## 過去の記録

過去の記録 ～05/25｜本日 05/26 | 今後の予定 05/27～

### 2015年11月26日(木)

#### Lie群論・表現論セミナー

17:00-18:45 数理科学研究科棟(駒場) 号室

Introduction to the cohomology of discrete groups and modular symbols 2 (English)

**Birgit Speh 氏**(Cornell University)Introduction to the cohomology of discrete groups and modular symbols 2 (English)

[ 講演概要 ]

The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.

On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.

In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.

On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.

In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

### 2015年11月25日(水)

#### 作用素環セミナー

16:45-18:15 数理科学研究科棟(駒場) 118号室

Combining Pseudodifferential and Vector Bundle Techniques, and Their Applications to Topological Insulators

**Max Lein 氏**(東北大AIMR)Combining Pseudodifferential and Vector Bundle Techniques, and Their Applications to Topological Insulators

#### 統計数学セミナー

14:55-18:00 数理科学研究科棟(駒場) 056号室

本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．

Learning theory and sparsity ～ Introduction into sparse recovery and compressed sensing ～

本講演は,数物フロンティア・リーディング大学院のFMSPレクチャーズとして行います．

**Arnak Dalalyan 氏**(ENSAE ParisTech)Learning theory and sparsity ～ Introduction into sparse recovery and compressed sensing ～

[ 講演概要 ]

In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.

In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.

#### FMSPレクチャーズ

14:55-18:00 数理科学研究科棟(駒場) 056号室

"Learning theory and sparsity" 全3回講演の(1)

(1)Introduction into sparse recovery and compressed sensing. (ENGLISH)

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

"Learning theory and sparsity" 全3回講演の(1)

**Arnak Dalalyan 氏**(ENSAE ParisTech)(1)Introduction into sparse recovery and compressed sensing. (ENGLISH)

[ 講演概要 ]

In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.

[ 参考URL ]In this introductory lecture, we will present the general framework of high-dimensional statistical modeling and its applications in machine learning and signal processing. Basic methods of sparse recovery, such as the hard and the soft thresholding, will be introduced in the context of orthonormal dictionaries and their statistical accuracy will be discussed in detail. We will also show the relation of these methods with compressed sensing and convex programming based procedures.

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

### 2015年11月24日(火)

#### 解析学火曜セミナー

16:50-18:20 数理科学研究科棟(駒場) 126号室

A local analysis of the swirling flow to the axi-symmetric Navier-Stokes equations near a saddle point and no-slip flat boundary (English)

**許 本源 氏**(東大数理)A local analysis of the swirling flow to the axi-symmetric Navier-Stokes equations near a saddle point and no-slip flat boundary (English)

[ 講演概要 ]

As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. One of the effective methods is numerical simulations. The swirling structure is significant both in mathematical analysis and the numerical simulations of tornado. In this joint work with H. Notsu and T. Yoneda we try to clarify the swirling structure. More precisely, we do numerical computations on axi-symmetric Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons occur only in the swirl case: The distance between the point providing the maximum velocity magnitude $|v|$ and the $z$-axis is drastically changing around some time (which we call it turning point). An ``increasing velocity phenomenon'' occurs near the boundary and the maximum value of $|v|$ is obtained near the axis of symmetry and the boundary when time is close to the turning point.

As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. One of the effective methods is numerical simulations. The swirling structure is significant both in mathematical analysis and the numerical simulations of tornado. In this joint work with H. Notsu and T. Yoneda we try to clarify the swirling structure. More precisely, we do numerical computations on axi-symmetric Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons occur only in the swirl case: The distance between the point providing the maximum velocity magnitude $|v|$ and the $z$-axis is drastically changing around some time (which we call it turning point). An ``increasing velocity phenomenon'' occurs near the boundary and the maximum value of $|v|$ is obtained near the axis of symmetry and the boundary when time is close to the turning point.

#### 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

On the cohomology ring of the handlebody mapping class group of genus two (JAPANESE)

Tea : Common Room 16:30 -- 17:00

**佐藤 正寿 氏**(東京電機大学)On the cohomology ring of the handlebody mapping class group of genus two (JAPANESE)

[ 講演概要 ]

The genus two handlebody mapping class group acts on a tree

constructed by Kramer from the disk complex,

and decomposes into an amalgamated product of two subgroups.

We determine the integral cohomology ring of the genus two handlebody

mapping class group by examining these two subgroups

and the Mayer-Vietoris exact sequence.

Using this result, we estimate the ranks of low dimensional homology

groups of the genus three handlebody mapping class group.

The genus two handlebody mapping class group acts on a tree

constructed by Kramer from the disk complex,

and decomposes into an amalgamated product of two subgroups.

