## Future seminars

Seminar information archive ～12/11｜Today's seminar 12/12 | Future seminars 12/13～

### 2017/12/13

#### Number Theory Seminar

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

Exponential motives (ENGLISH)

**Javier Fresán**(École polytechnique)Exponential motives (ENGLISH)

[ Abstract ]

What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the étale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums.

Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an étale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).

What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the étale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums.

Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an étale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).

#### FMSP Lectures

17:00-17:45 Room #470 (Graduate School of Math. Sci. Bldg.)

An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rahimov.pdf

**Anar Rahimov**(The Institute of Control Systems of ANAS and Baku State University)An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)

[ Abstract ]

We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.

[ Reference URL ]We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rahimov.pdf

### 2017/12/14

#### Algebraic Geometry Seminar

15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Algebraic curves and modular forms of low degree (English)

**Gerard van der Geer**(Universiteit van Amsterdam)Algebraic curves and modular forms of low degree (English)

[ Abstract ]

For genus 2 and 3 modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such modular forms for genus 2 and 3 using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.

For genus 2 and 3 modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such modular forms for genus 2 and 3 using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.

#### Applied Analysis

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

Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain

(English)

**I-Kun, Chen**(Kyoto University)Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain

(English)

[ Abstract ]

We consider the diffuse reflection boundary problem for the linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a $C^2$ strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. Velocity averaging effect for stationary solutions as well as observations in geometry are used in this research.

We consider the diffuse reflection boundary problem for the linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a $C^2$ strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. Velocity averaging effect for stationary solutions as well as observations in geometry are used in this research.

#### Algebraic Geometry Seminar

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Perfectoid test ideals (English)

**Linquan Ma**(University of Utah)Perfectoid test ideals (English)

[ Abstract ]

Inspired by the recent solution of the direct summand conjecture

of Andre and Bhatt, we introduce perfectoid multiplier/test ideals in mixed

characteristic. As an application, we obtain a uniform bound on the growth

of symbolic powers in regular local rings of mixed characteristic analogous

to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal

characteristic. This is joint work with Karl Schwede.

Inspired by the recent solution of the direct summand conjecture

of Andre and Bhatt, we introduce perfectoid multiplier/test ideals in mixed

characteristic. As an application, we obtain a uniform bound on the growth

of symbolic powers in regular local rings of mixed characteristic analogous

to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal

characteristic. This is joint work with Karl Schwede.

### 2017/12/18

#### Seminar on Geometric Complex Analysis

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

Gradient flow of the Ding functional

**Tomoyuki Hisamoto**(Nagoya University)Gradient flow of the Ding functional

[ Abstract ]

This is a joint work with T. Collins and R. Takahashi. We introduce the flow in the title to study the stability of a Fano manifold. The first result is the long-time existence of the flow. In the stable case it then converges to the Kähler-Einstein metric. In general the flow is expected to produce the optimally destabilizing degeneration of a Fano manifold. We confirm this expectation in the toric case.

This is a joint work with T. Collins and R. Takahashi. We introduce the flow in the title to study the stability of a Fano manifold. The first result is the long-time existence of the flow. In the stable case it then converges to the Kähler-Einstein metric. In general the flow is expected to produce the optimally destabilizing degeneration of a Fano manifold. We confirm this expectation in the toric case.

#### Operator Algebra Seminars

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

Isomorphism and Morita equivalence classes for crossed product of irrational rotation algebras by cyclic subgroups of $SL_2({\mathbb Z})$ (English)

**Zhuofeng He**(Univ. Tokyo)Isomorphism and Morita equivalence classes for crossed product of irrational rotation algebras by cyclic subgroups of $SL_2({\mathbb Z})$ (English)

### 2017/12/19

#### Numerical Analysis Seminar

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

#### Tuesday Seminar on Topology

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

Deformation of holomorphic quadratic differentials and its applications (JAPANESE)

**Hideki Miyachi**(Osaka university)Deformation of holomorphic quadratic differentials and its applications (JAPANESE)

[ Abstract ]

Quadratic differentials are standard and important objects in Teichmuller theory. The deformation space (moduli space) of the quadratic differentials is applied to many fields of mathematics. In this talk, I will develop the deformation of quadratic differentials. Indeed, following pioneer works by A. Douady, J. Hubbard, H. Masur and W. Veech, we describe the infinitesimal deformations in the odd (co)homology groups on the double covering spaces defined from the square roots of the quadratic differentials. We formulate the decomposition theorem for the infinitesimal deformations with keeping in mind of the induced deformation of the moduli of underlying complex structures. As applications, we obtain the Levi form of the Teichmuller distance, and an alternate proof of the Krushkal formula on the pluricomplex Green function on the Teichmuller space.

Quadratic differentials are standard and important objects in Teichmuller theory. The deformation space (moduli space) of the quadratic differentials is applied to many fields of mathematics. In this talk, I will develop the deformation of quadratic differentials. Indeed, following pioneer works by A. Douady, J. Hubbard, H. Masur and W. Veech, we describe the infinitesimal deformations in the odd (co)homology groups on the double covering spaces defined from the square roots of the quadratic differentials. We formulate the decomposition theorem for the infinitesimal deformations with keeping in mind of the induced deformation of the moduli of underlying complex structures. As applications, we obtain the Levi form of the Teichmuller distance, and an alternate proof of the Krushkal formula on the pluricomplex Green function on the Teichmuller space.

### 2017/12/21

#### Applied Analysis

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

### 2017/12/25

#### Operator Algebra Seminars

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

Kazhdan's property (T) and semidefinite programming

**Narutaka Ozawa**(RIMS, Kyoto University)Kazhdan's property (T) and semidefinite programming

### 2017/12/26

#### Algebraic Geometry Seminar

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

TBA (English)

**Kento Fujita**(RIMS)TBA (English)

[ Abstract ]

TBA

TBA

### 2018/01/15

#### Seminar on Geometric Complex Analysis

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

TBA

**Shinya Akagawa**(Osaka University)TBA

[ Abstract ]

TBA

TBA

### 2018/01/22

#### Seminar on Geometric Complex Analysis

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

TBA

**Yu Kawakami**(Kanazawa University)TBA

[ Abstract ]

TBA

TBA

### 2018/01/26

#### Colloquium

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yuta Koike**(Univ. Tokyo)(JAPANESE)

### 2018/02/23

#### Colloquium

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hiromu Tanaka**(Univ. Tokyo)(JAPANESE)