## Seminar information archive

Seminar information archive ～02/21｜Today's seminar 02/22 | Future seminars 02/23～

### 2017/03/06

#### Seminar on Geometric Complex Analysis

10:00-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Projective and c-projective metric geometries: why they are so similar (ENGLISH)

**Vladimir Matveev**(University of Jena)Projective and c-projective metric geometries: why they are so similar (ENGLISH)

[ Abstract ]

I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.

Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.

I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.

Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.

### 2017/02/24

#### Colloquium of mathematical sciences and society

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

### 2017/02/23

#### FMSP Lectures

13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

### 2017/02/20

#### Tuesday Seminar on Topology

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

The Verlinde formula for Higgs bundles (ENGLISH)

**Jørgen Ellegaard Andersen**(Aarhus University)The Verlinde formula for Higgs bundles (ENGLISH)

[ Abstract ]

In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will explain how all these dimensions fit into a one parameter family of 2D TQFT's, encoded in a one parameter family of Frobenius algebras, which we will construct.

In this talk we will present a Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. We further present a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks. We will explain how all these dimensions fit into a one parameter family of 2D TQFT's, encoded in a one parameter family of Frobenius algebras, which we will construct.

### 2017/02/16

#### Applied Analysis

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

Diffusive and inviscid traveling wave solution of the Fisher-KPP equation

(ENGLISH)

**Danielle Hilhorst**(CNRS / University of Paris-Sud)Diffusive and inviscid traveling wave solution of the Fisher-KPP equation

(ENGLISH)

[ Abstract ]

Our purpose is to study the limit of traveling wave solutions of the Fisher-KPP equation as the diffusion coefficient tends to zero. More precisely, we consider monotone traveling waves which connect the stable steady state to the unstable one. It is well known that there exists a positive constant c* such that there does not exist any traveling wave solution if c < c* and a unique (up to translation) monotone traveling wave solution of wave speed c for each c > c*.

We consider the corresponding inviscid ordinary differential equation where the diffusion coefficient is equal to zero and show that it possesses a unique traveling wave solution. We then fix c > 0 arbitrary and prove the convergence of the travelling wave of the parabolic equation with velocity c to that of the corresponding traveling wave solution of the inviscid problem.

Further research should involve a similar problem for monostable systems.

This is joint work with Yong Jung Kim.

Our purpose is to study the limit of traveling wave solutions of the Fisher-KPP equation as the diffusion coefficient tends to zero. More precisely, we consider monotone traveling waves which connect the stable steady state to the unstable one. It is well known that there exists a positive constant c* such that there does not exist any traveling wave solution if c < c* and a unique (up to translation) monotone traveling wave solution of wave speed c for each c > c*.

We consider the corresponding inviscid ordinary differential equation where the diffusion coefficient is equal to zero and show that it possesses a unique traveling wave solution. We then fix c > 0 arbitrary and prove the convergence of the travelling wave of the parabolic equation with velocity c to that of the corresponding traveling wave solution of the inviscid problem.

Further research should involve a similar problem for monostable systems.

This is joint work with Yong Jung Kim.

### 2017/02/13

#### Seminar on Geometric Complex Analysis

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

A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)

**Qi'an Guan**(Peking University)A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)

[ Abstract ]

In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.

This is joint work with Dr. Zhenqian Li.

In this talk, we will present that the germ of a complex analytic set at the origin in $\mathbb{C}^n$ is regular if and only if the related Ohsawa-Takegoshi extension theorem holds. We also present a necessary condition of the $L^2$ extension of bounded holomorphic sections from singular analytic sets.

This is joint work with Dr. Zhenqian Li.

#### Tokyo Probability Seminar

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

Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation

**Satoshi Yokoyama**(Graduate school of mathematical sciences, the university of Tokyo)Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation

### 2017/02/10

#### Algebraic Geometry Seminar

14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Stability theory of a klt singularity II (English)

**Chenyang Xu**(Beijing International Center of Mathematics Research)Stability theory of a klt singularity II (English)

[ Abstract ]

In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

### 2017/02/09

#### Discrete mathematical modelling seminar

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

Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)

**Dinh Tran**(University of New South Wales, Sydney, Australia)Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)

[ Abstract ]

We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.

We study growth of degrees of autonomous and non-autonomous lattice equations, some of which are known to be integrable. We present a conjecture that helps us to prove polynomial growth of a certain class of equations including $Q_V$ and its non-autonomous generalization. In addition, we also study growth of degrees of several non-integrable equations. Exponential growth of degrees of these equations is also proved subject to a conjecture. Our technique is to determine the ambient degree growth of the equations and a conjectured growth of their common factors at each vertex, allowing the true degree growth to be found. Moreover, our results can also be used for mappings obtained as periodic reductions of integrable lattice equations. We also study signatures of growth of degrees of lattice equations over finite fields.