We determine the integral cohomology ring of the genus two handlebody

mapping class group by examining these two subgroups

and the Mayer-Vietoris exact sequence.

Using this result, we estimate the ranks of low dimensional homology

groups of the genus three handlebody mapping class group.

#### Lie群論・表現論セミナー

17:00-18:45 数理科学研究科棟(駒場) 号室

Introduction to the cohomology of discrete groups and modular symbols 1 (English)

**Birgit Speh 氏**(Cornell University)Introduction to the cohomology of discrete groups and modular symbols 1 (English)

[ 講演概要 ]

The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.

On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.

In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.

The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.

On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.

In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.

### 2015年11月18日(水)

#### FMSPレクチャーズ

15:00-16:00,16:30-17:00 数理科学研究科棟(駒場) 大講義室号室

中央大学ENCOUNTER with MATHEMATICS共催

Crossroads of symplectic rigidity and flexibility (ENGLISH)

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

中央大学ENCOUNTER with MATHEMATICS共催

**Yakov Eliashberg 氏**(Stanford University)Crossroads of symplectic rigidity and flexibility (ENGLISH)

[ 講演概要 ]

The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

#### FMSPレクチャーズ

10:30-11:30 数理科学研究科棟(駒場) 056号室

Discretising systematically integrable systems (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani1118.pdf

**Alfred Ramani 氏**(Ecole Polytechnique)Discretising systematically integrable systems (ENGLISH)

[ 講演概要 ]

We present various methods for discretising integrable systerms inspired by the works of Hirota and Mickens. We apply these methods to the systematical discretisation of Painlevé equations.

[ 参考URL ]We present various methods for discretising integrable systerms inspired by the works of Hirota and Mickens. We apply these methods to the systematical discretisation of Painlevé equations.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani1118.pdf

#### 数理人口学・数理生物学セミナー

14:55-16:40 数理科学研究科棟(駒場) 128号室

Spatial population dynamics as a point pattern dynamics (JAPANESE)

http://www.ics.nara-wu.ac.jp/jp/staff/takasu.html

**高須夫悟 氏**(奈良女子大学理学部情報科学科)Spatial population dynamics as a point pattern dynamics (JAPANESE)

[ 講演概要 ]

Spatial population dynamics has been conventionally described as

dynamical system where population size (or population density) changes

with time over space as a continuous "real-valued" variable; these are

often given as partial differential equations as reaction-diffusion

models. In this approach, we implicitly assume infinitely large

population thereby population size changes smoothly and

deterministically. In reality, however, a population is a collection of

a certain number of individuals each of which gives birth or dies with

some stochasticity in a space and the population size as the number of

individuals is "integer-valued". In this talk, I introduce an approach

to reconstruct conventional spatial population dynamics in terms of

point pattern dynamics as a stochastic process. I discuss how to

mathematically describe such spatial stochastic processes using the

moments of increasing order of dimension; densities of points, pairs,

and triplets, etc. are described by integro-differential equations.

Quantification of a point pattern is the key issue here. As examples, I

introduce spatial epidemic SIS and SIR models as point pattern dynamics;

each individual has a certain "mark" depending on its health status; a

snapshot of individuals’ distribution over space is represented by a

marked point pattern and this marked point pattern dynamically changes

with time.

[ 参考URL ]Spatial population dynamics has been conventionally described as

dynamical system where population size (or population density) changes

with time over space as a continuous "real-valued" variable; these are

often given as partial differential equations as reaction-diffusion

models. In this approach, we implicitly assume infinitely large

population thereby population size changes smoothly and

deterministically. In reality, however, a population is a collection of

a certain number of individuals each of which gives birth or dies with

some stochasticity in a space and the population size as the number of

individuals is "integer-valued". In this talk, I introduce an approach

to reconstruct conventional spatial population dynamics in terms of

point pattern dynamics as a stochastic process. I discuss how to

mathematically describe such spatial stochastic processes using the

moments of increasing order of dimension; densities of points, pairs,

and triplets, etc. are described by integro-differential equations.

Quantification of a point pattern is the key issue here. As examples, I

introduce spatial epidemic SIS and SIR models as point pattern dynamics;

each individual has a certain "mark" depending on its health status; a

snapshot of individuals’ distribution over space is represented by a

marked point pattern and this marked point pattern dynamically changes

with time.

http://www.ics.nara-wu.ac.jp/jp/staff/takasu.html

#### 統計数学セミナー

17:00-18:10 数理科学研究科棟(駒場) 056号室

Order flow intensities for limit order book modelling

**Ioane Muni Toke 氏**(University of New Caledonia)Order flow intensities for limit order book modelling

[ 講演概要 ]

Limit order books are at the core of electronic financial markets. Mathematical models of limit order books use point processes to model the arrival of limit, market and cancellation orders in the order book, but it is not clear what a "good" parametric model for the intensities of these point processes should be.

