Created: 2014/08/12 08:45“ Mathematical Society of Japan
2014 AUTUMN MEETING

Titles and Short Summaries of the Talks

September, 2014
at Hiroshima University

Created: 2014/08/12 08:45

2014 Mathematical Society of Japan
AUTUMN MEETING
Dates: September 25th (Thu)–28th (Sun), 2014
Venue: Hiroshima University, Higashi-Hiroshima Campus
1–7–1, Kagamiyama, Higashi-Hiroshima City,
Hiroshima 739-8521
Contact to: Department of Mathematics,
Graduate School of Sciences, Hiroshima University
1–3–1, Kagamiyama, Higashi-Hiroshima City,
Hiroshima 739-8526
E-mail hiroshima14sept@mathsoc.jp
During session:

Phone +81 (0) 90 1791 3483

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

I
II
III
IV
V
VI
VII
VIII
IX
Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci. Fac. Int. Arts Sci.
K110
K108
K107
L101
L102
K211
K210
K201
K314

25th

ComplexAnalysisAlgebraGeometry

9:00–12:00
14:10–16:50

9:30–12:00
14:15–16:15

9:40–12:00
14:15–16:10

(Thu)

26th

Functional
Analysis

Functional
Equations

Topology

14:15–16:35

9:00–12:00
14:15–16:15

9:20–12:00
14:15–15:25

Featured Invited Talks

Statistics andApplied
Probability Mathematics
9:30–11:50

9:30–11:30
14:15–17:00

Infinite
Analysis
10:00–12:00
14:15–15:30

13:00–14:00

Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talks

Invited Talk

17:00–18:00

16:30–17:30

16:30–17:30

17:00–18:00

16:30–17:30

15:45–16:45

15:45–16:45

ComplexAnalysisAlgebraGeometry

Functional
Analysis

Functional
Equations

Topology

9:00–10:30

9:30–11:50

10:00–11:50

9:00–12:00

13:00–14:15

14:15–15:15
15:30–16:30

Statistics andApplied
Probability Mathematics
9:30–11:30

9:30–11:30

Infinite
Analysis
10:00–12:00

Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk

Invited Talk Invited Talk

13:20–14:20

13:00–14:00

13:20–14:20(Fri)

10:50–11:50
13:15–14:15

13:10–14:10

13:15–14:15

13:00–14:00

MSJ Prizes Presentation (Satake Memorial Hall) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14:50–15:20)
Plenary Talks(Satake Memorial Hall) MSJ Autumn Prize Winner · · · · · · · · · (15:30–16:30)
Ken’ichi Ohshika (Osaka Univ.) · · · · · · (16:45–17:45)
Oﬃcial Party(Saijo HAKUWA Hotel) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (18:15–20:15)

27th

Real
AnalysisAlgebraGeometry

Functional
Analysis

Functional
Equations

Topology

9:00–11:45
14:15–16:20

9:30–11:25
15:30–17:30

9:40–12:00
14:15–16:00

9:00–12:00
14:15–16:45

9:00–12:00
14:15–16:15

9:20–11:50
14:15–15:40

Statistics andApplied
Probability Mathematics
9:30–12:00

14:15–16:30

Found. of Math.
andHistory of Math.
9:30–11:40

Special Session 14:15–15:40
9:30–11:55(Sat)

Featured Invited Talks

13:00–14:00

Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talk Invited Talks Invited Talk Invited Talk

28th
(Sun)

16:40–17:40

14:15–15:15

Real
AnalysisAlgebra9:00–11:50
14:15–15:40

9:15–12:00

16:15–17:15

17:00–18:00

16:30–17:30

16:00–17:00

Functional
Equations

Topology

9:00–12:00
14:15–16:15

Featured Invited Talks

9:20–12:00

16:45–17:45

16:00–17:00

Statistics andApplied
Probability Mathematics

Found. of Math.
andHistory of Math.

9:30–11:20
14:15–16:10

9:30–11:30
15:00–16:10

14:15–15:15
15:30–16:30

9:30–11:50
14:15–16:15

13:00–14:00

Invited Talk Invited Talk

Invited Talk

Invited Talk

16:00–17:00

16:30–17:30

16:30–17:30

14:15–15:15

Created: 2014/08/12 08:45

Contents

Plenary Talks

1

Featured Invited Talks

1

Foundation of Mathematics and History of Mathematics

5

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8Algebra11

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

Geometry

22

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

Complex Analysis

30

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

Functional Equations

36

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

Real Analysis

55

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

Created: 2014/08/12 08:45

Functional Analysis

63

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Statistics and Probability

71

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Applied Mathematics

83

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

Topology

96

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

September 27th (Sat) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

100

September 28th (Sun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

104

Infinite Analysis

107

September 25th (Thu) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107

September 26th (Fri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

Created: 2014/08/12 08:45
1

Plenary Talks

Plenary Talks
September 26th (Fri) Satake Memorial HallMSJ Autumn Prize Winner····················································(15:30–16:30)

Ken’ichi Ohshika (Osaka Univ.)

Geometry of Kleinian groups and its applications · · · · · · · ·(16:45–17:45)

Summary: The study of Klenian groups using geometric method began with Thurston’s paradigm-making
work in 1980’s. During a few decades after then, many specialists in this field worked to solve problems raisedby Thurston. Now all of these problems are solved, and it is time to look further.
In this talk, I shall first explain what are Thurston’s problems and what are their significances, and summarise
how they have been solved. After that, I shall present how techniques developed in the process of solving
these problems are useful in the study of three-manifolds and discrete groups, taking results I have recently
obtained as examples.

Featured Invited Talks
September 25th (Thu)
Conference Room II
Ming-Lun Hsieh (Nat. Taiwan Univ.) ♭ Modular forms and Iwasawa theory · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: One of the most intriguing formulas in algebraic number theory is Dirichlet class number formula,which relates the analytic objects: special L-values and algebraic objects: class numbers and Selmer groups.
Many outstanding conjectures such as Bloch–Kato conjecture, Birch and Swinnerton-Dyer conjecture andIwasawa main conjectures all share the same flavour. Number theorists have been using modular forms
to study analytic or algebraic properties of special L-values by various period integral formulas and to
study associated Galois representations and Selmer groups via the development of Langlands correspondence.
One eﬀective way to make a connection between special L-values and Selmer groups is via the method ofcongruence among modular forms. In this talk, we would like to talk about successful examples of this method
as well as the recent progress on Iwasawa main conjectures and the application to Birch and Swinnerton-Dyer
conjecture.

Created: 2014/08/12 08:45
2

Featured Invited Talks

Conference Room V
Seiro Omata (Kanazawa Univ.)

Mathematical and numerical analysis of a droplet and bubble
motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: In this talk we discuss the motion of droplets or bubbles on a flat surface. This surface is represented
by a plane, which serves as an obstacle. The motion is controlled mainly by the surface tension and thecontact angle between the plane and the surface of the droplet. We introduce the governing equations forthe evolution of the droplet surface. The equations are of wave type (hyperbolic type) with an obstacle anda free boundary. Since the droplet should keep its volume throughout the evolution, we need to impose avolume-preserving constraint. To establish an existence theorem, we approximate the governing equations by
a discrete Morse flow.
Furthermore, we present an algorithm describing a motion of multiple bubbles, based on the so-called BMO
algorithm. We modify the BMO algorithm in order to handle multiphase mean curvature or mean curvatureacceleration problems under a volume constraint.

September 27th (Sat)
Conference Room II
Masaki Kashiwara (Kyoto Univ.)

Riemann Hilbert correspondence for irregular holonomic Dmodules · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13:00–14:00)

Summary: The original Riemann-Hilbert problem is to construct a liner ordinary diﬀerential equation withregular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categoricalequivalence between the category of regular holonomic D-modules and the category of perverse sheaves.
However it is a long standing problem to describe holonomic D-modules with irregular singularities in ageometric or topological language.
Recently, I, with Andrea D’Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which
are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived categoryof constructible sheaves with the enhanced sheaves category. This category is a quotient of the derived
category of ind-sheaves (or subanalytic sheaves) on the product of the base space and the real projective line.
Then we construct a fully faithful functor from the derived category of holonomic D-modules to the enhanced
sheaves category.

Created: 2014/08/12 08:45
3

Featured Invited Talks

Conference Room III
Toshitake Kohno (Univ. of Tokyo)

Iterated integrals and de Rham homotopy theory · · · · · · · ·(13:00–14:00)

Summary: The notation of iterated integrals of diﬀerential forms was initiated by K.-T. Chen in 1970’s. The
theory of iterated integrals provides a method to describe the de Rham cohomology of the loop spaces ofsimply connected manifolds. It also enables us to extract information about the nilpotent completion of thefundamental groups. The theory of iterated integrals is closely related to the rational homotopy theory due
to D. Quillen and the de Rham homotopy theory due to D. Sullivan.
After reviewing these historical aspects, I will focus on more recent developments concerning the theory of
iterated integrals. First, I describe the Kontsevich integral which gives a universal expression for finite typeinvariants of knots in terms of iterated integrals of logarithmic forms. The Kontsevich integral is relevent to
the Drinfel’d associator and multiple zeta values as well.
There is also a new aspect for the algebraic structure of the homology of free loop spaces in the framework ofstring topology. Such structures are related to iterated integrals by means of Hochschild homology. I describe
how loop products and the Batalin- Vilkovisky structure for the homology of free loop spaces are expressedin terms of iterated integrals. Finally, I will mention a description of volumes of spherical and hyperbolic
simplices by iterated integrals based on the Schläfli formula.

Conference Room V
Yasuo Komori-Furuya (Tokai Univ.)

Cauchy integral operator and related topics · · · · · · · · · · · · ·(13:00–14:00)

Summary: This talk is a survey for Cauchy integral operator and related topics. We recall the results by
Calderón and Coifman, McIntosh and Meyer: Lp boundedness of Cauchy integral operator. We consider close
relations between this problem and some problems in PDE: the Laplace equation on Lipschitz domains andKato’s square root problem.

September 28th (Sun)
Conference Room II
Ichiro Shimada (Hiroshima Univ.)

K3 surfaces and lattice theory · · · · · · · · · · · · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Thanks to the Torelli-type theorems for the period mapping, many geometric problems on K3
surfaces are reduced to computational problems in lattice theory, and the latter can often be solved by meansof computer. In this talk, we explain how to use the lattice theory and computer in the study of K3 surfaces.

Created: 2014/08/12 08:45
4

Featured Invited Talks

Conference Room III
Mitsuo Morimoto(Yokkaichi Univ. / Sophia Univ.⋆)

The 350th anniversary of Takebe Katahiro · · · · · · · · · · · · · ·(13:00–14:00)

Summary: Takebe Katahiro (1664-1739) is a Japanese mathematician in the Edo era, a student and acoworker of Seki Takakazu (ca 1642-1708). Takebe’s mathematical works include the Kenki Sanpō (1683), theEndan Genkai (1685) to the Hatsubi Sanpō (Seki Takakazu, 1674), the Genkai Taisei (1690) to the Chinesemathematics book Suanxue Qimeng (Zhu Shijie, 1299) and the Tetsujutsu Sankei (1722). He, together withhis master and his elder brother Kata’akira, conceives the Taisei Sankei, an encyclopedic monograph of allmathematics known to them. The project starts in 1683 and ends in 1711 after 28 years of compilation.
To celebrate his 350th anniversary, an international conference on the “Traditional Mathematics of East Asia
and Related Topics,” the Takebe Conference 2014, is organized on August 25-30 at Ochanomizu University.
The Takebe Conference 2014 is one of the satellite conferences of SEOUL ICM 2014 and supported by the
Mathematical Society of Japan.
In this talk, we survey the mathematics of Takebe Katahiro and the events of his 350th anniversary.

Created: 2014/08/12 08:45
5

Foundation of Mathematics and History of Mathematics

Foundation of Mathematics and History of Mathematics
September 27th (Sat)

Conference Room IX

9:30–11:40
1 Takashi Oyabu♭

Theory of H-theorems, and other 5 talks · · · · · · · · · · · · · · · · · · · · · · · · · · 5

Summary: 1. Constructible world. All sets are constructible::Then::Conntinuum problem::General contunuum Problem is true::We stand on Kantian philosophy: V == L : −problem :2. Theory of H-theorems. H-function in mathematics:Entropy concept in math... Then:: dH/dt =<0 ============> 0 :3. Representation theory. Representations of Diﬀ(M):::Aut(R):Poincaré conjectures hold:Real orthogonal
representations:
4. Fluctuation. Fluctuation and prigogine theory:H-theorems:δ-H theorems:Gibbs free energy::::Helmholtz
free energy:: H = SdAU (µ) : H = SdAΣU ilogU i : δ − H = SdAdU logdU : δ − H = SdAΣdU ilogdU i
5. Riemann surface. Taniyama–Simura conjecture:Auto-morphic functions:Modular functions:Modular
curves: X ===========> E : V :::::Morphism:
6. Maximal ideal space. R =====> SP EC(R) :: R =====> M (R) : M (R) = {Maximal ideals in R}
Topology:::Topological space:Introduce topology in M (R):This makes M (R)::::A manifold::

2 Yoshifumi Ito (Univ. of Tokushima⋆)

Definition and existence theorem of the concept of ordinal numbers· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper we give the new definition of the concept of ordinal numbers and prove its existence
theorem on the basis of the ZFC set theory. This is the generalization of Peano’s system of axioms of finite
ordinal numbers.

3 Makoto Kikuchi (Kobe Univ.)(Kobe Univ.)
Sakaé Fuchino

On the constructive nature of the incompleteness theorem · · · · · · · · · · · 15

Summary: The first incompleteness theorem consists of two statements. One is that the Gödel sentence ofa theory of arithmetic is unprovable if the theory is consistent, and the other is that the negation of theGödel sentence is unprovable if the theory satisfies a certain soundness condition. We discuss the diﬀerenceof the constructive nature of these two statements by interpreting their proofs in terms of the constructionsof primitive primitive recursive functions.

4 Makoto Kikuchi (Kobe Univ.)
Taishi Kurahashi(Kisarazu Nat. Coll. of Tech.)On theorems and proofs in nonstandard models of arithmetic · · · · · · · · 15

Summary: The set of theorems of arithmetic in a nonstandard model of arithmetic is equal to or is bigger
than the standard set of theorems of arithmetic. We firstly show that if the set of theorems in such amodel is bigger than the standard one, the set must contain true and untrue sentences. Then, we show theexistence of nonstandard models which satisfy the condition that set of theorems on their consistent initial
segments are always standard, and are always nonstandard. At last, we prove that there is a Rosser-type
provability predicate and a nonstandard model such that the theory defined by the provability predicate in
the model is true arithmetic.

Created: 2014/08/12 08:45
6

Foundation of Mathematics and History of Mathematics

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

Phase transitions and reverse mathematics · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: RM (reverse mathematics) and CMI (concrete mathematical independence) are two related areasof foundational interest which have emerged in mathematical logic. Recently, Andreas Weiermann innovateda new dichotomy principle called ‘phase transitions’ to illustrate an incompleteness phenomenon of CMI. In
this talk, we are going to present some finer versions of the phase transition principle via abounding resultsof RM. Thus we can cross-link RM and CMI for a better understading of foudational phenomena.

6 Toshio Suzuki (Tokyo Metro. Univ.)
Yoshinao Niida (Patent Result Co.)

Equilibrium points of an AND-OR tree: under constraints on probability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study a probability distribution d on the truth assignments to a uniform binary AND-OR
tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium
among independent distributions (ID) then d is an independent identical distribution (IID). We show astronger form of the above result. Given a real number r such that 0 < r < 1, we consider a constraint thatthe probability of the root node having the value 0 is r. Our main result is the following: When we restrict
ourselves to IDs satisfying this constraint, the above result of Liu and Tanaka still holds.

7 Kohtaro Tadaki (Chuo Univ.)

Reformulating quantum mechanics by algorithmic randomness · · · · · · · 15

Summary: The notion of probability plays a crucial role in quantum mechanics. It appears through theso-called Born rule. In modern mathematics which describes quantum mechanics, however, probability
theory means nothing other than measure theory, and therefore any operational characterization of thenotion of probability is still missing in quantum mechanics. In this sense, the current form of quantum
mechanics is considered to be imperfect as a physical theory which must stand on operational means. In thistalk, we present an alternative rule to the Born rule based on algorithmic randomness without reference tothe notion of probability. We use the notion of Martin–Löf randomness with respect to Bernoulli measurefor specifying the property of the results of quantum measurements in an operational way. We consider thevalidity of the new rule, in particular, based on the many-worlds interpretation of quantum mechanics.

8 Hiroyuki Ota (Univ. of Tokyo)
Akitoshi Kawamura (Univ. of Tokyo)

Small complexity classes for computable analysis · · · · · · · · · · · · · · · · · · · 15

Summary: Type-two Theory of Eﬀectivity (TTE) provides a general framework for computable analysis. To
refine it to polynomial-time computability while keeping as much generality as possible, Kawamura andCook recently proposed a modification to TTE using machines that have random access to an oracle andrun in time depending on the “size” of the oracle. They defined type-two analogues of P, NP, PSPACE andapplied them to real functions and operators. We further refine their model and study computation below
P: type-two analogues of the classes L, NC, and P-completeness under log-space reductions. As prototypicalapplications, we recast several facts (some in a stronger form than was known) about the complexity ofnumerical problems into our framework.

Created: 2014/08/12 08:45
7

Foundation of Mathematics and History of Mathematics

14:15–15:40(JAIST)
9 Takayuki Kihara
Arno Pauly (Univ. of Cambridge)

σ-homeomorphism types and point degree spectra of infinite dimensional spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The concept of a point degree spectrum links the study of degree structures in computability
theory to the study of dimension in descriptive set theory and topology. We answer an open question
whether there are more than two equivalence classes of perfect Polish spaces w.r.t. countable continuous
isomorphisms in the positive.

10 Sakaé Fuchino(Kobe Univ.)

Almost continuity of Baire functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Frankiewics and Kunen (1987) proved that the assertion “for any Baire space X and any
topological space Y with σ-disjoint open base, if f is a Baire function from X to Y then f is continuous ona co-meager subset of X” is independent over ZFC and the negation of the assertion is equi-consistent witha measurable cardinal. We shall discuss some results related to this theorem.

11 Hiroaki Minami(Kobe Univ.)
Hiroshi Sakai

The dominating number of Fσ ideals on Katětov–Blass order · · · · · · · · 15

Summary: We will talk about the dominating number of Fσ ideals on Katětov–Blass order is equal to thedominating number d which is the least size of cofinal subsets of the family of functions from the natural
numbers to the natural numbers ordered by the relation “alomost dominating”.

12 Yoshihiro Abe (Kanagawa Univ.)

Rigidity and weakly normal ideals on Pκ λ · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: On κ, selectivle ideals are rigid, and normal ideals selective. While on Pκ λ, all normal ideals are
not selective. We proved last year a weakly normal ideal is selective if the sup-function is one-to-one on ameasure one set. We show the same assumption gives the regidity to a weakly normal ideal.

13 Toshimichi Usuba (Kobe Univ.)

Set-theoretic geology in HOD · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Set-theorecit geology is a study of the structure of all ground models of the universe. We provethat under V = HOD or a bit weaker assumption, the structure of all ground models behaves well as under
V = L[A].

Created: 2014/08/12 08:45
8

Foundation of Mathematics and History of Mathematics

16:00–17:00

Talk Invited by Section on Foundation and History of Mathematics
Daisuke Ikegami (Kobe Univ.) Gödel’s program, large cardinals, and forcing axioms
Summary: After proving that one cannot refute the Continuum Hypothesis (CH) in Zermelo–Fraenkel set
theory with the Axiom of Choice (ZFC), Gödel suspected that one cannot decide the truth-value of CH
in ZFC, i.e., CH is independent from ZFC. To discuss the truth-values of CH and other mathematicalstatements, Gödel initiated the following program nowadays called Gödel’s Program: Decide the truth-

values of mathematically interesting statements independent from ZFC in “well-justified” extensions of
ZFC.
What Gödel had in mind at that time was the notion of large cardinals. He expected to decide the truth-valueof CH by assuming the existence of a certain large cardinal in ZFC.
After Cohen introduced forcing which is now a basic tool to argue the unprovability of statements in set
theory, it was shown by Lévy and Solovay that the existence of any large cardinal in ZFC cannot decide
the truth-value of CH. However, using large cardinals in ZFC, one can decide the truth-values of manymathematical statements which are independent from ZFC alone, and furthermore one can obtain a clear()
understanding of the theory of the second-order structure N, P(N), ∈ .
()
In this talk, we try to extend this understanding to the theory of the structure ω1 , P(ω1 ), ∈ where ω1 isthe least uncountable cardinal, by using large cardinals, forcing axioms, and some hypothesis from innermodel theory in ZFC. This is joint work with Matteo Viale.

September 28th (Sun)

Conference Room IX

9:30–11:30
14 Koichiro Ikeda(Hosei Univ.)

Simplicity and the strong order property of generic structures · · · · · · · 15

Summary: Evans and Wang proved that if an omega-categorical generic structure is not simple then it has
SOP3 . We consider a generalization of their result.

15 Hirotaka Kikyo(Kobe Univ.)

On model complete generic structures · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the model completeness of countably categorical structures constructed by Hrushovski’s
amalgamation method. We obtained some positive results in the ab initio case with coeﬃcient 1 for thepredimension function and with a ternary relation. We will discuss the cases with coeﬃcient other than 1.

16 Munehiro Kobayashi(Univ. of Tsukuba)
Akito Tsuboi (Univ. of Tsukuba)

On the equivalence of dividing and forking in NTP2 theories · · · · · · · · 15

Summary: In this talk, we see a new proof to Chernikov–Kaplan’s theorem which insists the equivalence ofdividing and forking over extension bases. We use indiscernible structures to prove the theorem, which are
more elementary notions than the ones used in Chernikov and Kaplan’s proof. The new proof was obtainedby improving Tsuboi’s idea.

17 Toshihiko Kurata (Hosei Univ.)

Categorical equivalence between concrete domains and sheaves · · · · · · · 15

Summary: We introduce a both-way translation between the category of concrete domains and a certain
category of sheaves, based on which we furthermore study the equivalence of these two categories.

Created: 2014/08/12 08:45
9Foundation of Mathematics and History of Mathematics

18 Katsuhiko Sano

(JAIST)

Cut-elimination theorem for Belnap–Dunn’s four-valued logic · · · · · · · · 15

Summary: This talk concerns a proof theory for Belnap–Dunn’s four-valued logic. First, we overview how
we can extract Dunn’s relational semantics for a given logical connective from a four-valued truth table forthe connective. Second, we provide inference rules for the connective in a sequent calculus of Belnap–Dunnlogic and establish an admissibility of the rule of cut in the expanded calculus with these rules.

19 Nobu-Yuki Suzuki (Shizuoka Univ.)

The independence of existence and disjunction properties in intermediate predicate logics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An intermediate predicate logic L is said to have the existence property (EP), if for every ∃xA(x),L ⊢ ∃xA(x) implies that there exists an individual variable v such that L ⊢ A(v). A logic L is said to havethe disjunction property (DP), if for every A and every B, L ⊢ A ∨ B implies either L ⊢ A or L ⊢ B. Since∃ is regarded as the generalized ∨, a natural question arises: Does EP imply DP? This is known as Ono’s
problem P52. We provide a negative solution to this problem. We also present an aﬃrmative partial result
under a natural condition for reasonable logics.

20 Ryo Kashima(Tokyo Tech)

On semilattice relevant logics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Urquhart’s semilattice relevant logic is defined to be the set of valid formulas in semilattice models.
We call it R0 , which is slightly diﬀerent from the orthodox relevant logic R. In this talk, semilattice models
are extended and a new logic, called R1 , is defined. R1 is a proper subset of R0 . The following formulas are
elements of R0 − R1 : ((p → r) ∧ (q → r)) → ((p ∨ q) → r), ((r → (p ∨ q)) ∧ (p → q)) → (r → q); the former isan axiom of R, and the latter is not provable in R. We study certain properties of R1 ; e.g., finding a soundand complete proof system.

11:30–12:00

Research Section Assembly

14:15–14:45

Mathematics History Team Meeting Part 1“On the map of Japan drawn under the direction of TAKEBE Katahiro with orders of Yoshimune,
the eighth Tokugawa shogun, during the Kyoho period”
Lecture by Minoru Kuge (Hiroshima Prefectural Museum of History) and discussion

15:00–16:10
21 Shunzi Horiguchi(Niigata Sangyo Univ.)
Tetsuaki Shimotomai

A discovery of the Shimizu style surveying secret book —Considerations
from the connections of the surveyors and religions— · · · · · · · · · · · · · · · 15

Summary: The Shimizu style surveying secret book of early stages in the Edo period (1603–1868) was foundin 2007 in Sapporo. We consider the surveying from the connections of the surveyors and religions.

Created: 2014/08/12 08:45
10

Foundation of Mathematics and History of Mathematics

22 Shotaro Tanaka♭

Methods for power series expansions of rational functions. Strictness
and handiness of their methods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Example: rational function: f (z) = (4z 2 −7z +11)/(2+5z)(2z −3)2 = 1/(2+5z)+1/(2z −3)2 . By∑∑
Wada’s theorem, power series: 1 : k = 1 → ∞, dp (k) ≡ (k+p−1)!/p!(k−1)!. 1 {d0 (k)(−1)k−1 (5k−1 /2k )+∑∑d1 (k)(2k−1 /31+k )}z k−1 (|z| < 2/5), 1 {d1 (k)(2k−1 /31+k )}z k−1 + 1 d0 (k)(−1)k−1 (2k−1 /5k )(1/z k ) (2/5 <∑|z| < 3/2), 1 {d0 (k)(−1)k−1 (2k−1 /5k ) + d1 (k)(3k−1 /21+k )(1/z)}(1/z k ) (3/2 < |z|). By Cauchy’s integralH∑formula,an (z − c)n : n = (−∞) → ∞, an = (1/2πi) {f (ζ)/(ζ − c)n+1 }dζ = (1/n!)f (n) (c). If c = 0, thenHan = (1/2πi) {f (ζ)/ζ n+1 }dζ = (1/n!)f (n) (0) is equal to the result from Wada’s. It is not easy to find thegeneral term from the recurring series.

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

La valeur particurière and the eigenvalue · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss the eigenvalue problem, especially, the coincidence between la valeur particulière andthe eigenvalue. The eigenvalue problem is the model of the Schrödinger equations or the quantum equations,
namely, the Sturm–Liouville type boundary value problem of heat diﬀusion is the model of the Schrödinger
equations. Sturm and Liouville discuss la valeur particulière, without its corresponding eigenspace, and thedefinition of eigenvalue and eigenspace/eigenfunction are introduced by Hilbert. This handling of the value
is traditionally relates to the sudies of linear diﬀerential equations, such as by Laplace, Fourier, Poisson,
Cauchy, et al. Especially, Poisson’s preceding studies contribute to the study of this type diﬀerential
equations by Sturm and Liouville and convergence of series in his heat theory.

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

Prévost’s study preceding Fourier of heat communication in the historyof physico-mathematics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss Prévost’s work on heat communication, which precedes Fourier. These situations owe
to the arrival of continuum, on which we summarize the topics as the background from the viewpoint ofmathematical history in 18–19th centuries as follows: 1) On the attraction and replusion of molecule, Navier
depends on Fourier’s principle of heat molecule. The then hysico-mathematicians had little evaluated Navier
until the top of 20th century. 2) Poisson points strongly out Fourier’s invalidity on the handling of De
Gua’s theory into the transcendental equations. 3) For formulation of heat motion in the fluid, Fourier had
submitted this paper, however, until his death, he has not published it, in which he seems to aim the unityof hydro- and thermodynamics. 4) The hydrodynamicists, like Poisson and Cauchy propose the equationsin unity of elasticity and fluid. Finally, we evaluate Prévost’s work on these background.

16:10–16:40

Mathematics History Team Meeting Part 2
Other topics

Created: 2014/08/12 08:45
11

AlgebraAlgebraSeptember 25th (Thu)

Conference Room II

9:30–12:00
1 Hiroko Yanaba (Hiroo Gakuen)
Takahiro Shishikura (Hiroo Gakuen)

On some results of the function associated with the Euler function φ(a)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Given a positive integer a, we have the Euler function φ(a). By s we denote the associatedfunction of φ(a), which is indicated by φ(a).
eGiven x, we consider the equation a − 2e+1 φ(a)e= x, e being a positive integer.
The main result is as follows.
If x = 0, then e = 1 and a = 2ε for some ε > 0. If x = 1 and e ≤ 4, then the equation has no solution.

On a function associated with σ(a) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

2 Shigeru Iitaka (Gakushuin Univ.⋆)

Summary: Associated with Euler tossile function, we introduced a new function φ(a),ewhich is defined to beφ(a)2s , s being the number of distinct prime factors of a.
Here, associated with divisor (sum) function σ(a), we introduce a yet another new function σe(a), which isdefined to be σ(a)
2s .
If 2e
σ (a) − a = −1 then a = 2e p, where p = 2e+1 + 1 is a prime.
Here e + 1 turns out to be 2m .

3 Yasutoshi Nomura∗

Primality and divisibility of Stirling numbers of the 2nd kind · · · · · · · · 10

Summary: We discuss in this talk when Stirling numbers S(n,k) are prime and when they are divisible byprime powers.

4 Isao Kiuchi (Yamaguchi Univ.) ∗ On a sum involving the Möbius function · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Makoto Minamide (Yamaguchi Univ.)
Yoshio Tanigawa (Nagoya Univ.)∑
Summary: Let cq (n) be the Ramanujan sum, i.e., cq (n) = d|(q,n) dµ(q/d), where µ is the Möbius function.
(∑)k∑Chan and Kumchev gave formulas for n≤y(k = 1, 2). In this our talk, we shall considerq≤x cq (n)(∑)k∑formulas for n≤ycq (n) (k = 1, 2).
n≤x b

5 Eiji Miyanohara (Waseda Univ.)

Transcendence of digital expansions generated by a cyclic permutationand k-adic expansion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove the transcendence of certain real numbers defined by using a cyclic permutation andk-adic expansion of natural numbers.

Created: 2014/08/12 08:45
12

Algebra6 Takeshi Kurosawa (Tokyo Univ. of Sci.)
Iekata Shiokawa (Keio Univ.⋆)

Algebraic independence of components of certain trigonometric functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let q ≥ 2 be an integer. We separate a given power series into q subseries, called q-components,
according to the residue classes mod q of their powers. We study algebraic independence for values at analgebraic point of q-components for a certain trigonometric functions.

7 Yohei Tachiya (Hirosaki Univ.)

Arithmetical properties of the values of the generalized divisor function
series · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10∑∞
Summary: Let q (|q| ≥ 2) and ℓ ≥ 2 be rational integers. Then the ℓ numbers 1, n=1 dk (n)q −n (k = 2, 3, ..., ℓ)
are linearly independent over Q, where dk (n) are the generalized divisor functions. This generalizes a resultof Erdos who treated the case ℓ = 2.

8 Kazuki Sato

(Tohoku Univ.)

Rational points on diagonal cubic surfaces · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a numerical suﬃcient condition for the existence of rational points on diagonal cubic
surfaces over the rationals under the assumption that the Tate–Shafarevich group of any elliptic curve over
the rationals is finite.

9 Akiko Ito(Kanagawa Univ.) ∗ On the 3-divisibility of the class numbers of certain quadratic fields (II)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let m1 and m2 be distinct square-free integers with 12 ∤ m1 m2 and let S+ , S− , S0 be mutually
disjoint finite sets of prime numbers not containing 2, 3, and the prime factors of m1 m2 . We show that there
exist infinitely many square-free integers d with gcd(m1 m2 , d) = 1 such that the class numbers of quadratic√√√
fields Q( m1 d) and Q( m2 d) are both divisible by 3, every prime number p ∈ S+ splits in Q( d), every√√
prime number p ∈ S− is inert in Q( d), and every prime number p ∈ S0 is ramified in Q( d).

(Nagoya Univ.) ∗ Mean values of multiple zeta-functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
10 Soichi Ikeda
Kaneaki Matsuoka (Nagoya Univ.)
Summary: We study mean values of the Euler–Zagier multiple zeta-functions.

11 Tomokazu Onozuka (Nagoya Univ.)

Zero-free regions of multiple zeta star functions · · · · · · · · · · · · · · · · · · · · 10

Summary: First, as a generalization of the classical notion of Dirichlet series, we define multiple Dirichlet
series and we give zero-free regions of multiple Dirichlet series. Next, we give zero-free regions of multiple
zeta star functions.

Created: 2014/08/12 08:45
13

Algebra12 Yumiko Hironaka (Waseda Univ.) ∗ Zeta functions of finite groups by counting numbers of subgroups · · · · 15
Summary: For a finite group G, we consider the zeta function ζG (s) =sugroups of G.

∑

H |H|

−s

, where H runs over theWe give examples of certain abelian p-group G and non-abelian p-group G′ of order pm , m ≥ 3 for odd p(resp. 2m , m ≥ 4) for which ζG (s) = ζG′ (s). Hence we see there are many non-abelian groups whose zetafunctions have symmetry and Euler product like the case of abelian groups.
On the other hand, we show that ζG (s) determines G within abelian groups.
We will explain some relation to the theory of Eisenstein series of of GLn and local densities of squarematrices.

14:15–16:15
13 Hiroto Inoue(Kyushu Univ.)

Expansion of the completed Riemann zeta function in Meixner–Pollaczek
polynomials and its zeros · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We will introduce the expansion of the completed Riemann zeta function in the Meixner–Pollaczek
polynomials, which satisfy the functional equation. It is showed that the expansion converses uniformly
in every compact set in the critical strip. Then we are interested in investigating the zeros of the partial
sums because these zeros approximate the nontrivial zeros of the Riemann zeta function. Furthermore,
we will have an observation that almost all the approximating zeros seem to lie on the real axis in anumerical calculation. For the last, we will mention the representation theoretical back ground of theMeixner–Pollaczek polynomials and the future works.

14 Yoshikatsu Yashiro (Nagoya Univ.) ∗ Distribution of zeros and zero-density estimate for the derivatives of
L-function attached to cusp form · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10(m)

Summary: Let Lf (s) the m-th derivative of L-function attached to cusp form. In this talk we shall give(m)(m)
the approximate formula of the number of zeros of Lf (s) and estimate the density of zeros of Lf (s) in
the right hand side of critical line.

15 Takahiro Wakasa (Nagoya Univ.) ∗ An explicit upper bound of the argument of Dirichlet L-functions on
the generalized Riemann hypothesis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We prove an explicit upper bound of the function S(t, χ), defined by the argument of Dirichlet
L-functions. An explicit upper bound of the function S1 (t), defined by the integral of the argument of the
Riemann zeta-function, have already been obtained by A. Fujii. Our result is obtained by applying an ideaof Fujii’s result on S1 (t). The constant part of the explicit upper bound of S(t, χ) in this paper does notdepend on a primitive Dirichlet character χ (mod q > 1).

16 Kohta Gejima(Osaka Univ.)

Shintani functions on SL(2, C) and Heun’s diﬀerential equations · · · · · 15

Summary: Shintani functions for the semisimple symmetric pair (SL(2, C), GL(1, C)) are defined for a pair(π, η) of representations. Here π is a non-unitary principal series representaition of SL(2, C) induced fromits parabolic subgroup, and η a character of GL(1, C). In this talk, we give explicit formulas of Shintani
functions of type (π, η), where π has a non-trivial minimal SU(2)-type Symn (C2 ) (n = 1, 2).

Created: 2014/08/12 08:45
14

Algebra17 Shingo Sugiyama (Osaka Univ.)
Masao Tsuzuki (Sophia Univ.)

