Final Version: 2015/02/24“ Mathematical Society of Japan
2015 ANNUAL MEETING

Titles and Short Summaries of the Talks

March, 2015
at Meiji University

Final Version: 2015/02/24

2015 Mathematical Society of Japan
ANNUAL MEETING
Dates: March 21st (Sat)–24th (Tue), 2015
Venue: Meiji University, Suruga-dai Campus (Liberty Tower)
Kanda Suruga-dai 1–1, Chiyoda-ku, Tokyo 101-8301
Contact to: Meiji University,
School of Interdisciplinary Mathematical Sciences
Nakano 4–21–1, Nakano-ku, Tokyo 164-8523
E-mail meiji15mar?mathsoc.jp
During session:

Phone +81 (0) 90 1791 3483

Mathematical Society of Japan
Phone +81 (0) 3 3835 3483

21st
(Sat)

Ia
1021 (2F)

IIa1022 (2F)

IIIa1031 (3F)

IVa1032 (3F)Va1063 (6F)

VIa1065 (6F)

AlgebraStatistics andProbability

Geometry

Topology

Functional
AppliedEquations Mathematics

Found. of Math.
Functional
and
Analysis
History of Math.

9:30–12:00
14:15–17:00

9:30–12:00
14:15–14:45

9:50–12:00
14:15–15:40

9:30–12:00
14:15–15:30

9:15–12:00
14:15–16:30

10:00–11:25
14:15–16:50

9:50–12:00
14:30–16:00

VII
VIII
IX
1126 (12F) 1133 (13F) 1136 (13F)

10:00–12:00

RealAnalysis
9:30–12:00
14:15–16:30

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

15:00–16:00
16:15–17:15

15:50–16:50
17:00–18:00

15:45–16:45

16:50–17:50

16:10–17:10

Ib1013 (1F)

VII
VIII
IX
IIb
IIIb
IVb
Vb
VIb
1123 (12F) 1001 (B1F) 1116 (11F) 1103 (10F) 1106 (10F) 1126 (12F) 1133 (13F) 1136 (13F)

AlgebraStatistics andProbability

9:30–12:00

9:30–11:30

Geometry

Topology

Functional
AppliedEquations Mathematics

9:30–12:00
13:00–14:15

9:30–12:00

9:15–12:00

9:30–11:30
13:00–13:50

17:00–18:00

14:15–15:15

Found. of Math.
Functional
and
Analysis
History of Math.
9:30–11:40

9:30–12:00

16:40–17:40

Real
Analysis
9:30–12:00

22nd Invited Talk

Invited Talk Invited Talk

Invited Talk Invited Talk Invited Talk

(Sun) 13:15–14:15

13:15–14:15

13:15–14:15

13:15–14:15

13:15–14:15

13:15–14:15

MSJ Prizes Presentation (1013 (1F)) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:40–15:00)
Plenary Talks(1013 (1F)) MSJ Spring Prize Winner · · · · · · · · · · · · · · · · · · · · · (15:15–16:15)
M. Kapranov (Univ. of Tokyo) · · · · · · · · · · · · · · · · · (16:45–17:45)
Oﬃcial Party(Kishimoto Tatsuo HALL (23F)) · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:00–20:00)
Ib
1013 (1F)IIa1022 (2F)

IIIa1031 (3F)

IVa1032 (3F)Va1063 (6F)

VIa1065 (6F)

AlgebraStatistics andProbability

Geometry

Topology

Functional
AppliedEquations Mathematics

ComplexAnalysis

Functional
AnalysisReal
Analysis

9:30–11:45
15:45–18:30

9:30–12:00
14:15–15:15

9:45–12:00
14:15–16:45

9:30–12:00
14:15–16:45

9:30–12:00
14:15–16:00

9:30–11:45
14:15–14:45

9:30–12:00
14:15–16:00

9:30–12:00

10:00–11:30
14:30–16:00

VII
VIII
IX
1126 (12F) 1133 (13F) 1136 (13F)

23rd
(Mon)

Infinite
Analysis
14:15–15:30

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

24th
(Tue)

14:30–15:30

15:30–16:30
16:45–17:45

17:00–18:00

17:00–18:00

16:20–17:20

16:15–17:15

15:10–16:10
16:25–17:25

Ib
1013 (1F)IIa1022 (2F)

IIIa1031 (3F)

IVa1032 (3F)Va1063 (6F)

VIa1065 (6F)VII
1126 (12F)

IX
1136 (13F)

AlgebraStatistics andProbability

Geometry

Topology

Functional
AppliedEquations Mathematics

ComplexAnalysisInfinite
Analysis

9:30–12:00
14:15–15:30

9:45–12:00
14:15–15:15

9:30–12:00
14:15–15:50

9:30–12:00

9:30–11:30
14:15–15:15

9:30–11:45
14:15–15:10

9:45–11:45
14:15–15:30

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

Invited Talk

Invited Talk

Invited Talk

15:45–16:45

16:00–17:00

15:30–16:30

9:45–11:45
14:15–15:45

16:00–17:00

15:30–16:30

16:30–17:30

15:45–16:45

15:45–16:45

Final Version: 2015/02/24

Contents

Plenary Talks

1

Featured Invited Talks

1

Foundation of Mathematics and History of Mathematics

5

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8Algebra11

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

Geometry

24

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

Complex Analysis

37

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

Functional Equations

42

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Real Analysis

59

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

Final Version: 2015/02/24

Functional Analysis

67

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

Statistics and Probability

74

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

Applied Mathematics

86

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

Topology

97

March 21st (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

March 22nd (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

100

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105

Infinite Analysis

108

March 23rd (Mon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

108

March 24th (Tue) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

Final Version: 2015/02/24
1

Plenary Talks

Plenary Talks
March 22nd (Sun) 1013 (1F)MSJ Spring Prize Winner····················································(15:15–16:15)

Mikhail Kapranov (Univ. of Tokyo)

Lie algebras and secondary polytopes · · · · · · · · · · · · · · · · · · ·(16:30–17:30)

Summary: Secondary polytopes, introduced by I.M. Gelfand, A.V. Zelevinsky and the speaker more than
twnety years ago, are convex polytopes whose vertices correspond to triagulations of other, “primary”
polytopes. The original motivation for their introduction was the study of discriminants of polynomials
in several variables. The talk, based on joint work with M. Kontsevich and Y. Soibelman, will discuss acompletely diﬀerent appearance of secondary polytopes, motivated by the study of Landau-Ginzburg models
in mathematical physics. Here, secodary poylytopes give rise to Lie algebra-type structures which can beused to deform triangulated categories with exceptional collections.

Featured Invited Talks
March 21st (Sat)
Conference Room IIa
Nariyuki Minami (Keio Univ.)

Questions in energy level statistics and the theory of point
processes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: Energy level statistics is a group of questions in mathematical physics in which one is interested
in statistical nature of the fluctuation of energy levels (i.e. eigenvalues of quantum Hamiltonians), rather
than their asymptotic or average distribution. In physics literature, it seems to be tacitly assumed that the
spectrum of a quantum Hamiltonian, after suitably normalized (or unfolded), and observed in thermodynamic
or semi-classical limit, looks like a typical realization of a stationary point process on the real line. In thistalk, I will present a purely phenomenological, and somewhat personal view of energy level statistics basedon the theory of point processes.

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2

Featured Invited Talks

Conference Room IIIa
Nobuhiro Honda (Tokyo Tech)

Geometry of twistor spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Consider an oriented 4-manifold. A Riemannian metric on the 4-manifold is said to be self-dual(or half-conformally flat) if the anti-self-dual component of the Weyl curvature tensor identically vanishes.
A conformally flat metric is an important example of self-dual metrics, but the notion of self-duality makes
sense only on 4-dimensional space. This notion originally arises from general relativity in physics, and plays
an important role in gauge theory.
The most characteristic property of self-dual metric is that, there always naturally associates a complex
3-manifold, fibered over the 4-manifold with typical fiber being a 2-sphere. This complex 3-manifold is called
the twistor space, and this is the main object of this talk.
In general, it is diﬃcult to construct self-dual metrics and twistor spaces over a compact manifold. But it is
known that such self-dual metrics (and therefore their twistor spaces) exist a lot. However, most of them are
not projective-algebraic. On the other hand, there are a lot of non-projective but algebraic twistor spaces.
These spaces may be investigated by a traditional method in complex algebraic geometry; namely a linear
system, a vanishing theorem (which holds under certain positivity of the metric), and intersection numbersof subvarieties. In this talk, we would like to discuss some explicit construction and classification of such
twistor spaces.

Conference Room Va
Kenji Yajima (Gakushuin Univ.)

Meeting points of Schrödinger equation and real analysis · ·(13:00–14:00)

Summary: There are many problems in the theory of Schrödinger equation and real analysis which areclosely connected: Strichartz estimates and the restriction theorem of Fourier transform onto the parabola,smoothness of solutions and changes of phases of generalized Fourier coeﬃcients, wave operators of scattering
theory and the transplantation and etc. I will discuss some of these examples, hoping to stimulate closer
collaboration between these disciplines.

March 23rd (Mon)
Conference Room Ib
Keiko Takahashi(Japan Agency for Marine-Earth Sci. and Tech.)

Mathematical issues on weather and climate variability prediction studies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: It is known that a prediction for ten days and longer term prediction for weather and climate
variability. One of reason for those diﬃculties is considered due to non-linear characteristics such as low orhigh atmospheric pressures having space scale of approximately 1,000km. I introduce our research activities
to improve predictability for ten-days more and seasonal phenomena.

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3

Featured Invited Talks

Conference Room IVa
Mitsuhiro Shishikura (Kyoto Univ.)

Continued fractions and the renormalization of dynamicalsystems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: We discuss the relationship between continued fractions for irrational numbers and dynamicalsystems via the idea called the renormalization.
Continued fraction is a way to express an irrational number α as the limit of a sequence of rational numbers.
There is a simple algorithm which generate this approximation.
Dynamical systems are mathematical models of time evolution. In some class of dynamical systems, one cantake a subdomain of the phase space and consider the first return map. The process assigning the return map
to the original dynamics is called “renormalization” and this can be regarded as a “meta-dynamics” definedon the space of dynamical systems. It is often important to consider the iteration of the renormalization andto study its fixed points and invariant sets, and the knowledge of their properties (such as the hyperbolicity)
leads to deep understanding of individual dynamical systems, such as universal structure in the phase space
and the parameter space and the rigidity.
In this talk, we focus on several types of “rotation-like dynamics” which is similar to or related to Rα :z 7→ e2πiα z on S1 = {z ∈ C : |z| = 1}, with irrational number α. For the rigid rotation Rα , the processof renormalization coincides with the algorithm for the continued fractions. General renormalizations forrotation-like dynamics can be considered as a nonlinear and infinite dimensional version of continued fractions.
We will see how to analyze the individual system via the properties of the meta-dynamics (renormalization)and the number theoretic properties of the rotation number α.

March 24th (Tue)
Conference Room Ib
Takashi Taniguchi (Kobe Univ.)

Average rank of elliptic curves —Fields medal award by Manjul Bhargava and future prespectives— · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: In a joint work with Shankar, Bhargava showed that the average rank of elliptic curves over therational number field, when ordered by height, is less than 1 (in fact, less than .885). Moreover, they
determined the average size of 2, 3, 4 and 5-Selmer groups for those elliptic curves. Their proof is based on
powerful new method in the geometry of numbers, dealing with the integer orbits of certain representationsof algebraic groups. This talk is an introduction to the theory. A brief discussion for future perspectives is
included.

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4

Featured Invited Talks

Conference Room Va
Izumi Takagi(Tohoku Univ.)

Mathematical approaches to biological pattern formation —Turing’s unfinished project— · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: In the seminal paper ”The chemical basis of morphogenesis” Alan Turing proposed the idea ofDiﬀusion-Driven-Instability as the basis of pattern formation in developmental biology, where a group of cells
develops spatially nontrivial structure spontaneously, starting from an almost uniform state. He assumed that
this patterning process is guided by a ”pre-pattern” appearing in the distribution of chemicals. He proved
that, when two chemicals with diﬀerent diﬀusion rates react, the spatially uniform state may become unstable
under spatially non-uniform disturbance. This will lead to an emergence of a spatial pattern. Inspired byTuring, many mathematical models have been proposed to explain various pattern formation observed in thenatural world.
In this talk we focus on the study of reaction-diﬀusion systems modeling pattern formation in developmental
biology, the phenomenon Turing wanted to analyse. As a case study we first review the mathematical results
concerning the activator-inhibitor system proposed by Gierer and Meinhardt. In particular, the eﬀect of
spatial heterogeneity on the resulting pattern has attracted much attention for the past decade. We shallreport recent development in this direction together with other types of models.

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5

Foundation of Mathematics and History of Mathematics

Foundation of Mathematics and History of Mathematics
March 21st (Sat)

Conference Room VII

10:00–11:25
1 Shigeru Masuda(Res. Workshop of Classical Fluid Dynamics)

The Correspondings as the Eigenvalue and the Eigenfunction/Eigenspace
before Hilbert · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The definition of eigenvalue and eigenfunction, based on the Sturm–Liouville type boundary value
problem of heat, is introduced by Hilbert 1904, however, la valeur particulière, the French corresponding
as the German Eigenwert have been traditionally discussed at least since Lagrange in the problem oftrigonometric series, After him, Fourier explains la valeur particulière on heat diﬀusion equations, Laplace
and Poisson use it on the secular perturbation equations. Gauss uses indole function in Latin. These
problems contain the linear diﬀerential equations or its integral equations. However, its corresponding
relation between the value and its function isn’t emphasized until Hilbert.

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

Poincaré’s Analytic Theory of Propagation of Heat, following after
Provést, Fourier and Poisson · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss Poincaré’s Analytic Theory of Propagation of Heat, following after Provést, Fourier
and Poisson. He introduces the harmonic function to prove the theorem of the existence of a function whichis expressed by a Fourier series, if the function satisfies with the Dirichlet condition. We talk comparatively
among them, about their characteristics and meanings in the history of physico-mathematics.

3 Michiyo Nakane

Osaka University and the establishment of the history of mathematics
in Japan · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: From 1950–1970, mathematicians in Japan mainly studied the history of western mathematics,
and Osaka University played an important role in establishment of this subject. In the 1950s, Koshiro
Nakamura began to teach the history of mathematics for graduate students in the mathematics department.
He had a close connection with the department of French literature and developed his original research onseventeenth century mathematics. Kokichi Hara, a professor of French literature, worked with Nakamura
and did excellent work on Pascal’s mathematics. This cooperation between mathematicians and French
literary men at Osaka University is one of the key factors that resulted in the establishment of the study ofthe history of mathematics in Japan.

4 Michiyo Nakane

Foundation and history of mathematics in Japan: From historical view
point · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Japan mathematical society has a foundation and history section, although these are diﬀerent
subjects. This paper analyzes the reason for this. From the 1940s to the 1960s, the foundation, philosophy,
and history of mathematics were discussed under the name ‘foundation.’ The nature of the foundationof mathematics, which was being developed in 1950s, suggested that mathematicians who studied thisfoundation would also have an interest in history.

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6

Foundation of Mathematics and History of Mathematics∗

5 Shotaro Tanaka

Methods of solving Rokuyaku power series and applying them to pyramidal power series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: 1. Wada, old Japanese mathematician made six kinds of power series, i.e., Rokuyaku; thirty eightproblems and solved them.
2. Example. 1 − 3x − 6x2 + 10x3 + 15x4 − − + + · · · = M , where 1 − − + +: types of operations, 1:∑
unit, −: subtraction, +: addition. Question: find M , Answer: M = (1 − 3x − 3x2 + x3 ) 1 d2 (k)xk−1 =(1 − 3x − 3x2 + x3 )/(1 − x2 )3 .
3. Pyramidal power series: pm (k) = (1/2)k(k + 1) + 1/6(m − 2)(k − 1)k(k + 1)(m ≥ 3). Example.
∑∑1
k−1
p6 (k): hexapyramidal number.
= (1 + 3x)
d3 (k)xk−1 = (1 + 3x)/(1 − x)4 , (|x| < 1),
1 p6 (k)xd3 (k) = (1/3!)k(k + 1)(k + 2).

11:30–12:00

Mathematics History Team Meeting

14:15–16:50
6 Hirotaka Kikyo(Kobe Univ.)

Model complete generic graphs I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a graph G, let V (G) denote the set of vertex of G, and E(G) the set of edges of G. Putδα (G) = |V (G)| − α|E(G)| for a real number α. Suppose 0 < α ≤ 1/2, α = p/m with positive integers p andm coprime. Let h be a real function on the set of real numbers such that h is concave, monotone increasing,unbounded, and for any positive integer x, h(x) + 1/m ≥ h(2x + c), where c is a constant determined by
α. Put Kα,h = {A : B ⊆ A ⇒ δ(B) ≥ h(|V (B)|)}. Then there is a (Kα,h , <)-generic structure M , andT h(M ) is model complete.

7 Koichiro Ikeda
Hirotaka Kikyo(Hosei Univ.)(Kobe Univ.)

A generic structure whose theory is not model complete · · · · · · · · · · · · 15

Summary: We construct an omega-categorical generic structure whose theory is not model complete.

8 Koichiro Ikeda(Hosei Univ.)

Near model completeness of generic structures · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show that if the theory of a generic structure M is ultra-homogeneous then M is nearly model
complete.

9 Kota Takeuchi (Univ. of Tsukuba)

n-dependent theories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: n-dependence is one of stability classes introduced by Shelah in 2009. In his papers, he asked
about the existence of suitable upper bound of the number of types over finite sets in n-dependent theories
and any simpler way reducting variables in a witness of n-dependence. In this talk we answer his questions byusing finite combinatorics, especially VC-dimension and Ramsey property of linearly ordered hypergraphs.

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Foundation of Mathematics and History of Mathematics

10 Munehiro Kobayashi(Univ. of Tsukuba)
Takayuki Kuriyama(Grad. Univ. for Adv. Stud.)
Kota Takeuchi (Univ. of Tsukuba)

VC-dimension and PAC-learnability for higher dimensional spaces · · · · 15

Summary: In computer learning theory, it is well known that finiteness of VC-dimension is equivalent to
PAC-learnability. On the other hand, the finiteness of VC-dimension is equivalent to the dependent property
in the context of model theory. Recently, a generalization of dependent property was introduced by Shelah.
In this talk we give a new learning theory correspondent to the generalization and discuss the relation to
VC-dimension.

11 Nobu-Yuki Suzuki (Shizuoka Univ.)

A note on weak variants of existence property in intermediate predicate
logics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss relationships between the existence property (EP) and its weak variants in intermediate
predicate logics. An intermediate predicate logic L is said to have the weak existence property (wEP), if
for every ∃xA(x), L ⊢ ∃xA(x) implies that L ⊢ A(v1 ) ∨ · · · ∨ A(vn ) for any finite set {v1 , ..., vn } of freevariables containing all free variables of ∃xA(x). An L is said to have the sentential existence property(sEP), if for every sentence ∃xA(x), L ⊢ ∃xA(x) implies that there exists a fresh individual variable v suchthat L ⊢ A(v). Then, it is easy to see that EP implies wEP, and that wEP implies sEP. We show that theconverses of these implications do not hold.

12 Takahiro Seki

(Niigata Univ.)

Halldén-completeness and Sahlqvist formulas · · · · · · · · · · · · · · · · · · · · · · 15

Summary: To prove Halldén-completeness in terms of Kripke semantics, the van Benthem–Humberstone
theorem is often used. The Sahlqvist theorem is one of the fundamental results on the correspondence
between modal formulas and frame postulates. Combining the Sahlqvist theorem and the van Benthem–
Humberstone theorem, we expect to obtain a range of Halldén-complete modal logics with Sahlqvist axioms.

13 Yoshihito Tanaka(Kyushu Sangyo Univ.)

A simple embedding of bounded semilattices with operators into Boolean
algebras with operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Sofronie–Stokkermans gives an embedding of bounded semilattices with operators into Boolean
algebras with operators. It is obtained by composing two injections, from bounded semilattices with operators
to bounded distributive lattices with operators and from bounded distributive lattices with operators to
Boolean algebras with operators. In this talk, we provide a simple embedding, which is defined directlyfrom a given bounded semilattice with operators. In fact, it is simple in the sense of algebra, either, as thecodomain of our embedding is a subalgebra of that of Sofronie–Stokkermans. Although the two codomains
are isomorphic if the given bounded semilattice with operators is finite, but in general cases, there exists an
example that the cardinality of our codomain is strictly smaller than that of Sofronie–Stokkermans.

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Foundation of Mathematics and History of Mathematics

The exact K4-models and the exact S4-models in S4 · · · · · · · · · · · · · · · 15

14 Katsumi Sasaki (Nanzan Univ.)

Summary: We treat modal logics S4 and K4, and consider related exact models. In MSJ spring meeting
2014, we gave a method to list all the exact K4-models for F(n) in S4, where F(n) is the set of modal
formulas with finite propositional variables p1 , · · · , pm and with finite modal degree ≤ n. Here, we give aneasier method to list them by using the exact S4-models listed in 2010. Specifically, for any exact K4-model
M = ⟨W, R, P ⟩ for F(n) in S4, we define a subset rep(M ) of W ; and prove the equivalence between thefollowing two conditions:(1) M ′ is an exact K4-model for F(n) in S4,(2) there exist an exact S4-model M = ⟨W, R, P ⟩ for F(n) in S4 an exact S4-model M = ⟨W, R, P ⟩ for
F(n) in S4 and a subset W ′ of rep(M ) such that M ′ = ⟨W, R − {(α, α) | α ∈ W ′ }, P ⟩.

17:00–18:00

Talk Invited by Section on Foundation and History of Mathematics

Katsuhiko Sano

(JAIST)

On coalgebraic modal logic and related topics

March 22nd (Sun)

Conference Room VII

9:30–11:40
15 Takashi Oyabu♭

Of parabolic type, and other 5 talks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: 1. Of parabolic typeIt was shown: that of parabolic type partial diﬀerential equations are closelly related to onsager scheme ofnon-equilibrium thermo-dynamics
2. Theory of H-theorems
Boltzmann’s H-function analogues are introduced and :maybe: dH/dt=<0===========>0:
Ut=============>0: Uit=============>0: Which is entropy increase law:
3. Non-equilibrium thermodynamnics
General schemes of non-equilibrium thermodynamics which are closelly related to Prigogine’s schemes:
4. w = dJ/dzdz = f (z)dz
Abelian diﬀerentials: Regular form: J::Modular:Elliptic curve:::Xo (1);;X(1);;;Xo (N )::X(N ): Modular
curve::Regular diﬀerential form=== Auto-morphic form of Xo (N ):5. Certain meta-physik
V==L::Problem: Godel’s L::Constructible set: V={x | x=x}::Class of set of all sets: And::Kantianphilosohy:Constructible world:Axiomatic set theory: ZF==========>Mathematics: ZF=L=V:::Ourscience:Constructible world:V::idea :as Greek philosophy
6. Isomorphism of Hilbert spaces: Laplacian
Hilbert spaces:H:∆:{Hn}::H’:∆′ :{Hn’} H==H’*Iso:<====>Spec(H)=Spec(H’): F:Hn========>Hn’:∆:Hn===========>Hn:∆′ :Hn’==============>Hn’:∆′ Hn’=λn’Hn’=λn’FHn:Hence: λn=λn’:F(∆Hn)=F(λnHn)=λnFHn:

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Foundation of Mathematics and History of Mathematics

16 Taishi Kurahashi(Kisarazu Nat. Coll. of Tech.)
Makoto Kikuchi (Kobe Univ.)

The incompleteness theorems for Σn definable theories of arithmetic· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that there is a complete consistent extension of Peano arithmetic which is Σ2
definable. Thus Gödel–Rosser’s first incompleteness theorem cannot be extended to Σn definable theories
directly. In this talk, we investigate the incompleteness phenomena for general Σn definable theories, andprove generalizations of first and second incompleteness theorems for Σn definable theories.

17 Makoto Fujiwara (Tohoku Univ.)

Uniform and intuitionistic provability in reverse mathematics · · · · · · · · 15

18 Kazuyuki Tanaka (Tohoku Univ.)
Florian Pelupessy (Tohoku Univ.)

Finitisations of second order principles · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This research is part of a project to examine relations between RM (reverse mathematics) and CMI(concrete mathematical independence). In this talk we will concentrate mostly on independent statementsfor (fragments of) Peano Arithmetic and their relation to second order logical principles within ACAo.
Many statements such as Ramsey’s theorem in dimension 2 are equivalent to their finitary versions over
WKLo, where for the converse direction RCAo is suﬃcient. Somewhat surprisingly, Koenig’s lemma itself
causes a peculier phenomenon in its finitisation.

19 Kohtaro Tadaki (Chuo Univ.)

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

Summary: The notion of probability plays an important role in almost all areas of science. In modern
mathematics, however, probability theory means nothing other than measure theory, and the operational
characterization of the notion of probability is not established yet. In this talk, based on the toolkit ofalgorithmic randomness we present an operational characterization of the notion of probability. Algorithmic
randomness, also known as algorithmic information theory, is a field of mathematics which enables us toconsider the randomness of an individual infinite sequence. We use the notion of Martin–Loef randomness
with respect to Bernoulli measure to present the operational characterization. As the first step of theresearch of this line, in this talk we consider the case of finite probability space, i.e., the case where thesample space of the underlying probability space is finite, for simplicity.

20 Kojiro Higuchi(Chiba Univ.)

On a theory of classes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present a theory of classes which is strictly stronger than Morse–Kelley set theory. The axiomsof our theory consist of only six axioms (or axiom schemes) including a new kind of axioms, Set Invention
Axiom (SIA). We see that our theory is strong enough to prove the axiom of universes, i.e., every set has its
smallest Grothendieck universe (as a set) containing the set.

21 Yasumichi Matsuzawa (Shinshu Univ.)

Complexity of the Weyl–von Neumann equivalence relation · · · · · · · · · · 15

Summary: The Weyl–von Neumann theorem states that two bounded self-adjoint operators on a Hilbert
space are unitarily equivalent modulo compacts if and only if they have the same essential spectrum. In the
talk we consider this result for unbounded operators using descriptive set theory. This is a joint work with
Hiroshi Ando.

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Foundation of Mathematics and History of Mathematics

22 Toshimichi Usuba (Kobe Univ.)

Large Lindelöf spaces with points Gδ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: By analyzing Dow’s construction, we introduce a general construction of regular Lindelöf spaces
with points Gδ . Using this construction, we prove the following: Suppose that either (1) there exists a
regular Lindelöf P-space of pseudocharacter ≤ ω1 and of size > 2ω , (2) CH and □(ω2 ) hold, or (3) CH holds
and there exists a Kurepa tree. Then there exists a regular Lindelöf space with points Gδ and of size > 2ω .

23 Hiroshi Sakai(Kobe Univ.)

On monadic second order theories of cardinals · · · · · · · · · · · · · · · · · · · · · 10

Summary: It is known, due to Büchi, that the monadic second order theories of ⟨ω, <⟩ and ⟨ω1 , <⟩ are bothdecidable. On the other hand, Gurevich–Magidor–Shelah proved that the decidability of the monadic second
order theory of ⟨ω2 , <⟩ is independent of ZFC. There are many open problems on the monadic second ordertheories of ⟨κ, <⟩ for κ ≥ ω2 . We give some of them and present some new results.

11:45–12:15

Research Section Assembly

13:15–14:15

Talk Invited by Section on Foundation and History of Mathematics

Daisuke Ikegami (Kobe Univ.)Gödel’s program, large cardinals, and forcing axioms

Summary: In the late 19th century, Cantor regarded infinity as “object”, not just a limit of finite objects,
and identified the notion of ordinals, cardinals, and the cardinality of sets. In 1938, he proved that the
cardinality of the set of real numbers (|R|) is strictly greater than that of the set of natural numbers (|N|),and then he conjectured that there is no cardinality of a set between |R| and |N|. This conjecture is
nowadays called the Continuum Hypothesis (CH).
In 1938, Gödel showed that one cannot refute CH in the standard axiom system of set theory so-called
Zermelo–Fraenkel set theory with the Axiom of Choice (ZFC). After that, he anticipated that one cannot
decide the truth-value of CH in ZFC, and in 1947, he announced the following research program nowadays
called Gödel’s Program:“Decide the truth-values of mathematically interesting statements in well-justified extensions of ZFC.”
What Gödel had in mind around that time for “well-justified extensions of ZFC” is the axiom systems ZFC+ large cardinal axioms. He expected to decide the truth-value of CH in ZFC + large cardinal axioms.
In 1963, Cohen showed that one cannot decide the truth-value of CH in ZFC by introducing a new method“forcing”. Using forcing, in 1967, Levy and Solovay proved that one cannot decide the truth-value of CH in
ZFC + ‘any’ large cardinal axiom.
However, it has been shown in these 30 years that one can decide the truth-values of many mathematicalstatements in ZFC + large cardinal axioms, and we now have a rigid understanding of the theory of thestandard second order arithmetic structure (N, P(N), ∈) under ZFC + large cardinal axioms.
In this talk, we try to extend this understanding to the theory of the second order structure (ω1 , P(ω1 ), ∈),where ω1 is the least uncountable cardinal, under ZFC + large cardinal axioms + forcing axioms. This is
joint work with Matteo Viale from University of Turin.

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AlgebraAlgebraMarch 21st (Sat)

Conference Room Ia

9:30–12:00
1 Akiyoshi Tsuchiya (Osaka Univ.)

The δ-vectors of reflexive polytopes and of the dual polytopes · · · · · · · 15

Summary: Let δ(P) be the δ-vector of a reflexive polytope P ⊂ Rd of dimension d and δ(P ∨ ) the δ-vector ofthe dual polytope P ∨ ⊂ Rd . In general, δ(P) = δ(P ∨ ) doesn’t hold. For each d ≥ 2, we show the existenceof a reflexive polytope of dimension d whose δ-vector equals the δ-vector of the dual polytope.

2 Akihiro Higashitani (Kyoto Univ.)

Unimodality of δ-vectors and two related properties · · · · · · · · · · · · · · · · 15

Summary: In this talk, we investigate two properties concerning the unimodality of the δ-vectors of lattice
polytopes, which are log-concavity and alternatingly increasingness. For lattice polytopes P of dimensiond, we prove that the dilated lattice polytopes mP have log-concave and alternatingly increasing δ-vectors ifm ≥ max{s, d + 1 − s}, where s is the degree of the δ-polynomial of P. We also provide several kinds of
unimodal (or non-unimodal) δ-vectors.

3 Akihiro Higashitani (Kyoto Univ.)
Benjamin Nill (Stockholm Univ.)
Akiyoshi Tsuchiya (Osaka Univ.)

Characterization of symmetric δ-trinomial · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give a necessary and suﬃcient for a trinomial 1 + (m − 2)tk + t2k , where m ≥ 3
and d ≥ 2 are integers, to be a δ-trinomial of a lattice polytope of dimension d.

4 Naoki Taniguchi (Meiji Univ.)

Sequentially Cohen–Macaulay Rees modules · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to study the question of when the Rees modules associated to arbitrary
filtration of modules are sequentially Cohen–Macaulay. Although this problem was originally investigatedby N. T. Cuong, S. Goto and H. L. Truong, their situation is quite a bit of restricted, so we are eager to try
the generalization of their results.

5 Yusuke Nakajima (Nagoya Univ.)

Ulrich modules over cyclic quotient surface singularities · · · · · · · · · · · · · 15

Summary: An Ulrich module is a certain class of maximal Cohen–Macaulay (= MCM) modules. Theirproperties are studied in several literatures. But it is not easy to decide which MCM module is an Ulrichone. In this talk, we investigate Ulrich modules over cyclic quotient surface singularities by using the notionof special CM modules.

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Algebra∗6 Hidefumi Ohsugi
Centrally symmetric configurations of order polytopes · · · · · · · · · · · · · · 15
(Kwansei Gakuin Univ.)
Kazuki Shibata (Rikkyo Univ.)
Takayuki Hibi (Osaka Univ.)
Kazunori Matsuda (Rikkyo Univ.)

Summary: It is shown that the toric ideal of the centrally symmetric configuration of the order polytope ofa finite partially ordered set possesses a squarefree quadratic initial ideal. It then follows that the convex
polytope arising from the centrally symmetric configuration of an order polytope is a normal Gorenstein
Fano polytope.

∗
7 Kei-ichiro Iima
On the locally Gorensteinness and Serre’s (Sn )-condition of modules(Nara Nat. Coll. of Tech.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Tokuji Araya (Okayama Univ. of Sci.)

Summary: In this talk, we shall characterize torsionfreeness of modules with respect to a semidualizing modulein terms of the Serre’s condition (Sn ). As an application we give a characterization of Cohen–Macaulayrings R such that Rp is Gorenstein for all prime ideals p with height less than n.

∗
8 Mitsuhiro Miyazaki
Actions of special linear groups to tensors of indeterminates and sagbi(Kyoto Univ. of Edu.) bases of the rings of invariants · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the action of the products of special linear groups to tensors of indeterminates ofsizes 2 × 2 × 3 and 2 × 2 × 4. And describe the rings of invariants by means of sagbi bases.

14:15–17:00
9 Takahisa Kawada(Nagoya Inst. of Tech.)Invariant code and its eﬃcient decoding · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: When a finite group acts on a curve, we construct an error-correcting code whose code length canbe larger but which is eﬃciently decoded if the errors are repeated in each sub-blocks. We call the code aninvariant code associated with the finite group. For these invariant codes, we evaluate the code parameters,
the computation complexities for decoding using the SV-algorithm. We have some examples of decoding on
a formula manipulation system.

10 Tetsuya Uematsu(Toyota Nat. Coll. of Tech.)

Uniform generators of the Brauer group of aﬃne diagonal quadrics · · · 10

Summary: In our previous studies, for a given family of varieties, we introduced the notion of uniform
generators of its Brauer group. They are elements in the Brauer group of the family whose specializations at
each variety in the family are generators of its Brauer group respectively. The main theorem of this work isthat there are no uniform generators of the Brauer group for the family of general aﬃne diagonal quadrics.
In this talk, we briefly explain the definition of specialization of Brauer groups and the precise statement of
this non-existence theorem.

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Algebra∗11 Tomohiro Iwami
Kawamata conjecture in the sense of Iskovskikh–Shokurov and variation(Kyushu Sangyo Univ.) of mixed Hodge structures for the associated algebraic fiber spaces · · · 10

Summary: In this talk, for Q-conic bundles of semistable type in the case of polarized log pairs, the author
would like to alternatively show a variant of rationality criterion for Q-conic bundles by using the moduli
part of the associated subadjunction,as succeeding to the author’s previous work “A Variant of Iskovskikh’s
rationality criterion for conic bundles in the case of polarized log pairs”, and moreover to partly prove“the finitely existence of the corresponding log models”, which is called as “Kawamata conjecture” by
Iskovskikh–Shokurov, by applying variation of mixed Hodge structures for the associated algebraic fiber
spaces to such a moduli part.

∗
12 Humihiko Watanabe
Twisted cohomology of the complement of theta divisors having normal(Kitami Inst. of Tech.) crossings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let D1 , . . . , DN be N distinct theta divisors on a principally polarized abelian surface X. We∑
assume that the divisor D =Dk has normal crossings. Set M = X − D. Let L be the locally constantsheaf associated to a many-valued function holomorphic on M , infinitely ramified along D. We discuss the
structure of the non-vanishing cohomology group H 2 (M, L).

