## Seminar information archive

Seminar information archive ～05/26｜Today's seminar 05/27 | Future seminars 05/28～

### 2015/06/26

#### Colloquium

16:50-17:50 Room #056 (Graduate School of Math. Sci. Bldg.)

Dimer models and mirror symmetry (JAPANESE)

**Kazushi Ueda**(Graduate School of Mathematical Sciences, University of Tokyo)Dimer models and mirror symmetry (JAPANESE)

### 2015/06/25

#### Infinite Analysis Seminar Tokyo

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Autonomous limit of the 4-dimensional Painlev¥.FN"e-type equations and degeneration of curves of genus two (JAPANESE)

**Akane Nakamura**(Tokyo University, Graduate School of Mathematical Sciences)Autonomous limit of the 4-dimensional Painlev¥.FN"e-type equations and degeneration of curves of genus two (JAPANESE)

[ Abstract ]

The Painlev¥.FN"e equations have been generalized from various aspects. Recently, the 4-dimensional Painlev¥N"e-type equations were classified by corresponding linear equations(Sakai, Kawakami-N.-Sakai, Kawakami). In this talk, I explain an attempt to characterize the 40 types of integrable systems obtained as the autonomous limit of the 4-dimensional Painlev¥N"e-type equations, by inspecting the degenerations of their spectral curves, which are curves of genus two.

The Painlev¥.FN"e equations have been generalized from various aspects. Recently, the 4-dimensional Painlev¥N"e-type equations were classified by corresponding linear equations(Sakai, Kawakami-N.-Sakai, Kawakami). In this talk, I explain an attempt to characterize the 40 types of integrable systems obtained as the autonomous limit of the 4-dimensional Painlev¥N"e-type equations, by inspecting the degenerations of their spectral curves, which are curves of genus two.

### 2015/06/24

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Gapped ground state phases, topological order and anyons

**Matthew Cha**(UC Davis)Gapped ground state phases, topological order and anyons

### 2015/06/23

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Box complexes and model structures on the category of graphs (JAPANESE)

**Takahiro Matsushita**(The University of Tokyo)Box complexes and model structures on the category of graphs (JAPANESE)

[ Abstract ]

To determine the chromatic numbers of graphs, so-called the graph

coloring problem, is one of the most classical problems in graph theory.

Box complex is a Z_2-space associated to a graph, and it is known that

its equivariant homotopy invariant is related to the chromatic number.

Csorba showed that for each finite Z_2-CW-complex X, there is a graph

whose box complex is Z_2-homotopy equivalent to X. From this result, I

expect that the usual model category of Z_2-topological spaces is

Quillen equivalent to a certain model structure on the category of

graphs, whose weak equivalences are graph homomorphisms inducing Z_2-

homotopy equivalences between their box complexes.

In this talk, we introduce model structures on the category of graphs

whose weak equivalences are described as above. We also compare our

model categories of graphs with the category of Z_2-topological spaces.

To determine the chromatic numbers of graphs, so-called the graph

coloring problem, is one of the most classical problems in graph theory.

Box complex is a Z_2-space associated to a graph, and it is known that

its equivariant homotopy invariant is related to the chromatic number.

Csorba showed that for each finite Z_2-CW-complex X, there is a graph

whose box complex is Z_2-homotopy equivalent to X. From this result, I

expect that the usual model category of Z_2-topological spaces is

Quillen equivalent to a certain model structure on the category of

graphs, whose weak equivalences are graph homomorphisms inducing Z_2-

homotopy equivalences between their box complexes.

In this talk, we introduce model structures on the category of graphs

whose weak equivalences are described as above. We also compare our

model categories of graphs with the category of Z_2-topological spaces.

### 2015/06/22

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Rational cohomology tori

(English)

http://webusers.imj-prg.fr/~marti.lahoz/

**Martí Lahoz**(Institut de Mathématiques de Jussieu )Rational cohomology tori

(English)

[ Abstract ]

Complex tori can be topologically characterised among compact Kähler

manifolds by their integral cohomology ring. I will discuss the

structure of compact Kähler manifolds whose rational cohomology ring is

isomorphic to the rational cohomology ring of a torus and give some

examples. This is joint work with Olivier Debarre and Zhi Jiang.

