied Mathematics

13 Akito Suzuki (Shinshu Univ.)
Etsuo Segawa (Tohoku Univ.)

The spectral mapping theorem and the generator of a quantum walk
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the spectral properties and asymptotic behaviour of a discrete time quantum walk in
an abstract form, which includes the Grover walk on a graph, possibly infinite. For given two Hilbert spaces
H and K, an abstract evolution U , which is a unitary operator acting on H, and its discriminant T , which
is a self-adjoint operator acting on K, are induced by a coisometry operator from H to K and a unitary
involution on H. We show a spectral mapping theorem form the discriminant T to the evolution U . We also
construct the generator H of the evolution U in terms of the discriminant T . The asymptotic behaviour ofsuch abstract quantum walks is classified in terms of the generators H.
14 Etsuo Segawa (Tohoku Univ.)
Yusuke Higuchi (Showa Univ.)

Birth eigenspace of the Grover walks on infinite trees · · · · · · · · · · · · · · · 15

Summary: It is known that any infinite trees never admit localization of the Grover walk while infinite regulartrees provide localization. We see that the derivation of the localization on the infinite tree is the overlap
between the initial state and the eigenspace which is independent of the underlying isotropic random walk.
This eigenspace is generated by infinite-length flows on the infinite tree. We suggest that the Grover walkon infinite trees is a limit of not so much the Grover walk on its n-th depth finite tree rather as a quantum
walk induced by the underlying random walk with the Dirichlet cut at the n-th depth.
15 Kaname Matsue (Inst. of Stat. Math.)
Osamu Ogurisu (Kanazawa Univ.)
Etsuo Segawa (Tohoku Univ.)

Simplicial quantum walks: construction and problems · · · · · · · · · · · · · · 15

Summary: We construct a new type of quantum walks on simplicial complexes as a natural extension of
the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks
possess linear spreading and localization as in the case of Grover walk on lattices. On the other hand, ourproposing quantum walk contains an intrinsic problem for exhibiting nontrivial behavior, which is not seenin typical quantum walks such as Grover walks on graphs.
16 Shin Harase (Ritsumeikan Univ.)
Takamitsu Kimoto(Recruit Holdings Co.)

On the SFMT pseudorandom number generators · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the 64-bit integer output sequences of the SFMT19937 pseudorandom number generator, which was developed by Saito and Matsumoto (2008). The SFMT generators are optimized under theassumption that one will mainly be using 32-bit output sequences, so that the dimensions of equidistribution
with v-bit accuuracy for 64-bit output sequences are much worse than those for 32-bit cases. We therefore
study the structure of SFMT19937 and point out its weaknesses. We also apply empirical statistical tests
to non-successive values of SFMT19937 and find that the generator fails them.
17 Momoko Hayamizu(Grad. Univ. for Adv. Stud./Inst. of Stat. Math.)
Kenji Fukumizu(Inst. of Stat. Math./Grad. Univ. for Adv. Stud.)

On minimum spanning tree-like metric spaces · · · · · · · · · · · · · · · · · · · · · 15

Summary: We attempt to shed new light on the notion of ‘tree-like’ metric spaces by focusing on an approachthat does not use the four-point condition. Our key question is: Given metric space M on n points, when
does a fully labelled positive-weighted tree T exist on the same n vertices that precisely realises M using its
shortest path metric? We introduce a fourth-point condition that is necessary and suﬃcient to ensure theexistence of T whenever each distance in M is unique, and present its connection to the minimum spanning
tree. We also discuss how to measure the goodness-of-fit of the minimum spanning tree to M , i.e., thespanning tree-likeness of M .

Final: 2015/08/20
76

Applied Mathematics

16:40–17:40

Talk Invited by Applied Mathematics Section

Haruhide Matsuda(Shibaura Inst. of Tech.)

On trees and connected factors of graphs

Summary: We’ll give a talk on a survey of trees in graphs. We mainly deal with spanning trees having someparticular properties concerning hamiltonian properties, for example, spanning trees with bounded degrees,with bounded number of leaves, or with bounded number of branch vertices. This topic is closely related
to a connected factor, in particular, a connected [1, k]-factor. For two integers a and b with a ≤ b, an[a, b]-factor is a spanning subgraph in which each vertex has degree between a and b. For an integer k ≥ 2,
a k-tree is a tree with the maximum degree at most k. Thus a graph G has a spanning k-tree if and only if
G has a connected [1, k]-factor.
We also consider the relationship between spanning trees with some properties and connected factors.

September 14th (Mon)

Conference Room III

9:15–11:45
18 Shunzi Horiguchi(Niigata Sangyo Univ.)

Expressions represented by the unevenness and curvature that compare
the convergences of expanded Halley method (Tsuchikura–Horiguchi–
Murase–Halley method) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Section 1 gives the definition of the function g(t) obtain from y = f (x). Section 2 gives theHalley method and extended Halley method (Tsuchikura–Horiguchi–Murase–Halley method). Section 3
gives expressions represented by the unevenness and curvature that compare the convergences of expanded
Halley method (Tsuchikura–Horiguchi–Murase–Halley method).
19 Shunzi Horiguchi(Niigata Sangyo Univ.)

Extensions of three types of Halley method · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Section 1 gives the definition of the function g(t) obtain from y = f (x). section 2 gives the
Newton method and extended Newton method (Tsuchikura–Horiguchi method). Section 3 gives the Halley
method and three types of extended Halley method. Section 4 gives convergences equation of the extended
Newton method and extended Halley method.
20 Takehito Yoshiki (Univ. of Tokyo)
Takashi Goda (Univ. of Tokyo)
Kosuke Suzuki (Univ. of Tokyo)

The improved order of the worst case error for α-smooth functions· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Quasi Monte Carlo(QMC) integration is one of the methods for numerical integration. We∑
approximate the integration value I(f ) of an integrable function f by the average IP (f ) = |P1 | x∈P f (x)over a finite point set P . We consider the function space Hα including functions whose mixed partial
derivatives up to order α in each variable are continuous. If we can find a point set P whose worst caseerror wce(H; P ) = supf ∈Hα ,∥f ∥Hα ≤1 |I(f ) − IP (f )| is small, the integration error for f ∈ Hα by P can besmall. Until now, the constructions of point sets satisfying wce(H; P ) ∈ O(N −α (log N )sα ) are known. In
s−1
this talk we give the existence of point sets satisfying wce(H; P ) ∈ O(N −α (log N ) 2 ), which improves theprevious result.

Final: 2015/08/20
77

Applied Mathematics

21 Josef Dick (Univ. New South Wales)
Kosuke Suzuki (Univ. of Tokyo)
Takashi Goda (Univ. of Tokyo)
Takehito Yoshiki (Univ. of Tokyo)

Construction of interlaced polynomial lattice rules achieving accelerating convergence for infinitely diﬀerentiable functions · · · · · · · · · · · · · · · · 15

Summary: We study multivariate integration over the s-dimensional unit cube in a weighted space of infinitely
diﬀerentiable functions. It is known from the recent result by Suzuki that there exists a good quasi-Monte
Carlo (QMC) rule which achieves an accelerating convergence of the worst-case error in this function space,and moreover, that this convergence behavior is independent of the dimension under a certain conditionon the weights. In this talk we provide a constructive approach to find a good QMC rule achieving
such a dimension-independent accelerating convergence of the worst-case error. Specifically we prove thatinterlaced polynomial lattice rules with an interlacing factor chosen properly depending on the number ofpoints and the weights can be constructed using a fast component-by-component algorithm to achieve adimension-independent accelerating convergence.
22 Endo(Watanabe) Takako(Ochanomizu Univ.)
Norio Konno (Yokohama Nat. Univ.)
Hideaki Obuse (Hokkaido Univ.)