13 Kenta Watanabe (Osaka Univ.) ∗ On the splitting of Lazarsfeld–Mukai bundles of rank 2 on K3 surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let X be a K3 surface, let C be a smooth curve on X, and let Z be a base point free pencil on
C. Then, the Lazarsfeld–Mukai bundle EC,Z of rank 2 associated to C and Z is given by an extension of
the torsion free sheaf JZ ⊗ OX (C) by OX , where JZ is the ideal sheaf of Z in X. We can easily see that if
C is very ample as a divisor on X, EC,Z is an ACM bundle with respect to OX (C). In this talk, by using
this fact, we will characterize a necessary condition for EC,Z to be given by an extension of two line bundles
on X, by ACM line bundles with respect to OX (C).

14 Kiwamu Watanabe (Saitama Univ.) ∗ Fano manifolds with nef tangent bundle and large Picard number · · · · 15
Summary: We study Fano manifolds with nef tangent bundle and large Picard number.

15 Tomoaki Shirato (Nagoya Univ.)

Frobenius splitting for some elliptic surfaces · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of Frobenius splitting was introduced by Mehta–Ramanathan to investigate thecohomology of Schubert varieties in positive characteristic. In Abelian varieties over an positive characteristic
field, Frobenius splitting is equivalent to the ordinarity. Therefore Frobenius splitting varieties are considered
as a generalization of ordinarity. In this talk, we consider that Frobenius splitting for some elliptic surfaces
in positive characteristic. Especially we considered the Frobenius splitting in fibered varieties , then we canlist up the Frobenius splitting elliptic surfaces without wild fibers.

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Algebra16 Yukiko Konishi (Kyoto Univ.)
Satoshi Minabe (Tokyo Denki Univ.)

Mixed Frobenius structure and local quantum cohomology · · · · · · · · · · 10

Summary: The Frobenius structure on a manifold, defined by Dubrovin, has been vigorously studied inrelation to mirror symmetry. We defined a generalization, called the mixed Frobenius sturucture (MFS), in
the aim of understanding local mirror symmetry. In this talk, we will show that a MFS naturally appears at
the nonequivariant limit of the equivariant cohomology of a smooth projective variety twisted by a concave
vector bundle.

Tannakian categories and chiral fermions · · · · · · · · · · · · · · · · · · · · · · · · · · 15

17 Makoto Sakurai

Summary: I have tried to define the chiral conformal field theories of Beilinson and Drinfeld by Hitchin’s
generalized complex geometry. However, I did not explain the chapter 1: Non-symmetric tensor category
and moduli of representable functors, which were casually used by Kapustin and Witten for the superYang–Mills–Higgs theory. I will re-examine the “tensor calculus” with regularity conditions on Riemannsurfaces (“worldsheet” of topological sigma model for N = (0, 2) super-symmetry) for insertions of chiralvertex algebras. The vanishing of gerbes to chiral de Rham complex is discussed in cases of complex smoothquasi-projective surfaces by blowups. Rational CFTs and the super-string compactification are briefly
explained for non-experts. No familiarity with diﬀerential geometry of Chern–Simons 3-forms or no “mixed
anomalies” of gauge- and gravitational- anomalies is assumed for audiences.

18 Tetsuya Ando

(Chiba Univ.)

Discriminants of homogeneous inequalities · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Consider a certain family of homogeneous polynomials f . If a polynomial φ of the coeﬃcients off essentially determines whether f ≥ 0 holds on a convex set A or not, then we call φ a discriminant. We
presnt a theory of discriminant.

19 Shigeru Iitaka (Gakushuin Univ.⋆)

Ultimate perfect numbers and φ- perfect numbers · · · · · · · · · · · · · · · · · · 10

Summary: Let σ(a) denote the sum of divisors of a positive integer a. Let P be a prime. If σ(P e ) is a prime
e+1
q, then a = P e q are called ultimate perfect numbers. In this case, q = P P −1 . Here P stands for P − 1.
P σ(a) − P a = (P − 2)M axp(a).
Here, M axp(a) denotes the maximal prime factor of a.

17:15–18:15

Talk Invited by Algebra Section

Kazushi Ueda

(Osaka Univ.) ♭ Moduli of relations of quivers

Summary: The derived category of coherent sheaves on an algebraic variety admitting a tilting object is
described in terms of a quiver with relations, and one can study not necessarily commutative deformationsof the algebraic variety by deforming the relations. In the talk, we will discuss the moduli space of noncommutative projective planes from the point of view of relations of the Beilinson quiver. This moduli space
is closely related to Shioda’s elliptic modular surface of level 3 and the moduli space of 3-qutrit states inquantum information theory. If the time permits, we will also discuss the moduli spaces of non-commutative
quadric surfaces and non-commutative cubic surfaces. The moduli space of non-commutative cubic surfaces
is 8-dimensional, and contains the configuration space of 6 points in general position as a locally closed
subscheme. This is a joint work with Tarig Abdelgadir and Shinnosuke Okawa.

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AlgebraMarch 22nd (Sun)

Conference Room Ib

9:30–12:00
20 Michio Yoshiwaki (Osaka City Univ.) ∗ Relative derived dimensions for cotilting modules · · · · · · · · · · · · · · · · · · 10
Summary: Let A be a finite-dimensional algebra over a field. We denote by mod A the category of finitely
generated right A-modules. For a module T ∈ mod A, we also denote by ⊥ T the left Ext-orthogonal
subcategory of mod A with respect to T . In this talk, we will show that for a given cotilting module
T ∈ mod A of injective dimension at least 1, the derived dimension of A with respect to ⊥ T is just the
injective dimension of T . This generalizes a result of Krause and Kussin.

21 Hirotaka Koga (Tokyo Denki Univ.)

Rings derived equivalent to Z · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show rings derived equivalent to Z are just Morita equivalent to it.

22 Satoshi Yamanaka (Okayama Univ.)

On weakly separable polynomials in skew polynomial rings · · · · · · · · · · 10

Summary: N. Hamaguchi and A. Nakajima introduced the notion of weakly separable extensions as a
generalization of separable extensions. They gave necessary and suﬃcient conditions for weakly separable
polynomials in the skew polynomial rings B[X; ρ] and B[X; D] when B is a integral domain. In this talk,we shall generalize their results for a non-commutative coﬃcient ring B.

23 Gahee Kim (Shizuoka Univ.)
Sho Matsuzawa (Shizuoka Univ.)

Calabi–Yau property of 3-dimensional quadratic AS-regular algebras· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: An AS-regular algebra is one of the main objects in noncommutative algebraic geometry. Let A
be a 3-dimensional quadratic AS-regular algebra, and A! a quadratic dual of A. It is known that A is aCalabi–Yau algebra if and only if the Nakayama automorphism of A! is the identity. Let φ be a gradedalgebra automorphism of A, and Aφ a twist of A by φ. It is also known that A and Aφ are graded Morita
equivalent. In this talk, we show that many 3-dimensional quadratic AS-regular algebras are graded Morita
equivalent to some Calabi–Yau algebras.

24 Kenta Ueyama (Hirosaki Univ.)

Cyclic ample groups acting on the graded down-up algebra A(0, 1) · · · 10

Summary: Recently, the notion of ampleness of a finite group action on a noetherian graded algebra wasintroduced by Mori and the speaker. They found some nice properties of fixed subalgebras of AS-regularalgebras under ample group actions. It is well-known that the down-up algebra A(0, 1) is an 3-dimensional
cubic AS-regular algebra. In this talk, we give a suﬃcient condition for the ampleness of cyclic groups acting
on the down-up algebra A(0, 1).

25 Yoshifumi Tsuchimoto (Kochi Univ.)

On structure of non commutative projective varieties as non commutative Kähler maifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We first define non commutative projective varieties as a non commutative Kähler manifolds.
Then we study some of their structure.

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Algebra26 Daiki Obara (Tokyo Univ. of Sci.)

On the Hochschild cohomology ring modulo nilpotence of the quiver
algebra defined by c cycles and a quantum-like relation · · · · · · · · · · · · · 15

Summary: We consider the quiver algebra A defined by c cycles and a quantum-like relation. We describe theminimal projective bimodule resolution of A, and determine the ring structure of the Hochschild cohomology
ring of A modulo nilpotence. And we introduce some results.

27 Tomohiro Itagaki (Tokyo Univ. of Sci.)
Katsunori Sanada (Tokyo Univ. of Sci.)

Notes on the Hochschild homology dimension and truncated cycles · · · 10m
for anSummary: In this talk, we show that if an algebra KQ/I with an ideal I of KQ contained in RQ

integer m ≥ 2 has an m-truncated cycle, then this algebra has infinitely many nonzero Hochschild homology
groups, where RQ denotes the arrow ideal. Consequently, such an algebra of finite global dimension has no
m-truncated cycles and satisfies an m-truncated cycles version of the no loops conjecture.

28 Ryo Kanda(Nagoya Univ.) ♭ Minimal atoms in Grothendieck categories · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The atom spectrum of a Grothendieck category is a generalization of the prime spectrum of acommutative ring. For a Grothendieck category with a noetherian generator, we show that the number ofminimal atoms is nonzero and finite.

29 Masashi Kosuda (Univ. of Ryukyus) ♭ Coxeter elements of the symmetric groups whose powers aﬀord thelongest · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We give a necessary and suﬃcient condition for Coxeter elements of the symmetric groups to
become the longest by being taken powers.

13:15–14:15

Talk Invited by Algebra Section

Jun-ichi Miyachi (Tokyo Gakugei Univ.) ♭ Homotopy categories and derived categories of N -complexes
Summary: We describe homological properties of N -complexes, that is, complexes with diﬀerentials dsatisfying dN = 0. The notion of N -complexes was introduced by Mayer in 1942. He studied the “generalized
homologies” of the N -complexes of simplicial complexes. Afterwards, Kapranov studied properties of thehomologies of N -complexes, homotopies of morphisms and the q-analog of homological algebra in 1991. In
this talk, we approach homology theory of N -complexes from the point of view of triangulated categories.
In particular we study the homotopy category KN (B) of N -complexes of an additive category B and thederived category DN (A) of N -complexes of an abelian category A. For a ring A we show that the derived
category DN (M odA) of N -complexes of right A-modules is triangle equivalent to D(M odTN −1 (A)), whereTN −1 (A) is the (N − 1)-dimensional upper triangular matrix ring of A.

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AlgebraMarch 23rd (Mon)

Conference Room Ib

9:30–11:45
30 Masanori Ando (Wakhok Univ.)

Odd number and tranpezoidal number · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We know that the Lecture hall partition theorem is generalization of Euler’s odd-strict theorem.
It’s binomial proof exists. We simplyfy this proof by considering finite set. And we add a new variable tothis proof.

31 Shuhei Kamioka (Kyoto Univ.)

Application of biorthogonal polynomials and the discrete two-dimensional
Toda molecule to rhombus tilings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A close relationship between rhombus tilings, and biorthogonal polynomials and an associatedintegrable system, the discrete two-dimensional (2D) Toda molecule, is revealed. It is shown that the famous
product formula by MacMahon for plane partitions, equivalently for rhombus tilings of a hexagonal region,
can be derived by solving an initial value problem of the discrete 2D Toda molecule.

32 Tsunekazu Nishinaka(Okayama Shoka Univ.)

On primitivity of non-noetherian group algebras · · · · · · · · · · · · · · · · · · · 10

Summary: A ring R is (right) primitive provided it has a faithful irreducible (right) R-module. In this talk,
we focus on a local property which is often satisfied by groups with non-abelian free subgroups:(∗) For each subset M of G consisting of finite number of elements not equal to 1, there exist three−1
distinct elements a, b, c in G such that whenever xi ∈ {a, b, c} and (x−1
1 g1 x1 ) · · · (xm gm xm ) = 1 for somegi ∈ M , xi = xi+1 for some i.

We get the following result: Let G be a non-trivial group which has a free subgroup whose cardinality is thesame as that of G. Suppose that G satisfies the condition (∗). If R is a domain with |R| ≤ |G|, then thegroup ring RG of G over R is primitive.

33 Kenichi Shimizu (Nagoya Univ.)

Frobenius properties of tensor functors · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For an extension A/B of finite-dimensional Hopf algebras, the relative modular function χA/B
and the relative Nakayama automorphism βA/B are defined in terms of the modular functions of A and B.
Fischman, Montgomery and Schneider showed that the extension A/B is β-Frobenius with β = βA/B , i.e.,there exists an isomorphism B AA ∼= β HomB (AB , BB ) of B-A-bimodules. I will talk about a generalizationof this theorem in the setting of finite tensor categories.

34 Hironori Oya (Univ. of Tokyo)

The representations of quantized function algebras and the transition
matrices between canonical bases and PBW bases · · · · · · · · · · · · · · · · · · 15

Summary: Let G be a complex simply connected simple algebraic group. Firstly, we study the relation
between the certain irreducible representations of the quantized function algebra Qq [G] and the positive
part Uq (n+ ) of the quantized enveloping algebra Uq (g), taking account into the right Uq (g)-algebra structureof Qq [G]. Next, using this relation, we prove that each canonical basis element is the N[q ±1 ]-linear
combination of the PBW basis elements when g is of type ADE. This is an another proof of Kato’s resultthat is a generalization of Lusztig’s result.

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Algebra(Kinki Univ.)
35 Fumihito Oda
Hokuto Idei (Yamagata Univ.)

The table of marks, the Kostka matrix, and the character table of thesymmetric group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We introduce a short proof of T = KC, where T is the table of marks with respect to the Young
subgroups, K is the Kostka matrix, and C is the character table of the symmetric group Sn . As a corollaryof the result, we could determine the explicit elements of the unit group of the generalized Burnside ringwith respect to the Young subgroups of Sn .

36 Hiroki Ishioka (Tokyo Univ. of Sci.)
Naoko Kunugi (Tokyo Univ. of Sci.)

Brauer indecomposability of Scott modules · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let k be an algebraically closed field of prime characteristic p, G a finite group and P a p-subgroupof G. We investigate the relationship between the fusion system FP (G) and the Brauer indecomposabilityof the Scott kG-module in the case that P is not necessarily abelian. We give an equivalent condition for
Scott kG-module with vertex P to be Brauer indecomposable.

37 Katsushi Waki (Yamagata Univ.)

Subgroups of J4 for amalgamation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I will show how to construct concrete subgroups of J4 for Amalgamation of Ivanov. We needs
these subgroups to make the 1333 dimansional simple J4 -module over the field with characteristic 3.

38 Masahiko Miyamoto(Univ. of Tsukuba)
Matthew Krauel (Univ. of Cologne)

Representation of regular commutant · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let V be a holomorphic vertex operator algebra and U a subVOA. We show that every simple
U -module appears in V if U and U c are both regular and (U c )c = U , where U c denotes the commutant ofU.

14:15–14:30

Presentation Ceremony for the 2015 MSJ Algebra Prize

14:30–15:30

Award Lecture for the 2015 MSJ Algebra Prize

Syu Kato(Kyoto Univ.)

On aﬃne highest weight categories arising from quantum groups andHecke algebras and its applications

15:45–18:30
39 Akinari Hoshi (Niigata Univ.)

Birational classification of fields of invariants for groups of order 128· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G be a finite group acting on the rational function field C(xg : g ∈ G) by C-automorphisms
h(xg ) = xhg for any g, h ∈ G. Noether’s problem asks whether the invariant field C(G) = k(xg : g ∈ G)G is
rational (i.e. purely transcendental) over C. We investigate the birational classification of C(G) for groups
G of order 128 with Brnr (C(G)) ̸= 0. Moravec showed that there exist exactly 220 groups G of order 128
with Brnr (C(G)) ̸= 0 forming 11 isoclinism families Φj . We show that if G1 and G2 belong to Φ16 , Φ31 ,Φ37 , Φ39 , Φ43 , Φ58 , Φ60 or Φ80 (resp. Φ106 or Φ114 ), then C(G1 ) and C(G2 ) are stably C-isomorphic with
Brnr (C(Gi )) ≃ C2 . Explicit structures of non-rational fields C(G) are given for each cases including also thecase Φ30 with Brnr (C(G)) ≃ C2 × C2 .

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Algebra40 Tomohiro Ooto (Univ. of Tsukuba)

Quadratic approximation in the field of formal Laurent series · · · · · · · · 10

Summary: In this talk, we study about Mahler’s exponent w2 and Koksma’s exponent w2∗ in the field offormal Laurent series over Fq . When 2 ̸ |q, we obtain that the set of values taken by w2 − w2∗ is including(0, 1]. Furthermore, we have a finiteness of a value of automatic continued fraction taken by w2∗ .

41 Hajime Kaneko (Univ. of Tsukuba)

On the nonzero digits of the beta expansions of algebraic numbers · · · 15

Summary: Rényi introduced the notion of β-expansions of real numbers for a real number base β > 1. It is
important to investigate the digits of algebraic numbers. For instance, Borel’s conjecture on the normalityof algebraic irrational numbers in an integral base b ≥ 2 is a well known open problem. In this talk, we
introduce lower bounds for nonzero digits of algebraic numbers in a Pisot or Salem number base β, which
gives partial results of normality.

42 Tomoya Machide(Nat. Inst. of Information)

On congruence identities of regularized multiple zeta values · · · · · · · · · 10

Summary: We prove congruence identities of regularized multiple zeta values involving a pair of index sets.
We also obtain a proof of the parity result, and a congruence sum formula for MZVs.

(Keio Univ.)
43 Masataka Ono
Shuji Yamamoto (Keio Univ.)

Shuﬄe product of finite multiple polylogarithms · · · · · · · · · · · · · · · · · · · 15

Summary: Finite polylogarithms were defined by Elbaz–Vincent and Gangl and studied by several authors.
In this talk, we will introduce a multiple version of finite polylogarithms and prove that a certain module
generated by finite multiple polylogarithms forms an algebra. This result is obtained by using a finite
analogue of the shuﬄe relation for the usual multiple polylogarithms. This is a joint work with Shuji
Yamamoto.

44 Shin-ya Kadota (Nagoya Univ.)

A certain weighted sum formula for multiple zeta values · · · · · · · · · · · · 10

Summary: Multiple zeta values are real numbers which are defined from the n-tuple of natural numbers.
Now, there are a lot of known linear relations among multiple zeta values. Eie–Liaw–Ong (2013) generalized
the weighted sum formula proved by Ohno–Zudilin (2008). In this talk, I’m going to introduce the weighted
sum formula with parameters, that is an extension of the weighted sum formula proved by Eie–Liaw–Ong.

45 Takuya Okamoto(Nippon Inst. of Tech.)
Tomokazu Onozuka (Nagoya Univ.)

Functional equation for the Mordell–Tornheim multiple zeta-function· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Matsumoto gave the functional equation for double zeta-functions of the Hurwitz–Lerch type,which includes the Euler–Zagier double zeta-function. As a generalization of the functional equation for
the Euler–Zagier double zeta-function, we gave the functional equation for the Mordell–Tornheim multiple
zeta-function.

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AlgebraOn the various mean values of the Dirichlet L-functions · · · · · · · · · · · · · 10

46 Takuya Okamoto(Nippon Inst. of Tech.)
Tomokazu Onozuka (Nagoya Univ.)

Summary: We give a method of obtaining explicit formulas for various mean values of Dirichlet L-functions
which are expressed in terms of the Riemann zeta-function, the Euler function and Jordan’s totient functions.

Combinatorial zetas and monoids · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1047 Hideaki Morita (Muroran Inst. of Tech.)

Summary: Combinatorial zetas are considered. Main examples are Ihara zeta functions for finite graphs, andArtin–Mazur zeta functions for finite dynamical systems. Their determinantal expressions are reviwed anda theorem of Foata–Zeilberger is introduced for giving a way of understanding these expressions in view of
Lyndon words. Finally, a similar way of construction is given for absolute Weil zetas.

Koyama–Nakajima’s L-functions and Ruelle zetas · · · · · · · · · · · · · · · · · · 15

48 Yukihiro Hattori(Muroran Inst. of Tech.)
Hideaki Morita (Muroran Inst. of Tech.)

Summary: S. Koyama and S. Nakajima introduce an L-function for each permutation matrice whose nonzero
entries are r-th roots of unity. Their L-functions are an generalization of Artin–Mazur zeta functions for
permutation matrices. In this talk, we will see that their L-functions are generating functions of exponential
type for quantities arising from certain finite discrete dynamical systems with weight functions.

(Nagoya Univ.) ♭ Power moments for the double zeta-function · · · · · · · · · · · · · · · · · · · · · · · 1049 Soichi Ikeda
Isao Kiuchi (Yamaguchi Univ.)
Kaneaki Matsuoka (Nagoya Univ.)
Summary: We study the even power moments for the double zeta-function of Euler–Zagier type.

50 Hidekazu Tanaka (Tokyo Tech) ♭ Transcendence of special values of log double sine function · · · · · · · · · · 10
Summary: In 2009, S. Gun, M. R. Murty, P. Rath studied transcendental values of the logarithm of the
gamma function. In this talk, we study transcendental values of log double sine function using their method.

March 24th (Tue)

Conference Room Ib

9:30–12:00
51 Kenichi Shimizu∗

On SP numbers (II) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We define a new number which we call an SP number. SP numbers are related to imaginary
quadratic fields. It seems that the number of SP numbers is less than prime numbers. We consider the
distribution of SP numbers.

52 Takafumi Miyazaki (Nihon Univ.) ∗ On the sum of consecutive k-th powers and Schäﬀer’s conjecture · · · · · 10
Summary: We consider the problem to ask when the sum of consecutive k-th powers is a perfect power. We
solve this in a special case. Our result gives an aﬃrmative answer to a classical conjecture of Schäﬀer.

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Algebra53 Takao Komatsu (Wuhan Univ.)

Restricted and associated Stirling numbers and Bernoulli numbers · · · 15

Summary: By using the associated and restricted Stirling numbers of the second kind, we give some
generalizations of the poly-Bernoulli numbers.

54 Ade Irma Suriajaya (Nagoya Univ.)

Two estimates on the zeros of L′ (s, χ) under the generalized Riemannhypothesis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Zeros of the Riemann zeta function and its derivatives have been studied by many mathematicians.
Among, the number of zeros and the distribution of the real part of non-real zeros of the derivatives of the
Riemann zeta function have been investigated by Berndt, Levinson, Montgomery, Akatsuka, and the author.
Berndt, Levinson, and Montgomery investigated the general case, meanwhile Akatsuka and the author gave
sharper estimates under the truth of the Riemann hypothesis. In this talk, we introduce similar results
related to the first derivative of the Dirichlet L-functions under the assumption of the generalized Riemannhypothesis.

55 Yuta Suzuki(Nagoya Univ.)

On the exceptional set for the Hardy–Littlewood conjecture under the
Generalized Riemann Hypothesis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 1923, Hardy and Littlewood conjectured that every suﬃciently large integer is either a squareor the sum of a prime and a square. In this talk, I will present a conditional estimate of the exceptional set
for this conjecture under GRH. It is an improvement of the previous results obtained by Mikawa (1993) orPerelli and Zaccagnini (1995).

56 Genki Shibukawa (Kyushu Univ.)

New trigonometric identities and reciprocity laws of generalized Dedekind
sums · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We obtain new trigonometric identities, which are product-to-sum type formulas for derivativeof the cotangent function. Further, from specializations of our formulas, we derive not only various known
reciprocity laws of generalized Dedekind sums but also new reciprocity laws of generalized Dedekind sums.

∗
57 Debika Banerjee
On squarefree integers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Harish-Chandra Research Inst.)
Makoto Minamide (Yamaguchi Univ.)

Summary: Let x, y be positive real numbers, p a prime. We consider two sums∑2n≤x,p|n⇒p>y µ (n), where µ is the Möbius function.

58 Akiko Ito∑n≤x,p|n⇒p>y µ(n) and(Kanagawa Univ.) ∗ The divisibility of the class number of the imaginary quadratic field√Q( 32e − 4k n ) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let k > 1 be an odd integer with 3 ∤ k and let n and e be positive integers with 32e < 4k n . We√show that the class number of the imaginary quadratic field Q( 32e − 4k n ) is divisible by n if k, n, and esatisfy certain conditions.

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Algebra∗59 Hirotaka SatoOn the anti-cyclotomic Zp -extension of an imaginary quadratic number(Tokyo Univ. of Foreign Stud.) field · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let K be an imaginary quadratic number field and L∞ be the ring class field of conductor
p∞ . Then p-part of Gal(L∞ /K) ≃ Zp ⊕ T , where T is a finite abelian p-group. In order to study theanti-cyclotomic Zp -extension of K, we characterize T in terms of the form class group of K.

60 Daisuke Shiomi (Yamagata Univ.) ∗ Unit indices of global function fields · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Let L be an imaginary bicyclic biquadratic function field over Fq (T ). Let QL be the unit indexof L. The main result of this talk is to give a necessary and suﬃcient condition for QL to be two.

61 Ryo Kato

(Kyoto Univ.) ♭ A remark on the Wiener–Ikehara Tauberian theorem · · · · · · · · · · · · · · · 10

Summary: Let {an } be a sequence of non-negative real numbers and L a Dirichlet series whose coeﬃcients are∑{an }. We give the asymptotic behavior of n≤X an as X → ∞ when Lm has a meromorphic continuation,and is holomorphic except for a pole of order l.

14:15–15:30
62 Kazuaki Tajima (Tohoku Univ.)

GIT stratification of reductive group actions in the non-split case · · · · 10

Summary: In early 80’s, Kirwan and Ness introduced the notion of GIT stratification of reductive group
actions in algebraic situation. If the group is split over k, their works tell us that these stratifications arerationally defined over a perfect ground field k. In this talk, we extend these stratifications for all (notnecessarily split) reductive algebraic groups over k.

63 Yu Yasufuku(Nihon Univ.)

Integer points in orbits in one- and higher-dimensions · · · · · · · · · · · · · · 15

Summary: We describe several recent results on S-integral points in orbits under maps on P1 as well as on
PN . How the map ramifies plays a key role. This talk is in part a joint work with H. Krieger, A. Levin, Z.
Scherr, T. Tucker, and M. Zieve.

64 Yoshiyasu Ozeki (Kyoto Univ.)

On weak Liu modules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give an answer to a Tong Liu’s question about the essential image of a functor on
weak Liu modules in most cases.

65 Mariko Ohara (Tohoku Univ.)

Algebraic K-theory of quasi-coherent modules over spectral schemes
and the representation in aﬃne case · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study K-theory of spectral schemes by using quasi-coherent sheaves. We regard the K-theory
as a functor K on the aﬃne spectral schemes and prove that the group completion ΩB(BGL) represents
the sheafification of K with respect to Zariski (resp. Nisnevich) topology, where we define BGL to be aclassifying space of a colimit of aﬃne spectral scheme GLn . We also prove K(Rb ) ≃ K(π0 Rb ) for connective
spectrum Rb which has only finitely many non-zero homotopy groups.

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Algebra66 Tomomi Ozawa (Tohoku Univ.)

Constant terms of Eisenstein series defined over a totally real field · · · 15

Summary: In this talk, we compute constant terms of Eisenstein series defined over a totally real field at all
cusps. M. Ohta defined and computed congruence modules related to Eisenstein series defined over Q in apaper published in 2003. His theory of congruence modules has been applied to several important problems
in number theory, particularly in Iwasawa theory. In his computation, the constant terms of Eisensteinseries over Q at all the equivalence classes of cusps are necessary. We explicitly describe the constant termsof Eisenstein series over a general totally real field in terms of special values of Hecke L-functions, at each
equivalence class of cusps.

15:45–16:45

Talk Invited by Algebra Section

Shunsuke Yamana (Kyushu Univ.) ♭ Exterior cube L-functions for GL(6)Summary: It is an interesting problem to ask when an automorphic L-function has a pole or when its central
critical value is nonvanishing. I will discuss this problem for the twisted exterior cube L-functions for GL(6).
I will determine the irreducible cuspidal automorphic representations of GL(6) whose twisted exterior cube
L-function has a pole. The proof is very short and uses quadratic base change. I will also review a conjecture
on its central critical value formulated by Ginzburg and Rallis. The twisted exterior cube L-function is very
similar to the triple product L-function, which was extensively studied by Piatetski-Shapiro, Rallis, Ikeda,
Kudla, Harris, Ichino, and also to the spin L-function for GSp(10), the half-spin L-function for GSO(12)and the standard L-function for GE7 .

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Geometry

Geometry
March 21st (Sat)

Conference Room IIIa

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

Drawing theorem and some compositions on the tangent of Doval (algebric 4th oder curve) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: We found the Tangent of Doval (The Oval of DEscartes) can be drawn by using Elementary
Geometry about 40 years ago, and found New Some Properties of The tangents. We already proved themethod are true, and this time, We show New composition of the tangent which consist of asymmetry axes
and Third Focus point of Doval, and consist of tangent-tangent closs points of Doval and second focus point.
We show these composition figure and show these Composition-constructions. We hope these properties of
Doval will be famila in order to apply Doval to many Mathematics field and Physics

2 Hirotaka Ebisui (Oval Research Center)

5 compositions of star star teorem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: We found Strange Compositions on Two Overlap Triangles. This have been already as ADE
theorem onrepoted Last MSJ2014 proceedind at Hirodai. That Composition has 5 Types. We show andexplain all of them Plase enjoy their figures.

3 Hiroaki Izumi (Hiroshima Univ.)

Mathematical formulization of phase transition and a branch of a concept or a power · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We succeed in mathematical formulization of business cycle, phase transition, symmetry breaking,scale transformation, rhythm phenomenon, synchronization, pattern and a branch of a concept or a power.
At first, I state what the key point of Nash Equilibrium is.
Next, I state mathematical formulization of a branch of a concept or a power.
To my thinking, that is the heart of the theory of history and the paper “First-order phase transition of avacuum and the expansion of the Universe” written by Katsuhiko Sato 1981.

4 Tomonori Fukunaga(Kyushu Sangyo Univ.)
Masatomo Takahashi(Muroran Inst. of Tech.)On convexity of frontals in the Euclidean plane · · · · · · · · · · · · · · · · · · · · 15

Summary: We study convexity of simple closed frontals in the Euclidean plane by using the curvature ofLegendre curves. We introduce a characterization of convexity of the simple closed frontal of a Legendre
curve by using the curvature.

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Geometry

5 Shun’ichi Honda(Muroran Inst. of Tech.)
Masatomo Takahashi(Muroran Inst. of Tech.)

Evolutes of framed curves in the Euclidean space · · · · · · · · · · · · · · · · · · · 15

Summary: The evolute of a regular curve is the classical object and may have singularities. By using amoving frame of a framed curve and the curvature of the framed curve, we can define an evolute of theframed curve in the Euclidean space. In this case, we can consider an evolute of evolutes and discuss
properties of them.

6 Kenji Kajiwara (Kyushu Univ.)
Toshinobu Kuroda (Kyushu Univ.)
Nozomu Matsuura (Fukuoka Univ.)

Conformal deformation of discrete plane curves and discrete Burgers
hierarchy I · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a discrete conformal deformation of discrete plane curves, which give rise to thediscrete Burgers hierachy. In this talk, we introduce the Burgers and the discrete Burgers hierarchies which
naturally appear in the geometric framework.

7 Nozomu Matsuura (Fukuoka Univ.)
Kenji Kajiwara (Kyushu Univ.)
Toshinobu Kuroda (Kyushu Univ.)

Conformal deformation of discrete plane curves and discrete Burgers
hierarchy II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a discrete conformal deformation of discrete plane curves, which gives rise to thediscrete Burgers hierachy. We also construct explicit formulas for the deformations by using the solution of
linear diﬀusion diﬀerential/diﬀerence equations.

8 Tomoshige Yukita (Waseda Univ.)

Classification of hyperbolic Coxeter polytopes with 6 faces and their
growth rates · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We classify hyperbolic Coxeter polytopes with 6 faces and show that their growth rates are Perron
numbers.

9 Yohei Komori (Waseda Univ.)

Coxeter garlands and 2-Salem numbers · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show that the growth rates of Coxeter garlands are 2-Salem numbers, where a real algebraic
integer α > 1 is called a 2-Salem number if it has a real conjugate β > 1 while other conjugates ω satisfy|ω| ≤ 1 and at least one of them is on the unit circle.

14:15–15:40∗
10 Atsufumi Honda
Duality of singularities for spacelike CMC surfaces in Minkowski space(Miyakonojo Nat. Coll. of Tech.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show the duality of singularities for spacelike CMC surfaces with singularities in the Lorentz–
Minkowski three-space.

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Geometry

11 Makoto Sakaki (Hirosaki Univ.) ∗ On the structure equations and the curvature ellipse of minimal surfaces
in product spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We discuss the structure equations and the curvature ellipse of minimal surfaces in product spaces.
We also give some related problems.

12 Norihisa Ikoma (Tohoku Univ.) ∗ Existence of Willmore type tori with small area · · · · · · · · · · · · · · · · · · · · 15
(SISSA)
Andrea Malchiodi
Andrea Mondino (ETH, Zürich)Summary: In this talk, we discuss the existence of Willmore type tori with small area embedded in 3dimensional closed Riemannian manifold. Here a Willmore type torus means a surface of genus 1 which isa critical point of the Willmore functional under the area constraint. Supposing some curvature conditions
for the ambient manifold, we shall show the existence of Willmore type tori having a small area.

13 Katsuhiro Moriya (Univ. of Tsukuba)

Simple factor dressing of a minimal surface · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Gauss map of a constant mean curvature surface in the Euclidean space is a harmonic map.
Theory of constant non-zero mean curvature surfaces is associated with theory of harmonic maps from asurface to the two-dimensional sphere. Dressing is a method to construct a harmonic map from a given one.
For a minimal surface, its conformal Gauss map is a harmonic map and it plays similar role to the gauss
map of a constant non-zero mean curvature surface. We define a simple factor dressing of a minimal surface
and explain the relationship between simple factor dressing, the associated family, the Goursat transform,
the Darboux transform and the Lopez-Ros deformations.

14 Yu Kawakami (Kanazawa Univ.)
Reiko Aiyama (Univ. of Tsukuba)
Kazuo Akutagawa (Tokyo Tech)

The Gauss map and total curvature of complete minimal Lagrangiansurfaces in the complex two-space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give an Osserman-type inequality and the precise maximal number of exceptional valuesof the Gauss map for a complete minimal Lagrangian surface with finite total curvature in the complex
two-space. Moreover, we prove that if the Gauss map of a complete minimal Lagrangian surface which is
not a Lagrangian plane omits three values, then it takes all other values infinitely many times.

15 Katsuei Kenmotsu (Tohoku Univ.⋆)

The classification of the surfaces with parallel mean curvature vector in
two-dimensional complex space forms, revisited · · · · · · · · · · · · · · · · · · · · 15

Summary: In the meeting of MSJ on March 1999, I claimed the classification result for those surfaces statedin the title of this talk. But it was incomplete. Today, I give the correction to the result as follows: A
parallel mean curvature surface in a complex two-dimensional complex space form depends on one realvalued harmonic function on the surface and five real constants if the ambient space is not flat, the mean
curvature vector does not vanish, and the Kähler angle is not constant.

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Geometry

15:50–16:50

Talk Invited by Geometry Section

Nozomu Matsuura (Fukuoka Univ.)

