## 過去の記録

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

Dipendra Prasad 氏 (Tata Institute of Fundamental Research)
Ext Analogues of Branching laws (ENGLISH)
[ 講演概要 ]
The decomposition of a representation of a group when restricted to a
subgroup is an important problem well-studied for finite and compact Lie
groups, and continues to be of much contemporary interest in the context
of real and $p$-adic groups. We will survey some of the questions that have
recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

### 2013年11月07日(木)

#### 作用素環セミナー

15:30-17:30   数理科学研究科棟(駒場) 123号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory III (JAPANESE)

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Bingyu Zhang 氏 (University of Cincinnati)
Maximum Regularity Principle for Conservative Evolutionary Partial Di erential Equations (ENGLISH)

#### Lie群論・表現論セミナー

13:30-14:20   数理科学研究科棟(駒場) 000号室

[ 講演概要 ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.

#### Lie群論・表現論セミナー

14:30-17:40   数理科学研究科棟(駒場) 000号室
Vaibhav Vaish 氏 (the Institute of Mathematical Sciences) 14:30-15:20
Weightless cohomology of algebraic varieties (ENGLISH)
[ 講演概要 ]
Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.
The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.
Yuichiro Tanaka 氏 (the University of Tokyo) 15:40-16:10
Visible actions on generalized flag varieties
--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)
[ 講演概要 ]
The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.

The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.
Pampa Paul 氏 (Indian Statistical Institute, Kolkata) 16:10-16:40
Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)
[ 講演概要 ]
Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.
Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.
Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the
complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.
There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.
If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.
If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.
In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.

Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.
Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.
Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).
Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.
In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.
Dipendra Prasad 氏 (Tata Institute of Fundamental Research) 16:50-17:40
Branching laws and the local Langlands correspondence (ENGLISH)
[ 講演概要 ]
The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.

### 2013年11月06日(水)

#### 作用素環セミナー

10:00-12:00   数理科学研究科棟(駒場) 122号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory II (JAPANESE)

### 2013年11月05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) 123号室
Tea: 16:00 - 16:30 コモンルーム
Carlos Moraga Ferrandiz 氏 (東京大学大学院数理科学研究科, 日本学術振興会)
The isotopy problem of non-singular closed 1-forms. (ENGLISH)
[ 講演概要 ]
Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.
A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

#### 作用素環セミナー

15:30-17:30   数理科学研究科棟(駒場) 118号室
Reiji Tomatsu 氏 (Hokkaido Univ.)
Introduction to the Ando-Haagerup theory I (JAPANESE)

### 2013年10月30日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室

Amenable minimal Cantor systems of free groups arising from
diagonal actions (JAPANESE)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 002号室
いつもと場所が異なりますのでご注意ください
Pierre Charollois 氏 (パリ第6大学)
Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)
[ 講演概要 ]
Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).
It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.
Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.

#### 古典解析セミナー

16:00-17:00   数理科学研究科棟(駒場) 122号室
Jacques Sauloy 氏 (Institute de Mathematiques de Toulouse, Universite Paul Sabatier)
The space of monodromy and Stokes data for q-difference equations (ENGLISH)
[ 講演概要 ]
Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.
However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.

### 2013年10月29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 コモンルーム
Daniel Matei 氏 (IMAR, Bucharest)
Fundamental groups of algebraic varieties (ENGLISH)
[ 講演概要 ]
We discuss restrictions imposed by the complex
structure on fundamental groups of quasi-projective
algebraic varieties with mild singularities.
We investigate quasi-projectivity of various geometric
classes of finitely presented groups.

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 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

[ 講演概要 ]
For a connected compact simple Lie group of type B or D,
we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on
a notion of visible actions on complex manifolds,
introduced by T. Kobayashi. The pairs we find exhaust
all the multiplicity-free pairs by an earlier
combinatorial classification due to Stembridge.

### 2013年10月28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

Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)
[ 講演概要 ]
We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.

#### 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

Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)
[ 講演概要 ]
We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.