In the first part of the talk, we show that despite their simplicity basic Poisson processes can be used to accurately model a few features of the order book that more advanced models reproduce with volume-dependent intensities.

In the second part of the talk we present ongoing investigations in a more advanced statistical modelling of these order flow intensities using in particular normal mixture distributions and exponential models.

Limit order books are at the core of electronic financial markets. Mathematical models of limit order books use point processes to model the arrival of limit, market and cancellation orders in the order book, but it is not clear what a "good" parametric model for the intensities of these point processes should be.

In the first part of the talk, we show that despite their simplicity basic Poisson processes can be used to accurately model a few features of the order book that more advanced models reproduce with volume-dependent intensities.

In the second part of the talk we present ongoing investigations in a more advanced statistical modelling of these order flow intensities using in particular normal mixture distributions and exponential models.

### 2015年11月17日(火)

#### 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

Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)

Tea : Common Room 16:30 -- 17:00

**片長 敦子 氏**(信州大学)Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)

[ 講演概要 ]

In this talk, we deal with hypersurface isolated singularities. First, we will recall

some topological results of singularities. Next, we will sketch the classification of

singularities in algebraic geometry. Finally, we will focus on the three-dimensional

case and discuss some results obtained so far.

In this talk, we deal with hypersurface isolated singularities. First, we will recall

some topological results of singularities. Next, we will sketch the classification of

singularities in algebraic geometry. Finally, we will focus on the three-dimensional

case and discuss some results obtained so far.

#### 代数学コロキウム

18:00-19:00 数理科学研究科棟(駒場) 117号室

いつもと曜日が異なりますのでご注意ください

The Tamagawa number formula over function fields. (English)

いつもと曜日が異なりますのでご注意ください

**Dennis Gaitsgory 氏**(Harvard University & IHES)The Tamagawa number formula over function fields. (English)

[ 講演概要 ]

Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.

The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.

The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

### 2015年11月16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

Towards the complex geometry of Teichmuller space with extremal length (English)

**宮地 秀樹 氏**(大阪大学)Towards the complex geometry of Teichmuller space with extremal length (English)

[ 講演概要 ]

In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.

In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.

#### FMSPレクチャーズ

15:00-16:00,16:30-17:00 数理科学研究科棟(駒場) 大講義室号室

中央大学ENCOUNTER with MATHEMATICS共催

Crossroads of symplectic rigidity and flexibility (ENGLISH)

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

中央大学ENCOUNTER with MATHEMATICS共催

**Yakov Eliashberg 氏**(Stanford University)Crossroads of symplectic rigidity and flexibility (ENGLISH)

[ 講演概要 ]

The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

#### 代数幾何学セミナー

15:30-17:00 数理科学研究科棟(駒場) 122号室

Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)

**Artan Sheshmani 氏**(IPMU/ Ohio State University)Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)

[ 講演概要 ]

I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.

I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.

### 2015年11月14日(土)

#### 調和解析駒場セミナー

13:00-18:00 数理科学研究科棟(駒場) 128号室

The sufficient condition for the Fatou property of weighted block spaces

(日本語)

空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性

(日本語)

**中村 昌平 氏**(首都大学東京) 13:30-15:00The sufficient condition for the Fatou property of weighted block spaces

(日本語)

[ 講演概要 ]

In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.

Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.

Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.

In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.

Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.

Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.

**町原 秀二 氏**(埼玉大学) 15:30-17:00空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性

(日本語)

[ 講演概要 ]

空間1次元Chern-Simons-Dirac方程式系の初期値問題の適切性をソボレフ空間で考える。問題が適切である指数の範囲と非適切である指数の範囲を紹介し、

方程式の構造やソボレフ空間の積評価との関係を観察する。証明は特に非適切性に関して紹介したい。特殊な初期値を設定することにより、解表示を得て、その解関数に対するソボレフ空間での取り扱いについて議論する。本研究は信州大学岡本葵氏との共同研究である。

空間1次元Chern-Simons-Dirac方程式系の初期値問題の適切性をソボレフ空間で考える。問題が適切である指数の範囲と非適切である指数の範囲を紹介し、

方程式の構造やソボレフ空間の積評価との関係を観察する。証明は特に非適切性に関して紹介したい。特殊な初期値を設定することにより、解表示を得て、その解関数に対するソボレフ空間での取り扱いについて議論する。本研究は信州大学岡本葵氏との共同研究である。

### 2015年11月13日(金)

#### FMSPレクチャーズ

15:00-16:00,16:30-17:30 数理科学研究科棟(駒場) 大講義室号室

中央大学ENCOUNTER with MATHEMATICS共催

Crossroads of symplectic rigidity and flexibility (ENGLISH)

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

中央大学ENCOUNTER with MATHEMATICS共催

**Yakov Eliashberg 氏**(Stanford University)Crossroads of symplectic rigidity and flexibility (ENGLISH)

[ 講演概要 ]

The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.