Relation between two-phase quantum walk and the topological numbers· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We treat two kinds of position-dependent quantum walks (QWs) in one dimension, which isconsidered as mathematical models of topological insulator. We call the QWs, “the complete two-phase
QW” and “the two-phase QW with one defect”. Both of the models have two diﬀerent time-evolution
operators in positive and negative parts, however, the complete two-phase QW does not have defect. We
exhibit two kinds of limit theorems concerning “localization” and “the ballistic spreading” which are thecharacteristic behaviors in the long-time limit for discrete-time QWs in one dimension. The analysis isbased mainly on the generating function methods. Next, we calculate the topological invariants fromthe time-evolution operator corresponding to the two spatial regions of the complete two-phase QW. We
note that the single defect prevents to apply the discussion of topological invariants directly, however, weshow that for the two-phase QW with defect, we can argue localization at the origin from a viewpoint of
topological insulator. Then, we give the relation between the localization of the complete two-phase QW
with topological invariants in concrete cases.
23 Hideo Mitsuhashi (Utsunomiya Univ.)
Norio Konno (Yokohama Nat. Univ.)
Iwao Sato (Oyama Nat. Coll. of Tech.)

The discrete-time quaternionic quantum walk on a graph · · · · · · · · · · · 15

Summary: The quaternionic quantum walk was formulated by the first author as a generalization of discretetime quantum walks recently. We treat the right eigenvalue problem of quaternionic matrices to analysis
the spectra of its transition matrix. The way to obtain all the right eigenvalues of a quaternionic matrix is
given. From the unitary condition on the transition matrix of the quaternionic quantum walk, we deducesome properties about it. Our main results determine all the right eigenvalues of a quaternionic quantum
walk by use of those of the corresponding weighted matrix.
(Keio Univ.)
24 Katsuhiro Ota
Yoshimi Egawa (Tokyo Univ. of Sci.)
Shinya Fujita (Yokohama City Univ.)
Tadashi Sakuma (Yamagata Univ.)

A degree condition for a graph to contain disjoint cycles of the sameeven length · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We have proved that for any k ≥ 2 there exists an integer ck such that if G is a graph of orderat least ck with minimum degree at least 2k + 1, then G contains k disjoint cycles of the same even length.
The minimum degree condition is sharp because (2k − 1)K1 + mK2 has minimum degree 2k but does notcontain k disjoint even cycles. Our result is an analogue of Egawa’s result on disjoint cycles of the samelength.

Final: 2015/08/20
78

Applied Mathematics

25 Yoshimi Egawa (Tokyo Univ. of Sci.)
Michitaka Furuya (Tokyo Univ. of Sci.)
Kenta Ozeki(Nat. Inst. of Information/JST ERATO)

The existence of a path-factor without small odd paths · · · · · · · · · · · · · 15

Summary: In this talk, we research a suﬃcient condition for the existence of a {P2 , P2k+1 }-factor. We prove∑that for k ≥ 3, there exists εk > 0 such that if a graph G satisfies 0≤j≤k−1 c2j+1 (G − S) ≤ εk |S| for all
S ⊆ V (G), then G has a {P2 , P2k+1 }-factor, where ci (G − S) is the number of components C of G − X with
|V (C)| = i. On the other hand, we construct infinitely many graphs having no {P2 , P2k+1 }-factor such that∑
16k+71
16k+710≤j≤k−1 c2j+1 (G − S) ≤ 36k−40 |S| + 72k−80 for all S ⊆ V (G).
26 Kiyoshi Ando(Nat. Inst. of Information/JST ERATO)

Conditions for k-connected graphs to have a contractible edge · · · · · · · 15

Summary: An edge in a k-connected graph is said to be k-contractible if the contraction of the edge results
in a k-connected graph. Let G be a k-connected graph with k ≥ 5. Ando and Kawarabayashi proved that if
G has neither K5− nor 5K1 + P3 and δ(G) ≥ k + 1, then G has a k-contractible edge. Yang and Sun provedthat if G has no K1 + C4 and degG (u) + degG (v) ≥ 2k + 2 for any adjacent vertices u and v, then G has ak-contractible edge. We give a common extension of the above two results.
13:15–14:15

Talk Invited by Applied Mathematics Section

Hiroyuki Ochiai(Kyushu Univ. / JST CREST)

Mathematics for image synthesis

Summary: Computer graphics (CG) is increasingly transforming every aspect of image creation and processing, and is an integration of technology and science. In this talk, we introduce our mathematical approach toCG, especially for making animations directable. A part of this talk is based on an experience in the CREST
project “Mathematics for Expressive Image Synthesis” (team leader: Ken Anjyo) approved by “Alliancefor breakthrough between mathematics and sciences” (research director: Yasumasa Nishiura) supported byJST.

September 15th (Tue)
9:30–11:55

Conference Room III

Special Session “Quantum walk and its related topics”

Norio Konno (Yokohama Nat. Univ.)

Mathematical structure of the quantum walk · · · · · · · · · · · · · · · · · · · · · · 45

Summary: The quantum walk is a quantum version of the classical random walk and has been largely
investigated for the last decade. The striking property of the quantum walk is the spreading property of
the walker. The standard deviation of the walker’s position grows linearly in time, quadratically faster thanclassical random walk, i.e., ballistic spreading. On the other hand, a walker stays at the starting position:
localization occurs. Interestingly, a quantum walker has both ballistic spreading and localization. A new
type of limit theorems explains this property. In this talk, we give a brief review of the quantum walk froma mathematical point of view.

Final: 2015/08/20
79

Applied Mathematics

Yutaka Shikano(Inst. for Molecular Sci./Chapman Univ./Tokyo Tech)

Discrete time quantum walk and quantum dynamical simulation · · · · · 45

Summary: Discrete-time quantum walks (DTQWs) are defined as quantum-mechanical analogues of classicalrandom walks. The concept of DTQWs was first considered by Feynman and then introduced in greater
generality by Gudder, Aharonov et al, Meyer, Ambainis et al. They have been realized experimentallyin various physical systems and are important in many fields, from fundamental quantum physics toquantum algorithm and condensed matter physics. It has been shown that several DTQWs on a line
admit a continuous limit identical to the propagation equations of a massive Dirac fermion and those of
massless Dirac fermion equations. Furthermore, the relationship between DTQWs and artificial electric andgravitational fields has been shown. Thus, DTQWs can be regarded as quantum dynamical simulators.
In this talk, I would like to introduce the physical implementation of DTQWs and the relationship between
the DTQWs and the quantum dynamical simulators.
Hideaki Obuse (Hokkaido Univ.)

Quantum walk meets topological insulators · · · · · · · · · · · · · · · · · · · · · · · · 45

Summary: A quantum walk (QW) describes quantum dynamics of particles, which corresponds to theclassical random walk when quantumness is lost. One of remarkable properties of QWs is localization whichstates that a probability to find walkers at an initial position in the infinite time limit is kept to be finite.
Since localization of QWs had been mathematically identified on the two-dimensional QW in 2004 first time,
this phenomenon has been intensively studied. So far, it is mathematically clarified that localization occurs
even in the one-dimensional QW on a half line or a spatially inhomogeneous QW.
Recently, localization of QWs has attracted attentions from a quite diﬀerent direction, that is, topologicalinsulators. The topological insulator is new topological states of quantum matter, which have been oneof the central research issues in the condensed matter physics since a discovery of the corresponding newmaterial in 2005, though the first (rather old) example of topological insulators is the integer quantum
Hall insulator found in 1980. The wave function of these new materials exhibits a finite integer (or Z2 )topological number. When the topological number is discontinuously varied in space, i.e., by attaching twomaterials whose topological numbers are diﬀerent or exposing the material in vacuum whose topologicalnumber is zero, there appear surface states localized near the interface. Now, it gets to understand thatseveral examples of localization of QWs can be related to the surface states of topological insulators.
In this talk, I will explain the relation between localization of QWs and the topological insulator and present
recent developments in this direction.
14:15–17:25
27 Ippei Obayashi (Tohoku Univ.)
Marcio Gameiro (Univ. de São Paulo)
Yasuaki Hiraoka (Tohoku Univ.)

Continuation of point clouds via persistence diagrams · · · · · · · · · · · · · · 15

Summary: In this talk, we present a mathematical and algorithmic framework for the continuation of point
clouds by persistence diagrams. The persistence diagram represents homological information of an input
point cloud (a coordinate data of finite points in a Euclidean space). This framework solves the inverse
problem from persistence diagrams to point cloud data by deforming the point cloud data.
28 Genki Kusano (Tohoku Univ.)
Yasuaki Hiraoka (Tohoku Univ.)
Kenji Fukumizu (Inst. of Stat. Math.)