[ Reference URL ]Complex tori can be topologically characterised among compact Kähler

manifolds by their integral cohomology ring. I will discuss the

structure of compact Kähler manifolds whose rational cohomology ring is

isomorphic to the rational cohomology ring of a torus and give some

examples. This is joint work with Olivier Debarre and Zhi Jiang.

http://webusers.imj-prg.fr/~marti.lahoz/

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Amoebas and Horn hypergeometric functions

**Susumu Tanabé**(Université Galatasaray)Amoebas and Horn hypergeometric functions

[ Abstract ]

Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.

There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the

analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.

As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.

This is a collaboration with Timur Sadykov.

Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.

There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the

analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.

As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.

This is a collaboration with Timur Sadykov.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Lamplighter random walks on fractals

**Chikara Nakamura**(Research Institute for Mathematical Sciences, Kyoto University)Lamplighter random walks on fractals

### 2015/06/17

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Self-adjointness of bound state operators in integrable quantum field theory

**Yoh Tanimoto**(Univ. Tokyo)Self-adjointness of bound state operators in integrable quantum field theory

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)

(Japanese)

**Norifumi Seki**(University of Tokyo)Hodge-Tate weights of p-adic Galois representations and Banach representations of GL_2(Q_p)

(Japanese)

#### Mathematical Biology Seminar

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

A conservation law and time-delay for viral infection dynamics (JAPANESE)

**Yusuke Kakizoe**(Graduate school of systems life sciences, Kyushu University)A conservation law and time-delay for viral infection dynamics (JAPANESE)

### 2015/06/16

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Stable maps and branched shadows of 3-manifolds (JAPANESE)

**Masaharu Ishikawa**(Tohoku University)Stable maps and branched shadows of 3-manifolds (JAPANESE)

[ Abstract ]

We study what kind of stable map to the real plane a 3-manifold has. It

is known by O. Saeki that there exists a stable map without certain

singular fibers if and only if the 3-manifold is a graph manifold. According to

F. Costantino and D. Thurston, we identify the Stein factorization of a

stable map with a shadow of the 3-manifold under some modification,

where the above singular fibers correspond to the vertices of the shadow. We

define the notion of stable map complexity by counting the number of

such singular fibers and prove that this equals the branched shadow

complexity. With this equality, we give an estimation of the Gromov norm of the

3-manifold by the stable map complexity. This is a joint work with Yuya Koda.

We study what kind of stable map to the real plane a 3-manifold has. It

is known by O. Saeki that there exists a stable map without certain

singular fibers if and only if the 3-manifold is a graph manifold. According to

F. Costantino and D. Thurston, we identify the Stein factorization of a

stable map with a shadow of the 3-manifold under some modification,

where the above singular fibers correspond to the vertices of the shadow. We

define the notion of stable map complexity by counting the number of

such singular fibers and prove that this equals the branched shadow

complexity. With this equality, we give an estimation of the Gromov norm of the

3-manifold by the stable map complexity. This is a joint work with Yuya Koda.

### 2015/06/15

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Boundedness of the KSBA functor of

SLC models (English)

http://www.math.utah.edu/~hacon/

**Christopher Hacon**(University of Utah/RIMS)Boundedness of the KSBA functor of

SLC models (English)

[ Abstract ]

Let $X$ be a canonically polarized smooth $n$-dimensional projective variety over $\mathbb C$ (so that $\omega _X$ is ample), then it is well-known that a fixed multiple of the canonical line bundle defines an embedding of $X$ in projective space. It then follows easily that if we fix certain invariants of $X$, then $X$ belongs to finitely many deformation types. Since canonical models are rarely smooth, it is important to generalize this result to canonically polarized $n$-dimensional projectivevarieties with canonical singularities. Moreover, since these varieties specialize to non-normal varieties it is also important to generalize this result to semi-log canonical pairs. In this talk we will explain a strong version of the above result that applies to semi-log canonical pairs.This is joint work with C. Xu and J. McKernan

