## 過去の記録

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
[ 講演概要 ]
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.

#### FMSPレクチャーズ

13:00-16:20   数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books II
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf

### 2015年01月26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

On the uniform birationality of the pluriadjoint maps (Japanese)
[ 講演概要 ]
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.

#### 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
Jungkai Chen 氏 (National Taiwan University)
Positivity in varieties of maximal Albanese dimension (ENGLISH)
[ 講演概要 ]
Given a variety of maximal Albanese dimension, it is known that the holomorphic Euler characteristic is non-negative. It is an interesting question to characterize varieties with vanishing Euler characteristic.

In our previous work (jointly with Debarre and Jiang), we prove that Ein-Lazarsgfeld's example is essentially the only variety of maximal Albanese and Kodaira dimension with vanishing Euler characteristic in dimension three. In the recent joint work with Jiang, we prove a decomposition theorem for the push-forward of canonical sheaf. As a consequence, we are able to generalized our previous characterization. The purpose of this talk is give a survey of these two works.

#### FMSPレクチャーズ

12:30-13:30   数理科学研究科棟(駒場) 128号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups III
[ 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

9:30-10:30   数理科学研究科棟(駒場) 122号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Nontempered Characters
[ 講演概要 ]
In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf

#### FMSPレクチャーズ

13:00-17:00   数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books I
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf

#### FMSPレクチャーズ

11:00-12:00   数理科学研究科棟(駒場) 122号室
Raul Gomez 氏 (Cornell University)
Local Theta lifting of generalized Whittaker models.
[ 講演概要 ]
In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf

### 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.