## 過去の記録

### 2015年01月25日(日)

#### FMSPレクチャーズ

12:30-13:30   数理科学研究科棟(駒場) 126号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups II
[ 講演概要 ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf

#### FMSPレクチャーズ

11:00-12:00   数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Harmonic Analysis
[ 講演概要 ]
In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf

#### FMSPレクチャーズ

9:30-10:30   数理科学研究科棟(駒場) 126号室
Raul Gomez 氏 (Cornell University)
Generalized and degenerate Whittaker models associated to nilpotent orbits.
[ 講演概要 ]
In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications.
This is joint work with Dmitry Gourevitch and Siddhartha Sahi.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf

### 2015年01月24日(土)

#### FMSPレクチャーズ

13:00-14:00   数理科学研究科棟(駒場) 126号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups I
[ 講演概要 ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf

#### FMSPレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Tempered Characters
[ 講演概要 ]
In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R).
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf

#### FMSPレクチャーズ

14:30-15:30   数理科学研究科棟(駒場) 126号室
Raul Gomez 氏 (Cornell University)
The Tor and Ext functors for smooth representations of real algebraic groups.
[ 講演概要 ]
Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf

### 2015年01月23日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 大講義室号室
Luc Illusie 氏 (Université de Paris-Sud)
Grothendieck and algebraic geometry
[ 講演概要 ]
Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.

### 2015年01月22日(木)

#### 東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 002号室

Dynamical braceを用いたダイナミカル・ヤン・バクスター写像の構成について (JAPANESE)
[ 講演概要 ]
ダイナミカル・ヤン・バクスター写像はダイナミカル・ヤン・バクスター方程式の集合論的解として導入された概念である．本講演では，brace(積$a*b:=ab+a+b$に関して群構造を持つ環$(R,+,¥cdot)$の一般化として得られる代数系)をダイナミカル化した代数系dynamical braceを導入し，ユニタリ条件を満たす右非退化なダイナミカル・ヤン・バクスター写像を構成する方法について述べる．またdynamical braceの性質と分類およびbraceとの関係についても紹介をする予定である．

ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成 (JAPANESE)
[ 講演概要 ]
FelderやEtingof-Varchenkoは，量子ダイナミカル・ヤン・バクスター方程式の解であるダイナミカルR行列から，ホップ代数の一般化であるホップ亜代数を構成した．この構成方法に現れる量子ダイナミカル・ヤン・バクスター方程式は一般化されており，その解もダイナミカル・ヤン・バクスター写像という名前でいくつか求められている．そこで本講演では，ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成について紹介する．さらに時間が許せば，ダイナミカル・ヤン・バクスター写像に付随して定まる有限次元L-operator全体のなすテンソル圏
(これは，対応するホップ亜代数のある種の有限次元表現全体のなすテンソル圏と見なせる) がリジッドとなることを説明したい．

#### 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
Arnaud Ducrot 氏 (ボルドー大学)
On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data
(ENGLISH)
[ 講演概要 ]
In this talk we discuss the asymptotic behaviour of a multi-dimensional Fisher-KPP equation posed in an asymptotically homogeneous medium and supplemented together with a compactly supported initial datum. We derive precise estimates for the location of the front before proving the convergence of the solutions towards travelling front. In particular we show that the location of the front drastically depends on the rate at which the medium become homogeneous at infinity. Fast rate of convergence only changes the location by some constant while lower rate of convergence induces further logarithmic delay.

### 2015年01月21日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Ofer Gabber 氏 (CNRS, IHES)
[ 講演概要 ]
(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.
(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.)

#### 古典解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Remarks on the number of accessory parameters (JAPANESE)
[ 講演概要 ]

このような作用素(の族)の大域的な構造を考察する上で,
アクセサリーパラメータは重要な役割を果たす.

このアクセサリーパラメータに関する考察を行う.

### 2015年01月20日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Italo Capuzzo Dolcetta 氏 (Università degli Studi di Roma "La Sapienza")
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)
[ 講演概要 ]
In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.
The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.
We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.

#### トポロジー火曜セミナー

16:30-17:30   数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room

On Lagrangian caps and their applications (JAPANESE)
[ 講演概要 ]
In 2013, Y. Eliashberg and E. Murphy established the $h$-principle for
exact Lagrangian embeddings with a concave Legendrian boundary. In this
talk, I will explain a modification of their $h$-principle and show
applications to Lagrangian submanifolds in the complex projective spaces.