Existence of Hilbert cusp forms with non-vanishing L-values · · · · · · · · · 15

Summary: We give a derivative version of the relative trace formula on PGL(2) studied in our previous work,and obtain a formula of an average of central values (derivatives) of automorphic L-functions for Hilbert
cusp forms. As an application, we prove existence of Hilbert cusp forms with non-vanishing central values(derivatives) such that the absolute degrees of their Hecke fields are suﬃciently large.

18 Shuichi Hayashida(Joetsu Univ. of Edu.)

Generalizations of the Maass relation of Siegel modular forms · · · · · · · 15

Summary: This talk is related to lifts to Siegel modular forms of half-integral weight. The Maass relation
is a certain relation among Fourier coeﬃcients of a certain kind of Siegel modular forms of degree two.
This relation characterizes the image of the Saito–Kurokawa lift. In particular, Siegel–Eisenstein series ofdegree two satisfy the Maass relation. In the end of 80’s T. Yamazaki obtained generalizations of the Maass
relation for Siegel–Eisenstein series of integral weight of arbitrary degrees. In the present talk I would liketo explain some refinements of Yamazaki’s results and give also a generalization of the Maass relation forSiegel cusp forms and Siegel modular forms of half-integral weight of arbitrary degrees. As an applicationof the generalized Maass relation we obtain lifts from pairs of two elliptic modular forms to Siegel modular
forms of half-integral weight of even degrees.

19 Hirotaka Kodama (Kinki Univ.)
Shoyu Nagaoka (Kinki Univ.)

On the mod p kernel of the theta operator · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In the previous meeting, it was reported that the image by the theta operator of Igusa cusp form
χ35 vanishes mod 23. However, the reason why such a phenomenon exists was not clarified. Therefore, we
consider whether it can be shown that there exist Siegel modular forms with a similar property. In thismeeting, we report that we can construct a family of Siegel modular forms satisfying such property in thecase of odd degree.

20 Hidehiko Mishou (Tokyo Denki Univ.)
Hirofumi Nagoshi (Gunma Univ.)

Joint d-universality for Dirichlet L-functions with real characters andmulti-dimensional denseness of quadratic class numbers · · · · · · · · · · · · · 10

Summary: We establish the joint universality theorem for a set of Dirichlet L-functions
L(s, χd1 d ), . . . , L(s, χdr d ) with real primitive characters in the d-aspect. We also obtain a multi-dimensional
denseness result concerning class numbers of quadratic fields.

Created: 2014/08/12 08:45
15

Algebra16:30–17:30

Talk Invited by Algebra Section

Hidehiko Mishou (Tokyo Denki Univ.)

An overview of the theory of universality for zeta functions

Summary: Let X and Y be a topological space and Tι : X → Y (ι ∈ I) be continuous mappings. An elementx ∈ X is called universal for {Tι }, if the set {Tι x ∈ Y | ι ∈ I} is dense in Y .
In the 1910s and later, the existence of universal objects have been comfirmed for many operators in thespace of entire functions. In 1975, S. M. Voronin obtained the first explicit example of universal objects.
Roughly speaking he showed that any non-vanishing and holomorphic function on the strip 1/2 < ℜs < 1
can be uniformly approximated by a suitable vertical translation ζ(s + iτ ) of the Riemann zeta function
ζ(s).
In the talk, I will summarize the results and the applications in the theory of universality for arithmetic zetafunctions. Also, I will talk about my recent works on the joint universality for sets of several zeta functions.

September 26th (Fri)

Conference Room II

9:30–11:50
21 Sin-Ei Takahasi (Toho Univ.) ∗ The structure of ordered topological semigroups on the real space R
Yuji Kobayashi (Toho Univ.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(
)
Open
Univ.
of
Japan
Yasuo Nakasuji
Makoto Tsukada (Toho Univ.)
Summary: This is a research report about the classification problem of the structure of ordered topologicalsemigroups on the space R of all real numbers, which is an old and new problem. We determine the structureof semigroups on R if they are Archimedean and satisfy a certain very weak cancellation law. Moreover weshow that exactly 3 cancellative topological semigroups exist on R and also exactly 8 ordered topologicalbands exist on R up to isomorphism.

22 Shuhei Kamioka (Kyoto Univ.)

Tilings of the Aztec diamonds and biorthogonal polynomials · · · · · · · · 15

Summary: On tiling problems of the Aztec diamonds Stanley exhibited a multivariate generalization of the
Aztec diamond theorem by Elkies, Kuperberg, Larsen and Propp (1992). (See Ciucu (1998).) In this talka new proof of Stabley’s multivariate generalization of the Aztec diamond theorem is shown in terms ofbiorthogonal polynomials and determinants.

23 Hiro-Fumi Yamada (Okayama Univ.)
Hiroshi Mizukawa(Nat. Defense Acad. of Japan)

A partition identity and the character table of the symmetric groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For an integer r greater than 1, an identity is presented which counts the number of parts modulo
r of the r-class regular partitions. This identity is applied for computing the determinant of the regularcharacter table of the symmetric group.

Created: 2014/08/12 08:45
16

Algebra24 Akiyoshi Tsuchiya (Osaka Univ.)
Akihiro Higashitani (Kyoto Univ.)
Takayuki Hibi (Osaka Univ.)
Koutarou Yoshida (Osaka Univ.)

Ehrhart polynomials with negative coeﬃcients · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is shown that, for each d ≥ 4, there exists an integral convex polytope P of dimension d suchthat each of the coeﬃcients of n, n2 , . . . , nd−2 of its Ehrhart polynomial i(P, n) is negative.

25 Takayuki Hibi (Osaka Univ.)
Akihiro Higashitani (Kyoto Univ.)

Facets of (0,1)-polytopes with squarefree initial ideals · · · · · · · · · · · · · · · 15

Summary: Let P ⊂ Rd be a (0, 1)-polytope of dimension d which contains the origin of Rd . Suppose that theconfiguration A arising from P satisfies ZA = Zd+1 and that the toric ideal IA of A possesses a squarefree
initial ideal with respect to the reverse lexicographic order induced by an ordering of the variables for which
the variable corresponding to the origin is the weakest. It is then proved that the equation of each facet of∑d
P is of the form i=1 ai zi = b, where each ai is an integer and where b ∈ {0, 1}.

26 Kazunori Matsuda (Rikkyo Univ.) ∗ Reverse lexicographic Gröbner bases and strongly Koszul toric rings
Hidefumi Ohsugi· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Kwansei Gakuin Univ.)
Summary: In this talk, we give a suﬃcient condition for a toric ring K[A] to be strongly Koszul in terms of
the reverse lexicographic Gröbner bases of its toric ideal IA . This is a partial extension of a result given by
Restuccia and Rinaldo.
In addition, we show that any strongly Koszul toric ring generated by squarefree monomials is compressed.
Using this fact, we show that our suﬃcient condition for K[A] to be strongly Koszul is both necessary andsuﬃcient when K[A] is generated by squarefree monomials.

27 Tomohiro Okuma (Yamagata Univ.) ∗ Good ideals and pg -ideals for two-dimensional normal singularities · · · 10
Kei-ichi Watanabe (Nihon Univ.)
Ken-ichi Yoshida (Nihon Univ.)
Summary: We introduced the notion of pg ideals for two-dimensional normal local domain. In this talk, wetalk about several properties of pg ideals, and give an existence of pg ideals. As an application, we prove an
existence theorem for good ideals for any two-dimensiona Gorenstein normal local domain. Moreover, weclassify Ulrich ideals for minimally (simple) elliptic singularities.

∗
28 Futoshi Hayasaka
A computation of Buchsbaum–Rim functions of two variables · · · · · · · · 10
(Hokkaido Univ. of Edu.)

Summary: In this talk, we will compute Buchsbaum–Rim functions of two variables associated to a parameter
matrix of a special form over a one-dimensional Cohen–Macaulay local ring, and will determine when thefunction coincides with the Buchsbaum–Rim polynomial. As a consequence, we have that there exists thecase where the function does not coincide with the polynomial function, which should be contrasted withthe ordinary Buchsbaum–Rim function of single variable.

Created: 2014/08/12 08:45
17

Algebra29 Tadahito Harima (Niigata Univ.) ∗ Completely m-full ideals and componentwise linear ideals · · · · · · · · · · · 10
Junzo Watanabe (Tokai Univ.)
Summary: We show that the class of completely m-full ideals coincides with the class of componentwise linear
ideals in a polynomial ring over an infinite field.

13:20–14:20

Talk Invited by Algebra Section

Masato Okado (Osaka City Univ.)

Tetrahedron equation and quantum groups

Summary: Tetrahedron equation is a 3 dimensional analogue of the Yang–Baxter equation in 2 dimensional
solvable lattice models. Recently, new connections between its solutions and quantum groups have beenfound. They are intertwiners of the quantum coordinate ring associated to SL3 or Sp4 , Poincaré–Birkhoﬀ–
Witt type basis of the nilpotent part of a quantized enveloping algebra associated to finite-dimensional
simple Lie algebras, and a new infinite-dimensional representation, which we call q-oscillator representation,of quantum aﬃne algebras. In my talk I will explain what are interesting from the viewpoint of representation
theory of quantum groups.

September 27th (Sat)

Conference Room II

9:30–11:25
30 Yugen Takegahara(Muroran Inst. of Tech.)2-adic properties for the numbers of involutions in the alternating groups· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Inv(n) be the set consisting of the identity and all involutions in the alternating groups ofdegree n. D. Kim and J. S. Kim determined the largest power of 2 in ♯Inv(n), where n = 4k, 4k + 2, or
4k + 3. They also conjectured that the largest power of 2 in ♯Inv(4k + 1), k = 1, 2, ..., are concerned with acertain 2-adic integer. We can give an aﬃrmative answer to this conjecture.

31 Yuki Kanakubo (Sophia Univ.) ♭ Cluster variables on double Bruhat cells and monomial realizations ofToshiki Nakashima (Sophia Univ.) crystal bases · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: For semi simple simply connected algebraic group G and elements u, v of its Weyl group, it
is known that the coordinate ring C[Gu,v ] of the double Bruhat cell Gu,v has the structure of an upper
cluster algebra and the generalized minors ∆(k, i) are the cluster variables ([A. Berenstein, S. Fomin,l(u)+l(v)A. Zelevinsky]). In this talk, for G = SLr+1 (C), we consider ∆(k, i) as the functions on C̸=0
bycoordinate transformation. Then they become Laurent polynomials with coeﬃcient 1. And we can express
each monomial in those polynomials in terms of monomial realization of crystal.

32 Toshiyuki Abe (Ehime Univ.)
Hiromichi Yamada (Hitotsubashi Univ.)

A commutant of a 4-cyclic permutation orbifold model of aﬃne vertex
operator algebra of type A1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: I will talk on a structure of a vertex operator algebra given as a commutant in the cyclic orbifold
model of Lsl2 (1, 0) of order 4.

Created: 2014/08/12 08:45
18

Algebra33 Kenichiro Tanabe (Hokkaido Univ.)

On modules with logarithmic terms over vertex algebras · · · · · · · · · · · · 15

Summary: I will introduce a generalization of modules over vertex algebras and give some examples of such
modules.

34 Masahide Konishi (Nagoya Univ.)

Basicalization of KLR algebras · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: KLR algebras are introduced to categorify the negative part of the associated quantum group.
From another point of view, they are a class of infinite dimensional algebra, defined by two data: a quiver
and a weight on its vertices. It is not so pathological, therefore we know we can obtain a basic algebra
Morita equivalent to a KLR algebra as a quiver with relations in principle. In this talk, I will explain an
explicit algorithm for that in some special cases.

35 Ayako Itaba (Tokyo Univ. of Sci.)
Takahiko Furuya (Meikai Univ.)
Katsunori Sanada (Tokyo Univ. of Sci.)

On the decomposition of the Hochschild cohomology group of a monomial algebra satisfying a separability condition · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the finite connected quiver Q having two subquivers Q(1) and Q(2) with
(1)

(2)

(1)

(2)

Q = Q(1) ∪Q(2) = (Q0 ∪Q0 , Q1 ∪Q1 ). Suppose that Q(i) is not a subquiver of Q(j) where {i, j} = {1, 2}.
For a monomial algebra Λ = kQ/I obtained by the quiver Q, when the associated sequence of paths given
by I satisfies a certain separability condition, we propose the method so that we easily construct a minimal
projective resolution of Λ as a right Λe -module and calculate the Hochschild cohomology group of Λ.

36 Tomohiro Itagaki (Tokyo Univ. of Sci.)

On the cyclic homology of an algebra associated with a cyclic quiver
and a monic polynomial · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The Hochschild homology and the cyclic homology of an algebra K[x]/(f (x)) over a commutative
ring K is given by the Buenos Aires cyclic homology group, where f (x) is a monic polynomial. We consider
an algebra A associated with a cyclic quiver and a monic polynomial which generalizes K[x]/(f (x)). In thistalk, we give the module structure of the Hochschild homology and the cyclic homology of A.

11:30–12:00

Research Section Assembly

14:15–15:15

Talk Invited by Algebra Section

Hiroyuki Minamoto (Osaka Pref. Univ.) ♭ Derived bi-duality and DG-completion
Summary: Duality and bi-duality are basic operations and has played prominent role in algebra and representation theory. Recently the concern with the derived duality and derived bi-duality have been growing.
We show that a derived bi-duality DG-module is obtained as a tautological homotopy limit. This result
gives unified proofs and generalizations of previous known results about derived bi-duality. We will also
discuss derived double centralizer property, which relates to a notion of DG-completion.

15:30–17:30
37 Hiroki Miyahara (Univ. of Yamanashi)

A constraction of Auslander-regular rings and its application · · · · · · · · 10

Created: 2014/08/12 08:45
19

Algebra38 Mitsuo Hoshino (Univ. of Tsukuba)
Noritsugu Kameyama (Shinshu Univ.)
Hirotaka Koga (Tokyo Denki Univ.)

Group-graded and group-bigraded rings · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let I be a non-trivial finite multiplicative group with the unit element e and A = ⊕x∈I Ax an
I-graded ring. We construct a Frobenius extension Λ of A and study when the ring extension A of Ae canbe a Frobenius extension. Also, formulating the ring structure of Λ, we introduce the notion of I-bigradedrings and show that every I-bigraded ring is isomorphic to the I-bigraded ring Λ constructed above.

39 Kazutoshi Koike(Okinawa Nat. Coll. of Tech.)Self-duality of finite triangular extensions · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Azumaya conjectured that every exact ring has a self-duality. The conjecture is related to selfduality of finite triangular extensions. We obtain self-duality of finite triangular extensions of skew fields
under certain conditions.

40 Hirotaka Koga (Tokyo Denki Univ.)

On standard derived equivalences · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we provide another suﬃcient condition to guarantee the existence of standard derived
equivalences for derived equivalent rings.

41 Satoshi Yamanaka (Okayama Univ.) ♭ On Morita equivalence in ring extensions · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: It seems that Morita invariance judges of the important of classes of ring extensions concerned.
The notion of Morita equivalence in ring extensions was introduced by Y. Miyashita, and he showed thatthe classes of G-Galois extensions and Frobenius extensions are Morita invariant. After that, S. Ikehata
showed that the classes of symmetric extensions, QF-extensions, separable extensions, and Hirata separable
extensions are Morita invariant. The purpose of this talk is to show that some classes of ring extensions
are Morita invariant. Further, we will give an example of the class of ring extensions which is not Morita
invariant. It may seem that the classes of almost all ring extensions are Morita invariant. But, there is aclass of ring extensions which we do not know weather that is Morita invariant or not.

42 Ryo Kanda(Nagoya Univ.) ♭ Classification of categorical subspaces of locally noetherian schemes · · 15

Summary: We classify the prelocalizing subcategories of the category of quasi-coherent sheaves on a locallynoetherian scheme. In order to give the classification, we introduce the notion of a local filter of quasicoherent subsheaves of the structure sheaf. We also classify the localizing subcategories and the closed
subcategories in terms of filters.

43 Shunsuke Tsuchioka (Univ. of Tokyo)
Anton Evseev (Univ. of Birmingham)

On graded generalized Cartan invariants of the symmetric groups · · · · 15

Summary: We propose graded analogue of Hill’s conjecture and Külshammer–Olsson–Robinson’s conjecture
concerning generalized Cartan invariants of the symmetric groups and discuss implications between themand their variants. As a support, we see our conjectures are compatible with certain localization andspecialization of the base ring Z[v, v −1 ].

Created: 2014/08/12 08:45
20

Algebra44 Taiki Shibata (Univ. of Tsukuba)

On integrals for algebraic supergroups · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let k be a base field. An aﬃne group scheme is a representable functor from the category ofcommutative k-algebras to the category of groups. If “algebras” are replaced with “superalgebras”(= Z2 graded algebras), then we obtain the notion of an aﬃne supergroup scheme (or simply, supergroup). Let A
be the Hopf superalgebra corresponding to an algebraic supergroup G. A non-zero k-linear map ϕ : A → k
is called an integral for G if ϕ is A-colinear. It is known that the integral plays an important role in the
representation theory of G. In this talk, we will discuss the existence and properties of integrals.

September 28th (Sun)

Conference Room II

9:15–12:00∗
45 Tomohiro Iwami
An analogue of Clemens–Griﬃths components for certain three-dimensional(Kyushu Sangyo Univ.) log pairs in the weak sense and the associated rationality criterion · · · 10

Summary: Succeeding to the author’s previous work “A variant of Iskovskikh’s rationality criterion for conic
bundles in the case of polarized (log) pairs”, in which the author slightly gave a rationality criterion for
Q-conic bundles, as resulting datum of running log minimal model program for certain three-dimensional log
pairs under several assumptions, the author will try to induce an analogue of Clemens–Griﬃths components
in the sense of A. Kuznetsov for rational Q-conic bundles, with regards to Chow motives,contributing to sucha rationality,in the induced Chow–Kunneth decomposition for such conic bundles, also by some methods
related to phantom categories.

46 Jo Suzuki(Osaka Univ.)

Klein’s fundamental second kind 2-form for the Cab curves · · · · · · · · · · 15

Summary: In this paper, we derive the exact formula for symplectic basis of cohomology and its associatedKlein’s fundamental second kind 2-form for so-called Cab curves. Previously, a similar result was obtainedfor hyper-elliptic curves. Thus far, the symplectic bases were calculated numerically by solving equations
because no such a formula was known for more general curves.

47 Yoshifumi Tsuchimoto (Kochi Univ.)

Non commutative Kähler maifolds · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We define non commutative counterpart of projective variety equipped with a Kähler structure.

(Nagoya Univ.) ∗ On the classification of involutions on Enriques surfaces · · · · · · · · · · · · · 15
48 Hiroki Ito
Hisanori Ohashi (Tokyo Univ. of Sci.)
Summary: We classify involutions on Enriques surfaces with the help of lattice theory due to Nikulin. We
also give geometric realizations to all types by mainly Horikawa construction. This is a joint work with
Hisanori Ohashi.

49 Yuki Yamamoto (Kanazawa Univ.)

Divisorial contractions to cDV points with discrepancy > 1 · · · · · · · · · · 15

Summary: I show that every divisorial contraction to cDV point with discrepancy > 1 is a weighted blow-up,
except for a few cases.

Created: 2014/08/12 08:45
21

Algebra50 Hirokazu Nasu

(Tokai Univ.)

Obstructions to deforming space curves lying on a smooth quartic
surface · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a suﬃcient condition for a first order infinitesimal deformation of a curve on a 3-fold to be
obstructed. As an application, we give a new example of a generically non-reduced irreducible componentsof the Hilbert scheme of space curves, whose general member is contained in a smooth quartic (K3) surface.
Our proof is based on a calculation of the obstructions (cup products).

51 Daizo Ishikawa (Waseda Univ.)

Weak Fano bundles of rank 2 on cubic threefolds · · · · · · · · · · · · · · · · · · · 15

Summary: We classified weak Fano bundles of rank 2 on nonsingular cubic hypersurfaces in projective
4-spaces.

52 Ryo Kawaguchi (Nara Medical Univ.)

A characterization of toric Fano threefolds · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In a recent research, we obtain a lower bound for the self-intersection number of an ample divisor
on a three-dimensional toric threefold. In this talk, we will see that this bound is attained if and only if ourdivisor is the anti-canonical divisor on a toric Fano threefolds.

53 Akihiro Higashitani (Kyoto Univ.)

Equivalent classes for toric Fano 5-folds and higher dimensions · · · · · · · 15

Summary: Let Fn be the set of isomorphism classes of toric Fano n-folds. We say that X and Y in Fn are
F-equivalent if there exists a sequence of equivariant blow-ups or blow-downs from X to Y through toricFano n-folds. In this talk, we will present the results on F-equvalent classes and some other equivalentclasses for F5 . We also consider a higher dimensional analogue of the results on equivalent classes for F5 .

14:15–15:15

Talk Invited by Algebra Section

Isamu Iwanari (Tohoku Univ.) ♭ Tannaka duality for higher categories
Summary: I will discuss Tannaka duality theory for stable infinity-categories; a higher categorical analogueof triangulated categories. I’ll describe its backgrounds, motivations, applications to mixed motives, andprospects.

Created: 2014/08/12 08:45
22

Geometry

Geometry
September 25th (Thu)

Conference Room III

9:40–12:00
1 Hirotaka Ebisui (Oval Research Center)

About theorem in an-Desargues-system (ADE Theorem) · · · · · · · · · · · · 15

Summary: We have two systems for overraping two triangles that can be called as non Desargues andDesargues systems. Namely, in Desargues system, 3 lines connected 3 corresponding vertexs of triangle, areconcurrence, and in non-Desargues system, they are not concurrence. Oppositly, we call this relation as that
two triangles are in Desargues or non-Desargues system. Now we can say easyly that the Desargues theorem
is in Desargues system. And Hexagon theorem which was found and reported in MSJ2011 at Shinshu Univ
by H. Ebisui, is defined as a theorem in non(an)-Desargues system. About this fact, we show again Hexagon
theorem which is drawn or constructed in new geometry system so called non(an)-Desargues system,andsome corresponding theorems.

2 Akitoshi Kawamura (Univ. of Tokyo)
Yoshio Okamoto(Univ. of Electro-Comm.)
Takeshi Tokuyama (Tohoku Univ.)

Weight balancing on boundaries and skeletons · · · · · · · · · · · · · · · · · · · · · 15

Summary: Given a polygonal region containing a target point (which we assume is the origin), it is not hard
to see that there are two points on the perimeter that are antipodal, i.e., whose midpoint is the origin. We
prove three generalizations of this fact. (1) For any polygon (or any bounded closed region with connectedboundary) containing the origin, it is possible to place a given set of weights on the boundary so that theirbarycenter (center of mass) coincides with the origin, provided that the largest weight does not exceed
the sum of the other weights. (2) On the boundary of any 3-dimensional bounded polyhedron containing
the origin, there exist three points that form an equilateral triangle centered at the origin. (3) On the
1-skeleton of any 3-dimensional bounded convex polyhedron containing the origin, there exist three points
whose center of mass coincides with the origin. This talk is partly based on work presented at the 30th
Annual Symposium on Computational Geometry (SoCG 2014) jointly with 10 other authors.

3 Shuzo Izumi(Kinki Univ.)

Suﬃciency of simplex inequalities · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let z0 , ..., zn be the facet areas an n-simplex. Then we have the simplex inequalities: zp <z0 + ... + zp−1 + zp+1 + ... + zn (0 ≤ p ≤ n), generalizations of triangle inequalities. Conversely, suppose that
numbers z0 , ..., zn > 0 satisfy these inequalities. Does there exist an n-simplex with facet areas z0 , ..., zn ?
Kakeya solved this problem aﬃrmatively in the case n = 3 and conjectured that the assertion is aﬃrmative
also for n ≥ 4. We assert that this is always aﬃrmative.

4 Shiho Ogata(Fukuoka Univ.)

Gap theorems of complete λ-hypersurfaces · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Since n-dimensional λ-hypersurfaces in Euclidean space are critical points of the weighted areafunctional for the weighted volume-preserving variations, in this talk, we talk about the rigidity properties ofcomplete λ-hypersurfaces. We give a gap theorem of complete λ-hypersurfaces with polynomial area growth.
By making use of the generalized maximum principle for λ-hypersurfaces, we prove a rigidity theorem ofcomplete λ-hypersurfaces. This is a joint work with Professor Q.-M. Cheng and Professor G. Wei.

Created: 2014/08/12 08:45
23

Geometry

5 Makoto Sakaki (Hirosaki Univ.) ∗ Surfaces with mean curvature vector of constant length in productspaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Deforming rotation surfaces with constant mean curvature in S 3 and H 3 to S 3 × R and H 3 × R
respectively, we give four classes of surfaces with mean curvature vector of constant length in S 3 × R andH 3 × R. Also we obtain minimal 2-tori in S 3 × S 1 .

6 Hiroshi Iriyeh (Tokyo Denki Univ.) ∗ On Hamiltonian stable Lagrangian tori which are not Hamiltonian
Hajime Ono (Saitama Univ.) volume minimizing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In 1993, Y.-G. Oh proposed a problem whether standard Lagrangian tori in C n are volume
minimizing under Hamiltonian isotopies of C n . We prove that most of them do not have such property if
the dimension n is greater than two.

(Meijo Univ.)
7 Norio Ejiri
Shoichi Fujimori (Okayama Univ.)
Toshihiro Shoda (Saga Univ.)

Limits of triply periodic minimal surfaces · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider limits of triply periodic minimal surfaces in R3 . We prove that some important
examples of doubly periodic minimal surfaces can be obtained as limits of triply periodic minimal surfaces.

8 Naoyuki Koike (Tokyo Univ. of Sci.)

A holonomy invariant anisotropic surface energy functional · · · · · · · · · · 15

Summary: In this paper, we investigate a holonomy invariant anisotropic surface energy (functional) in acomplete Riemannian manifold, where “holonomy invariant” means that the parametric Lagrangian (onthe tangent bundle of the Riemannian manifold) used to define the anisotropic surface energy is constantalong each holonomy subbundle of the tangent bundle. First we obtain the first variational formula for
the functional. Next we shall introduce the notions of an anisotropic convex hypersurface, an anisotropic
equifocal hypersurface and an anisotropic isoparametric hypersurface for the functional, and give examplesof these hypersurfaces in the case where the ambient space is a symmetirc space. Also, we prove that theanisotropic equifocality is equivalent to the anisotropic isoparametricness in the case where the ambient
space is a symmetric space of non-negative curvature.

9 Norihito Koiso (Osaka Univ.) ♭ Bi-harmonic submanifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Hajime Urakawa (Tohoku Univ.)
Summary: A map f : (M, g) → (X, h) is called a bi-harmonic map if it is a solution of the variational problem
defined by the square integral of the tension field τ . A submanifold Y of (X, h) is called a bi-harmonic
submanifold if the inclusion map ι is a bi-harmonic map with respect to the induced metric ι∗ h. The
equation of bi-harmonic submanifold is over-determind, but has many solutions: all minimal submanifolds
are bi-harmonic submanifolds. B. Y. Chen conjectured that there are no bi-harmonic submanifolds in
Euclidean spaces except minimal submanifolds. In this talk, we show that the conjecture is true for
hypersurfaces under a certain generic condition.

Created: 2014/08/12 08:45
24

Geometry

14:15–16:10
10 Yusuke Masatani (Nagoya Univ.)

On unbounded diameter of the space of Lagrangian submanifolds in
bi-disks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: By using S. Seyfaddini’s idea, we prove unboundedness of Lagrangian Hofer metric associatedwith uncountably many Lagrangian submanifolds in standard bi-disks (D2 × D2 , ω̄0 ).

11 Mitsuhiro Imada (Keio Univ.)

On complex almost contact metric structures on complex hypersurfacesof C2n · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Complex contact manifolds, whose definition is analogous to that of real contact manifolds, arealso expected to be important, but few examples of complex contact manifolds are known so far. In thisreport, we show that the (standard) hyperkähler structures on C2n induce complex almost contact metricstructures on some complex hypersurfaces of C2n . Also, we discuss whether those structures satisfy thenormality defined by Ishihara and Konishi.

12 Isami Koga

(Kyushu Univ.) ∗ Classification of some submanifolds of the complex Grassmannian manifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let M → Grp (Cn ) be a holomorphic isometric immersion of a compact Kähler manifold into thecomplex Grassmannian manifold. We assume that the pull-back bundle of the universal quotient bundle
Q → Grp (Cn ) over the complex Grassmannian manifold is projectively flat. In this talk, we classify such
submanifolds with parallel second fundamental form.

13 Sadahiro Maeda (Saga Univ.) ∗ Naturally reductive homogeneous real hypersurfaces in a nonflat comHiroshi Tamaru (Hiroshima Univ.) plex space form · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, we give some geometric characterizations of naturally reductive homogeneous real
hypersurfaces in a nonflat complex space form.

14 Kazumi Tsukada (Ochanomizu Univ.)

Totally complex submanifolds of a complex Grassmann manifold of
2-planes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A complex Grassmann manifold G2 (Cm+2 ) of all 2-dimensional complex subspaces in Cm+2 has
two nice geometric structures —the Kähler structure and the quaternionic Kähler structure. We study
totally complex submanifolds of G2 (Cm+2 ) with respect to the quaternionic Kähler structure. We showthat the projective cotangent bundle P(T ∗ CP m+1 ) of a complex projective space CP m+1 is a twistor spaceof the quaternionic Kähler manifold G2 (Cm+2 ). Applying the twistor theory, we construct maximal totallycomplex submanifolds of G2 (Cm+2 ) from complex submanifolds of CP m+1 . Then we obtain many interesting
examples.

15 Hiroshi Iriyeh (Tokyo Denki Univ.)
Takashi Sakai (Tokyo Metro. Univ.)
Hiroyuki Tasaki (Univ. of Tsukuba)

On the structure of the intersection of quaternionic flag manifolds in acomplex flag manifold · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study antipodal structure of the intersections of two real forms in complex flag manifolds. In
particular, in the complex flag manifold consisting of sequences of complex subspaces in a complex vector
space we describe the intersection of real forms consisting of sequences of quaternionic subspaces.

Created: 2014/08/12 08:45
25

Geometry

16 Hiroyuki Tasaki (Univ. of Tsukuba)

Sequences and estimates of antipodal subsets · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let Pk (n) be the set consisting of all subsets of cardinalities k in {1, . . . , n}. A subset A of Pk (n)is antipodal, if for any α and β in A the cardinality of α − β = {i ∈ α | i ∈/ β} is even. An antipodal
subset of Pk (n) is related to an antipodal set of the oriented real Grassmann manifold G̃k (Rn ), which wasintroduced by Chen–Nagano. We have already obtained the classification of maximal antipodal subsets of
Pk (n) for k ≤ 4. We construct sequences of antipodal subsets of Pk (n). Using this we show estimates of the
cardinalities of antipodal subsets of P5 (n).

17 Kazuyoshi Kiyohara (Okayama Univ.) ∗ The conjugate locus on ellipoid and D4+ Lagrangean singularity · · · · · · 15
Jin-ichi Itoh (Kumamoto Univ.)
Summary: In the 2008 annual meeting of MSJ we talked that, on ellipsoids with distinct axes (or moregenerally on certain Liouville manifolds), the conjugate locus of a “general point” has three components ofsingularities and they are cuspidal edges. In this talk we show that the end points of those cuspical edges are
D4+ Lagrangean singularities (of Arnold) and no other type of singularities do appear. The D4+ singularities
appear exactly at the points where the multiplicity of the conjugacy is greater than one.

16:30–17:30

Talk Invited by Geometry Section

Osamu Ikawa (Kyoto Inst. Tech.) ∗ Foundations and applications of symmetric triads
Summary: The notion of a symmetric triad with multiplicities is a generalization of that of an irreducible rootsystem with multiplicities. We shall construct symmetric triads with multiplicities from compact symmetric
triads with certain conditions. We apply symmetric triads into two directions:(1) The orbits of Hermann actions. A Hermann action is a generalization of the isotropy action of acompact symmetric space. We describe the orbit spaces of Hermann actions using symmetric triads withmultiplicities, and we also study the properties of each orbit such as regular, minimal, austere and totally
geodesic orbit.
(2) The intersection of two real forms in an irreducible Hermitian symmetric space of compact type, which
is a joint work with M. S. Tanaka and H. Tasaki. They proved that the intersection is an antipodal set if
it is discrete. We will describe the necessary and suﬃcient condition that two real forms intersect discretely
using a symmetric triad.

September 26th (Fri)

Conference Room III

10:30–10:45

Presentation Ceremony for MSJ Geometry Prize 2014

10:50–11:50

Award Lecture for MSJ Geometry Prize 2014

—Celebrating Professor Masatake Kuranishi—(Osaka Univ.) Kuranishi’s masterpieces and their developments in deformation theory
Ryushi Goto(
Kagoshima
Univ.⋆) and CR-geometry
Kimio Miyajima
Summary: In this talk, we discuss Kuranishi’s works and their developments focussing on deformation theory
and CR-geometry.

Created: 2014/08/12 08:45
26

Geometry

13:15–14:15

Talk Invited by Geometry Section
Takumi Yokota (Kyoto Univ.) Convex functions and barycenter on CAT(1)-spaces of small radii
Summary: CAT(1)-spaces are metric spaces of curvature at most 1 in the sense of Alexandrov defined interms of geodesic triangles. CAT(0)-spaces are a generalization of simply-connected complete Riemannian
manifolds of non-positive curvature and convexity of their distance functions yields many interesting results.
In this talk, we discuss convexity of certain functions on small metric balls in CAT(1)-spaces. This function
is discovered by W. Kendall and is similar to the one used by W. Jäger and H. Kaul in the proof of
uniqueness of harmonic maps between Riemannian manifolds.
As an application, we prove that any Borel probability measure on a complete CAT(1)-space of small radius
admits a unique Karcher mean which is also a unique barycenter. We also see that our Karcher mean on
CAT(1)-spaces shares various properties, such as Jensen’s inequality, with barycenter on CAT(0)-spaces.
This is a generalization of preceding results on CAT(0)-spaces and CAT(1)-spaces of small diameters by
K.-T. Sturm, K. Kuwae, S.-i. Ohta, etc.
Finally, we use our barycenter to formulate an analogue of Banach–Saks property for general metric spaces.
We prove that complete CAT(1)-spaces with small radii enjoy this property. This can be regarded as anextension of Kakutani’s theorem on uniformly convex Banach spaces.

September 27th (Sat)

Conference Room III

9:40–12:00
18 Kazuhiro Okumura(Asahikawa Nat. Coll. of Tech.)

Real hypersurfaces admitting ϕ-invariant Ricci tensors in a nonflat
complex space form · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider real hypersurfaces with ϕ-invariant Ricci tensors in a non-flat complex
fn (c). In particular, we classify Hopf hypersurfaces having weakly ϕ-invariant Ricci tensor inspace form M
fn (c).
M

19 Dounnu Sasaki (Waseda Univ.)

An intersection functional on the space of subset currents on a freegroup · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Kapovich and Nagnibeda introduced the space SCurr(FN ) of subset currents on a free group
FN of rank N ≥ 2, which can be thought of as a measure-theoretic completion of the set of all conjugacy
classes of finitely generated subgroups of FN . We define a product N (H, K) of two finitely generated
subgroups H and K of the free group FN by the sum of the reduced rank rk(H ∩ gKg −1 ) over all double
cosets HgK (g ∈ FN ), and extend the product N to a continuous symmetric R≥0 -bilinear functional on
SCurr(FN ) × SCurr(FN ).

20 Oliver Goertsches (Univ. Hamburg)
Hiraku Nozawa (Ritsumeikan Univ.)
Dirk Töben (Fed. Univ. of São Carlos)

On localization of Chern–Simons type invariants of Riemannian foliations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We will present an Atiyah–Bott–Berline–Vergne type localization formula in the context ofequivariant basic cohomology for certain Riemannian foliations on compact manifolds. It localizes some
Chern–Simons type invariants, for example the volume of Sasakian manifolds or secondary characteristicclasses of Riemannian foliations, to the union of closed leaves. We give various examples to illustrate ourmethod.

