## 過去の記録

### 2017年02月20日(月)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Jørgen Ellegaard Andersen 氏 (Aarhus University)
The Verlinde formula for Higgs bundles (ENGLISH)
[ 講演概要 ]
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年02月16日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Diffusive and inviscid traveling wave solution of the Fisher-KPP equation
(ENGLISH)
[ 講演概要 ]
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年02月13日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Qi'an Guan 氏 (北京大学)
A Characterization of regular points by Ohsawa-Takegoshi Extension Theorem (ENGLISH)
[ 講演概要 ]
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.

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

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

### 2017年02月10日(金)

#### 代数幾何学セミナー

14:00-15:30   数理科学研究科棟(駒場) 002号室
Chenyang Xu 氏 (Beijing International Center of Mathematics Research)
Stability theory of a klt singularity II (English)
[ 講演概要 ]
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年02月09日(木)

#### 離散数理モデリングセミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Dinh Tran 氏 (University of New South Wales, Sydney, Australia)
Growth of degrees of lattice equations and its signatures over finite fields (ENGLISH)
[ 講演概要 ]
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年02月07日(火)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 117号室
Chenyang Xu 氏 (Beijing International Center of Mathematics Research)
Stability theory of a klt singularity I (English)
[ 講演概要 ]
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年02月03日(金)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 118号室

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

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室
Otani Yul 氏 (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)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室

(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室

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

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 126号室

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)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 126号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

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)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室

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年02月02日(木)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 118号室

Homology pro stability for pro unital rings, and relative algebraic K-theory (副単位的環のホモロジー副安定性と相対代数的K理論） (JAPANESE)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 118号室

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

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室

Representation theory of Drinfeld doubles (ドリンフェルトダブルの表現論） (JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室

Radon transform for twisted D-modules on partial flag varieties (一般旗多様体上の捻られたD-加群のラドン変換）
(JAPANESE)