Deformations of discrete curves

Summary: It is well-known that there are deep connections between the diﬀerential geometry and the theoryof integrable systems, and various integrable diﬀerential equations arise as the integrability condition ofgeometric objects. In order to develop its discrete analogue, the studies of discrete diﬀerential geometry(DDG) started from the mid 1990s. One of the themes of DDG is to construct the geometric framework,
which is consistent with the theory of discrete integrable systems. Some of the motivations to study
DDG may be, for example, an expectation that discrete systems may be more fundamental and haverich mathematical structures as was clarified in the theory of integrable systems, or the development oftheoretical infrastructure for the visualization or the simulation of large deformation of geometric objects.
The purpose of this talk is to present a discrete analogue of the deformation theory of curves in space or inplane from the viewpoint of DDG.

17:00–18:00

Talk Invited by Geometry Section♭
Wenjiao Yan
Isoparametric foliation and Yau’s conjecture on the first eigenvalue(Tohoku Univ./Beijing Normal Univ.)

Summary: A well known conjecture of S. T. Yau states that the first eigenvalue of every closed minimal
hypersurface in the unit sphere is just its dimension. We show that Yau’s conjecture is true for minimal
isoparametric hypersurfaces. Moreover, a more fascinating result is that the first eigenvalues of the focal
submanifolds (which are minimal submanifolds in the unit sphere ) are equal to their dimensions in the
non-stable range.

March 22nd (Sun)

Conference Room IIIb

9:30–12:00
16 Tuerxunmaimaiti Yaermaimaiti ∗ (p, q)-Laplacians of regular Kaehler graphs · · · · · · · · · · · · · · · · · · · · · · · · 15
(Nagoya Inst. of Tech.)Toshiaki Adachi (Nagoya Inst. of Tech.)
Summary: A Kaehler graph is a compound graph and is a discrete model of a Kaehler manifold admitting
Kaehler magnetic fields. We define Laplacians corresponding to the random walk of (p, q)-step bicoloredpaths on this graph, give a condition that they are selfadjoint, and study their eigenvalues when the graphis finite.

17 Keita Kunikawa (Tohoku Univ.)

Bernstein theorem for ancient solutions to the mean curvature flow
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A solution of mean curvature flow which is defined on all negative time is called ancient solution.
Ancient solutions are good models of singularities of the mean curvature flow. For example, all self-shrinkers
and translators are ancient solutions. It is important to study these solutions to investigate the shapes of
singularities. In this talk, I give a non-existence theorem of entire graphic ancient solutions.

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Geometry

18 Keita Kunikawa (Tohoku Univ.)

Bernstein theorem of translating solitons in higher codimension · · · · · · 10

Summary: In this talk, I give a Bernstein-type theorem of entire graphs of translating solitons in higher
codimension. In the case of hypersurfaces, Bao–Shi showed that a translating soliton whose image of theGauss map is contained in a compact subset in an open hemisphere is a hyperplane. This means that there
is no nontrivial translating soliton whose slope is bounded. In the present article, we generalize this theorem
in a higher codimensional case. Moreover we obtain an optimal growth condition which allows unboundedslopes.

19 Hajime Koba (Waseda Univ.) ∗ On fluid-flow on an evolving hypersurface · · · · · · · · · · · · · · · · · · · · · · · · · 15
Yoshikazu Giga (Univ. of Tokyo)
Chun Liu (Pennsylvania State Univ.)
Summary: We consider fluid-flow on an evolving hypersurface. We focus on kinetic and dissipation energies toderive governing equations for the motion of incompressible viscous flow on an evolving hypersurface. Moreprecisely, we use a variational approach to derive the incompressible Euler and Navier–Stokes equations on
a prescribed evolving hypersurface.

20 Tatsuyoshi Hamada(Fukuoka Univ./Osaka City Univ.)

On star-Ricci flat real hypersurfaces of complex space forms · · · · · · · · · 10

Summary: In this article, we studied star-Ricci flat real hypersurfaces of non-flat complex space forms.

21 Makoto Kimura (Ibaraki Univ.)

Gauss map of real hypersurfaces in complex projective space and submanifolds in complex 2-plane Grassmannian · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We define Gauss map g from real hypersurfaces M in complex projective space CP n to complex
2-plane Grassmannian G2 (C n+1 ). If M is a Hopf hypersurface, then g(M ) is a half-dimensional totallycomplex submanifold in G2 (C n+1 ) with respect to quaternionic Kähler structure. Conversely, from a halfdimensional totally complex submanifold in G2 (C n+1 ), we can construct Hopf hypersurface in CP n by using
twistor space of G2 (C n+1 ).

22 Sadahiro Maeda (Saga Univ.) ∗ Some remarks on ruled real hypersurfaces in a nonflat complex space
Toshiaki Adachi (Nagoya Inst. of Tech.) form · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, we clarify geometric properties of ruled real hypersurfaces in a nonflat complex spaceform.

23 Kazuyuki Hasegawa (Kanazawa Univ.)

Twistor holomorphic aﬃne surfaces and projective invariants · · · · · · · · 10

Summary: We study aﬃne immersions from surfaces with twistor lifts and their projective invariants. In
particular, aﬃne immersions with holomorphic twistor lifts are considered. In the case of compact surfaces
with holomorphic twistor lifts, we see a quantization phenomenon for a projective invariant. Moreover, we
prove that a real analytic twistor holomorphic aﬃne surface with the symmetric Ricci tensor with respect
to both complex structures is totally geodesic or totally umbilic.

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Geometry

24 Masaro Takahashi(Kurume Nat. Coll. of Tech.)
Oscar Macia (Univ. of Valencia)
Yasuyuki Nagatomo (Meiji Univ.)

Holomorphic isometric embeddings of the projective line into quadrics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss holomorphic isometric embeddings of the projective line into quadrics from theviewpoint of gauge theory. We get a description of their moduli spaces up to image and gauge–equivalence.

13:00–14:15
25 Naoyuki Koike (Tokyo Univ. of Sci.)

Homogeneity by a Banach Lie group action of infinite dimensionalanti-Kähler isoparametric submanifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, we proved that, if a full irreducible infinite dimensional anti-Kähler isoparametricsubmanifold of codimension greater than one has J-diagonalizable shape operators, then it is an orbit of a
Banach Lie group action consisting of isometries of the ambient space whose associated holomorphic Killingfields are defined on the whole of the ambent space. In this talk, we explain the result and the outline ofthe proof.

26 Kotaro Kawai (Univ. of Tokyo)

Some associative submanifolds of the squashed 7-sphere · · · · · · · · · · · · · 15

Summary: The squashed 7-sphere S 7 is a 7-sphere with an Einstein metric given by the canonical variationand its cone R8 − {0} has full holonomy Spin(7). There is a canonical calibrating 4-form Φ on R8 − {0}. A
minimal 3-submanifold in S 7 is called associative if its cone is calibrated by Φ.
We classify two types of fundamental associative submanifolds in the squashed S 7 . One is obtained by theintersection with a 4-plane and the other is homogeneous. Then we study their infinitesimal associative
deformations and explicitly show that all of them are integrable.

27 Hideya Hashimoto (Meijo Univ.)
Misa Ohashi (Nagoya Inst. of Tech.)

On G2 , Spin(7)-orbit decomposition of Stiefel manifolds related toOctonions and its applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We investigate the real Stiefel manifolds Vk (Rn ) = SO(n)/SO(n − k) for n = 7 or n = 8.
If we identify R7 and R8 with ImC and C, respectively, then we have V2 (R7 ) = G2 /SU (2), V2 (R8 ) =Spin(7)/SU (3), and V3 (R8 ) = Spin(7)/SU (2). These real Stiefel manifolds can be represented as a orbit of
the action of the Lie group G2 or Spin(7). In this paper, we give the orbit decomposition of the another
Stiefel manifolds related to the octonions C under the action of Lie group G2 and Spin(7).

28 Takayuki Okuda (Hiroshima Univ.)
Osamu Ikawa (Kyoto Inst. Tech.)
Hiroshi Iriyeh (Tokyo Denki Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Hiroyuki Tasaki (Univ. of Tsukuba)

The intersection of two real flag manifolds in a complex flag manifold· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show a necessary and suﬃcient condition for the intersection of two real flag manifolds in acomplex flag manifold to be discrete. In the case where the intersection is discrete we prove that it is anantipodal set and describe it as an orbit of a certain Weyl group.

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Geometry

March 23rd (Mon)

Conference Room IIIa

9:45–12:00
29 Shigehiro Sakata (Waseda Univ.)

The location of centers of a body with the outer cone condition · · · · · · 15

Summary: We consider the renormalized Riesz potential of a body with the outer cone condition. We call amaximizer of the potential a radial center of a body. It is well-known that all radial centers are containedin the heart of the body. In this talk, we show that we can restrict the location of the centers into a smaller
region contained in the heart of the body.

30 Akifumi Sako (Tokyo Univ. of Sci.) ∗ Feature of gauge theory on noncommutative homogeneous Kähler manToshiya Suzuki
ifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Kushiro Nat. Coll. of Tech.)
Hiroshi Umetsu(Kushiro Nat. Coll. of Tech.)
Summary: We construct a gauge theory on a noncommutative homogeneous Kähler manifold by using thedeformation quantization with separation of variables for Kähler manifolds. A model of noncommutative
gauge theory that is connected with an ordinary Yang–Mills theory in the commutative limit is given. As
examples, we construct noncommutative CP N and noncommutative CH N and gauge thoeories on them.
We track the phenomena that local gauge symmetry breaks down under noncommutative deformation by
an obserbation of concreate model and explicit geometrical calculations. As a result, topological symmetries
are also broken by higher quantum collection by the deformation.

31 Masanori Adachi(GAIA, POSTECH/Nagoya Univ.)

A CR proof for a global estimate of the Diederich–Fornaess index ofLevi-flat real hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Yet another proof is given for a global estimate of the Diederich–Fornaess index of relatively
compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocalof the dimension of the ambient space. This proof reveals that this kind of estimate makes sense and holds
also for abstract compact Levi-flat CR manifolds.

32 Daisuke Tarama (Kyoto Univ.)

Stability analysis for the free rigid body dynamics on normal andcompact real forms of complex semi-simple Lie algebras · · · · · · · · · · · · · 15

Summary: This talk is based on a joint work with Tudor Ratiu (EPFL). The stability of the isolated equilibria
is considered for the generalized free rigid body dynamics on the normal and the compact real forms ofcomplex semi-simple Lie algebras, by using the results of Bolsinov and Oshemkov. It is shown that all theisolated equilibria on generic orbits for the system on normal real forms are hyperbolic and that those forthe system on compact real forms are elliptic.

∗
33 Hiroshi Sawai
Necessary conditions for LCK structures on compact solvmanifolds · · · 15
(Numazu Nat. Coll. of Tech.)

Summary: In this talk, we give necessary conditions for locally conformal Kähler structures with non-parallel
Lee from on compact solvmanifolds. Moreover, we construct a locally conformal symplectic solvmanifold
without a locally conformal Kähler structure.

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Geometry

34 Hisashi Kasuya(Tokyo Tech) ♭ Flat bundles and hyper-Hodge decomposition on solvmanifolds · · · · · · 10

Summary: By using Hodge theoretical properties for all topologically trivial rank 1 flat bundles, we represent
the structure theorem of Kähler solvmanifolds as extensions of Hasegawa’s result and Benson–Gordon’sresult for nilmanifolds.

35 Hisashi Kasuya(Tokyo Tech) ♭ Cohomologies of Sasakian groups and Sasakian solvmanifolds · · · · · · · · 10

Summary: We show certain symmetry of the dimensions of cohomologies of the fundamental groups of
comapct Sasakian manifolds and show that Sasakian solvmanifolds are finite quotients of Heisenberg
nilmanifolds.

36 Hisashi Kasuya(Tokyo Tech) ♭ Tamed symplectic structures of solvmanifolds · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the existence of tamed symplectic structures on solvmanifolds with left-invariant complex
structures.

14:15–16:45
37 Hikaru Yamamoto (Univ. of Tokyo)

Ricci-mean curvature flows in gradient shrinking Ricci solitons · · · · · · · 15

Summary: G. Huisken studied asymptotic behavior of a mean curvature flow moving in a Euclidean spacewhen it develops a singularity of type I, and proved that its parabolic rescaled flow converges to a selfshrinker in the Euclidean space. In this talk, we generalize this result for Ricci-mean curvature flows ingradient shrinking Ricci solitons.

38 Ryosuke Takahashi (Nagoya Univ.)

On the modified Futaki invariant of complete intersections in projective
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let M be a Fano manifold. We call a Kähler metric ω ∈ c1 (M ) a Kähler–Ricci soliton if itsatisfies the equation Ric(ω) − ω = LV ω for some holomorphic vector field V on M . It is known thata necessary condition for the existence of Kähler–Ricci solitons is the vanishing of the modified Futaki
invariant introduced by Tian–Zhu. In a recent work of Berman–Nyström, it was generalized for (singular)
Fano varieties and the notion of algebro-geometric stability of the pair (M, V ) was introduced. In thispaper, we propose a method of computing the modified Futaki invariant for Fano complete intersections inprojective spaces.

39 Shunsuke Saito (Univ. of Tokyo)

On the vanishing of the modified Futaki invariants · · · · · · · · · · · · · · · · · 10

Summary: In 2002, G. Tian and X. Zhu defined the modified Futaki invariant, which is an obstruction to
the existence of Kähler–Ricci solitons. This is a KRS analogue of the Futaki invariant. Using this, they
proved that there exists a unique holomorphic vector field such that the invariant associated to this vector
field vanishes on the reductive part of the Lie algebra of all holomorphic vector fields. Meanwhile, they
asked whether this obstruction vanishes on the unipotent part. Except for the toric case, there has been no
investigation for this. Hence, their question has been still open.
In this talk, we prove that the modified Futaki invariant vanishes on the unipotent part. This gives anaﬃrmative answer to the Tian–Zhu problem.

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Geometry

40 Homare Tadano (Osaka Univ.)

Gap theorems for Harmonic-Ricci solitons · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we shall give some gap theorems for Harmonic-Ricci solitons, which show somenecessary and suﬃcient conditions for Harmonic-Ricci solitons to be Harmonic-Einstein. Our results extend
the recent work by H. Li (Arch. Math. (Basel) 91: 187–192, 2008), and M. Fernández-López and E.
Garcı́a-Rı́o (Internat. J. Math. 23: 1250072, 2012).

41 Homare Tadano (Osaka Univ.)

A lower bound for the generalized scalar curvature of Harmonic-Ricci
solitons · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we shall give a lower bound for the generalized scalar curvature on complete domain
manifolds of certain Harmonic-Ricci solitons. Our results extend the recent work on a lower bound for thescalar curvature on gradient Ricci solitons by Chow, Lu and Yang (C. R. Acad. Sci. Paris, Ser. I 349:
1265–1267, 2011), and Fernández-López and Garcı́a-Rı́o (Proc. Amer Math. Soc. 141: 2145–2148, 2013).

42 Takayuki Moriyama (Mie Univ.)

Smoothness of deformations of submanifolds characterized by diﬀerential forms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We provided the smoothness theorem for deformations of submanifolds characterized by a sytemof diﬀerential forms on Riemannian manifolds in the previous talk. In this talk, we show the “refined”
smoothness theorem.

∗
43 Mamoru Doi
A new example of Calabi–Yau 3-folds by the doubling construction
Naoto Yotsutani (Fudan Univ.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a diﬀerential-geometric construction and examples of Calabi–Yau 3-folds, at least oneof which is new. Ingredients in our construction are admissible pairs, which were dealt with by Kovalev
and further studied by Kovalev and Lee. An admissible pair (X, D) consists of a 3-dimensional compactKähler manifold X and a smooth anticanonical K3 divisor D on X. If two admissible pairs (X 1 , D1 ) and(X 2 , D2 ) satisfy the gluing condition, we can glue X 1 \ D1 and X 2 \ D2 together to obtain a Calabi–Yau
3-fold M . In particular, if (X 1 , D1 ) and (X 2 , D2 ) are identical to an admissible pair (X, D), then the gluing
condition holds automatically, so that we can always construct a Calabi–Yau 3-fold from a single admissible
pair (X, D) by doubling it. Furthermore, we can compute all Betti and Hodge numbers of the resulting
Calabi–Yau 3-folds in the doubling construction.

∗
44 Mamoru Doi
Doubling construction of Calabi–Yau 4-folds from toric Fano 4-folds
Naoto Yotsutani (Fudan Univ.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We use our doubling construction to obtain Riemannian 8-manifolds with holonomy containedin Spin(7). In order to construct Calabi–Yau 4-folds, we use an admissible pair (X, D) consisting of a4-dimensional compact Kähler manifold X and a smooth anticanonical Calabi–Yau divisor D on X. As inthe doubling construction of Calabi–Yau 3-folds, smooth Fano 4-folds give admissible pairs (X, D) which
are said to be of Fano type. We can construct a Calabi–Yau 4-fold by the doubling construction from anyof the 124 types of smooth toric Fano 4-folds by showing that the Â-genus of the resulting manifold is equal
to 2.

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Geometry

45 Kota Hattori(Keio Univ.) ∗ Compact special Lagrangian submanifolds embedded in hyper-Kähler
manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct smooth families of compact special Lagrangian submanifolds embedded in some toric
hyper-Kähler manifolds, which never become holomorphic Lagrangian submanifolds via any hyper-Kähler
rotations. These families converge to special Lagrangian immersions with self-intersection points in thesense of current. To construct them, we apply the desingularization method developed by Joyce.

17:00–18:00
Yuji Odaka

Talk Invited by Geometry Section(Kyoto Univ.) ∗ Moduli of Kähler–Einstein manifolds and their canonical compactifications

Summary: After the development of the last half century of Kähler geometry [(..Poincare, Koebe..), Calabi,
Matsushima, Yau, Futaki, Mabuchi, Tian, Donaldson etc], now it is a theorem that existence of a “canonicalmetric” —Kähler–Einstein metrics— on a fixed complex manifold is equivalent to an algebro-geometricnotion called K-stability [Tian, Donaldson] of the manifold, which is essentially “infinite” variant of GIT
stability of David Mumford.
The protagonist of this talk would be Moduli space of those manifolds (rather than metric itself) —we willshow partially from our results as well as from [Fujiki, Donaldson etc], how the above stories of metrics fits
to, or can be applied to, construction of their nice moduli spaces. Furthermore, we get algebro-geometricnice compactifications of the moduli spaces, in a Gromov–Hausdorﬀ manner where interesting tractablesingularities appear.
I would (only) briefly explain algebro-geometric aspect, which is actually my origin. Algebro-geometrically,
the program above is to construct moduli of K-stable varieties (which I call “K-moduli”), which in turnoriginally came from my following observations: K-stability directly links to the theory of the minimal-modelprogram (“MMP”) in birational algebraic geometry, and thus the recent Kollár–Shepherd–Barron–Alexeev’s
higher dimensional generalisation of M̄g (the Deligne–Mumford compactification of moduli of compact
Riemann surfaces) are examples of K-moduli.

March 24th (Tue)

Conference Room IIIa

9:30–12:00
46 Vasile Sorin Sabau (Tokai Univ.)
Jin-ichi Itoh (Kumamoto Univ.)

On the cut locus of a family of Finsler manifolds · · · · · · · · · · · · · · · · · · · 15

Summary: Firstly we show that if (M, g) is a complete Riemannian manifold, then by an appropriate choiceof a function f : M → R we can construct a Finsler structure of Randers type F = α + df such that the cut
locus of this Randers metric coincides with the cut locus of the Riemannian metric (M, g) as set of points.
As application, we show that there are Finsler (and Riemannian) structures on some spheres whose cut
locus is a fractal, provided these structures are not C ∞ -structures.

47 Tetsuya Nagano (Univ. of Nagasaki)

On reversible geodesics in Finsler space · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Geodesics in Finsler space depend on a direction, in general. Namely, the geodesic from p to q is
diﬀerent from the geodesic from q to p. We call it “reversible” when the forward geodesic coincides with the
backward geodesic. In this lecture, existence conditions for reversible geodesics are stated.

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Geometry

48 Nobuhiro Innami (Niigata Univ.)

Geodesics in a Finsler 2-torus of revolution · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We first discuss three distances induced from a Finsler metric F . It motivates us to decompose F
into its symmetric part and skew-symmetric part. We show a condition of the reversibility of geodesics in(M, F ) by using the skew-symmetric part when it is a 1-form. We introduce Busemann–Pedersen’s results
concerning geodesics in tori with one-parameter group of motions. After that, we give two exmples ofRanders metrics on tori with one-parameter group of motions and study the behaviors of geodesics in their
universal covering planes.

49 Mitsuhiro Itoh (Univ. of Tsukuba)
Hiroyasu Satoh (Nippon Inst. of Tech.)Fisher information geometry of geodesics and barycenter map · · · · · · · 10

Summary: We investigate geometrical properties of geodesics defined on a space of probability measures on acompact smooth manifold in terms of Fisher information metric. It is known that geodesics are all periodic,of period 2π, non-complete by T. Friedrich. However, we obtain a new simple explicit formula for geodesics
from which we conclude that any two measures can be joined by a geodesic. We also apply the simple
formula to a barycenter map which is associated to probability measures defined on ideal boundary of an
Hadamard manifold.

50 Mitsuhiro Itoh (Univ. of Tsukuba)
Hiroyasu Satoh (Nippon Inst. of Tech.)Harmonic Hadamard manifolds and Gauss hypergeometric diﬀerential
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we would like to report a recent geometrical study of harmonic Hadamard manifolds,
which we call as those being of hypergeometric type, on which the inversion formula for Fourier sphericaltransform can be defined.

51 Kei Kondo (Yamaguchi Univ.)
Minoru Tanaka (Tokai Univ.)

Bi-Lipschitz diﬀeomorphism theorem via the notion of nonsmooth analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We recently proved that if a bi-Lipschitz map between compact manifolds and its inverse map
have no singular point in the sense of F. H. Clarke, respectively, then they are diﬀeomorphic. We will
introduce this result to you.

52 Ryunosuke Ozawa (Tohoku Univ.)

Metric on the space of quantum metric measure spaces · · · · · · · · · · · · · 15

Summary: In this talk, I talk about metric on the space of quantum metric measure spaces. We define thedistance between two quantum metric measure spaces and consider relation between Gromov’s box distancefunction on the space of metric measure spaces and it. We also generalize the concentration function
for quantum metric measure space and consider the relation between the convergence of quantum metricmeasure spaces and it.

53 Takashi Shioya (Tohoku Univ.)

Estimate of isodiametric constant for closed surfaces · · · · · · · · · · · · · · · · 10

Summary: We give an explicit estimate of the area of a closed surface by the diameter and a lower bound ofcurvature. This is better than Calabi–Cao’s estimate for a nonnegatively curved two-sphere.

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Geometry

54 Ayato Mitsuishi (Tohoku Univ.) ∗ Collapsing three-dimensional Alexandrov spaces with boundary · · · · · · 15
Takao Yamaguchi (Kyoto Univ.)
Summary: Alexandrov spaces are complete length spaces with the notion of curvature bounds. They naturally
appear in collapsing phenomena of Riemannian manifolds with a lower curvature bound, and have played
important roles in the study of collapsing Riemannian manifolds with a lower curvature bound. In thistalk, I will announce that the topologies of collapsing compact Alexandrov three-spaces with nonempty
boundaries are determined.

14:15–15:50
55 Tatsuki Seto

(Nagoya Univ.)

Toeplitz operators and the Roe–Higson type index theorem · · · · · · · · · 15

Summary: In 1988, Roe proved some index theorem on a complete Riemannian manifold M which ispartitioned by a closed hypersurface N . His theorem states that Connes’ pairing of Roe’s cyclic one cocyclewith the Cayley transform of a Dirac operator on M is calculated by the Fredholm index of the Dirac
operator DN on N . Higson gave a simple proof of Roe’s index theorem in 1991.
If M is even dimensional, Roe–Higson’s index theorem is trivial in some sense since the Fredholm index of
DN is always zero. In this talk, I will show another non-trivial index formula with Toeplitz operators as aneven dimensional analogue of Roe–Higson’s theorem.

56 Mamoru Tanaka (Tohoku Univ.)

Property (TLΦ ) for Orlicz spaces LΦ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A finitely generated group is said to have Property (F H) if every aﬃne isometric action on a real
Hilbert space has a fixed point. It is well known that Property (F H) is equivalent to Kazhdan’s Property(T ). These properties ware generalized to properties (FB ) and (TB ) for Banach spaces B, and they are wellstudied when B are Lp spaces. We give some relations between (TLΦ ) and (T ), and between (FLΦ ) and(F H) for Orlicz spaces LΦ , which are generalization of Lp spaces.

57 Ryosuke Mineyama (Osaka Univ.)
Shin-ichi Oguni (Ehime Univ.)

Coarse geometry of the Hilbert metric · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a necessary and suﬃcient condition for which the natural boundary of a Hilbert geometry
to be a corona, i.e., it admits a continuous surjection from the Higson corona. In addition, we show that theHilbert geometry is with coarse bounded geometry. As a consequence of this we see that the coarse Novikov
conjecture holds for Hilbert geometries whose boundaries are coronae. On the other hand, we determine theasymptotic dimension of 2-dimensional Hilbert geometries and 2-dimensional Hadamard manifolds.

58 Tomohiro Fukaya (Tohoku Univ.)

Coronae of product spaces and the coarse Baum–Connes conjecture· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the coarse Baum–Connes conjecture for product spaces and product groups. We showthat a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy someassumptions on peripheral subgroups, satisfies the coarse Baum–Connes conjecture. For this purpose, weconstruct and analyze an appropriate compactification and its boundary, “corona”, of a product of proper
metric spaces.

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Geometry

59 Masato Mimura (Tohoku Univ.) ∗ Group approximations in Cayley topology and coarse geometry: part II:(Niigata Univ.) Fibered coarse embeddings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hiroki Sako
Summary: We study “fibered coarse embeddings”, in the sense of Chen–Wang–Yu, of a sequence of finite
Cayley graphs in terms of the convergence in the space of marked groups of Grigorchuk.

16:00–17:00

Talk Invited by Geometry Section

Ayato Mitsuishi (Tohoku Univ.) ♭ Topology of Alexandrov spaces
Summary: In this talk, I will discuss about some naive problem on topology of Alexandrov spaces. Here,
Alexandrov spaces are complete metric space having a lower curvature bound in the sense that theysatisfy triangle comparison, which are generalized objects of complete Riemannian manifolds having a lower
sectional curvature bound. They naturally appear in convergence and collapsing phenomena of Riemannian
manifolds with a lower curvature bound, and have played important roles in the study of collapsingRiemannian manifolds with a lower curvature bound. So, it is important to study geometric and topologicalstructures of Alexandrov spaces.
I will talk about the following topics on topology of Alexandrov spaces. (1) Several notions of “orientability”
of Alexandrov spaces are considered. I will announce that they are equivalent. (2) For every closed
Alexandrov space, its orientability (in the sense of (1)) implies and is implied by the existence of fundamental
homology class. (3) Orientable closed Alexandrov spaces satisfy “Poincaré duality” in special degrees. It
follows from this study that every orietable closed Alexandrov space of positive curvature has trivial integral
homology of codimension one.

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Complex Analysis

Complex Analysis
March 23rd (Mon)

Conference Room VII

9:30–11:45∗
1 Saburou Saitoh
New meanings of the division by zero and interpretations on 100/0= 0(Gunma Univ.⋆/Inst. of Reproducing Kernels) and on 0/0=0 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Masao Kuroda (Gunma Univ.⋆)
Hiroshi Michiwaki (NejiLaw Inc.)
Masami Yamane(Inst. of Reproducing Kernels)

Summary: We shall give simple and natural, however, the surprising identities 100/0=0 and 0/0 =0 by anatural extension of fractions with the concept of Tikhonov regularization using the theory of reproducing
kernels. We shall give interpretations and the situation of the results.

∗
2 Saburou Saitoh
A new concept for the point at infinity and the division by zero z/0=0⋆(Gunma Univ. /Inst. of Reproducing Kernels) (note) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hiroshi Michiwaki (NejiLaw Inc.)
Masako Takagi(Inst. of Reproducing Kernels)

Summary: We shall introduce a new concept for the point at infinity on the Riemann sphere and the zero
division z/0=0. As a typical result, we shall derive the surprising result: At an isolated singular point ofan analytic function, it takes a definite value with a natural meaning. As the important applications of thisresult, the extension formula of functions with analytic parameters may be obtained and singular integrals
may be interpretated with the division by zero, naturally.

∗
3 Rikio Yoneda
The Fredholm Toeplitz operator and the Berezin transform · · · · · · · · · · 10
(Otaru Univ. of Commerce)

Summary: In this talk, we study the Fredholm Toeplitz operator on the Bergman spaces using the Berezintransform.

4 Kiyoki Tanaka (Osaka City Univ.)
Masaharu Nishio (Osaka City Univ.)

Boundary behavior of harmonic Bergman kernels · · · · · · · · · · · · · · · · · · 15

Summary: We deal with radial measure weighted harmonic Bergman spaces on the ball. For two radialmeasures, we introduce an averaging function, to give the condition for corresponding Toepitz operators to
be bounded and compact. We discuss the boundary behavior of harmonic Bergman kernels.

5 Hiroaki Aikawa (Hokkaido Univ.)

Construction of a domain which fails to satisfy the global boundary
Harnack principle with the aid of the Helmholtz equation · · · · · · · · · · · 15

Summary: We study the Poisson representation for the Helmholtz equation in the half space and give aprecise estimate of the Poisson integrals. This estimate is applied to show the sharpness of the modulus ofcontinuity of a function f for which the domain above the graph of f satisfies the global boundary Harnack
principle.

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Complex Analysis∗
6 Nobushige Toda
On the defect relation for holomorphic curves · · · · · · · · · · · · · · · · · · · · · · 15
(Nagoya Inst. of Tech.⋆)Summary: Let f be a transcendental holomorphic curve from C into the n-dimensional complex projective
space P n (C) and a ∈ C n+1 \ {0}, where f is linearly non-degenerate over C. If a has multiplicity m for f ,we put µ(a, f ) = (1 − n/m)+ , where m = ∞ when (a, f ) = a1 f1 + · · · + an+1 fn+1 has no zero. Let X be asubset of C n+1 \ {0} in N -subgeneral position, where N ≥ n, M 1 the set of a ∈ X for which µ(a, f ) = 1∑
and ∆ = a∈X µ(a, f ). We estimate ∆ when ∆ > N + 1, ♯M 1 is relatively large and ♯M 1 ≤ N .

7 Hiroki Sumi

(Osaka Univ.)

Randomness-induced phenomena and negativity of Lyapunov exponents
in random dynamical systems of complex polynomials · · · · · · · · · · · · · · 15

Summary: We show that for a generic random dynamical system of complex polynomials of degree two
or more, the Lyapunov exponents are negative and the chaoticity is much weaker than a usual iteration
dynamical system of a single polynomial. This is due to a non-trivial eﬀect of randomness. We call suchphenomena “randomness-induced phenomena”.

8 Shunsuke Morosawa (Kochi Univ.)

On dynamics of rational semigroups whose Julia sets are Cantor targets· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider dynamics of rational semigroups whose Julia sets are Cantor targets.

14:15–14:45
9 Hideki Miyachi (Osaka Univ.)

Spirals and the asymptotic Teichmüller space · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I will discuss the Bers density problem for the asymptotic Teichmüller space of the unit disk. I
will show that the Schwarzian derivative for Gehring’s spiral domain is asymptotically equivalent to the
Schowarzian derivative of a Jordan domain which is in the closure of the universal Teichmüller space. I will
also observe that the asymptotic class of the Schwarzian derivative of Flinn’s domain is not contained in theclosure of the asymptotic Teichmüller space.

10 Hiromi Ohtake (Kyoto Univ. of Edu.) ∗ On isometric mappings from the unit disk to Teichmüller spaces · · · · · 15
Summary: We can show that if h1 , h2 are two distance non-increasing mappings from the unit disk D withhyperbolic metric to itself, and if the mapping (h1 , h2 ) from D to the polydisk D2 is isometric, then either
h1 or h2 is isometric. From this results, we can show that new result on isometric mappings from the unit
disk to Teichmüller spaces.

15:10–16:10

Talk Invited by Complex Analysis Section

Hiroshige Shiga (Tokyo Tech)

On the deformation spaces of Kleinian groups

Summary: Let G be a non-elementary Kleinian group. We consider the deformation space D(G) of G, thespace of quasiconformal deformations of G, and its complex analytic properties. We show some analytic
properties of D(G) which are improvements of results obtained by Bers, Kra, Maskit and McMullen. In
particular, we clarify that the structures for Kleinian groups with non-simply connected components are
diﬀerent from those for Kleinian groups without non-simply connected components.

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Complex Analysis

16:25–17:25

Award Lecture for 2014 Analysis Prize

Hidetaka Hamada(Kyushu Sangyo Univ.)

Approximation of holomorphic mappings on spirallike domains in Cn

Summary: In this talk, we will show that any domain D in Cn which is spirallike with respect to a linear
operator A, where m(A) > 0, is Runge. We also show the local uniform approximation of biholomorphic
mappings on a spirallike domain D with respect to A, where k+ (A) < 2m(A), by automorphisms of Cn .
Finally, as an application of the above result, we will show that any Loewner PDE in a complete hyperbolic
spirallike domain D with respect to A, where k+ (A) < 2m(A), of Cn admits an essentially unique univalentsolution with values in Cn .

March 24th (Tue)

Conference Room VII

9:30–11:45
11 Atsuhira Nagano (Waseda Univ.)

Icosahedral invariants and Shimura curves · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Shimura curves are the moduli space of principally polarized abelian surfaces with quaternion
multiplication. In this talk, we obtain explicit and simple models of Shimura curves with small discriminant.
Our Shimura curves appear as divisors in a weighted projective space whose coordinates are given byicosahedral invariants.

12 Atsuhira Nagano (Waseda Univ.)

Icosahedral invariants and CM points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We shall give an example of the unramified class field over a quartic CM field. Our class fieldis generated by special values of analytic functions in two variables which have an expression coming from
icosahedral invariants.

13 Takayuki Koike (Univ. of Tokyo) ∗ On the minimality of canonically attached singular Hermitian metrics
on certain nef line bundles · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle
L. Especially we study minimal singular metrics of L, metrics of L with the mildest singularities among
singular Hermitian metrics of L whose local weights are plurisubharmonic. In some situations, we determine
a minimal singular metric of L. As an application, we give new examples of (strictly) nef line bundles which
admit no smooth Hermitian metric with semi-positive curvature.

14 Katsusuke Nabeshima(Univ. of Tokushima)
Shinichi Tajima (Univ. of Tsukuba)

An extended ideal membership algorithm in a local ring · · · · · · · · · · · · 15

Summary: It is known that a membership problem of ideals in a local ring, is solved by local cohomology. In
this talk, an extended ideal membership algorithm is considered in the ring of convergent power series. The
key of the proposed method is to compute syzygyies in a polynomial ring (global ring) and the use of local
cohomology.

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Complex Analysis

15 Shinichi Tajima (Univ. of Tsukuba)
Katsusuke Nabeshima(Univ. of Tokushima)

Integral dependence relations and local cohomology · · · · · · · · · · · · · · · · 15

Summary: Integral dependence relations are considered in the ring of convergent power series for the Jacobi
ideal of an isolated hypersurface singularity. An eﬀective algorithm of computing integral dependence
relations is described. The key of the proposed method is the use of local cohomology and of Grothendiecklocal duality theorem.

