## 過去の記録

### 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 ]

[ 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.
[ 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.

[ 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.

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 470号室
kazufumi Ito 氏 (North Carolina State University)
Fluid-structure interaction model and Levelset method (ENGLISH)
[ 講演概要 ]
We derive a weak form and weak solution of the level set formulation of Cottet and Maitre for fluid-structure interaction problems with immersed surfaces. The method in particular exhibits appealing mass and energy conservation properties and a variational formulation of Peskin’s Immersed Boundary methods.

### 2013年10月16日(水)

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Peter Scholze 氏 (ボン大学)
Shimura varieties with infinite level, and torsion in the cohomology of locally symmetric spaces (ENGLISH)
[ 講演概要 ]
We will discuss the p-adic geometry of Shimura varieties with infinite level at p: They are perfectoid spaces, and there is a new period map defined at infinite level. As an application, we will discuss some results on torsion in the cohomology of locally symmetric spaces, and in particular the existence of Galois representations in this setup.

(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.)

#### 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

#### 統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 052号室

[ 講演概要 ]

[ 参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/03.html

### 2013年10月15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

Desingularizing special generic maps (JAPANESE)
[ 講演概要 ]
This is a joint work with Osamu Saeki (IMI, Kyushu University).
A special generic map is a generic map which has only definite
fold as its singularities.
We study the condition for a special generic map from a closed
n-manifold to the p-space (n+1>p), to factor through a codimension
one immersion (or an embedding). In particular, for the cases
where p = 1 and 2 we obtain complete results.
Our techniques are related to Smale-Hirsch theory,
topology of the space of immersions, relation between the space
of topological immersions and that of smooth immersions,
sphere eversions, differentiable structures of homotopy spheres,
diffeomorphism group of spheres, free group actions on the sphere, etc.

### 2013年10月12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
このセミナーは,月に1度程度,不定期に開催されます.

The global Cauchy problems for nonlinear dispersive equations on modulation spaces
(JAPANESE)
[ 講演概要 ]

て考える.
その具体例のひとつであるシュレディンガー方程式では

その一方で, 解空間にモジュレーション空間を用いれば
その上限を超えて大域解の一意存在性を述べることが出来る.

しかし, この事実はシュレディンガー方程式のみでしか述べられていない.
そこで本公演では,より一般の非線形分散型方程式の初期値問題に対しても

(JAPANESE)
[ 講演概要 ]
Feynmanによる経路積分の導入から始め、

1.(Lagrange型)経路積分が数学的に意味をもつ汎関数のクラスを与える。

このクラスに属する任意の汎関数を振幅とする経路積分の時間分割近似法が、

この汎関数のクラスは基本的な汎関数を含み、

このため、

さらに、この経路積分にお いて微分積分学の基本定理、
Riemann-Stieljes積分やlimとの順序交換定理、

[1] N. Kumano-go,
“Feynman path integrals as analysis on path space by time slicing approximation
”,
Bull. Sci. Math. vol. 128 (2004).
[2] D. Fujiwara and N. Kumano-go,
“Smooth functional derivatives in Feynman path integral by time slicing
approximation”,
Bull. Sci. Math. vol. 129 (2005).

2.相空間(Hamilton型)経路積分が数学的に意味をもつ2つの汎関数のクラス
を与える。

このため、相空間経路積分可能な多くの汎関数を創ることができる。
さらに、使用する際に注意が必要であるが、
この相空間経路積分において、

Hamilton型の準古典近似が成立する。

[3] N. Kumano-go and D. Fujiwara,
“Phase space Feynman path integrals via piecewise bicharacteristic paths
and their semiclassical approximations”,
Bull. Sci. math. vol. 132 (2008).
[4] N. Kumano-go,
“Phase space Feynman path integrals with smooth functional derivatives
by time slicing approximation”,
Bull. Sci. math. vol. 135 (2011).