[ Reference URL ]Let $X$ be a canonically polarized smooth $n$-dimensional projective variety over $\mathbb C$ (so that $\omega _X$ is ample), then it is well-known that a fixed multiple of the canonical line bundle defines an embedding of $X$ in projective space. It then follows easily that if we fix certain invariants of $X$, then $X$ belongs to finitely many deformation types. Since canonical models are rarely smooth, it is important to generalize this result to canonically polarized $n$-dimensional projectivevarieties with canonical singularities. Moreover, since these varieties specialize to non-normal varieties it is also important to generalize this result to semi-log canonical pairs. In this talk we will explain a strong version of the above result that applies to semi-log canonical pairs.This is joint work with C. Xu and J. McKernan

http://www.math.utah.edu/~hacon/

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)

**Saotome Takanari**The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)

[ Abstract ]

We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.

We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

**Hiroshi Takahashi**(College of Science and Technology, Nihon University)#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Parallel energy-preserving methods for Hamiltonian systems (日本語)

**Yuto Miyatake**(Nagoya University)Parallel energy-preserving methods for Hamiltonian systems (日本語)

### 2015/06/12

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)

**Kota Hattori**(Keio University)The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)

[ Abstract ]

For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.

For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.

### 2015/06/11

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

### 2015/06/10

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Dynamics, dimension, and $C^*$-algebras

**David Kerr**(Texas A&M Univ.)Dynamics, dimension, and $C^*$-algebras

### 2015/06/09

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Symplectic displacement energy for exact Lagrangian immersions (JAPANESE)

**Manabu Akaho**(Tokyo Metropolitan University)Symplectic displacement energy for exact Lagrangian immersions (JAPANESE)

[ Abstract ]

We give an inequality of the displacement energy for exact Lagrangian

immersions and the symplectic area of punctured holomorphic discs. Our

approach is based on Floer homology for Lagrangian immersions and

Chekanov's homotopy technique of continuations. Moreover, we discuss our

inequality and the Hofer--Zehnder capacity.

We give an inequality of the displacement energy for exact Lagrangian

immersions and the symplectic area of punctured holomorphic discs. Our

approach is based on Floer homology for Lagrangian immersions and

Chekanov's homotopy technique of continuations. Moreover, we discuss our

inequality and the Hofer--Zehnder capacity.

### 2015/06/08

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)

**Hisashi Kasuya**(Tokyo Institute of Technology)Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)

[ Abstract ]

By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.

By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

On a stochastic Rayleigh-Plesset equation and a certain stochastic Navier-Stokes equation

**Satoshi Yokoyama**(Graduate School of Mathematical Sciences, The University of Tokyo)On a stochastic Rayleigh-Plesset equation and a certain stochastic Navier-Stokes equation

### 2015/06/05

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Veech groups of Veech surfaces and periodic points

(日本語)

**Yoshihiko Shinomiya**(Shizuoka University)Veech groups of Veech surfaces and periodic points

(日本語)

[ Abstract ]

Flat surfaces are surfaces with singular Euclidean structures. The Veech group of a flat surface is the group consisting of all matrices inducing affine mappings of the flat surface. In this talk, we give relations between some geometrical values of flat surfaces and the signatures of Veech groups as Fuchsian groups. As an application of these relations, we estimate the numbers of periodic points of certain flat surfaces.

Flat surfaces are surfaces with singular Euclidean structures. The Veech group of a flat surface is the group consisting of all matrices inducing affine mappings of the flat surface. In this talk, we give relations between some geometrical values of flat surfaces and the signatures of Veech groups as Fuchsian groups. As an application of these relations, we estimate the numbers of periodic points of certain flat surfaces.

#### Seminar on Probability and Statistics

16:20-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

### 2015/06/03

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

The Furstenberg boundary and $C^*$-simplicity

**Narutaka Ozawa**(RIMS, Kyoto Univ.)The Furstenberg boundary and $C^*$-simplicity

#### Mathematical Biology Seminar

14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Population dynamics of fish stock with migration and its management strategy

**Shigehide Iwata**(The graduate school of marine science and technology, Tokyo University of Marine Science and Technology)Population dynamics of fish stock with migration and its management strategy

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