Kernel function on persistence diagrams · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Persistent homology and its application to topological data analysis for the actual data are studied
in recent years. However, a study of statistical data analysis using persistent homology is developing.
Here, we apply kernel methods, which are widely used in machine learning, for persistence diagrams, a
representation of persistent homology. In this talk, we construct a kernel function on persistence diagrams
and show the stability theorem for the kernel function.

Final: 2015/08/20
80

Applied Mathematics

29 Akane Kawaharada (Univ. of Shizuoka)

Fractal feature analysis of the patterns created by 2D cellular automata· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we study fractal feature analysis of the spatio-temporal patterns created by thesymmetric two-dimensional elementary cellular automata. We find that six patterns of all spatio-temporal
patterns are represented by Lebesgue’s singular function, which is a self-aﬃne map. The relation among thesix patterns are also discussed.
30 Kaname Matsue (Inst. of Stat. Math.)

Slow shadowing: an eﬀective technique for tracing trajectories near slow
manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We provide an eﬀective tracing method for computing trajectories near slow manifolds in fast-slow
systems. Our method is based on a topological tool called covering relations. The result leads to an analogueof shadowing lemma in fast-slow systems. This technique not only prove the existence of trajectories nearslow manifolds but also gives us easy implementations for validating such trajectories in a wide range, via
rigorous numerics. Our procedure is available to validate trajectories not only for suﬃciently small ϵ > 0
but all ϵ in a given half-open interval (0, ϵ0 ].
31 Shigetoshi Yazaki (Meiji Univ.)
Satoh Kentaro (Fuji Soft Incorporated)
Petr Pauš
(Meiji Univ./Czech Tech. Univ. in Prague)

Comparison study of an image segmentation by means of a direct
method and level-set method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A direct method and a level-set method of an image segmentation will be studied.
32 Tadashi Nakajima (Tokyo Denki Univ.) ∗ The duration problem of an insurer · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Kunio Nishioka (Chuo Univ.)
Sadao Sato (Tokyo Denki Univ.)
Summary: Let {X(t)} be the Lévy process which consists of a constant positive drift and a negative compound
Poisson Process whose common distribution is F . We consider that the first hitting time T0 of {X(t)} to
the negative domain. In the Lundberg model, the T0 is a ruin time of an insurer.
In this lecture, we present an exact formula of the Laplace–Fourier transform of the joint distribution of thefirst hitting time and the first hitting place[]v(x) ≡ Ex e−α T0 +i β X(T0 ) ,x ≥ 0, α ≥ 0, β ∈ R1 ,where F is a “linear combination of delta measures.”
33 Takaaki Aoki

(Kyoto Univ.)

Optimal control problem with quasi-geometric discounting revisited · · 15

Summary: In the previous paper, I characterized some dynamic aspects on dynastic utility incorporating
two-sided altruism with discrete-time OLG settings. In its extension, here I formulate the continuoustime version of the optimal control problem with quasi-geometric discounting as well as the corresponding
Hamilton–Jacobi–Bellman equation, and derive some results in a time-consistency context. Fixed points
and contraction arguments in some functional spaces are also shown.
34 Masaji Watanabe (Okayama Univ.)
Fusako Kawai (Kyoto Inst. Tech.)

Mathematical formulation for exogenous type microbial depolymerization process · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An exogenous type microbial depolymerization process is studied. A mathematical model is
described. Inverse problems for a time factor and a molecular factor are formulated. Numerical techniques
are illustrated, and numerical results are introduced.

Final: 2015/08/20
81

Applied Mathematics

35 George Miyake(Ube Nat. Coll. of Tech.)
Yuji Katsuta (Ube Nat. Coll. of Tech.)

A computational method of a tanget bifurcation set by using the bisection method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Newton method in calculations of a bifurcation set requires diﬀerential coeﬃcients of second
order, which make its dimension of diﬀerential coeﬃcients extremely large in size, consequently it is diﬃcult
to deal with the coeﬃcients. A computational algorithm using the bisection method for a bifurcation set isapplied to a tangent bifurcation of a equilibrium point.
36 Aoi Honda (Kyushu Inst. of Tech.)
Yoshiaki Okazaki(Fuzzy Logic Systems Inst.)

Inclusion-exclusion integral —Integral with respect to nonadditive monotone measure— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An integral with respect to the nonadditive monotone measure is proposed. This integral is a
generalization of the Lebesgue integral and also the Choquet integral. It has appropriate properties as anintegral and can be applicable to real data analysis.
37 Fuminori Sakaguchi (Univ. of Fukui)

Two possible relationships between rapidly converging generalized continued fractions and an integer-type algorithm for ODEs using quasiorthogonalizations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, we observe two possible relationships between rapidly converging generalized
continued fractions and an integer-type high-accuracy algorithm for linear higher-order ODEs using quasiorthogonalizations of integer-valued vectors which was proposed recently by the author and M. Hayashi.
One possible relationship is between continued fractions and numerical ratios among expansion coeﬃcients
calculated by the algorithm, where numerical ratios often coincide just with convergents of canonicalcontinued fractions of true analytical ratios. The other is an application of rapidly converging generalized
continued fractions to high-accuracy calculation of eigenvalues of diﬀerential operators by means of theinteger-type algorithm.

September 16th (Wed)Conference Room III

9:30–12:00
38 Masahiro Watari(Okinawa Nat. Coll. of Tech.)

Branching pattern models of two subtropical tree species in Okinawa
Island I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Watanabe studied the branching patterns and the subsequent elongations of Psychotria rubra andPsychotria manillensis in Okinawa Island. By using Watanabe’s results, we introduce branching patternmodels for shrub Psychotria species in Okinawa Island. We also construct a deterministic algorithm forthese branching pattern models.
39 Masahiro Watari(Okinawa Nat. Coll. of Tech.)

Branching pattern models of two subtropical tree species in Okinawa
Island II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In the previous talk entitled “Branching pattern models of two subtropical tree species in Okinawa
Island I”, we introduced branching pattern models for shrub Psychotria species in Okinawa Island. The
deterministic algorithm was also constructed. In this talk, We determine the datum of the first, second andthird year branching pattern models for Psychotria species by applying the algorithm. For two Psychotria
species P. rubra and P. manillensis, we also compute the occurrence probabilities of them.

Final: 2015/08/20
82

Applied Mathematics

40 Ryusuke Kon (Univ. of Miyazaki)

Bifurcation of cycles in nonlinear semelparous Leslie matrix models · · 15

Summary: A species is said to be semelparous if it reproduces only once in its lifetime immediately before
death. The semelparous life cycle is known as one of the key factors generating population cycles. In orderto understand the situation that such population cycles appear stably, we establish a general method forevaluating the stability of cycles bifurcating from the extinction equilibrium point in nonlinear semelparous
Leslie matrix models. The method is established by justifying a continuation approximation method thatderives a certain Lotka-Volterra equation from a nonlinear semelparous Leslie matrix model. We also givesome applications for the general method.
41 Takeshi Gotoda (Kyoto Univ.)

Existence of enstrophy dissipating solution for 3-body problem in α
point vortex system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is considered that enstrophy dissipation in weak solutions of Euler equations are closely relatedwith the turbulence phenomena in two dimension. However, it is uncertain what kind of weak solutions
can dissipate. Under such a background, I am trying to gain such dissipating solutions by using Eulerα equations. Specially, I am studying the α-point-vortex system (α-PV) which is derived from Euler-α
equations with Delta function initial data. In 3-body problem for α-PV, enstrophy dissipating solutions havealready been constructed with assistance of numerical calculation, which is not rigorous mathematically. I
proved the existence of such dissipating solutions rigorously.
42 Yoshitaro Tanaka (Meiji Univ.)
Hirokazu Ninomiya (Meiji Univ.)
Masayasu Mimura (Meiji Univ.)