Created: 2014/08/12 08:45
27

Geometry

21 Tomoyo Kanazawa(Tokyo Univ. of Sci.)
Akira Yoshioka (Tokyo Univ. of Sci.)

An S 1 -reduction of non-formal star product · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We studied and talked about a star product and besides its characteristic equation to obtain theenergy-eigenspace of the MIC-Kepler problem. At present, we are going to find a shape in the star productwhich should produce its characteristic equation for the Hamiltonian of the MIC-Kepler problem, because
we reached our solutions by means of reduction of Hamiltonian systems. Since we used the Moyal producton the cotangent bundle of the principal U(1)-bundle whose base space is the three-dimensional Euclidean
space except the origin, we tried to research into the reduction of star products; we would like to make areport about a reduced algebra which may be endowed with a star product derived from the Moyal product.

22 Daisuke Tarama (Kyoto Univ.)

Stability analysis for the free rigid body dynamics on U (n) · · · · · · · · · · 15

Summary: The free rigid body dynamics, which is the geodesic flow on SO(3) with respect to a left-invariant
metric, is a typical solvable example in analytical mechanics. The stability of its equilibria is well known. In
this talk, a natural extension of the free rigid body dynamics to the unitary group U (n) is considered. The
dynamics is described by Euler equation on the Lie algebra u(n), which has a bi-Hamiltonian structure, andit can be restricted to the adjoint orbit. The complete integrability and the stability of the equilibria on thegeneric orbits are considered by using the results of Bolsinov and Oshemkov. In particular, it is shown that
all the equilibria on generic orbits are Lyapunov stable.

23 Masaya Kawamura(Tokyo Metro. Univ.)

A priori estimates for the Monge–Ampère equation related to supersymmetry and Gauduchon conjecture · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Supersymmetry is the symmetry between Bosons and Fermions in superstring theory. Yau andothers showed that supersymmetry requires that there exists a balanced metric (i.e., Hermitian metrics
satisfying d(ω n−1 ) = 0) whose Chern–Ricci curvature (Bismut curvature) vanishes on compact complex
manifolds. Gauduchon conjecture is Calabi conjecture for Gauduchon metrics (i.e., Hermitian metrics¯ n−1 ) = 0) on compact complex manifolds. We study on a priori estimates for the Monge–
satisfying ∂ ∂(ω
Ampère equation closely related to supersymmetry and Gauduchon conjecture under an estimate of Laplacianof a smooth solution. These estimates are important for applying continuity method to obtain a solution.

24 Yasushi Homma (Waseda Univ.)

Twisted Dirac operators and generalized gradients · · · · · · · · · · · · · · · · · 15

Summary: Generalized gradients are the first order diﬀerential operators naturally defined on Riemannianor spin manifolds. It is known that there exist commutation relations for gradients called Weitzenböck
formulas. In this talk, we show the other commutation relations by using twisted Dirac operators and PRV
theorem in representation theory. We also give some applications.

25 Kenta Tottori (Tohoku Univ.) ∗ Calabi’s gradient metric on the space of Kähler metrics · · · · · · · · · · · · · 10
Summary: Calabi’s gradient metric is a Riemannian metric on the space of Kähler metrics H. Since H is an
infinite dimensional space, the existence of a geodesic is not trivial. In this talk, we will show the Cauchy
problem for the geodesic equation has a short time solution. Furthermore, we will show Calabi’s gradient
metric defines a distance function on H.

Created: 2014/08/12 08:45
28

Geometry

26 Shin Nayatani (Nagoya Univ.)

Rumin–Bochner formular for 1-forms on a CR manifold · · · · · · · · · · · · · 15

Summary: Around 1990, Michel Rumin defined a diﬀerential complex for a contact manifold, and developed
the associated harmonic theory for a strongly pseudoconvex CR manifold with a fixed contact form. Rumin
proved a Bochner-type formula for a harmonic one-form on such a manifold. In this talk, I discuss the
sharpness of Rumin’s formula with an explicit example and an application of the formula to the eigenvalue
estimate of the subelliptic Laplacian. I’ll also discuss a generalization of the formula to the case of two-forms.

14:15–16:00
27 Ryosuke Takahashi (Nagoya Univ.)

Modified Kähler–Ricci flow on projective bundles · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we propose a method of studying the modified Kähler–Ricci flow on special projective
bundles, called admissible bundles, from the view point of symplectic geometry. As a result, we canreduce the modified Kähler–Ricci flow to a simple PDE for a time-dpendent function on the interval[−1, 1]. Moreover, we show that the solution of this evolution equation converges uniformly to the function
corresponding to a GQE metric in exponential order under some assumptions.

28 Homare Tadano (Osaka Univ.)

A lower diameter bound for closed domain manifolds of shrinking Ricciharmonic solitons · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we remark that the arguments by Futaki–Sano (Asian J. Math. 17, 17–31, 2013)
and Futaki et al (Ann. Global Anal. Geom. 44, 105–114, 2013) also work well for closed domain manifoldsof shrinking Ricci-harmonic solitons and the arguments also give a lower diameter bound for the domain
manifolds.

29 Yohei Sakurai (Univ. of Tsukuba)

Rigidity of manifolds with boundary under a lower Ricci curvaturebound · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and alower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop–Gromov
type concerning the volumes of the metric neighborhoods of the boundaries. We conclude several rigidity
theorems. As one of them, we obtain a volume growth rigidity theorem. We also obtain a splitting theoremof Cheeger–Gromoll type under the assumption of the existence of a single ray.

30 Tsukasa Takeuchi (Tokyo Univ. of Sci.)

Integrability in the geodesic flow for the Berger mertic · · · · · · · · · · · · · · 10

Summary: The (1,1)-tensor field on symplectic manifold that satisfies some integrability conditions is calleda recursion operator. It is known the recursion operator is a characterization for integrable systems, andgives constants of motion for integrable systems. Our aim is to construct recursion operators for the geodesic
flow for the Berger metric.

31 Yu Kitabeppu (Kyoto Univ.)(HCM)
Sajjad Lakzian

A finite generation of the fundamental groups on metric measure spaces
with small linear diameter growth · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove a finite generation of the fundamental groups on metric measure spaces with smalllinear diameter growth. This is done by using the Abresch–Gromoll inequality on RCD spaces. Another key
idea is the local to global property of nonnegative Ricci curvature bound in the non-smooth setting.

Created: 2014/08/12 08:45
29

Geometry

32 Junichi Mukuno (Nagoya Univ.) ∗ On the fundamental group of a complete globally hyperbolic Lorentzianmanifold with a lower bound for the curvature tensor · · · · · · · · · · · · · · · 10
Summary: In this talk, we prove the finiteness of the fundamental group of a certain class of complete
globally hyperbolic Lorentzian manifolds with the positivity of the curvature tensor.

33 Hideki Miyachi (Osaka Univ.) ∗ Rigidity of a coarsification of isometries on Teichmuller space · · · · · · · · 15
Summary: In this talk, I will give a coarsification (discretization) of isometries on Teichmuller space. I will
discuss a rigidity property of the coarsification. If time permits, I will also give a motivation on this work.

16:15–17:15

Talk Invited by Geometry Section

Shin-ichi Oguni (Ehime Univ.) ∗ The coarse Baum–Connes conjecture and coarse algebraic topology
Summary: Coarse geometry studies unbounded proper metric spaces, for example, non-compact completeriemannian manifolds and finitely generated infinite groups with word metrics, from a large-scale geometricviewpoint.
In general, a Dirac-type operator on a non-compact complete riemannian manifold is not a Fredholm
operator and thus we cannot take the Fredholm index. John Roe defined an ‘index’ in the K-group of
the Roe algebra. The K-group of the Roe algebra depends only on the coarse structure of the manifold
and thus can be treated in coarse geometry. Moreover, by regarding the operator as a cycle of the coarse
K-homology, John Roe encoded taking the coarse geometric index for the operator as the coarse assembly
map. The coarse assembly map from the coarse K-homology to the K-group of the Roe algebra is definedfor any proper metric space, and then the coarse Baum–Connes conjecture claims that the coarse assembly
map is an isomorphism for any ‘nice’ proper metric space.
In this talk, first I will explain why the coarse Baum–Connes conjecture is interesting. Indeed I will
introduce some applications to diﬀerential topology and explain that the conjecture is natural in view ofcoarse algebraic topology. Next I will report known results on the conjecture. Also I will confirm that theconjecture is true for some simple examples by using coarse algebraic topology as one of main tools. Finally
I will introduce a result by our joint work with Tomohiro Fukaya (Tohoku University), which claims thatthe coarse Baum–Connes conjecture is true for the product of finitely many groups which consist of some of
CAT (0) groups, hyperbolic groups, polycyclic groups and appropriate relatively hyperbolic groups. Also I
will explain ideas for its proof.

Created: 2014/08/12 08:45
30

Complex Analysis

Complex Analysis
September 25th (Thu)

Conference Room I

9:00–12:00
1 Shigeyoshi Owa (Yamato Univ.) ∗ Notes on Carathéodory functions involving Möbius transformations · · 15
Summary: Let A be the class of functions p(z) which are analytic in the open unit disk U with p(0) = 1. Ifp(z) ∈ A satisfies Rep(z) > 0 (z ∈ U), then p(z) is said to be Carathéodory function in U. For p(z) ∈ A, we
introduce three subclasses P(α) for α < 1, P(β) for β > 1, and P(α, β) for α < 1 and β > 1 of A. Applying
Möbius transformations w(ζ) for p(z), we discuss some properties for Carathéodory functions p(z).

2 Masanori Amano (Tokyo Tech)

On the limit value of the Teichmüller distance between Jenkins–Strebel
rays · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins–
Strebel diﬀerentials. We give the limit value of the Teichmüller distance between the rays. In particular, we
obtain a condition under which the rays are asymptotic.

3 Yoshihiko Shinomiya (Waseda Univ.)

On the numbers of periodic points on Veech surfaces · · · · · · · · · · · · · · · 15

Summary: A Veech surface is a flat surface whose Veech group is a lattice in PSL(2, R). A Veech surface isarithmetic if the Veech group is commensurable with PSL(2, Z). Otherwise, the Veech surface is called an
non-arithmetic Veech surface. It is known that the number of periodic points on an non-arithmetic Veech
surface is finite. We will give upper bounds of the numbers of periodic points on non-arithmetic Veech
surfaces.

4 Masahiro Yanagishita (Waseda Univ.)

Weil–Petersson metric on square integrable Teichmüller spaces · · · · · · · 15

Summary: The square integrable Teichmüller space is the metric subspace of the Teichmüller space composedof the Teichmüller equivalence classes with square integrable Beltrami coeﬃcient. Since this subspace has
a complex structure modeled on a Hilbert space, we can introduce a Hermitian metric, which is called theWeil–Petersson metric. In this talk, we discuss its Kählerity.

5 Hiroshige Shiga (Tokyo Tech)

On rigidity and finiteness for Teichmüller curves · · · · · · · · · · · · · · · · · · · 15

Summary: Let f be a holomorphic map from a Riemann surface C of finite type to the moduli space ofRiemann surfaces. If the map f is a locally isometry, then the pair (C, f ) is called a Teichmüller curve. We
show a rigidity theorem and a finiteness theorem for Teichmüller curves.

6 Hiroshige Shiga (Tokyo Tech)

Conformal invariants defined by harmonic functions on Riemann surfaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider conformal invariants defined by various spaces of harmonic functions on Riemannsurfaces. The Harnack distance is a typical one. We give sharp inequalities comparing those invariants withthe hyperbolic metric on the Riemann surface and we determine when equalities hold. We also describe theHarnack distance in terms of the Martin compactification and discuss some properties of the distance.

Created: 2014/08/12 08:45
31

Complex Analysis

7 Hiroshige Shiga (Tokyo Tech)

Deformation spaces of Kleinian groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let G0 be a non-elementary Kleinian group. We consider the deformation space of D(G0 ), thespace of quasiconformal deformations of G0 , and their complex analytic properties. We show some analytic
structures of D(G0 ) which are improvements of results by Bers, Kra, Maskit and McMullen. In particular,
we clarify that the structures for Kleinian groups with non-simply connected components are diﬀerent fromthose for Kleinian groups without non-simply connected components.

8 Ikkei Hotta(Tokyo Tech)

Ld -Loewner chains with quasiconformal extensions · · · · · · · · · · · · · · · · · 15

Summary: Recently, a new approach in Loewner theory has been proposed which gives a unified treatment ofboth the radial and chordal version of the Loewner equations. The notion of Loewner chains are generalized
in this framework, called a Loewner chain of order d. In this talk we discuss a suﬃcient condition thata Loewner chain of order d has a quasiconformal extension to the Riemann sphere. It is provided as a
generalization of Becker’s quasiconformal extension theorem.

9 R. Michael Porter (CINVESTAV)
Hirokazu Shimauchi (Tohoku Univ.)

Discrete quasiconformal maps via a linear system · · · · · · · · · · · · · · · · · · 15

Summary: We propose a discretization method for the quasiconformal mappings from the unit disk to itself.
The disk is triangulated in a simple way and the quasiconformal mappings are approximated by piecewise
linear mappings; the images of the vertices of the triangles are defined by an overdetermined system of
linear equations. The linear system is sparse and its solution is obtained by standard least-squares. The
least-squares solution is unique and its mapping sequence converges to the true solution in some certain
cases.

10 Hideki Miyachi (Osaka Univ.) ∗ A dynamical approach to the theory of infinitesimal spaces of quasiconformal mappings · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, I will study the infinitesimal spaces of quasiconformal mappings on the plane via
continuous flows on the space of quasiconformal mappings.

11 Masakazu Shiba (Hiroshima Univ.⋆)
Hiroshi Yamaguchi (Shiga Univ.⋆)

Conformal embeddings of an open Riemann surface into closed ones
—Extremal property of period matrices— · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let R be an open Riemann surface of positive finite genus g and {Aj , Bj }gj=1 be a canonicalhomology basis modulo dividing cycles. For each t ∈ (−1, 1] and each j there exists a unique holomorphic
diﬀerential φtj on R such that exp(−πit/2)φtj is canonical semiexact in the sense of Kusunoki and the Aktperiod is equal to δjk . Let τjk
be the Bk period of ϕtj and fix any real g vector a = (a1 , a2 , . . . , ag ). Then∑gtt
describes a circle when t moves in (−1, 1], and that the circle has an
we show that τa := j,k=1 aj ak τjkinteresting extremal property in the set of compact continuations of R.

Created: 2014/08/12 08:45
32

Complex Analysis

14:10–16:50
12 Yuuki Tadokoro(Kisarazu Nat. Coll. of Tech.)

The period matrix of the hyperelliptic curve w2 = z 2g+1 − 1 · · · · · · · · · 15

Summary: Let Cg be the hyperelliptic curve defined by the aﬃne equation w2 = z 2g+1 −1 for genus g ≥ 2. We
explicitly obtain the period matrix of this curve whose all entries are elements of the (2g + 1)-st cyclotomic
field.

13 Junghun Lee(Nagoya Univ.)

J-stability of immediately expanding polynomial maps in p-adic dynamics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Given a family {fλ }λ∈Λ of polynomial maps of degree d where Λ is the set of parameters, apolynomial map fλ0 is called J-stable in Λ if there exists a neighborhood of λ0 in Λ such that for any
element λ in the neighborhood, there exists a conjugacy between the dynamics on the Julia sets of fλ andfλ0 . The aim of this paper is to show that a polynomial map fλ0 over the field Cp of p-adic complex numbers
is J-stable in the set of polynomial maps over Cp if fλ0 is immediately expanding.

14 Masashi Kisaka (Kyoto Univ.)

Transcendental entire function of slow growth with prescribed polynomial dynamics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct a transcendental entire functions of arbitrarily slow growth which has a given
polynomial dynamics as its subdynamics. We also show several applications of the result, one of which isthe following: there exists a transcendental entire function which has a Cremer point but its Julia set islocally connected.

15 Hiroyuki Inou (Kyoto Univ.)
Shizuo Nakane(Tokyo Polytechnic Univ.)

An implosion arising from saddle connection in 2D complex dynamics· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: It is known that the fiber Julia set of a skew product is discontinuous if there exist two saddle
fixed points one of whose stable manifold intersects the unstable manifold of the other. We will explain this
discontinuity by an analogous argument as in the parabolic implosion.

16 Sachiko Hamano (Fukushima Univ.)

Reproducing kernels for the spaces of holomorphic semiexact diﬀerentials on annuli · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a precise representation of a reproducing kernel for the Hilbert space of all holomorphic
semiexact diﬀerentials on an annulus by using the calculation of the L1 -constants with two logarithmic
poles. We give an example such that the pseudoconvex variation of the annulus with complex parameter t
yields the subharmonicity of the L1 -constant with t.

17 Masanori Adachi (Nagoya Univ.)
Judith Brinkschulte (Univ. Leipzig)

A global estimate for the Diederich–Fornaess index of weakly pseudoconvex domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A uniform upper bound for the Diederich–Fornaess index is given for weakly pseudoconvex
domains whose Levi-form of the boundary vanishes in ℓ-directions everywhere.

Created: 2014/08/12 08:45
33

Complex Analysis

18 Satoru Shimizu (Tohoku Univ.) ♭ Holomorphic equivalence problem for a class of unbounded Reinhardt
domains containing the origin · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this talk, I talk about the holomorphic equivalence problem for (essentially) unbounded
pseudoconvex Reinhardt domains. When the domains contain no coordinate hyperplanes, an aﬃrmative
answer was already given. As an opposite case to such a case, we discuss a class of unbounded Reinhardt
domains containing the origin, which are said to be of broadened type. The main purpose of this talk is to
give an aﬃrmative answer to the holomorphic equivalence problem for them by making use of the way of a
Liouville foliation.

19 Hiroaki Aikawa (Hokkaido Univ.)(Tokyo Tech)
Tsubasa Itoh

Averaging property of capacity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the distribution of a subset of Rn with respect to the p-capacity. Stegenga investigatedthe distribution with respect to the logarithmic capacity and he proved that the averaging property holds
for logarithmic capacity. We show that the same averaging property holds for the p-capacity.

(Oita Univ.) ∗ Trudinger’s exponential integrability for Riesz potentials of functions in
20 Takao Ohno
Yoshihiro Mizuta
generalized grand Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Hiroshima Inst. of Tech.)
Summary: Our aim in this talk is to discuss Trudinger’s exponential integrability for Riesz potentials offunctions in generalized grand Morrey spaces. Our result will imply the boundedness of the Riesz potential
operator from a grand Morrey space to a Morrey space.

(Oita Univ.) ∗ Trudinger’s inequality for Riesz potentials of functions in Musielak–
21 Takao Ohno
Tetsu Shimomura (Hiroshima Univ.) Orlicz spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we are concerned with Trudinger’s inequality for Riesz potentials of functions inMusielak–Orlicz spaces.

17:00–18:00

Talk Invited by Complex Analysis Section

Yoshihiro Mizuta(Hiroshima Inst. of Tech.)

Function spaces of variable exponent and Sobolev’s theorem

Summary: First we show the well-known Sobolev type inequality, and then extend it to the variable exponent
settings.

Created: 2014/08/12 08:45
34

Complex Analysis

September 26th (Fri)

Conference Room I

9:00–10:30
22 Yukinobu Adachi∗

On the Julia directions of the value distribution of nondegeneratetransendental holomorphic maps of C2 to C2 · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We prove that for a nondegenerate holomorphic map F = (f (x, y), g(x, y)) where f and g are entire
functions and f is a transendental one, there exists a ray J(θ) = {(x, y); x = t exp(iθ), y = kt exp(iθ)(0 ≦t < ∞)} where k is an arbitrarily fixed complex number except Lebesgue measure zero set and θ is somereal number depending on value k, such that F (x, y), in any open cone in C2 with vertex (0, 0) containing
J(θ), does not omit any algebraic curve with three irreducible components in a general position.

23 Yukinobu Adachi∗

On a high dimensional Rieman’s removability theorem · · · · · · · · · · · · · · 15

Summary: Let M be a (connected) complex manifold and E be a closed capacity zero set. Let X be a(connected) complex compact Kobayashi hyperbolic space whose universal covering is Stein and let f be aholomorphic map of M − E to X. Then f be extended holomorphically to a map of M to X.

24 Yukinobu Adachi∗

On a high dimensional Riemann’s mapping theorem · · · · · · · · · · · · · · · · 10

Summary: We prove that the domain D in Γ × Cz where Γ is a polydisk centered at (0) and the fiber ofD over every point of Γ is a simply connected domain in Cz which contains a small disk {|z| ≤ ε}, where
ε is independent of every point of Γ, is biholomorphic to some complete Hartogs domain. And we give
applications of the uniformization of some fiber spaces.

25 Masataka Tomari (Nihon Univ.) ∗ On maximal ideal cycle and fundamental cycle of normal two-dimensional
Tadashi Tomaru (Gunma Univ.) singularities with star-shaped resolution, and graded singurities · · · · · · 15
Summary: We study the maximal ideal cycle and the fundamental cycle for normal two-dimensional singularities with star-shaped resolution. Our interest is the identification of these. If the cordinated ringof singularity have a homogeneous reduced element in the minimal degree, then the identification can be
regarded at the central curve. We can show that this condition is satisfied for Brieskorn complete intersection
singularity.

26 Tatsuhiro Honda(Hiroshima Inst. of Tech.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)

Growth and distortion theorems for pluriharmonic mappings · · · · · · · · 15

Summary: In this talk, we give growth and distortion theorems for aﬃne and linearly invariant families ofpluriharmonic mappings of the unit ball B into Cn . Also, we obtain two-point distortion theorems.

Created: 2014/08/12 08:45
35

Complex Analysis

27 Tatsuhiro Honda(Hiroshima Inst. of Tech.)
Hidetaka Hamada(Kyushu Sangyo Univ.)
Gabriela Kohr (Babeş-Bolyai Univ.)
Kwang Ho Shon (Pusan Nat. Univ.)

Strongly starlike mappings in several complex variables · · · · · · · · · · · · · 10

Summary: Let f be a normalized biholomorphic mapping on the Euclidean unit ball in Cn and let α ∈ (0, 1).
In this talk, we will show that if f is strongly starlike of order α in the sense of Liczberski and Starkov, thenit is also strongly starlike of order α in the sense of Kohr and Liczberski. We also give an example whichshows that the converse of the above result does not hold in dimension n ≥ 2.

13:20–14:20

Talk Invited by Complex Analysis Section

Yukitaka Abe (Univ. of Toyama) ∗ Analytic study of singular curves
Summary: We study singular curves from analytic point of view.

We reformulate the Serre duality, ageneralized Abel’s theorem etc. in quite natural way from our view point, and give completely analytic
proofs of them. We also reconsider Picard varieties, Albanese varieties and generalized Jacobi varieties of
singular curves analytically. We call an Albanese variety considered as a complex Lie group an analytic
Albanese variety. We investigate them in detail and construct several examples. We think that an analytic
Albanese variety is suitable for a generalized Jacobi variety because it has similar properties to those of theJacobi variety for a compact Riemann surface.

Created: 2014/08/12 08:45
36

Functional Equations

Functional Equations
September 25th (Thu)

Conference Room V

9:00–12:00
1 Hiroshi Ogawara (Kumamoto Univ.)

Diﬀerential transcendency of a formal Laurent series satisfying a rational
linear q-diﬀerence equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We report that a formal Laurent series satisfying a rational linear q-diﬀerence equation of firstorder does not satisfy any nontrivial algebraic diﬀerential equation over the rational function field unless
it represents a rational function. This also provides an algebraic proof of Ishizaki’s theorem on diﬀerential
transcendency for a meromorphic function satisfying a linear q-diﬀerence equation, and then slightly relaxes
the assumption of the theorem. We also report diﬀerential transcendency of non-rational solutions of arational q-diﬀerence Riccati equation and a rational linear homogeneous q-diﬀerence equation of second
order that have rational solutions.

2 Junya Nishiguchi (Kyoto Univ.)

Stabilization of unstable steady solutions by delayed feedback control:
Approach by Lambert W function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The delayed feedback control is a method for changing the structure and nature of solutions oforiginal diﬀerential systems by adding a delay term. In this talk, I consider stabilization of unstable steadysolutions of an ordinary diﬀerential equation ẋ(t) = f (x(t)) on the Euclidean space by the delayed feedback
control. Here a delayed feedback term is represented by K(x(t − τ ) − x(t)) using a constant matrix K
and a positive number τ . Adding this term, the original ODE becomes a delay diﬀerential equation, andwe can expect the change of dynamics of the diﬀerential equation. For this purpose, I use the Lambert
W function, which is the multi-valued inverse of the complex function zez . A main theorem shows thatthe stabilization is always possible if unstable eigenvalues of the steady solution consist of a unique pair ofcomplex conjugates.

3 Kazuki Hiroe(Josai Univ.)

Local Fourier transform and blowing up · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a resolution of ramified irregular singularity of formal meromorphic connections on
disk via local Fourier transforms as an analogy of the blowing up of the singularity of plane curve germs.
A necessary and suﬃcient condition for an irreducible connection to have a resolution of singularity will
be determined. A relationship between Komatsu-Malgrange irregularity of connections and some curve
invariants will also be discussed.

4 Kohei Iwaki(Kyoto Univ.)

On WKB theoretic transformations for Painlevé transcendents on degenerate Stokes segments · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show that the second Painlevé equation (PII) and the third Painlevé equation (PIII’(D7))
of type D7 give a normal form of Painlevé equations on a degenerate Stokes segments connecting two
diﬀerent simple turning points and on a degenerate Stokes segment of loop-type, respectively. That is, any
2-parameter formal solution of a Painlevé equation is reduced to a 2-parameter formal solution of (PII) or(PIII’(D7)) on these degenerate Stokes segments by the transformation.

Created: 2014/08/12 08:45
37

Functional Equations

5 Hiroshi Yamazawa(Shibaura Inst. of Tech.)

Existence of holomorphic and singular solutions of q-analogue of Briot–
Bouquet type diﬀerence-diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 1990, Gérard–Tahara introduced the Briot–Bouquet type partial diﬀerential equation t∂t u =F (t, x, u, ∂x u), and they determined the structure of holomorphic and singular solutions provided that thecharacteristic exponent ρ(x) satisfies ρ(0) ̸∈ N∗ . In this talk we consider holomorphic and singular solutionsof the following type of diﬀerence-diﬀerential equations tDq u = F (t, x, u, ∂x u).

6 Hiroshi Yamazawa(Shibaura Inst. of Tech.)
Hidetoshi Tahara (Sophia Univ.)

q-Analogue of summability of formal solutions of some linear q-diﬀerencediﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let q > 1. In this talk we considers a linear q-diﬀerence-diﬀerential equation: it is a q-diﬀerence
equation in the time variable t, and a partial diﬀerential equation in the space variable z. Under suitableconditions and by using q-Borel and q-Laplace tranforms, we consider that if it has a formal power series
solution X̂(t, z) one can construct an actual holomorphic solution which admits X̂(t, z) as a q-Gevrey
asymptotic expansion of order 1.

7 Tetsutaro Shibata (Hiroshima Univ.) ∗ Asymptotic behavior of the bifurcation diagrams for semilinear problems with cubic-like nonlinearity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider the nonlinear ordinary diﬀerential equation with a parameter λ and cubic-likenonlinear term f (u). It is known that under the suitable conditions on f (u), there are three bifurcation
curves λ = λj (ξ) (j = 1, 2, 3) which are parameterized by the maximum norm ξ of the solution uλ associatedwith λ. The purpose of this talk is to study the precise global structures of λj (ξ) (j = 1, 2, 3).

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

Global bifurcation structure of stationary solutions to a cell polarization
model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We are interesting in wave-pinning in a reaction-diﬀusion model for cell polarization proposed
by Y. Mori, A. Jilkine and L. Edelstein-Keshet in SIAM J. Appl. Math (2011). Wave-pinning meansa phenomenon that a wave of activation of one of the species is initiated at one end of the domain,
moves into the domain, decelerates, and eventually stops inside the domain, forming a stationary front.
Several mathematical bifurcation results of stationary solutions are obtained by Kuto and Tsujikawa in
DCDS Supplement (2013). We propose a method to represent a bifurcation sheet of a shadow-system. It
determines the global bifurcation structure of stationary solutions of the shadow-system completely including
even secondary bifurcation branches.

Created: 2014/08/12 08:45
38

Functional Equations

9 Takasi Yamasaki (Shimane Univ.)
Jitsuro Sugie (Shimane Univ.)

Smith-type criterion for the asymptotic stability based on the weighted
damping · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The equations considered in this talk are x′′ + h(t) x′ + ω 2 x = 0 and its generalization x′′ +h(t)|x′ |q−2 x′ + ω 2 x = 0, q ≥ 2, where the prime denotes d/dt, the damping coeﬃcient h(t) is continuousand nonnegative for t ≥ 0, and the restoring coeﬃcient ω is positive. A necessary and suﬃcient condition
for the asymptotic stability of the equilibrium is obtained in consideration of the weighted damping. Our
result includes many previous ones. Some examples are presented to illustrate the main result.

10 Mitsuru Shibayama (Osaka Univ.)

Variational proof of the existence of the super-eight solution in thefour-body problem · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Using the variational method, Chenciner and Montgomery proved the existence of an eight-shaped
periodic solution of the planar three-body problem with equal masses. Just after the discovery, Gerver havenumerically found a similar periodic solution called “super-eight” in the planar four-body problem withequal mass.
In this talk I will prove the existence of the super-eight orbit by using the variational method. The diﬃcultyof the proof is to eliminate the possibility of collisions. In order to solve it, we apply the scaling techniqueestablished by Tanaka and investigate the asymptotic behavior of a binary collision.

11 Tomoyuki Tanigawa (Kumamoto Univ.)

Asymptotic behavior of positive solutions of third order Emden–Fowler
diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we devote to the asymptotic analysis of third order Emden–Fowler diﬀerential equationx′′′ + q(t)|x|γ sgn

x = 0,

q(t) > 0,0<γ<1

in the framework of regular variation. It is shown that in case function q(t) is nearly regularly varying
accurate information can be acquired about the existence of possible positive solutions of the equation andtheir asymptotic behavior at infinity.

12 Hiroyuki Usami(Gifu Univ.) ∗ Applications of ordinary diﬀerential equations to hyperbolic equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We introduce applications of asymptotic theory of ODEs to that of one-dimensional hyperbolic
equations via Fourier analysis. In particular, we give suﬃcient conditions which ensure the existence of limit
functions of solutions to some hyperbolic problems.

13 Hiroyuki Usami (Gifu Univ.) ♭ Global solution of an inverse blow-up problem · · · · · · · · · · · · · · · · · · · · · 10
Yutaka Kamimura(Tokyo Univ. of Marine Sci. and Tech.)
Summary: An inverse blow-up problem is discussed. We establish a global continuation result showing thata nonlinearity realizing a blow-up time for large initial data can be continued in the direction of smaller
initaial data as long as the blow-up time is Lipschitz continuous.

Created: 2014/08/12 08:45
39

Functional Equations

14 Shingo Takeuchi(Shibaura Inst. of Tech.)Complete p-elliptic integrals and computation of π3 · · · · · · · · · · · · · · · · 10

Summary: Complete p-elliptic integrals are introduced and applied to compute π3 , a generalization of π. The
strategy is same as those of Salamin (1976) and Brent (1976), but the Legendre relation and the Landen
transformation are required for these new integrals.

∗
15 Katsuyuki Nishimoto
The solutions to the Laplace’s homogeneous ordinary diﬀerential equa(Descartes Press Co.) tions by means of the N-fractional calculus · · · · · · · · · · · · · · · · · · · · · · · · 4

Summary: In this article, the solutions to the homogeneous ordinary diﬀerential equations with linear
coeﬃcients,
φ2 · (az + b) + φ1 · (gz + h) + φ · (pz + q) = 0,(φν = dν φ/dz ν for ν > 0, φ0 = φ = φ(z),a, b, g, h, p, q; constants, agp ̸= 0,)
which are called as “the Laplace’s ordinary diﬀerential equations”, are discussed by means of the N(Nishimoto’s)-fractional calculus (NFC-Method) (The calculus in the 21th Century).

14:15–16:15
16 Ichiro Tsukamoto (Toyo Univ.) ∗ On an asymptotic expression of a positive solution of x′′ = tαλ−2 x1+α(α = λ0 , λ > 0) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We state an asymptotic expression of a positive solution of the diﬀerential equation denoted in
the title. This expression is valid as t tends to +0 and improves the exression stated in the meeting of theMathematical Society of Japan at Kyoto University in 2013.

17 Tokinaga Namba (Univ. of Tokyo)
Atsushi Nakayasu (Univ. of Tokyo)
Nao Hamamuki (Waseda Univ.)

On cell problems for Hamilton–Jacobi equations with non-coercive
Hamiltonians and its application to homogenization problems · · · · · · · · 10

Summary: We study the solvability of a cell problem arising in a homogenization problem for a Hamilton–
Jacobi equation whose Hamiltonian is not coercive because of its boundedness. By using a certain function,a necessary and suﬃcient condition to solve the cell problem is given. As its application, we also give ahomogenization result.

18 Haruya Mizutani (Osaka Univ.)
Nikolay Tzvetkov(Univ. Cergy-Pontoise)

Strichartz estimates for non-elliptic Schrödinger equations · · · · · · · · · · · 10

Summary: We consider the Schrödinger equation on compact manifolds equipped with possibly degenerate
metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends onthe degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, thesame Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for the Riemannian
Laplacian. We also investigate the optimality of the result for the case on a product of compact Lie groups.

Created: 2014/08/12 08:45
40

Functional Equations

19 Takuya Suzuki (Univ. of Tokyo)

Analyticity of semigroups generated by higher order elliptic operatorsin spaces of bounded functions on C 1 domains · · · · · · · · · · · · · · · · · · · · · 10

Summary: Our goal is to establish the analyticity of semigroups generated by higher order divergence typeelliptic operators in spaces of bounded functions with the Dirichlet condition when the domain is uniformly
C 1 domain. We mainly consider resolvent estimates in L∞ type spaces and also consider the existence anduniqueness of the resolvent equations in order to show the generation of analytic semigroups. Masuda–
Stewart’s method is a well known method to show the analyticity of semigroups, but this method may need
the assumption that the boundary of a domain is uniformly C 2m . We relax the smoothness assumption ofboundaries to uniformly C 1 by applying resolvent estimates in L∞ type spaces obtained by a contradiction
argument and a blow up argument.

20 Takanobu Hara (Tokyo Metro. Univ.)

Potential estimates for elliptic equations with drift terms · · · · · · · · · · · · 10

Summary: We consider divergence form elliptic equations with a strongly singular drift term −∇ · (A∇u) +⃗b · ∇u = µ in a domain Ω ⊂ Rn (n ≥ 3). We give a weak-type L1 − Ln/(n−2),∞ estimate for a solution to
the Dirichlet problem with the homogeneous boundary condition. Moreover, we give a two-sided pointwise
potential estimate for a weak solution.

21 Nobuyuki Kato (Nippon Inst. of Tech.) ∗ Uniform Hölder continuity of approximate solutions to parabolic systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: By means of the discrete Morse flow method we construct approximate solutions to parabolic systems and generete a Cauchy–Euler polygon. From Campanato-type estimates for the approximate solutions,
we derive Hölder continuity of the Cauchy–Euler polygon uniformly with respect to the approximation.

22 Tatsuki Kawakami (Osaka Pref. Univ.) ∗ When does the heat equation have a solution with a sequence of similar
Shigeru Sakaguchi (Tohoku Univ.) level sets? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider an overdetermined Cauchy problem for the heat equation. We prove that if the
problem has a non-trivial non-negative solution with a certain sequence of similar level sets, then thesolution must be radially symmetric.

