## Future seminars

Seminar information archive ～12/12｜Today's seminar 12/13 | Future seminars 12/14～

### 2018/12/14

#### Algebraic Geometry Seminar

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

On the birationality of quint-canonical systems of irregular threefolds of general type (English)

**Zhi Jiang**(Fudan)On the birationality of quint-canonical systems of irregular threefolds of general type (English)

[ Abstract ]

It is well-known that the quint-canonical map of a surface of general type is birational.

We will show that the same result holds for irregular threefolds of general type. The proof is based on

a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi

type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.

It is well-known that the quint-canonical map of a surface of general type is birational.

We will show that the same result holds for irregular threefolds of general type. The proof is based on

a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi

type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.

### 2018/12/17

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)

**Joe Kamimoto**(Kyushu University)Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)

[ Abstract ]

This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.

This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.

The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.

### 2018/12/18

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Dynamics of singular vortex patches (English)

**In-Jee Jeong**(Korea Institute for Advanced Study (KIAS))Dynamics of singular vortex patches (English)

[ Abstract ]

Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.

This is joint work with Tarek Elgindi.

Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.

This is joint work with Tarek Elgindi.

#### Tuesday Seminar on Topology

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

Discrete G-spectra and a model for the K(n)-local stable homotopy category (JAPANESE)

**Takeshi Torii**(Okayama University)Discrete G-spectra and a model for the K(n)-local stable homotopy category (JAPANESE)

[ Abstract ]

The K(n)-local stable homotopy categories are building blocks for the stable homotopy category of spectra. In this talk I will construct a model for the K(n)-local stable homotopy category, which explicitly shows the relationship with the Morava E-theory E_n and the stabilizer group G_n. We consider discrete symmetric G-spectra studied by Behrens-Davis for a profinite group G. I will show that the K(n)-local stable homotopy category is realized in the homotopy category of modules in discrete symmetric G_n-spectra over a discrete model of E_n.

The K(n)-local stable homotopy categories are building blocks for the stable homotopy category of spectra. In this talk I will construct a model for the K(n)-local stable homotopy category, which explicitly shows the relationship with the Morava E-theory E_n and the stabilizer group G_n. We consider discrete symmetric G-spectra studied by Behrens-Davis for a profinite group G. I will show that the K(n)-local stable homotopy category is realized in the homotopy category of modules in discrete symmetric G_n-spectra over a discrete model of E_n.

### 2018/12/19

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements

**Rei Mizuta**(Univ. Tokyo)Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements

#### Number Theory Seminar

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

Cohomology vanishing for automorphic vector bundles (ENGLISH)

**Jean-Stefan Koskivirta**(University of Tokyo)Cohomology vanishing for automorphic vector bundles (ENGLISH)

[ Abstract ]

A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.

A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.

### 2018/12/21

#### Algebraic Geometry Seminar

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Degenerations of p-adic volume forms (English)

**Mattias Jonsson**(Michigan)Degenerations of p-adic volume forms (English)

[ Abstract ]

Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.

Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.

### 2018/12/25

#### Tuesday Seminar of Analysis

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

Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)

**MASAKI Satoshi**(Osaka University)Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)

[ Abstract ]

In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.

In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.

#### Infinite Analysis Seminar Tokyo

16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Q-operators for generalised eight vertex models associated

to the higher spin representations of the Sklyanin algebra. (ENGLISH)

**Takashi Takebe**(National Research University Higher School of Economics (Moscow))Q-operators for generalised eight vertex models associated

to the higher spin representations of the Sklyanin algebra. (ENGLISH)

[ Abstract ]

The Q-operator was first introduced by Baxter in 1972 as a

tool to solve the eight vertex model and recently attracts

attention from the representation theoretical viewpoint. In

this talk, we show that Baxter's apparently quite ad hoc and

technical construction can be generalised to the model

associated to the higher spin representations of the

Sklyanin algebra.

The Q-operator was first introduced by Baxter in 1972 as a

tool to solve the eight vertex model and recently attracts

attention from the representation theoretical viewpoint. In

this talk, we show that Baxter's apparently quite ad hoc and

technical construction can be generalised to the model

associated to the higher spin representations of the

Sklyanin algebra.

### 2019/01/09

#### Number Theory Seminar

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

Formal groups and p-adic dynamical systems (ENGLISH)

**Laurent Berger**(ENS de Lyon)Formal groups and p-adic dynamical systems (ENGLISH)

[ Abstract ]

A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.

A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.

### 2019/01/16

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)

**Lei Fu**(Yau Mathematical Sciences Center, Tsinghua University)p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)

[ Abstract ]

Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.

Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.

### 2019/01/22

#### Tuesday Seminar of Analysis

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

TBA (Japanese)

**KATO Keiichi**(Tokyo University of Science)TBA (Japanese)

### 2019/01/28

#### Tokyo Probability Seminar

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

TBA (JAPANESE)

**Yosuke Kawamoto**(FUKUOKA DENTAL COLLEGE)TBA (JAPANESE)

### 2019/01/29

#### Algebraic Geometry Seminar

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

Logarithmic good reduction and the index (TBA)

**Kentaro Mitsui**(Kobe)Logarithmic good reduction and the index (TBA)

[ Abstract ]

A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.

A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.