Singular limit problem in a reaction diﬀusion model for phyllotactic
formation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, manymathematical models using the theoretical inhibitory eﬀect were proposed to reproduce these phyllotactic
patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in
reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biologicalexperiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator. Then, there
arises a natural question as to how the inhibitory eﬀect can be related to the auxin. In this presentation, we
propose a reaction diﬀusion model based on auxin behavior in plant tips. The relationship between Douady
and Couder’s model and our model is shown by singular limit analysis.
43 Hirofumi Izuhara (Univ. of Miyazaki)
Kuto Kousuke(Univ. of Electro-Comm.)
Tohru Tsujikawa (Univ. of Miyazaki)

Pattern formation in a chemotaxis-growth system · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we deal with a chemotaxis-growth system which includes a nonlinear growth termwith Allee eﬀect from the viewpoint of pattern formation. We discuss global structures of stationary
solutions of the system.
44 Koichi Anada(Waseda Univ. Senior High School/Shibaura Inst. of Tech.)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)

On Type II Blow-up Solutions to a quasi-linear parabolic partial diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a quasi-linear parabolic partial diﬀerential equations which has blow-up faster than
the rate of self similar solutions. We call them “Type II blow-up solutions”. In this talk, we provide someprofile for “Type II blow-up solutions”.

Final: 2015/08/20
83

Applied Mathematics

45 Hisasi Tani

(Meiji Univ.)

Inertial eﬀect on weakly nonlinear analysis for two-phase Hele-Shaw
problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Fingering patterns, formed by a radially growing interface in a Hele-Shaw cell, are investigatedin case of taking the inertial eﬀect into consideration. Compared with the previous studies which havebeen carried out under the assumption that the eﬀect of inertia is negligible, some experimental results
suggested that it is not always negligible even for the case of the small Reynolds number. We here carryout weakly nonlinear stability analysis, and then investigate the eﬀect of inertia on the fingering patterns.
Our numerical results indicate that the inertial eﬀect stabilizes the interface and suppresses the tip-splitting
phenomena of the fingers.
46 Shigetoshi Yazaki (Meiji Univ.)
Koya Sakakibara (Univ. of Tokyo)

Structure-preserving numerical scheme for Hele-Shaw problems by themethod of fundamental solutions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The solutions to the one-phase interior or the classical Hele-Shaw problem are discretized inspace by means of the method of fundamental solutions combined with the discrete asymptotic uniform
distribution method, and then a system of ordinary diﬀerential equations is obtained, which is solved by theusual fourth order Runge–Kutta method. The one-phase interior Hele-Shaw problem has curve-shortening(CS), area-preserving (AP) and barycenter-fixed (BF) properties. Under our numerical scheme, a descrete
version of CS-, AP- and BF-properties hold, while simple boundary element method does not satisfy theseproperties in general. The one-phase exterior Hele-Shaw problem and the one-phase interior Hele-Shaw
problem with sink/source points can also be treated. In each problem, a non-trivial exact solution isconstructed and an experimental order of convergence is shown.
14:15–16:45
47 Issei Oikawa(Waseda Univ.)

On finite element solutions when triangles are almost flat · · · · · · · · · · · 15

Summary: We consider finite element solutions when triangles are almost flat. Since the maximum angle
condition is violated in this case, the convergence of them is not obvious. We will show that the solutions
converge weakly in H 1 to some function which may be completely diﬀerent from the exact solution.
48 Takiko Sasaki (Univ. of Tokyo)
Masahito Ohta (Tokyo Univ. of Sci.)

Error analysis of splitting methods for abstract Cauchy problems · · · · 15

Summary: We consider splitting methods for abstract Cauchy problems. A large number of articles are
devoted to the numerical study of splitting methods for the various PDEs. However, there are only a few
general results concerning the order of convergence. We will show that a second order convergence of aStrang type splitting scheme for abstract Cauchy problems.
49 Akitoshi Takayasu (Waseda Univ.)
Kaname Matsue (Inst. of Stat. Math.)
Takiko Sasaki (Univ. of Tokyo)
Kazuaki Tanaka (Waseda Univ.)
Makoto Mizuguchi (Waseda Univ.)
Shin’ichi Oishi (Waseda Univ.)

Verified numerical enclosure of blow-up time for ODEs · · · · · · · · · · · · · · 15

Summary: This talk is concerned with a blow-up problem of an autonomous system of ordinary diﬀerential
equations (ODEs). We introduce a numerical method for rigorously enclosing the blow-up time of solutions
to ODEs. Our method is based on the Poincaré compactification and verified numerical computations. The
method verifies whether a solution of ODEs blows-up in finite time. Then the blow-up time is enclosed in atime interval.

Final: 2015/08/20
84

Applied Mathematics

50 Yoshitaka Watanabe(Kyushu Univ. / JST CREST)

Some consideration of numerical verifications for the Kolmogorov problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows arepresented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like operator
with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial
solution. When discussing the numerical results, we consider the eﬀects of rounding errors in the floating
point computations. This is a continuation of our study that was presented in J. Comp. Appl. Math. 223(2009) 953–966.
51 Takehiko Kinoshita(Kyoto Univ. / Kyoto Univ.)
Yoshitaka Watanabe(Kyushu Univ. / JST CREST)
Mitsuhiro T. Nakao(Sasebo Nat. Coll. of Tech.)Some remarks for the solutions of Poisson equations with H 3 regularities
on the polygonal domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1052 Tomoya Kemmochi (Univ. of Tokyo)

On the discretization of an adhesive obstacle problem with a higher
order term · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider an adhesive obstacle problem with a higher order term. This problem models theshape of membranes on a ripped surface. From the view point of material science, this problem should be
simulated. However, it has many diﬃculties and thus we cannot apply conventional computational methods
straightforward. Therefore, we deal with the problem in the framework of Γ-convergence.
In this talk, we discretize the functional for this problem on the space of piecewise linear continuous functions.
We also regularize the characteristic function appearing in the adhesion term, since the characteristic function
is not diﬀerentiable. Then, we get the discretized and regularized functional. We show that this functional
Γ-converges to the original functional in the Sobolev space H 1 .
53 Yusuke Imoto (Kyushu Univ.)
Daisuke Tagami (Kyushu Univ.)

Error estimates of a time implicit particle method for the heat equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Error estimates of a time implicit particle method for the heat equation are established. The
particle method is a general class describing particle methods used practically as Smoothing Particle
Hydrodynamics. By virtue of a stability analysis based on an energy inequality by a discrete Sobolev
norm with respect to the space, the error estimates with unconditional stability are obtained if the time
discretization is implicit.
54 Xuefeng Liu(Niigata Univ.)

Verified lower eigenvalue bound for self-adjoint diﬀerential operator · · 15

Summary: For eigenvalue problems of self-adjoint diﬀerential operators, a universal framework is proposed
to give verified lower and upper bounds for their eigenvalues. In the case of the Laplacian operator, byapplying Crouzeix–Raviart finite elements, an eﬃcient algorithm is developed to bound the eigenvalues for
the Laplacian defined in 1D, 2D and 3D spaces. For eigenvalue problem of Biharmonic operator, Fujino–Morley finite element is used to give explicit lower bounds. Particularly, for nonconvex domains, for whichcase there may exist singularities of eigenfunctions around re-entrant corners, the proposed algorithm caneasily provide eigenvalue bounds.

Final: 2015/08/20
85

Applied Mathematics

55 Koya Sakakibara (Univ. of Tokyo)
Shigetoshi Yazaki (Meiji Univ.)

On the charge simulation method using dummy points and weightedaverage condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The charge simulation method is a fast numerical technique for solving potential problems. In
this talk, we investigate the charge simulation method using dummy points and weighted average condition.
By using dummy points, we can obtain invariant numerical scheme without assuming so-called zero-average
condition. Then we can add one more condition. One candidate is to assume some weighted-average
condition. We show some mathematical and numerical aspect, and apply it to other problem such as
biharmonic problem.
17:00–18:00

Talk Invited by Applied Mathematics Section

Tomoyuki Miyaji (Meiji Univ.)