23 Takayoshi Ogawa (Tohoku Univ.) ∗ Maximal L1 -regularity for a Cauchy problem to parabolic equations
Senjo Shimizu (Shizuoka Univ.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider maximal L1 -regularity of the Cauchy problem for parabolic equations in the Besov
0space Ḃp,1(Rn ) with 1 ≤ p ≤ ∞. The estimate obtained here is not available by abstract theory for theclass of UMD since the end-point Besov space is included. We consider the endpoint estimate obtainedby Danchin and show that the estimate is indeed, optimal. Besides, we discuss the optimality of maximal
regularity in L1 for the linear parabolic equation for the variable coeﬃcient case.

24 Shuichi Jimbo (Hokkaido Univ.) ∗ Eigenvalues of 2nd order elliptic operators in a domain with a thintubular hole · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk I consider an eigenvalue problem of a 2nd order elliptic operator in a domain with athin tubular hole. I present an asymptotic formula for the behavior of the eigenvalue when the hole shrinks
to a lower dimensional manifold.

Created: 2014/08/12 08:45
41

Functional Equations

16:30–17:30

Talk Invited by Functional Equations Section

Naoki Sioji (Yokohama Nat. Univ.)

A generalized Pohozaev identity and uniqueness of positive radial solutions for an elliptic equation

Summary: We introduce a generalized Pohozaev identity related to an elliptic equation. By using it, westudy the uniqueness of positive radial solutions of the equation in a ball (or in Rn ) under the Dirichletboundary condition. We also study its nondegeneracy in a space of radial functions and in a space which
involves nonradial functions. We apply our results to various examples like the scalar field equation, theBrezis–Nirenberg problem on a spherical cap, etc.

September 26th (Fri)

Conference Room V

9:00–12:00
25 Motohiro Sobajima (Univ. of Salento)
Giorgio Metafune (Univ. of Salento)
Chiara Spina (Univ. of Salento)

Weighted Calderón–Zygmund and Rellich inequalities · · · · · · · · · · · · · · · 10

Summary: We find necessary and suﬃcient conditions for the validity of weighted Rellich and Calderón–
Zygmund inequalities with respect to Lp -norm (1 ≤ p ≤ ∞) for functions in the whole space. Moreover,weighted Rellich and Calderón–Zygmund inequalities with respect to the operators L = ∆+c|x|−2 x·∇−b|x|−2(c, b ∈ R) are also considered.

26 Yoshifumi Mimura (Tohoku Univ.)

A priori bounds of stationary solutions of two dimensional Keller–Segelsystem on polygonal domains · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider stationary solutions of two dimensional Keller–Segel system on polygonal domains
and prove that a priori bounds of the solutions fail for specific parameters determined by the position of
singular points and angles of domains. The similar results are already proved by Senba and Suzuki in 2000
when domains are open sets in R2 with smooth boundaries. The novelty is that foregoing specific parameters
depend on angles of domains.

27 Norisuke Ioku (Ehime Univ.)
Bernhard Ruf (Univ. di Milano)
Elide Terraneo (Univ. di Milano)

Existence, non-existence, and unconditional uniqueness for a heat equation with exponential nonlinearity in R2 · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, a heat equation with exponential nonlinearity in R2 is discussed. We prove a nonexistence result for some initial data in an Orlicz space exp L2 (R2 ). In order to consider the existence of
local solutions and unconditional uniqueness, we introduce the closure of C0∞ (R2 ) in exp L2 (R2 ).

Created: 2014/08/12 08:45
42

Functional Equations

28 Shoichi Hasegawa (Tohoku Univ.)

Liouville theorem for Hénon type equation on the hyperbolic space· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we study the Liouville result of nontrivial stable solutions of the equation(H)−∆H u = (sinh dH (0, x))α |u|p−1 u in BN ,where α > 0, p > 1, N ≥ 3. Here the operator ∆H denotes the Laplace–Beltrami operator on the hyperbolic
space BN and dH (0, x) is the hyperbolic distance from the origin to x ∈ BN . We show that there exists an
exponent pc (α, N ) such that the equation (H) has no nontrivial stable solutions for 1 < p < pc . We can
expect that pc will be critical from the asymptotic behavior of the radial solutions of (H) for p ≥ pc large
enough.

29 Aya Ishizeki (Saitama Univ.) ∗ Variational formulae of decomposed Möbius energy and estimates · · · · 10
Takeyuki Nagasawa (Saitama Univ.)
Summary: The Möbius energy can be decomposed into three parts, each of which is invariant under Möbiustransformations. The third part is the absolute constant. Hence when we consider the energy as a variational
problem, we may deal with first two parts only. We find some similarities between these parts and relatively
easily get variational formulae and applicable estimates.

30 Kousuke Kuto
(Univ. of Electro-Comm.)

Limiting structure of shrinking solutions to the stationary SKT modelwith large cross-diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We are concerned with the limiting behavior of the coexistence steady-states to the Lotka–
Volterra competition model as one of the cross-diﬀusion terms tends to infinity. Under the Neumannboundary condition, Lou–Ni (1999) derived a couple of shadow systems which characterize the limiting
behaviors of the coexistence steady-states. One of the shadow system charcterizing the segregation of thecompeting species has been studied by Lou–Ni–Yotsutani (2004) in detail. This talk focuses on the othershadow system characterizing the shrinking of the species not endowed with the cross-diﬀusion eﬀect. The
bifurcation structure of nonconstant solutions to the shadow system will be stated. In particular for the 1D
case, we obtain an unbounded connected set of nonconstant solutions.

31 Yasuhito Miyamoto (Univ. of Tokyo)

Intersection properties of radial solutions and global bifurcation diagrams for supercritical quasilinear elliptic equations · · · · · · · · · · · · · · · · 10

Summary: We study the positive solution u(r, ρ) of the quasilinear elliptic equationr−γ (rα |u′ |β u′ )′ + |u|p−1 u = 0, 0 < r < ∞,
u(0) = ρ > 0, u′ (0) = 0.
This class of diﬀerential operators includes the usual Laplace, m-Laplace, and k-Hessian operators in thespace of radial functions. The equation has a singular positive solution u∗ (r). A generalized Joseph–
Lundgren exponent, which we denote by p∗JL , is obtained. We study the intersection numbers betweenu(r, ρ) and u∗ (r) and between u(r, ρ0 ) and u(r, ρ1 ), and see that p∗JL plays an important role.

Created: 2014/08/12 08:45
43

Functional Equations

32 Mieko Tanaka (Tokyo Univ. of Sci.) ∗ Generalized eigenvalue problem for (p, q)-Laplacian with indefinite weight
Dumitru Motreanu· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Univ. de Perpignan)
Summary: We provide existence and non-existence results of a positive solution for the (p, q)-Laplace equation
under the Dirichlet boundary condition, with 1 < q < p.

33 Mieko Tanaka (Tokyo Univ. of Sci.) ∗ Bifurcation of positive solutions for the one dimensional (p, q)-Laplace(Saga Univ.) equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Ryuji Kajikiya
Satoshi Tanaka (Okayama Univ. of Sci.)
Summary: In this talk, we consider the bifurcation of positive solutions for the one dimensional (p, q)-Laplace
equation under the Dirichlet boundary condition. We investigate the shape of the bifurcation diagram
near the bifurcation point and near infinity. As a consequence, we prove the existence of multiple positive
solutions and show the uniqueness of positive solutions for a bifurcation parameter in a certain range.

34 Daisuke Naimen (Osaka City Univ.)

On the multiple solutions of a nonlinear elliptic problem with the
Dirichlet energy · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider a nonlinear elliptic equation involving the Dirichlet energy. We introduce
a new approach which enables us to get multiple (possibly infinitely many) solutions. In addition, we put apositive answer to the solvability of the critical problem in high dimension which has never been solved.

35 Masato Hashizume (Osaka City Univ.)

A minimization problem with a sign changing condition · · · · · · · · · · · · · 10

Summary: In this talk,we consider a minimization problem with a sign changing condition. This problem isrelated with “Lp Lyapunov inequality”. The author proves the existence of the minimizer of the minimization
problem.

36 Yasuhiro Fujita (Univ. of Toyama) ∗ Log-Sobolev inequality for locally Lipschitz continuous functions · · · · · 10
Summary: We discuss a logarithmic Sobolev inequality for locally Lipschitz continuous functions on Rn .

37 Atsushi Kosaka (Osaka City Univ.)
Yoshitsugu Kabeya (Osaka Pref. Univ.)
Tatsuki Kawakami (Osaka Pref. Univ.)
Hirokazu Ninomiya (Meiji Univ.)

Asymptotic behavior of eigenvalues to the Laplace–Beltrami operator
on a spherical cap in SN · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this conference, we speak of the linear eigenvalue problem of the Laplace–Beltrami operator
on a large spherical cap. If a spherical cap is suﬃciently large, then we can treat the eigenvalue problem as
the perturbation of the eigenvalue problem on a unit sphere.
In this study, we obtained asymptotic formulas of eigenvalues. By using the asymptotic formulas, we canexactly see the multiplicity of eigenvalues of the Laplace–Beltrami operator on a large spherical cap. This
result is applied for, e.g., the investigation of a local bifurcation structure of semilinear elliptic problems on
a spherical cap.

Created: 2014/08/12 08:45
44

Functional Equations

38 Soohyun Bae (Hanbat Nat. Univ.)(Ehime Univ.)Yūki Naito

Critical phenomena in the separation property for semilinear elliptic
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the semilinear elliptic equation, and study separation phenomena of positive radialsolutions. With respect to intersection and separation, we establish a classification of the solution structures,and investigate the structures of intersection, partial separation and separation.

39 Futoshi Takahashi (Osaka City Univ.)
Massimo Grossi(Univ. di Roma “La Sapienza”)

On the location of two blow up points on an annulus for the mean field
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the mean field equation on two-dimensional annular domains, and prove that if P1
and P2 are two blow up points of a blowing-up solution sequence of the equation, then we must haveP1 + P2 = 0.

13:15–14:15

Talk Invited by Functional Equations Section♭
Hideo Nakazawa
Scattering problems for wave equations with dissipation and related(Nippon Medical School) topics

Summary: In this talk, we shall overview several results related to the scattering problem for wave equations
with dissipation. Our topics are given as followings. The problem of decay and non-decay of the total energyof the solution, the existence of a scattering state and the principle of limiting absorption, non-uniform
decay with linear dissipation of spatial anisotropy, traveling wave solution and exponential decay of the totalenergy with special Coulomb-type dissipation, spectral analysis of the Schrödinger and wave equation with
non-self-adjoint perturbation of rank 1, uniform resolvent estimate for stationary equation in 2D exterior
domain and their applications to smoothing estimate and the principle of limiting amplitude. We shall also
discuss several unsolved problems.

September 27th (Sat)

Conference Room V

9:00–12:00
40 Hiroyoshi Mitake (Hiroshima Univ.) ∗ Analysis on the large-time behavior by the nonlinear adjoint method:Hung V. Tran (Univ. of Chicago) obstacle problems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Cagnetti, Gomes, Mitake and Tran (2013) introduced a new idea to study the large time behavior
for degenerate viscous Hamilton–Jacobi equations. In this talk, we apply the method to study the large-time
behavior of the solution to the obstacle problem for degenerate viscous Hamilton–Jacobi equations. We
establish the convergence result under rather general assumptions.

41 Hiroyoshi Mitake (Hiroshima Univ.) ∗ Weakly coupled systems of the infinity Laplace equations: existence,
Hung V. Tran (Univ. of Chicago) uniqueness, comparison with generalized cones · · · · · · · · · · · · · · · · · · · · · 10
Summary: We derive the weakly coupled systems of the infinity Laplace equations via a tug-of-war gameintroduced by Peres, Schramm, Sheﬃeld, and Wilson (2009). We establish existence, uniqueness results ofthe solutions, and introduce a new notion of “generalized cones” for systems. By using “generalized cones”
we analyze blow-up limits of solutions.

Created: 2014/08/12 08:45
45

Functional Equations

42 Masashi Aiki (Tokyo Univ. of Sci.)(Keio Univ.)
Tatsuo Iguchi

Motion of a vortex filament in an external flow · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a nonlinear model equation describing the motion of a vortex filament immersed in
an incompressible and inviscid fluid. In the present problem setting, we also take into account the eﬀectof external flow. We prove the unique solvability, locally in time, of an initial value problem posed on the
one-dimensional torus. The problem describes the motion of a closed vortex filament.

43 Okihiro Sawada(Gifu Univ.) ∗ On the shear flows of the Euler equations · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The nonstationary incompressible inviscid flow of ideal fluids in the whole space is considered.
This is described as the Cauchy problem of the Euler equations. The mathematical meaning of the shear flow
and its application are discussed. It is proved that the shear flow is a unique global-in-time strong solution
in certain class due to the argument of renormalization solutions. The proof is based on the boundedness ofthe solutions to the linear transport equation, component-wisely.

44 Tsuyoshi Yoneda (Tokyo Tech)
Gerard Misiolek (Univ. of Notre Dame)

1
Local ill-posedness of the Euler equations in B∞,1
· · · · · · · · · · · · · · · · · · 10

Summary: We show that the incompressible Euler equations are not locally well-posed in the sense of1. Our approach relies on the technique of Lagrangian deformations ofHadamard in the Besov space B∞,1
1
leads
Bourgain and Li. We show that the assumption that the data-to-solution map is continuous in B∞,1
1,pto a contradiction with a well-posedness result in W
of Kato and Ponce.

45 Erika Ushikoshi (Tamagawa Univ.) ∗ Hadamard variational formula for the eigenvalue of the Stokes equations
Shuichi Jimbo (Hokkaido Univ.) with the Dirichlet boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider the eigenvalue problem of the Stokes equations in a bounded domain. Under thedomain perturbation keeping its topological type, we establish the Hadamard variational formula for the
eigenvalues of the Stokes equations with the Dirichlet boundary condition. Our result covers the case whenthe eigenvalue has multiplicity.

46 Ken Abe(Nagoya Univ.) ∗ On estimates for the Stokes flow in a space of bounded functions · · · · · 10

Summary: We consider the composition operator S(t)P∂ for the Stokes semigroup S(t) and the Helmholtz
projection P in a space of bounded functions. It is well known that this composition plays a fundamentalrole for studying the nonlinear Navier–Stokes equations on Lp . The situation is diﬀerent for the case p = ∞since in this case the Hemlholtz projection does not acts as a bounded operator anymore. In this talk, weshow that some a priori estimate is valid for the composition operator on a space of bounded functions.

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

On local well-posedness of incompressible two-phase flows with phasetransitions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The basic model for incompressible two-phase flows with phase transitions where the interface
is nearly flat in the case of non-equal densities is considered. The local well-posedness of the model in
Lp -setting was proved by Prüss and Shimizu. We prove local well-posedness of the model Lp in time Lq in
space setting.

Created: 2014/08/12 08:45
46

Functional Equations

48 Hirokazu Saito (Waseda Univ.)
Yoshihiro Shibata (Waseda Univ.)

Global well-posedness of a free boundary problem for the Navier–Stokes
equations in the Lp -Lq framework · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we show the global well-posedness of a free boundary problem for the Navier–Stokes
equations in the Lp -Lq framework, and large time behavior of solutions. There are many results about
free boundary problems for the Navier–Stokes equations in the L2 -L2 framework, and also in the Lp -Lpframework more generally. On the other hand, the Lp -Lq framework will be used in our argument. We notethat it is essential to control integrability of solutions with respect to time t.

49 Takayuki Kubo (Univ. of Tsukuba)
Yoshihiro Shibata (Waseda Univ.)

Maximal Lp -Lq regularity of the compressible-incompressible two phaseproblem, without surface tension and phase transition case · · · · · · · · · · 10

Summary: We consider the compressible-incompressible viscous two phase problem without surface tension
and phase transition case. In this talk, we would like to report Maximal Lp -Lq regularity of our problem.
The essential point of our proof is to show the existence of R-boundedness of solution operator to theresolvent problem corresponding to our problem.

50 Takayuki Kubo (Univ. of Tsukuba)
Yoshihiro Shibata (Waseda Univ.)

Local and global well-posedness of the compressible-incompressible twophase problem, without surface tension and phase transition case · · · · 10

Summary: We consider the compressible-incompressible viscous two phase problem without surface tension
and phase transition case. In this talk, we would like to report local and global well-posedness of ourproblem. Our proof is based on Banach’s fixed point theorem and maximal Lp − Lq estimate of linearlized
problem corresponding to our problem.

51 Miho Murata (Waseda Univ.)
Yoshihiro Shibata (Waseda Univ.)

On the global well-posedness for a compressible viscous fluid flow · · · · 10

Summary: We show a global in time unique existence theorem for a compressible viscous fluid flow with aslip boundary condition in the Lp in time and Lq in space framework with 2 < p < ∞ and N < q < ∞under the assumption that the domain is bounded and initial data are small. Kobayashi and Zaja̧czkowski
proved the global well-posedness for a compressible viscous fluid flow with slip boundary condition in theL2 framework. One of the merits of our approach is less regularity on initial data.

52 Yasunori Maekawa (Tohoku Univ.)

Large time asymptotics for two-dimensional exterior flows with small
circulation at infinity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the incompressible Navier–Stokes equations in a two-dimensional exterior domain Ω,with no-slip boundary conditions. Our initial data are of the form u0 = αΘ0 + v0 , where α ∈ R and Θ0 is
the Lamb–Oseen vortex with unit circulation at infinity, and v0 is a solenoidal perturbation belonging to
L2 (Ω)2 . When |α| is suﬃciently small we show that the solution behaves asymptotically in time like theself-similar Lamb–Oseen vortex with circulation α. This is a global stability result, in the sense that the
perturbation v0 can be arbitrarily large.

Created: 2014/08/12 08:45
47

Functional Equations

53 Toshiaki Hishida (Nagoya Univ.) ♭ Stability of time-dependent Navier–Stokes flow and algebraic energy
Maria Schonbek
decay · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
(Univ. California, Santa Cruz)
Summary: Specific decay rates of energy of disturbance around time-dependent NS flow are discussed.

14:15–16:15
54 Itsuko Hashimoto(Toyama Nat. Coll. of Tech.)

Asymptotic stability of rarefaction wave of radially symmetric solutions
for Burgers equation in several space dimensions · · · · · · · · · · · · · · · · · · · 10

Summary: We present recent results on large-time behavior of the radially symmetric solution for Burgers
equation on the exterior of a ball in multi-dimensional space, where boundary data at the far field areprescribed.
In this talk, we prove that for radially symmetric solution to the Burgers equation on multi-dimensional
space, the asymptotic states are classified into four cases.
The proof is given by a standard L2 energy method.

55 Shouta Enomoto (Kyushu Univ.)
Yoshiyuki Kagei (Kyushu Univ.)

On linearized stability of stationary solutions to the compressible
Navier–Stokes equation in a periodic layer · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the stability of stationary solutions to the compressible Naver–Stokes equation in aperiodic layer of R3 . There exists a spatially periodic stationary solution if the external force is spatiallyperiodic and is suﬃciently small in some Sobolev space. We show that the linearized semigroup decays in1
the L2 -norm in the order t− 2 if the initial data belongs to L1 and L2 . Furthermore, it is shown that theasymptotic leading part of the semigroup is given by a 2-D heat semigroup.

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

Decay property for the Timoshenko system with thermal eﬀects: Cattaneo versus Fourier’s law · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the Timoshenko system with thermal eﬀects in the one-dimensional whole space. We
investigate the dissipative structure of the system and derive the optimal L2 decay estimate of the solutions
in a general situation. Our decay estimate is based on the detailed pointwise estimate of the solutions in
the Fourier space and we observe that the decay property is of the regularity-loss type.

57 Naofumi Mori (Kyushu Univ.)

Global existence and energy decay of solutions of the nonlinear Timoshenko system with memory · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the initial value problem for the nonlinear Timoshenko system with a memory term.
The main purpose is to investigate the global existence and the optimal decay of the solutions to thenonlinear problem by employing L2 energy method. Y. Liu and S. Kawashima (2013) showed them by
employing a time-weighted L2 energy method. We show that they can be proved without employing atime-weighted L2 energy method under less assumptions on the initial data than those which were neededin Y. Liu and S. Kawashima (2013).

Created: 2014/08/12 08:45
48

Functional Equations

58 Kentarou Fujie (Tokyo Univ. of Sci.)
Michael Winkler (Univ. Paderborn)
Tomomi Yokota (Tokyo Univ. of Sci.)

Blow-up prevention by logistic sources in a parabolic-elliptic Keller–
Segel system with singular sensitivity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This talk is concerned with the parabolic-elliptic Keller–Segel system with singular sensitivity χv0
and logistic source ru − µu2 in a smoothly bounded domain Ω ⊂ R2 , where χ > 0, r ∈ R, µ > 0. It is shownthat in this two-dimensional setting, the absorptive character of the logistic kinetics is suﬃcient to enforce
global existence of classical solutions even for arbitrarily large χ0 > 0 and any µ > 0 and r ∈ R. It is
moreover shown that if in addition r > 0 is suﬃciently large then all these solutions are uniformly bounded.

59 Kentarou Fujie (Tokyo Univ. of Sci.)

Boundedness in a fully parabolic chemotaxis system with singular sensitivity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This talk deals with a fully parabolic chemotaxis system with singular sensitivity χv0 . The main
result solves the open problem that the solution is uniform-in-time bounded for suﬃciently small χ0 > 0,
which was conjectured by Winkler (2011).

60 Sachiko Ishida (Tokyo Univ. of Sci.)

Global existence for a 2D quasilinear chemotaxis-Navier–Stokes systemwith rotation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We deal with a degenerate chemotaxis-Navier–Stokes system with rotation on a bounded domain
in 2 dimension. As to the known result, Tao–Winkler (2012) proved global existence and boundedness in achemotaxis-Stokes system with arbitrary porous medium diﬀusion. This talk extends the result for global
existence of weak solutions to that for a chemotaxis-Navier–Stokes system with rotation.

61 Masanari Miura (Kyushu Univ.)
Yoshie Sugiyama (Kyushu Univ.)

On uniqueness theorem on weak solutions to the parabolic-parabolic
Keller–Segel system of degenerate and singular types · · · · · · · · · · · · · · · 10

Summary: In this talk, we shall bring a focus onto the parabolic-parabolic and parabolic-elliptic Keller–Segelsystems of the singular and degenerate types and show uniqueness of weak solutions in the class of Hoelder
continuous functions.

62 Noriko Mizoguchi(Tokyo Gakugei Univ.)

A new proof to finite-time blowup in the parabolic-parabolic Keller–
Segel system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It has remained open for several decades whether finite-time blowup is a generic feature in theparabolic-parabolic Keller–Segel system in two dimensional domains. An aﬃrmative answer was recently
given by the speaker and Winkler. However their proof cannot work in the degenerate Keller–Segel systemin the higher dimensions. In this talk, we give a new proof to their theorem which can be applied also tosuch a case.

Created: 2014/08/12 08:45
49

Functional Equations

63 Noriko Mizoguchi(Tokyo Gakugei Univ.)
Philippe Laurençot(Univ. de Toulouse / CNRS)

Finite-time blowup for the parabolic-parabolic Keller–Segel system withcritical diﬀusion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It is known that a similar phenomenon to that in the two-dimensional Keller–Segel system appears
in the parabolic-elliptic simplification with degenerate critical diﬀusion in the higher dimensions. One cantake the same approach for the global existence of solution even in the parabolic-parabolic system. However
there have been no results on the existence of solutions blowing up in finite time in the parabolic-parabolic
system. In this talk, we give a criterion for finite-time blowup to initial data and then show that the criterion
is satisfied by a large class of initial data.

16:30–17:30

Talk Invited by Functional Equations Section

Kotaro Tsugawa (Nagoya Univ.)

Local well-posedness for fifth-order nonlinear dispersive equations

Summary: We consider the Cauchy problem for fifth order dispersive equations on the torus. We assume
that the nonlinear part is a polynomial of u, ∂x u, ∂x2 u and ∂x3 u and does not include any constants and linear
terms. The equations include the fifth order KdV equation, the fifth order modified KdV equation andsome equations in physics. In this talk, we discuss on conditions to the nonlinear terms. We first give anecessary and suﬃcient condition for the local well-posedness when the initial data is suﬃciently smooth.
Next, we show the local well-posedness with low regularity initial data when the nonlinear term satisfy acancellation property. In both studies, the main diﬃculty comes from the derivative loss in the nonlinear
terms. Remark that the linear part does not have any smoothing eﬀect since the torus is compact. It seems
diﬃcult to show the well-posedness by the standard energy method or the standard fixed point argument
when the nonlinear part include ∂x2 u or ∂x3 u. To avoid the diﬃculty, we combine the energy method andthe normal form reduction in the first result and combine the fixed point argument and the normal form
reduction in the second result.

September 28th (Sun)

Conference Room V

9:00–12:00
64 Takashi Kagaya (Hokkaido Univ.)

A local existence on a free boundary problem for quasilinear parabolic
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove a local existence on a free boundary problem for quasilinear parabolic equation whose
spatial dimension is one. The parabolic equation has Dirichlet and Neumann boundary conditions at eachboundary points. This free boundary problem arises in various applications such as the heat equation andthe curvature flow. If the equation has no lower order term, the local existence on this free boundary
problem is well known. We consider the case for the equation with lower order terms, and examine how the
maximal existence time depends on initial data and lower order terms.

Created: 2014/08/12 08:45
50

Functional Equations

65 Kurumi Hiruko (Tohoku Univ.)

A dynamical aspect of hybrid system describing intermittent androgen
suppression therapy of prostate cancer · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Since a prostate tumor is influenced by androgen, continuous androgen suppression (CAS) therapy
is the most famous therapy of prostate cancer in Japan. However the relapse of tumors often occurs in spiteof under CAS therapy. Recently, clinical studies suggested that intermittent androgen suppression (IAS)
therapy may delay or prevent the relapse. In the IAS therapy, medication is stopped when the size of tumor
decreases less than a lower threshold, and resumed when the size exceeds an upper threshold. We deal witha hybrid system describing IAS therapy and prove mathematically that the size of tumor remains in somebounded interval for any time under IAS therapy.

66 Motohiro Sobajima (Univ. of Salento)
Noboru Okazawa (Tokyo Univ. of Sci.)
Tomomi Yokota (Tokyo Univ. of Sci.)

Existence of solutions to heat equations with singular lower order terms· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we consider the solvability for the Cauchy problem of heat equations in RN (N ≥ 2)with singular lower order terms ∂u/∂t = ∆u − β|x|−2 x · ∇u + c|x|−2 u + f , where β ∈ R, c ≤ (N − 2 − β)2 /4,
u0 is an initial value and f is an inhomogeneous term. We give a result which generalizes the one of Barasand Goldstein (1984) from β = 0 to β ̸= 0 and improves the one of Arendt, Goldstein and Goldstein (2006).

67 Junichi Harada (Akita Univ.) ∗ Blow-up set for a parabolic system equation · · · · · · · · · · · · · · · · · · · · · · · 8
Summary: We discuss blow-up problems for a semilinear parabolic system equation. We characterize theblow-up set by using the zero of solutions.

68 Tomoro Asai (Univ. of Tokyo) ∗ On self-similar solutions to the surface diﬀusion flow equations with
Yoshikazu Giga (Univ. of Tokyo) contact angle boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider the surface diﬀusion flow equation on the half line when the curve is represented
by the graph of a smooth function. We impose two boundary conditions. The first boundary conditionis the contact angle condition and the second boundary condition is the linearized version of the no-flux
condition. We construct a bounded self-similar solution to this problem. We further prove the stability ofthis self-similar solution.

69 Masashi Mizuno (Nihon Univ.) ∗ A singular limit problem of the Allen–Cahn equation with Neumann
Yoshihiro Tonegawa (Hokkaido Univ.) boundary conditions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We study a singular limit problem of the Allen–Cahn equation with Neumann boundary conditions
and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit
energy measures is Brakke’s mean curvature flow with a generalized right angle condition on the boundary.

Created: 2014/08/12 08:45
51

Functional Equations

70 Keisuke Matsuya (Univ. of Tokyo) ♭ Existence of blow-up solutions for a discrete semilinear heat equation
Tetsuji Tokihiro (Univ. of Tokyo)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Existence of blow-up solutions to initial value problems for a discrete analogue of a d-dimensional
semilinear heat equation is investigated. We prove that a parameter α in the partial diﬀerence equation
plays exactly the same role as the parameter of nonlinearity does in the semilinear heat equation. That is,
we prove non-existence of non-blow-up solutions for 0 < α ≤ 2/d, and, for α > 2/d, existence of non-blow-up
solutions for suﬃciently small initial data.

∗
71 Hiroshi Matsuzawa
Spreading speed and sharp asymptotic profiles of solutions in free(Numazu Nat. Coll. of Tech.) boundary problems for nonlinear diﬀusion equations · · · · · · · · · · · · · · · · 10
Yihong Du (Univ. of New England)
Maolin Zhou (Univ. of Tokyo)

Summary: We study free boundary problems of nonlinear diﬀusion equations. For monostable, bistable, andcombustion types of nonlinearities, Du and Lou (to appear in J. Eur. Math. Soc.) obtained a rather
complete description of the long-time dynamical behavior of the problem and revealed sharp transition
phenomena between spreading (u(t, x) → 1 as t → ∞) and vanishing (u(t, x) → 0 as t → ∞). They also
determined the asymptotic spreading speed of the fronts when spreading happens. In this talk, we give amuch sharper estimate for the spreading speed, and we show that the asymptotic profile of solution depends
only on the nonlinearity when spreading happens.

72 Jin Takahashi
Eiji Yanagida(Tokyo Tech)(Tokyo Tech)

Solutions with time-dependent singularities for a semilinear heat equation with absorption · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider a semilinear heat equation with a nonlinear absorption term. It is shownthat if the power of the nonlinearity is in some range, there is no time-dependent singular solution. On
the other hand, in other range, two types of time-dependent singular solutions exist, and any singularity isremovable if it is weaker than the order of the fundamental solution of the Laplace equation.

73 Masakazu Yamamoto (Hirosaki Univ.)
Yuusuke Sugiyama(Tokyo Univ. of Sci.)
Keiichi Kato (Tokyo Univ. of Sci.)

Asymptotic expansion of solutions to the drift-diﬀusion equation withcritical dissipation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The initial value problem for the drift-diﬀusion equation in the whole space is studied. The
dissipation on this equation is given by the half Laplacian. It is proved that the solution to this equation
decays as time variable tends to infinity. Moreover the asymptotic expansion of the solution is established.

∗
74 Kazushige Nakagawa
Global behavior of solutions to degenerate drift diﬀusion system in(Fukushima Univ.) between two critical exponents · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Takayoshi Ogawa (Tohoku Univ.)
Atsushi Kimijima (Tohoku Univ.)

Summary: We are concerned with the time global behavior of solutions to the degenerate drift-diﬀusion
system. Our aim is to classify the global existence of the weak solution and the finite time blow up of thesolution by the initial condition in between two critical exponents.

Created: 2014/08/12 08:45
52

Functional Equations♭
75 Masaki Kurokiba
Two dimensional drift-diﬀusion system in a critical weighted space · · · 10
(Muroran Inst. of Tech.)

Summary: We establish the time local well-posedness of a multi-component parabolic-elliptic drift-diﬀusion
model in two space dimensions in a scaling critical weighted space. In order to show the critical wellposedness, we introduce a refined version of Brezis–Gallouet inequality in term of the Besov space and apply
it to the some weighted estimate in two dimensions.

76 Masaharu Taniguchi (Okayama Univ.)

Convex compact sets in RN −1 give traveling fronts of cooperationdiﬀusion systems in RN · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: This paper studies traveling fronts to cooperation-diﬀusion systems in RN for N ≥ 3. We consider(N − 2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN −1 , and define anequivalence relation between them. We prove that there exists a traveling front associated with a given
surface and that it is asymptotically stable for given initial perturbation. The associated traveling fronts
coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.

77 Takashi Suzuki (Osaka Univ.) ♭ Compactness of 2D normalized Ricci flow orbit —an analytic proof of
Hamilton’s theorem— · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We show compactness of 2D normalized Ricci flow orbit for any compact Riemannian surface
without boundary. Hence if the stationary state admits only the trivial solution, then the non-stationary
solution converges to a constant. This is an improvement of our previous result in 2010.

14:15–16:15
78 Mamoru Okamoto (Shinshu Univ.)
Shuji Machihara (Saitama Univ.)

Remarks on ill-posedness of the Cauchy problem for the Chern–Simons–
Dirac system in one dimension · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider ill-posedness of the Cauchy problem for the Chern–Simons–Dirac system in one spatial
dimension. Bournaveas, Candy, and Machihara proved that local in time well-posedness in H s (R) × H r (R)with −1/2 < r ≤ s ≤ r + 1. We showed well-posedness holds if s and r satisfy |s| < 1/2, r = −1/2 or s = 0,
−1 ≤ r ≤ −1/2. In this talk, we show that these results are optimal in the sense that the Cauchy problem
is ill-posed in H s (R) × H r (R) if s and r do not satisfy these conditions. We deal with both massless andmassive cases for the ill-posedness.

79 Nobu Kishimoto (Kyoto Univ.)

Normal form reduction for the unconditional uniqueness of periodic
nonlinear dispersive equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We study the unconditional uniqueness property for periodic nonlinear dispersive equations by
successive applications of integration by parts in the time variable, which we call Normal Form Reduction(NFR). We first give an abstract framework of infinite NFR scheme, and then apply it to the nonlinear
Schrödinger equations (NLS) with power-type nonlinearities of odd order, a cubic NLS with a derivative in
the nonlinearity, and the modified Benjamin–Ono equation.

Created: 2014/08/12 08:45
53

Functional Equations

80 Hironobu Sasaki (Chiba Univ.) ∗ Remark on the scattering operator for the cubic nonlinear Dirac equation in three space dimensions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We study the scattering operator S for the three dimensional Dirac equation with a cubic
nonlinearity. It has been proved that S can be defined on a neighborhood of 0 in the Sobolev space
H s0 (R3 ; C4 ) for any s0 > 1. We prove that for any M ∈ N and s ≥ max{s0 , M }, there exists someneighborhood U of 0 in the weighted Sobolev space H s,M (R3 ; C4 ) such that S(U ) ⊂ H s,M (R3 ; C4 ).

(Kyoto Univ.)
81 Takahisa Inui
Masahiro Ikeda (Kyoto Univ.)

Remark on the lifespan of solutions and non-existence of local solution
for a nonlinear Schrödinger equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the nonlinear Schrödinger equation with p-th power absolute value nonlinearlity. Let
the initial value λf belong to H s (Rd ) where λ > 0 is a parameter and s = 0 or 1. It is well known that
this is locally well-posed in H s when 1 < p ≤ 1 + 4/(d − 2s). In the case 1 < p ≤ 1 + 4/(d − 2s), we
prove that if λ is suﬃciently large and f ∈ H s has a singularity near the origin, then the H s -solution blows
up in finite time and the lifespan has the upper bound by a polynomial order of λ. In the opposite casep > 1 + 4/(d − 2s), we also prove that if f ∈ H s has a singularity near the origin, then the local H s -solution
does not exist.

82 Kota Uriya(Tohoku Univ.) ∗ Final state problem for a system of nonlinear Schrödinger equations
with three wave interaction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the final state problem for a system of nonlinear Schrödinger equations
with three wave interaction in two dimensions. In our previous study, we constructed a solution of a two
component system which describes the mass transition phenomenon by using the hyperbolic functions. We
show the existence of a solution to a three component system describing the mass transition phenomenon
periodically in time by using the Jacobi elliptic functions.