16 Kohei Ueno

(Daido Univ.) ∗ Böttcher coordinates at superattracting fixed points of holomorphic
skew products · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let f : (C2 , 0) → (C2 , 0) be a germ of holomorphic skew product with a superattracting fixed
point at the origin. If it has a suitable weight, then we can construct a Böttcher coordinate which conjugatesf to the associated monomial map. This Böttcher coordinate is defined on an open set whose interior orboundary contains the origin.

17 Tomoko Shinohara(Tokyo Metro. Coll. of Ind. Tech.)

Local dynamics at an indeterminate point of Newton’s method · · · · · · 15

Summary: In this talk, consider the local dynamics at an indeterminate point of Newton’s method. Y.
Yamagishi studied that Newton’s method of some holomorphic function of two variables. He showed that
there exists a neighborhood of its indeterminate point that is divided into three subsets A, B and C, where
A is an attracting set, B is a bursting set and C is a Cantor bouquet. By using a sequence of blow ups, we
try another approach to the construction of a local dynamics of its indeterminate point.

18 Junichi Mukuno (Nagoya Univ.)
Yoshikazu Nagata (Nagoya Univ.)

On the automorphism groups of unbounded homogeneous domains withthe boundaries of light cone type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we determine the automorphism groups of some unbounded homogeneous domains
with the boundaries of light cone type.

19 Atsushi Yamamori (POSTECH)(POSTECH)
Hyeseon Kim(POSTECH)
Van Thu Nihn

The autormophism group of a certain unbounded Reinhardt domain· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we give a description of the holomorphic automorphism group of a certain unbounded
Reinhardt domain.

14:15–15:10
20 Akio Kodama (Kanazawa Univ.) ♭ On the holomorphic automorphism group of a generalized Hartogs
triangle and a related question · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, we completely determine the structure of the holomorphic automorphism group of
a generalized Hartogs triangle and obtain natural generalizations of some results due to Landucci and
Chen–Xu. These give aﬃrmative answers to some open problems posed by Jarnicki and Pflug. Also we
discuss some related question with our results.

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Complex Analysis

21 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 National Univ.)

Suﬃcient conditions for univalence and starlikeness in complex Banach
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss some suﬃcient conditions for univalence and starlikeness of normalized
holomorphic mappings on the unit ball in a complex Banach space.

22 Sachiko Hamano (Fukushima Univ.) ∗ Hyperbolic span and pseudoconvexity · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Masakazu Shiba (Hiroshima Univ.⋆)
Hiroshi Yamaguchi (Shiga Univ.⋆)
Summary: The planar open Riemann surface R admits Schﬀer span s(R, ζ) with pole ζ ∈ R. M. Shibashowed that the open Riemann surface of genus one admits the hyperbolic span σh (R). We establish
the variation formula of σH (t) := σH (R(t)) for the moving open Riemann surface R(t) of genus one withcomplex parameter t in a disk ∆. This formula implies the following intimite relation between the hyperbolic
span and the pseudoconvexity: If the total space R = ∪t∈∆ (t, R(t)) is a two dimensional Stein manifold,then σH (t) is subharmonic on ∆. Further, σH (t) is harmonic on ∆ iﬀ R is biholomorphic to the product∆ × R(0).

15:30–16:30

Talk Invited by Complex Analysis Section

Yusaku Tiba

(Tokyo Tech)

A minimum principle of a maximal plurisubharmonic function and its
application to the complex Monge–Ampère equation

Summary: In this talk, we study a geometric property of a solution of the Monge–Ampère equation which
has a convex level set by using our minimum principle of a maximal plurisubharmonic function. We also
show a relation between the supports of the Monge–Ampère currents and complex extreme points of closed
balls for the Kobayashi distance in a bounded convex domain in Cn .

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42Functional Equations

Functional Equations
March 21st (Sat)

Conference Room Va

9:15–12:00
1 Mika Tanda
Takashi Aoki

(Kinki Univ.)(Kinki Univ.)

The hypergeometric function and WKB solutions · · · · · · · · · · · · · · · · · · 10

Summary: We consider the relation between the hypergeometric function and WKB solutions of the hypergeometric diﬀerential equation with a large parameter. The hypergeometric function is equal to a constantmultiple of the Borel sum of the WKB solution recessive at the origin. We give the multiplicative constantin some cases. These results yield some formulas that describe asymptotic expansions of the hypergeometricfunction with respect to the large parameter.

2 Toshinori Takahashi (Kinki Univ.)(Kyoto Univ.)
Kohei Iwaki(Kinki Univ.)
Takashi Aoki

Exact WKB analysis of Schrödinger equation with a Stokes curve ofloop type · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a Schrödinger-type ordinary diﬀerential equation with a large parameter in thecomplex domain. Our main interest is the Stokes phenomena of WKB solutions of the equation associatedwith a Stokes curve of loop type. To analyze them, we employ a modified Bessel equation as a canonicalform and compute the Voros coeﬃcient of the equation. Combining the formula describing the Stokes
automorphism for the Voros coeﬃcient and the formal coordinate transformation connecting the Schrödingertype equation and the modified Bessel equation, we have some formula concerning parametric Stokes
phenomena for WKB solutions.

3 Yoshiaki Goto

(Kobe Univ.)

Contiguity relations of Lauricella’s FD and contingency tables · · · · · · · 10

Summary: In this talk, I would like to give contiguity relations of Lauricella’s FD , in terms of the twisted
cohomology group and the intersection form. Our formulas are applied to the numerical evaluation of thenormalizing constant of the hypergeometric distribution on the 2 × (m + 1) contingency tables with a fixedmarginal sums.

4 Youko Umeta (Tokyo Univ. of Sci.)
Shinichi Tajima (Univ. of Tsukuba)
Toshinori Oaku
(Tokyo Woman’s Christian Univ.)

On the monodromy structure of holonomic D-modules associated withsimple line singularities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We construct algebraic local cohomology solutions for holonomic D-modules associated withsimple line singularities and we study the monodromy structure of holonomic D-modules.

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5 Masafumi Yoshino (Hiroshima Univ.)
Yoshinari Tanaka(Nat. Inst. for Environ. Stud.)behavior of the system for three species with evolutional character · · · 10

Summary: We will study global properties of evolutional Lotka–Volterra system. We assume that the
predatory eﬃciency is a function of a character of species whose evolution obeys a quantitative genetic
model. We will show that the structure of a solution is rather diﬀerent from that of a non-evolutional
system. We will analytically show new ecological features of the dynamics.

6 Masafumi Yoshino (Hiroshima Univ.)
Hiroshi Yamazawa(Shibaura Inst. of Tech.)

Borel summability of formal solutions of system of semilinear partial
diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we are interested in the Borel summability of formal solutions with a parameter offirst order semilinear system of partial diﬀerential equations with n independent variables. In [1], Balser andKostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter
for a linear equation with one independent variable. We will extend their results to a semilinear system of
equations with general independent variables.

7 Yoshikatsu Sasaki (Hiroshima Univ.)
Yoshino Masafumi (Hiroshima Univ.)

Nonintegrability of Hamiltonian system perturbed from integrable system with two singular points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a Hamiltonian system equivalent to confluent Okubo equation, and show that acertain perturbation destroys the integrability of it.

8 Kodai Fujimoto (Osaka Pref. Univ.)
Naoto Yamaoka (Osaka Pref. Univ.)

Existence of limit cycles for Liénard type systems with mean curvature
operator · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the system ẋ = φ−1
C (y), ẏ = −f (x)y − g(x) which is equivalent to the Liénard type√equation (φC (ẋ))˙ + f (x)φC (ẋ) + g(x) = 0, where φC (x) = x/ 1 + x2 , and f (x) and g(x) are smoothfunctions. Since the range of φC is bounded, some solutions of the system may not be global solutions.
Using phase plane analysis, time maps and Poincaré–Bendixson Theorem, we obtain a suﬃcient conditon
under which the system has at least one limit cycles.

9 Tomoyuki Tanigawa (Kumamoto Univ.)

Existence of positive solutions of fourth order sub-half-linear diﬀerential
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The feature of the present work is to demonstrate that the method of regular variation can beeﬀectively applied to fourth order sub-half-linear diﬀerential equations providing full information about theexistence and the precise asymptotic behavior of all possible postive solutions.

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Functional Equations

10 Tetsutaro Shibata (Hiroshima Univ.)

Global and local behavior of oscillatory bifurcation curve · · · · · · · · · · · · 10

Summary: We consider the positive solutions for the equation u′′ (t) + λf (u(t)) = 0, t ∈ I =: (−1, 1) with theboundary condition u(±1) = 0, where λ > 0 is a parameter. We know that under the suitable conditions on
f (u), the bifurcation curve λ = λ(α) (α = ∥uλ ∥∞ > 0) is a continuous function of α > 0 and λ(α) → π 2 /4
as α → 0 and α → ∞. Furthermore, it intersects the line λ = π 2 /4 infinitely many times as α → 0. We
show that the bifurcation curve λ(α) does not intersect the line λ = π 2 /4 infinitely many times as α → ∞by establishing the precise asymptotic formula for λ(α) as α → ∞.

11 Hiroyuki Usami (Gifu Univ.) ∗ Asymptotic behavior of solutions of a Lanchester-type model · · · · · · · · 10
Huyen Trang Tran Thi (Gifu Univ.)
Summary: We consider asymptotic behavior of all solutions of initial value problems to a Lanchester-typemodel. We can show how they behave at the infinity depending on initial data.

12 Seiji Saito(Doshisha Univ.)

On Graef–Qian’s theorem of diﬀerence equations · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we show an extension of Graef–Qian’s theorem which is concerning the globally
asymptotic stability of diﬀerence equations.

13 Motohiro Sobajima (Univ. of Salento)
Giorgio Metafune (Univ. of Salento)
Noboru Okazawa (Tokyo Univ. of Sci.)
Chiara Spina (Univ. of Salento)

Analytic semigroups generated by |x|α ∆ with singular lower-order terms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we deal with generation of analytic semigroups on Lp = Lp (RN ) (1 < p < ∞) by
elliptic operators of the form L = |x|α ∆ + c|x|α−2 x · ∇ − b|x|α−2 (x ∈ RN \ {0}), where c, b ∈ R and α ∈ Rwith α ̸= 2 are fixed constants. We give the necessary and suﬃcient condition for generation of positive andanalytic semigroups.

14 Motohiro Sobajima (Univ. of Salento)
Giorgio Metafune (Univ. of Salento)

Spectral properties of non-selfadjoint extensions of Calogero Hamiltonian · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we consider the Calogero Hamiltonian in L2 (R+ ) (R+ = (0, ∞)), that is, we deald2bwith one-dimensional Schrödinger operators with inverse-square potentials H = − dr
2 + r 2 (r ∈ R+ ), whereb < −1/4. We give the spectrum of all realizations of H having non-empty resolvent sets.

15 Fumihiko Hirosawa (Yamaguchi Univ.)
Marcelo Rempel Ebert(Univ. de São Paulo)
Fitriana Laila (Yamaguchi Univ.)

On the energy estimates of the wave equation with time dependent
propagation speed asymptotically monotone functions · · · · · · · · · · · · · · 10

Summary: We consider the energy estimates for the wave equation with time dependent propagation speed.
It is known that the asymptotic behavior of the energy is determined by the interactions of the propertiesof the propagation speed: smoothness, oscillation and the diﬀerence from a reference function. The main
purpose of our talk is that if the propagation speed behaves asymptotically a monotone decreasing function,then we can extend the preceding results to allow faster oscillating coeﬃcients. Moreover, we prove that theregularity of the initial data in the Gevrey class can essentially contribute for the energy estimate.

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14:15–16:30
16 Wataru Ichinose (Shinshu Univ.)

The Feynman path integral for the Dirac equation (1), the electron
going across the infinite past and future · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Feynman path integral for the Dirac equation has been determined mathematically in theform of the sum-over-histories satisfying the superposition principle. That is, it is given in the form of the“sum” of the probability amplitudes with a common weight, over all possible paths that go in any direction
at any speed forward and backward in time. In this talk we show that the path space taken into accountcan be made of paths going across the infinite past and future. Considering the path space like this will be
important for the Feynman path integral to be applied to the theory of quantum electrodynamics.

17 Wataru Ichinose (Shinshu Univ.)

The Feynman path integral for the Dirac equation (2), Causality (finite
propagation property not exceeding c) · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Feynman path integral for the Dirac equation has been determined mathematically in theform of the sum-over-histories satisfying the superposition principle over the path space. The path space
is made of all possible paths that go in any direction at any speed forward and backward in time, and go
across the infinite past and future. In this talk we show directly that the Feynman path integral has the
propagation speed not exceeding the velocity of light c and so that causality is preserved under the Lorentz
transformation. It is well known in the theory of the partial diﬀerential equations that the Dirac equation
has the propagation speed not exceeding c.

18 Sojiro Murai (Univ. of Electro-Comm.) ∗ Smoothing and Strichartz estimates for wave equation in an exterior
Kiyoshi Mochizuki
domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Tokyo Metro. Univ.⋆ /Chuo Univ.)
Summary: In this talk we shall show the smoothing and Strichartz estimates for the wave equation withlarge potential in an exterior domain. The fundamental tool is the uniform estimate for the resolvent of the
Schrödinger operators.

19 Masato Hashizume (Osaka City Univ.)
Futoshi Takahashi (Osaka City Univ.)

Lp -Lyapunov inequality on Neumann boundary condition · · · · · · · · · · · 10

Summary: Lyapunov inequality is a necessary condition for some ordinary diﬀerential equation. Cañada,
Montero and Villegas considered this problem in partial diﬀerential equations which is Lp -Lyapunov
inequality. In this talk, the author introduce the result of Lp -Lyapunov inequality in Neumann deta case.

20 Shinji Adachi (Shizuoka Univ.)
Tatsuya Watanabe(Kyoto Sangyo Univ.)

Asymptotic uniqueness of ground states of quasilinear elliptic equations
with H 1 -supercritical exponent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we show the asymptotic uniqueness of ground states for a class of quasilinear elliptic
equations with H 1 -supercritical exponent. To this aim, the uniqueness and the non-degeneracy of positive
solutions of the corresponding limit equation, which is a zero mass problem, play important roles. Thus
we also show the uniqueness and non-degeneracy result for a class of zero mass problems by applying ODE
techniques.

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Functional Equations(Saitama Univ.) ∗ Remark on Nehari type condition for a least energy solution of semi21 Yohei Sato
Masataka Shibata (Tokyo Tech) linear elliptic equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: To study existence of solutions for semi-linear elliptic equation, Nehari manifold is useful. We
introduce that we can find the Nehari-type variational structure under the general assumption than former
results. We also give applications.

22 Kenichiro Umezu (Ibaraki Univ.) ∗ On the role of indefinite weights in the positive solutions set for an
Humberto Ramos Quoirin
elliptic boundary value problem with convex-concave mixed nonlinearity(Univ. de Santiago de Chile)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we consider some indefinite superlinear elliptic boundary value problem with anonlinear boundary condition, having convex-concave mixed nonlinearity. The goal is to understand therole of indefinite weight functions included in the problem in determining the structure of its nontrivial
non-negative solutions. Variational and bifurcation approaches are both used in our argument.

23 Ryo Takahashi (Osaka Univ.)
Takashi Suzuki (Osaka Univ.)(Osaka Univ.)
Xiao Zhang

Extremal boundedness of a variational functional in point vortex mean
field theory associated with probability measures · · · · · · · · · · · · · · · · · · · 10

Summary: We study a variational functional of Trudinger–Moser type associated with one-sided Borel
probability measure. Its boundeness at the extremal parameter holds when the residual vanishing occurs.

24 Kotaro Watanabe(Nat. Defense Acad. of Japan)
Naoki Shioji (Yokohama Nat. Univ.)

Lp elastic closed curves and flat-core solutions on S2 (G) · · · · · · · · · · · · 10

Summary: In this talk, we consider Lp elastica problem on S2 (G), where G is a Gaussian curvature.
Especially, we show the existence of flat-core type solution if p > 2.

25 Atsushi Kosaka (Osaka City Univ.)
Yasuhito Miyamoto (Univ. of Tokyo)

Structure of solutions to the Emden–Fowler equation on a spherical cap· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we speak of the result on the structure of positive and radial solutions to the Emden–
Fowler equation defined on a spherical cap. In our problem, the structure of solutions is qualitatively diﬀerent
from the structure of solutions to a similar problem defined on the Euclidean space or the hyperbolic space,especially, the exponent of a nonlinear term is greater than the critical Sobolev exponent. Hence we focus
our attention on our problem, and obtain the result on the global structure of solutions.

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26 Yasuhito Miyamoto (Univ. of Tokyo)

Nonradial maximizers for a Hénon type problem and Liouville–Gel’fandproblem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the radiality and nonradiality of the maximizers of
{∫
}
∫
2
sup
|x|α (eu − 1)dx; u ∈ H01 (D),|∇u| dx = β 2DDfrom a viewpoint of the bifurcation diagram of the Euler–Lagrange equation∆u + β 2 ∫|x|α eu= 0 in D,|x|α ueu dx
D

u = 0 on ∂D,

where D := {x ∈ R2 ; |x| < 1}.

27 Ryuji Kajikiya(Saga Univ.)

Symmetric mountain pass lemma and sublinear elliptic equations · · · · 10

Summary: In this lecture, we study the p-Laplace elliptic equations under the Dirichlet boundary condition
and give a general and weak suﬃcient condition for the existence of a sequence of solutions converging tozero. This result is proved by applying the symmetric mountain pass lemma obtained in our earlier paper.

16:50–17:50

Talk Invited by Functional Equations Section

Kazuyuki Yagasaki (Kyoto Univ.)

Existence and bifurcation of positive radial solutions in elliptic equations

Summary: In this talk I review my recent results on existence and bifurcation of positive radial solutions in
elliptic equations, including collaborations with Profs. Miyamoto and Nawa.

March 22nd (Sun)

Conference Room Vb

9:15–12:00
28 Toshiharu Kawasaki (Tamagawa Univ.)
Masashi Toyoda (Tamagawa Univ.)

Fixed point theorem and fractional diﬀerential equation with multiple
delays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we show a new fixed point theorem which is a generalization of both of Lou’s fixed
point theorem and de Pascale and de Pascale’s fixed point theorem. Moreover our result can be applied
existence theorem of a unique solution for fractional diﬀerential equations with multiple delays. Using theexistence theorem, we discuss a unique solution for the fractional chaos neuron model.

29 Tatsuya Miura (Univ. of Tokyo)

Singular limit of an adhesive obstacle problem · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider an obstacle problem of a total energy consisting of a bending energy,
tension, and an adhesion energy. This problem corresponds to, for example, determining the shape ofmembranes or filaments on some substrates. In this case, the total energy functional is not convex andthere may exist multiple minimizers. We give some results about the shape of minimizers in the case thatthe bending energy is negligible. Moreover, we also give a singular limit of this energy when the bending
energy is small.

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30 Toshikazu Kuniya (Kobe Univ.)

Asymptotic behavior of age-structured SIS epidemic models with spatial
heterogeneity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we are concerned with some age-structured SIS epidemic models with spatial
heterogeneity. By virtue of the monotonicity of semiflows defined by their solutions, we can prove theexistence, uniqueness and global attractivity of the nontrivial endemic equilibrium in the case where thespectral radius of a linear operator is greater than unity. Concretely, a model with patch structure (asdiscrete spatial heterogeneity) and a model with diﬀusion (as continuous spatial heterogeneity) are planned
to be presented.

31 Saori Nakamori (Hiroshima Univ.)
Kazuhiro Takimoto (Hiroshima Univ.)

Bernstein type theorem for the parabolic k-Hessian equation · · · · · · · · 10

Summary: In this talk, we are concerned with the characterization of entire solutions to the parabolic kHessian equation of the form −ut Fk (D2 u) = 1 in Rn × (−∞, 0]. We prove that for 1 ≤ k ≤ n, any strictly
parabolically convex solution u = u(x, t) ∈ C 4,2 (Rn × (−∞, 0]) to −ut Fk (D2 u) = 1 in Rn × (−∞, 0] must
be a linear function of t plus a quadratic polynomial of x, under some growth assumptions on u.

32 Masato Iida (Univ. of Miyazaki)
Hideki Murakawa (Kyushu Univ.)
Harunori Monobe (Meiji Univ.)
Hirokazu Ninomiya (Meiji Univ.)

Generalization of fast reaction limit for a two-component system · · · · · 10

Summary: In this talk, we consider the fast reaction limit of a two-component system which corresponds
approximately to the system studied by Hilhorst et al., where the system has diﬀerent reaction terms. Our
goal is to show that the propagation speed of free boundary arising from the fast reaction limit become zero,
finite or infinity, depending on the combination of two reaction terms in the system. This talk is based on a
joint work with M. Iida, H. Murakawa and H. Ninomiya.

33 Hiroshi Matsuzawa(Numazu Nat. Coll. of Tech.)
Yuki Kaneko (Waseda Univ.)

Spreading speed and sharp asymptotic profiles of solutions in freeboundary problems for nonlinear advection-diﬀusion equations · · · · · · · 10

Summary: In this talk we are interested in free boundary problems for nonlinear advection-diﬀusion equationsof the form ut −uxx +βux = f (u) for t > 0, g(t) < x < h(t), where x = g(t) and x = h(t) are free boundaries.
Such a problem may be used to describe the spreading of a biological or chemical species with the freeboundaries representing the expanding fronts. When f is a logistic nonlinearity, it has been shown by Gu,
Lin and Lou that the asymptotic spreading speeds of the two fronts h(t) and g(t) are diﬀerent due to theadvection term. In this paper, for monostable, bistable and combustion types nonlinearities, we give a muchsharper estimate for the diﬀerent spreading speeds of the fronts, and also prove that the solution converges
to a semi-wave in C 2 -norm as t → ∞ when spreading happens.

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

Profile of global bifurcation sheet and diagrams of a reaction-diﬀusion
model for cell polarization · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We are interesting in a reaction diﬀusion model for cell polarization proposed by Y. Mori, A.
Jilkine and L. Edelstein-Keshet in SIAM J.Appl Math (2011). Several mathematical bifurcation results ofstationary solutions are obtained by Kuto and Tsujkawa in DCDS Supplement (2013). We have obtained
exact expressions of all the solution for it and a bifurcation sheet by using the Jacobi’s elliptic functions andcomplete elliptic integrals. In this talk, we prove properties of profile of the global bifurcation sheet.

35 Noriaki Umeda(Meiji Univ.)On blow-up at space infinity for semilinear heat equations with inhomogeneous terms · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a solution of a Cauchy problem for a semilinear heat equation with inhomogeneousterms. We study the solution which does not blow up in the total space at the blow-up time. It does onlyat space infinity.

36 Hiroshi Kamiya (Osaka Pref. Univ.)

Life span of solutions for a semilinear heat equation with a large
exponent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem of a semilinear heat equation ∂t u = ∆u + up in the whole space.
For initial data φ with ∥φ∥L∞ > 1, we investigate the asymptotic behavior of the life span Tp of the classicalsolution u as p → ∞.

37 Junichi Harada (Akita Univ.) ∗ Possibility of nonsimultaneous blow-up for a complex valued semilinear
heat equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We study blow-up problems for a complex-valued semilinear heat equation. A goal of this talkis to discuss the possibility of a non-simultaneous blow-up from the view point of the asymptotic forms of
blow-up solutions.

38 Goro Akagi(Kobe Univ.)

Stability of non-isolated asymptotic profiles for fast diﬀusion · · · · · · · · 10

Summary: The stability of (possibly non-isolated) asymptotic profiles of solutions to the Cauchy–Dirichletproblem for the fast diﬀusion equation is discussed for general smooth bounded domains.

39 Kazuhiro Ishige (Tohoku Univ.)
Ryuichi Sato (Tohoku Univ.)

Heat equation with a nonlinear boundary condition and uniformly local
Lr spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We establish the local existence and the uniqueness of solutions of the heat equation with anonlinear boundary condition for the initial data in uniformly local Lr spaces. Furthermore, we study the
sharp lower estimates of the blow-up time of the solutions with the initial data λψ as λ → 0 or λ → ∞ andthe lower blow-up estimates of the solutions.

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40 Yohei Fujishima (Osaka Univ.) ∗ On the eﬀect of higher order derivatives of initial data on the blow-up
set for a semilinear heat equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk, we consider a semilinear heat equation with large initial data, and study the locationof the blow-up set of the solution for the case where the initial function has several maximum points. In
particular, we discuss the relationship between the location of the blow-up set and higher order derivativesof initial data.

41 Shigeru Sakaguchi (Tohoku Univ.) ∗ Stationary isothermic surfaces and curves have some symmetry · · · · · · 10
Summary: Let S and C be a smooth hypersurface and a smooth curve both of which are properly embedded
in RN with N ≧ 3 and consider their tubular neighborhoods N . We show that, if some heat flow over N
has S (or C) as a stationary isothermic surface (or a stationary isothermic curve), then S (or C) must havesome symmetry.

13:15–14:15

Talk Invited by Functional Equations Section

Hiroyoshi Mitake (Hiroshima Univ.) ♭ Large-time asymptotics and selection problems for degenerate viscous
Hamilton–Jacobi equations
Summary: In the talk, I will present recent results about (i) large-time asymptotics and (ii) selection problems
for Hamilton–Jacobi equations with possibly degenerate diﬀusion terms. We derive new estimates on longtime averaging eﬀects and stochastic Mather measures by the nonlinear adjoint method which has been
recently developed. We then apply them to establish new results of the asymptotic analysis on the above(i), (ii). These are the first general ones concerning equations which are neither uniformly parabolic nor
first order. These are joint works with F. Cagnetti, D. A. Gomes, and H. V. Tran.

March 23rd (Mon)

Conference Room Va

9:30–12:00
42 Koichi Osaki (Kwansei Gakuin Univ.) ∗ Lp -estimates of solutions to n-dimensional parabolic-parabolic chemotaxis system with weak degradation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Etsushi Nakaguchi(Tokyo Med. Dent. Univ.)
Summary: We study the global existence of solutions to an n-dimensional parabolic-parabolic chemotaxis
system with weak degradation of population and sublinear production of chemoattractant. We will show
the global existence of solutions in Lp space (p > n) under certain relations between the degradation andproduction orders, applying the theory of semilinear parabolic evolution equations in Banach spaces.

43 Sachiko Ishida (Tokyo Univ. of Sci.)

Boundedness in chemotaxis-Navier–Stokes systems with position dependent sensitivity in 2D domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This talk presents boundedness in degenerate Keller–Segel–Navier–Stokes systems with position
dependent sensitivity on 2D bounded domains Ω. In MSJ Autumn Meeting 2014, we dealt with the same
system and showed global existence. However, L∞ (Ω)-bounds of the solution depended on the time variable
even if we knew the uniform in time bounds in Lp (Ω) for any p ∈ [1, ∞). So, we prove the uniform in time
L∞ -bounds of the weak solution.

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Functional Equations

44 Kentarou Fujie (Tokyo Univ. of Sci.)
Takasi Senba (Kyushu Inst. of Tech.)Global existence and boundedness in a parabolic-elliptic Keller–Segelsystem with general sensitivity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This talk is concerned with a parabolic-elliptic Keller–Segel system with signal-dependent sensitivity χ(v) under homogeneous Neumann boundary condition in a smoothly bounded domain Ω ⊂ R2 with
nonnegative initial data u0 ∈ C 0 (Ω̄), ̸≡ 0. In the special case χ(v) = χ0 log v (χ0 > 0), global existence andboundedness of the solution to the system was proved under some smallness condition on χ0 by Biler (1999)
and Fujie, Winkler and Yokota (2014). In this talk, global existence and boundedness in the system will beestablished for general χ ∈ C 2 ((0, ∞)) satisfying χ′ > 0 and χ′ (s) → 0 as s → ∞. The main idea in thederivation of our result is in estimation in a neighborhood of each point.

45 Noriko Mizoguchi(Tokyo Gakugei Univ.)Type II blowup in the doubly parabolic Keller–Segel system in the twodimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It was recently shown that finite-time blowup occurs for a large class of radial initial data in theparabolic-parabolic Keller–Segel system in the two dimention. However type of blowup has been unknown
except a peculiar solution given by Herrero and Velazquez. In this talk, we show that each blowup is of type
II in the system in the radial case.

46 Yuta Wakasugi (Osaka Univ.) ∗ Critical exponent for a system of semilinear damped wave equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Kenji Nishihara (Waseda Univ.)
Summary: We consider the Cauchy problem for the weakly coupled semilinear damped wave system with
k-components. We show that there exists a unique global solution for small data in supercritical cases forany space dimension.

(Mie Univ.) ∗ Combined eﬀects of two nonlinearities in lifespan of small solutions to
47 Kunio Hidano
Chengbo Wang (Zhejiang Univ.) semi-linear wave equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Kazuyoshi Yokoyama(Hokkaido Univ. of Sci.)
Summary: We discuss combined eﬀects of two nonlinearities in lifespan of small solutions to semi-linear wave
equations. Using the method of vector fields in Klainerman (Comm. Pure Appl. Math. 38 (1985), 321–332)
together with some of techniques developed in Li and Zhou (Indiana Univ. Math. J. 44 (1995), 1207–1248),
we show that the upper bound on the lifespan recently obtained by Han and Zhou (Comm. Partial Diﬀerential
Equations 39 (2014), 651–665) is sharp in general, at least in space dimensions n = 2, 3. Moreover, we also
study the threshold case and show that the equation admits global (in time) solutions.

48 Shigehiro Sakata (Waseda Univ.)
Yuta Wakasugi (Osaka Univ.)

Movement of spatial maximizers of the solution of the damped wave
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Cauchy problem for the damped wave equaiton in Euclidean space. We investigate
the shape of the graph of the solution. In particular, we study the asymptotic behavior of spatial maximizersof the solution.

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49 Hiroshi Takeda (Fukuoka Inst. of Tech.) ∗ Large time behavior of solutions for a nonlinear damped plate equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we consider the initial value problem for a nonlinear plate equation with the weakdamping term. We show the unconditional global well-posed result in a weighted Sobolev space for small
data. Moreover we prove decay estimates of the solution in the same framework.

50 Takamori Kato (Nagoya Univ.)

Invariant measure for the periodic fourth order Schrödinger equation· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove the invariant measure of the Gibbs measure for the periodic forth order Schrödinger
equation.

51 Shinya Kinoshita (Nagoya Univ.) ∗ The Cauchy problem of nonlinear Schrödinger equations below L2 · · · · 10
Summary: This paper is concerned with the Cauchy problem of Hartree (HNLS) and pure power nonlinear
Schrödinger equations (PNLS) with L2 -subcritical regularity. It is known that the global well-posedness
in the scale invariant homogeneous Sobolev space with radially symmetry or some angular regularity wasestablished provided that the initial data have small norm. We generalize these results by new weighted
Strichartz estimates.

(Tohoku Univ.) ∗ On the ill-posedness for a quadratic nonlinear Schrödinger equation
52 Kota Uriya
Tsukasa Iwabuchi (Chuo Univ.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We are concerned with the ill-posedness issue for the nonlinear Schrödinger equation with thequadratic nonlinearity |u|2 and prove the norm inflation in the dimensions 1 ≤ n ≤ 3. This is theextension of the ill-posedness result by Kishimoto–Tsugawa in one dimension and also a remaining case of
Iwabuchi–Ogawa.

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

Scattering problem for Hartree equations with inverse-square potentials· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

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

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

If a = 0, then Hayashi–Tsutsumi(1987) studied the asymptotic behavior in time and the scattering theory.
In a way similar to this we study for (HE)a with careful application of contraction principle.

14:15–16:00∗
Global existence and asymptotic behavior of solutions to some nonlinear
54 Yoshihisa Nakamura(Kumamoto Univ.) systems of Schrödinger equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Akihiro Shimomura (Univ. of Tokyo)
Satoshi Tonegawa (Nihon Univ.)

Summary: We study the global existence and the large time behavior of solutions to the coupled system of
the Schrödinger equations with cubic nonlinearities in one space dimension. We construct modified wave
operators to the system for small final data.

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55 Yohei Yamazaki (Kyoto Univ.) ∗ Transverse instability for nonlinear Schrödinger equation with a linear
potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider the transverse instability for a nonlinear Schrödinger equation with a linear potential
on R × TL , where 2πL is the period of the torus TL . Rose and Weinstein showed the existence of a stable
standing wave for a nonlinear Schrödinger equation with a linear potential on R. We regard the standing
wave of nonlinear Schrödinger equation on R as a line standing wave of nonlinear Schrödinger equation on
R × TL . We show the result of the stability of line standing waves for all L > 0.

56 Gaku Hoshino (Waseda Univ.)
Tohru Ozawa (Waseda Univ.)

Space-time analytic smoothing eﬀect for the global solutions to thepseudo conformally invariant Schrödinger equations · · · · · · · · · · · · · · · · 10

Summary: We study the global Cauchy problem for the mass critical NLS. We prove the global existence ofanalytic solutions in both space and time variables for suﬃciently small and exponentially decaying data.
The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms.

57 Reinhard Farwig (TU Darmstadt) ∗ Initial values for the Navier–Stokes equations in spaces with weights inYoshikazu Giga (Univ. of Tokyo) time · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Tokyo Tech)
Penyuan Hsu
Summary: We consider the nonstationary Navier–Stokes system in a smooth bounded domain Ω ⊂ R3 withinitial value u0 ∈ L2σ (Ω). It is an important question to determine the optimal initial value condition inorder to prove the existence of a unique local strong solution satisfying Serrin’s condition. In this paper, we
introduce a weighted Serrin condition that yields a necessary and suﬃcient initial value condition to guarantee∫Tthe existence of local strong solutions u(·) contained in the weighted Serrin class 0 (τ α ∥u(τ )∥q )s dτ < ∞with 2s + 3q = 1 − 2α, 0 < α < 12 . Moreover, we prove a restricted weak-strong uniqueness theorem in thisSerrin class.

(Nagoya Univ.)
58 Ken Abe
Yoshikazu Giga (Univ. of Tokyo)
Katharina Schade (TU Darmstadt)
Takuya Suzuki (Univ. of Tokyo)

On the Stokes semigroup in some non-Helmholtz domains · · · · · · · · · · · 10

Summary: This presentation is concerned with a joint work with Dr. Ken Abe, Professor Yosikazu Giga, and
Ms. Katharina Schade. Our work is related to the initial boundary problem for the Stokes system underzero Dirichlet boundary condition with initial condition. We establish that Lp -Helmholtz decomposition
is not necessary to get the analyticity of the Stokes semigroup in C0,σ , the L∞ -closure of the space of
all compactly supported smooth solenoidal vector fields. In fact, in a sector-like domain for which the
Lp -Helmholtz decomposition does not hold, the analyticity of the Stokes semigroup in C0,σ is proved.

(Tokyo Tech)
59 Tsubasa Itoh
Hideyuki Miura (Tokyo Tech)
Tsuyoshi Yoneda (Tokyo Tech)

Remark on single exponential bound of the vorticity gradient for thetwo-dimensional Euler flow around a corner · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, the two dimensional Euler flow under a simple symmetry condition with hyperbolic√√
structure in a unit square D = {(x1 , x2 ) : 0 < x1 + x2 < 2, 0 < −x1 + x2 < 2} is considered. It is shownthat the Lipschitz estimate of the vorticity on the boundary is at most single exponential growth near thestagnation point.