A billiard problem in nonlinear and nonequilibrium problem: a computerassisted analysis

Summary: We study a system of ordinary diﬀerential equations in R4 , which is a mathematical model for
describing a two-dimensional motion of a camphor disk floating on water. The camphor disk moves as if it
is a billiard ball: it repeats a uniform motion and a reflection. Unlike an ordinary billiard ball, the camphor
disk reflects without hitting against a wall, and an angle of reflection is smaller than that of incidence.
As a result, when the domain is square, it tends to a limit cycle whose trajectory approaches each wallin turn drawing a square-like shape. Since this “billiard ball” is driven by nonlinear and nonequilibrium
phenomenon, we call it a nonequilibrium billiard ball. In this talk, we consider the case where the domain
is a rectangular and vary its aspect ratio as a bifurcation parameter. Previous studies by Mimura et al.
showed that a quasi-periodic motion and a chaotic motion can arise depending on the aspect ratio. We
apply the bifurcation theory and numerical computation to reveal why and how such a motion occurs. We
find that the key is a Hopf–Hopf bifurcation with D2 -symmetry.

Final: 2015/08/20
86

Topology

Topology
September 13th (Sun)

Conference Room V

9:50–12:00
1 Yusuke Takimura(Gakushuin Boys’ Junior High School)(Waseda Univ.)
Noboru ItoStrong and weak (1, 2, 3) homotopies on knot projections · · · · · · · · · · · 15

Summary: An image of a generic immersion from a circle into a 2-spehre is called a knot projection. It is
well-known that any two knot projections are related by a finite sequence consisting of local replacementsof knot projections of three types, called Reidemeister moves. This study introduces an equivalence relation
for knot projections called weak (1, 2, 3) homotopy, which consists of Reidemeister moves of type 1, weaktype 2, and weak type 3 and defines the first non-trivial invariant under weak (1, 2, 3) homotopy. By using
this invariant, we show that there exists an infinite number of weak (1, 2, 3) homotopy equivalence classesof knot projections. By contrast, if we choose the other variants of a triple type, all equivalence classes ofknot projections are contractible.
2 Noboru Ito(Waseda Univ.)

Based chord diagrams for spherical curves · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This study suggests the first approach for developing a frame work to produce invariants ofbase-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based
chord diagrams. A chord diagram is a configuration of paired points on a circle, while a based chord diagram
is a chord diagram having a base point. Though base-point-free invariants are considered for the framework,
using based chord diagrams is advantageous. Reidemeister moves are local replacements that consist of five
local moves: first, strong second, weak second, strong third, and weak third. Here, weak moves do notchange Seifert circles obtained by spherical curves. Our invariants not only contain a linear sum of Arnold’s
invariants but also new invariants.
3 Tomo Murao (Univ. of Tsukuba)

On the extension of a fundamental theorem in braid theory for handlebody-braids · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Trivalent braids and handlebody-braids are extensions of braids. Ishihara and Ishii proved thatthe map taking a regular neighborhood induces a one-to-one correspondence between the set of the IHequivalence classes of trivalent braids and that of the equivalence classes of handlebody-braids. Birman
proved that two braids are equivalent if and only if their presentations are related by the braid relations.
However such a theorem has not been established yet for handlebody-braids. In this talk, we show such atheorem for trivial handlebody-braids obtained from 3-braids with bind maps.
4 Masaaki Suzuki
Jae Choon Cha(Meiji Univ.)(POSTECH)

Non-meridional epimorphisms of knot groups · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show that there are infinitely many pairs of prime knots which admit non-meridional epimorphisms but do not admit meridional epimorphisms.
5 Masakazu Teragaito (Hiroshima Univ.)

Quasi-alternating links and Kauﬀman polynomials · · · · · · · · · · · · · · · · · 10

Summary: We study the relation between the maximum z-degree of Kauﬀman polynomial and the determinant for a quasi-alternating link. This gives a stronger criterion for deciding whether a non-alternating
link is quasi-alternating or not than the known criterion in terms of Q-polynomials. Also, we determine allquasi-alternating links with determinant 5.

Final: 2015/08/20
87

Topology

6 Teruaki Kitano(Soka Univ.)

The first cohomology of a knot group with C2 -coeﬃcients twisted by anSL(2; C)-representation and twisted Alexander polynomial · · · · · · · · · · 10

Summary: The first cohomology of a knot group with sl (2; C)-coeﬃcients is isomorphic to the Zariski tangent
space of the space of conjugacy classes of representations. In this talk we consider C2 -coeﬃcients cases.
Because SL(2; C) can be considered to be a subgroup of the extended group SL(2; C) ⋉ C2 , then C2 coeﬃcients cohomology can be consider as a subspace of the one with sl (2; C) ⊕ C2 . Furthermore the twisted
Alexander polynomial can be appeared as an obstruction of deformations of an irreducible representation.
7 Tetsuya Itoh

(Kyoto Univ.)

Generalized Jones–Kawamuro conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a generalization of Jones–Kawamuro conjecture, an inequality between the self-linking
number and the braid indices of closed braids, for general open books.
8 Atsushi Ishii (Univ. of Tsukuba)
Scott Carter (Univ. of South Alabama)
Masahico Saito (Univ. of South Florida)
Kokoro Tanaka (Tokyo Gakugei Univ.)

Group, quandle, and mixed (co)homologies · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A multiple conjugation quandle is a quandle with partial group operations. A multiple conjugation
quandle was introduced for colorings of a handlebody-knot, whose diagram is a diagram of a spatial trivalentgraph. We introduce homology theory for a multiple conjugation quandle. The homology theory unifies
homology theories for groups and quandles. We also introduce a cocycle invariant for handlebody-knots.
9 Kouki Sato

(Tokyo Tech)

Heegaard Floer d-invariant of 1-surgeries of (2, q)-cablings · · · · · · · · · · · 10

Summary: Heegaard Floer d-invariant (correction term) is an invariant of rational homology 3-spheres
associated with Spinc structure. In particular, the d-invariant of 1-surgeries along knots in S 3 has been
investigated as a (2Z-valued) knot concordance invariant d1 . In this talk, we give an evaluation of d1 forthe (2, q)-cable of any knot K. This evaluation does not depend on the knot type of K, and if K belongs toa certain class which contains any negative knot, then the equality holds. As a corollary, we show that therelationship between d1 and Heegaard Floer τ -invariant is very weak in general.
10 Shinya Harada(Tokyo Tech)

Hasse–Weil zeta functions of SL2 -character varieties of certain closedarithmetic hyperbolic 3 manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Hasse–Weil type zeta functions of the hyperbolic components of the SL2 -character varieties ofcertain closed arithmetic hyperbolic 3 manifolds are shown to be equal to the Dedekind zeta functions of
their trace fields under some conditions.
11 Yuichi Yamada(Univ. of Electro-Comm.)
Motoo Tange (Univ. of Tsukuba)

Four dimensional manifolds constructed by lens space surgeries · · · · · · 10

Summary: We study pairs of Dehn surgeries along distinct knots that yield the same (orientation-preservedor -reversed) lens spaces. We decide the complete list of pairs of which one is a torus knot and the other isa Type VII or VIII knot (called “knots in genus one fibered surfaces”). It consists of six sequences. This isrelated to lens spaces smoothly embedded in the connected sum of two copies of complex projective planes.
14:15–15:15

Talk Invited by Topology Section
Yuichi Nohara (Kagawa Univ.) Lagrangian fibrations on Grassmannians and mirror symmetry
Summary: Mirror symmetry is a duality between symplectic geometry on a Käler manifold X and complex
geometry on another Kähler manifolds X ∨ (and vice versa). Strominger, Yau, and Zaslow conjectured thatX ∨ can be obtained by dualizing Lagrangian torus fibers of a (special) Lagrangian fibration on X. Fukaya,
Oh, Ohta, and Ono developed Lagrangian intersection Floer theory for Lagrangian torus fibers of toric
moment maps and mirror symmetry for compact toric manifolds. In this talk we discuss Lagrangian torus
fibrations on the Grassmannian of two planes in Cn and relation to mirror symmetry.

