## 過去の記録

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

Kエネルギーの coercivity に由来する安定性 (Japanese)
[ 講演概要 ]
S. Boucksom氏とM. Jonsson氏との共同研究について話します。Kエネルギーのcoercivityという有名な増大度条件があります。我々はこのcoercivity に対応するJ一様K安定性の概念を導入し、J一様K安定性が従来のK安定性よりも真に強い定義でありながら、Kähler-Einstein多様体などについて実際に成り立つことを示しました。さらに最近Berman-Boucksom-Jonssonによって、J一様K安定性から出発すればCheeger-Coldingの非崩壊理論を用いることなくKähler-Einstein計量を得られることが明らかにされました。時間が許せばこのあたりについても解説したいと思います。

### 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
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.

### 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
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

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.

#### 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)
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.
[ 講演参考URL ]
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)
[ 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.

#### 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)
[ 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.

#### 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
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.

### 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

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.
[ 講演参考URL ]
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
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.
[ 講演参考URL ]
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)
[ 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.
[ 講演参考URL ]
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
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.

### 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)
[ 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.

#### 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
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.)

### 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)
[ 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.

#### 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

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.
[ 講演参考URL ]
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
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.

### 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)
[ 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.

(日本語)
[ 講演概要 ]

### 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

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.
[ 講演参考URL ]
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)
[ 講演概要 ]

### 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)
[ 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.

### 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)
[ 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.

### 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)
[ 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.

#### 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

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.

### 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)
[ 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.