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60 Yasunori Maekawa (Tohoku Univ.)
Hideyuki Miura (Tokyo Tech)

On Ukai-type solution formula for the Stokes system in a domain withgraph boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the Stokes system for viscous incompressible flows in a domain with graph boundary.
We provide an approach using the isomorphism between X(Ω)n−1 and Xσ (Ω), where X(Ω) is a Banach
space of functions in the domain Ω ⊂ Rn , while Xσ (Ω) is the space of solenoidal vector fields in Ω. Our
approach reduces the Stokes system to the system of n − 1 unknowns, and in particular, it is shown that
this reduction yields a Ukai-type solution formula for the Stokes semigroup, which is known when Ω is thehalf space, to the case of the curved boundary.

61 Teppei Kobayasi (Meiji Univ.) ∗ A stationary solution of the Navier–Stokes equations in a perturbed
layer domain in R3 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Many mathematicians treat stationary problems of the Navier–Stokes equations in various unbounded domains with compact and noncompact boundaries. For example, exterior domains, half spaces,
aperture domains, channels. In this paper we prove that for a perturbed layer domain there exists a
stationary solution of the Navier–Stokes equations approaching the Poiseuille flow with the restrictedcondition.

62 Toshiaki Hishida (Nagoya Univ.) ♭ Asymptotic structure of steady Stokes flow around a rotating obstacle
in two dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We provide asymptotic structure at spatial infinity of plane Stokes flow in exterior domains when
the obstacle is rotating.

16:20–17:20

Award Lecture for 2014 Analysis Prize

Kazuhiro Ishige (Tohoku Univ.)

Concavity properties of solutions for parabolic equations

Summary: This talk is based on the joint works with Professor Paolo Salani (University of Florence, Italy)
and it is concerned with concavity properties of the solutions for parabolic equations. We first prove thatthe super-level set convexity property is not necessarily preserved by the heat flow. Next we give a suﬃcientcondition for the solutions of parabolic equations to be parabolically power concave. Furthermore, we findrelationship among the Minkowski addition of convex domains and the parabolic Minkowski convolution of
the solutions of parabolic equations.

March 24th (Tue)

Conference Room Va

9:30–11:30
63 Tetu Makino (Yamaguchi Univ.) ∗ On spherically symmetric solutions to the Einstein–Euler equations · · 10
Summary: We consider spherically symmetric solutions to the Einstein equations with the energy-momentum
tensor of the barotropic perfect fluid with realistic equations of state. Equilibria are given by the Tolmann–
Oppenheimer–Volkoﬀ equations, around which there are time-periodic solutions of the linearized problem.
We can construct true solutions near that with physical boundary with the vacuum, applying the Nash–
Moser(–Hamilton) theorem.

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64 Naofumi Mori (Kyushu Univ.)
Shuichi Kawashima (Kyushu Univ.)

Dissipative structure and nonlinear stability for the dissipative Timoshenko
system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the nonlinear Timoshenko system with frictional damping in one dimensional whole
space. We introduce the Sobolev space H 2 (critical index), and show the global existence and uniqueness ofthe solutions only by assuming the initial data in H 2 : We employ the energy method and apply the refined
Lyapnov function of the linear system to this nonlinear system. Moreover, we show the optimal decay t−1/4
under the assumption of the initial data in H 2 ∩ L1 . The key to the optimal decay result is to use theL2 -Lq -Lr type decay estimate eﬀectively.

65 Hirotada Honda (Keio Univ.)(Keio Univ.⋆)
Atusi Tani

Large-time solvability of primitive equations for the ocean with freesurface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We construct a global-in-time strong solution of the primitive equations for the ocean. The freeboundary problem in 3-dimensional strip-like region for the ocean is studied, that is to say, the interface
between the atmosphere and ocean is free, not rigid lid approximated. Our proof for the existence of astrong solution is given in Sobolev–Slobodetskii spaces.

66 Hiroki Ueno
Tatsuo Iguchi(Keio Univ.)(Keio Univ.)

A mathematical justification of the thin film approximation for the flow
down an inclined plane · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider two-dimensional motion of liquid film of a viscous incompressible fluid down an
inclined plane in the influence of the gravity and the surface tension. In order to investigate such a motion, amethod of the thin film approximation is often used. It is the approximation by the perturbation expansionof the solution for the non-dimensional parameter δ defined by ratio between the thickness of the liquidfilm and the typical wave length. In this study, we will give the error estimate between the solution of
the original Navier–Stokes equations and that of Burgers equation when the Reynolds number, the angle ofinclination, and the initial date are suﬃciently small.

67 Noboru Chikami (Tohoku Univ.) ∗ On the well-posedness of the full compressible Navier–Stokes system inRaphaël Danchin (Univ. Paris-Est) critical Besov spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We are concerned with the Cauchy problem of the full compressible Navier–Stokes equations
satisfied by viscous and heat conducting fluids in the whole space. We focus on the so-called critical Besov
regularity framework. After recasting the whole system in Lagrangian coordinates, and working with “thetotal energy along the flow” rather than with the temperature, we discover that the system may be solved
by means of Banach fixed point theorem in a critical functional framework whenever the space dimension isgreater than two. Back to Eulerian coordinates, this allows to improve the range of the Lebesgue exponent
for which the system is locally well-posed, compared to previous results.

68 Kazuyuki Tsuda (Kyushu Univ.)

Time-periodic problem for the compressible Navier–Stokes–Korteweg
system on the whole space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The existence of a time periodic solution of the compressible Navier–Stokes–Korteweg system on
the whole space is shown for suﬃciently small time periodic external force when the space dimension isequal to 3. The time periodic solution is shown to be asymptotically stable under suﬃciently small initial
perturbations and the L∞ norm of the perturbation decays as time goes to infinity.

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69 Ryouta Oomachi (Kyushu Univ.)

Stability of time periodic solution of incompressible Navier–Stokes equation on the half-space under oscillatory moving boundary condition · · 10

Summary: We consider initial boundary value problem for the Navier–Stokes equation on the half space
under oscillatory moving boundary condition. We prove the existence of the time periodic solution which
depends only on time variable and vertical variable. The aim of our study is to investigate the stability ofthe time periodic solution. It is proved that the time periodic solution is asymptotically stable under thesuﬃcient small initial perturbations when the boundary data is suﬃcient small.

70 Yoshiyuki Kagei (Kyushu Univ.)
Takaaki Nishida (Kyoto Univ.)

Instability of plane Poiseuille flow in viscous compressible gas · · · · · · · · 10

Summary: We consider the stability of plane Poiseuille flow in viscous compressible gas. We will establish
a condition for the Reynolds and Mach numbers in order for plane Poiseuille flow to be unstable. It will
be shown that plane Poiseuille flow is unstable for Reynolds numbers much less than the critical Reynolds
number for the incompressible flow when the Mach number is suitably large.

71 Miho Murata (Waseda Univ.)
Matthias Hieber (TU Darmstadt)

On the local in time unique existence to the Fluid–Rigid body interaction problem for compressible fluids · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the system of equations describing the motion of a rigid body immersed in a viscous,
compressible fluid within the barotropic regime. It is shown that this system admits a unique, local strong
solution within the Lp -Lq framework. Boulakia and Guerrero proved an existence result for strong solution
to the coupled system within the L2 framework as long as no collisions occurs. One of the merits of ourapproach is the less compatibility condition and regularity on initial data.

72 Senjo Shimizu (Shizuoka Univ.)
Shintaro Yagi (Shizuoka Univ.)

On local Lp -Lq well-posedness of incompressible two-phase flows withphase transitions: Non equal densities with large initial data · · · · · · · · 10

Summary: The basic model for incompressible two-phase flows with phase transitions where the interface isnearly flat in the case of non-equal densities is considered. The local well-posedness of the model in Lp intime Lq in space settting was proved in [2] under smallness assumption for initial data. We remove thesmallness assumption for initial data.

14:15–15:15
73 Hirokazu Saito (Waseda Univ.)
Matthias Hieber (TU Darmstadt)

Strong solutions for two-phase free boundary problems for a class of
non-Newtonian fluids · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider incompressible two phase flows for generalized Newtonian fluids as aclass of non-Newtonian fluids. The flows are described as some free boundary problem of the incompressible
Navier–Stokes equations mathematically. By using optimal regularity theorems, concerning the linearized
problem, established by Prüss and Simonett ’10 and ’11, we show the unique existence theorem of strong
solutions to the free boundary problem locally in time for suﬃciently small initial data.

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74 Yoshihiro Shibata (Waseda Univ.)

Local well-posedness of compressible-incompressible two-phase flows
with phase transitions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I would like to talk about the local well-posedness of compressible-incompressible two-phase flows
with phase transitions when the intersurface is close to the flat surface. The point is to represent the massdensity along the characteristic curve, so that the equations transfer to the quasilinear parabolic equations.
The local well-posedness is proved for given time with small initial data with the help of Lp -Lq maximal
regularity theorem for the linearized equations. This is a joint work with Maria Schonbek, Department ofMath., Univ. California, Santa Cruz.

75 Yoshihiro Shibata (Waseda Univ.)

On the Lp -Lq maximal regularity theorem arising in the study of thecompressible-incompressible two phase flow with phase transition · · · · 10

Summary: I would like to talk about the Lp -Lq maximal regularity theorem which enable us to prove
local well-posedness of the interface problem for the Navier–Stokes equations describing the compressibleincompressible two-phase flows with phase transitions. To prove it, I proved the existence of R bounded
solution operators of the corresponding generalized problem, which, combined with the Weis operator valued
Fourier multiplier theorem, implies the requiared maximal regularity theorem.

76 Yoshihiro Shibata (Waseda Univ.)

On strong dynamics of compressible nematic liquid crystals · · · · · · · · · 10
2−1/r

domain and the global
Summary: I would like to talk about the local wellposedness in a uniform Wr
wellposedness in a bounded domain with small initial data for the strong solutions of simplicied Ericksen–
Leslie model describing the motion of a viscous compressible liquid crystal flow. This is a joint work with
Dr. Katharina Schade, Department of Mathematic, TU Darmstadt who is a member of IRTG program ofGermany. After the Lagrange transformation, we solved the problem by using the Lp -Lq maximal regularity
theorem for the linearized equations.

77 Yoshihiro Shibata (Waseda Univ.)

On the global wellposedness of strong dynamics of compressible nematic
liquid crystals in RN · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I would like to talk about the global wellposedness of the initial problem for the viscous incompressible liquid crystal flow in the N -dimensional Euclidean space RN . The proof is done by combining
Lp -Lq maximal regularity results and Lp -Lq decay estimates for the Stokes equations and heat equations.
We need essentially two Lebesgue spaces in time with value Lq in space. This is somehow first result
concerning global well-posedness for strong soluutions with small initial data for the quasilinear parabolic
equations in unbounded domains. I need two diﬀerent p’s.

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15:30–16:30

Talk Invited by Functional Equations Section

Satoshi Masaki (Hiroshima Univ.) ♭ On mass-subcritical nonlinear Schrödinger equation
Summary: Recently, there is much progress on analysis of time global behavior of solutions to nonlinear
Schrödinger equation based on a so-called concentration compactness/rigidity type argument, after apioneering work by Kenig and Merle. In energy-critical case, mass-critical case, and intermediate cases ofthese two, behavior of solutions around ground states are precisely analyzed, and it is clearly understoodthat ground state solutions are thresholds. In this talk, I would like to introduce my attempt to apply theargument to mass-subcritical cases, in which case the ground states are known to be orbitally stable.
More specifically, as a first step, we investigate a threshold phenomenon between scattering and nonscattering, and give a sharp suﬃcient condition for scattering by showing existence of a special solution suchthat; (1) the solution does not scatter for positive time; (2) the solution has minimum size at the initialtime, in a suitable sense, among all solutions satisfying property (1). In mass-critical case, the ground stateis the solution satisfies these two properties. However, in mass-subcritical case, the above threshold solution
is not a ground state solution, or any other standing-wave solutions.

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Real Analysis
March 21st (Sat)

Conference Room IX

9:30–12:00
1 Noriaki Yoshino (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

An operator theoretic approach to a quasi-linear degenerate parabolicelliptic Keller–Segel system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we present an operator theoretic approach to a quasi-linear degenerate parabolicelliptic Keller–Segel system. Under some conditions we will show local existence of weak solutions.

2 Kentarou Fujie (Tokyo Univ. of Sci.)

Global existence and asymptotic behavior in a chemotaxis-growth modelfor tumor invasion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: This talk is concerned with global existence and asymptotic behavior of solutions to a chemotaxisgrowth system in a smoothly bounded domain Ω ⊂ Rn , n ≤ 3. Without the logistic source ru − µuα , r >0, µ > 0, α > 1, the stabilization of this system has been shown by Fujie, Ito, Winkler and Yokota (preprint),
whereas especially about asymptotic behavior, the logistic source disturbs applying this method directly. In
this talk, a way out of this diﬃculty is introduced and the asymptotic behavior of solutions to the systemwith logistic source is precisely determined.

3 Yutaka Tsuzuki (Tokyo Univ. of Sci.)

Solvability of heat equations with hysteresis coupled with Navier–Stokes
equations in 2D and 3D domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is concerned with a system of heat equations with hysteresis and Navier–Stokes equations.
Recently, an existence result for the problem with the Navier–Stokes equation in a weak sense has beenobtained. This result does not include uniqueness for the problem. This talk establishes existence anduniqueness for the problem with the Navier–Stokes equation in a stronger sense by introducing the fractional
power of the Stokes operator.

4 Kota Kumazaki(Tomakomai Nat. Coll. of Tech.)

On a system of parabolic type equations with a hysteresis operator· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider a system of some parabolic type equation with a hysteresis operator as amathematical model of concrete carbonation process in three dimensions. This system consists of a diﬀusion
equation of moisture transport involving a hysteresis relation between moisture and the degree of saturation
and a diﬀusion equation of carbon dioxide transport. In this talk, we discuss the existence and uniquenessof a solution for a initial boundary value problem of this system.

5 Akio Ito(Kinki Univ.)

Asymptotic behavior of global-in-time solutions to 1D tumor invasion
model of Chaplain–Anderson type with quasi-variational structure · · · 15

Summary: We consider a one-dimensional tumor invasion model of Chaplain–Anderson type with quasivariational structure. One object is to show the existence of global-in-time solutions by using the limit
procedure for suitable approximate solutions. The other is to consider the asymptotic behaviors of global-intime solutions as time goes to ∞. Actually, we construct at least one global-in-time solution, which enables
us to consider the onvergence to a certain constant steady-state solution as time goes to ∞ whenever the
initial data satisfy suitable conditions.

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Real Analysis

6 Hirokazu Komatsu (Kinki Univ.)(Kinki Univ.)
Akio Ito
Hiroyuki Nakajima (Kinki Univ.)

Non-negativity and boundedness of solutions to non-autonomous ordinary diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The state variables of ordinary diﬀerential equations that describe dynamics in chemical reaction
systems or ecosystems are required to be non-negative and bounded. In the present report, suﬃcientconditions for the solutions to non-autonomous diﬀerential equations to be non-negative are given in twotheorems: one is for the case the function that describes the equation is continuous with respect to the time
variable, and the other is for the case the equation is with an external force term that is not assumed to becontinuous with respect to the time variable. The later theorem is applied to proving the non-negativity andboundedness of the solutions to the system of equations that describes the dynamics of cardiac hypertrophy.

(Kinki Univ.)
7 Akio ItoAtsushi Kadoya(Hiroshima Shudo Univ.)
Kazuhiko Yamamoto (Kinki Univ.)

Numerical simulation of the systems of ordinary diﬀerential equations
arising from Cardiac hypertrophy-related factor network · · · · · · · · · · · · 15

Summary: We study the mechanism of cardiac hypertrophy by the cooperation with mathematical science,molecular biology and systems biology. From the viewpoint of theoretical analysis and numerical analysis,
we analyze the factors concerned with cardiac hypertrophy comprehensively by using systems biology. From
the approach of systems biology, we derive the original systems of ordinary diﬀerential equations as themathematical model. We propose a new model in which two new eﬀects are given to the original system ofordinary diﬀerential equations from the mathematical point of view. We analyze a new model theoreticallyand numerically, and obtain some interesting numerical results.

8 Keisuke Takasao (Kanagawa Univ.) ∗ Existence of mean curvature flow via Allen–Cahn equation with constraints · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In 1978, Brakke proved the existence of weak solutions defined by using geometric measure theory,
for the mean curvature flow. The weak solution is called Brakke’s mean curvature flow. In 1993, Ilmanen
proved the existence of Brakke’s mean curvature flow by using the phase-field method. In this talk we show
the existence of Brakke’s mean curvature flow via a singular limit of solutions for Allen–Cahn equation withconstraint.

9 Noriaki Yamazaki (Kanagawa Univ.)
Takeshi Fukao (Kyoto Univ. of Edu.)
M. Hassan Farshbaf-Shaker (WIAS)

Numerical simulations of Allen–Cahn equation with constraints via
Lagrange multiplier · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we give some numerical experiments of Allen–Cahn equation with constraint by using
the properties of the Lagrange multiplier. Also, we consider the approximation problem of Allen–Cahn
equation with constraint by using the Yosida approximation. Then, we show the numerical results of theapproximation problem. Also, we clarify the diﬀerence between these numerical results.

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Real Analysis

14:15–16:30
10 Shoji Shimizu (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

Solvability of complex Ginzburg–Landau equation in a general domain· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The main purpose of this talk is to study the initial boundary value problem for complex
Ginzburg–Landau equation (CGL) in a general domain. In former studies, (CGL) is always treated ina bounded domain since Rellich’s theorem is used to derive the convergence of approximate solutions.
However, in a general domain case, one cannot apply Rellich’s theorem directly. So here by using the
diagonal argument we construct a sequence of approximate solutions which converges weakly and a.e. in
the whole domain and strongly in any bounded sub-domains. By this approach we can show that a weaklimit of approximate solutions gives the desired solution of (CGL).

11 Shun Uchida (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

Exponential attractor of some autonomous double-diﬀusive convection
system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the large time behavior of solutions of some system which describes double-diﬀusive
convection phenomena in some porous medium. In our previous work, it has been already showed that thissystem possesses the global attractor. In this talk, we show that our system has an exponential attractor by
applying “smoothing property” between two distinct solutions. Moreover, using this smoothing property,
we can also derive the upper estimate of fractal dimension of the global attractor.

12 Hiroshi Watanabe (Salesian Polytech.)

Solvability of strongly degenerate parabolic equations with variable
coeﬃcients · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial value problem (CP) for strongly degenerate parabolic equations withvariable coeﬃcients. Strongly degenerate parabolic equations are regarded as a linear combination of thetime-dependent conservation laws (quasilinear hyperbolic equations) and the porous medium type equations(nonlinear degenerate parabolic equations). Thus, this equations has both properties of hyperbolic equationand those of parabolic equations and describes various nonlinear convective diﬀusion phenomena such as
filtlation problems, Stefan problems and so on.
In this talk, we employ an entropy triplet to define entropy solutions asociated with (CP). Our purpose isto prove the uniquneness and existence of the entropy solution in the space BV.

13 Takeshi Fukao (Kyoto Univ. of Edu.)(Pavia Univ.)
Pierluigi ColliSome equations and dynamic boundary conditions of Cahn–Hilliard
type with singular potentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The well-posedness of a system of partial diﬀerential equations and dynamic boundary conditions,both of Cahn–Hilliard type, is discussed. The existence of a weak solution and its continuous dependence
on the data are proved using the suitable setting for the conservation of a total mass in the bulk puls theboundary. A very general class of double-well like potentials is allowed.

(Kochi Univ.)
14 Risei Kano(
Takeshi Fukao Kyoto Univ. of Edu.)

The existence of solutions for the model of perfect plasticity with timedependent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: we discuss the solvability of the perfect plasticity model with time dependent.

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Real Analysis

15 Yusuke Murase (Meijo Univ.)
Masahiro Kubo (Nagoya Inst. of Tech.)

Solvability of quasi-variational inequalities generated by a quasi-subdifferential operator · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss a solvability of a functional inclusion which corresponds to elliptic variational andquasi-variational inequalities. Our functional inclusion is generated by so-called “quasi-subdiﬀerential
operator”. “quasi-subdiﬀerential operator” is a extension of sub diﬀerential operator in some sense. We
show you a existence result under a certain assumptions.

16 Ken Shirakawa (Chiba Univ.)
Hiroshi Watanabe (Salesian Polytech.)Phase-field models of grain boundary motions under non-isothermal
settings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, a system of PDEs which is based on a non-isothermal phase-field model of planar
grain boundary motion, proposed in [Warren, J. A. et al.; Acta Materialia, 51 (2003), 6035–6058]. On thebasis of the previous study in isothermal cases, the existence result for the non-isothermal system will bedemonstrated as the main theorem in this talk.

17 Toyohiko Aiki (Japan Women’s Univ.)
Oleh Krehel (TU Eindhoven)
Adrian Muntean (TU Eindhoven)

Homogenization for diﬀerential equations describing change of mass of
colloids · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider a system of partial diﬀerential equations describing a mass conservation
law for colloids in a porous medium having periodic structure. Here, we treat the Smoluchowski population
balance equation as a reaction rate of generation of colloid particles on the domain. For this problem
we have already shown the results concerned with existence and uniqueness for each period. The aim of
this talk is to discuss a homogenization process for these equations. Namely, as the period tends to 0 thesequence of solutions has a limit and the limit solves some partial diﬀerential equations in a weak sense.

16:40–17:40

Talk Invited by Real Analysis Section

Koichi Osaki (Kwansei Gakuin Univ.)

Nonlinear analysis for a chemotaxis-growth system

Summary: We are concerned with nonlinear analysis for the solutions to a parabolic-parabolic chemotaxis
system with logistic growth: ut = ∆u − χ∇(u∇v) + u − µuα , τ vt = ∆v − v + u(u + 1)β−1 , in a boundeddomain in Rn . Under some relations between the degradation and secretion orders α(≤ 2) and β(≤ 1), we
have shown global existence of solutions, and also existence of attractors by obtaining some a priori uniform
estimates. For a typical case of orders α = 2 and β = 1, we have also shown pattern formation of solutions,exhibiting several spatial patterns, including stripe or hexagonal patterns, in a rectangle by using the local
bifurcation theory. In this talk we will review the results and show the analysis in detail.

March 22nd (Sun)

Conference Room IX

9:30–12:00
18 Yōhei Yamasaki (Yamato Univ.) ∗ The limit and “singular integrals of 1 veriables” · · · · · · · · · · · · · · · · · · · · 15
Summary: In 2009, the presenter gave a talk to clarify the condition to commute with limit for singular
integrals of 1 variable. This talk clarifies the condition to commute with limit for singular integrals of 1
variable.

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19 Yoshifumi Ito (Univ. of Tokushima⋆)

Fourier transformation of distributions in D′ · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we study the Fourier transformation of distributions in D′ .
We prove the several structure theorems by virtue of the Paley–Wiener theorem for the Fourier transformation of distributions with compact support.

20 Yoshifumi Ito (Univ. of Tokushima⋆)

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

Summary: In this paper, we study the Fourier transformation of L2loc -functions by virtue of the Fouriertransformation of distributions in D′ .
Thereby we determine the space of functions to where the all solutions of any type of Schrödinger equations
belong.

21 Youhei Tsutsui (Univ. of Tokyo)

Div-curl lemma with critical power weights in dimension three · · · · · · · 15

Summary: This talk presents an endpoint case of div-curl lemma in dimension three with Hardy spaces
associated with Herz spaces. The proof relies on that the continuity of solutions to the Neumann problem ofPoissonn equations and a generalization of Feﬀerman–Stein vector-valued inequality for Hardy–Littlewood
maximal operator.

22 Shinya Moritoh (Nara Women’s Univ.)

Ostrowski’s inequalities and some examples · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider Ostrowski’s inequalities and some examples. This is a continuation of the talk givenin the previous meeting of MSJ.

23 Hironari Miyoshi (Waseda Univ.)
Masayoshi Tsutsumi (Waseda Univ.)

Lifting problems for a hyperbolic surface in Sobolev spaces · · · · · · · · · · 10

Summary: We consider the lifting and density problems for a hyperboloid of one sheet in fractional Sobolev
spaces. Using the higher order diﬀerentiation formula of the composite function and the higher order
diﬀerence formula of the composite function, we solve the lifting question and show the density of thesmooth mapping in fractional Sobolev spaces into a hyperboloid of one sheet.

24 Takuya Sobukawa (Waseda Univ.)(Ibaraki Univ.)
Eiichi Nakai

Generalization of local Morrey–Campanato type spaces and their interpolation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15uSummary: The purpose of this talk is to introduce Bw(E)-funciton spaces which unify many function spaces,
Lebesgue, Morrey–Campanato, Lipschitz, Bp, CMO, local Morrey-type spaces, etc. We investigate theuinterpolation property of Bw(E)-funciton spaces and apply it to the boundedness of linear and sublinear
operators, for example, the Hardy–Littlewood maximal operator, singular and fractional integral operators,uand so on, which contains previous results and extends them to Bw(E)-funciton spaces.

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25 Yoshiaki Okazaki(Kyushu Inst. of Tech.)

A linear quasi-metric structure of the function space Mp (µ) · · · · · · · · · 15

Summary: The function space Mp (µ) and the quasi-metric |u − v|p is introduced on Mp (µ). The topologicallinear structure of (Mp (µ), |u − v|p ) is studied. (Mp (µ), |u − v|p ) is a complete topological linear quasi-metricspace. The necessary and suﬃcient condition for Mp (µ) = Lp (µ) is given.

26 Yoshihiro Sawano (Tokyo Metro. Univ.) ♭ Morrey-type spaces on Gauss measure spaces and boundedness of singular integrals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We aim to show that Morrey spaces with non-doubling measures defined earlier appear in anatural context. In the probability setting, the Gauss measure is of importance and we can realize oursetting in the context of the Gauss measure.

27 Yoshihiro Sawano (Tokyo Metro. Univ.) ♭ Weak type inequalities for some integral operators on generalized nonhomogeneous Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We discuss weak type inequalities for some integral operators, especially generalized fractional
integral operators, on generalized Morrey spaces of non-homogeneous type. The inequality for generalized
fractional integral operators is proved by using two diﬀerent techniques: one uses the Chebyshev inequality
and some inequalities involving the modified Hardy–Littlewood maximal operator, and another uses a
Hedberg type inequality and weak type inequalities for the modified Hardy–Littlewood maximal operator.

13:15–14:15
Neal Bez

Talk Invited by Real Analysis Section(Saitama Univ.)

Some inequalities from geometric and harmonic analysis via inductionon-scales

Summary: Induction-on-scales is a powerful technique which has been a key ingredient in a number ofimportant developments on the Restriction Conjecture for the Fourier transform and related geometricinequalities, including the Kakeya Conjecture and the family of Brascamp–Lieb inequalities. In this talk, I
will discuss an induction-on-scales approach to certain nonlinear generalisations of the classical Brascamp–
Lieb inequalities, and applications of these inequalities to multilinear restriction estimates and multilinear
Radon-like transform estimates. A somewhat closely related approach has recently been employed by Larry
Guth to give a remarkably short proof of multilinear Kakeya estimates, and this will also be covered during
the talk.

March 23rd (Mon)

Conference Room IX

9:30–12:00
28 Ryotaro Tanaka (Niigata Univ.)
Kichi-Suke Saito (Niigata Univ.)

Recent progress on the duality of James constant · · · · · · · · · · · · · · · · · · 15

Summary: It is known that the James constant of a Banach space does not coincide with that of its dual
space in general. In this talk, we study conditions that guarantee the coincidence. A suﬃcient condition is
given.

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29 Kichi-Suke Saito (Niigata Univ.)
Ryotaro Tanaka (Niigata Univ.)

New geometric properties of Banach spaces · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce new geometric properties of Banach spaces that generalize p-uniform
smoothness and q-uniform convexity. To characterize these properties, we also study generalized Beckner
inequalities.

30 Sachiko Atsushiba(Univ. of Yamanashi)

Convergence theorems for some classes of nonlinear mappings · · · · · · · 15

Summary: In this talk, we introduce the concept of k-acute points of a mapping for k ∈ [0, 1]. We study
some properties of k-acute points and relations among k–acute points, attractive points and fixed points.
We also study properties of some classes of nonlinear mappings by using these concepts. Then, we provesome weak and strong convergence theorems for nonlinear mappings.

31 Hiroyasu Mizuguchi (Niigata Univ.)

Measurements of diﬀerences between orthogonalities in normed spaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The notion of orthogonality for vectors in inner product spaces is simple, interesting and fruitful.
When moving to normed spaces, we have many possibilities to extend this notion. Recently, some constants
which measure the diﬀerences between two orthogonality notions in normed space have been investigated.
However, these constant are considered only in the unit sphere SX of the normed space X. In this talk,
we introduce new constants to measure the diﬀerence between Birkhoﬀ and isosceles orthogonalities in theentire normed space X.

32 Koji Aoyama(Chiba Univ.)

Viscosity approximation methods with a sequence of contractions · · · · 15

Summary: The aim of this talk is to prove that every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence
generated by the Halpern type iterative method. Then we show some convergence theorems for fixed point
problems.

33 Toshiharu Kawasaki (Nihon Univ.)

Criteria for the improper Lebesgue integral · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we will give new criteria for the improper Lebesgue integral.

34 Nobusumi Sagara (Hosei Univ.)
Mohammed Ali Khan(Johns Hopkins Univ.)
Suzuki Takashi (Meiji Gakuin Univ.)

An Exact Fatou Lemma for Gelfand Integrals: Equivalence of theSaturation and Fatou Properties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We establish an exact version of Fatou’s lemma for Gelfand integrals of functions and multifunctions in dual Banach spaces without any order structure, and under the saturation property on theunderlying measure space. The necessity and suﬃciency of saturation for the Fatou property is demonstrated. Our result has a direct application to the equilibrium existence result for saturated economies
without convexity assumptions.

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35 Kiyohisa Tokunaga(Yamaguchi Univ./Fukuoka Inst. of Tech.)Double integration by parts based on a triangular element method · · · 15

Summary: The well-known theorem of single integral by parts for 1-variable functions is derived as the limit
at infinity of Abel’s lemma on summation by parts. Two of the terms are defined by the Stieltjes integral.
The Stieltjes integral is extended to the Stieltjes triangular double integral. Double integration by parts
based on a triangular element method is also derived as the limit at infinity of Abel’s lemma on summation
by parts.

36 Toshikazu Watanabe (Nihon Univ.)
Hiroki Saito (Saitama Univ.)

Pseudometric generating property and continuity of non-additive measure taking value in an ordered vector space · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we discuss the pseudometric generating property and the continuity of non-additive
measure µ taking values in an ordered vector space V . It is known that the pseudometric generating
property plays important roles in fuzzy measure theory and many authors investigate this property andprogress toward establishing a unified theory of fuzzy or non-additive measures. The purpose of this talk is
to consider this property on vector valued non-additive measures and establish its characteristic.

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Functional Analysis
March 21st (Sat)

Conference Room VIII

10:00–12:00
1 Hiroyuki Yamagishi(Tokyo Metropolitan Coll. of Indus. Tech.)
Kohtaro Watanabe(Nat. Defense Acad. of Japan)
Yorimasa Oshime (Doshisha Univ.)

The best constant of Lp Sobolev inequality corresponding to periodic
and Neumann boundary value problem for (−1)M (d/dx)2M · · · · · · · · · 15

Summary: We study the best constant of Lp Sobolev inequality including j-th derivative with periodic or
Neumann boundary condition. The best constants are expressed as Lq norm of Bernoulli polynomial.

2 Takeshi Wada (Shimane Univ.)
Makoto Nakamura (Yamagata Univ.)

The Cauchy problem for nonlinear Schrödinger equation in fractional
order Sobolev spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Cauchy problem for nonlinear Schrödinger equation is considered in the Sobolev space of
fractional order. An improved Strichartz estimate is constructed and applied to the problem to obtain small
global solutions with less regularity assumption for the nonlinear term.

3 Atsuhide Ishida (Otemon Gakuin Univ.)

Non-existence of the wave operators for the repulsive Hamiltonians · · · 15

Summary: We consider the scattering theory for the Schrödinger equation with the repulsive Hamiltonian.
In this quantum system, we can see the characteristic property in which the free dynamics of the particle
disperse in an exponential order in time. This fact indicates that the borderline between the short-range
and long-range has to be the log-type decaying. I will report in this talk that we can decide this borderline
aﬃrmatively by finding concrete counter-example such that the wave operators do not exist.

4 Akito Suzuki
Shogo Ito

(Shinshu Univ.)(Shinshu Univ.)

Hidden spectra of the discrete Schrödinger operators with density zeropotentials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the discrete Schrödinger operators H on Zd with density zero potentials. We showthat for a class of density zero potentials, H has a hidden spectrum that does not contribute to the densityof states.

5 Hajime Moriya (Shibaura Inst. of Tech.)

Univalence superselection rule · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We discuss univalence superselection rule for many electron systems. We do not merely assume
this, rather, we shall dereive this fundamental rule rigorously.

6 Shûichi Ohno (Nippon Inst. of Tech.) ∗ Weighted composition operators on the minimal Möbius invariant space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We will characterize the boundedness and compactness of weighted composition operators on theminimal Möbius invariant space.

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7 Hideyuki Ishi

(Nagoya Univ.) ∗ The Gindikin–Wallach set for a non-homogeneous cone · · · · · · · · · · · · · 15

Summary: We introduce the Gindikin–Wallach set for a regular cone of positive definite symmetric matrices
with prescribed zero-components. Under a certain condition for the zero-pattern, we describe the Gindikin–
Wallach set.

14:15–15:15

Talk Invited by Functional Analysis Section

Hidetoshi Tahara (Sophia Univ.)

q-Analogues of Laplace and Borel transforms with application to qdiﬀerence equations

Summary: Certain q-analogues of Laplace and Borel transforms are discussed, and a new inversion formula
between q-Laplace and q-Borel transforms is given. q-Analogues of Watson type lemma and convolution
operators are also discussed. These results give a new framework of the summability of formal solutionsof q-diﬀerence equations. As an application, the summability of formal power series solution of a typical
q-diﬀerence equation is proved.

March 22nd (Sun)

Conference Room VIII

9:30–12:00
8 Mariko Giga (Nippon Medical School)
Mitsuru Uchiyama (Ritsumeikan Univ.)
Atsushi Uchiyama (Yamagata Univ.)

Superadditivity and derivative of operator functions · · · · · · · · · · · · · · · · 15

Summary: We consider bounded linear operators on Hilbert space. We first show an equivalence for operators∑∑∑
Ai ≥ 0 (i = 1, 2, · · · , n) among (i)i g(Ai ) for every operator convex
i Ai ) ≥i̸=j Ai Aj ≥ 0, (ii) g(∑∑function g(t) on [0, ∞) with g(0) ≤ 0, (iii) f ( i Ai ) ≤ i f (Ai ) for every non-negative operator monotonefunction f (t) on [0, ∞). Next, let A, B ≥ 0 and A be invertible. Then the followings are equivalent (i)AB + BA ≥ 0, (ii) the Fréchet derivative Df (sA)(B) is decreasing with respect to s > 0 for every operator
monotone function f (t) on (0, ∞), (iii) Dg(sA)(B) is increasing with respect to s > 0 for every operator
convex function g(t) on (0, ∞).