### 2017/02/07

#### Algebraic Geometry Seminar

15:30-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Stability theory of a klt singularity I (English)

**Chenyang Xu**( Beijing International Center of Mathematics Research)Stability theory of a klt singularity I (English)

[ Abstract ]

In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In the talks, we will discuss a series of recent works started by Chi Li, and then by Harold Blum, Yuchen Liu and myself, in which we want to establish an algebro-geometric stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. metric tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

### 2017/02/03

#### thesis presentations

9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical modeling for synchronization of cardiac muscle cells (心筋細胞の拍動同期現象に関する数理モデル）

(JAPANESE)

**林 達也**(東京大学大学院数理科学研究科)Mathematical modeling for synchronization of cardiac muscle cells (心筋細胞の拍動同期現象に関する数理モデル）

(JAPANESE)

#### thesis presentations

10:45-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Characteristic class and the ε-factor of an étale sheaf (エタール層の特性類とε因子） (JAPANESE)

**梅崎 直也**(東京大学大学院数理科学研究科)Characteristic class and the ε-factor of an étale sheaf (エタール層の特性類とε因子） (JAPANESE)

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On modularity of elliptic curves over abelian totally real fields (総実アーベル拡大体上の楕円曲線の保型性について）

(JAPANESE)

**吉川 祥**(東京大学大学院数理科学研究科)On modularity of elliptic curves over abelian totally real fields (総実アーベル拡大体上の楕円曲線の保型性について）

(JAPANESE)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces (K3曲面の導来自己同型を用いた超ケーラー多様体上の正エントロピー自己同型の構成について） (JAPANESE)

**大内 元気**(東京大学大学院数理科学研究科)Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces (K3曲面の導来自己同型を用いた超ケーラー多様体上の正エントロピー自己同型の構成について） (JAPANESE)

#### thesis presentations

9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Entanglement Entropy in Algebraic Quantum Field Theory (代数的場の量子論におけるエンタングルメント・エントロピー）

(JAPANESE)

**Otani Yul**(東京大学大学院数理科学研究科)Entanglement Entropy in Algebraic Quantum Field Theory (代数的場の量子論におけるエンタングルメント・エントロピー）

(JAPANESE)

#### thesis presentations

10:45-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

A Categorical Approach for Freeness of Group Actions on C*-algebras （C*-環への群作用の自由性に対する圏論的アプローチ）

(JAPANESE)

**窪田 陽介**(東京大学大学院数理科学研究科)A Categorical Approach for Freeness of Group Actions on C*-algebras （C*-環への群作用の自由性に対する圏論的アプローチ）

(JAPANESE)

#### thesis presentations

12:45-14:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Applications of Fraïssé theory to operator algebras (Fraïssé理論の作用素環への応用） (JAPANESE)

**増本 周平**(東京大学大学院数理科学研究科)Applications of Fraïssé theory to operator algebras (Fraïssé理論の作用素環への応用） (JAPANESE)

#### thesis presentations

10:45-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Study of the Kähler-Ricci Flow and its Application in Algebraic Geometry (ケーラー・リッチ流の研究とその代数幾何学における応用）

(JAPANESE)

**野村 亮介**(東京大学大学院数理科学研究科)Study of the Kähler-Ricci Flow and its Application in Algebraic Geometry (ケーラー・リッチ流の研究とその代数幾何学における応用）

(JAPANESE)

#### thesis presentations

12:45-14:00 Room #126 (Graduate School of Math. Sci. Bldg.)

A cohomological study of the existence problem of compact Clifford-Klein forms (コンパクトClifford-Klein形の存在問題のコホモロジー的研究） (JAPANESE)

**森田 陽介**(東京大学大学院数理科学研究科)A cohomological study of the existence problem of compact Clifford-Klein forms (コンパクトClifford-Klein形の存在問題のコホモロジー的研究） (JAPANESE)

#### thesis presentations

14:15-15:30 Room #126 (Graduate School of Math. Sci. Bldg.)

On the quantitative shadowing property of topological dynamical systems (位相的力学系の量的擬軌道追跡性について) (JAPANESE)

**川口 徳昭**(東京大学大学院数理科学研究科)On the quantitative shadowing property of topological dynamical systems (位相的力学系の量的擬軌道追跡性について) (JAPANESE)

#### thesis presentations

9:15-10:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Semigroups generated by higher order elliptic operators and the Stokes operators in end point spaces (端点型空間上の高階楕円型作用素やストークス作用素により生成される半群） (JAPANESE)

**鈴木 拓也**(東京大学大学院数理科学研究科)Semigroups generated by higher order elliptic operators and the Stokes operators in end point spaces (端点型空間上の高階楕円型作用素やストークス作用素により生成される半群） (JAPANESE)

#### thesis presentations

10:45-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematical analysis of the method of fundamental solutions with its application to fluid mechanics and complex analysis (基本解近似解法の数学解析およびその流体力学，複素解析への応用） (JAPANESE)

**榊原 航也**(東京大学大学院数理科学研究科)Mathematical analysis of the method of fundamental solutions with its application to fluid mechanics and complex analysis (基本解近似解法の数学解析およびその流体力学，複素解析への応用） (JAPANESE)

#### thesis presentations

12:45-14:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Numerical Analysis for Interface and Nonlinear Boundary Value Problems for the Stokes Equations (ストークス方程式に対するインターフェースおよび非線形境界値問題の数値解析） (JAPANESE)

**杉谷 宜紀**(東京大学大学院数理科学研究科)Numerical Analysis for Interface and Nonlinear Boundary Value Problems for the Stokes Equations (ストークス方程式に対するインターフェースおよび非線形境界値問題の数値解析） (JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Meta-continuation Semantics via Meta-lambda Calculus (メタラムダ計算を用いたメタ継続意味論) (JAPANESE)

**戸澤 一成**(東京大学大学院数理科学研究科)Meta-continuation Semantics via Meta-lambda Calculus (メタラムダ計算を用いたメタ継続意味論) (JAPANESE)

### 2017/02/02

#### thesis presentations

10:45-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Stability of anti-canonically balanced metrics(反標準的平衡化計量の安定性）

(JAPANESE)

**斎藤 俊輔**(東京大学大学院数理科学研究科)Stability of anti-canonically balanced metrics(反標準的平衡化計量の安定性）

(JAPANESE)

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