83 Makoto Nakamura (Yamagata Univ.) ∗ On the Cauchy problem for nonlinear Schrödinger equations in de Sitter
spacetime · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: The Cauchy problem for Schrödinger equations with weighted nonlinear terms is considered. Local
and global solutions are shown in Sobolev spaces.

84 Yuta Wakasugi (Osaka Univ.) ∗ Critical exponent for the Cauchy problem to the weakly coupled damped
Kenji Nishihara (Waseda Univ.) wave system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk, we consider a system of weakly coupled semilinear damped wave equations. We
determine the critical exponent for any space dimensions. We also give estimates of the lifespan of solutions
from above for subcritical nonlinearities.

Created: 2014/08/12 08:45
54

Functional Equations

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

Convergence of hydrodynamical limits for generalized Carleman models· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider a generalized Carleman’s model describing the time evolution of one dimensional
gas composed of two kinds of particles that move parallel to x-axis with constant and equal speeds, either
in the positive x-direction with density u, or in the negative x-direction with density v with initial andhomogeneous boundary conditions. The existence of time global solutions in L1 (0, 1) × L1 (0, 1) and anonlinear diﬀusion limit under the usual parabolic scaling is established for this problem.

86 Kyouhei Wakasa (Hokkaido Univ.) ∗ The lifespan of solutions to nonlinear wave equations with weighted
functions in 1D · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: We consider the initial value problem for nonlinear wave equations with weighted functions in
one space dimension. Kubo & Osaka & Yazici (2013) showed that the solution exists globally in time if theinitial data are odd functions. On the other hand, they showed that the solution blows up in finite time if
the initial data are not odd functions. Also, they have obtained the estimate of the lifespan which is the
maximal existence time of solutions, however the sharpness was not clarified. Our aim in this talk is to get
the sharp upper and lower bounds of the lifespan in such case.

87 Koichi Taniguchi (Chuo Univ.) ∗ Scattering problem for semilinear wave equation with a potential in an
Tsukasa Iwabuchi (Chuo Univ.) exterior domain · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Tokio Matsuyama (Chuo Univ.)
Summary: We consider the scattering problem for the initial-boundary value problem to semilinear wave
equation with a potential in an exterior domain Ω. Here, Ω is a compliment of a convex and compact
obstacle O in R3 . First, we will inform global existence theorems, and then, wave operators and scattering
operators will be constructed.

16:30–17:30

Talk Invited by Functional Equations Section
Shinya Okabe (Tohoku Univ.) ♭ A fourth order parabolic obstacle problem
Summary: In this talk, we show a recent joint work with M. Novaga (Pisa University) on the obstacle
problem for the parabolic biharmonic equation. We let Ω ⊂ RN be a bounded domain with smoothboundary, and we let f : Ω → R be the obstacle function satisfying
f ∈ C 2 (Ω̄),
f <0on ∂Ω.
For an initial datum u0 : Ω → R such thatu0 ∈ H02 (Ω),
u0 ≥ fa.e. in Ω,
we shall consider the following fourth order parabolic obstacle problem:ut (x, t) + ∆2 u(x, t) ≥ 0
ut (x, t) + ∆2 u(x, t) = 0

ininΩ × R+ ,{(x, t) ∈ Ω × R+ | u(x, t) > f (x)},u(x, t) = 0, ∇u(x, t) · ν Ω (x) = 0
u(x, t) ≥ f (x)u(x, 0) = u0 (x)

on
in
in

∂Ω × R+ ,Ω × R+ ,Ω,

where ν Ω denotes the unit outer normal of ∂Ω.
The purpose of this talk is to investigate the regularity properties of solutions to the obstacle problem
via an implicit time discretization. Since our motivation for the problem rose from a geometric obstacle
problem, we wish to mention the geometric obstacle problem.

Created: 2014/08/12 08:45
55

Real Analysis

Real Analysis
September 27th (Sat)

Conference Room I

9:00–11:45
1 Toshikazu Watanabe (Nihon Univ.)
Masashi Toyoda (Tamagawa Univ.)

On fixed point theorems for generalized contractive type mappings inpartially ordered sets · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Nieto and Lopez consider fixed point theorems for contractive mappings in partially orderedsets. On the other hand, Weissinger proved the contractive mapping which include the Banach contraction
mappings. In this paper, we consider fixed point theorems for Weissinger type contractive mappings andKannan mappings in partially ordered sets.

2 Yasunori Kimura (Toho Univ.)

Approximation of a common fixed point of mappings on a complete
geodesic space · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The shrinking projection method is an approximation scheme of a common fixed point of mappings,
and it is known that this method has a kind of rigidness toward the calculation errors. In this talk, we
consider the shrinking projection method with errors in the setting of complete geodesic spaces and discuss
the convergence property of this scheme.

3 Shin-ya Matsushita (Akita Pref. Univ.)(Akita Pref. Univ.)
Li Xu

On Douglas–Rachford method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we are concerned with the Douglas–Rachford method for solving the convex feasibility
problem.

4 Sachiko Atsushiba(Univ. of Yamanashi)

Convergence theorems for nonlinear mappings by Halpern’s type iterations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study Halpern’s type iterations for nonlinear mappings in Banach spaces. Then,
we prove strong convergence theorems for uniformly asymptotically regular nonexpansive semigroups in
Banach spaces. Furthermore, we give some convergence theorems for the nonlinear mappings.

5 Mikio Kato (Kyushu Inst. of Tech.⋆)Takayuki Tamura (Chiba Univ.)

On the uniform non-ℓn1 -ness of direct sums of Banach spaces · · · · · · · · · 15

Summary: We shall characterize the uniform non-ℓn1 -ness of direct sums of Banach spaces.

6 Kiyohisa Tokunaga(Fukuoka Inst. of Tech.)

Proof of integral by parts based on the definition of Riemann integral· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The definite integral is defined as the limit at infinity of sum of sequences. The well-known
theorem of single integral by parts for a 1-variable function is derived from this definition.

Created: 2014/08/12 08:45
56

Real Analysis

7 Jun Kawabe(Shinshu Univ.)

Bounded convergence theorem for distribution-based nonlinear integral
functionals · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce a new notion of the perturbation of nonlinear integral functionals to formulate afunctional form of the convergence theorems for nonlinear integrals in nonadditive measure theory. As its
direct consequences, we obtain the bounded convergence theorems for typical nonlinear integrals, which showthat the autocontinuity of a nonadditive measure is equivalent to the validity of the bounded convergence
theorems for the Choquet, the Sugeno, and the Shilkret integrals as well as their symmetric and asymmetricextensions.

8 Shinya Moritoh (Nara Women’s Univ.)

Ostrowski’s inequality and its discretization · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A comparison of integral and discrete Ostrowski’s inequalities in the plane is considered. An
integral inequality is described by Legendre’s elliptic integrals. A natural discrete analogue of the inequality
is also given. The main point is to find a suitable decomposition of the radius in polar coordinates.

9 Yoshifumi Ito (Univ. of Tokushima⋆) ♭ Laws of natural statistical physics · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: In this paper we propose the laws of natural statistical physics and give the new formulations in
the following three cases :(1) The case where the Schrödinger operator has only the discrete spectrum.
(2) The case where the Schrödinger operator has only the continuous spectrum.
(3) The case where the physical system is composed of particles moving periodically.

10 Yoshifumi Ito (Univ. of Tokushima⋆)

Concept of natural probability · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we study the concepts of natural probability and natural random variable and givethe new formulations.
For a given normalized L2 -function ψ on Rn , (n ≥ 1), we define the orthogonal probability measureψA = χA ψ on the probability space (Rn , Mn , µ) to be a natural probability measure. Here Mn is theσ-additive family of all Lebesgue measurable sets on Rn and µ is the σ-additive measure∫µ(A) = A |ψ(r)|2 dr, (A ∈ Mn ).
We define the vector-valued natural random variable r = r(ω) on a certain probability space Ω(B, P ) whose
probability distribution law is defined by the L2 -density ψ so that the fundamental relation P ({ρ ∈ Ω; r(ρ) ∈A}) = µ(A) holds. Further we study the fundamental properties of these concepts.
Further we study two other cases of these concepts.

Created: 2014/08/12 08:45
57

Real Analysis

12:10–12:30

Presentation Ceremony for MSJ Analysis Prizes 2014

14:15–16:20
11 Hiroki Saito(Saitama Univ.)

Kakeya maximal operator (no dilation) with radial weights on the plane· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider the weighted “small” Kakeya maximal operator is defined to be∫1aKN,w f (x) := sup|f (y)|w(y) dyx∈R w(R) R

where the supremum is taken over all rectangles with sizes a × aN containing x. In this talk, we shall provea∥KN,w
f ∥L2 (w) ≤ C√

log N ∥f ∥L2 (w) ,for a certain radial weight w.

12 Takeshi Iida
(Fukushima Nat. Coll. of Tech.)

Weighted estimates of higher order commutators generated by BM Ofunctions and the fractional integral operator on Morrey spaces · · · · · · 15

Summary: The purpose of this paper is to investigate the weighted estimates of commutators generated by
BM O-functions and the fractional integral operator on Morrey spaces. In particular, the conditions of
indices is the Olsen type conditions. The main result is generalized the Sawano Sugano and Tanaka result
to a weighted setting.

∗
13 Satoko Sugano
On a Calderón–Zygmund operator of higher order Schrödinger type
(Kobe City Coll. of Tech.)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider higher order Schrödinger type operators with nonnegative potentials. We assume
that the potential belongs to the reverse Hölder class which includes nonnegative polynomials. We showthat an operator of higher order Schrödinger type is a Calderón–Zygmund operator.

14 Katsuo Matsuoka (Nihon Univ.)

On the generalization of fractional integrals and λ-CMO spaces · · · · · · 10

Summary: In this talk, we will extend the boundedness of fractional integrals Iα for the non-homogeneous
central Morrey spaces B p,λ (Rn ) over the whole of λ such that −n/p ≤ λ < ∞. In order to show the above,(d)
we will introduce the generalized λ-CMO spaces Λp,λ (Rn ) and the generalized fractional integrals I˜α,d .

15 Yoshihiro Sawano (Tokyo Metro. Univ.) ♭ Atomic decomposition for Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Takeshi Iida
(Fukushima Nat. Coll. of Tech.)
Hitoshi Tanaka (Univ. of Tokyo)
Summary: We propose here a non-smooth decomposition of Morrey spaces. We content ourselves withstating two main decomposition results.

16 Yoshihiro Sawano (Tokyo Metro. Univ.) ♭ Wavelet characterization and modular inequalities for weighted Lebesgue
Mitsuo Izuki (Okayama Univ.) spaces with variable exponent · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Ibaraki Univ.)
Eiichi Nakai
Summary: We consider the wavelet characterization of the space Lp(·) (w) with w ∈ Ap(·) .

Created: 2014/08/12 08:45
58

Real Analysis

17 Fumi-Yuki Maeda (Hiroshima Univ.⋆) ∗ Sobolev and Trudinger type inequalities for potentials of functions in
Yoshihiro Mizuta
grand Musielak–Orlicz–Morrey spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Hiroshima Inst. of Tech.)(Oita Univ.)
Takao Ohno
Tetsu Shimomura (Hiroshima Univ.)
Summary: We define (generalized) grand Musielak–Orlicz–Morrey space on a bounded open set in RN andgive a Sobolev type inequality as well as a Trudinger type inequality for potentials of functions in such
spaces.

18 Fumi-Yuki Maeda (Hiroshima Univ.⋆) ∗ Growth properties of Musielak–Orlicz integral means for Riesz potenYoshihiro Mizuta
tials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Hiroshima Inst. of Tech.)
Tetsu Shimomura (Hiroshima Univ.)
Summary: In this talk we are concerned with growth properties of integral means for Riesz potentials offunctions in Musielak–Orlicz spaces.

16:40–17:40

Talk Invited by Real Analysis Section

Kenichi Mitani (Okayama Pref. Univ.)

On geometrical constants of Banach spaces

Summary: In this talk, we describe some recent results on James constant, von Neumann–Jordan constantand the skewness of Banach spaces. These constants play an important role in the description of various
geometrical structures of Banach spaces. We first discuss James and von Neumann–Jordan constants forabsolute normalized norms. We also exhibit some connections between the skewness and James constantfor general Banach spaces.

September 28th (Sun)

Conference Room I

9:00–11:50(Kinki Univ.)
19 Akio Ito
Nobuyuki Kenmochi (Bukkyo Univ.)
Yusuke Murase (Meijo Univ.)

Optimal control problems for mathematical model for the process ofbrewing Japanese Sake with unknown terminal time · · · · · · · · · · · · · · · · 15

Summary: Our mathematical model for the process of brewing Japanese Sake is a system of diﬀerential
equations with a constraint condition, and whose terminal time is depend upon the solution self. The
system was solved by Y. Murase and A. Ito in 2013 with putting homogeneous Neumann boundary
conditions and Robin boundary condition for heat equation. Our next objective is optimal control problem
for the model. In this talk, we talk about existence theorem of optimal control and optimal solution
characterized by certain cost function which is corresponding to phenomena.

Created: 2014/08/12 08:45
59

Real Analysis

20 Kentarou Fujie (Tokyo Univ. of Sci.)(Kinki Univ.)
Akio Ito
Michael Winkler (Univ. Paderborn)
Tomomi Yokota (Tokyo Univ. of Sci.)

Global existence and asymptotic behavior of solutions to a model fortumor invasion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with a chemotaxis system modeling tumor invasion in a smoothly bounded domainΩ ⊂ RN , N ≤ 3. This system was recently proposed as a modified tumor invasion model in which therole of an active extracellular matrix is taken into consideration. Moreover, the existence and uniquenessof local-in-time classical solutions to the model was proved in the general case N ∈ N. This talk clarifies
boundedness and asymptotic behavior of solutions to the model in the physically relevant case when N ≤ 3.

21 Tomomi Yokota (Tokyo Univ. of Sci.)
Noriaki Yoshino (Tokyo Univ. of Sci.)

Operator-theoretic approach to a quasilinear nondegenerate parabolicelliptic Keller–Segel system with growth term · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with the chemotaxis system with nonlinear diﬀusion and superlinear growth termf (b) = |b|α−1 b when n ≤ 3. It is shown that if α ≤ 4 (n = 1), α < 1 + n4 (n = 2, 3), then there exists
a local solution to this system for any large data. In the case of Lipschitz growth, Marinoschi (J. Math.
Anal. Appl. 2013; 402: 415–439) established the existence of local solutions to this system with suﬃciently
small initial data and showed that under a stronger assumption on the chemotactic sensitivity there exists a
global solution with large initial data. This talk develops the local solvability with Lipschitz growth to theone with superlinear growth and allows the system to have a local solution with large initial data without
any stronger assumption. The key to including the superlinear growth lies in the Yosida approximation off.

22 Shoji Shimizu (Waseda Univ.)
Mitsuharu Ôtani (Waseda Univ.)

The solvability of complex Ginzburg–Landau equation focusing onparabolicity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The main purpose of this talk is to study Cauchy problem for complex Ginzburg–Landau equation(CGL) by focusing on its parabolicity. In former studies, (CGL) is always treated as a single equation overcomplex spaces. However in this approach, one can not make most use of the parabolicity of (CGL). So
here we regard the real part of (CGL) as the principal part governed by the subdiﬀerential operator and thepure imaginary part as its perturbations. By this approach we can show a new smoothing eﬀect of (CGL)
which ameliorates former results.

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

Global 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 in some porous medium. In our previous works, it has already been showed that there exist a
unique global solution of this system under the homogeneous Dirichlet or Neumann boundary condition.
In this talk, we discuss the existence of global attractor of the system. Especially, for the homogeneous
Neumann boundary condition case, we need some restriction on the external forces and mass of the initial
data. We focus on the diﬀerences between two cases, i.e. Dirichlet and Neumann boundary condition cases.

Created: 2014/08/12 08:45
60

Real Analysis

24 Yutaka Tsuzuki (Tokyo Univ. of Sci.)

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

Summary: This talk is concerned with a system of heat equations with hysteresis and Navier–Stokes equations
in two-dimensional domains. There are some studies on the system of heat equations and Navier–Stokes
equations in which the temperature (the solution to heat equations) is controlled by obstacle functions. In
this talk, the control of the temperature is precisely described by introducing hysteresis. This talk provides
the existence of solutions along the abstract theory for evolution equations with subdiﬀerential operators.

(Kobe Univ.)
25 Goro Akagi
Giulio Schimperna (Univ. di Pavia)

Doubly nonlinear evolution equations in variable exponent Lebesgue
spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk is concerned with the Cauchy–Dirichlet problem for a doubly nonlinear parabolic
equation involving variable exponents and provides some theorems on existence and regularity of strong
solutions. In the proof of these results, we also analyze the relations occurring between Lebesgue spaces ofspace-time variables and Lebesgue–Bochner spaces of vector-valued functions, with a special emphasis on
measurability issues and particularly referring to the case of space-dependent variable exponents.

26 Toshitaka Matsumoto(Hiroshima Univ.)
Naoki Tanaka (Shizuoka Univ.)

Abstract Cauchy problem for weakly continuous operators · · · · · · · · · · 15

Summary: The abstract Cauchy problem for weakly continuous operators is discussed in a general Banach
space. A class of weakly continuous operators is introduced by using sets of functionals. An existence
theorem for weakly diﬀerentiable solutions and its applications to concrete PDEs are given.

27 Dai Noboriguchi (Waseda Univ.)
Kazuo Kobayasi (Waseda Univ.)

An existence theorem for a nonhomogeneous Dirichlet problem for astochastic scalar conservation law · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the initial-boundary value problem for a randomly forced scalar conservation law
with a multiplicative noise on a bounded convex domain D in Rd : du + div(A(u)) dt = Φ(u) dW (t) in(0, T ) × D, u(0, ·) = u0 (·) on D, u ∼= ub on (0, T ) × ∂D. We introduce a notion of kinetic formulations inwhich the kinetic defect measures on the boundary of a domain are truncated. In such a kinetic formulation
we give a result of uniqueness and existence.

28 Motohiro Sobajima (Univ. of Salento)

Lp -theory for second-order elliptic operators with unbounded coeﬃcients in an endpoint class · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The m-accretivity and m-sectoriality of the minimal and maximal realizations of second-order
elliptic operators of the form Au = −div(a∇u) + F · ∇u + V u in Lp (RN ) are shown, where the coeﬃcientsa, F and V are unbounded. The result may be regarded as an endpoint assertion of my previous result in2012 and an improvement of that in Metafune et al. (2010). Moreover, an Lp -generalization of a self-adjoint
problem posed by T. Kato in 1981 is also discussed.

Created: 2014/08/12 08:45
61

Real Analysis

14:15–15:40
29 Hiroshi Watanabe (Salesian Polytech.)
Ken Shirakawa (Chiba Univ.)

Large time behavior for mathematical models of grain boundary motions
involving isothermal solidifications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider coupled systems of Allen–Cahn type equations and PDE models of grain boundary
motions. In this light, these systems can be regarded as interactive mathematical models of the grainboundaries motions under isothermal solidifications. In this talk, we discuss the large time behaviorof solutions to our systems. Moreover, we also mention about some improvements to approximatingarguments, associated with the Γ-convergence of governing energies.

30 Ken Shirakawa (Chiba Univ.)
Hiroshi Watanabe (Salesian Polytech.)

Energy-dissipative solutions to models of grain boundary motions underisothermal solidifications · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider parabolic type systems of the ϕ-η-θ model, that is known as a phase-fieldmodel of grain boundary motion under an isothermal solidification. The main objective is to confirm thereproduction ability of the smoothing eﬀect and energy-dissipation in our systems. With this view, the main
results will be concerned with the existence of special kind of solution, called energy-dissipative solution.
Although each of our systems has specific diﬃculties in mathematics, the main results are proved on thebasis of the time-discretization for a common approximating problem. As a consequence, we provide a
uniform finding method for energy-dissipative solutions to wide scope of nonstandard parabolic systems,
associated with the ϕ-η-θ model.

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

Singular limit of Allen–Cahn equation with constraints and its Lagrange
multiplier · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the Allen–Cahn equation with constraint. Our constraint is the subdiﬀerential of
the indicator function on the closed interval, which is the multivalued function. In this talk we give thecharacterization of the Lagrange multiplier to our equation. Moreover, we consider the singular limit of oursystem and clarify the limit of the solution and the Lagrange multiplier to our problem.

32 Takeshi Fukao (Kyoto Univ. of Edu.)
Pierluigi Colli (Univ. di Pavia)

Cahn–Hilliard equation with dynamic boundary conditions and massconstraints on the boundary · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The well-known Cahn–Hilliard equation has the structure of the mass conservation under thesuitable boundary condition. In the case when the equation is treated with the dynamic boundary
condition, the total mass on the inside of the domain and its trace on the boundary should be conserved.
The new issue is the setting of the mass constraint on the boundary. The eﬀet of this additional constraint
is characterized by the Lagrange multiplier, that is, there are two Lagrange multipliers, one is for the insideof the domain, the other is for the boundary.

Created: 2014/08/12 08:45
62

Real Analysis

33 Toyohiko Aiki (Japan Women’s Univ.)
Yusuke Murase (Meijo Univ.)

Large time behavior of a solution to the free boundary problem describing adsorption phenomena · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk we consider the free boundary problem which is a mathematical model for adsorption
phenomena in porous media. On this problem the modeling process was proposed and the well-posedness
was already discussed. Here, under some condition for the growth rate of wetting area we show a resulton large time behavior of a solution to the problem. Also, we can provide some conjectures on the rate ofconvergence of the solution for large time from observations for our numerical results.

16:00–17:00

Talk Invited by Real Analysis Section

Kentarou Yoshii (Tokyo Univ. of Sci.)

On the hyperbolic type linear evolution equations

Summary: Set I := [0, T ]. Let {A(t); t ∈ I} be a family of closed linear operators in a complex Hilbert space
X. Then we consider the abstract Cauchy problem for linear evolution equations of the form(d/dt)u(t) + A(t)u(t) = f (t), t ∈ I,
(ACP)
u(0) = u ∈ Y.
0

Here Y is another Hilbert space, embedded densely and continuously in X.
One of those methods to solve (ACP) depends on the unique existence of evolution operator for (ACP){U (t, s); 0 ≤ s ≤ t ≤ T }.
If the evolution operator for (ACP) is known, then it is expected that the function u(·) given by the Duhamel
formula∫tu(t) := U (t, 0)u0 +U (t, s)f (s) ds
0is a unique solution of (ACP).
Our purpose in this talk is to obtain the suﬃcient condition guaranteeing the existence of evolution operator.

Created: 2014/08/12 08:45
63

Functional Analysis

Functional Analysis
September 25th (Thu)

Conference Room IV

14:15–16:35∗
1 Hiroaki Niikuni
Spectral band structure of periodic Schrödinger operators on generalized(Maebashi Inst. of Tech.) degenerate zigzag nanotubes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we consider periodic Schrödinger operators on the dumbell-like metric graph, which
is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period cell. We
see the relationship between the structure of graph and the band-gap spectrum.

2 Hironobu Sasaki (Chiba Univ.)(Tokyo Tech)
Shoji Shimizu
Akito Suzuki (Shinshu Univ.)

Spectral analysis for mean-field Schrödinger opearators · · · · · · · · · · · · · 10

Summary: We consider a time-dependent Schrödinger operator Ht which appears in recent study for meanfeild analysis of quantum many-body systems. We show some basic spectral properties of Ht .

3 Shougo Ito
Akito Suzuki(Shinshu Univ.)(Shinshu Univ.)

The spectrum of a discrete Schrödinger operator with a non-decaying
potential · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study the spectrum of a discrete Schrödinger operator H = H0 + V on Zd (d ≥ 2)∑with a potential defined by V = v xn =(n,0,...,0), n∈Z |xn ⟩⟨xn | (v > 0). In the case of d = 2, 3, there exists
a positive γd+ such that: (1) if v ≤ γd+ , then the spectrum σ(H) equals [−2d, λ+ ] with some λ+ > 2d; (2) if
v > γd+ , then σ(H) = [−2d, 2d] ∪ [λ− , λ+ ] with some λ+ > λ− > 2d. For d ≥ 4, there exists a positive γd−such that σ(H) = [−2d, 2d] holds if v ≤ γd− .

4 Hiroshi Ito(Ehime Univ.)

The nonrelativistic limit for Dirac operators with a potential diverging
at infinity · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider Dirac operators with a bounded magnetic potential and an unbounded electric
potential diverging at infinity. Under the assumption that the potentials are dilation analytic, resonancesof the operator are defined as eigenvalues of the dilated operator. In this talk we show that if the speedof light goes to infinity (the nonrelativistic limit), resonances of the Dirac operator exist near resonances of
two Pauli operators.

5 Mitsuteru Kadowaki (Ehime Univ.)
Hiroshi Isozaki (Univ. of Tsukuba)
Michiyuki Watanabe (Niigata Univ.)

Asymptotic behavior in far field of the resolvent for wave propagationin two-layered media · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we report a result for asymptotic behavior in far field of the resolvent for wave
propagation in two-layered media of three dimensions. It is well-known that asymptotic behavior in far fieldof the resolvent for wave propagation in homogeneous medium of whole space. Moreover that is very usefulto study obstacle or Schrödinger scattering and inverse scattering problem. However, it was not establishedthat sharp study for asymptotic behavior in far field of the resolvent for wave propagation in two-layered
media because of the existence of refracted (transmitted) waves.

Created: 2014/08/12 08:45
64

Functional Analysis

6 Shinichiro Futakuchi (Hokkaido Univ.)
Kouta Usui (Hokkaido Univ.)

Time-ordered exponential on the complex plane for unbounded operators and Gell-Mann–Low formula · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The time-ordered exponential plays a fundamental role in perturbative calculation. We introduce
a method for constructing the time-ordered exponential on the complex plane for unbounded operators, andits applications to quantum field theory.

7 Daiju Funakawa (Hokkaido Univ.)

Existence of ground states for a Wess–Zumino model · · · · · · · · · · · · · · · 10

Summary: Supersymmetry is a symmetry corresponding to replacing bosons by fermions. We investigate
the Wess–Zumino model which is one of the simplest example of supersymmetric quantum field theory. We
show the existence of the ground state in two diﬀerent cases: where the particles are massive and wherethese are massless.

8 Takahiro Hasebe (Hokkaido Univ.)
Franz Lehner (Graz Univ. of Tech.)

Cumulants for free Lie algebras and Campbell–Hausdorﬀ formula · · · · 15

Summary: We find a relation between cumulants in noncommutative probability and the Campbell–Hausdorﬀ
formula in free Lie algebras. Combinatorics of set compositions (or ordered set partitions) is the main toolin the result.

9 Kenjiro Yanagi (Yamaguchi Univ.)

Uncertainty relations for non-hermitian type · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently Dou and Du obtained several uncertainty rlations for non-hermitian type. We show that
their results can be given as corollaries of our uncertainty relations for generalized metric adjusted skew
informations.

17:00–18:00

Talk Invited by Functional Analysis Section

Tetsu Mizumachi (Kyushu Univ.)

Stability of line solitons for the KP-II equation

Summary: In this talk, we discuss nonlinear stability of line soliton solutions of the KP-II equation. The
KP-II equation is a two dimensional generalization of the KdV equation which takes into account of slow
variations of waves in the transversal direction.
If the perturbation to line solitons are periodic in the transversal direction, the line soliton solution is stablein the same manner as 1-soliton solutions of the KdV equation.
However, with respect to localized transversal perturbations in R2 , the modulating speed and the phase shiftcannot be uniform in the transversal direction. Modulation equations of the local amplitude and the local
phase shift of the crest of the line solitons are described by a system of 1D wave equations with diﬀraction
terms.

Created: 2014/08/12 08:45
65

Functional Analysis

September 26th (Fri)

Conference Room IV

10:00–11:50
10 Ryo Tabata (Hiroshima Univ.)

The behavior of n × n Immanants as n → ∞ · · · · · · · · · · · · · · · · · · · · · · 15

Summary: When λ is a Young diagram, Tλ = max Tλ (A) = maxA≥0 (dλ (A) − det A)/(perA − det A) measures
how large dλ (A) can be on the determinant-permanent line segment. The celebrated permanental dominanceconjecture asserts that Tλ ≤ 1 for all λ. Conjecturally the maximum value is attained by Yn = (n/(n −1)δij − 1/(n − 1)) and we study the behavior of Tλ (Yn ) as |λ| → ∞. We give precise values when λ’s
are hooks, random young diagrams, and limn→∞ T(kn ) (Yn ). We also discuss the relation with Pierce’s
conjecture, which says that the maximum permanent of singular correlation matrices is attained bu Yn .

11 Hideto Nakashima (Kyushu Univ.)

Explicit formula of the basic relative invariants of homogeneous cones· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In a study of homogeneous convex cones, the basic relative invariants play an important role. It
is known that they are obtained inductively as the irreducible factors of Vinberg polynomials (Ishi 2001). In
this talk, we give an explicit formula which calculates the basic relative invariants all at once with Vinberg
polynomials by using data related to the homogeneous cones.

12 Toshihiko Matsuki (Ryukoku Univ.)

Classification of orthogonal multiple flag varieties of finite type · · · · · · 15

Summary: Let G be the split orthogonal group of degree 2n + 1 over an arbitrary field F of characteristic
not 2. In this talk, we classify multiple flag varieties G/P1 × · · · × G/Pk of finite type. Here a multiple flag
variety is called of finite type if it has a finite number of G-orbits with respect to the diagonal action of G
when |F| = ∞.

13 Toshihiko Matsuki (Ryukoku Univ.)

Orbits on orthogonal triple flag varieties · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G be the split orthogonal group of degree 2n + 1 over a field F of characteristic not 2. In thistalk, we describe G-orbits on the triple flag variety M = Fl(α) × Fl(β) × Fl(n) . Here Fl(α) denote the flag
variety consisting of α-dimensional isotropic subspaces in F2n+1 .

14 Atsumu Sasaki(Tokai Univ.)

A Cartan decomposition for Cayley type homogeneous spaces · · · · · · · 15

Summary: We explain how to find an abelian B satisfying G = KBH for Cayley type homogeneous spaces
G/H. Here, K is a maximal compact subgroup of G. We note that G/H is non-symmetric. Then, ourresult gives a kind of generalizations of Cartan decomposition for symmetric spaces to non-symmetric ones.

15 Hideyuki Ishi

(Nagoya Univ.) ∗ Siegel type integral on a regular convex cone · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Laplace transform of a power of the determinant over the cone of positive definite symmetricmatrices is called the Siegel integral. The formula is generalized to integrals over general homogeneous cones
by Gindikin, while the analogous integrals are considered over regular cones of symmetric matrices withprescribed zeros by Roverato. In this talk, we introduce a new class of regular convex cones and consider
the Siegel type integral over the cones, which unifies Gindikin’s and Rovelato’s formulas.

Created: 2014/08/12 08:45
66

Functional Analysis

13:10–14:10

Talk Invited by Functional Analysis Section

Hiroshi Oda (Takushoku Univ.)

Connections between representation theories for real reductive Liegroups and graded Hecke algebras

Summary: The representation theory for real reductive Lie groups G and that for graded Hecke algebras H
are very similar. For example, the Langlands classification for G versus Evens’ classification of irreducible
H-modules, and the Helgason–Fourier transform versus the Opdam–Cherednik transform. In addition
Ciubotaru and Trapa constructed for various classical G functors sending G-modules to modules of thecorresponding H. We unify many parallel objects and phenomenons in two representation theories byintroducing the notion of radial pair s. A radial pair is a pair of a (gC , K)-module and an H-module satisfying
axioms which are formally the same as a generalized Chevalley restriction theorem and a generalized radial
part formula. Related to this we construct three functors sending H-modules to (gC , K)-modules.

September 27th (Sat)

Conference Room IV

9:00–12:00
16 Hiromichi Miyake

On compactness in L1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, we discussed a method of constructing a separated locally convex topology τ on L1
with the assumption that the reference measure is σ-finite. In this talk, we show a characterization ofcompactness for the weak topology of L1 associated with the topology τ and apply similar arguments tostudy some conditions for strong and weak compactness in L1 , respectively. We also discuss (weak) almost
periodicity of linear contractions on L1 .

17 Kazuyuki Wada (Hokkaido Univ.)

Existence of a ground state for a self-interaction model of a complex
scalar field with spacial cut-oﬀ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the Hamiltonian H of a charged scalar field with seif-interaction. Here, we assume
that the mass of boson is just zero. By introducing a spacial cut-oﬀ function, H is realized as a linear
operator on a boson Fock space. Under certain conditions, H is bounded-below, self-adjoint. Moreover, H
has a ground state for arbitrary coupling constants under an infrared regularily condition.

18 Kei Ji Izuchi (Niigata Univ.) ∗ Topological structure of the space of weighted composition operators
Shûichi Ohno (Nippon Inst. of Tech.) between diﬀerent Hardy spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We consider properties related to weighted composition operators boundedly acting from theclassical Hardy space H p to H q for 1 ≤ q < p < ∞. Especially, we shall completely determine pathconnected components in the set of weighted composition operators and explicitly characterize by functiontheoretic properties of analytic self-maps.

19 Shûichi Ohno (Nippon Inst. of Tech.) ∗ Composition operators related to the Dirichlet space · · · · · · · · · · · · · · · 10
Summary: The Hilbert–Schmidtness of composition operators acting between the classical Hilbert Hardy
space and the Dirichlet space is known. We here consider boundedness and compactness of composition
operators acting between their spaces.

Created: 2014/08/12 08:45
67

Functional Analysis

20 Kouhei Izuchi (Yamaguchi Univ.)

Ranks of backward shift invariant subspaces of Hardy space over thebidisk · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let {φn (z)}n≥0 be a sequence of inner functions satisfying that ζn (z) := φn (z)/φn+1 (z) ∈ H ∞ (z)for every n ≥ 0 and {φn (z)}n≥0 has no nonconstant common inner divisors. Associated with it, we havea Rudin type invariant subspace M of H 2 (D2 ). The ranks of M ⊖ wM for Fz and Fz∗ respectively are
determined, where Fz is the fringe operator on M ⊖ wM. Let N = H 2 (D2 ) ⊖ M. It is also proved that therank of M ⊖ wM for Fz∗ equals to the rank of N for Tz∗ and Tw∗ .

21 Yasuyuki Oka(Kushiro Nat. Coll. of Tech.)

A characterization of the tempered distributions supported by a regularclosed set on the Heisenberg group · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will give the characterization of the tempered distributions supported by a regularclosed set on the Heisenberg group by means of the heat kernel method.

22 Shigeru Furuichi (Nihon Univ.)

On bounds for relative operator entropies · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy.
In this talk, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds ofrelative operator entropy.

23 Junichi Fujii (Osaka Kyoiku Univ.)

On basic operator entropies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: As a tangent vector for the geodesics of a certain geometry of positive-definite matrices, relative
entropies for operators were introdused and have been discussed. So I introduce basic entropies for operators(or matrices) corresponding to those in the classical information theory. We observe some good properties
for these entropies.

24 Yuki Seo (Osaka Kyoiku Univ.)

Matrix power means due to Lawson–Lim–Pálfia for 1 < t < 2 · · · · · · · · 10

Summary: For −1 ≤ t ≤ 1, Lim–Pálfia defined a new family of operator power means of positive definite
matrices and subsequently by Lawson–Lim their notion and most of their results extend to the setting of
positive invertible operators on a Hilbert space. Each of these means except t ̸= 0 arises as a unique positive
invertible solution of a non-linear operator equation and satisfies all desirable properties of power arithmetic
means of positive real numbers. The purpose of this talk is to extend the range in which operator powermeans due to Lawson–Lim–Pálfia are defined. We investigate some properties of operator power means fort ∈ (−2, 2)\[−1, 1].