9 Haruka Watanabe (Chiba Univ.)
Albania Nugraha Imam (Chiba Univ.)
Masaru Nagisa (Chiba Univ.)

Examples of operator monotone functions · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider functions with special forms (here, we call them of Szabó type). Using the result of
M. Nagisa and S. Wada, their oerator monotonicity is decided by the computation of their some quantity.
By this idea, we will completely decide the operator monotonicity of some classes of functions of Szabó type.

10 Sin-Ei Takahasi (Toho Univ.) ∗ An order-preserving function on a quotient space of strictly monotone
Yasuo Nakasuji (Open Univ. of Japan) functions and its applications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: This is a research report about an order-preserving average function on a certain space. We
introduce an order in a quotient space of strictly monotone continuous functions on a finite interval of real
numbers and show that a new average function on this quotient space is order-preserving. We also apply
this new order-preserving function to derive a finite form of Jensen type inequality with negative weights.

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

Shannon type inequalities of a relative operator entropy including Tsallis
and Rényi ones · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we introduce a relative operator entropy of operator distributions including Tsallis
and Rényi ones, and we obtain generalizations of Shannon type inequalities shown by Furuta, Yanagi–
Kuriyama–Furuichi and ourselves.

12 Yuki Seo (Osaka Kyoiku Univ.)

Hadamard product and Karcher mean of positive definite matrices · · · 10

Summary: In this talk, we show several operator inequalities involving the Hadamard product and the
Karcher mean of n positive definite matrices, which are regarded as n-variable version of results due toAndo and Aujla–Vasudeva. As an application, we show an estimate from above to an n-variable version of
the Fiedler type inequality and an n-variable version of majolization relation for the Hadamard product via
the Karcher mean.

13 Toshikazu Abe (Niigata Univ.)
Osamu Hatori (Niigata Univ.)

On generalized gyrovector spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a notion of generalized gyrovector sapces and give an example of it.

14 Toshikazu Abe (Niigata Univ.)
Osamu Hatori (Niigata Univ.)

On a Mazur–Ulam theorem for generalized gyrovector spaces and its
application · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We show a Mazur–Ulam theorem for generalized gyrovector spaces. As an application of it wegive the form of Thompson type isometries on the set of positive invertible elements in unital C ∗ -algebras.

15 Junichi Fujii (Osaka Kyoiku Univ.)

On holonomies for the curve of the operator geometric means · · · · · · · · 15

Summary: Motivated by TQC (the topological quantum computing), I discuss again the holonomies on
the geometry of the positive-definite matrices by Corach–Porta–Recht where the geodesic is the operator
geometric means in the sense of Kubo–Ando. It is shown that the holonomy group is the special unitary
one SU(n) which plays an important role in TQC. We give a horizontal lift of any geodesic to the principal
bundle and its parallel transport along the geodesic. Approximating any diﬀerential curve by the polygonsof geodesics, we can obtain any holonomies.

16 Yoichi Udagawa (Tokyo Univ. of Sci.)
Shuhei Wada
(Kisarazu Nat. Coll. of Tech.)Takeaki Yamazaki (Toyo Univ.)
Masahiro Yanagida(Tokyo Univ. of Sci.)

A family of operator means including the power, power diﬀerence andStolarsky means · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We shall introduce a new way to make a family of operator means. We shall also give a concrete
application which interpolates the power, power diﬀerence and Stolarsky means.

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13:15–14:15

Talk Invited by Functional Analysis Section

Hiroyuki Osaka (Ritsumeikan Univ.)

Gap problems of matrix monotone functions and matrix convex functions and their applications

Summary: Let I be an open interval in the real line R and f be a real valued continuous function definedin I. For a pair of self-adjoint matrices A and B in Mn , n by n matrix algebra, with spectra in I we say
the function f is a matrix monotone function of degree n, n-monotone in short if f (A) ≤ f (B) wheneverA ≤ B. When f is n-monotone for an arbitrary n, it is called operator monotone. We say that the function
f is convex of degree n, n-convex in short if
f (λA + (1 − λ)B) ≤ λf (A) + (1 − λ)f (B)for 0 ≤ λ ≤ 1. Similarly, when f is n-convex for an arbitrary n, it is called operator convex. Denote theseclasses of functions as P∞ (I), and Pn (I) (resp. as K∞ (I) and Kn (I)).
In this talk we will present the problems of gaps between Pn (I) and Pn+1 (I) as well as Kn (I) and Kn+1 (I)and show their applications to matrix inequalities and quantum entropies.

March 23rd (Mon)

Conference Room VIII

9:30–12:00
17 Tatsuya Tsurii (Osaka Pref. Univ.)
Satoshi Kawakami (Nara Univ. of Edu.)
Satoe Yamanaka (Nara Univ. of Edu.)

A hypergroup arising from representations of a finite group and its
subgroup · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a pair of a finite group G and its subgroup G0 , one can obtain a graph (Dinkin diagram)D(G ⊃ G0 ) by restrictions of irreducible representations of G and by inducing of irreducible representationsof G0 owing to Frobenius reciprocity theorem. We introduce a hypergroup associated with this graph
D(G ⊃ G0 ).

18 Satoe Yamanaka (Nara Univ. of Edu.)
Satoshi Kawakami (Nara Univ. of Edu.)
Tatsuya Tsurii (Osaka Pref. Univ.)A hypergroup arising from representations of a hypergroup and its
subhypergroup · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a pair of a hypergroup L and its subhypergroup L0 , one can obtain a graph (Dinkin diagram)
D(L ⊃ L0 ) by restrictions of irreducible representations of L and by inducing of irreducible representationsof L0 . We introduce a hypergroup associated with this graph D(L ⊃ L0 ) and twisted by a hypergroup oforder two.

19 Ryosuke Nakahama (Univ. of Tokyo)

Norm computation and analytic continuation of vector-valued holomorphic discrete series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk the speaker presents the result on the norm computation of the holomorphic discrete
series representations. From this, we can determine when the highest weight modules is unitarizable. Today
we mainly deal with G = Sp(r, R) case.

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20 Toshihisa Kubo (Univ. of Tokyo)

Covariant diﬀerential operators and the Rankin–Cohen bracket · · · · · · 15

Summary: The goal of this talk is to find explicit formulas for certain SL(2, R)-intertwining diﬀerential
operators from C ∞ (R2 ) ⊕ C ∞ (R2 ) to C ∞ (R). The Rankin–Cohen bracket, Jacobi polynomials, andGegenbauer polynomials play a key role.

21 Kyo Nishiyama (Aoyama Gakuin Univ.)

Enhanced orbit embedding · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a theory of orbit embeddings and some examples.

22 Kyo Nishiyama (Aoyama Gakuin Univ.)
Lucas Fresse (Univ. Lorraine)

Nilpotent variety of double flag varieties · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a definition of nilpotent variety for a double flag variety associated with a symmetric pairand prove there are finitely many K-orbits.

23 Koichi Shimada (Univ. of Tokyo)

Classification of actions of compact abelian groups on subfactors withindex less than 4 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We classify actions of discrete abelian groups on some inclusions of von Neumann algebras which
may not be factors, up to cocycle conjugacy. As a corollary, we classify actions of compact abelian groups
on inclusions of AFD factors with index less than 4, up to stable conjugacy.

24 Yosuke Morita (Univ. of Tokyo)

A topological obstruction for the existence of compact quotients ofhomogeneous spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Extending the idea of Kobayashi–Ono, we provide a necessary condition, which is written in termsof relative Lie algebra cohomology, for that a given homogeneous space G/H admits a compact Cliﬀord–
Klein form. Using the Chern–Weil theory of characteristic classes, we classify the irreducible symmetricspaces satisfying this necessary condition.

14:15–16:00
25 Takeshi Miura (Niigata Univ.)
Tomas Tonev (Univ. of Montana)

Generalizations of multiplicatively spectrum preserving maps on function algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We characterize mappings Si , Ti , not necessarily linear, from parameter sets Ji , i = 1, 2, onto
multiplicative subsets of function algebras, subject to the following conditions on the peripheral spectra oftheir products: σπ (S1 (a)S2 (b)) ⊂ σπ (T1 (a)T2 (b)) and σπ (S1 (a)S2 (b)) ∩ σπ (T1 (a)T2 (b)) ̸= ∅, a ∈ J1 , b ∈ J2 .
As a direct consequence we obtain a large number of previous results about mappings subject to various
spectral conditions.

26 Yasuo Watatani (Kyushu Univ.) ∗ General Brenner decomposition of the relative position of three subMasatoshi Enomoto
spaces of a Hilbert space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 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 generalcondition that the Brenner type decomposition holds.

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Functional Analysis

27 Yuki Arano (Univ. of Tokyo)
Yosuke Kubota (Univ. of Tokyo)

A categorical approach to the Atiyah–Segal completion theorem in
KK-theory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a new perspective on the Atiyah–Segal completion theorem and generalize it toequivariant KK-theory. The homological algebra of the Kasparov category, which is developed by Ralf
Meyer and Ryzard Nest, plays a central role. It contains most of known generalizations of the Atiyah–Segal
completion theorem. Moreover, as a corollary, an analogue of McClare’s result on the restriction maps isalso proved and applied to the stability of the Baum–Connes conjecture under extensions.

∗
28 Kengo Matsumoto
Full groups of Cuntz–Krieger algebras and Higman–Thompson groups(Joetsu Univ. of Edu.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Chiba Univ.)
Hiroki Matui

Summary: We will study presentations of the continuous full group ΓA of a one-sided topological Markov
shift (XA , σA ) for an irreducible matrix A with entries in {0, 1} as a generalization of the Higman–Thompson
groups VN , 1 < N ∈ N. We will show that the group ΓA can be represented as a group Γtab
A of matrices,Lof right
called A-adic tables, with entries in admissible words of the shift space XA , and a group ΓPAcontinuous piecewise linear functions, called A-adic PL functions, on [0, 1] with finite singularities.

29 Tsuyoshi Kajiwara (Okayama Univ.)
Yasuo Watatani (Kyushu Univ.)

Analysis of the cores of C*-algebras associated dynamical systems with
branched points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we report new results for the analysis of the cores of the C*-algebras associated withdynamical systems with branched points. We determine the dimensions of GNS representations given by
the model traces of the core of the C*-algebras associated with rational functions. We define the shift mapon the cores, and calculate its action on the set of discrete traces and K0 -groups. We clarify the relation
between the shift map and the dimension groups which have been defined for C*-algebras associated with
Markov chain.

30 Shuhei Masumoto (Univ. of Tokyo)

The countable chain condition and tensor products of operator algebras· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The countable chain condition has been fairly studied in set theory, being related to the behaviorof cardinals in forcing extensions. An appropriate interpretation of this condition in the setting of operator
algebras gives a generalization of σ-compactness for measure spaces. We shall present that ZFC does notdetermine whether this condition is preserved under minimal tensor products of operator algebras, whichshould be contrasted with the fact that σ-compactness is preserved under Cartesian products.

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Functional Analysis

16:30–17:30

Talk Invited by Functional Analysis Section

Kenji Taniguchi(Aoyama Gakuin Univ.)

Composition series of the standard Whittaker (g, K)-modules

Summary: For a real reductive linear Lie group G, the space of Whittaker functions is the representation spaceinduced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. The speaker defined
the standard Whittaker (g, K)-modules, which are K-admissible submodules of the space of Whittaker
functions. They are characterized by (1) infinitesimal character, (2) right action of the stabilizer of thecharacter of nilpotent subgroup, (3) moderate growth condition at infinity. In this talk, we discuss the(g, K)-module structure of them.
We first explain the case when the infinitesimal character characterizing such module is generic. In this case,this module is completely reducible, and its structure is explicitly determined. On the other hand, if theinfinitesimal character is integral, very little is known about the structure of the standard Whittaker (g, K)modules so far. In the second part of this talk, we exhibit the cases when G = U (n, 1) or G = Spin(n, 1) inwhich the module structures are completely determined even if the infinitesimal character is regular integral.
Studies of higher rank cases are now in progress. We want to introduce some parts of them, if possible.

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Statistics and Probability

Statistics and Probability
March 21st (Sat)

Conference Room IIa

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

Unbiased estimator related to some integral equations · · · · · · · · · · · · · · 15

Summary: We have already constructed a probabilistic solution to a certain class of deterministic nonlinear
integral equations. Related to the same equations, we show that there exist a suitable sequence of randomvariables and a proper functional such that the functional is a realizable unbiased estimator of the solutions
to the above-mentioned integral equations.

2 Taro Murayama (Kanazawa Univ.) ∗ The zero-mass limit problem for three relativistic Schrödinger heat
semigroups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: Heat semigroups for three magnetic relativistic Schrödinger operators can be represented by
Feynman–Kac–Itô type path integral. We discuss convergences of these semigroups by using their path
integral representations if mass-parameter goes to zero.

3 Naotaka Kajino (Kobe Univ.)
Alexander Grigor’yan(Univ. of Bielefeld)

Localized heat kernel upper bounds for diﬀusions via a multiple Dynkin–
Hunt formula · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The aim of this talk is to present the authors’ result on obtaining heat kernel upper bounds fordiﬀusion processes from assumptions on the behavior of the process only within a fixed open subset of thestate space. The proof is based on a seemingly new formula, which we call a multiple Dynkin–Hunt formula,expressing the transition function of the diﬀusion process on the whole space in terms of that of the partprocess on a given open set. This result has an application to heat kernel analysis for the canonical diﬀusion
in a certain random geometry, called the Liouville Brownian motion.

4 Shigeyoshi Ogawa (Ritsumeikan Univ.)
Hideaki Uemura (Aichi Univ. of Edu.)

On the identification of noncausal functions from the SFCs · · · · · · · · · · 15

Summary: Let f (t, ω) be a noncausal random function. We consider the stochastic Fourier coeﬃcient (SFC
∫1∫
in abbr.) f˜n of f (t, ω) defined by 0 f (t, ω)en (t)dWt , where {en (t)} is a CONS and dWt stands for somestochastic integral. The question whether we can identify the original function f (t, ω) by its SFCs arises
spontaneously. We study this problem under the condition that en (t) is the trigonometric function and∫dWt is the Ogawa integral, and give an aﬃrmative answer.

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Statistics and Probability

5 Shigeyoshi Ogawa (Ritsumeikan Univ.)

BPE and a noncausal counterpart of Girsanov’s theorem · · · · · · · · · · · · 10

Summary: The BPE (Brownian particle equation) is a class of SPDEs (stochastic partial diﬀerential equation)of the first order including the white noise, at least in its principal part.
The equation was first introduced by the author in 1973 as a model that serves as a bridge between PDEs of
two diﬀerent types; the PDE of the first order on one hand and the PDE of parabolic type and this programis realized in the framework of the noncausal calculus
In this talk we are to show first some recent results on basic properties of the Brownian particle equation
and results in the noncausal calculus. As an application of the theory, we will show an elementary derivationof a noncausal counterpart of Girsanov’s theorem.

6 Yuji Kasahara (Univ. of Tsukuba)
Shin’ichi Kotani(Kwansei Gakuin Univ.)

Asymptotic behavior of the transition density of Bessel-like diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Linear diﬀusions which are not far from Bessel diﬀusions will be discussed. We talk on someresults on the asymptotic behavior of the transition denssity in the large time.

7 Yasuki Isozaki (Kyoto Inst. Tech.)First hitting time of the integer lattice by symmetric stable processes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For one-dimensional Brownian motion, the first hitting time of a point has infinite mean while
the exit time from an interval has finite exponential moments. In this note we establish its counterparts forsymmetric stable processes. The Laplace transform of the first hitting time of the integer lattice is obtained.

8 Dai Taguchi (Ritsumeikan Univ.)
Arturo Kohatsu-Higa(Ritsumeikan Univ.)
Jie Zhong (Univ. of Central Florida)

Parametrix method for skew diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we prove a Gaussian upper bound for the density of a skew diﬀusion. The idea of
proof is the parametrix method for skew diﬀusion which is a Taylor-like expansion for a semigroup. This
expansion leads to a probabilistic representation which can be used Monte Carlo simulation.

9 Yusuke Nakamura (Hiroshima Univ.)
Akihiko Inoue (Hiroshima Univ.)
Shingo Moriuchi(Bizen Ryokuyo High School)

A Vasicek-type short rate model with memory eﬀect · · · · · · · · · · · · · · · · 15

Summary: We introduce a Vasicek-type short rate model with memory eﬀect. The model can describe
more complex yield curves than those the original Vasicek model can. We derive two types of explicit
representations of bond prices in this term-structure model. The second one is of Markovian type, whence
would be useful in numerical calculations.

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Statistics and Probability

14:15–14:45
10 Ryoki Fukushima (Kyoto Univ.)(UCLA)
Marek Biskup(WIAS)
Wolfgang König

Eigenvalue fluctuations for lattice Anderson Hamiltonians · · · · · · · · · · · 10

Summary: We study a homogenization problem for the eigenvalues of discrete random Schrödinger operator.
The operator is restricted to a lattice approximation of a smooth domain and we consider the asymptotics
as the mesh-size tending to zero. It is shown that the eigenvalues converges to those of a natural limiting
operator and also that the fluctuation of them around the means obeys Gaussian limit law.

11 Ryoki Fukushima (Kyoto Univ.)
Francis Comets (Univ. Paris 7)
Nobuo Yoshida (Nagoya Univ.)

Limiting results for the free energy of directed polymers in random
environment with unbounded jumps · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study asymptotic behaviors of the free energy for the directed polymer in random environment.
The polymer is allowed to make unbounded jumps and the environment is given by the Bernoulli variables.
We first establish the continuity including the negative infinity value of the coupling constant β. Secondly,
we identify the asymptotics of the free energy at β = −∞ in the limit of the success probability of the
Bernoulli variables tending to one.

12 Katusi Fukuyama (Kobe Univ.) ∗ On permutational invariance of the metric discrepancy results · · · · · · · 5(Kobe Univ.)
Yutaro Noda
Summary: If a sequence of non-zero real numbers {nk } satisfies |nk+1 /nk | → ∞, then the law of the iterated
logarithm for discrepancies of {nk x} is permutational invariant.

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Statistics and Probability

15:00–16:00

Talk Invited by Statistics and Probability Section

Naotaka Kajino (Kobe Univ.)

Heat kernel analysis for Brownian motion of 2-dimensional Liouvillequantum gravity

Summary: This talk is mainly based on a joint work with Sebastian Andres (Universität Bonn).
Liouville quantum gravity is a mathematical model for 2-dimensional quantum gravity proposed in theoreticalphysics, which is formally given by “multiplying” a prescribed Riemannian metric g on a 2-dimensionalsurface (say R2 ) by a random “weight function” of the form eγX(·) for a Gaussian free field X(·) and apositive parameter γ. Since X(·) is only a random distribution because of the logarithmic singularity of
its covariance kernel, the “function” eγX(·) is a highly ill-defined object and it has not yet been suﬃciently
well-understood even what such a “weighted Riemannian metric” should mathematically mean.
In recent years there have been researches attempting to make rigorous sense of various objects which should
be given rise to by such a “weighted Riemannian metric”. On the basis of Kahane’s construction (in 1985!)
22of the associated volume measure Mγ (dz) := “eγX(z)−γ E[X(z) ]/2 dz”, γ ∈ (0, 2), the canonical diﬀusion
process associated with this “metric”, called the Liouville Brownian motion, has been rigorously constructed
recently by Garban, Rhodes and Vargas and in a weaker form also by Berestycki. Mathematically it is an
Mγ -symmetric diﬀusion defined as the time change of the 2-dimensional Brownian motion by the positive
continuous additive functional with Revuz measure Mγ .
In this talk I will present a detailed analysis of the heat kernel pt (x, y) of the Liouville Brownian motion.
The results include its joint continuity, a locally uniform sub-Gaussian upper bound of the form pt (x, y) ≤
(
(
) 1 )
β
C1 t−1 log(t−1 ) exp −C2 |x−y|t ∧1 β−1 for t ∈ (0, 12 ] and an on-diagonal lower bound of the form pt (x, x) ≥()−η
C3 t−1 log(t−1 )for small (depending heavily on x) t > 0 for Mγ -a.e. x with some concrete constantη > 0. As immediate corollaries it then turns out that the pointwise spectral dimension equals 2 Mγ -a.e.
and that the global spectral dimension is also 2.

16:15–17:15

Award Lecture for 2014 Analysis Prize

Hirofumi Osada (Kyushu Univ.)

Stochastic dynamics and geometry for infinite particle systems

Summary: We discuss infinite particle systems in Rd controlled by free potential Φ(x) and interacting potentials Ψ(x, y). Such systems, from view point of stochastic geometry, are governed by (Φ, Ψ) quasi-Gibbs
measures, and the associated stochastic dynamics are given by infinite-dimensional stochastic diﬀerential
equations called interacting Brownian motions in infinite dimensions. We give general theorems to constructunique, strong solutions of infinite-dimensional stochastic diﬀerential equations describing interacting Brownian motions. As applications, we construct infinite-dimensional labeled dynamics naturally arising fromrandom matrices. The associated unlabeled dynamics are reversible with respect to random point fields
related to random matrices. Typical examples are Dyson (Sineβ ), Airy, and Bessel random point fields,
and the Ginibre random point field. All canonical Gibbs measures with Ruelle’s class interaction potentials(satisfying suitable marginal assumptions) are covered by our theorems. We detect the infinite-dimensional
stochastic diﬀerential equations describing the stochastic dynamics related to Airy random point fields with
β = 1,2,4. When β = 2, this dynamics coincides with that given by the space-time correlation functions
constructed by Spohn, Johansson, and others. Interacting Brownian motions arising from random matrix
theory have logarithmic interaction potentials. Because of the long range nature of this potential, thesystems have geometric and dynamic rigidity. I show novel and surprisingly interesting phenomena ofinteracting Brownian motions in infinite-dimensions with logarithmic interaction potentials.

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Statistics and Probability

March 22nd (Sun)

Conference Room IIb

9:30–11:30
13 Shin-Ichiro Takazawa (Kobe Univ.) ∗ The convergence rate of the strong law of large numbers by a finite
number of strategies in the unbounded forecasting game II · · · · · · · · · · 10
Summary: We consider the convergence rate of the strong law of large numbers in the framework of gametheoretic probability of Shafer and Vovk. We prove that in the unbounded forecasting game with double
hedges Skeptic can weakly force the strong law of large numbers by two strategies.

14 F. Alberto Grünbaum (UC Berkeley)(JSPS)
Takuya Machida

A long-time limit distribution of a 3-period time-dependent quantum
walk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Quantum walks are quantum analogs of random walks and have a background of quantum physics.
Also, their applications have largely headed for quantum computers. From the view point of mathematics,
the long-time limit theorems of quantum walks have been studied to mention the behavior of the walker
after a lot of evolutions. In this talk, our focus is put on a discrete-time quantum walk on the line. The
walker determines its evolution by unitary operators which are chosen depending on time. The new result
presented this time is a long-time limit distribution for a 3-period time-dependent quantum walk. The limit
distribution shows an interesting behavior which we have never seen in a time-independent quantum walkor a 2-period time-dependent quantum walk.

15 Akihito Hora (Hokkaido Univ.)

Hydrodynamic limit for restriction-induction chains and free probability· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We use notions of free probability to describe time evolution of the rescaled Young diagrams
through hydrodynamic limit for restriction-induction chains.

16 Takayoshi Setokuchi(Setokuchi Roof Tile Factory Co. Ltd.)
Keizo Takashima(Okayama Univ. of Sci.)

Discrepancies of irrational rotations based on numbers having single
isolated large partial quotient · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give some refinements of results of Schoissengeier on the discrepancies of irrational rotations.
Using these refinements, we give general mathematical explanations for the appearances of several parabolalike hills in behaviors of discrepancies of irrational rotations having single isolated large partial quotient intheir continued fraction expansion.

17 Shintaro Suzuki (Osaka Univ.)

The Artin–Mazur zeta function of generalized beta transformations · · 15

Summary: In this talk, we consider the generalized beta-transformation, introduced by Pawl Gora in 2007
and study analytic properties of its Artin–Mazur zeta function. We state that it can be extended to theopen unit disk as a meromorphic function which is expressed by using the f-expansion of 1. The main
theorem enables us to study the analytic properties of its poles.

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Statistics and Probability

18 Hiroki Takahashi (Keio Univ.) ∗ Zero temperature limit for the Hénon map at the first bifurcation · · · · 15
Summary: We develop a thermodynamic formalism for a strongly dissipative Hénon-like map at the firstbifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside
the limit set. For any t ∈ R we prove the existence of an invariant Borel probability measure which
minimizes the free energy associated with a non continuous geometric potential −t log J u , where J u denotes
the Jacobian in the unstable direction. Under a mild condition, we show that these measures accumulate as
t → +∞ to measures which minimize the unstable Lyapunov exponent. We also show that the equilibrium
measures converge to a Dirac measure as t → −∞.

19 Michael Keane (Wesleyan Univ.)
Masato Takei (Yokohama Nat. Univ.)

On the number of infinite clusters in percolation on a class of fractal-likegraphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the site percolation problem on a class of fractal-like graphs in the d-dimensional
space, and show that for every such graph the critical probability lies strictly between zero and one, and thenumber of the infinite cluster is at most two with probability one. Moreover for almost every such graph,
the number of the infinite cluster is at most one with probability one.

11:30–12:00

Research Section Assembly

March 23rd (Mon)

Conference Room IIa

9:30–12:00
20 Naoto Nakano(JST PRESTO/ Hokkaido Univ.)
Masaru Inatsu (Hokkaido Univ.)
Seiichiro Kusuoka (Tohoku Univ.)
Yoshitaka Saiki (Hitotsubashi Univ.)

Ensemble predictability estimate of vector-valued time-series analysis
based on stochastic diﬀerential equation model · · · · · · · · · · · · · · · · · · · · 15

Summary: Ensemble predictability estimate of vector-valued time-series analysis based on stochastic diﬀerential equation (SDE) model is studied. Here, we regard the time-series as one realization of a solution pathof a SDE of the Markovian type. We can obtain the coeﬃcient of the SDE by using empirical evaluating
formulae, and we can perform numerical simulations by the use of the empirically estimated SDE. Comparing
the ensemble variance of the result of the simulations to that of the reference time-series, we validate theframework of this study and estimate the predictability of the time-series.

21 Fumiya Akashi (Waseda Univ.)

GMM estimator for symmetric α-stable linear processes and its secondorder asymptotic properties · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk focuses on the parameter estimation problem of the symmetric α-stable linear process.
In particular, we make use of the empirical characteristic function and apply the generalized method of
moments (GMM) estimator for characteristic exponent α, scale parameter σ and the coeﬃcients of thestable process. It is shown that the estimator has consistency and asymptotic normality, and the stochastic
expansions are given up to second-order. We also provide the bias adjustment procedure for the estimator,and give some theoretical and numerical examples.

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Statistics and Probability

22 Yan Liu(Waseda Univ.)

Asymptotic theory for minimum contrast estimation in time series
analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study asymptotic distributions of minimum contrast estimators which naturally
originated in time series analysis. Generally, the Whittle estimator for Gaussian process is a special form of
the minimum contrast estimators in time series analysis. The estimator has been extended to the several
classes of minimum contrast estimators. The extension, however, cannot be explained in the statisticalsense. We focused on the statistical errors (e.g. prediction error, interpolation error, etc.), which has to beminimized, and defined a new class of the minimum contrast estimators. We examined the properties of theclass for the spectral densities and investigated asymptotic distribution of the estimators.

23 Shintaro Hashimoto (Univ. of Tsukuba)
Ken-ichi Koike (Univ. of Tsukuba)

Reference priors with maximum divergence for multiparameter nonregular models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we derive reference priors which maximize a general divergence measure (called
α-divergence) in multiparameter non-regular models in presence of nuisance parameter. In non-regular case,the prior is diﬀerent from the reference prior given in Bernardo (1979). The comparison between regularand non-regular cases is also discussed.

24 Koji Tsukuda(Grad. Univ. for Adv. Stud.)

A functional central limit theorem in an L2 space for the Ewens sampling
formula · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A new functional central limit theorem for the number of a partition by the Ewens sampling
formula is presented. As a framework of the weak convergence, the L2 space is argued, whereas the
Skorokhod space is argued in existing functional CLTs for random combinatorial structures. It enables us
to treat a weight function, which requires new methods of proofs, and the limit law becomes a weighted
Brownian motion.

25 Jo Suzuki(Osaka Univ.)

A generalized BIC without assuming either discrete or continuous · · · · 15

Summary: In any database, some fields are continuous and others discrete. However,in any statistics, when
we consider dependency among the variables, they are assumed to be either all Gaussian or all discrete.
In this paper, we consider to estimate the model that expresses its dependency based on maximizing theposterior probability from examples w.r.t. a given prior probability. We show that such a model is always
obtained and converges with probability one. The same idea can be applied to obtain dependency among
variables in the same way as BIC even when a continuous variable is contained.

26 Masafumi Akahira (Univ. of Tsukuba)
Nao Ohyauchi (Univ. of Tsukuba)

Asymptotic loss of the MLE of a truncation parameter for a one-sided
truncated exponential family of distributions · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In a similar way to Akahira (2013, in revision in Ann. Inst. Statist. Math.), for a truncatedexponential family of distributions with a truncation parameter and a natural parameter as a nuisanceparameter, the bias-adjusted maximum likelihood estimators (MLEs) S and T of the truncation parameter
when the natural parameter is known and unknown, respectively, are obtained, and their stochastic
expansions are derived. Further, the second order asymptotic variances of S and T are obtained and thesecond order asymptotic loss of T relative to S is also given.

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Statistics and Probability

27 Nao Ohyauchi (Univ. of Tsukuba)
Masafumi Akahira (Univ. of Tsukuba)

Asymptotic loss of the MLE of a truncation parameter for a two-sided
truncated exponential family of distributions · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In a similar way to Akahira et al. (2014, to appear in Comm. Stat. Theor. Meth.), for a two-sided
truncated exponential family of distributions with two truncation parameters and a natural parameter as
a nuisance parameter, the bias-adjusted MLE S of one of the truncation parameters when the naturalparameter and another truncation parameter are known and the bias-adjusted MLE T of the truncation
parameter when they are unknown, are obtained, and their stochastic expansions are derived. Further,
the second order asymptotic variances of S and T are obtained and the second order asymptotic loss of T
relative to S is also given.

14:15–15:15
28 Yuri Sekiya (Hokkaido Univ. of Edu.)
Nobuhiro Taneichi (Kagoshima Univ.)

On an application of a discontinuous term of the asymptotic expansion
for distribution of multinomial goodness-of-fit test statistic · · · · · · · · · · 15

Summary: In the multinomial goodness-of-fit test, Siotani and Fujikoshi (1984) derived an asymptotic
expansion for the null distribution of the loglikelihood ratio statistic under a simple null hypothesis. They
proposed an expression as an approximation of the lower probability of the loglikelihood ratio statistic. The
expression consists of continuous and discontinuous terms. We consider a new test using the discontinuous
term.

29 Seiichi Iwamoto (Kyushu Univ.⋆)
Yutaka Kimura (Akita Pref. Univ.)

Is Da Vinci Code in itself optimal? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is shown that Da Vinci Code —the first eight Fibonacci numbers— is in itself optimal for two
quadratic programming problems under linear constraints. This result applies to Fibonacci Code —theconsecutive Fibonacci numbers—. Some relations to reversed problem and dual problem are discussed.

30 Seiichi Iwamoto (Kyushu Univ.⋆)

Three dual approaches to least squares method · · · · · · · · · · · · · · · · · · · · 15

Summary: The least squares method results in solving a quadratic convex programming problem without
constraint. In this talk, it is shown that its dual problem, together with equality condition, is derived
through three approaches —(1) dynamic method, (2) plus-minus method, and (3) inequality method. (1)applies Lagrange duality for mathematical programming under linear constraints. (2) is an improvement ofFenchel duality. (3) is a series of applications of arithmetic mean— geometric mean inequality under theconstraints.

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Statistics and Probability

15:30–16:30

Talk Invited by Statistics and Probability Section

Taka-aki Shiraishi (Nanzan Univ.)

Advanced theory of multiple comparison procedures in multi-sample
modelsSummary: We consider multiple comparison procedures in k sample models. Suppose under the i-thtreatment a random sample Xi1 , · · · , Xini of size ni is taken (i = 1, · · · , k), where Xij ’s are independent.
Furtheremore assume that Xij has a distribution function Fi (x) with finite mean µi = E(Xij ). Then we canderive the following conclusions (i)–(v). (i) Suppose that Fi (x) is a normal distribution function with mean
µi and unkown variance σ 2 . Then, for the diﬀerences among mean responses, from a mathematical theory,the closed testing procedure proposed by Shiraishi (2011a) is superior to the single step Tukey–Kramer test
(Tukey (1953), Kramer (1956)). By a simulation, the power of the former is fairy higher than the latter.
The confidence region of µ ≡ (µ1 , · · · , µk ) derived from the closed testing procedure is equivalent to a single
step simultaneous confidence intervals of {µi − µi′ : 1 ≤ i < i′ ≤ k}. (ii) Suppose that the simple order
restriction of µ1 ≤ µ2 ≤ · · · ≤ µk is satisfied under the condition of the above (i). Then, for the diﬀerencesamong mean responses, a closed testing procedure is superior to the single step Hayter’s test (Hayter(1990)). To compute the upper 100αth percentiles of the distributions of statistics maxi<i′ (−tii′ ), the sincmethod described in Lund and Bowers (1992) and Stenger (1993) is utilized. (these contents are statedin Shiraishi (2014a) and Shiraishi and Sugiura (2015)) (iii) Suppose that Fi (x) is a normal distributionfunction with mean µi and unkown variance σi2 . Then, for the diﬀerences among mean responses, Shiraishi
and Hayakawa (2015) propose a closed testing procedure superior to the single step Games–Howell test
(Games and Howell (1976)). By a simulation, the power of the former is fairy higher than the latter. (iv)
Suppose that Fi (x) = F (x − µi ) holds. Then nonparametric multiple comparison procedures are discussed
corresponding to the above (i) and (ii). (these contents are stated in Shiraishi (2008), (2011b), (2014a)) (v)Suppose that Fi (x) is Bernoulli, Poisson, or exponential. Then the theory of multiple comparison procedures
are constructed. (these contents are stated in Shiraishi (2009), (2011c), (2012a), (2012b), (2013), (2014b))

16:45–17:45

Talk Invited by Statistics and Probability Section

Masashi Hyodo (Tokyo Univ. of Sci.)

Estimation of the probabilities of misclassification for a linear discriminant function in high-dimensional settings

Summary: In this talk we consider the estimation of the probabilities of misclassification for a linear
discriminant function in high-dimensional settings. We discuss misclassification probability for Fisher’slinear discriminant function and Euclidean distance-based linear discriminant function. Based on thelarge sample theory, Lachenbruch and Mickey (1968) proposed the asymptotic unbiased estimator of
misclassification probability for Fisher’s linear discriminant function. Since this method is based on large
sample asymptotic results, it does not perform well in high dimensional settings. We treat the estimation of
misclassification probability for Fisher’s linear discriminant function and related topics when the dimension,p, of the observation vectors is less than the total number, N , of observation vectors from the two groups,
but both p and N tend to infinity with the same order. On the other hand, we are interested to explore thediscrimination procedure that can accommodate p > N cases. In this case, Euclidean distance-based linear
discriminant function is often used. We introduce the consistent estimator of misclassification probabilities
when the dimension of the vector, p, may exceed the sample size, N , and the underlying distribution need
not necessarily be normal.