### 2013年10月25日(金)

#### 統計数学セミナー

14:50-16:00   数理科学研究科棟(駒場) 006号室

スパースコーディングと構造化辞書学習 (JAPANESE)
[ 講演概要 ]
スパースコーディングは,多次元の観測データを複数並べた観測行列を2つの行列の積に分解する問題として,主成分分析・独立成分分析などと統一的な枠組で扱うことができ,その性質の違いは分解される行列に課される制約に依存する. 本講演では,画像を対象とした応用などを例に取り,スパースコーディング特有の性質について議論する. また,他の分解手法にはない特殊な問題として構造化された辞書の学習問題を取り上げ,そのアルゴリズムの性質について議論する.
[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/05.html

### 2013年10月24日(木)

#### 幾何コロキウム

10:00-11:30   数理科学研究科棟(駒場) 122号室

Some Uniqueness Theorems for Smoothing Singularities in Special Lagrangian Geometry (JAPANESE)
[ 講演概要 ]
Special Lagrangian submanifolds are area-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. I'll talk mainly about the singularities of two special Lagrangian planes intersecting transversely. I'll determine a class of smoothing models for the singularities.
By some results of Abouzaid and Smith one can determine the smoothing models up to quasi-isomorphism in a Fukaya category. I'll combine it with a technique of Thomas and Yau.

### 2013年10月23日(水)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室

Classification of quantum homogeneous spaces (ENGLISH)

#### 統計数学セミナー

13:00-15:30   数理科学研究科棟(駒場) 006号室

Mark Podolskij 氏 (Universität Heidelberg)
Limit theorems for ambit processes (ENGLISH)
[ 講演概要 ]
We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.

[ 講演参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/04.html

### 2013年10月22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

Armin Schikorra 氏 (MPI for Mathematics in the Sciences, Leipzig)
Fractional harmonic maps and applications (ENGLISH)
[ 講演概要 ]
Fractional harmonic mappings are critical points of a generalized Dirichlet Energy where the gradient is replaced with a (non-local) differential operator.
I will present aspects of the regularity theory of (non-local) fractional harmonic maps into manifolds, which extends (and contains) the theory of (poly-)harmonic mappings.
I also will mention, how one can show regularity for critical points of the Moebius (Knot-) Energy, applying the techniques developed in this theory.

#### 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 コモンルーム

Cluster algebra and complex volume of knots (JAPANESE)
[ 講演概要 ]
The cluster algebra was introduced by Fomin and Zelevinsky around
2000. The characteristic operation in the algebra called `mutation' is
related to various notions in mathematics and mathematical physics. In
this talk I review a basics of the cluster algebra, and introduce its
application to study the complex volume of knot complements in S^3.
Here a mutation corresponds to an ideal tetrahedron.
This talk is based on joint work with Kazuhiro Hikami (Kyushu University).

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Louisiana State University (USA))
Representation Theory and Microlocal Analysis (ENGLISH)
[ 講演概要 ]
Suppose $H\\subset K$ are compact, connected Lie groups, and suppose $\\tau$ is an irreducible, unitary representation of $H$. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of $Ind_H^K\\tau$ by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on $K$. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation $\\pi$ of a reductive Lie group $G$ when restricted to a reductive subgroup $H$. One of his key ideas was to restrict $\\pi$ to a representation of a maximal compact subgroup $K\\subset G$, view $\\pi$ as a subrepresentation of $L^2(K)$, and then use ideas similar to those developed by Kashiwara and Vergne.

In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group $G$ by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of $G$, viewed as continuous functions on the (possibly noncompact) Lie group $G$. In this talk, we will outline the main results of this paper and give additional conjectures.

### 2013年10月18日(金)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Björn Gustavsson 氏 (KTH Royal Institute of Technology)
Some applications of partial balayage (ENGLISH)
[ 講演概要 ]
Partial balayage is a rather recent tool in potential theory. One of its origins is the construction of quadrature domains for subharmonic functions by Makoto Sakai in the 1970's. It also gives a convenient way of describing weak solutions to a moving boundary problem for Hele-Shaw flow (Laplacian growth), and recently Stephen Gardiner and Tomas Sjödin have used partial balayage to make progress on an inverse problem in potential theory. I plan to discuss some of these, and related, matters.

### 2013年10月17日(木)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 470号室
Fikret Goelgeleyen 氏 (Bulent Ecevit University)
Stability for Inverse problems for Ultrahyperbolic Equations (ENGLISH)
[ 講演概要 ]
In this work, we consider inverse problems of determining a coefficient or a source term in an ultrahyperbolic equation by some lateral boundary data.
We prove Hoelder estimates which are global and local and the key is Carleman estimates.