Created: 2014/08/12 08:45
68

Functional Analysis

25 Hiroaki Tohyama(Maebashi Inst. of Tech.)
Hiroshi Isa (Maebashi Inst. of Tech.)
Masatoshi Ito (Maebashi Inst. of Tech.)
Eizaburo Kamei
Masayuki Watanabe(Maebashi Inst. of Tech.)Operator valued α-divergence and noncommutative ratio · · · · · · · · · · · · 15

Summary: Kamei showed some kind of the additivity for relative operator entropy S(A|A ♯t B) = tS(A|B)
for t ∈ [0, 1]. In regard to this, we show some results which have been obtained for operator valued
α-divergence. Recently, we have introduced an notion of noncommutative ratio on the path A ♮w B. In thistalk, we also show some results obtained by applying noncommutative ratio to operator valued α-divergence.

26 Masaru Nagisa (Chiba Univ.)
Albania Nugraha Imam (Chiba Univ.)

Characterization of diagonality of operators · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We can consider Shur product of bounded linear operators on a Hilbert space. Using this product,
we have already get the condition for an operator, which implies its diagonality. In this talk, we consider
the algebra B(ℓp , ℓq ) (1 ≤ q ≤ p ≤ ∞) of bounded linear operators which has a usual product (compositionof maps) and a Schur product, and has two structures as a Banach algebra. So we can also consider thesimilar condition of an operators in B(ℓp , ℓq ), which implies its diagonality.

14:15–16:45∗
27 Kengo Matsumoto
Continuous orbit equivalence of topological Markov shifts and dynami(Joetsu Univ. of Edu.) cal zeta functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
(Chiba Univ.)
Hiroki Matui

Summary: For continuously orbit equivalent one-sided topological Markov shifts (XA , σA ) and (XB , σB ), we
B
A
). We
) and (H̄ B , H̄+directly construct an isomorphism between their ordered cohomology groups (H̄ A , H̄+show that the cocycle functions for the continuous orbit equivalences give rise to positive elements of theirordered cohomology groups, so that the zeta functions of continuously orbit equivalent topological Markov
shifts are related. The set of Borel measures is shown to be invariant under continuous orbit equivalence of
one-sided topological Markov shifts.

28 Yasushi Nagai(Keio Univ.)

Distribution of patches in tilings and properties of spectrum of thecorresponding dynamical systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Tiling is a cover of Euclidean space by tiles such as polygons that overlap only on their borders.
Given a tiling, one can construct a topological dynamical system. This dynamical system is often uniquely
ergodic, namely it admits a unique invariant measure. In this talk we investigate a relation between tilingand the spectrum of this measure theoretic dynamical system. It is known that we can deduce pure discrete
spectrum of this dynamical system from information of distribution of patches in certain tiling. Here a patch
is a configuration that appears in a tiling. In this talk we conversely deduce a property on distribution ofpatches from a spectral property of the corresponding dynamical system.

Created: 2014/08/12 08:45
69

Functional Analysis

29 Takuya Takeishi (Univ. of Tokyo) ♭ Bost–Connes system for local fields of characteristic zero · · · · · · · · · · · · 15
Summary: The Bost–Connes system, which describes the relation between quantum statistical mechanics andclass field theory, was first constructed by Bost and Connes for the rational field, and generalized for arbitrary
number fields by the contribution of many researchers. In this talk, we will introduce a generalization of theBost–Connes sysmtem for local fields of characteristic zero, and introduce some properties.

30 Yuhei Suzuki (Univ. of Tokyo)

Amenable minimal Cantor systems of free groups arising from diagonal
actions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study amenable minimal Cantor systems of free groups. We show for every free group,(explicitly given) continuum many Kirchberg algebras are realized as the crossed product of an amenable
minimal Cantor system of it. In particular this shows there are continuum many Kirchberg algebras suchthat each of which is decomposed to the crossed products of amenable minimal Cantor systems of any
virtually free group. We also give computations of K-groups for the diagonal actions of the boundary action
and the odometer transformations. These computations with Matui’s theorem classify their topological fullgroups.

31 Hiroyuki Osaka (Ritsumeikan Univ.)
Tamotsu Teruya (Gunma Univ.)

The Jiang–Su absorption for inclusions of unital C*-algebras · · · · · · · · 15

Summary: In this talk we will introduce the tracial Rokhlin property for an inclusion of separable simple
unital C*-algebras P ⊂ A with finite index in the sense of Watatani, and prove theorems of the following
type. Suppose that A belongs to a class of C*-algebras characterized by some structural property, such as
the Jiang–Su absorption. Then P belongs to the same class. We show that an action α from a finite group
G on a simple unital C*-algebra A has the tracial Rokhlin property in the sense of Phillips if and only if thecanonical conditional expectation E : A → AG has the tracial Rokhlin property for an inclusion AG ⊂ A.

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

Maximal abelian subalgebras of C ∗ -algebras generated by complex dynamical systems and continuous orbit equivalence · · · · · · · · · · · · · · · · · · 15

Summary: We consider a pair of the C ∗ -algebra generated by a complex dynaical system and its maximalabelian subalgebra. We study a relation between isomorphisms of such pairs and continuous orbit equivalence.

33 Yasuo Watatani (Kyushu Univ.)
Masatoshi Enomoto

Relative position of three subspaces in a Hilbert space and Brennertype decomposition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the relative position of three subspaces in a infinite-dimensional Hilbert space. We givea condition that it has a Brenner type decomposition with a finite-dimensional double triangle part.

34 Rui Okayasu (Osaka Kyoiku Univ.)
Reiji Tomatsu (Hokkaido Univ.)

Haagerup approximation property and positive cones associated with avon Neumann algebra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We discuss various definitions of the Haagerup approximation property for an arbitrary von
Neumann algebra. As a consequence, we give a simple and direct proof that the definition given by M.
Caspers and A. Skalski is equivalent to our original one defined by using the standard form. Our strategy is
to use the one-parameter family of positive cones due to H. Araki. This is based on a joint work with Reiji
Tomatsu.

Created: 2014/08/12 08:45
70

Functional Analysis

17:00–18:00

Talk Invited by Functional Analysis Section

Yasuhiko Sato

(Kyoto Univ.) ♭ Classification theorem of C*-algebras and the Toms–Winter conjecture

Summary: In 1989, G. A. Elliott showed that a certain class of amenable C*-algebras can be classified
by their K-groups. Following this success, he initiated the program to classify amenable C*-algebras via
K-theoretic invariants. In his program, it has become necessary to invoke some regularity property of theclassifiable C*-algebras in various manners, after the appearance of pathological examples constructed byVilladsen, Rørdam and Toms.
With the aim of characterizing classifiable C*-algebras, in 2008, Toms and Winter have conjectured thatthe following three fundamental properties are equivalent for all separable, simple, amenable C*-algebras:strict comparison, absorption of the Jiang–Su algebra, and finite nuclear dimension (or finite decomposition
rank for stably finite cases). Recently, this conjecture has attracted a fair amount of attention fromexperts in operator algebras. Actually, it is known that an aﬃrmative answer to this conjecture induces
a solution of Rosenberg’s conjecture and also of the Blackadar–Kirchberg conjecture, which are concernedwith quasidiagonality of amenable C*-algebras.
In my talk, I report on the recent progress of the Toms–Winter conjecture and its application to theclassification theorem for amenable C*-algebras.

Created: 2014/08/12 08:45
71

Statistics and Probability

Statistics and Probability
September 25th (Thu)

Conference Room VII

9:30–11:50
1 Takahiro Hasebe (Hokkaido Univ.)
Steen Thorbjørnsen (Univ. of Aarhus)

Unimodality of freely selfdecomposable distributions · · · · · · · · · · · · · · · · 15

Summary: We show that any freely selfdecomposable probability distribution is unimodal. This is the freeprobabilistic analog of Yamazato’s result in [Ann. Probab. 6 (1978), 523–531].

2 Isamu Dôku(Saitama Univ.)

Construction of probabilistic solutions to a class of deterministic integral
equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider a class of deterministic nonlinear integral equations. We begin with constructing abranching model, define a star-product and construct a tree-based star-product functional. By stydying
mathematical structure of the functional, we prove that the function given by expectation of the functionalwith respect to the law of a branching process satisfies the original integral equations.

3 Keita Owari(Univ. of Tokyo)

On the Lebesgue property of monotone convex functions on Orlicz-likespaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In financial mathematics, it is known as Jouini–Schachermayer–Touzi’s theorem that for any
convex risk measure on L∞ with the σ-additive dual representation, (1) the Lebesgue property (ordercontinuity), (2) the weak compactness of sublevels of the conjugate on L1 and the attainment of thesupremum in the dual representation are equivalent. We provide a couple of generalization of this result
which applies to any finite-valued monotone convex function on a lattice ideal of L0 (including all Orlicz
spaces) forming a dual pair with its order-continuous dual space with slightly diﬀerent a priori lower
semicontinuity assumptions and the choice of penalty function.

4 Go Yuki(Ritsumeikan Univ./JST CREST)

Consistency of the positive semi-definite Fourier type estimators · · · · · 10

Summary: To estimate volatilities of d-dimensional Itô semi-martingales, Malliavin and Mancino proposed
Fourier series type estimators composed of the finite observations of d-dimensional Itô semi-martingale.
Recently, Akahori et al. introduced Fourier series type estimators which are positive semi-definite. We
discuss about the consistency of these positive semi-definite Fourier type estimators for the volatility.

Created: 2014/08/12 08:45
72

Statistics and Probability

5 Shigeyoshi Ogawa (Ritsumeikan Univ.)

A direct inversion formula for natural SFT · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We are concerned with the question whether and how a random function f (t, ω) is determinedby its image of a stochastic transformation called SFT (stochastic Fourier transformation) T∗ f (t, ω), which
was introduced by the author in 1990, in the study of stochastic integral equation of Fredholm type. The
question of inversibility of the SFT has been studied again in the framework of homogeneous chaos andsome aﬃrmative answers as well as the inversion schemes were given (cf. Ogawa 2013, Ogawa–Uemura 2013,2014). In this talk, by limitting ourselves to the case of causal functions and trigonometric basis, we are toshow an elementary approach to the question, an approach that does not rely on the homogeneous chaos
framework, and give a direct formula for the inversion of the natural SFT.

∗
6 Hiroya Hashimoto
A note on convergence rates for stability problems of SDEs under(Sanwa Kagaku Kenkyusho Co.) Nakao–Le Gall condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Takahiro Tsuchiya (Univ. of Aizu)

Summary: We consider the stability problems of one dimensional stochastic diﬀerential equations when thediﬀusion coeﬃcients satisfy the so called Nakao–Le Gall condition. A bounded rate of strong convergencein the sense of L1 are given by the Yamada–Watanabe method.

7 Hideki Tanemura (Chiba Univ.)
Hirofumi Osada (Kyushu Univ.)

Infinite-dimensional stochastic diﬀerential equations arising from Airyrandom point fields · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We identify infinite-dimensional stochastic diﬀerential equations (ISDEs) describing the stochastic
dynamics related to Airy random point fields with β = 1, 2, 4. We prove the existence and uniqueness of the
ISDEs.

8 Hideki Tanemura (Chiba Univ.)
Hirofumi Osada (Kyushu Univ.)

Strong solutions of infinite-dimensional stochastic diﬀerential equations
and tail σ-fields · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We present a new method to construct unique strong solutions of infinite-dimensional stochastic
diﬀerential equations (ISDEs) describing interacting Brownian motions (IBMs). Our method can be applied
to IBMs related to random matrix theory.

9 Takafumi Amaba (Ritsumeikan Univ.)

An integration by parts on space of loops · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider to construct a measure on space of loops in C∗ (strictry speaking, a space of paths
in a coeﬃcient body), surrounding the origin by employing the utility of the (alternate) Loewner–Kufarev
equation. We discuss about a simple integration by parts formula under the measure.

(Kyoto Univ.)
10 Kouji Yano
Yuko Yano (Kyoto Sangyo Univ.)

Renormalized zero resolvents for one-dimensional diﬀusions · · · · · · · · · · 15

Summary: For a one-dimensional diﬀusion on an interval for which 0 is the regular reflecting left boundary,
the renormalized zero-resolvent, denoted by h0 , is studied. It is reported that, for the process stopped uponhitting 0, the function h0 is excessive and the h0 -transform can be regarded as a conditional process to avoidzero.

Created: 2014/08/12 08:45
73

Statistics and Probability

14:15–15:15

Talk Invited by Statistics and Probability Section

Atsushi Takeuchi (Osaka City Univ.)

Integration by parts formula for jump processes

Summary: It is well known that the Malliavin calculus is a powerful tool in stochastic analysis, and theintegration by parts formula plays a crucial role in the argument. Most of works concern only diﬀusion
processes without any jumps. Although it is a natural question whether a similar approaches can be taken
in case of jump processes, there are a lot of diﬀuculties to do it. Moreover, there are some approaches to theMalliavin calculus for jump processes, depending on the interests. In this talk, we shall give a brief review
of some recent results concerning the integration by parts formula for jump processes.

15:30–16:30

Talk Invited by Statistics and Probability Section

Hiroki Takahashi (Keio Univ.) ∗ On the destruction of Smale’s horseshoe in the Henon map (and whatcomes afterwards)
Summary: An important problem in dynamics (qualitative theory of ordinary diﬀerential equations) is todescribe how Smale’s horseshoe loses its stability through continuous modifications of the system. The
loss of stability of Smale’s horseshoe through homoclinic bifurcations is modeled by a certain parametrizedfamily of planar diﬀeomorphisms, called the Henon maps. I will talk about recent results on the dynamics
of the strongly dissipative Henon maps around the first bifurcation parameter, with special emphasis on
their geometric and probabilistic aspects.

September 26th (Fri)

Conference Room VII

9:30–11:30
11 Masahiro Kobayashi(Tokyo Univ. of Sci.)
Hiroshi Shimizu (Nihon Unisys)
Masakiyo Miyazawa(Tokyo Univ. of Sci.)

Structure-reversibility of a two dimensional reflecting random walk · · · 15

Summary: We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is
assumed that this reflecting random walk has skip free transitions. We are concerned with its time reversed
process assuming that the stationary distribution exists. In general, the time reversed process may not be
a reflecting random walk. In this paper, we derive necessary and suﬃcient conditions for the time reversed
process also to be a reflecting random walk. These conditions are diﬀerent from but closely related to the
product form of the stationary distribution.

12 Izumi Okada(Tokyo Tech)

The inner boundary of random walk range · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We deal with the inner boundary of random walk range, that is, the set of those points in arandom walk range which have at least one neighbor site outside the range. We consider the number of theinner boundary points of random walk range and the question; how many times does a simple random walkrevisit the most frequently visited site among the inner boundary points?

Created: 2014/08/12 08:45
74

Statistics and Probability

13 Naotaka Kajino (Kobe Univ.)
Janna Lierl (Univ. Illinois UC)

Neumann heat kernel estimates on inner uniform domains in pointrecurrent strongly local symmetric Dirichlet spaces · · · · · · · · · · · · · · · · · 15

Summary: For a strongly local regular Dirichlet space arising from a resistance form and with a complete
geodesic metric and a sub-Gaussian type two-sided heat kernel estimate, we present a two-sided estimateof the Neumann heat kernel on inner uniform subdomains in terms of the natural inner geodesic metric ofthe domains. Besides the change of the metric, the Neumann heat kernel estimate involves no diﬀerence
from the global heat kernel estimate. This result is meant mainly for inner uniform domains of fractals
with spectral dimension less than 2 and is applicable to Brownian motion on aﬃned nested fractals and2-dimensional generalized Sierpiński carpets.

∗
14 Christoph Aistleitner
The law of the iterated logarithm for lacunary series with bounded gaps
(Graz Univ. of Tech.) II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
Katusi Fukuyama (Kobe Univ.)

Summary: For every positive number σ, there exists a sequence {nk } of intergers satisfying nk+1 −nk ∈ {0, 1}∑
such that the law of the iterated logarithm forcos(2πnk x) with limsup constant σ holds.

15 Masato Takei (Yokohama Nat. Univ.)

On crossing probabilities for Ising percolation on the triangular lattice· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We consider the percolation problem for spin configurations of the Ising model on the triangularlattice. We derive an RSW-type bound for crossing probabilities when the external field is zero and theinverse temperature is not more than the critical one. As an application, we can obtain power estimatesof the one-arm probability and the two-point connectivity function from below, at the critical inverse
temperature.

16 Seiichiro Kusuoka (Tohoku Univ.)
Hiroshi Takahashi (Nihon Univ.)(Keio Univ.)
Yozo Tamura

Recurrence and transience properties of multi-dimensional diﬀusion
processes in semi-selfsimilar random environments · · · · · · · · · · · · · · · · · · 15

Summary: We consider limiting behaviors of multi-dimensional diﬀusion processes in multi-parameter random
environments, which are sets of values at diﬀerent d points of one-dimensional α-stable or (r, α)-semi-stableLévy processes. They imply conditions of random environments for the dichotomy of recurrence andtransience of multi-dimensional diﬀusion processes formed by d independent one-dimensional diﬀusion
processes in α-stable or (r, α)-semi-stable Lévy processes. Their limiting behaviors are quite diﬀerent
from those of multi-dimensional standard Brownian motions. We also consider a direct product of aone-dimensional diﬀusion process in a reflected non-positive Brownian environment and a one-dimensional
standard Brownian motion. For the two-dimensional diﬀusion process, we show the transience property.

17 Makoto Nakashima (Univ. of Tsukuba)

On the estimates of the free energy of directed polymers in random
environment in 1+2 dimension at high temperature · · · · · · · · · · · · · · · · 15

Summary: We consider the free energy of the directed polymers in random environment in 1+2 dimension.
It is known that the free energy is strictly negative if the inverse temperature β is not zero when spatial
dimension d is 1 or 2. In this talk, we give new bounds of the free energy as β > 0 small.

Created: 2014/08/12 08:45
75

Statistics and Probability

18 Takeyuki Sasai (Univ. of Tokyo)
Kenshi Miyabe (Meiji Univ.)
Akimichi Takemura (Univ. of Tokyo)

A game-theoretic proof of Erdős–Feller–Kolmogorov–Petrowsky law of
the iterated logarithm for fair coin tossing · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We give a game-theoretic proof of the celebrated Erdős–Feller–Kolmogorov–Petrowsky law of theiterated logarithm for fair coin tossing. As many other game-theoretic proofs of the laws in probability
theory, our game-theoretic proof is explicit and gives insights on what happens when the law is violated.

11:45–12:15

Research Section Assembly

September 27th (Sat)

Conference Room VII

9:30–12:00
19 Satoshi Suzuki (Shimane Univ.)
Daishi Kuroiwa (Shimane Univ.)

Surrogate duality and its constraint qualifications · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we study a constraint qualification which completely characterizes surrogate strong
and min-max duality for quasiconvex programming. We show that the closed cone constraint qualification
for surrogate duality is a necessary and suﬃcient constraint qualification for surrogate strong and min-max
duality via quasiconvex programming. Also, we compare our constraint qualification with previous ones for
Lagrange and surrogate duality.

20 Toshiharu Fujita(Kyushu Inst. of Tech.)

Mutually dependent Markov decision processes with associative criteria· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this study, we consider in mutually dependent Markov decision processes (MDMDP) withassociative criteria. The MDMDP model is structured upon finite-stage Markov decision processes. At
each stage, the reward in one decision process is given by the optimal values of other decision process,whose initial state is determined by the current state and decision in the original process. We introduce
an associative criterion to each MDMDP and derive recursive equations by dynamic programming with aninvariant imbedding technique.

21 Yoshihiro Suto (Waseda Univ.)(Waseda Univ.)
Yan Liu
Masanobu Taniguchi (Waseda Univ.)

Parameter estimation by a contrast function based on interpolation
error · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Interpolation is an important issue for a variety of fields in statistics (e.g., missing data analysis).
In this research, the asymptotics of a contrast function estimator defined by pseudo interpolation error for
Gaussian stationary process are investigated. We estimate parameters of the process by minimizing thepseudo interpolation error written in terms of a fitted parametric spectral density and the periodogram
based on observed stretch. The estimator has the consistency and asymptotic normality. Although thecriterion for the interpolation problem is known as the best in the sense of smallest mean square error forpast and future extrapolation, it is shown that the estimator is asymptotically ineﬃcient in general, whichleads to an unexpected result.

Created: 2014/08/12 08:45
76

Statistics and Probability

22 Fumiya Akashi (Waseda Univ.)

On the second-order asymptotic eﬃciency of frequency domain GMM
estimators · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We elucidate the second-order asymptotic properties of frequency domain generalized method of
moments (GMM) estimators for second order stationary processes. The process concerned is essentiallynonparametric one, and we focus on the estimation problem of the pivotal quantity of the process, which
is defined as a solution of over-identified spectral restrictions. The Edgeworth expansion for the GMM
estimator up to second-order is given. We also discuss asymptotic eﬃciency of the GMM estimator bymaking a comparison between the limit distributions of the GMM estimator and a quasi-maximum likelihood
estimator.

23 Yan Liu(Waseda Univ.)

Quantile estimation in frequency domain · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Nowadays, the quantile estimation becomes a notable method in statistics for its robustness
against the existence of moments of random variables. In this talk, we extend the idea of quantile in time
domain to that in frequency domain. The objective function for the quantile estimator in time domain
can be naturally extended into frequency domain. The quantile estimator in frequency domain has theconsistency. However, asymptotic normality of the quantile estimator based on the bare periodogram does
not hold, which is obviously diﬀerent from the quantile theory for time domain. We give the asymptotic
properties of the estimator. The modified estimator for asymptotic normality will also be provided.

24 Koji Tsukuda(Grad. Univ. for Adv. Stud.)
Yoichi Nishiyama(Inst. of Stat. Math./Grad. Univ. for Adv. Stud.)

Testing the time-homogeneity of ergodic stochastic processes by an L2
space approach · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A general approach to test the time-homogeneity of ergodic stochastic process models is presented.
It is based on weak convergences of stochastic integrals taking values in L2 spaces, and it enables us to
use the Anderson–Darling type weight function which cannot be treated by a weak convergence theory formartingales taking values in ℓ∞ spaces. The result is applied to some time-homogeneity testing problems ofergodic diﬀusion processes and stress release models with continuous observations.

25 Yoshihide Kakizawa (Hokkaido Univ.)

Bootstrap-based Bartlett-type adjustment · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For the LR statistic, the Bartlett adjustment is applicable, i.e., a simple mean adjustment throughmultiplication by a constant of the form 1+b/N yields an improvement of the null distribution. On theother hand, the Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared
approximation to the null distributions of various statistics rather than the LR statistic. In this talk, we
propose a bootstrap-based Bartlett-type adjustment, which is an extension of a bootstrap-based Bartlett
adjustment for the LR statistic.

Created: 2014/08/12 08:45
77

Statistics and Probability

26 Yoshihiko Maesono (Kyushu Univ.)

Higher order asymptotic representation of kernel estimator of hazard
function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we obtain an asymptotic representation a kernel type estimator of a hazard function.
The hazard function estimator takes a form of a ratio of two kernel type estimators. The convergence ratesof them are diﬀerent, and so we cannot see an eﬀect of the slow order rate estimator under an ordinal
asymptotic setting. Using the higher order asymptotic representation, we can discuss an eﬀect of the slow
order rate estimator.

27 Hirokazu Yanagihara (Hiroshima Univ.)

On asymptotically KL loss eﬃciency of a log-likelihood-based information criterion in high-dimensional normal multivariate linear regression
models · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: This paper deals with a variable selection procedure in a multivariate linear regression model withnormality assumption, which is called a normal multivariate linear regression model, by minimizing a model
selection criterion. A model selection criterion considered in this paper is a log-likelihood-based information
criterion which is defined by adding a penalty term to the negative twofold maximum log-likelihood. A
purpose of this paper is to clarify a suﬃcient condition of the penalty term in the log-likelihood-based
information criterion to satisfy an asymptotically Kullback–Leibler (KL) loss eﬃciency property from the
HD asymptotic framework, such that (n, p) → ∞ simultaneously under the condition p/n → c0 ∈ (0, 1).
Then, we can study whether AIC, AICc , BIC, CAIC and HQC are asymptotically KL loss eﬃcient or not,when the HD asymptotic framework is used.

28 Takanori Ayano (Osaka Univ.)(Osaka Univ.)
Joe Suzuki

Asymptotic property of MDL information criterion for continuous data
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: It is very important to estimate the probability of the data series accurately for applying MDL
information criterion. For discrete data, it is known that the methods based on universal coding in
information theory have high precision (universal Bayesian measures) and they are used in MDL. Recently,
Ryabko extended the universal Bayesian measures for discrete data to continuous data and one gets to beable to apply MDL for not only discrete data but also continuous data. In this presentation, we give therates of convergence for the generalization error of the universal Bayesian measures for continuous data andshow that they achieve the optimal rate under a certain condition.

Created: 2014/08/12 08:45
78

Statistics and Probability

14:15–15:15

Talk Invited by Statistics and Probability Section

Hironori Fujisawa (Inst. of Stat. Math.)

Divergence-based robust statistics

Summary: Many estimation methods have been proposed for robust statistics. In this talk, some divergecebased methods are discussed. The density power divergence was proposed by Basu et al. (1998). Thisis based on the idea that the density values for outliers are small. The largest characteristic is that thedensity power divergence is easily applicable for any continuous probability density function. The density
power divergence belongs to a separable class of Bregman divergences. Fujisawa and Eguchi (2008) proposed
another type of divergence, which was called the gamma-divergence. This divergence belongs to a larger
class of Bregman divergence. The robust estimator based on the gamma divergence can show a suﬃciently
small latent bias even if the ratio of outlier is not small. This solves an important open problem that has
not been unsolved for a long time. Kanamori and Fujisawa (2014) proposed an extended class of divergencefrom the point of view of aﬃnce invariance of data transformation, which was called the Hölder divergence.
This divergence does not belong to a class of Bregman divergence. Recently, Kanamori and Fujisawa (2014)
pointed out a close relation between the gamma and Hölder divergences by virtue of unnormalized model.

15:30–16:30

Talk Invited by Statistics and Probability Section

Yoichi Miyata(Takasaki City Univ. of Econ.)

On asymptotic properties of Bayesian type estimators

Summary: Roughly speaking, nonstationary processes can be classified into three main groups: (i) nonstationary mixing processes, (ii) processes with deterministic trends, and (iii) unit root processes. In this talk,we will consider general conditions and rather easily verified conditions that ensure asymptotic posterior
normality, strong consistency of the Bayesian type estimators and their asymptotic normality in possibly
misspecified models for stationary processes, (i), and (ii). We will illustrate our main results with aheterogeneous AR model, a Logit model, and a finite mixture model.

September 28th (Sun)

Conference Room VII

9:30–11:20
29 Hidekazu Tanaka (Osaka Pref. Univ.)
Nabendu Pal(Univ. Louisiana at Lafayette)
Wooi K. Lim (William Paterson Univ.)

Some results on gamma parameter estimation · · · · · · · · · · · · · · · · · · · · · 15

Summary: This talk deals with improved estimation of gamma parameters from a decision-theoretic point ofview. First, we study the second order properties of three estimators of shape parameter —(i) the maximum
likelihood estimator (MLE), (ii) a bias corrected version of the MLE, and (iii) an improved version (interms of mean squared error) of the MLE. It is shown that all the three estimators mentioned above aresecond order inadmissible. Also, we obtain second order admissible estimators which are second order better
than the above three estimators. Similarly, in estimating scale parameter, we consider the second orderadmissibilities of some estimators and propose second order admissible estimators.

Created: 2014/08/12 08:45
79

Statistics and Probability

30 Kiyotaka Iki (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Point-symmetric multivariate density function and decomposition · · · · 10

Summary: For a T -variate density function, we define the point-symmetry, quasi-point-symmetry of orderk (< T ) and the marginal point-symmetry of order k, and gives the theorem that the density function is
T -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of orderk. The theorem is illustrated for the multivariate normal density function.

31 Makoto Inokuchi (Hiroshima Univ.)
Hirokazu Yanagihara (Hiroshima Univ.)

Asymptotical comparison with LSE and MLE of coeﬃcient matrices inhigh-dimensional GMANOVA model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper, we asymptotically compare with the least square estimator (LSE) and the maximum
likelihood estimator (MLE) of coeﬃcient matrices in high-dimensional GMANOVA model, when the sample
size n and the number of response variables p simultaneously approach ∞ under the condition thatcn,p = p/n → c0 ∈ [0, 1).

(Univ. of Tsukuba)
32 Aki Ishii
Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

Equality test of covariance matrices in high-dimension, low-sample-size
context · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A common feature of high-dimensional data is the data dimension is high, however, the sample
size is relatively low. We call such data HDLSS data. Ishii et al. (2014) gave an asymptotic distribution of
the largest eigenvalue estimator derived by the noise-reduction methodology that was created by Yata andAoshima (2012). In this talk, we provide an estimator of the first eigenvector by using the noise-reduction
methodology. We show that the estimator enjoys the consistency property in a mild condition. We consider
testing the equality of covariance matrices between two classes and propose a new test statistic by applying
both the largest eigenvalue estimator and the first eigenvector estimator. We verify the proposed test
statistic improves the power as the dimension grows.

33 Ayaka Yagi (Tokyo Univ. of Sci.)
Takashi Seo (Tokyo Univ. of Sci.)

A test for the mean vector with k-step monotone missing data · · · · · · · 15

Summary: We consider the problem of testing the mean vector in one-sample problem when the data havek-step monotone pattern missing observations. Jinadasa and Tracy (1992) obtained closed form expressions
for the maximum likelihood estimators of the mean vector and the covariance matrix of a multivariate
normal distribution with a k-step monotone missing data pattern. We propose a simplified Hotelling’s T 2
type statistic by evaluating the covariance matrix of the maximum likelihood estimator of the mean vector
in the case of a k-step monotone missing data. Further, we give an approximate upper percentile of the T 2
type statistic and investigate the accuracy by Monte Carlo simulation.

Created: 2014/08/12 08:45
80

Statistics and Probability

34 Kazuyoshi Yata (Univ. of Tsukuba)
Makoto Aoshima (Univ. of Tsukuba)

High-dimensional PCA for a mixture model and its applications · · · · · 15

Summary: In this talk, we consider PCA (Principle Component Analysis) for mixture models in highdimension, low-sample-size (HDLSS) settings. We show that the first true eigenvalue, eigenvector and its
PC scores hold consistency properties when the underlying distribution has a two-class mixture model.
Next, we derive a geometric representation of the dual sample covariance matrix constructed by HDLSS
data from the mixture model. With the help of the geometric representation, we propose a new clustering
method for a high-dimensional mixture distribution. Finally, we extend the clustering method to a generalcase when three or more classes are mixed.

35 Masato Naganawa (Tokyo Univ. of Sci.)
Kouji Tahata (Tokyo Univ. of Sci.)
Sadao Tomizawa (Tokyo Univ. of Sci.)

Extended linear asymmetry model for square contingency tables withordered categories · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The issues of various symmetry rather than independence arise naturally for the analysis of squarecontingency tables. So the models, that indicate the structure of symmetry and asymmetry, have been
proposed, for example, the symmetry model (Bowker, 1948), the quasi-symmetry model (Caussinus, 1965),
and the marginal homogeneity model (Stuart, 1955). In this talk, we propose the models that indicate thestructure of asymmetry. The model includes various symmetry and asymmetry models in the special cases.
An example is given.

14:15–16:10
36 Masanori Sawa

(Kobe Univ.)

Developing the theory of designs on measure spaces, I · · · · · · · · · · · · · · 15

Summary: In this talk, I introduce the notion of cubature formulas or designs on measure spaces, generalizing
various related objects in statistical experiments, numerical analysis, and algebraic combinatorics. Many
examples will be given emphasizing how general our notion is. The idea of cubature on measure spaces
originally goes back to an outstanding work by Kôno in 1962 on the construction of optimal experimental
designs on the cube.

37 Masatake Hirao (Aichi Pref. Univ.)
Masanori Sawa (Kobe Univ.)

Characterizing optimum designs in terms of finite irreducible reflectiongroups, II · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we give a geometric characterization of D-optimal experimental designs on the unit
ball that consist of corner vectors associated with finite irreducible reflection groups An and Dn .

38 Kohei Yamada (Nagoya Univ.)

Some results related to a remark of Graham and Lovász · · · · · · · · · · · · 10

Summary: Let G be an undirected connected graph without loops and multiedges, and let n+ (G) and n− (G)be the number of positive and negative eigenvalues, respectively, of the distance matrix of G. Graham andLovász [Adv. in Math., Vol.78, 1978] posed a problem of whether there exists a graph with n− (G) < n+ (G).
Recently, Azarija [Discrete Math.,315-316, pp.65–68, 2014] proved that the Paley graph of order at least 13
is such an example. In this talk, I present some observations on graphs with n+ (G) = n− (G).

Created: 2014/08/12 08:45
81

Statistics and Probability

39 Shoko Chisaki (Tokyo Univ. of Sci.)
Nobuko Miyamoto (Tokyo Univ. of Sci.)

Diﬀerence systems of sets with size 2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Diﬀerence systems of sets (DSS) are combinatorial structures introduced by Levenshtein in 1971,
which are a generalization of cyclic diﬀerence sets and arise in connection with code synchronization. A DSS
is a collection of t disjoint subsets Qi , 0 ≤ i ≤ t − 1, of any finite abelian group G of order q = ef + 1 suchthat every element of G\{0} appears at least ρ times in the multiset {a − b|a ∈ Qi , b ∈ Qj , 0 ≤ i ̸= j ≤ t − 1}.
In this talk, we will talk about parameter ρ of DSS with e = 4, 6. Additionally, we define new blocks withsize 2 and present the conditions that these blocks form a DSS.

40 Xiao-Nan Lu (Nagoya Univ.)
Masakazu Jimbo (Nagoya Univ.)

Aﬃne-invariant strictly cyclic Steiner quadruple systems and related
hypergraphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A Steiner quadruple system denoted by SQS(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 blocks or quadruples, such that each 3-subset of V appears
exactly once in B. An SQS(v) admitting a cyclic permutation whose stabilizer of any block is trivial is said
to be strictly cyclic, denoted by sSQS(v). In this talk, we consider an sSQS(2p) over Z2p admitting all theunits of Z2p as multipliers, which is said to be aﬃne-invariant. We show that the blocks of an aﬃne-invariantsSQS(2p) can be obtained from a rainbow 1-factor of a special kind of hypergraphs.

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

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

Summary: We consider a fractional 2m factorial design derived from a simple array (SA) such that the(ℓ + 1)-factor and higher-order interactions are assumed to be negligible, where ℓ = 2, 3. Under thesesituations, if the main eﬀect is estimable, and furthermore some of the remaining non-negligible factorialeﬀects may or may not be estimable, then a design is said to be of resolution R∗ ({1} | Ωℓ ). Using thealgebraic structure of the TMDPB association scheme, we give a necessary and suﬃcient condition for an
SA to be a balanced fractional 2m factorial design of resolution R∗ ({1} | Ωℓ ), where the number of assemblies
is less than the number of non-negligible factorial eﬀects.

42 Kazuki Matsubara (Hiroshima Univ.)
Sanpei Kageyama(Hiroshima Inst. of Tech.)

An asymptotic existence of pairwise additive minimal BIB designs · · · 15

Summary: The existence of pairwise additive balanced incomplete block (BIB) designs, denoted by
PAB(v, k, λ), has been discussed with direct and recursive constructions in Matsubara et al. (2007,2013). Especially, when k is an odd integer, PAB(v, k, (k − 1)/2) are said to be minimal. On the other hand,
Wilson (1975) proved an asymptotic existence of pairwise balanced designs. In this talk, an asymptotic
existence of pairwise additive minimal BIB designs is shown by use of Wilson’s theorem.

Created: 2014/08/12 08:45
82

Statistics and Probability∗
43 Sanpei Kageyama
An aﬃne α-resolvable triangular design is not of simple type · · · · · · · · 10
(Hiroshima Inst. of Tech.)