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March 24th (Tue)

Conference Room IIa

9:45–12:00
31 Akira Shibuya (Tokyo Univ. of Sci.)
Kiyotaka Iki (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Orthogonal decomposition of extended diagonal exponent symmetry
model in square contingency tables with ordered categories · · · · · · · · · · 15

Summary: For square contingency tables with ordered categories, we propose new models, which are theextension of Tomizawa’s (1992) diagonal exponent symmetry model. Also we give the orthogonal decomposition of proposed model.

32 Mana Aizawa (Tokyo Univ. of Sci.)
Kouji Yamamoto (Osaka Univ.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Decompositions of sum-symmetry model for square contingency tables
with ordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For square contingency tables, Yamamoto et al. (2013) proposed the sum-symmetry (SS) model.
We propose three kinds of symmetry model, and give two kinds of decompositions of the SS model.

33 Kouji Tahata (Tokyo Univ. of Sci.)
Masato Naganawa (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Decomposition of symmetry based on extended linear asymmetry model
for square contingency tables with ordered categories · · · · · · · · · · · · · · · 10

Summary: For the analysis of square contingency tables with ordered categories, it may be useful to apply
some kinds of asymmetry model when the symmetry model does not hold. In this talk, the symmetry model
is separated into two models. One is the extended linear asymmetry model and the other is a model whichindicates both global symmetry and moment equality. Also, the relationship between test statistics is given.

34 Shoko Chisaki (Tokyo Univ. of Sci.)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

On a diﬀerence systems of set from a family of subsets in Fp · · · · · · · · · 10

Summary: A regular diﬀerence systems of set is a collection of t disjoint m-subsets Qi , 0 ≤ i ≤ t−1, of Zn suchthat every element of Z∗n appears at least ρ times in the multiset {a − b|a ∈ Qi , b ∈ Qj , 0 ≤ i ̸= j ≤ t − 1}.
A DSS is perfect if every element of Z∗n is contained in exactly ρ times in the above multiset. In this talk,we will show a condition that a family of subsets in a finite field of order p forms a regular DSS, where p is
an odd prime. Additionally, we will give a lower bound on the parameter ρ of the DSS and talk about acondition that the DSS is perfect.

35 Masanori Sawa

(Kobe Univ.)

Developing the theory of designs on measure spaces II —a generalizationof Tchakaloﬀ’s Theorem— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An existence theorem is given for cubature formulas for finite-dimensional spaces of L1 -integrable
functions, designed as a natural generalization of Tchakaloﬀ’s Theorem for classical polynomial-type cubature formulas. Statistically, this result states that any probability measure can be represented by adiscrete probability measure over a finite-dimensional space of L1 -integrable functions. One more statisticalapplication will also be discussed in connection with optimal experimental designs.

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36 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.)
Kazuma Ozoe (Okayama Univ. of Sci.)

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

Summary: Consider a fractional factorial design with m factor each at two levels, which is derived froma simple array (SA), where m ≥ 8, and the five-factor and higher-order interactions are assumed to be
negligible. Under these situations, if the main eﬀect and the two-factor interaction are estimable, andfurthermore some of the remaining non-negligible factorial eﬀects may or may not be estimable, then adesign is said to be of resolution R∗ ({1, 2}|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 resolutionR∗ ({1, 2}|Ω4 ), where the number of assemblies is less than the number of non-negligible factorial eﬀects.

37 Kazuki Matsubara(Matsunaga High School)
Masatake Hirao (Aichi Pref. Univ.)
Sanpei Kageyama(Hiroshima Inst. of Tech.)

The existence of 2 pairwise additive cyclic BIB designs with an evennumber of points · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

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, we
provide 2 PACB(32, 2, 1) found out by use of a computer, and then it is shown that 2 PACB(2m , 2, 1) for anym ≥ 2 and 2 PACB(2m t, 2, 1) with any integer m ≥ 2 and any odd integer t ≥ 1 such that gcd(t, 27) ̸= 3, 9
can be constructed.

38 Xiao-Nan Lu (Nagoya Univ.)
Masakazu Jimbo (Nagoya Univ.)

Unifying some graphs related to quadruple systems · · · · · · · · · · · · · · · · · 15

Summary: A quadruple system denoted by QSλ (v), is a pair (V, B), where V is a finite set of v elements,
and B is a set of 4-subsets of V , called block, such that each 3-subset of V appears exactly λ times in B.
Moreover, (V, B) is said to be cyclic if it admits an automorphism consisting of a cycle of length v. By
identifying V with Zv (the additive group of integers mod v), if every unit of Zv is a multiplier, then (V, B)
is said to be aﬃne-invariant. It is known that some constructions of cyclic and aﬃne-invariant QS’s are
related to graphs. In this talk, we unify these graphs related to QS’s, such that progresses to the existence
problem of aﬃne-invariant QS’s can be made from the point of view of number theory.

14:15–15:15
39 Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Asymptotic properties of the extended cross-data-matrix methodology
for high-dimensional data and their applications · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider the extended cross-data-matrix methodology (ECDM) developed by Yataand Aoshima (2013). By applying the ECDM, we give a variety of unbiased estimators for parameters inhigh-dimensional inference. We show that the estimators enjoy the consistency property when the data
dimension grows. Also, we show that the test statistics by the ECDM are asymptotically distributed as anormal distribution under certain conditions. Finally, we study the performance of the ECDM in actual
high-dimensional data analyses.

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40 Akimichi Takemura (Univ. of Tokyo)
Constantin Siriteanu (Osaka Univ.)
Satoshi Kuriki (Inst. of Stat. Math.)

Some recent results on complex non-central Wishart distribution inapplication to wireless communication · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We review some recent results on complex non-central Wishart distribution, which came fromproblems of statistical models in wireless communicationss.

41 Hirofumi Wakaki (Hiroshima Univ.)

A variable selection criterion for GMANOVA model with random coefficient · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A variable selection criterion is derived for GMANOVA model with random coeﬃcient.

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Applied Mathematics
March 21st (Sat)

Conference Room VIa

9:50–12:00
1 Nobuo Shindo(Kyoto Gaidai Nishi High School)

3-color resolution of the edges of maximum plane graph —by “peninsula” method— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I prove that edges of every maximum plane graph G are 3-color resoluble. G does not containany separate triangle. To prove this theorem, I prove the supportive theorem that if edges of the maximum
plane graph without any single triangle are 3-colors resoluble, the edges of the maximum plane graph asa whole are 3-color resoluble, too. To prove the main theorem, I reflect number of cases, covering the
maximum plane graph G with chains of triangles, a number of which is 1/2f. f is the number of the facesof G. At least one case of 3-color resolution of the edges of the graph G exists, through constructing the“peninsula” which contains almost of the chains of triangles.

2 Kenta Noguchi(Keio Univ.)

Control of cycle parities of quadrangulations · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A triangulation is a simple graph on a surface where every face is triangular. A quadrangulation
is a simple graph on a surface where every face is quadrilateral. Quadrangulations has an algebraic structure
called cycle parities. Let F be a set of all quadrangulations on a fixed non-orientable closed surface
Nk . It is known that the cycle parity divides F into four congruence classes. In this talk, we focus on
quadrangulations as a subgraph of triangulations. For a given triangulation G on Nk , we try to find aquadrangulation with any type of cycle parities as a subgraph of G.

3 Masato Mimura (Tohoku Univ.) ∗ Cayley verifiable expander · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We show that any Cayley graph Gamma of a group with “Kazhdan’s property (T)” is a “Cayley
verifiable expander.” That means, there exists a radius R such that any Cayley graph Lambda with thesame R-ball as Gamma has a first positive Laplace eigenvalue which is bounded away from zero uniformly
on Lambda.

4 Takuya Ikuta (Kobe Gakuin Univ.)
Akihiro Munemasa (Tohoku Univ.)

Complex Hadamard matrices coming from 4-class association schemes· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let q be a power of 2. Let n be odd and n ≥ 3. Consider the vector space V (n, q) with anondegenerate quadratic form. Last year, Frédéric Vanhove noted that in Brouwer, Cohen and Neumaier,“Distance-Regular Graphs”, Theorem 12.1.1 is incorrect for n ≥ 5, and showed that the existence of a 4-classassociation scheme for (n, q) = (5, 4). After that, Andries E. Brouwer generalized his result for any n and q.
In this talk, we are to give an infinite families of complex Hadamard matrices attached to such association
schemes.

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5 Kohei Yamada (Nagoya Univ.)
Masanori Sawa (Kobe Univ.)
Masakazu Jimbo (Nagoya Univ.)

Graham and Lovász’s problem on the inertia of distance matrix andquasi-symmetric designs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let n+ (G) and n− (G) be the number of positive and negative eigenvalues of the distance matrix ofa graph G, respectively. Graham and Lovász (1978) asked whether there exists an undirected and connected
graph G with n+ (G) > n− (G). Azarija (2014) proved that every conference graph of order v > 9 satisfies
n+ (G) = n− (G) + 1. In this talk, we mainly present another class of graphs with n+ (G) > n− (G) which is
not strongly regular in connection with quasi-symmetric combinatorial 2-designs.

6 Ryoko Oishi-Tomiyasu(High Energy Accelerator Res. Organ.)

Application of reduction theory of quadratic forms to a lattice determination problem in crystallography · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: When P ⊂ R3 is a periodic point set with the period lattice L, an eﬃcient method to determine
the equivalent class of L from the average theta series of P has a useful application to the problem known
as “powder indexing” in crystallography. By using the C-type reduction theory of quadratic forms, we
succeeded in developing an algorithm robust against loss and errors of information due to observational
problems, suppressing the computation time. We introduce how the C-type reduction theory was used in
the method.

7 Michiaki Kabe
(Kanto Polytechnic Coll.)

Solution for soil improvement problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Every plant produced in the field requires appropriate own cultivate soil. We solve the so-calledsoil improvement problem which means the way to improve the soil in order to produce plants afterinvestigating the present soil. Then using the solution, we develop the software system to improve the soilfor plants.

14:30–16:00
8 Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Etsuo Segawa (Tohoku Univ.)
Yusuke Higuchi (Showa Univ.)

Quantum graph walk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: By giving attention to a common point of the scattering matrix of a quatum graph and thetime evolution (transition matrix) of a discrete-time quantum walk on a graph, we consider a discrete-timequantum walk on a graph with the scattering matrix of a quatum graph as its transition matrix, and define
a quantum graph walk on a graph. Through a quantum graph walk, we discuss the relation between aquatum graph and a discrete-time quantum walk on a graph. Furthermore, we generalize the scatteringmatrix of a quatum graph.

9 Norio Konno (Yokohama Nat. Univ.)
Masato Takei (Yokohama Nat. Univ.)

On stationary measures for discrete-time quantum walks in one dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider stationary measures of the one-dimensional discrete-time quantum walks with twochiralities, which is defined by a 2 × 2 unitary matrix U . By a simple argument, we show that any uniform
measure becomes a stationary measure. If U is diagonal, then any stationary measure is uniform. Except
the diagonal case, we can construct several non-uniform stationary measures.

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10 Shunsuke Nakamura(Tokyo Univ. of Sci.)
Keiko Kotani (Tokyo Univ. of Sci.)

The number of contractible edges in a 4-connected graph having a small
number of edges not contained in triangles · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G be a 4-connected graph, and let Ẽ(G) denote the set of those edges of G which are
not contained in a triangle and let Ec (G) denote the set of contractible edges of G. Ando and Egawa
proved that if |Ẽ(G)| ≥ 15, then |Ec (G)| ≥ (|Ẽ(G)| + 8)/4. In this talk, we prove if |Ẽ(G)| ≥ 7, then|Ec (G)| ≥ (|Ẽ(G)| + 8)/4.

11 Kiyoshi Ando(Nat. Inst. of Information/JST ERATO)

A forbidden subgraph condition for 5-contractible edges · · · · · · · · · · · · · 15

Summary: An edge of k-connected graph is said to be k-contractible if the contraction of it results in ak-connected graph. Kawarabayashi showed that for each odd integer k, every k-connected graph with noK4− has a k-contractible edge, where K4− stands for the graph obtained from K4 by deleting one edge. We
prove every 5-connected graph with no K1 +(K2 ∪P3 ) has a 5-contractible edge. Since K4− ⊂ K1 +(K2 ∪P3 ),this is an extension of Kawarabayashi’s result in case of k = 5.

12 Kazuhiko Ushio (Kinki Univ.)

Balanced C7 -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
C7 -foil designs and related designs.

16:10–17:10

Talk Invited by Applied Mathematics Section
Midori Kobayashi (Univ. of Shizuoka) Dudeney’s round table problem —a survey—

Summary: Dudeney’s round table problem was proposed about one hundred years ago. It has already beensolved when the number of people is even, but it is still unsettled when the number of people is odd, except
in only a few cases. Here is a statement of the problem. A set of n people sits at a round table on each of(n − 1)(n − 2)/2 consecutive days. Is it possible to arrange the seating such that no person has the sametwo neighbours twice?
We survey the history of the problem, known results on the problem, generalization and some related topics
such as 3-designs, perfect 1-factorizations and perfect sets of Hamilton decompositions. We also mention
some open problems.

March 22nd (Sun)

Conference Room VIb

9:30–11:30
13 Minoru Fujimoto (Seika Science Lab.)
Kunihiko Uehara (Tezukayama Univ.)

Twin prime theorem fixed · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

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. We may conclude that there exist infinitely many 2d
diﬀerent primes including the twin primes in case of d = 1 because we can give the lower bounds of theexistence density for them in this algorithm. We also discuss the Hardy–Littlewood conjecture about them.

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14 Minoru Fujimoto (Seika Science Lab.)
Kunihiko Uehara (Tezukayama Univ.)

Legendre’s conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the existence density of the Sophie Germain primes and the primes constellation likeas primes triplet and primes quadruplet by using a simple algorithm for getting the 2d diﬀerent primes.
After we refer to the Legendre’s conjecture which is known as one of the Landau problems: “Does there
always exist at least one prime between consecutive perfect squares?”.

(Nihon Univ.)
15 Akira Saito
Liming Xiong (Beijing Inst. of Tech.)

The Ryjáček closure and a forbidden subgraph · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Ryjáček closure is a powerful tool in the study of hamiltonian properties of claw-free graphs.
Because of its usefulness, we may hope to use it in the classes of graphs defined by another forbidden
subgraph. In this talk, we give a negative answer to this hope, and report that the claw is the only forbidden
subgraph that produces non-trivial results on hamiltonicity by the use of the Ryjáček closure.

16 Kiyoshi Yoshimoto (Nihon Univ.)
Hui DuOn long disjoint paths joining two specified vertices and a vertex subset· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Enomoto conjectured that if G is a graph of order n and the minimum degree δ ≥ n2 + 1, thenfor any two vertices x and y in G, there exists a Hamilton cycle C of G such that dC (x, y) = ⌊ n2 ⌋, wheredC (x, y) is the distance between x and y in C. In this talk, we consider several conjectures which generalize
Enomoto’s conjecture and show several results relating to the conjectures.

17 Shinya Fujita (Yokohama City Univ.)
Gary MacGillivray (Univ. of Victoria)
Tadashi Sakuma (Yamagata Univ.)

Safe set problem on graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let G = (V (G), E(G)) be a connected graph. A non-empty subset S ⊂ V (G) is called a safe set,
if for every component C of G[S] and every component of G − S, we have |C| ≥ |D| whenever C is adjacent
to D in G. We discuss this new concept in this talk.

18 Shoichi Tsuchiya (Keio Univ.)
Guantao Chen (Georgia State Univ.)
Jie Han (Georgia State Univ.)(Georgia State Univ.)
Suil O
Songling Shan (Georgia State Univ.)

On spanning Halin subgraph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A fundamental problem in graph theory is deciding whether a graph has a particular type ofspanning subgraph. It was conjectured that every 4-connected plane triangulation has a spanning Halin
subgraph, but it was disproved. In this talk, we introduce recent results on the spanning Halin subgraphproblem.

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19 Masataka Kaneko (Toho Univ.)
Satoshi Yamashita(Kisarazu Nat. Coll. of Tech.)
Kazushi Ahara (Meiji Univ.)
Akira Iritani(Iwataminami High School)(Toho Univ.)
Setsuo Takato

Eﬀective TeX drawing with dynamic geometry software · · · · · · · · · · · · · 15

Summary: In this talk, we will introduce some new methodology to generate fine graphics on TeX documents
using Cinderella, which is one of the most popular dynamic geometry softwares. Our strategy is to transfer
the data and process for drawing on Cinderella into (1) TeX graphical codes, or (2) command lines ofcomputer algebra systems to generate them. Using the resulting package “KETCindy”, more simple andmore interactive drawing on TeX should be enabled.

13:00–13:50
20 Kosuke Suzuki (Univ. of Tokyo)

Accelerating convergence and the tractability of multivariate integration
for the Walsh spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study multivariate integration for a weighted Walsh space for which the b-adic Walsh coeﬃcients decay as |fb(k)| ∈ b−µa (k) , where µa is the weighted Dick weight and b is an integer larger than 1. Thisfunction space is closely related to a criterion WAFOM, which is used in quasi-Monte Carlo integration. In
this talk, we study accelerating convergence of the minimal worst-case error and accelerating convergencewith polynomial and strong tractability.

21 Norihiro Nakashima(Toyota Tech. Inst.)
Hajime Matsui (Toyota Tech. Inst.)

A decoding algorithm for projective Reed–Muller codes by DFT and
BMS algorithm · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Projective Reed–Muller (RM) codes were introduced as a generalization of RM codes, and thelowest wight and the dual code of PRM codes are known. Roughly speaking, a PRM code is divided into
the direct sum of RM codes. Then we may considered syndromes related to PRM codes as syndromes
related to corresponding RM codes. By using Berlekamp–Massey–Sakata algorithm and discrete Fouriertransformation, we construct a decoding method for PRM codes.

(Tokyo Tech)
22 Shin Harase
Takamitsu Kimoto (Tokyo Tech)

Implementing 64-bit maximally equidistributed Mersenne Twister pseudorandom number generators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In Monte Carlo simulations, Mersenne Twister pseudorandom number generators are widely used.
Mersenne Twisters are based on linear recursions on the two-element field, and we can assess the quality
criterion k(v) called the dimension of equidistribution with v-bit accuracy. Recently, we often use 64-bit
computers, so 64-bit generators are preferable. Up until now, there has been no 64-bit long-period linear
pseudorandom number generator with optimal k(v)’s. In this talk, we introduce an implementation of 64-bit
Mersenne Twisters with optimal k(v)’s.

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13:50–14:10

Presentation Ceremony for the 2014 MSJ Prize for Excellent Young Applied
Mathematicians

March 23rd (Mon)

Conference Room VIa

10:00–11:30
23 Shunzi Horiguchi(Niigata Sangyo Univ.)

Tsuchikura–Horiguchi–Murase–Halley method (Expansion of Halley
Method) and the convergences II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give expansions of Halley method (Tsuchikura–Horiguchi–Murase–Halley method). Next wegive the formula of the comparison of the speeds of convergences for the Halley method and the expansions.

24 Shunzi Horiguchi(Niigata Sangyo Univ.)

Numerical Calculations of Convergences II of Tsuchikura–Horiguchi–
Murase–Halley’s method (Expansion of Halley’s Method) · · · · · · · · · · · 10

Summary: We perform the numerical calculations of the comparisons of the speeds of convergences of theHalley method and the expansions for elementary functions.

25 Shy Der Lin(Chung Yuan Christian Univ.)
H. M. Srivastava (Univ. of Victoria)

Some special properties and application of fractional calculus · · · · · · · · 15

Summary: In recent years, various operators of fractional calculus have been investigated and applied inmany remarkably diverse fields. The main object of this paper is to consider some miscellaneous properties
and applications. We first investigate various families of series identities which emerged in connection withsome of these fractional diﬀer-integral formulas. By using such operators of fractional calculus, a number ofintegral formulas as well as fractional diﬀer-integral formulas involving inverse hyperbolic functions are also
evaluated.

26 Pin-Yu Wang (Nanya Inst. of Tech.) ♭ The N-Fractional Calculus of The Functions 1/f (z) and log f (z), andIdentities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this article, the N-fractional calculus are discussed. Moreover, some identities that are derived
from them are reported.

27 Fumio Nakajima (Iwate Univ.) ∗ Harmonic function property of the geometry of the surface of Mt. Fuji
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We shall propose the fundamental problem whether the height of a mountain may be describedby a harmonic function , and answer this problem to Mt. Fuji by inspecting its contour map statistically.

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14:30–16:00
28 Ryuichi Ohori (Univ. of Tokyo)

Optimization of digital nets for Walsh figure of merit with parameterof growth of derivatives · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 13

Summary: Walsh figure of merit (WAFOM) is a criterion for digital nets, a quasi-Monte Carlo (QMC)
method for numerical integration on [0..1)s . It has been introduced by Matsumoto, Saito and Matoba, andgives an upper bound on QMC integration error for a space of functions defined by Dick. We propose that
we change the function space according to the amount of resources available and optimize point sets foreach function space.

29 Takehito Yoshiki (Univ. of Tokyo)
Kosuke Suzuki (Univ. of Tokyo)

Extra expansion of Walsh coeﬃcients · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Quasi Monte Carlo integration for a function f is the approximation of the integration f by theaverage of f over a finite point set P . In the study of Quasi Monte Carlo integration for a function f overan unit cube by a digital net, it is important to obtain a good point set P which makes the integration
error small. For this purpose, it is important to estimate the upper bound of Walsh coeﬃcients fˆ(k) of afunction f . For a function f in a Sobolev space, the upper bound of fˆ(k) by Dick is known. In this talk,
we introduce the extra expansion of fˆ(k). By using this, we get the improved result in some cases.

30 Jin Hatomoto(Tokyo Nat. Coll. of Tech.)Hitting time distributions for diﬀeomorphisms with weak hyperbolic
product structure · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study an invertible map which admits a weak hyperbolic product structure region, whichis the intersection of two transeversal families of weak stable and weak unstable disks, with countably
many branches and integrable return times. We introduce that for such maps the hitting time distributions
converge to an exponential distribution. Applications of our resutls are some almost Anosov diﬀeomorphisms.

31 Masaji Watanabe (Okayama Univ.)
Fusako Kawai (Kyoto Inst. Tech.)

Modeling and simulation for exogenous type microbial depolymerization· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Microbial depolymerization processes are categorized into exogenous type and endogenous type.
Monomers are separated from the terminals of molecules in an exogenous depolymerization processes.
Polymers depolymerized in exogenous type depolymerization processes include polyethylene and polyethylene
glycol. Molecules reduce by arbitrary scission in an endogenous type depolymerization process. Polymers
depolymerized in endogenous type depolymerization processes include polyvinyl alcohol and polylactic acid.
In this presentation, a mathematical model for an exogenous type depolymerization process is described,
inverse problems for a time factor and a molecular factor of a degradation rate are illustrated, and numericalresults based on experimental results are introduced.

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16:15–17:15

Talk Invited by Applied Mathematics Section

Elliott Ginder (Hokkaido Univ.)

Methods for approximation of constrained interfacial dynamics

Summary: From cavitation, to the motion of DNA strands and soap bubbles, oscillating and constrainedinterfacial motions are a recurrent theme in nature and which play an important role in applications. The
need for approximation schemes treating these topics is clear and our focus is on the development of methods
for multiphase interfacial motions, including possible volume and contact angle constraints. Particularemphasis is on methods of the thresholding dynamical type, of which we have developed an algorithm forapproximating acceleration dependent interfacial motions (the so-called hyperbolic mean curvature flow).
Here we have found that minimizing movements (MM) provide one with a natural framework for bothanalyzing constrained evolutionary equations, as well as for realizing the computational implementation of
our approximation schemes. In particular, by discretizing time, this approach allows one to construct timelocal approximations of the target evolutionary equation as the Euler–Lagrange equations of corresponding
energy functionals. In turn, we will show how this variational aspect allows one, by controlling the set ofadmissible functions for each minimization, to design evolutions with prescribed constraints.

March 24th (Tue)

Conference Room VIa

9:45–11:45
32 Hidenori Ogata(Univ. of Electro-Comm.)
Koya Sakakibara (Univ. of Tokyo)
Masashi Katsurada (Meiji Univ.)

Approximations of complex analytic functions by the charge or dipole
simulation method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present an application of the charge or dipole simulation methods, which are known as
numerical solvers of boundary value problems of the Laplace equation, to the approximations of the complex
analytic functions.

33 Akitoshi Takayasu (Waseda Univ.)
Makoto Mizuguchi (Waseda Univ.)
Takayuki Kubo (Univ. of Tsukuba)
Shin’ichi Oi(Waseda Univ. / JST CREST)

A method of verified computations for solutions to semilinear parabolic
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk presents a numerical method of verifying existence and local uniqueness of a solution
for semilinear parabolic equations. The main theorem of this talk gives a suﬃcient condition for enclosing
the solution in a neighborhood of a numerical solution.

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34 Yoshitaka Watanabe (Kyushu Univ.)
Takehiko Kinoshita (Kyoto Univ.)
Mitsuhiro T. Nakao(Sasebo Nat. Coll. of Tech.)Constructive norm bounds of Laplacian for second-order elliptic operators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk presents constructive L2 -norm estimates of Laplacian for second-order elliptic operatorswith Dirichlet boundary condition. They are applications of the authors’ previous result related to aposteriori estimates of inverse operators. These norm estimations are expected to provide invaluabe
information for explicit H 2 -estimates and pointwise bounds for solutions of second-order elliptic boundary
value problems.

35 Daisuke Koyama(Univ. of Electro-Comm.)
Fumio Kikuchi (Univ. of Tokyo⋆)

On the robustness of a hybridized DGFEM for nearly incompressible
elasticity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We can overcome volume locking if we use our hybridized DGFEM with regular triangulations. To
prove this fact, we reformulate the elasticity problem as a Stokes problem with nonzero divergence constrain,
and establish a uniform inf-sup condition by constructing a Fortin operator. This inf-sup condition implies
that one can use a discontinuous Pk approximation for velocity and a discontinuous Pk−1 approximation forpressure (∀k ∈ N) in our hybridized DGFEM for the Stokes problem with the divergence free constraint.

36 Hirofumi Notsu (Waseda Univ.)
Masahisa Tabata (Waseda Univ.)

Error estimates of Galerkin-characteristics finite element schemes fornatural convection problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Error estimates of Galerkin-characteristics finite element schemes for natural convection problems
are proved. A conventional scheme with P2/P1/P2 element and a stabilized scheme with P1/P1/P1 element
are considered. The results are optimal and are proved by mathematical induction.

37 Tomoya Kemmochi (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

An application of discrete maximal regularity to the semilinear heat
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Maximal regularity is a very significant property for parabolic partial diﬀerential equations. It
is widely used for analysis of quasilinear parabolic equations and the Navier–Stokes equation. Thus, it isimportant to consider whether the discrete analogy holds when the equation is discretized for numericalcomputations. If this is the case, it is expected that the discrete version of maximal regularity can beapplied to the error analysis of the numerical approximation for nonlinear equations.
From the above perspective, we have studied the discrete analogy of maximal regularity for abstract linear
Cauchy problems. In this talk, we apply these results to the finite element approximation of the semilinear
parabolic equation. The time variable is discretized by the backward Euler method. We shall report an
optimal error estimate.

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14:15–15:45
38 Ippei Obayashi(Kyoto Univ. / JST CREST)

Formation mechanism of basin of attraction for simple bipedal walking
models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this presentation, I will talk about the stability of simple bipedal walking models. Especially,
I focus on the geometric structure of basin of attraction. By some numerical computations for the basin of
attraction, interesting and complex geometric structures, for example, the region is thin and fractal-like, but
the formation mechanism is not known. I will explain the formation mechanism of the basin of attraction
using the saddle property and hybridness of bipedal walking models.

39 Takeshi Gotoda (Kyoto Univ.)

The α point vortex system and enstrophy variations · · · · · · · · · · · · · · · · 15

Summary: It is considered that enstrophy dissipation in weak solutions of the Euler equations are closely
related with the turbulence theory in two dimension. However, it is uncertain what kind of weak solutions
can dissipate. Under such a background, I am studying the Euler-alpha equations, specially the alpha-pointvortex system (alpha-PV). Since the alpha-PV is a regularization of the point-vortex system (PV), there isa possibility of obtaining the dissipating solutions of the PV by utilizing the alpha-PV. I will talk about thealpha-PV and the relationship between the alpha-PV and the PV in terms of enstrophy dissipation.

(Hokkaido Univ.)
40 Kei Nishi
Yasumasa Nishiura (Tohoku Univ.)
Takashi Teramoto(Asahikawa Medical Univ.)

On the motion of the two interacting interfaces of a pulse solution in abistable reaction-diﬀusion system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The dynamics of a pulse solution arising in a bistable reaction-diﬀusion system is investigatedfrom a viewpoint of bifurcation theory, by deriving a finite-dimensional ODEs for the motion of the twopulse interfaces. Application to a spatially heterogeneous case will be also mentioned if time permits.

41 Sungrim Seirin Lee (Hiroshima Univ.)

Application of Phase-field method for elucidating the pattern formationof life · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce two novel applications of phase-field method to life sciences. One is a mathematicalmodeling which elucidate the mechanism of chromatin pattern formation in the nucleus. The other is theapplication for multi-scaling modeling of the cells.

42 Masakazu Akiyama (Hokkaido Univ.)
Tomonori Ayukawa (Akita Univ.)
Masakazu Yamazaki (Akita Univ.)

A mathematical model of planar cell polarity · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Many cells within epithelial tissues display polarity along a particular axis. This axis is perpendicular to the tissue plane and apicobasal axis (from top to bottom of tissues) of the cell. This phenomenon
is called “planar cell polarity, PCP”, and is a common phenomenon found in many multicellular organisms.
For example, hair cells in the inner ear of humans have many hairs on each individual cell, and since thehairs are regularly arranged on the cell plane, we can hear the sound. Not only hair cells, but fish scales,
and body hair on mammals and the wings of birds etc., have cell polarity. As a result, these creatures carryout macroscopic morphogenesis.
In this talk, we will introduce our mathematical model and simulation result. Despite of our model is very
simple formulation, it can reproduce various aspects of the PCP.

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16:00–17:00

Talk Invited by Applied Mathematics Section

Yuichiro Wakano (Meiji Univ.)

Dynamics and its mathematical analysis in evolutionary biology

Summary: Evolution occurs when individuals carry diﬀerent genes, some individuals are more successful inreproduction than others and hence some genes increase in the next generation. Evolutionary dynamics iscomplicated if the reproductive success of a focal individual depends not only on her own gene but also
on the distribution of genes in the whole population (i.e., evolutionary game theory). Many biologicallyinteresting topics (e.g., cooperative behavior, speciation, viral pathogenesis) have been modeled and studied
by using individual-based model (IBM). Several results have been obtained by computer simulations of IBM.
In order to fully understand the behavior of IBMs, however, we need a simplified and analytically tractablemodel which grasps the essence of IBMs. Adaptive Dynamics is one of such models. In this talk, I introduce
some important concepts in Adaptive Dynamics; invasion fitness, singular point, convergence stability (CS)and evolutionary stability (ES). Then, replicator-mutator equation, which is a kind of integro-diﬀerential
equations, is introduced. This formalism allows us to define CS and ES in a straightforward manner by
rewriting replicator-mutator equation (single integro-diﬀerential equation) with central moment equations(infinite-dimensional ODE). When we adopt the Gaussian distribution assumption, the moment equations
become a 2-dimensional ODE system and the traditional result in Adaptive Dynamics are naturally derived.
The validity of the Gaussian distribution assumption is discussed.

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Topology
March 21st (Sat)

Conference Room IVa

9:30–12:00
1 Shouta Tounai (Univ. of Tokyo) ∗ Homotopy types of Frobenius complexes · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: An aﬃne monoid is an additive monoid which is cancellative, pointed, and finitely generated. A
Frobenius complex is the order complex of an open interval of an aﬃne monoid with respect to a certain
partial order. Frobenius complexes were introduced by Laudal and Sletsjøe to compute torsion groups
and Poincaré–Betti series of some monoid algebras. Clark and Ehrenborg determined homotopy types of
Frobenius complexes of some aﬃne monoids by using discrete Morse theory. I extended their result by using
basic properties of homotopy colimits, and compute some examples.

(Kochi Univ.)
2 Ryo Kato
Katsumi Shimomura (Kochi Univ.)

On harmonic invertible spectra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We introduce some new results around of the Hopkins’ Picard group of the stable homotopy
category of harmonic spectra. In particular we define the notion of normal invertible spectra, and then it isshown that the group has no such spectrum.

3 Masaki Nakagawa (Okayama Univ.)
Hiroshi Naruse (Okayama Univ.)

A Gysin formula for the universal Schur functions · · · · · · · · · · · · · · · · · · 15

Summary: It is known that the usual Schur functions can be characterized via the Gysin homomorphism forthe flag bundle in the ordinary cohomology theory. In this talk, we introduce a universal analogue of theusual Schur functions, which we call the “universal Schur functions”, and give a similar characterization via
the Gysin homomorphism for the flag bundle in the complex cobordism theory.

4 Takahito Naito (Univ. of Tokyo)

The Sullivan’s coproduct on the homology of free loop spaces · · · · · · · · 10

Summary: In the theory of string topology, Sullivan defined a coproduct on the loop homology which is
diﬀerent from the loop coproduct constructed by Cohen and Godin. In this talk, we give computations of
the Sullivan’s coproduct and show that the coproduct is a nontrivial operation.

5 Misako Yokoyama (Shizuoka Univ.)

The fundamental pregroupoids, the fundamental semi-groups, and thefundamental groupoids of orbifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we consider b-paths and constant paths in orbifolds, and introduce the fundamental
pregroupoids(or category), the fundamental semi-groups, and the fundamental groupoids of orbifolds. The
fundamental pregroupoids, semi-groups, groupoids of orbifolds are isomorphism invariants, but not bhomotopy invariants. The fundamental pregroupoids of a discal 2-orbifold and an ordinal 2-disc are notisomorphic, and those of D2 (3) and D2 (2) are not isomorphic.

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6 Satoshi Murai(Osaka Univ.)

On tight triangulations of products of spheres · · · · · · · · · · · · · · · · · · · · · 15

Summary: In 1987, Brehm and Kühnel proved that every combinatorial triangulation of the product ofspheres Si × Sj has at least i + 2j + 4 vertices. Kühnel and Lutz conjectured that a combinatorial
triangulation of Si × Sj has exactly i + 2j + 4 vertices if and only if it is a tight triangulation. In this talk,we present some partial aﬃrmative answers to the conjecture of Kühnel and Lutz.

7 Shosaku Matsuzaki (Waseda Univ.)
Makoto Ozawa (Komazawa Univ.)

Impossibility of embeddings of 2-dimensional complexes into the 3sphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider an embedding of a 2-dimensional CW complex into the 3-sphere, and construct its
dual graph. Then we obtain a homogeneous system of linear equations from the 2-dimensional CW complex
in the first homology group of the complementof the dual graph. By the non-existence of an integer solution
for the homogeneous system of linear equations, we show that some 2-dimensional CW complexes cannot
be embedded into the 3-sphere.