In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.

http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html

#### 幾何コロキウム

10:00-11:30 数理科学研究科棟(駒場) 126号室

ランダム閉３次元写像トーラスの対称性について (Japanese)

**正井 秀俊 氏**(東京大学)ランダム閉３次元写像トーラスの対称性について (Japanese)

[ 講演概要 ]

閉曲面の写像類群上のランダムウォークを考え，それらから得られる写像トーラスをランダム写像トーラスと呼ぶ．ランダム写像トーラスは漸近的に確率１で閉双曲多様体になることが知られている．また，閉双曲多様体の写像類群は有限群となることが知られている．この講演ではランダム写像トーラスの写像類群は漸近的に確率１で自明となることを証明する.

閉曲面の写像類群上のランダムウォークを考え，それらから得られる写像トーラスをランダム写像トーラスと呼ぶ．ランダム写像トーラスは漸近的に確率１で閉双曲多様体になることが知られている．また，閉双曲多様体の写像類群は有限群となることが知られている．この講演ではランダム写像トーラスの写像類群は漸近的に確率１で自明となることを証明する.

### 2015年11月10日(火)

#### トポロジー火曜セミナー

17:30-18:30 数理科学研究科棟(駒場) 056号室

Tea : Common Room 17:00 -- 17:30

Topological T-duality for "Real" circle bundle (JAPANESE)

Tea : Common Room 17:00 -- 17:30

**五味 清紀 氏**(信州大学理学部)Topological T-duality for "Real" circle bundle (JAPANESE)

[ 講演概要 ]

Topological T-duality originates from T-duality in superstring theory,

and is first studied by Bouwkneght, Evslin and Mathai. The duality

basically consists of two parts: The first part is that, for any pair

of a principal circle bundle with `H-flux', there is another `T-dual'

pair on the same base space. The second part states that the twisted

K-groups of the total spaces of principal circle bundles in duality

are isomorphic under degree shift. This is the most simple topological

T-duality following Bunke and Schick, and there are a number of

generalizations. The generalization I will talk about is a topological

T-duality for "Real" circle bundles, motivated by T-duality in type II

orbifold string theory. In this duality, a variant of Z_2-equivariant

K-theory appears.

Topological T-duality originates from T-duality in superstring theory,

and is first studied by Bouwkneght, Evslin and Mathai. The duality

basically consists of two parts: The first part is that, for any pair

of a principal circle bundle with `H-flux', there is another `T-dual'

pair on the same base space. The second part states that the twisted

K-groups of the total spaces of principal circle bundles in duality

are isomorphic under degree shift. This is the most simple topological

T-duality following Bunke and Schick, and there are a number of

generalizations. The generalization I will talk about is a topological

T-duality for "Real" circle bundles, motivated by T-duality in type II

orbifold string theory. In this duality, a variant of Z_2-equivariant

K-theory appears.

### 2015年11月09日(月)

#### 代数幾何学セミナー

15:30-17:00 数理科学研究科棟(駒場) 122号室

3-dimensional McKay correspondence (English)

**伊藤由佳理 氏**(名古屋大学)3-dimensional McKay correspondence (English)

[ 講演概要 ]

The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.

The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.

### 2015年11月05日(木)

#### 代数幾何学セミナー

15:30-17:00 数理科学研究科棟(駒場) 126号室

いつもと部屋と曜日が違います。The day of the week and room are different from usual.

Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)

いつもと部屋と曜日が違います。The day of the week and room are different from usual.

**大川新之介 氏**(阪大)Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)

[ 講演概要 ]

I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.

I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.

#### 応用解析セミナー

16:00-17:30 数理科学研究科棟(駒場) 123号室

部屋が普段と異なるのでご注意ください

The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)

部屋が普段と異なるのでご注意ください

**Henri Berestycki 氏**(フランス高等社会科学院(EHESS))The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)

[ 講演概要 ]

I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.

I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.

### 2015年11月02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

A class of non-Kahler manifolds (Japanese)

**下部 博一 氏**(大阪大学)A class of non-Kahler manifolds (Japanese)

[ 講演概要 ]

We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.

We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.

#### 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

Concentrations for the travel cost of the simple random walk in random potentials

**久保田 直樹 氏**(日本大学理工学部)Concentrations for the travel cost of the simple random walk in random potentials

[ 講演概要 ]

多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．

このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが

原点からある点へ移動するために必要とするコスト(到達コスト)を考える．

到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．

そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，

到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．

多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．

このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが

原点からある点へ移動するために必要とするコスト(到達コスト)を考える．

到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．

そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，

到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．

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