Summary: The validity of aﬃne α-resolvability in 2-associate PBIB desings is considered. Some history isreviewed. Finally we will show that there does not exist an aﬃne α-resolvable triangular design with λ1 = 0or λ2 = 0.

Created: 2014/08/12 08:45
83

Applied Mathematics

Applied Mathematics
September 25th (Thu)

Conference Room VIII

9:30–11:30
1 Hiroshi Nozaki (Aichi Univ. of Edu.)

Linear programming bounds for regular graphs · · · · · · · · · · · · · · · · · · · · 15

Summary: We develop a linear programming method to obtain bounds for the number of vertices of aconnected regular graph. This method especially need only the information of the distinct eigenvalues of agraph. As an application of this bound, we prove that a connected k-regular graph satisfying g > 2d − 1
has the minimum second largest eigenvalue of all k-regular graphs of the same size, where d is the numberof distinct non-trivial eigenvalues, and g is the girth.

2 Toshiaki Adachi (Nagoya Inst. of Tech.) ∗ Kähler graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Tuerxunmaimaiti Yaermaimaiti(Nagoya Inst. of Tech.)
Summary: As a discrete model of a Kähler manifold admitting Kähler magnetic fields, we introduce thenotion of Kähler graphs. We show some examples of Käher graphs and give a condition that we canconstruct a vertex-transitive finite Kähler graphs.

3 Toshiaki Adachi (Nagoya Inst. of Tech.) ∗ (1,1)-Laplacians for Kähler graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Tuerxunmaimaiti Yaermaimaiti(Nagoya Inst. of Tech.)
Summary: For Kähler graphs we define their (p, q)-Laplacians by use of (p, q)-colored paths. We particularly
consider (1, 1)-Laplacians and study eigenvalues for Kähler graphs defined by complement graphs and thoseof product types. We give examples of pairs of (1, 1)-isospectral Kähler graphs.

4 Iwao Sato (Oyama Nat. Coll. of Tech.)
Norio Konno (Yokohama Nat. Univ.)
Yusuke Higuchi (Showa Univ.)
Etsuo Segawa (Tohoku Univ.)

A zeta function with respect to the transition matrix of a discrete-timequantum walk on a graph · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to beclosely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph,
which is closely related to, as to say, the square of the evolution matrix of a quantum walk. Then we giveto such a function two types of determinant expressions and derive from it some geometric properties of afinite graph. As an application, we illustrate the distribution of poles of this function comparing with thoseof the usual Ihara zeta function.

5 Yuusuke Suzuki (Niigata Univ.)(Keio Univ.)
Kenta Noguchi

Extension to triangulations with some properties from quadrangulations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: For a given triangulation G on a surface F 2 , we can extend G to a triangulation T by adding a
diagonal edge in every face of G. Now the problem is to find a triangulation T with some properties. In
this talk, we show that for a given simple 2-connected planar quadrangulation G with |V (G)| ≥ 6, we can
extend G to a 4-connected triangulation.

Created: 2014/08/12 08:45
84

Applied Mathematics

6 Ginji Hamano (Tokyo Denki Univ.)
Takayuki Hibi (Osaka Univ.)
Hidefumi Ohsugi(Kwansei Gakuin Univ.)

Existence of a regular unimodular triangulation of the edge polytopesof finite graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let G be a fundamental FHM-graph and PG the edge polytope of G. Ohsugi has obtained anecessary and suﬃcient condition for PG to possess a regular unimodular triangulation. However, thiscondition is not so easy to apply to a given graph only by looking at the graph.
In this lecture, for a fundamental FHM-graph G, we will give several criteria for the existence of a regular
unimodular triangulation of PG in terms of some simple data of the graph. We also apply our criteria tosome examples, including the complete graph K6 with 6 vertices, and show that their edge polytopes possessa regular unimodular triangulation.

7 Yusuke Suyama (Osaka City Univ.)

Numbering of vertices of simplicial 2-spheres · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let K be a triangulation of the 2-sphere. We assign numbers to vertices of K on the basis of acertain rule. We determine the number of triangulations with at most 9 vertices, such that all vertices canbe numbered by the rule.

8 Kenta Ozeki(Nat. Inst. of Information/JST ERATO)
Dong Ye (Middle Tennessee State Univ.)

A decomposition of cubic graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A decomposition of a graph G is a set E1 , . . . , Ek of disjoint edges such that the union of them
form the edge set E(G) of G. It was conjectured by Hoﬀmann–Ostenhof that every cubic graph has adecomposition E1 , E2 , E3 such that E1 is a spanning tree, E2 is a matching, and E3 is a family of cycles.
(Note that a matching and a family of cycles desired here are not necessarily spanning subgraphs.) We
prove that the conjecture is true for 3-connected plane cubic graphs.

14:15–17:00
9 Kazuhiko Ushio (Kinki Univ.)

Balanced C5 -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
C5 -foil designs and related designs.

(Keio Univ.)
10 Jun Fujisawa
Hiroki Seno (Yokohama Nat. Univ.)

Matching extension in projective planar graphs · · · · · · · · · · · · · · · · · · · · 15

Summary: A matching M of G is said to be extendable in G if M is a subset of a perfect matching of G, anda graph with at least 2m + 2 vertices in which every matching of size m is extendable is called m-extendable.
Moreover, a graph with at least 2m + 2 vertices is said to be distance d m-extendable if any matching M
with |M | = m in which the edges lie pair-wise distance at least d is extendable. In this talk we introduce
the following result: Every 5-connected triangulation of the projective plane with an even order is distance
3 7-extendable, and there exist infinitely many 5-connected triangulations of the projective plane with aneven order which are not distance 3 8-extendable.

Created: 2014/08/12 08:45
85

Applied Mathematics

11 Kiyoshi Yoshimoto (Nihon Univ.)
Ralph J. Faudree (Univ. of Memphis)(Univ. de Paris Sud)
Hao Li

Locating sets of vertices on Hamiltonian cycles · · · · · · · · · · · · · · · · · · · · 15

Summary: Let k ≥ 2 be a positive integer and X = {x1 , . . . , xk } and Y = {y1 , . . . , yk } be a pair of disjoint
sets of vertices in a graph G. In this talk, we consider the existence of a Hamiltonian cycle of G such that
all of the vertices of X precede the vertices of Y for appropriate initial vertex and orientation of the cycle.

12 Akira Saito
Kazuki Sano

(Nihon Univ.)(Nihon Univ.)

Spanning trees homeomorphic to a small tree · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we will present a suﬃcient condition for a connected graph to have a spanning tree
which is homeomorphic to a tree of a bounded order. The result is a natural extension of a classical result
for the existence of a hamiltonian path, known as Ore’s Theorem. We also discuss the sharpness of theresult.

13 Kiyoshi Ando(Nat. Inst. of Information/JST ERATO)

A degree sum and forbidden subgraph condition for k-contractible edges· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: If a k-connected graph G has no K1 + C4 and the degree sum of each connected subgraph of G
of order 3 is greater than 3k + 1, then G has a k-contractible edge.

14 Atsuhiko Mizusawa (Waseda Univ.)
Diogo Kendy Matsumoto(Waseda Univ.)

A construction of smooth travel groupoids on finite graphs · · · · · · · · · · 15

Summary: In this talk, we show a way to construct smooth travel groupoids from given finite graphs. This
gives an answer to Ladislav Nebeský’s question “does there exists a connected graph that has no smooth
travel groupoid?” on finite graphs.

15 Shinya Fujita (Yokohama City Univ.)
Michitaka Furuya (Tokyo Univ. of Sci.)
András Gyárfás(A. Rényi Inst. of Math.)Ágnes Tóth (A. Rényi Inst. of Math.)

A note on covering edge colored hypergraphs by monochromatic components · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For r ≥ 2, α ≥ r − 1 and k ≥ 1, let c(r, α, k) be the smallest integer c such that the vertex set of
any non-trivial r-uniform k-edge-colored hypergraph H with α(H) = α can be covered by c monochromaticconnected components. Here α(H) is the maximum cardinality of a subset A of vertices in H such that A
does not contain any edges. An old conjecture of Ryser is equivalent to c(2, α, k) = α(r − 1) and a recent
result of Z. Kiraly states that c(r, r − 1, k) = ⌈ kr ⌉ for any r ≥ 3.
Here we make the first step to treat non-complete hypergraphs, showing that c(r, r, r) = 2 for r ≥ 2 andc(r, r, r + 1) = 3 for r ≥ 3.

Created: 2014/08/12 08:45
86

Applied Mathematics

16 Takahiro Matsushita (Univ. of Tokyo)

On the topology of neighborhood complexes and the chromatic numbersof graphs · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Lovasz introduced the neighborhood complex N (G) of a graph G. He showed that for a graph G,
the connectivity of N (G) gives a lower bound for the chromatic number χ(G) of G. Then a natural question
arises: how eﬀective is to detemine the topology of the neighborhood complex to compute the chromatic
number? For example, is there a topological invariant which is equivalent to the chromatic number? In thistalk, we discuss such a problem.

17 Katsuhiko Kuribayashi (Shinshu Univ.)

On the strong homotopy for quasi-schemoids · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A quasi-schemoid is a small category with a particular partition of the set of morphisms. We
define a homotopy relation on the category of quasi-schemoids and study the fundamental properties of thehomotopy.

18 Sho Suda (Aichi Univ. of Edu.)
Michio Seto (Shimane Univ.)
Tetsuji Taniguchi(Matsue Coll. of Tech.)Gram matrices of reproducing kernel Hilbert spaces over graphs I · · · · 10

Summary: We will define a structure of reproducing kernel Hilbert spaces for simple connected graphs. Sincegraphs are isomorphic if and only if corresponding Hilbert spaces are isomorphic, studying the space isimportant. In this talk, using the data of the corresponding Gram matrix, we obtain the inequalities forsome values on graphs and characterize the some graphs as objects which attain the inequalities.

19 Michio Seto (Shimane Univ.) ∗ Gram matrices of reproducing kernel Hilbert spaces over graphs II · · · 10
Sho Suda (Aichi Univ. of Edu.)
Tetsuji Taniguchi(Matsue Coll. of Tech.)
Summary: We study graph homomorphisms from a viewpoint of reproducing kernel Hilbert space theory. In
particular, de Branges–Rovnyak theory is introduced into graph theory. We describe graph homomorphisms
with Gram matrices of de Branges–Rovnyak spaces.

September 26th (Fri)

Conference Room VIII

9:30–11:30
20 Ryuichi Ohori (Univ. of Tokyo)
Takehito Yoshiki (Univ. of Tokyo)

Walsh figure of merit is eﬃciently approximable · · · · · · · · · · · · · · · · · · · · 10

Summary: Walsh figure of merit (WAFOM) is a quality criterion for a quasi-Monte Carlo integration method,
introduced by Matsumoto, Saito and Matoba. They define WAFOM as the sum over the orthogonal
complement of the digital net, and compute WAFOM by iterating over the digital net itself. As a further
improvement of their method we show an eﬀective approximation method which is easier to implement andfaster in computation.

Created: 2014/08/12 08:45
87

Applied Mathematics

21 Kosuke Suzuki (Univ. of Tokyo)
Takehito Yoshiki (Univ. of Tokyo)

On the decay of the Walsh coeﬃcients of smooth functions · · · · · · · · · · 15

Summary: For the study of quasi-Monte Carlo (QMC) rules for numerical integration of high smooth
integrands defined over the s-dimensional unit cube, to analyze the decay of the b-adic Walsh coeﬃcients isimportant. Josef Dick gave the decay of the Walsh coeﬃcients of functions in Sobolev spaces in 2008. In
this talk, we introduce another method to analyze the decay of the Walsh coeﬃcients of smooth functions
using iterate integration by parts which improves the bound on Walsh coeﬃcients in some cases.

22 Takehito Yoshiki (Univ. of Tokyo)
Takashi Goda (Univ. of Tokyo)
Ryuichi Ohori (Univ. of Tokyo)
Kosuke Suzuki (Univ. of Tokyo)

The mean square quasi-Monte Carlo error for digitally shifted point sets
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A digitally shifted point set is a point set which can be identified with a subset P + σ for anelement σ ∈ Zbs×n and a subgroup P ⊂ Zbs×n , where Zb denotes the cyclic group of order b. We shall choose
σ uniformly and randomly from σ ∈ Zbs×n . The randomized QMC integration by P + σ is the approximation∫∑of I(f ) := x∈[0,1)s f (x) dx by IP +σ (f ) := 1/|P + σ| x∈P +σ f (x). In this talk, we consider the root mean∑square error M EP (f ) := 1/bsn σ∈Z s×n (I(f ) − IP +σ (f ))2 . If M EP (f ) is small, IP +σ (f ) can be smallbaveragely. For a suﬃciently smooth integrand f , we obtain a quality measure called Walsh figure of merit
W (P ; µ), which gives an upper bound for M EP (f ). We show that W (P ; µ) is computable, and find a point
set P with W (P ; µ) small by computer search.

23 Shin Harase(Tokyo Tech)

Projections of Sobol’ sequences · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider multivariate numerical integration by quasi-Monte Carlo methods. Typical quasiMonte Carlo point sets are low-discrepancy point sets based on the t-values of (t, m, s)-nets. In particular,
Sobol’ sequences are famous examples and widely used in computational finance. In this talk, we focus
on Sobol’ sequences with better two-dimensional projections constructed by Joe and Kuo (2008). We
investigate the t-values of higher dimensional projections, and give some remarks.

24 Toshiaki Murofushi (Tokyo Tech)
Takafumi Horio (Tokyo Tech)

A computational approach for testing additive decomposability of monotone, supermodular set functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this paper we consider additive decompositions by proper monotone set functions, i.e., monotone
set functions with proper support, and investigate whether it is possible to have such decompositions
for monotone, supermodular set functions, which we call a “decomposability question”. We propose acomputational approach by formulating the polytope of monotone, supermodular set functions by meansof hyperplanes, and by examining the corresponding vertices of polytope for further decomposability overproper monotone set functions. This enables us to numerically resolve the decomposability question ina finite steps of procedure. We have tested the proposed method for five- and six-element sets; we haveobtained a positive answer to the question for a five-element set, and a negative one for a six-element set.

Created: 2014/08/12 08:45
88

Applied Mathematics

25 Minoru Fujimoto (Seika Science Lab.)
Kunihiko Uehara (Tezukayama Univ.)

NP Complete problem by quadratic residue problem · · · · · · · · · · · · · · · · 15

Summary: We study the quadratic residue problem known as an NP complete problem by way of the prime
number and show that a nondeterministic polynomial process does not belong to the class P because of arandom distribution of solutions for the quadratic residue problem.

26 Takuya Ikuta (Kobe Gakuin Univ.)

Complex Hadamard matrices attached to some association schemes · · 15

Summary: Recently, we classified type-II matrices attached to some association schemes. We have 6 infinite
families of type-II matrices, among which are 4 families of our complex Hadamard matrices. To check
whether our complex Hadamard matrices are inequivalent to the tensor product of known examples, we
introduce the Haagerup set for type-II matrices and the Nomura algebra for our complex Hadamard matrices.
In this talk, we mainly present how to compute the Haagerup set and the Nomura algebra for our complex
Hadamard matrices. This is based on a joint work with Akihiro Munemasa.

13:00–14:00

Talk Invited by Applied Mathematics Section

Etsuo Segawa (Tohoku Univ.)

Spectral mapping of quantum walks

Summary: For a given finite graph G = (V, E), we present a spectral mapping theorem onto a discrete-timequantum walk on ℓ2 (D) from the underlying cellar automaton on ℓ2 (V ), where D is the set of the symmetricarcs generated by E. Firstly, we show that the cellar automaton satisfies a diﬀerence of a wave equation, andprovides the real parts of the spectrum of the quantum walk at each time n ∈ N. We denote this inherited
eigenspace of the quantum walk from the underlying cellar automaton by L. Secondly, we show that in
the Grover walk case, which is intensively studied from the view points of quantum search algorithms andscattering theories, the orthogonal complement eigenspace L is generated by a homological structure of thegraph. Finally, we extend our notion to an infinite abelian covering graph. As an application, we discuss
the following typical stochastic properties of quantum walks; localization and linear spreading.

September 27th (Sat)9:30–11:55

Conference Room VIII

Special Session “Moving boundary problems and its numerical and mathematical analysis”

Tetsuya Ishiwata(Shibaura Inst. of Tech.)

Motion of polygonal curves by crystalline curvature flow · · · · · · · · · · · · 45

Summary: In this talk we consider the motion of planar polygonal curves governed by generalized crystalline
curvature flow with a driving force: β(Nj )Vj = U − g(Hj ), where Vj , Nj and Hj denote an outward velocity,
an outward normal vector and a crystalline curvature of the j-th facet of solution curve, respectively. Here,“facet” means a lines segment of solution curve Γ(t). The positive function β and U describe an anisotropyof the mobility and a driving force, respectively. We consider 2 cases. One is the case when solution curves
are closed. The other is the case when solution curves have infinity length. For both cases, we disuss abehavior of polygonal curves, especially, we mainly consider a deformation of solution curves.

Created: 2014/08/12 08:45
89

Applied Mathematics

Masato Kimura (Kanazawa Univ.)

Generalization of crystalline motion · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 45

Summary: We consider a polygonal analogue of the Hele-Shaw moving boundary problem with surface
tension based on a framework of polygonal motion proposed by Benes–Kimura–Yazaki (2009). This is a
generalization of the crystalline motion for the curvature flow which was originally proposed by Angenent–
Gurtin (1989) and J. E. Taylor (1993).
A key idea is to introduce a polygonal Dirichlet-to-Neumann map. We study variational properties of thepolygonal Dirichlet-to-Neumann map and show that our polygonal Hele-Shaw problem is an almost complete
analogue of the original problem. Local solvability of a polygonal Hele-Shaw problem is proved by means of
the variational structure. We also give several polygonal versions of moving boundary problems such as thecurvature flow, the Hele-Shaw flow and the Stokes flow etc. with some numerical examples. Our polygonal
motions exactly satisfy properties of curve shortening and/or area preservation.
This is a joint work with Shigetoshi Yazaki (Meiji University) and Daisuke Tagami (Kyushu University).

Masahisa Tabata (Waseda Univ.)

Numerical analysis of multiphase flows · · · · · · · · · · · · · · · · · · · · · · · · · · · · 45

Summary: Multifluid and multiphase flows with surface tension are encountered frequently in scientific andengineering problems. Recently we have developed an energy-stable Galerkin-characteristics scheme to
two-fluid flow problems with surface tension, where each flow is governed by the Navier–Stokes equations.
After presenting excellent features of this scheme, we simulate numerically some multiphase flow problems
such as rising bubbles and falling droplets by the use of it.

14:15–16:30
27 Shingo Iwami (Kyushu Univ.)

Quantitative analysis of virus infection dynamics with distributed delay
diﬀerential equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this study, we were interested in quantifying and modeling the ecliptic phase during virus
infection. One simple mathematical approach describing this phase is modeling by delay diﬀerential
equations (DDE). However, unfortunately, the distribution of the ecliptic phase was poorly understood.
Here, from cell culture experiments with simian/human immunodeficiency virus (SHIV), we quantified the
distribution of the ecliptic phase and found that the phase obeys gamma distribution. Based on thisexperimental result, we made a mathematical model including the distribution by DDE and estimated viralparameters from previously published experimental data. Our analyses showed that modeling the ecliptic
phase aﬀected estimation of the virus infection rate (therefore, basic reproductive number) but not the virus
production rate and the death rate of infected cells.

28 Toshikazu Kuniya (Kobe Univ.)

Analysis of an age-structured SIS epidemic model with spatial diﬀusion· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we focus on an age-space-structured SIS epidemic model which is formulated as anonlinear diﬀusion system of partial diﬀerential equations. In order to apply a traditional approach of
integral operators, we use the Feynman–Kac formula in probability theory and express the solution of thesystem explicitly in terms of expected value. After that we reformulate the problem of existence of thesolution to a fixed-point problem for a nonlinear operator and show that such a fixed-point exists if and only
if the spectral radius of the next generation operator, that is, the well-known basic reproduction number R0
is greater than unity.

Created: 2014/08/12 08:45
90

Applied Mathematics

29 Yasuaki Hiraoka (Kyushu Univ.)
Emerson G. Escolar (Kyushu Univ.)

Persistence modules on commutative ladder quivers · · · · · · · · · · · · · · · · 15

Summary: In this talk, we generalize the concept of persistence modules on An quivers to commutative ladder
quivers. This class of persistence modules frequently appears in topological data analysis, and the theory
and algorithm proposed in this talk can be applied to these practical problems. A new algebraic frameworkdeals with persistence modules as representations on associative algebras and the Auslander-Reiten theory
is applied to develop the theoretical and algorithmic foundation.

30 Emerson Gaw Escolar (Kyushu Univ.)
Yasuaki Hiraoka (Kyushu Univ.)

Computing persistence modules on commutative ladders of finite type
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In topological data analysis, the idea of persistence modules on commutative ladders is a recent
development extending the ideas of persistent homology to a more general setting. In particular, it
can be used to study common robust topological features. In this talk, we discuss the computation of
persistence modules on commutative ladders of finite type, focusing on the use of Morse reductions to reduce
computation times.

31 Genki Kusano (Kyushu Univ.)
Yasuaki Hiraoka (Kyushu Univ.)

An application of persistent homology to a coverage problem in sensor
networks · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A coverage problem in sensor networks was partially solved by V. de Silva and R. Ghrist by using
homology. In this talk, we apply persistent homology to the coverage problem, and present a coveragetheorem with perturbation.

32 Satoru Takagi (Kogakuin Univ.)
Hiroaki Uesu (Waseda Univ.)

An analysis of students’ needs for undergraduate mathematics lectures
applying the Kano model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: At universities, mathematics lecturers have to change their teaching materials and methods
according to students’ mathematical skills, and also have to make them understand mathematics. In thispaper, we apply the questionnaire analysis in some undergraduate mathematics lectures for the method ofstudents’ needs analysis using the Kano model, and report the results.

33 Kazuaki Nakane (Osaka Univ.)

Image analysing method via homology —for cancer area detection—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Development of technology for detecting of the cancer lesions from digitized pathological specimens
has been studied for a long time. This type of system has been developed based on the pattern recognition
technology. Because the cancer tissues have too various forms, this technology does not work well.
Here we introduce a new method. By using a mathematical theory (homology theory), our system has been
designed. Our method can estimate the contact degree of elements in the tissue of unit area. We may
consider that, by the loss of contact inhibition, cancer lesions are included in high contact degree area. We
have tried this method to pathological images and obtained satisfactory good results.

Created: 2014/08/12 08:45
91

Applied Mathematics

34 Kazuaki Nakane (Osaka Univ.)

Image analysing method via homology II —for general structures—· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: There are structures that are formed with a certain order. For these kind of structures, research
is progressing from both the theory and experiment. There are many examples we cannot find the ruleof structures at first glance. In these cases, it is diﬃcult to make mathematical description. Some of thestructures, we apply the topological method and attempt to classify. The structures are constituted by thecontact between the components. Homology can also be considered the concept of evaluating the degreeof contact. We set the size of the unit area and calculate the indexes which are depended on the Betti
numbers. This is the principle that quantify the degree of contact.

16:45–17:45

Talk Invited by Applied Mathematics Section

Yoshihito Oshita (Okayama Univ.)

Motion of droplets driven by curvature and potential

Summary: We consider the motion of small droplets driven by the curvature and the potential in a boundeddomain and show that the center of the droplets moves along a solution of some reduced equation in a small
volume fraction limit and compare its homogenization limit as well.

September 28th (Sun)

Conference Room VIII

9:30–11:50
35 Shunzi Horiguchi(Niigata Sangyo Univ.)

The conditional expressions III which compare convergences of Ttsuchikura–
Horiguchi method (the first extended recurrence formula of Yoshimasu
Murase–Newton’s type) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We obtained extension of Newton–Raphson method (Ttsuchikura–Horiguchi method). We givethe conditional expressions III which compare convergences of Ttsuchikura–Horiguchi method (the firstextended recurrence formula of Yoshimasu Murase–Newton’s type).

36 Shunzi Horiguchi(Niigata Sangyo Univ.)

The numerical computations of the conditional expressions III which
compare convergences of Ttsuchikura–Horiguchi method (the first extended recurrence formula of Yoshimasu Murase–Newton’s type) · · · · · 10

Summary: We give the numerical computations of the conditional expressions III which compare convergencesof Ttsuchikura–Horiguchi method (the first extended recurrence formula of Yoshimasu Murase–Newton’stype).

37 Issei Oikawa(Waseda Univ.)

A hybridized discontinuous Galerkin method with reduced stabilization· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In this talk, we propose reduced stabilization of the hybridized discontinuous Galerkin methods.
We show error estimates and numerical results. A new theoretical tool for analysis of the proposed method
is also proposed.

Created: 2014/08/12 08:45
92

Applied Mathematics

38 Shinya Uchiumi (Waseda Univ.)
Masahisa Tabata (Waseda Univ.)

Analysis of a finite element scheme free from quadrature errors for the
Navier–Stokes equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We consider the characteristics finite element method for the Navier–Stokes equations. The
conventional scheme cannot be implemented precisely because the composite function terms are not polynomials. In the analysis of the conventional scheme, however, it is assumed that the terms are integrated
exactly. We have developed a scheme free from quadrature errors that can be precisely implemented forthe convection-diﬀusion equations. Here we show that the scheme can be extended to the Navier–Stokes
equations to achieve an optimal convergence result.

39 Takahito Kashiwabara (TU Darmstadt)
Guanyu Zhou (Univ. of Tokyo)
Issei Oikawa (Waseda Univ.)

Penalty method to the Stokes problem with slip boundary condition· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The penalty method for Stokes problem with slip boundary condition is concerned. We derive
the optimal error estimate of penalty method. The smooth boundary is approximated by straight polygonallines, then finite element method is applied to solve the penalty problem. The error estimate of finite element
approximation is achieved. Some numerical experiments are presented to verify our theoretical results.

40 Tomoya Kemmochi (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

Discrete maximal regularity for abstract Cauchy problems and its application to finite element methods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Maximal regularity is one of fundamental concepts in theory of partial diﬀerential equations. It,
for example, provides us a convenient way to establish the well-posedness for a wide class of nonlinear
equations. Therefore, it is natural to ask whether a discrete analogue of maximal regularity is available.
Furthermore, we are interested in application of discrete maximal regularity to error analysis of various
discretization of nonlinear equations. In this paper, we first prove a maximal regularity result for timediscrete abstract Cauchy problem in a UMD space. Then, we also report an application of such discrete
maximal regularity result to the finite element method for the heat equation and obtain reasonable a priori
estimate.

41 Yoshiki Sugitani (Univ. of Tokyo)
Guanyu Zhou (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

Finite element approximation for the Stokes equations under a unilateralboundary condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: As an open boundary condition (a kind of artificial boundary conditions) for viscous incompressible
fluids flow simulation, we propose a unilateral boundary condition. With our boundary condition, the Navier–Stokes equation satisfies an energy inequality so that we can avoid numerical instability in 3D simulations.
In this paper, we restrict ourselves to a model Stokes problem and report some results on the finite element
approximation.

Created: 2014/08/12 08:45
93

Applied Mathematics

42 Yuuki Ueda (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

On a high-accurate successive time-discretization method based on Bspline interpolation functions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Recently, K. Takizawa and T. Tezduyar proposed a new time discretization method, which theycall space-time computation techniques with continuous representation in time (ST-C), for fluid-structureinteraction problem. The method is based on B-spline interpolation functions and, consequently, is highly
accurate. In this paper, we examine the successive projection technique (SPT), which is a most basic
technique among ST-C, and report the well-posedness of the algorithm and a certain error estimation.

43 Khoji Ohtsuka(Hiroshima Kokusai Gakuin Univ.)

Solution of the shape optimization problem with Generalized J-integral
by adjoint method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Let Ω be a domain on which the boundary value problem is defined and u(Ω) the solution. We
study the shape optimization problem to find the shape which is optimal in that it minimizes the cost∫functional Ω g(u(Ω))dx with the volume constraint, |Ω|=constant. In this study, we talk how to solve shape
optimization problems with Generalized J-integral coming from fracture mechanics, H1-gradient method
proposed by Prof. Azegami and adjoint method.

14:15–16:15
44 Koichi Anada(Waseda Univ. Senior High School)
Tetsuya Ishiwata(Shibaura Inst. of Tech.)Some features for blow-up solutions of a nonlinear parabolic equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In previous studies we have shown some conjectures for behavior of blow-up solutions to a nonlinear
parabolic equations. They are very important features to investigate behavior of solutions near their blow-up
time. The purpose of our paper is to prove one of them that we call weak eventual monotonicity.

45 Takiko Sasaki (Univ. of Tokyo)
Norikazu Saito (Univ. of Tokyo)

Blow-up of finite diﬀerence solutions for nonlinear Schrödinger equations· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The purpose of this paper is to establish a numerical method for computing blow-up solutions of
one-dimensional nonlinear Schrödinger equations with power nonlinearlities. There are various techniques
for computing blow-up solutions of nonlinear heat and wave equations. However, a little is known for the
nonlinear Schrödinger equations. In this paper, we propose a finite diﬀerence scheme that can approximate
the blow-up phenomena. Thus, after having established converge results, we show that the numericalblow-up time actually converges to the blow-up time of the the nonlinear Schrödinger equation underconsideration.

46 Daisuke Tagami (Kyushu Univ.)

An iterative domain decomposition method for eddy current problems
with the gauge condition · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: An iterative domain decomposition method is introduced into eddy current problems, which
is formulated by a mixed method with the Lagrange multiplier. By introducing the mixed method, atwo-subdomain problem is equivalent to the conventional one-domain problem, and yields an interative
domain decomposition method of eddy current problems. Moreover, to mathematically justify the previous
formulation, the formulation based on the mixed method has been established a connection with the previousone.

Created: 2014/08/12 08:45
94

Applied Mathematics

47 Koya Sakakibara (Univ. of Tokyo)
Shigetoshi Yazaki (Meiji Univ.)

Numerical computation of the one phase Hele-Shaw flow based on the
charge simulation method · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We construct the variational structure-preserving numerical scheme for the one phase Hele-Shaw
flow and examine its eﬀectivity numerically. We modify the CSM invariant scheme in order to satisfy thearea-preserving property by posing a condition that the weighted average of charges is equal to 0.

48 Tomoyuki Miyaji (Kyoto Univ.)

Computer-assisted analysis to dynamical systems with four-leaf orbits· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study a three-dimensional dynamical system defined by ordinary diﬀerential equations. Craik
has shown that an exact solution to 3D Navier–Stokes equation is constructed by using a solution to theequations. Craik and Okamoto have found out that almost all orbits of the system are unbounded andan unstable periodic orbit plays an important role in determining the destination of an unbounded orbit.
We prove the existence of such a periodic orbit by a method of numerical verification based on intervalarithmetic. When passing through the vicinity of the periodic orbit, an orbit draws a four-leaf. If one adds
damping terms to the system, one can observe a four-leaf chaotic attractor. We also study the route tofour-leaf chaos.

49 George Miyake(Ube Nat. Coll. of Tech.)
Yuji Katsuta (Ube Nat. Coll. of Tech.)

A method of computing parameter values for shaping a limit cycle into
a separatrix loop · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Where there is an adhesion of a stable or unstable limit cycle to a saddle equilibrium point innonlinear systems, the limit cycle is made up into separatrix loop. It is known the computational methodof parameter values for shaping the limit cycle into the separatrix loop by using numerical integration on
the alpha branch streaming out from the equilibrium point. The alpha branch is likely to happen because
the instability of the alpha branch is to prevent the branch returning to in the neighborhood of equilibrium
point, as a result a new computational method using bisection method is brought in.

50 Ayuki Sekisaka (Tohoku Univ.)

The relationship between the stability of pulse and the absolute spectrum in reaction diﬀusion system · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Can two unstable waves make a stable pulse? This problem was solved aﬃrmatively by Nii andSandstede–Scheel, independently. In particular, The stability of pulse is connected with absolute spectrum.
But, their results depends on the codimension of a bifurcation. In this talk, we show that an extension
between the stability of pulse and the absolute spectrum with higher codimension bifurcation.

Created: 2014/08/12 08:45
95

Applied Mathematics

16:30–17:30

Talk Invited by Applied Mathematics Section

Takeshi Takaishi(Hiroshima Kokusai Gakuin Univ.)

A phase-field model for crack growth and its numerical verification

Summary: A phase field model for crack growth in two or three dimensional isotropic elastic material is
proposed by the author and Kimura. A phase-field to represent the shape of the crack with a regularization
parameter ϵ > 0 is introduced in the model. The phase field model is derived as a gradient flow of thisregularized energy that is approximated by the Francfort–Marigo type energy using the idea of Ambrosio
and Tortorelli. The model is convenient to study the mathematical property of crack growth for theoreticaland numerical analysis, such as the equilibrium profiles of the phase-filed. Numerical results shows the twoor three-dimensional structure of crack surface.

Created: 2014/08/12 08:45
96

Topology

Topology
September 25th (Thu)

Conference Room VI

9:20–12:00(Kochi Univ.)
1 Kazuaki Higa
Ryo Kato
Katsumi Shimomura (Kochi Univ.)

A surviving condition on permanent cycles in the Adams E2 -term · · · · 10

Summary: For a nontrivial element in the Adams spectral sequence, we give a new condition for surviving
to the stable homotopy groups of spheres. It may be seen as a generalization of many works of Xiugui Liu
and collaborators.

2 Kentaro Miyazawa (Kochi Univ.)
Katsumi Shimomura (Kochi Univ.)

On the action of Greek letter element β1 in the stable homotopy groupsof spheres · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk, we consider the action of β1 in the stable homotopy groups of spheres using themethod’s of Ravenel’s small descent spectral sequence.

3 Norihiko Minami(Nagoya Inst. of Tech.)On the Beilinson–Rosenblyum isogeny theorem of the Hurewicz functor
for infinite loop spaces · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: I shall oﬀer a slightly streamlined proof of the Beilinson–Rosenblyum isogeny theorem of the
Hurewicz functor for infinite loop spaces. Universal torsion order estimates of the kernel and the cokernelof the Hurewicz homomorphism functor are also slightly improved.

4 Saki Itagaki
Yutaka Hemmi(Kochi Univ.)(Kochi Univ.)

Correspondence between categories of finite topological spaces and finite
simplicial complexes · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: There is a functor from the category of finite topological spaces Ftop to the category of finite
simplicial complexes. This functor is faithful but is not full. To make this functor full, we consider a weakerversion of continuity of maps between finite topological spaces and consider an extend category Ftopexof Ftop. Moreover, we can define the homotopy in Ftopex so that two finite topological spaces have thesame homotopy type in Ftopex if and only if the corresponding simplicial complexes have the same strong
homotopy type.

5 Takahiro Matsushita (Univ. of Tokyo)

The simplicial sets related to the Hom complexes of graphs · · · · · · · · · · 10

Summary: For a positive integer r, an r-set we say in this talk is a set X with a subset of the r-times direct
product X r of X. For r-sets X and Y , we construct the poset Hom(X, Y ) called the Hom complex, andthe simplicial set Sing(X, Y ) called the singular complex. We show that their geometric realizations are
homotopy equivalent. The Hom complex of r-sets is the generalization of the Hom complexes of graphs
which have been applied to the graph coloring problem in graph theory.