8 Michihiko Fujii (Kyoto Univ.)

The growth series for pure Artin groups of dihedral type · · · · · · · · · · · · 10

Summary: I consider the kernel of the natural projection from the Artin group of dihedral type to thecorrespoding Coxeter group, which we call a pure Artin group of dihedral type, and present rational
function expressions for both the spherical growth series and the geodesic growth series of the pure Artin
group of dihedral type with respect to a natural generating set. Moreover, I show that their growth rates
are Pisot numbers.

9 Motoko Kato (Univ. of Tokyo)

The relative number of ends of the higher-dimensional Thompson groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor
set C. Brin defined higher dimensional Thompson groups nV as a generalization of V . It is a subgroup of
the homeomorphism group of C n . We prove that the number of ends of nV is equal to 1 and there is a
subgroup of nV such that the relative number of ends is ∞. This is the generalization of the corresponding
result of Farley on Thompson group V . As a corollary, nV has Haagerup property and does not have thestructure of Kähler group.

(Kobe Univ.)
10 Kentaro Saji
Luciana de Fátima Martins(São Paulo State Univ.)

Geometric foliations on a cuspidal edge · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the topological configurations of lines of curvature, the asymptotic and characteristic
curves on a cuspidal edge, in the domain of a parametrisation of this surface as well as on the surface itself.
Such configuration is characterized in terms of the 3-jet of the map.

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14:15–15:30
11 Miho Hatanaka (Osaka City Univ.)

Spin toric manifolds associated to pseudographs · · · · · · · · · · · · · · · · · · · 15

Summary: We describe a necessary and suﬃcient condition for a toric manifold to admit a spin structure.
This implies that a toric manifold admits a spin structure if and only if its real part is orientable. It is known
that a Delzant polytope can be constructed from a pseudograph, so that one can associate a toric manifold
to a pseudograph. We characterize pseudographs whose associated toric manifolds admit spin structures.

12 Hideya Kuwata (Osaka City Univ.)

On finiteness of global sections of a certain line bundle on a nicetopological toric manifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Topological toric manifolds was introduced as an analogue of compact smooth toric varieties in
the category of closed smooth manifolds by H. Ishida, Y. Fukukawa, M. Masuda. Considering an appropriate
line bundle and sections for nice topological toric manifolds, we will show that the space of global sections
is finite dimensional.

13 Kazumasa Inaba (Tohoku Univ.)

On deformations of isolated singularities of polar weighted homogeneousmixed polynomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we deform isolated singularities of a certain class of polar weighted homogeneousmixed polynomials, and show that there exists a deformation which has only definite fold singularities andmixed Morse singularities.

14 Takefumi Nosaka (Kyushu Univ.)

Ddiagrammatic computation for the Blanchfield pairing and twisted
Milnor signature · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I introduce a summary of diagrammatic computation for the Blanchfield pairing and twisted
Milnor signature, from the viewpoint of quandle theory. These results are corollaries of the previous results,
which I talked in the plenary session of the last year.

15:45–16:45

Talk Invited by Topology Section

Shoji Yokura (Kagoshima Univ.)

On characteristic classes of singular spaces —from a viewpoint ofcounting—

Summary: I will give a survey on characteristic classes of singular spaces, in particular the three well-known
theories of characteristic classes of singular varieties: MacPherson’s Chern class (Ann. of Math., 1974),
Baum–Fulton–MacPherson’s Todd class (Publ. IHES., 1975) and Cappell–Shaneson’s L-class (J. Amer.
Math. Soc., 1991) (cf. Goresky–MacPherson’s L-class (Topology, 1980) , and a “unification” of them. I will
start by reviewing counting.

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March 22nd (Sun)

Conference Room IVb

9:30–12:00
15 Hisashi Kasuya(Tokyo Tech) ♭ Cohomology of polycyclic groups and algebraic groups · · · · · · · · · · · · · · 15

Summary: We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous
cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic
groups.

16 Hisashi Kasuya(Tokyo Tech) ♭ Cohomology of algebraic groups and Sullivan’s minimal models · · · · · · 15

Summary: We obtain explicit Sullivan’s minimal models of certain diﬀerential graded algebras defined on
simplicial classifying spaces of torsion-free virtually polycyclic groups and we give de Rham homotopy
theorem for simplicial complexes with torsion-free virtually polycyclic fundamental groups.

17 Hisashi Kasuya(Tokyo Tech) ♭ Cohomology of proalgebraic groups and 1-minimal models · · · · · · · · · · · 10

Summary: On a simplicial complex or manifold with the fundamental group Γ, for a representation ρ : Γ → T
into a reductive algebraic group T with the Zariski-dense image, considering the diﬀerential graded algebraof diﬀerential forms with values in the coordinate ring of T as a local system, we show that the 1-minimalmodel of this diﬀerential graded algebra is the dual of the Lie algebra of the prounipotent radical of theρ-relative completion by using the cohomology of proalgebraic groups.

18 Tatsuhiko Yagasaki (Kyoto Inst. Tech.)Taras Banakh(Ivan Franko Nat. Univ. of Lviv)

Diﬀeomorphism groups of non-compact manifolds endowed with the
Whitney C ∞ -topology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss topological type of the diﬀeomorphism group D(M ) of any non-compact connectedsmooth n-manifold M without boundary endowed with the Whitney C ∞ -topology. It is shown that theidentity connected component D(M )0 of D(M ) is homeomorphic to N × R∞ for some ℓ2 -manifold N . For
example, if n = 1, 2 or n = 3 and M 3 is orientable and irreducible, then D(M )0 is homeomorphic toℓ2 × R∞ .

19 Katsuhisa Koshino (Univ. of Tsukuba)

The property of being a Baire space of certain function space · · · · · · · · 15

Summary: Let X be a compact metrizable space and Y be a non-degenerate dendrite with a distinguished∪
end point 0. For each function f : X → Y , we define the hypo-graph ↓ f = x∈X {x} × [0, f (x)] of f ,where [0, f (x)] is the unique arc between 0 and f (x) in Y . We can regard ↓ C(X, Y ) = {↓ f | f : X →Y is continuous} as a subspace of the hyperspace consisting of non-empty closed subsets in X × Y endowedwith the Vietoris topology. In this talk, we show that ↓ C(X, Y ) is a Baire space if and only if the set of
isolated points of X is dense.

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20 Naoki Kato

(Univ. of Tokyo)

Lie foliations transversely modeled on nilpotent Lie algebras · · · · · · · · · 15

Summary: We talk about the following two problems of realization for Lie foliations. (i) Which pair of Liealgebras (g, h) can be realized as a Lie g-foliation with the structure Lie algebra h? (ii) Which pair (g, m)
can be realized as a Lie g-flow with the structure Lie algebra Rm ? In this talk, we give a complete answer
to (i) in the case where g is a nilpotent Lie algebra and give a complete answer to (ii) in the case where g isa nilpotent Lie algebra with a rational structure.

21 Naoki Kato

(Univ. of Tokyo)

Classification of solvable Lie flows of codimension 3 · · · · · · · · · · · · · · · · 15

Summary: É. Ghys proved that any Lie g-flow is homogeneous if g is a nilpotent Lie algebra. In the casewhere g is solvable, we expect that any Lie g-flow is homogeneous. In this talk, we talk about this problem
in the case where g is a three-dimensional solvable Lie algebra.

22 Atsuhide Mori (Osaka City Univ.) ∗ Spinnable foliations of the 5-sphere · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We can deform the standard contact structure of the 5-sphere into the spinnable foliations
associated to certain Milor fibrations. A topological construction of such foliation will be presented.

13:15–14:15

Talk Invited by Topology Section
Anton Alekseev (Univ. of Geneva) Geometry and Topology of Lie-group valued moment maps

Summary: A Hamiltonian G-space is a symplectic manifold which carries an action of a connected Liegroup G preserving the symplectic structure and generated by the moment map with values in the
dual of the Lie algebra of G. The classical moment map theory is built around several extraordinary
results including the Marsden–Weinstein Reduction Theorem, the Atiyah–Guillemin–Sternberg and Kirwan
convexity Theorems, the Duistermaat–Heckman localization and the Guillemin-Sternberg “Quantization
commutes with Reduction” principle.
In this talk, we will introduce the theory of Lie group-valued moment maps where the moment map takes
values in the group G (instead of the dual of its Lie algebra) and the 2-form on the manifold is relatively
closed (rather than closed). Surprisingly, this new theory preserves all the good features of the classicalmoment map theory while relaxing a number of topological restrictions. Interesting examples for this newformalism are provided by moduli spaces of flat connections on orientable 2-dimensional manifolds.

March 23rd (Mon)

Conference Room IVa

9:30–12:00
23 Erika Kuno

(Osaka Univ.)

Uniform hyperbolicity for curve graphs of nonorientable surfaces · · · · · 10

Summary: Let C(N ) be a curve graph of a compact connected nonorientable surface N . Bestvina-Fujiwara
in 2007 and Masur–Schleimer in 2013 showed that C(N ) is (Gromov) hyperbolic. On the other hand,
Aougab, Bowditch, Clay–Rafi–Schleimer, and Hensel–Przytycki–Webb independently proved that curve
graphs of orientable surfaces are uniformly hyperbolic in 2013. In this talk, we prove that C(N ) is uniformly
17-hyperbolic applying the Hensel–Przytycki–Webb’s argument to the case of nonorientable surfaces, andespecially we describe about the diﬀerences between the orientable case and the nonorientable case.

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Topology

24 Yuichi Kabaya(Kyoto Univ.)

Exotic components in linear slices of quasi-Fuchsian groups · · · · · · · · · · 15

Summary: The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some
simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks,
and it has one ‘standard’ component containing Fuchsian groups. Komori–Yamashita proved that there
exist non-standard components if the length is suﬃciently large. In this talk, I will give another proof basedon the theory of complex projective structures.

25 Kenta Hayano (Hokkaido Univ.)
Refik İnanç Baykur(Univ. of Massachusetts)

Multisections of Lefschetz fibrations and topology of symplectic 4manifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A multisection of a Lefschetz fibration is a 2-dimensional submanifold in the total space on which
the restriction of the fibration is a simple branched covering. Recently we gave a way to understand topology
and configuration of multisections in a combinatorial way via mapping class groups. In this talk we will
explain applications of this result to the problems on topology of symplectic 4-manifolds.

26 Takayuki Morifuji (Keio Univ.)

Reducibility of automorphisms of Hurwitz surfaces and the η-invariant· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we discuss a relationship between the surface symmetry and the spectral asymmetry.
More precisely we show that an automorphism of the Macbeath surface of genus 7, or one of the three
Hurwitz surfaces of genus 14 is reducible if and only if the η-invariant of the corresponding mapping torus
vanishes.

27 Naoyuki Monden(Osaka Electro-Comm. Univ.)
R. Inanc Baykur(Univ. of Massachusetts)
Jeremy Van Horn-Morris(Univ. of Arkansas)

Positive factorizations of mapping classes · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study which surface mapping classes can be factorized into arbitrarily large number of
positive Dehn twists or only of a fixed number. In connection to fundamental questions regarding theuniform topology of symplectic 4-manifolds/Stein fillings of contact 3-manifolds coming from the topology
of Lefschetz pencils/open books on them, we completely determine when a boundary multitwist admits
arbitrarily long positive Dehn twist factorizations along nonseparating curves, and which mapping classgroups contain elements with such factorizations.

28 Jun Murakami (Waseda Univ.)

Volumes of hyperbolic and spherical polyhedrons · · · · · · · · · · · · · · · · · · · 10

Summary: Formulas for volumes of hyperbolic and spherical polyhedrons are given by using the volume
formula for hyperbolic and spherical tetrahedrons. Here a polyhedron is parametrized by its combinatorics
and the dihedral angles at every edges. In these formulas some auxiliary parameters are introduced andwe have to solve a system of equations with respect to these parameters. If the faces of the polyhedron is
given actually, we don’s need to solve such equations and we have closed formulas for the volumes of suchpolyhedrons. These formulas are based on the face model of the Uq (sl2 ) quantum invariant for knottedgraphs. This is a joint work with A. Kolpakov.

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Topology

29 Ken’ichi Yoshida (Univ. of Tokyo)

Stable presentation length of 3-manifold groups · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce the stable presentation length of a finitely presented group. The stable presentation
length of the fundamental group of a 3-manifold is an analogue of the simplicial volume. We explain somesimilarities of them.

30 Teruaki Kitano(Soka Univ.)

Reidemeister torsion of a homology 3-sphere obtained by n1 -Dehn
surgery along the figure-eight knot for SL(2, C)-irreducibe representation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let M be a homology 3-sphere and ρ : π1 M → SL(2, C) an irreducible representation. Here weassume that M is obtained by n1 -Dehn surgery along the figure-eight knot. We take and fix an elementm ∈ π1 M which is corresponding to a meridian of the group of the figure-eight knot. We give the explicit
formula of Reidemeister torsion of M for ρ in terms of the trace of ρ(m).

31 Yoshikazu Yamaguchi (Akita Univ.)

The asymptotics of the Reidemeister torsion for Seifert manifolds andPSL2 (R)-representations of Fuchsian groups · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I will talk about the asymptotic behavior of the Reidemeister torsion for Seifert manifolds startingwith PSL2 (R)-representations of Fuchsian groups.

14:15–16:45
32 Shunsuke Tsuji (Univ. of Tokyo) ∗ The action of Dehn twists and the Johnson kernel on the skein modules· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We give an explicit formula for the action of the Dehn twists on the completed skein modules interms of the action of the completed skein algebra of the surface. As an application, we describe the actionof the Johnson kernel on the completed skein modules.

33 Wataru Yuasa(Tokyo Tech) ∗ Skein quantization and Poisson algebras of curves on bordered surfaces· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We define Poisson algebras of curves on bordered surfaces. A bordered surface is a surface withboundaries which have marked points on the boundaries. Curves on the bordered surface are oriented loops
and oriented arcs with its endpoints in marked points. The Poisson bracket is defined on the symmetricalgebra on the vector space spanned by the homotopy classes of curves on the bordered surface. This bracket
is an extension of the Goldman bracket, Kawazumi–Kuno’s action of loops on arcs and Labourie’s swapping
bracket. We also define a Poisson cobracket on the Poisson algebra. Therefore, we get a bi-Poisson bialgebra.
The Poisson algebra contains the Poisson algebra of unoriented curves. We show that the Kauﬀman bracket
skein algebra of a bordered surface defined by Muller is a quantization of the Poisson algebra of unoriented
curves on the bordered surface.

34 Nariya Kawazumi (Univ. of Tokyo)

A tensorial description of the Turaev cobracket on compact genus 0
surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a tensorial description of the Turaev cobracket on any compact genus 0 surface throughthe standard exponential expansion.

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Topology

35 Takefumi Nosaka (Kyushu Univ.)

Finite presentations of centrally extended mapping class groups · · · · · · 10

Summary: We describe a finite presentation of Tg,r for g ≥ 3. Here Tg,r is the universal central extension of
the mapping class group of the surface of genus g with r-boundaries.

36 Ryoma Kobayashi (Tokyo Univ. of Sci.)

On a finite presentation of the level 2 principal congruence subgroup ofGL(n; Z) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Γ2 (n) denote the kernel of the natural homomorphism GL(n; Z) → GL(n; Z2 ). We call Γ2 (n)the level 2 principal congruence subgroup of GL(n; Z). In our work, we obtain an explicit finite presentationof Γ2 (n). We note that a finite presentation of Γ2 (n) has been independently obtained also by Fullarton andMargalit–Putman recently.

37 Ryoma Kobayashi (Tokyo Univ. of Sci.)
Susumu Hirose (Tokyo Univ. of Sci.)

On a normally generating set for the Torelli group of a non-orientableclosed surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Ng denote a genus-g non-orientable closed surface, that is, Ng is a connected sum of g realprojective planes, and let I(Ng ) be the subgroup of the mapping class group of Ng consisting of elements
acting trivially on H1 (Ng ; Z). We call I(Ng ) the Torelli group of Ng . In our work, we obtain a normallygenerating set for I(Ng ).

(Tokyo Tech)
38 Genki Omori(
Tokyo
Univ. of Sci.)
Ryoma Kobayashi

A finite presentation for the automorphism group of the first homology
of a non-orientable surface over Z2 preserving the mod 2 intersection
form · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Ng be a closed non-orientable surface of genus g and let · be the mod 2 intersection form on
the first homology group H1 (Ng ; Z2 ) with Z2 coeﬃcient of Ng . Then we denote the group of automorphismson H1 (Ng ; Z2 ) preserving the intersection form · by Aut(H1 (Ng ; Z2 ), ·). It is known that Aut(H1 (Ng ; Z2 ), ·)is finitely presented. In this talk, we give an explicit presentation for Aut(H1 (Ng ; Z2 ), ·). As applications we
calculate the second homology group of Aut(H1 (Ng ; Z2 ), ·) for g = 7 and g ≥ 9, by applying the discussionsof Pitsch and using the result of Stein.

39 Takuya Sakasai (Univ. of Tokyo)
Masaaki Suzuki (Meiji Univ.)
Shigeyuki Morita(Univ. of Tokyo⋆ / Tokyo Tech⋆)

On a structure of the symplectic derivation Lie algebra of genus 1 · · · · 15

Summary: We give an observation of a structure of the symplectic derivation Lie algebra of genus 1 bycomparing it with higher genus cases.

40 Yuta Nozaki (Univ. of Tokyo)

An extension of the LMO functor · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Cheptea, Habiro and Massuyeau constructed the LMO functor, which is defined on a certain
category of cobordisms between two surfaces with at most one boundary component. In this talk, we extend
the LMO functor to the case of any number of boundary components.

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Topology

17:00–18:00

Talk Invited by Topology Section

Yusuke Kuno

(Tsuda Coll.) ∗ Fatgraph complexes and mapping class groups

Summary: The fatgraph complex associated to an orientable surface is a combinatorial tool to study theTeichmuller space and the mapping class group action on it. This talk is about the study of the fatgraphcomplex with emphasis on its application to the low dimensional cohomology of the mapping class groups.

March 24th (Tue)

Conference Room IVa

9:30–12:00
41 Keiji Tagami
Tetsuya Abe(Tokyo Tech)(Tokyo Tech)

Annulus presentations compatible with fiber surfaces · · · · · · · · · · · · · · · 10

Summary: Inspired by Osoinach’s and Teragaito’s works, Abe, Jong, Omae and Takeuchi introduced thenotion of a certain presentation of a knot which is called an annulus presentation. In this talk, we consider
annulus presentations of fibered knots and introduce the notion of annulus presentations compatible withthe fiber surfaces. Moreover, we describe a relation between the monodromies and the twistings along theannuli. This is a joint work with Tetsuya Abe.

42 Louis H. Kauﬀman(Univ. of Illinois at Chicago)
Eiji Ogasa (Meiji Gakuin Univ.)

Local moves on knots and products of knots · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Suppose that a 1-knot J is obtained from a 1-knot K by one crossing-change. Then the (2ν + 1)submanifold J ⊗ν [2] ⊂ S 2ν+3 is obtained from the (2ν + 1)-submanifold K ⊗ν [2] ⊂ S 2ν+3 by one twist-move.
([2] is the empty knot of degree two. [2] ⊗ [2] is the Hopf link.)
A 1-knots J and K are pass-move equivalent if and only if the (2ν + 1)-submanifolds J⊗µ (the Hopf link)
and K⊗µ (the Hopf link)⊂ S 2ν+3 are (2µ + 1, 2µ + 1)-pass-move equivalent.
Let Sn be the set of n-dimensional simple knots. We assign K⊗(the Hopf link) to an n-knot K. It makes
a bijective map Sn −→ Sn+4 , where n ≧ 5 if n is odd and n ≧ 8 if n is even. (If n takes the other values,
some results are obtained by the authors.)

43 Kanako Oshiro (Sophia Univ.)

An interpretation of finite-degree connected Alexander quandle colorings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Fox p-colorings of a knot K are interpreted as group representations from the fundamental groupof the double branched cover of S 3 with branch set K to Zp . The interpretation is extended for quandle
colorings by connected Alexander quandles of the form Zp [t]/(tk + ak−1 tk−1 + · · · + a1 t + a0 ).

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Topology

44 Makoto Ozawa (Komazawa Univ.)
Yuya Koda (Hiroshima Univ.)

Knot homotopy in subspaces of the 3-sphere · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We say that a knot in a subspace of the 3-sphere is transient if it is moved by a homotopy within
the subspace to the trivial knot in the 3-sphere. We show that every knot in a subspace of the 3-sphere istransient if and only if the exterior of the subspace is a disjoint union of handlebodies. Using the notionof transient knot, we define an integer-valued invariant of knots in the 3-sphere that we call the transientnumber. We then show that the union of the sets of knots with unknotting number one and those withtunnel number one is a proper subset of that with transient number one.

45 Yusuke Takimura(Gakushuin Boy’s Junior High School)(Waseda Univ.)
Noboru Ito

Sub-chord diagrams of knot projections · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we introduce a new integer-valued invariant of spherical curves under RI and strong
RIII that provides a complete classification of prime reduced spherical curves with up to at least seven
double points. The invariant produces the necessary and suﬃcient condition that spherical curves can be
related to a simple closed curve by a finite sequence consisting of RI and strong RIII.

46 Shosaku Matsuzaki (Waseda Univ.)(Waseda Univ.)
Noboru Ito

Circle arrangements on spherical curves · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we introduce definitions of circle arrangements for multi-component spherical curves
and circle numbers of oriented links. This talk gives a necessary and suﬃcient condition that any two
spherical curves have the same circle arrangements. We also show that every odd (resp. even) component
link has circle number one (resp. two).

47 Tetsuya Abe
Keiji Tagami(Tokyo Tech)(Tokyo Tech)

Fibered knots with the same 0-surgery and the slice-ribbon conjecture· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We prove that if the slice-ribbon conjecture is true, then (modified) Akbulut–Kirby’s conjecture
on knot concordance is false. We also give a fibered potential counterexmaple to the slice-ribbon conjecture.
This is a joint work with Keiji Tagami.

48 Motoo Tange (Univ. of Tsukuba)

A traversable theorem of Alexander polynomial of lens space knot · · · · 15

Summary: The Alexander polynomial of a knot yielding lens space has remarkable properties. The coeﬃcientsis ±1 or 0 and the non-zero coeﬃcients are alternating. We will show the below. Lining the coeﬃcients of
Alexander polynomial in the plane, we can find a curve which is traversing on the non-zero coeﬃcients. Let(n1 > n2 > n3 > · · · ) be the non-zero coeﬃcients of Alexander polynomial of K. By using the curve, weshow the distribution of n1 , n2 , n3 , n4 . As a result, it follows that the adjacent 1, −1 are not so far awayeach other.

49 Masakazu Teragaito (Hiroshima Univ.)

Quasi-alternating links and Q-polynomials · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Qazaqzeh and Chbili showed that for any quasi-alternating link, the degree of the Q-polynomialis less than its determinant. We give a refinement of their evaluation.

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Topology

50 Taizo Kanenobu (Osaka City Univ.)

Oriented Gordian distance of two-component links · · · · · · · · · · · · · · · · · 10

Summary: The oriented Gordian distance between two oriented links is the minimal number of crossingchanges needed to deform one into the other. We compile a table of oriented Gordian distances between
2-component non-splittable links with up to six crossings.

51 Kazuhiro Ichihara (Nihon Univ.)(Nihon Univ.)
Yuki Temma

Non left-orderable surgeries on twisted torus knots · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider Dehn surgeries on knots in the 3-sphere which yield 3-manifolds with nonleft-orderable fundamental groups, and report a result that certain twisted torus knots admit such surgeries.

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Infinite Analysis

Infinite Analysis
March 23rd (Mon)

Conference Room IX

14:15–15:30
1 Takuya Matsumoto(Nagoya Univ. / Nagoya Univ.)

Classical r-matrices and the deformed gravity solutions · · · · · · · · · · · · · 15

Summary: In this talk, we will explain the Yang–Baxter sigma models proposed by Klimcik, which providea systematic way of the integrable deformation of the principal chiral model by utilizing the classical rmatrices. Then, we apply this formulation for the superstring action on the AdS5 ×S5 background. We willshow that some of the deformed backgrounds correspond to the well-known deformed gravity solutions suchas Lunin–Maldacena backgrounds. This talk is based on the collaboration works with Kentaroh Yoshida(Kyoto U.) and P. Marcos Crichigno (Utrecht U.).

2 Yas-Hiro Quano(Suzuka Univ. of Med. Sci.)

Form factors of spin 1 analogue of the eight-vertex model · · · · · · · · · · · 15

Summary: The spin 1 analogue of the eight-vertex model (21-vertex model) is considered on the basis of freefield representations of vertex operators in the 2 × 2-fold fusion SOS model and vertex-face transformation.
Correlation functions and form factors in the 21-vertex model can be expressed in terms of type I and type
II vertex operators of the corresponding fused SOS model and so-called tail operators. We need the tailoperators in order to translate correlation functions and form factors in SOS model into those of elliptic
vertex model. For correlation functions we use the tail operators for diagonal matrix elements with respect
to the ground state sectors, and for form factors we use the ones for oﬀ diagonal matrix elements. In thistalk we will construct the free field representations of the tail operators for oﬀ diagonal matrix elements withrespect to the ground state sectors. As a result, integral formulae for form factors of any local operators in
the 21-vertex model can be obtained, in principle.

3 Ayumu Hoshino(Kagawa Nat. Coll. of Tech.)
Masatoshi Noumi (Kobe Univ.)
Jun Shibahara (Univ. of Tokyo)
Jun’ichi Shiraishi (Univ. of Tokyo)

Tableau foumula for Macdonald polynomials of type Cn with one row
diagrams · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present explicit formulas for Macdonald polynomials of type Cn with one row diagrams which
are called “tableau formulas”. For the construction of tableau formulas, we give some transformation
formulas of the basic hypergeometric series. We note the relation between Macdonald polynomials and thedeformed W algebras.

4 Masatoshi Noumi (Kobe Univ.)
Yasushi Komori (Rikkyo Univ.)
Yasuho Masuda (Kobe Univ.)

Duality transformation formulas for multiple elliptic hypergeometricseries of type BC · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: New duality transformation formulas are proposed for multiple elliptic hypergeometric series oftype BC and of type C. Various transformation and summation formulas are derived as special cases torecover some previously known results.

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Infinite Analysis

5 Masahiko Ito (Tokyo Denki Univ.)
Masatoshi Noumi (Kobe Univ.)

Derivation of a BCn elliptic summation formula via the fundamental
invariants · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will explain a way to derive a BCn elliptic summation formula from the fundamental invariants.

15:45–16:45

Talk Invited by Infinite Analysis Special Session

Shintarou Yanagida (Kyoto Univ.)

Motivic Hall algebras and quantum toroidal algebras

Summary: For a smooth projective curve defined over a finite field, one can construct Ringel–Hall algebra
associated to the abelian category of the coherent sheaves on the curve considered. By Kapranov’s work in
the late 1990s, a certain subalgebra (so-called the composition subalgebra) of the Ringel–Hall algebra forthe projective line is isomorphic to the positive half of the quantum aﬃne algebra for sl2 . By the work of
Burban and Schiﬀmann in the 2000s, an analogue of Kapranov’s result holds for the elliptic curve, and thecorresponding algebra is the so-called Ding–Iohara–Miki algebra (or the quantum toroidal gl∞ ).
In this talk I consider the Ringel–Hall algebras and their composition subalgebras for the singular fibers in
the elliptic surfaces. The first main result is that the composition subalgebras for the cycles of the projectivelines turns out to be isomorphic to the quantum toroidal gln .
The second main result is that these Ringel–Hall algebras have non-trivial symmetry. In the case of thecycle of the projective lines, our non-trivial automorphism coincides with the one found by Miki for thequantum toroidal gln .
In order to prove the second result, it is convenient to consider not the original Ringel–Hall algebra but the
motivic Hall algebra. The latter one can be introduced for the curves defined over the complex number field.
For elliptic surfaces defined over the complex number field, one can consider the relative Fourier–Mukai
transforms, and the non-trivial automorphisms mentioned above are the ones induced by these transforms
on the Drinfeld doubles of the motivic Hall algebras.

March 24th (Tue)

Conference Room IX

9:45–11:45
6 Yoko Shigyo(Tsuda Coll.)Plücker coordinates of the BKP hierarchy · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, I describe the Plücker coordinates of the BKP hierarchy. This Plücker coordinatessatisfy the Giambelli type formula. I prove that a formal power series tau(x) is a solution of the BKP
hierarchy if and only if the Plücker coordinates satisfy the Giambelli type formula.

7 Saburo Kakei(Rikkyo Univ.)

Hirota bilinear method and GUE, NLS, Painlevé IV · · · · · · · · · · · · · · · · 15

Summary: Tracy and Widom showed that a Fredholm determinant associated with the Gaussian unitaryensemble (GUE) is related to a particular solution of the fourth Painlevé equation. We reconsider thisproblem from the viewpoint of Hirota’s bilinear method in soliton theory and present another proof.

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Infinite Analysis

8 Yoshihiro Takeyama(Univ. of Tsukuba)

A deformation of aﬃne Hecke algebra and integrable stochastic particle
system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a deformation of the aﬃne Hecke algebra of type GL which describes the commutation relations of the divided diﬀerence operators found by Lascoux and Schützenberger and the multiplication
operators. Making use of its representation we construct an integrable stochastic particle system. It is a
generalization of the q-Boson system due to Sasamoto and Wadati. We also construct eigenfunctions of its
generator using the propagation operator. As a result we get the same eigenfunctions for the (q, µ, ν)-Boson
process obtained by Povolotsky.

9 Taichiro Takagi(Nat. Defense Acad. of Japan)

Tropical periodic Toda lattice and Kerov–Kirillov–Reshetikhin bijection· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The tropical periodic Toda lattice (trop p-Toda) is a dynamical system attracting attentions in
the interplay of integrable systems and tropical geometry. We show that the Young diagrams associatedwith trop p-Toda given by two very diﬀerent definitions are identical. The first definition is given via a Lax
representation of discrete periodic Toda lattice, and the second one is associated with a generalization of
the Kerov–Kirillov–Reshetikhin bijection in combinatorics of Bethe ansatz. By means of this identification,
it is shown for the first time that the Young diagrams given by the latter definition are preserved under thetime evolution. This result is regarded as an important first step to clarifying the iso-level set structure ofthis dynamical system in general cases, i.e. not restricted to generic cases.

10 Masataka Kanki (Rikkyo Univ.)
Tetsuji Tokihiro (Univ. of Tokyo)(Nihon Univ.)
Jun Mada

Co-primeness condition of the periodic discrete Toda equation · · · · · · · 15

Summary: We reformulate the singularity confinement of the discrete Toda equation. We prove that the
co-primeness condition, which has been introduced as a new integrability criterion, is satisfied for thediscrete Toda equation under several types of boundary conditions (semi-infinite, molecule, and periodic).
In particular, we focus on the equation with the periodic boundary condition, and explain how to define theτ -functions compatibly with the boundary condition. We provide a sketch of a proof of irreducibility of theτ -functions. The main theorem on the co-primeness follows from the irreducibility of the τ -functions.

11 Tomoki Nakanishi (Nagoya Univ.)

On generalized cluster algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study generalized cluster algebras introduced by Chekhov and Shapiro. When the coeﬃcientssatisfy the normalization and quasi-reciprocity conditions, one can naturally extend the structure theory ofseeds in the ordinary cluster algebras by Fomin and Zelevinsky to generalized cluster algebras. As the main
result, we obtain formulas expressing cluster variables and coeﬃcients in terms of c-vectors, g-vectors, andF-polynomials. Furthermore, quantization can be formulated using the generalized quantum dilogarithms.

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Infinite Analysis(Kyoto Univ.)
12 Kohei Iwaki
Tomoki Nakanishi (Nagoya Univ.)

Exact WKB analysis and cluster algebras II · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This is a continuation of developing mutation theory in exact WKB analysis using the frameworkof cluster algebras. Here we study the Schrodinger equation on a compact Riemann surface with turning
points of simple-pole type. We show that the orbifold triangulations by Felikson, Shapiro, and Tumarkinprovide a natural framework of describing the mutation of Stokes graphs, where simple poles correspondto orbifold points. We then show that under the mutation of Stokes graphs around simple poles the Voros
symbols mutate as the variables of generalized cluster algebras introduced by Chekhov and Shapiro.

14:15–15:30
13 Takeshi Morita (Osaka Univ.)

A bilateral extension of the Ramanujan entire function · · · · · · · · · · · · · 15

Summary: In this talk, we introduce a bilateral extension of the Ramanujan entire function. We study theconnection problem on the q-diﬀerence equation which the extended function satisfies. We also define the“extended” q-Borel–Laplace transformations to study the connection problem.

14 Toshiyuki Mano (Univ. of Ryukyus) ∗ Flat structure on the space of isomonodromic deformations · · · · · · · · · · 15
Mitsuo Kato (Univ. of Ryukyus)
Jiro Sekiguchi(Tokyo Univ. of Agri. and Tech.)
Summary: In this talk, we show the extence of a flat structure without potential on the space of isomonodromic
deformations, which implies the equivalence between a generalization of the WDVV equation and the (fullparameter) Painlevé VI equation as a particular case.
We also show the existence of a flat generator system of the ring of invariant polynomials of a finite
irreducible complex reflection group, which corresponds to an algebraic solution of a (higher-order) Painlevé
type equation.

15 Hideshi Yamane(Kwansei Gakuin Univ.)

Asymptotic analysis for the integrable discrete nonlinear Schrödinger
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the asymptotic behavior of a solution to the defocusing integrable discrete nonlinear
Schrödinger equation (Ablowitz–Ladik model). We employ the inverse scattering transform and the Deift–
Zhou nonlinear steepest descent method.

16 Takao Suzuki(Kinki Univ.)(1)

Drinfeld–Sokolov hierarchy of type A5 and Simpson’s even four hypergeometric function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In a recent work, the sixth order Painlevé system which contains Simpson’s even four hypergeometric function as a particular solution has been proposed. In this talk, we investigate its relationship to(1)

the Drinfeld–Sokolov hierarchy of type A5

17 Hiroyuki Kawamuko (Mie Univ.)
Yoshiaki Ushiku (Mie Univ.)

corresponding to a partition (2, 2, 2) of natural number 6.

Initial value space of the second Matrix Painlevé equation · · · · · · · · · · · 10

Summary: We construct the initial value space of the second Matrix Painlevé equation by using Backlundtransformations.

Final Version: 2015/02/24
112

Infinite Analysis

15:45–16:45

Talk Invited by Infinite Analysis Special Session

Hidetaka Sakai (Univ. of Tokyo)

Studies on the Painlevé equations

Summary: We will look over theories on the Painlevé equations. The Painlevé equations are expected todefine new special functions as their solutions, next to elliptic functions and hypergeometric functions.
The Painlevé equations were originally defined as second order algebraic ODE’s of normal form, satisfying
the Painlevé property. But if we only present a set of eight nonlinear ODE’s, we seem to be unable toconvey true figure of the equations. They are natural generalizations of elliptic functions, and this kind ofgeneralization is only the eight Painlevé equations. In this talk, we see them as a non-autonomous analog
of biquadratic Hamiltonian system, which is solved by elliptic functions.
From this formulation, we naturally obtain a correspondence to certain rational surfaces, and we canunderstand symmetries of equations, or particular solutions called Riccati solutions, by using the surfaces’
theory.
The Painlevé equations are also derived from a deformation theory of linear ODE’s. This is the second
foundation of studies on the Painlevé equations. In this talk, we will see this concept connecting to a
generalization to higher dimensional case.