Final: 2015/08/20
88

Topology

15:30–17:15
12 Inasa Nakamura (Univ. of Tokyo)

On addition of 1-handles with chart loops to 2-dimensional braids · · · · 10

Summary: A 2-dimensional braid over an oriented surface-knot F is presented by a graph called a chart on asurface diagram of F . We consider 2-dimensional braids obtained from addition of 1-handles equipped withchart loops. We investigate how much we can simplify such 2-dimensional braids.
13 Takahiro Oba(Tokyo Tech)

Compact Stein surfaces and braided surfaces · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Loi and Piergallini showed that any compact Stein surface is the total space of a simple branchedcovering of a 4-ball whose branch set is a positive braided surface. They also showed that the opposite is true.
Unfortunately, although the fact is well-known, little is known about how Stein structures behave towards
positive braided surfaces. In this talk, we give an infinite family of positive braided surfaces as branch setsof simple branched coverings whose total spaces are all diﬀeomorphic but admit mutually diﬀerent Steinstructures.
14 Akiko Shima
Teruo Nagase(Tokai Univ.)(Tokai Univ.⋆)

C-minimal 5-charts with four crossings · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A chart represents a surface-link in 4-space. We show that there does not exist any C-minimal
5-chart with exactly four crossings which represents a disjoint union of spheres.
15 Kenta Hayano (Hokkaido Univ.)
Noriyuki Hamada (Univ. of Tokyo)

A monodromy of a genus-3 Lefschetz pencil on the 4-torus · · · · · · · · · · 15

Summary: Smith constructed a genus-3 Lefschetz pencil on the 4-torus by taking a branched covering of asingular variety. In this talk, we will give vanishing cycles of this pencil explicitly.
(Tokyo Tech)
16 Genki Omori
Ryoma Kobayashi(Ishikawa Nat. Coll. of Tech.)

A finite generating set for the level 2 twist subgroup of the mappingclass group of a closed non-orientable surface · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We obtain a finite generating set for the level 2 twist subgroup of the mapping class group of aclosed non-orientable surface. The generating set consists of crosscap pushing maps along non-separating
two-sided simple loops and squares of Dehn twists along non-separating two-sided simple closed curves. Asan application, we calculate the first homology group of the level 2 twist subgroup for genus g ≥ 5 andg = 3.
17 Yasushi Kasahara(Kochi Univ. of Tech.)On simple closed curves and a visualization of the linerarity for mappingclass group of surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the set of simple closed curves on a surface as a subset of its mapping class groupand derive a condition equivalent to its linearity. We also apply our argument to show that an arbitrary
homomorphism of the mapping class group is injective up to center if and only if it can detect the geometricintersection among the simple closed curves.
18 Takuya Sakasai (Univ. of Tokyo)
Masaaki Suzuki (Meiji Univ.)
Shigeyuki Morita(Univ. of Tokyo⋆ / Tokyo Tech⋆)

Tautological algebra of mapping class group and representation theory· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study relations in the tautological algebra of the mapping class group by using representation
theory.

Final: 2015/08/20
89

Topology

September 14th (Mon)

Conference Room X

10:30–10:45

Presentation Ceremony for the 2015 MSJ Geometry Prize

10:50–11:50

Award Lecture for the 2015 MSJ Geometry Prize

Hiroshi Iritani(Kyoto Univ.)

Mirror symmetry for toric varities

Summary: I will explain a mirror construction for the big equivariant quantum cohomology of toric varieties
via shift operators of equivariant parameters. Shift operators in equivariant quantum cohomology havebeen introduced in the work of Braverman, Okounkov, Maulik and Pandharipande and can be regarded as
equivariant lifts of the Seidel representation. These operators naturally define a mirror Landau–Ginzburg
potential and a primitive form. I will also explain that shift operators are closely related to the Gamma
structure in quantum cohomology.
13:15–14:15

Award Lecture for the 2015 MSJ Geometry Prize

Osamu Saeki(Kyushu Univ.)

Stable maps and topology of manifolds

Summary: In this talk, we consider generic smooth maps, called stable maps, between manifolds that are
singular in general, and see how their topology and their singularities are related to the diﬀerential topologyof the manifolds over which the maps are defined. When the singularities are relatively mild, we will seethat the existence of such maps gives strong restrictions to the topology of the manifolds. We also review
the theory of singular fibers of stable maps and present its applications to the cobordism theory of maps
and manifolds together with applications to the visualization of scientific data.

September 15th (Tue)

Conference Room V

9:50–12:00
19 Hiromichi Nakayama(Aoyama Gakuin Univ.)

Surface diﬀeomorphisms with connected but not path-connected minimal sets containing arcs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Warsaw circle is obtained by joining the boundary of the closure of the graph of sin 1/x(−1/π ≤ x ≤ 1/π). It is well-known as an example of a connected but not path-connected compact set.
Inserting such components almost everywhere along the circle, we obtain the Warsaw circle with infinitely
many singular arcs, denoted by X. In 1955, Gottschalk and Hedlund introduced a minimal homeomorphismon this set. However this homeomorphism is defined only on this set. In 1991, Walker first constructeda homeomorphism of the cylinder whose minimal set is X. However, his homeomorphism cannot be adiﬀeomorphism. In this talk, we will construct a C ∞ diﬀeomorphism of the cylinder with a compact
connected but not path-connected minimal set containing arcs.
20 Takahiro Yamamoto(Kyushu Sangyo Univ.)

Cobordism group of Morse functions on surfaces with boundary · · · · · · 15

Summary: This is a joint work with Osamu Saeki. We consider Morse functions on compact manifolds
possibly with boundary, and define their admissible cobordism group, based on generic maps into the planethat are submersions near the boundary. Furthermore, we show several cobordism groups of such Morsefunctions.

Final: 2015/08/20
90

Topology

21 Naohiko Kasuya(Aoyama Gakuin Univ.)
Antonio Jose Di Scala(Politecnico di Torino)(KIAS)
Daniele Zuddas

Almost complex submanifolds in the even dimensional Euclidean spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We prove that any compact almost complex manifold (M, J) of real dimension 2m admits a
pseudo-holomorphic embedding in (R4m+2 , J ′ ) for some positive almost complex structure J ′ . Moreover,
we give a necessary and suﬃcient condition, expressed in terms of the total Chern class c(M, J), for the
existence of an embedding or an immersion in (R4m , J ′ ) for some J ′ .
22 Naohiko Kasuya(Aoyama Gakuin Univ.)
Antonio Jose Di Scala(Politecnico di Torino)(KIAS)
Daniele Zuddas

Non-Kähler complex structures on R4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct uncountably many complex structures J defined on R4 and a surjective holomorphic
map f : (R4 , J) → CP 1 such that the only singular fiber is an immersed holomorphic sphere, and the regularones are either holomorphic tori or holomorphic annuli. Such complex structures are not Kähler, can not
be covered by a single complex coordinate system and the only holomorphic functions are the constants.
23 Kouichi Yasui (Hiroshima Univ.)

Corks, exotic 4-manifolds and knot concordance · · · · · · · · · · · · · · · · · · · 15

Summary: We give a method for producing framed knots which represent homeomorphic but nondiﬀeomorphic (Stein) 4-manifolds, using corks and satellite maps. To obtain the method, we introduce
a new description of cork twists. As an application, we construct knots with the same 0-surgery which are
not concordant for any orientations. This disproves the Akbulut–Kirby conjecture given in 1978.
24 Selman Akbulut (Michigan State Univ.)
Kouichi Yasui (Hiroshima Univ.)

Contact 5-manifolds admitting open books with exotic Stein pages · · · 10

Summary: We construct a contact 5-manifold supported by infinitely many distinct open books with theidentity monodromy and pairwise exotic Stein pages (i.e. pages are pairwise homeomorphic but nondiﬀeomorphic Stein fillings of a fixed contact 3-manifold), moreover we describe a process of generatinge 3 (n ≥ 2) weinfinitely many such examples. In contrast to this result, on each of #n S 2 × S 3 and #n S 2 ×Sconstruct infinitely many open books with pairwise exotic Stein pages (and identity monodromy) supporting
mutually distinct contact structures.
25 Tomohiro Horiuchi (Chuo Univ.)
Yoshihiko Mitsumatsu (Chuo Univ.)