Created: 2014/08/12 08:45
97

Topology

6 Naoya Suzuki (Nagoya Univ.)

The Dixmier–Douady class in a simplicial de Rham complex · · · · · · · · · 15

Summary: Let G be a Lie group and BG a classifying space of G. Then we can recognize a characteristicclass of principal G-bundles as an element in H*(BG). In general BG is a very huge space so we can not use
the ordinary de Rham cohomology theory on it. However if use the simplicial de Rham theory due to mainly
Bott–Shulman–Stasheﬀ and Dupont, we can exhibit a cocycle which represents an element in H*(BG) as adiﬀerential form on a simplicial manifold NG. In this presentation I will exhibit a cocycle in a simplicial de
Rham complex which represents the Dixmier–Douady class in the sense of Carey–Crowley–Murray. It is acharacteristic class of a principal G-bundle whose fiber has a central U(1)-extension.

7 Hirokazu Nishinobu (Kochi Univ.)
Toshihiro Yamaguchi (Kochi Univ.)

Certain examples of posets of rational Gottlieb subgroups · · · · · · · · · · · 10

Summary: Let Gξ∗ (X) be the fibre-restricted Gottlieb group with respect to a fibration ξ : X → E → Y in
CW complexes. It is a subgroup of the Gottlieb group G∗ (X) of X. When Y = BS 1 and X is the productof odd-spheres, we illustrate a variety of Gottlieb poset, which is the poset of subspaces Gξ∗ (X) ⊗ Q in
G∗ (X) ⊗ Q.

8 Katsuhiko Kuribayashi (Shinshu Univ.)

Loop products on Noetherian Hopf spaces · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We investigate the loop homology of a simply-connected Noetherian Hopf spaces. It turns outthat non-triviality of the loop product characterizes the finiteness of the cohomology of such Hopf spaces.

9 Miho Hatanaka (Osaka City Univ.)

Spin toric manifolds associated to graphs · · · · · · · · · · · · · · · · · · · · · · · · · 10

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 simple graph, so that one can associate a toric
manifold to a simple graph. We characterize simple graphs whose associated toric manifolds admit spin
structures.

10 Hiraku Abe (Osaka City Univ.)

Young diagrams and intersection numbers for toric manifolds arisingfrom root systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study intersection numbers in the toric manifold associated with the fan determined by the
Weyl chambers for the root system of type A. We give a combinatorial formula for intersection numbers ofcertain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe
the ring structure of the cohomology of the toric manifold.

Created: 2014/08/12 08:45
98

Topology

11 Tatsuya Horiguchi (Osaka City Univ.)
Megumi Harada (McMaster Univ.)
Mikiya Masuda (Osaka City Univ.)

The equivariant cohomology rings of Peterson varieties · · · · · · · · · · · · · 10

Summary: Let G be a complex semisimple linear algebra group and let Pet be the Peterson variety in theflag variety G/B. The main theorem gives an eﬃcient presentation of the S-equivariant cohomology ring of
the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials.
Here the group S is a certain circle subgroup of a maximal torus T of G. Our description of the ideal
J uses the Cartan matrix and is uniform across Lie types. Our result generalizes a previous theorem of
Fukukawa–Harada–Masuda, which was only for Lie type A.

12 Takayuki Yamaguchi (Hiroshima Univ.)
Tomonori Fukunaga (Hokkaido Univ.)
Takaaki Yamanoi (Hokkaido Univ.)

Complete classification of Gauss words of rank less than or equal to 5
by universal finite type invariant · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We show complete classification of Gauss words of rank less than or equal to 5, which is obtainedby the universal finite type invariant of degree 7. We also show truncated Polyak algebras of Gauss wordsof rank less than or equal to 7. The invariant and the truncated Polyak algebras have been calculated byour computer program.

14:15–15:25
13 Yukinobu Yajima (Kanagawa Univ.) ∗ The D-space property of infinite products · · · · · · · · · · · · · · · · · · · · · · · · · 10
Yasushi Hirata (Kanagawa Univ.)
Summary: It is proved by an elementary submodel that any countable product of subparacompact DC-likespaces is a D-space. More generally, we prove that any uncoutable product of subparacompact DC-likespaces is a D-space if and only if each factor of the product is compact except contably many ones.

14 Tatsuhiko Yagasaki (Kyoto Inst. Tech.)Taras Banakh(Ivan Franko Nat. Univ. of Lviv)
Kotaro Mine (Univ. of Tokyo)
Katsuro Sakai (Kanagawa Univ.)

Homeomorphism groups of non-compact surfaces endowed with the
Whitney topology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study topological type of the homeomorphism group H(M ) of any non-compact connectedsurface M endowed with the Whitney topology and show that the identity connected component H0 (M ) of
H(M ) is homeomorphic to the product l2 × R∞ .

15 Takashi Shimomura(Nagoya Univ. of Econ.)Ergodic measures and graph circuits of a sequence of covers · · · · · · · · · 10

Summary: We have shown that every 0-dimensional system is an inverse limit of a sequence of finite directed
graph covers. In this expression, all invariant measures are expressed as a limit of barycenters of circuitsof each finite directed graph. Consider the case in which each system of all circuits of a graph is linearly
independent. Then, a condition for the invariant measure to be ergodic is given. This condition seems tomean that the time average and the space average coincide.

Created: 2014/08/12 08:45
99

Topology

16 Takashi Shimomura(Nagoya Univ. of Econ.)

Combinatorial construction of completely scrambled compact system· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Since Li and Yorke developed the notion of scrambled sets in the study of chaotic systems, there
has been some discussion as to how large such sets can be. In 1997, Mai reported a non-compact example
that is completely scrambled, i.e., the scrambled set is the whole space, and conjectured that there was nocompact example. Huang and Ye later disputed this conjecture. They constructed a compact, 0-dimensional
completely scrambled system. They also reported the existence of locally equicontinuous transitive examples.
We construct a set of examples that are completely scrambled, transitive and not locally equicontinuous.

17 Takamitsu Yamauchi (Ehime Univ.)

On coarse geometric infinite-dimensionality of the countable direct sumof the integers · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: Asymptotic property C is an infinite-dimensional property in coarse geometry in the sense thatevery metric space with finite asymptotic dimension has asymptotic property C. It was introduced by
Dranishnikov as a coarse geometric analogue of Haver’s property C in dimension theory. In this talk, we
discuss a question of Dranishnikov and Zarichnyi which asks whether the countable direct sum of the integers
has asymptotic property C.

15:45–16:45

Talk Invited by Topology Section∗
Brian Bowditch
Rigidity results for spaces associated to a surface(Univ. of Warwick / Tokyo Tech)

Summary: A quasi-isometry between two metric spaces is a map which preserves their large-scale geometry,or more precisely, distances to within fixed linear bounds. An important aspect of geometric group theory
is to describe the possible quasi-isometries between various naturally occurring spaces. For example, it
was shown recently by Behrstock, Kleiner, Minsky and Mosher that (apart from a few exceptional cases)
the mapping class group of a compact orientable surface is quasi-isometrically rigid. That is, any selfquasi-isometry of (a Cayley graph of) the mapping class group agrees, up to bounded distance, with left
multiplication by an element of the group. We aim to describe some of the ideas behind this, as well assome strengthenings and variations to other spaces such at the Weil–Petersson metric on Teichmüller space.
Our approach makes use of the theory of median algebras.

September 26th (Fri)

Conference Room III

10:30–10:45

Presentation Ceremony for MSJ Geometry Prize 2014

10:50–11:50

Award Lecture for MSJ Geometry Prize 2014

—Celebrating Professor Masatake Kuranishi—(Osaka Univ.) Kuranishi’s masterpieces and their developments in deformation theory
Ryushi Goto(
Kagoshima
Univ.⋆) and CR-geometry
Kimio Miyajima
Summary: In this talk, we discuss Kuranishi’s works and their developments focussing on deformation theory
and CR-geometry.

Created: 2014/08/12 08:45
100

Topology

Conference Room VI
13:00–14:15
18 Masaaki Suzuki (Meiji Univ.)
Takuya Sakasai (Univ. of Tokyo)
Shigeyuki Morita(Univ. of Tokyo⋆ / Tokyo Tech⋆)Integral Euler characteristic of Out F11 · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The integral Euler characteristic of Out F11 is −1202.

19 Shunsuke Tsuji (Univ. of Tokyo) ♭ The logarithms of Dehn twists on non-orientable surfaces · · · · · · · · · · · 15
Summary: We introduce a Lie algebra associated with a non-orientable surface, which is an analogue for theGoldman Lie algebra of an oriented surface. As an application, we deduce an explicit formula of the Dehn
twist along an annulus circle on the surface as in Kawazumi–Kuno and Massuyeau–Turaev.

20 Nariya Kawazumi (Univ. of Tokyo)

The Turaev cobracket, the Enomoto–Satoh traces and the divergencecocycle in the Kashiwara–Vergne problem · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We interpret the divergence cocycle in the Kashiwara–Vergne problem and the Enomoto–Satohobstructions for the surjectivity of the Johnson homomorphisms as some part of a regular homotopy versionof the Turaev cobracket.

21 Tomohiko Ishida (Kyoto Univ.)
Masatoshi Sato (Gifu Univ.)

A twisted first homology of the handlebody mapping class group · · · · · 10

Summary: We compute first homology of the handlebody mapping class group with twisted coeﬃcient.

22 Tomohiko Ishida (Kyoto Univ.)

Vanishing of volume flux groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We give a suﬃcient condition for vanishing of volume flux groups, which was first proved byKȩdra–Kotschick–Morita in another way.

September 27th (Sat)

Conference Room VI

9:20–11:50
23 Inasa Nakamura (Univ. of Tokyo)

Two-dimensional braids over a surface link · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: For an oriented surface link S, we can take a satellite construction called a 2-dimensional braidover S, which is a surface link in the form of a covering over S. We demonstrate that 2-dimensional braids
over surface links are useful for showing the distinctness of surface links.

Created: 2014/08/12 08:45
101

Topology

24 Shin Satoh(Kobe Univ.)

Crossing changes unknot a welded knot · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We prove that any descending diagram presents a trivial welded knot. This implies that thecrossing change is an unknotting operation in the category of welded knots. As an application, we provethat there is an embedding of the product of a θ-graph and a circle whose constituents present three given
ribbon knotted torus in 4-space.

25 Seiichi Kamada (Osaka City Univ.)

Cords and 1-handles attached to surface-knots · · · · · · · · · · · · · · · · · · · · · 10

Summary: Boyle classified 1-handles attached to surface-knots, that are closed and connected surfaces
embedded in the Euclidean 4-space, in the case that the surfaces are oriented and 1-handles are orientablewith respect to the orientations of the surfaces. We classify 1-handles attached to surface-knots in the casethat the surface-knots are oriented and 1-handles are non-orientable, and in the case that the surface-knots
are non-orientable.

26 Tetsuya Abe
In Dae Jong

(Tokyo Tech)(Kinki Univ.)

Annulus twist and diﬀeomorphic 4-manifolds II · · · · · · · · · · · · · · · · · · · · 15

Summary: We solve a strong version of Kirby’s problem 3.6 (D), that is, we show that for any integer γ,
there exist infinitely many mutually distinct knots such that 2-handle additions along them with framing γ
yield the same 4-manifold.

27 Masatsuna Tsuchiya (Gakushuin Univ.)

On homotopy K3 surface constructed by two left handed trefoil knots· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We define Xn to be the 4-dimentional handlebody represented by the Kirby diagram which is a
simple link of two left handed trefoil knots with framing (0, n), and define Mn to be the boudary of Xn .
Note that Mn is a homology 3-sphere. It is known that M−6 bounds a contractible 4-manifold. First weshow that we can get a homotopy K3 surface by using M−6 and Kirby Calculus. Next we show that aknot is not a slice knot and if n is larger than 0, Mn does not bound any contractible 4-manifolds by using
adjunction inequality.

28 Noriyuki Hamada (Univ. of Tokyo)

On sections of the Matsumoto–Cadavid–Korkmaz Lefschetz fibration· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: In the study of (topological, 4-dimensional) Lefschetz fibrations, to investigate (−1)-sections ofa given Lefschetz fibration is a fundamental and important problem concerning Lefschetz pencils, hence
symplectic topology. On the other hand, Yukio Matsumoto originally constructed a genus-2 Lefschetz
fibration with eight singular fibers, and then, Cadavid and Korkmaz independently generalized it to thehigher genera. Those Lefschetz fibrations has played a great role in the development of the theory. In thistalk, we show explicit monodromies of those fibrations which describe a set of disjoint (−1)-sections. The
number of the (−1)-sections involved is the largest ever known, and possibly maximal.

Created: 2014/08/12 08:45
102

Topology

29 Takuya Ukida(Tokyo Tech)

A genus zero Lefschetz fibration on the Akbulut cork · · · · · · · · · · · · · · · 10

Summary: We construct a genus zero positive allowable Lefschetz fibration over the disk (a genus zero PALF
for short) on a cork introduced by Akbulut and describe the monodromy as a positive factorization in the
mapping class group of a fiber. We also examine the monodromies of genus zero PALFs on infinitely many
exotic pairs of compact Stein surfaces such that one is obtained by applying a cork twist to the other.

30 Takahiro Oba(Tokyo Tech)Diﬀeomorphism types of Stein fillings and mapping class groups · · · · · 15

Summary: Classification of Stein fillings of a given contact manifold has been discussed as a crucial problem
in contact geometry. In particular, it is important to examine which contact manifold has a unique Steinfilling. Uniqueness of Stein fillings had often been clarified by symplectic geometry before 2010, while itis sometimes proved by using combinatorics in mapping class groups after 2010. In this talk, considering
Lefschetz fibrations over D2 and mapping class groups, I will present a condition for a Stein fillable integral
homology 3-sphere to have a unique Stein filling. Moreover I will mention a result of weak fillings of thesame manifold.

31 Naohiko Kasuya (Univ. of Tokyo)

On contact submanifolds of the odd dimensional Euclidean spaces · · · · 15

Summary: We prove that a closed co-oriented contact 3-manifold can be a contact submanifold of somecontact structure on R5 , if and only if the first Chern class is trivial. We also prove that a closed co-oriented
contact (2m + 1)-manifold (M 2m+1 , ξ) can be a contact submanifold of the standard contact structure on
R4m+1 , if it satisfies one of the following conditions: (1) m is odd (m ≥ 3) and H1 (M 2m+1 ; Z) = 0, (2) m iseven (m ≥ 4) and M 2m+1 is 2-connected, (3) m = 2 and M 5 is simply-connected.

32 Tomohiro Horiuchi (Chuo Univ.)

Leafwise holomorphic automorphisms of Reeb components · · · · · · · · · · 15

Summary: The aim of this study is to classify the structures of the Reeb component as a Levi flat CR
manifold, by considerating the leafwise holomorphic automorphisms.

14:15–15:40
33 Kuniyuki Takaoka (Waseda Univ.)

LR number of spherical closed curves · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Given an oriented spherical closed curve with n transverse crossing points, we assign a cyclic wordof length 2n on two letters L standing left and R standing right by reading the crossing sign so that eachcrossing point is read once L and once R. The LR number is the number of appearence of the subword
LR. In this talk, we completely determine oriented spherical closed curves whose LR number is less than orequal to three.

Created: 2014/08/12 08:45
103

Topology(Waseda Univ.)
34 Noboru Ito
Yusuke Takimura(Gakushuin Boy’s Junior High School)

Triple chords and strong (1, 2) homotopy · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A triple chord is a circle and three chords whose endpoints are on the circle and any two chords
are mutually intersect. A chord diagram of a spherical curve consists of a circle and chords, each of whichconnects the preimages for every double point. In this talk, we consider a relationship between the numberof triple chords as sub-chord diagrams and an equivalence relation called strong (1, 2) homotopy for sphericalcurves.

(Waseda Univ.)
35 Noboru Ito
Yusuke Takimura(Gakushuin Boy’s Junior High School)

Strong and weak (1, 2) homotopies on spherical curves and new invariants · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The second Reidemeister move can be decomposed into two types, respectively called strong or
weak. This talk gives a necessary and suﬃcient condition that two spherical curves are equivalent by a finite
sequence consisting of the first and the strong second Reidemeister moves. Similarly, we obtain a necessary
and suﬃcient condition in the weak case. We also define an integer-valued invariant with respect to the first
and the strong second Reidemeister moves.

36 Kenta Hayano (Hokkaido Univ.)(Waseda Univ.)
Noboru Ito

A new aspect of the Arnold invariant J + from a global viewpoint · · · · 15

Summary: The Arnold invariant J + for generic plane curves counts the number of local moves called direct
self-tangency perestroika in a generic regular homotopy from a standard curve to a given one. In this talkwe will give infinitely many regular homotopic curves with the same J + which cannot be mutually relatedby any generic regular homotopies without direct self-tangency perestroika.

37 Keiichi Sakai(Shinshu Univ.)

Lin–Wang type formula for Haefliger invariant · · · · · · · · · · · · · · · · · · · · · 15

Summary: Long embeddings R4k−1 ,→ R6k are classified by Haefliger invariant. We show that Haefliger
invariant behaves as it is of order two. As a byproduct we obtain an invariant for long generic immersions
R4k−1 ↬ R6k−1 which can be lifted to embeddings R4k−1 ,→ R6k .

38 Yusuke Mizota (Kyushu Univ.)
Takashi Nishimura(Yokohama Nat. Univ.)

Is the module of lowerable vector fields finitely generated? · · · · · · · · · · · 10

Summary: The notion of lowerable vector field was introduced by Arnol’d for studying bifurcations of wave
front singularities. Is the module of lowerable vector fields finitely generated in general? In this talk, wegive a partial aﬃrmative answer to this problem.

Created: 2014/08/12 08:45
104

Topology

16:00–17:00

Talk Invited by Topology Section

Masaharu Ishikawa (Tohoku Univ.)

Stable maps and branched shadows of 3-manifolds

Summary: The stable maps play an important role in the study of smooth manifolds, especially used for
obtaining topological information of the source manifold from the types of their singularities as seen in Morsetheory. We are studying stable maps from orientable 3-manifolds to a plane. A shadow is a polyhedronequipped with a half integer on each region. The 3-manifold represented by a shadow is a kind of circle
bundle over the polyhedron. F. Costantino and D. Thurston regarded the Stein factorization of a stable
map as a shadow and used it to construct a shadow from a triangulation of a 3-manifold.
The aim of our study is to get information of “complexity” of 3-manifolds from stable maps. We show thatthe stable map complexity is equal to the branched shadow complexity for a compact orientable 3-manifold
possibly with torus boundaries; the former is the minimal number of singular fibers of codimension 2 ofstable maps of the 3-manifold and the latter is the minimal number of vertices of its branched shadows.
These complexities estimate the volume from above and below in case the manifold is hyperbolic. We alsoclassify hyperbolic links in the 3-sphere whose exteriors have the complexity 1 in terms of Dehn surgeries.
This is joint work with Yuya Koda.

September 28th (Sun)

Conference Room VI

9:20–12:00
39 Naoko Kamada (Nagoya City Univ.)

The writhes of a twisted knot · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: The odd writhe is a numerical invariant of virtual knots defined by L. Kauﬀman. S. Satoh and
K. Taniguchi introduced a series of numerical invariants of a virtual knot, called n-writhes. They are arefinement of the odd writhe. The n-writhes are related to the index polynomial defined by Y. Im, K.
Lee and Y. Lee and A. Henrich and the aﬃne index polynomial definined by Kauﬀman. We discuss ageneralization of them to a twisted knot.

40 Takuji Nakamura(Osaka Electro-Comm. Univ.)
Yasutaka Nakanishi (Kobe Univ.)(Kobe Univ.)
Shin SatohOn the set of virtual knots with a given state number · · · · · · · · · · · · · · 10

Summary: A state of a virtual knot diagram D is a union of circles obtained from D by splicing all real
crossings. Let sn (D) be the number of states of D consisting of n circles. The n-state number of a virtual
knot K is the minimal number of sn (D) for all possible virtual knot diagrams of K. In this talk, we consider
a set of virtual knots whose n-state number is equal to i for each non-negative integer i and study thefiniteness of the set.

Created: 2014/08/12 08:45
105

Topology

41 Yasutaka Nakanishi (Kobe Univ.)
Yoko Sakamoto (Kobe Univ.)(Kobe Univ.)
Shin SatohDelta-crossing number for knots · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: A Delta-crossing tangle is a tangle of three arcs with three crossings, which is appeared in a Delta
move. A Delta-crossing diagram is a diagram which can be decomposed into Delta-crossing tangles joined bysimple arcs. We prove that every knot has a Delta-crossing diagram, and then investigate the Delta-crossing
number which is the minimum number of Delta-crossing tangles among all Delta-crossing diagrams of thegiven knot. We obtain upper and lower bounds on the number in terms of the ordinal crossing number andgenus.

42 Shosaku Matsuzaki (Waseda Univ.)

On arrangements of component-trivial links on planes · · · · · · · · · · · · · · 15

Summary: Let L = L1 ∪ L2 ∪ ... ∪ Ln be a link in R3 such that Li is a trivial link for each 1 ≤ i ≤ n. Let P1 ,P2 , ..., Pn be mutually distinct flat planes in R3 such that no two of them are parallel. Then there is a link
L′ = L′1 ∪ L′2 ∪ ... ∪ L′n in R3 such that L is ambient isotopic to L′ and L′i ⊂ Pi for each 1 ≤ i ≤ n.

43 Atsushi Ishii (Univ. of Tsukuba)

Circulatory orientations and handlebody-links · · · · · · · · · · · · · · · · · · · · · 10

Summary: A handlebody-knot is a handlebody embedded in the 3-sphere. It is a fundamental problem
to give a suitable orientation for handlebody-knot. We introduce a circulatory orientation and discuss
fundamental moves for handlebody-knots.

44 Toshio Saito (Joetsu Univ. of Edu.)

Essential tangle spheres of knots · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In 1998, it was shown by Ozawa that if a knot in the 3-sphere admits an essential free 2-tangle
sphere, then its essential tangle sphere is unique. We discuss if the result above could be generalized.

45 Yoshiyuki Nakagawa (Ryukoku Univ.)
Yasushi Yamashita(Nara Women’s Univ.)
Makoto Tamura (Osaka Sangyo Univ.)

The growth of torus link groups · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: Let G be a finitely generated group with a finite generating set S. For g ∈ G, let lS (g) be thelength of the shortest word over S representing g. The growth series of G with respect to S is the series∑∞
A(t) = n=0 an tn , where an is the number of elements of G with lS (g) = n. If A(t) can be expressed as arational function of t, then G is said to have a rational growth function.
We calculate explicitly the rational growth functions of (p, q)-torus link groups for any p, q > 1. As anapplication, we show that their growth rates are Perron numbers.

46 Yuka Kotorii (Univ. of Tokyo)

On relation between the Milnor’s µ-invariant and HOMFLYPT polynomial · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: Milnor introduced a family of invariants for ordered oriented links, called µ̄-invariants. Moreover,
Habegger–Lin showed that Milnor’s invariants are invariants of string link, called µ-invariants. Polyak
showed a relation between the µ̄-invariants of length 3 sequence and Conway polynomials. We show thatany µ-invariant of length ≤ k can be represented as a combination of HOMFLYPT polynomials if allµ-invariant of length ≤ k − 2 vanish. This result is an extension of Polyak’s result.

Created: 2014/08/12 08:45
106

Topology

47 Yasuyoshi Tsutsumi(Oshima Nat. Coll. of Maritime Tech.)

Negativity of the third Ohtsuki invariants of the Brieskorn–Hamm
homology 3-spheres · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: We calculate the third Ohtsuki inavariant of every Brieskorn–Hamm manifold which is a rational
homology 3-sphere. By the result, we show that the third Ohtsuki invariants of Brieskorn–Hamm homology
3-spheres are negative.

48 Takayuki Morifuji (Keio Univ.) ∗ Parabolic representations of 2-bridge knots and twisted Alexander polyAnh T. Tran (Ohio State Univ.) nomials · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk we discuss the twisted Alexander polynomial associated to parabolic representationsof 2-bridge knots. We also give an aﬃrmative answer to a conjecture of Dunfield, Friedl and Jackson for
infinitely many hyperbolic knots.

49 Teruaki Kitano(Soka Univ.)

Reidemeister torsion of a homology 3-sphere surgeried along a torus
knot for SL(2, C)-irreducible representaions · · · · · · · · · · · · · · · · · · · · · · · 10

Summary: In this talk we consider a homology 3-sphere M obtained by Dehn surgery along a torus knot
and a SL(2, C)-irreducible representation of π1 (M ). Here Reidemeister torsion τρ (M ) can be defined as
a complex number. By using Reidemeister torsion τρ (M ) for ρ, we define the semi-torsion plolynomial∏σM (t) = ρ (t − 21 τρ ). In 1980’s D. Johnson computed this polynomial for the homology 3-sphere surgeriedalong (2,3)-torus knot. In this talk we give a formula for this polynomial for a homology 3-sphere along atorus knot. It is a generalization of D. Johnson’s formula.

50 Takamichi Sushida (Meiji Univ.)
Akio Hizume (Ryukoku Univ.)
Yoshikazu Yamagishi (Ryukoku Univ.)

Shape limit in Voronoi spiral multiple tilings · · · · · · · · · · · · · · · · · · · · · · 15√

Summary: We study Voronoi diagrams with the spiral sequence S = {ζ j = rj e −1jθ : j ∈ Z} of a covering
space Mv of C∗ := C\{0}, where v ∈ Z\{0}. They are intimately related to the phyllotaxis and continued
fractions. Generically, the tiles are hexagons, while they are quadrilaterals in the degenerate case. For each
multiplicity v, the set Bv of generators ζ ∈ Mv of quadrilateral multiple tilings is the union of branches∪of real algebraic curves parameterized by θ. Their union B = v Bv is a dense subset of the unit disk.
Moreover, we consider the shapes of quadrilateral tiles when θ/2πv is fixed and r tends to 1. If θ/2πv isa quadratic irrational, then the limit set of the shape parameters is a finite set. In particular, if θ/2πv is√linearly equivalent to the golden section τ = 1+2 5 , then the limit shape is the square.

51 Hirotaka Akiyoshi (Osaka City Univ.)

Side parameter for the torus with a single cone point · · · · · · · · · · · · · · · 10

Summary: Let M be the cone manifold obtained as the product of the torus with a single cone point ofcone angle θ ∈ (0, 2π) and the interval. We introduce the side parameter for the space of cone hyperbolic
structures on M whose holonomy representations are real.

Created: 2014/08/12 08:45
107

Infinite Analysis

Infinite Analysis
September 25th (Thu)

Conference Room IX

10:00–12:00
1 Genki Shibukawa (Kyushu Univ.)

Multivariate Meixner, Charlier and Krawtchouk polynomials · · · · · · · · 15

Summary: We introduce some multivariate analogues of Meixner, Charlier and Krawtchouk polynomials,
and establish their main properties, that is, duality, degenerate limits, generating functions, orthogonality
relations, diﬀerence equations, recurrence formulas and determinant expressions. A particularly importantand interesting result is that “the generating function of the generating function” for the Meixner polynomials
coincides with the generating function of the Laguerre polynomials, which has reviously not been known evenfor the one variable case. Actually, main properties for the multivariate Meixner, Charlier and Krawtchouk
polynomials are derived from some properties of the multivariate Laguerre polynomials by using this key
result.

2 Yusuke Ohkubo (Nagoya Univ.)

Existence and orthogonality of generalized Jack symmetric functions
arising from AGT conjecture and its q-deformation · · · · · · · · · · · · · · · · · 15

Summary: We investigate the existence and the orthogonality of the generalized Jack symmetric functions
which play an important role in the proof of the AGT conjecture. We show their orthogonality by deforming
them to the generalized Macdonald symmetric functions. In addition we talk about a possibility to describe
the q-deformed AGT conjecture with help of the generalized Macdonald symmetric functions.

3 Kouichi Takemura (Chuo Univ.)

Multi-indexed Jacobi polynomials and Maya diagrams · · · · · · · · · · · · · · 15

Summary: Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions ofa deformed Pöschl–Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials
and pairs of Maya diagrams, and we show that any multi-indexed Jacobi polynomial is essentially equal
to some multi-indexed Jacobi polynomial of two types of eigenfunction. As an application, we show a
Wronskian-type formula of some special eigenstates of the deformed Pöschl–Teller Hamiltonian.

4 Ayumu Hoshino(Kagawa Nat. Coll. of Tech.)
Masatoshi Noumi (Kobe Univ.)
Junichi Shiraishi (Univ. of Tokyo)

Fourfold series expression for Askey–Wilson polynomial · · · · · · · · · · · · · 15

Summary: We present a fourfold series expansion representing the Askey–Wilson polynomials. To obtain
the result, a sequential use is made of several summation and transformation formulas for the basic
hypergeometric series, including the Verma’s q-extension of the Field and Wimp expansion, Andrews’
terminating q-analogue of Watson’s 3 F2 sum, Singh’s quadratic transformation.

Created: 2014/08/12 08:45
108

Infinite Analysis

5 Ayumu Hoshino(Kagawa Nat. Coll. of Tech.)
Masatoshi Noumi (Kobe Univ.)
Junichi Shiraishi (Univ. of Tokyo)

An explicit formula for Koornwinder polynomial with one row diagram
and a proof of Lassalle’s conjectures · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We present an explicit formula for the Koornwinder polynomial of type BCn with one row
diagram. When the parameters are specialized, we recover Lassalle’s formula for Macdonald polynomials oftype Bn , Cn and Dn with one row diagram, thereby proving his conjectures.

6 Yosuke Saito(Tohoku Univ.)

Modular double of the Ding–Iohara–Miki algebra obtained from the
double sine function · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: From the kernel function defined by the double sine function, we obtain two free field realizationsof the Ding–Iohara–Miki algebra which commute with each other. Similar situations have been observed instudies of modular doubles of quantum groups.

14:15–15:30
7 Youichi Shibukawa (Hokkaido Univ.)

Hopf algebroids associated with dynamical Yang–Baxter maps · · · · · · · 15

Summary: We introduce construction of Hopf algebroids by means of dynamical Yang–Baxter maps.

8 Youichi Shibukawa (Hokkaido Univ.)

Rigid tensor categories associated with dynamical Yang–Baxter maps
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We introduce rigid tensor categories associated with dynamical Yang–Baxter maps.

9 Masanori Ando (Wakhok Univ.) ∗ An understanding and its application of the similarity in the generating
functions of partitions and strict partitions · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: The generating functions of partitions and strict partitions are similar. It is trivial in thegenerating function. However we understand this similarity as combinatorics using simple set theory. And
we generalize it to q-identity called Uchimura type.

10 Saburo Kakei (Rikkyo Univ.)
Kenji Kajiwara (Kyushu Univ.)

Toda hierarchy and motion of plane curves by modified KdV hierarchy· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A relation between the Goldstein–Petrich hierarchy for plane curves and the Toda lattice hierarchy
is investigated. A representation formula for plane curves is given in terms of a special class of τ -functionsof the Toda lattice hierarchy.

Created: 2014/08/12 08:45
109

Infinite Analysis

15:45–16:45

Talk Invited by Infinite Analysis Special Session
Soichi Okada (Nagoya Univ.) Schur-type Pfaﬃans and their applications to symmetric function
Summary: The evaluation of determinants or Pfaﬃans plays a key role in combinatorics, representation

theory, infinite analysis, and so on. In this talk, we consider generalizations of Schur’s Pfaﬃans Pf((xi −xj )/(xi +xj )) and Pf((xi −xj )/(1−xi xj )). We can express these Schur-type Pfaﬃans in terms of generalized
Vandermonde determinants. By using these formulae, we derive King’s column-length restricted version of
Littlewood’s identities for summations of Schur functions, and Worley’s formulae expressing near-staircase
Schur’s P -functions in terms of Schur functions. Also we discuss extensions and variations of them.

September 26th (Fri)

Conference Room IX

10:00–12:00
11 Takeshi Morita (Osaka Univ.)

A relation between the divergent bilateral basic hypergeometric series
2 ψ2 (a, 0; b1 , b2 ; q, x) and the basic hypergeometric series · · · · · · · · · · · · · 15

Summary: We give the new relation between the bilateral basic hypergeometric series around the origin
and the unilateral basic hypergeometric series around the origin by the using of the q-Borel–Laplacetransformations.

12 Shin Isojima(Hosei Univ.)

Ultradiscrete limit of special function solutions of the Painlevé III
equation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: The Painlevé III equation possesses a class of special solutions in a determinantal form with the
Bessel function elements. In this talk, its ultradiscrete analog is constructed by procedure of ultradiscretization with parity variables.

13 Tomoyuki Takenawa(Tokyo Univ. of Marine Sci. and Tech.)

Schlesinger transformations and diﬀerence Painlevé equations · · · · · · · · 15

Summary: Schlesinger transformations are algebraic transformations of a Fuchsian system that preserve its
monodromy representation and act on the characteristic indices of the system by integral shifts. One of theimportant reasons to study such transformations is the relationship between Schlesinger transformations
and discrete Painlevé equations. Based on a recent work with A. Dzhamay and H. Sakai, we derive discrete
Schlesinger evolution equations describing discrete dynamical systems generated by elementary Schlesinger
transformations and give their discrete Hamiltonian description w.r.t. the standard symplectic structure on
the space of Fuchsian systems. As an application, we explicitly derive diﬀerence Painlevé equations of type
(1)
(1)∗
(1)∗
D4 , A2 and A1 from Schlesinger transformations.

(Kyoto Univ.)
14 Kohei Iwaki
Tomoki Nakanishi (Nagoya Univ.)

Exact WKB analysis and cluster algebras · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We develop the mutation theory in the exact WKB analysis using the framework of cluster
algebras. As we vary the phase of Stokes curves, the Stokes graph changes the topology when a Stokes
segment appears. We call this phenomenon the mutation of Stokes graphs. Such a mutation of the
Stokes graph causes a Stokes phenomenon for Voros symbols. We show that the Voros symbols mutate asvariables of a cluster algebra with surface realization. As an application, we obtain the identities of Stokes
automorphisms associated with periods of cluster algebras.

Created: 2014/08/12 08:45
110

Infinite Analysis

15 Masataka Kanki (Rikkyo Univ.)
Tetsuji Tokihiro (Univ. of Tokyo)
Takafumi Mase (Univ. of Tokyo)(Nihon Univ.)
Jun Mada

Co-primeness condition as an integrability criterion for discrete equations · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: We study the Laurent property, the irreducibility and co-primeness of discrete integrable andnon-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence,
and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility andco-primeness hold only in the integrable case. Next we apply this method to the nonlinear partial diﬀerence
equations, such as the discrete KdV equation and the discrete Toda equation. We conclude that co-primenessof the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of theconfinement of singularities in discrete equations.

16 Akishi Kato (Univ. of Tokyo)
Yuji Terashima (Tokyo Tech)

Quiver mutation loops and partition q-series · · · · · · · · · · · · · · · · · · · · · · · 15

Summary: A quiver mutation loop is a loop in a quiver exchange graph. We define partition q-series forquiver mutation loops, and show that they enjoy various remarkable properties such as pentagon identities,
and modular properties, and relation with fermionic character formulas of certain conformal field theories.
The partition q-series are defined solely in terms of combinatorial data and are independent of the details of
the system under study.

13:00–14:00

Talk Invited by Infinite Analysis Special Session

Yousuke Ohyama (Osaka Univ.)

Classical Analysis on the q-Painlevé equations

Summary: The Painlevé equations are found by Paul Painlevé in 1898. He classified all of second ordernonlinear ordinary diﬀerential equations without movable branch points. Sakai showed that all of initialvalue spaces of the Painlevé equations are rational surfaces with some condition. He classified all of such
surfaces, and showed that all of elliptic, q-analogue, diﬀerence and diﬀerential Painlevé equations can be
unified in his classification.
There are many researches on the q-Painlevé equations in these twenty years, such that Bc̈klund transformations, special solutions and their determinant representations. But the properties of generic transcendental
solutions are unrevealed. In this talk, we study analytic properties of the q-Painlevé transcendents. We
review the Riemann–Hibert–Birkhoﬀ correspondence and study connection formula of the q-Painlevé equations.