### 2015年01月19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) 126号室

Hyperbolic span and pseudoconvexity (Japanese)
[ 講演概要 ]
We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
コンピュータによる数値計算においては、浮動小数点演算による丸め誤差、級数展開・ 反復の打ち切り誤差、連続問題の離散化誤差など、レベルの異なる誤差が発生すること があります。本講演では、「計算の品質」の観点から、何らかの方法で得られた近似解 に対し、真の解との誤差限界を数学的に厳密に見積もる数値計算手法について、特に残 差の果たす役割に注目しながら、分かりやすく紹介できればと思います。

#### 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

Crepant resolutions of Slodowy slice in nilpotent orbit closure in sl_N(C) (JAPANESE)
[ 講演概要 ]
Nilpotent orbit closures and their intersections with Slodowy slices are typical examples of symplectic varieties. It is known that every crepant resolution of a nilpotent orbit closure is obtained as a Springer resolution. In this talk, we show that every crepant resolution of a Slodowy slice in nilpotent orbit closure in sl_N(C) is obtained as the restriction of a Springer resolution and explain how to count the number of crepant resolutions. The proof of the main results is based on the fact that Slodowy slices can be described as quiver varieties.

### 2015年01月16日(金)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 126号室

Degeneration and curves on K3 surfaces (Japanese)
[ 講演概要 ]
There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of quartic K3 surfaces whose members fulfil the conjecture.

#### 統計数学セミナー

14:00-15:30   数理科学研究科棟(駒場) 052号室
Ajay Jasra 氏 (National University of Singapore)
A stable particle filter in high-dimensions
[ 講演概要 ]
We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.

This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).
[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html

### 2015年01月15日(木)

#### 東京無限可積分系セミナー

15:00-18:30   数理科学研究科棟(駒場) 002号室

On Gram matrices of the Shapovalov form of a basic representation of a
quantum affine group (ENGLISH)
[ 講演概要 ]
We consider Gram matrices of the Shapovalov form of a basic
representation
of a quantum affine group. We present a conjecture predicting the
invariant
factors of these matrices and proving that it gives the correct
invariants
when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in
certain ways.
This generalizes Evseev's theorem which settled affirmatively
the K\"{u}lshammer-Olsson-Robinson conjecture that predicts
the generalized Cartan invariants of the symmetric groups.
This is a joint work with Anton Evseev.
Alexander Tsymbaliuk 氏 (SCGP (Simons Center for Geometry and Physics)) 17:00-18:30
Continuous and Infinitesimal Hecke algebras (ENGLISH)
[ 講演概要 ]
In the late 80's V. Drinfeld introduced the notion of the
degenerate affine Hecke algebras. The particular class of those, called
symplectic reflection algebras, has been rediscovered 15 years later by
[Etingof and Ginzburg]. The theory of those algebras (which include also
the rational Cherednik algebras) has attracted a lot of attention in the
last 15 years.
In this talk we will discuss their continuous and infinitesimal versions,
introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those
classical algebras to the simplest 1-block finite W-algebras.

### 2015年01月14日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Laurent Berger 氏 (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
[ 講演概要 ]
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Canonical cyclic group actions on noncommutative tori

### 2015年01月13日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room

Stable presentation length of 3-manifold groups (JAPANESE)
[ 講演概要 ]
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Wojciech Zajączkowski 氏 (Institute of Mathematics Polish Academy of Sciences)
Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)
[ 講演概要 ]
We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.

### 2015年01月10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

Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
[ 講演概要 ]

スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)
[ 講演概要 ]
Hardyの不等式は，劣臨界指数の場合には伸縮に関するスケール不変性を持つ事が知られている．一方，臨界指数の場合には対数型の特異性に起因して通常の伸縮不変性は破綻する． 本講演では，「伸縮に関するスケール不変性を持つ平均振動型の臨界Hardyの不等式」および「非線形スケール不変性を持つ対数補正型臨界 Hardyの不等式」の二種を導出する．更にその最良定数は達成されないことを，対応する変分問題を解析することで証明する.

### 2015年01月07日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Sandra Rozensztajn 氏 (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
[ 講演概要 ]
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.