Reeb components of leafwise complex foliations and their symmetries· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We determine the group of leafwise holomorphic smooth automorphisms for Reeb components ofcertain type in the case of complex leaf dimension 1 and 2.
26 Atsuhide Mori (Osaka City Univ.) ∗ Contact structures and leafwise symplectic foliations · · · · · · · · · · · · · · · 15
Summary: Suppose that a 1-form α and a 2-form ω on a closed oriented (2n + 1)-manifold M satisfy
α ∧ ω n > 0. Then, putting τ = ω − dα, we say that the pair (α, τ ) is a twisted Jacobi structure. If (α, ετ )is a twisted Jacobi structure for any ε ∈ (0, 1], we say that α is an ετ -confoliation form. Suppose that thebinding N of a supporting open-book decomposition of a contact manifold M admits a non-singular closed
1-form ν such that, for a suitable contact form α of N , the half-line ν + tα (t ≥ 0) consists of ϵτ -confoliation
forms. Then we show that the half-line extends to a non-linear family of ϵτ -confoliation forms which starts
from a leafwise (almsot) symplectic foliation and goes through adapted contact forms on M .

Final: 2015/08/20
91

Topology

14:15–15:45
27 Eiichi Matsuhashi (Shimane Univ.)
Benjamin Espinoza(Univ. of Pittsburgh at Greensburg)

Arcwise increasing maps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A surjective continuous map f : [0, 1] → X is called an arcwise increasing map if for every two
closed subintervals A and B of [0, 1] such that A is a proper subset of B, f (A) is a proper subset of f (B).
A continuum X is said to admit an arcwise increasing map if there is an arcwise increasing map from [0, 1]
onto X. In this talk I will talk about a characterization of Peano continua with no free arcs using arcwise
increasing maps. Also, a characterization of dendrites that admit arcwise increasing maps are presented.
28 Huhe Han (Yokohama Nat. Univ.)
Takashi Nishimura(Yokohama Nat. Univ.)

The spherical dual transform is an isometry for spherical Wulﬀ shapes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A spherical Wulﬀ shape is the spherical counterpart of a Wulﬀ shape which is the well-known
geometric model of a crystal at equilibrium introduced by G. Wulﬀ in 1901. As same as a Wulﬀ shape,
each spherical Wulﬀ shape has its unique dual. The spherical dual transform for spherical Wulﬀ shapes
is the mapping which maps a spherical Wulﬀ shape to its spherical dual Wulﬀ shape. In this talk, it ispresented that the spherical dual transform for spherical Wulﬀ shapes is an isometry with respect to thePompeiu–Hausdorﬀ metric.
29 Takayuki Masuda (Osaka Univ.)

A gluing theorem of Lorentzian transformation groups · · · · · · · · · · · · · · 10

Summary: We introduce a new parameter, the aﬃne twist parameter for the aﬃne Lorentz deformation of a
hyperbolic surface. We show that two aﬃne Lorentz deformation can be glued by aﬃne twist parameter.
We also show that the aﬃne Lorentz deformation space can be parametrized by Margulis invariants andaﬃne twist parameters. The aﬃne twist parameter is canonically regarded as a correspondence to the
Fenchel–Nielsen twist parameter in Teichmüller theory.
30 Kenshi Ishiguro (Fukuoka Univ.)
Takahiro Koba (Fukuoka Univ.)

Modular invariants and Weyl groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The modular representations of some Weyl groups are considered. If two compact connected Liegroups are locally isomorphic, the complex representations of their Weyl groups are equivalent. However,
the integral representations need not be equivalent. Under the mod 2 reductions, we consider the structureof invariant rings for symplectic groups.
31 Yusuke Suyama (Osaka City Univ.)

Simplicial 2-spheres obtained from non-singular complete fans · · · · · · · 10

Summary: We show that a simplicial 2-sphere satisfying a certain condition is the underlying simplicial
complex of a non-singular complete fan in R3 .
32 Miho Hatanaka (Osaka City Univ.)

On the relation between root systems and facet vectors of graph associahedrons · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We can construct a simple polytope from a finite simple graph by truncating faces of a simplex.
The resulting simple polytope is called a graph associahedron, and is a Delzant polytope. We can associate atoric manifold with a finite simple graph through this construction. In this talk, we characterize a connectedfinite simple graph for which the set of facet vectors of the graph associahedron is a root system.

Final: 2015/08/20
92

Topology

33 Mikiya Masuda (Osaka City Univ.) ♭ The cohomology of regular Hessenberg varieties and representations of
Hiraku Abe
the symmetric group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Osaka City Univ./Univ. of Toronto)
Megumi Harada (McMaster Univ.)
Tatsuya Horiguchi (Osaka City Univ.)
Summary: Hessenberg varieties (in type A) are subvarieties of the full flag variety. Their geometry andtopology have been studied since the late 1980s by De Mari, Shayman, Procesi. This subject lies at theintersection of, and makes connections between, many research areas such as: geometric representation
theory, combinatorics, and algebraic geometry and topology. In this talk we consider two extreme cases: oneis regular nilpotent and the other is regular semisimple. We give an explicit description of the cohomology
ring of regular nilpotent Hessenberg varieties and then explain its relation to the cohomology ring of regularsemisimple Hessenberg varieties.
16:15–17:15
Zhi LuTalk Invited by Topology Section(Fudan Univ.)

Equivariant unitary bordism and equivariant cohomology Chern numbers

Summary: By using the universal toric genus and the Kronecker pairing of bordism and cobordism, we showthat the integral equivariant cohomology Chern numbers completely determine the equivariant geometricunitary bordism classes of closed unitary G-manifolds, which gives an aﬃrmative answer to the conjecture
posed by Guillemin–Ginzburg–Karshon in their book [Moment maps, cobordisms, and Hamiltonian group
actions. Mathematical Surveys and Monographs, 98. American Mathematical Society, Providence, RI,
2002], where G is a torus. As a further application, we also obtain a satisfactory solution of [Question (A),
§1.1, Appendix H] of the above book on unitary Hamiltonian G-manifolds. In particular, our approach canalso be applied to the study of (Z2 )k -equivariant unoriented bordism. This is a joint work with Wei Wang.

Final: 2015/08/20
93

Infinite Analysis

Infinite Analysis
September 13th (Sun)

Conference Room IV

9:30–12:00
1 Yusuke Ohkubo (Nagoya Univ.)
Hidetoshi Awata (Nagoya Univ.)
Hiroki Fujino (Nagoya Univ.)

Crystallization of the level 2 representation of the Ding–Iohara algebra· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will explain the q → 0 limit of the level 2 representation of the Ding–Iohara
algebra. We call works at this limit “crystallization” after one of the quantum groups. This specialization
also correspond to the limit from Macdonald polynomials to Hall–Littlewood polynomials. Using the theoryof Hall–Littlewood polynomials, in the crystallized case we can solve some problems. For example, we obtaina formula of the 4 point correlation function of a certain operator.
2 Takuya Matsumoto(Nagoya Univ. / Nagoya Univ.)

Quantum aﬃne algebra associated with the centrally extended Lie
superalgebra sl(2|2) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We propose a quantum aﬃne algebra associated with the centrally extended Lie superalgebrasl(2|2). This algebra plays important roles in both the gauge/gravity (AdS/CFT) correspondence and one
dimensional Hubbard model. After reviewing the physical motivations, we define the quantum aﬃne algebrain terms of the Chevalley–Serre generators. If time allows, we also discuss the Yangian degeneration when
the deformation parameter q goes to 1.
3 Kanehisa Takasaki (Kinki Univ.)
Toshio Nakatsu (Setsunan Univ.)

Open string amplitudes of topological string theory on closed vertex· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The partition function, or open string amplitude, of topological string theory on the so called“closed vertex” was calculated some ten years ago by an algebro-geometric method and the method of
topological vertex. This talk presents two results on open string amplitudes thereof. First, part of open
string amplitudes can be calculated by the method of topological vertex. Second, single-variate generating
functions of these amplitudes satisfy a q-diﬀerence equation. The result on the q-diﬀerence equation showsa similarity with the A-polynomials of knot invariants.
4 Atsuo Kuniba (Univ. of Tokyo)
Shouya Maruyama (Univ. of Tokyo)
Masato Okado (Osaka City Univ.)

Multispecies TASEP and the tetrahedron equation · · · · · · · · · · · · · · · · · 15

Summary: We identify the algorithm for constructing steady states of the n-species totally asymmetricsimple exclusion process (TASEP) on L site periodic chain by Ferrari and Martin with a composition ofb L ) in crystal base theory. Based on this connection
combinatorial R for the quantum aﬃne algebra Uq (sland the factorized form of the R matrix derived recently from the tetrahedron equation, we establish a new
matrix product formula for the steady state of the TASEP which is expressed in terms of corner transfer
matrices of the q-oscillator valued five-vertex model at q = 0.
5 Tomoki Nakanishi (Nagoya Univ.)

Quantum generalized cluster algebras and quantum dilogarithms ofhigher degrees · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Generalized cluster algebras were introduced by Chekhov and Shapiro around 2011. It has been
known since then that they are as good as ordinary cluster algebras in various aspects. In this talk I explain
how to quantize the y-variables of generalized cluster algebras using generalizations of quantum dilogarithm,
following the method of Fock and Goncharov for ordinary cluster algebras. As a byproduct we obtain ageneralized dilogarithm identity associated with any period of a quantum cluster algebra.

Final: 2015/08/20
94

Infinite Analysis

6 Takeshi Ikeda (Okayama Univ. of Sci.)
Tomoo Matsumura(Okayama Univ. of Sci.)

Pfaﬃan sum formula for the symplectic Grassmannians · · · · · · · · · · · · · 15

Summary: For the symplectic Grassmannians, we prove a closed formula for the torus equivariant Schubertclasses. More precisely, the corresponding double Schubert polynomial is expressed as a sum of Pfaﬃans
with entries written in terms of the double theta polynomials introduced by E. Wilson. The result gives
a proof to the conjecture of Wilson which states that the formula written in terms of raising operators
represents the equivariant Schubert class.
7 Takeshi Ikeda (Okayama Univ. of Sci.)
Tomoo Matsumura(Okayama Univ. of Sci.)
Hiroshi Naruse (Univ. of Yamanashi)Thomas Hudson(Pohang Univ. of Sci. and Tech.)

K-theoretic degeneracy loci of the symplectic vector bundle · · · · · · · · · 15

Summary: For a vector bundle with a symplectic structure over a smooth variety, we consider the degeneracyloci with respect to a fixed isotropic flag. We obtained an explicit formula for the structure sheaves of thedegeneracy loci in the Grothendieck group of algebraic vector bundles on the base variety. The formula iswritten as a sum of Pfaﬃans with entry given in terms of K-theoretic Segre classes of the vector bundles
involved.
14:15–15:15

Talk Invited by Infinite Analysis Special Session

Toshiro Kuwabara(Higher School of Economics)

Jet bundles on symplectic manifolds and vertex algebras

Summary: For a symplectic manifold, the Jet bundle (of its structure sheaf) is an infinite-dimensional vector
bundle equipped with a structure of a sheaf of vertex Poisson algebra, which is induced from the Poisson
algebra structure given by the symplectic form. In this talk, we discuss sheaves of (h-adic) vertex algebras
which are obtained as a deformation-quantization of the Jet bundle.

September 14th (Mon)

Conference Room IV

9:30–12:00
8 Yoshikatsu Sasaki (Hiroshima Univ.)

Weierstrass’ elliptic function solution to the autonomous limit of thestring equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we study the string equation of type (2,2n+1), which is derived from 2D gravity
theory or the string theory. We consider the equation as a 2n-th order analogue of the first Painlevé
equation, take the autonomous limit, and find its solutions concretely expressed by the Weierstrass’ elliptic
function ℘(z).
9 Hidehito Nagao (Akashi Coll. of Tech.)

The Padé approximation method applied to q-Painlevé equations · · · · 15

Summary: We study Padé approximation problems of the diﬀerential grid, related to all the q-Painlevé(1)equations of types from E6 to (A2 + A1 )(1) . Then, by solving those problems, we can derive the evolution
equations, the scalar Lax pairs and the determinant formulae of special solutions for the corresponding
q-Painlevé equations.
10 Tetsu Masuda (Aoyama Gakuin Univ.)(1)

Construction of rational solutions to the q-Sasano system of type D7· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(1)

Summary: We construct rational solutions to the q-Sasano system of type D7 . We observe that a family ofLaurent polynomials appear, which are invariant under the aciton of Weyl group of type D5 .

Final: 2015/08/20
95

Infinite Analysis

11 Masahiko Ito (Tokyo Denki Univ.)
Masatoshi Noumi (Kobe Univ.)

A generalization of the Sears–Slater transformation and elliptic Lagrange interpolation of type BCn · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will show a connection formula for the Jackson integral of type BCn in the form of a
Sears–Slater type expansion. The coeﬃcients of this expansion are expressed by certain elliptic Lagrange
interpolation functions. Analyzing basic properties of the elliptic Lagrange interpolation functions, anexplicit determinant formula is provided for a fundamental solution matrix of the associated system of
q-diﬀerence equations.
12 Satoshi Tsujimoto (Kyoto Univ.)

Exceptional Bannai–Ito polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will introduce a new exceptional orthogonal polynomial system from the Bannai–Ito polynomials through the generalized Darboux transformation.
13 Kimio Ueno

(Waseda Univ.)

Dilogarithm function and monodromy preserving deformation · · · · · · · 15

Summary: We present solutions to monodromy preserving deformation which are expressed in terms of
dilogarithm function.
(Chiba Univ.)
14 Rei Inoue
Thomas Lam (Univ. of Michigan)
Pavlo Pylyavskyy (Univ. of Minnesota)

Toric network and generalized discrete Toda lattice · · · · · · · · · · · · · · · · · 15

Summary: We introduce a family of commutative rational maps on a toric network, by using the double
aﬃne Weyl group action on the network. We show that the maps are linearized on the Jacobian variety ofthe spectral curve, and solve the initial value problem using Riemann theta functions.
15 Shinsuke Iwao (Aoyama Gakuin Univ.)
Kyo Nishiyama (Aoyama Gakuin Univ.)
Noboru Ogawa (Tokai Univ.)

The full Kostant–Toda hierarchy, totally nonnegative matrices andsingular curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will discuss the relation between the totally positive part of the iso-spectral set of classicalintegrable systems and the positive structure of singular curves. In this talk, I will deal with the specificcase of the full Kostant–Toda hierarchy.
13:00–14:00

Talk Invited by Infinite Analysis Special Session

Gen Kuroki(Tohoku Univ.)

On canonical quantization of τ -functions for Painlevé systems

Summary: Consider the Kac–Moody algebra associated to any symmetrizable generalized Cartan matrix.
Denote the lower Chevalley generators by fi (dependent variables), the coroots by αi∨ (parameter variables),(1)

and the exponentials of the fundamental weights by τi (τ -variables). These variables of type Al for
l = 1, 2, 3 are identified with the corresponding variables of the Painlevé II, IV, and V, respectively. Thenthe commutative Poisson algebra generated by these variables is naturally defined and a certain birational
Weyl group action on the Poisson algebra is also constructed. The τ -variables are the exponentials of
the canonically conjugate variables of the parameter variables. (Note that the parameter variables are
not Poisson-central.) Elements of the orbit of the τ -variables are called the classical τ -functions and are
Poisson-polynomials in the dependent variables. We shall canonically quantize this situation. We shalldefine the non-commutative algebra generated by the same (but non-commutative) variables and constructa certain birational Weyl group action on the non-commutative algebra. The quantized τ -variables commute
with the quantized dependent variables and satisfy the commutation relations τi αj∨ τi−1 = αi∨ + δij . Then
we shall obtain the quantized τ -functions as elements of the orbit of quantized τ -variables and can prove
the polynomiality of the quantized τ -functions. The main ingredients of the proof of the polynomiality are
the translation functors in the representation theory of the Kac–Moody algebra. We can generalize theseresults to the case of the quantized enveloping algebra.