## 過去の記録

### 2014年01月10日(金)

#### FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory II (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

### 2014年01月09日(木)

#### FMSPレクチャーズ

14:50-16:20   数理科学研究科棟(駒場) 056号室
Rinat Kashaev 氏 (University of Geneva)
Lectures on quantum Teichmüller theory I (ENGLISH)
[ 講演概要 ]
Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.
In these lectures it is planned to address the following subjects:
1) Penner’s coordinates in the decorated Teichmüller space.
2) Ratio coordinates.
3) Quantization.
4) The length spectrum of simple closed curves.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

### 2014年01月08日(水)

#### 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

Dow's metrization theorem and beyond (JAPANESE)

#### 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

[ 講演概要 ]
We give an explicit and intrinsic description of (the torsor defined by the 12th roots of) the discriminant of an elliptic curve using the group of its 12-torsion points and the Weil pairing. As an application, we extend a result of Coates (which deals with the characteristic 0 case) to the case where the characteristic of the base field is not 2 or 3. This is a joint work with Kohei Fukuda.

### 2013年12月26日(木)

#### 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

Countable Chain Condition for $C^*$-algebras (ENGLISH)

### 2013年12月25日(水)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Nonconvex Optimization Problems (ENGLISH)
[ 講演概要 ]
A general class of nonsmooth nonconvex optimization problems is discussed. A general existence theory of solutions, the Lagrange multiplier theory and sensitivity analysis of the optimal value function are developed. Concrete examples are presented to demonstrate the applicability of our approach.

### 2013年12月24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
Tirasan Khandhawit 氏 (Kavli IPMU)
Stable homotopy type for monopole Floer homology (ENGLISH)
[ 講演概要 ]
In this talk, I will try to give an overview of the
construction of stable homotopy type for monopole Floer homology. The
construction associates a stable homotopy object to 3-manifolds, which
will recover the Floer groups by appropriate homology theory. The main
ingredients are finite dimensional approximation technique and Conley
index theory. In addition, I will demonstrate construction for certain
3-manifolds such as the 3-torus.

### 2013年12月20日(金)

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Determination of the magnetic field in an anisotropic Schrodinger equation (ENGLISH)
[ 講演概要 ]
This talk is devoted to the study of the following inverse boundary value problem: given a Riemannian manifold with boundary, determine the magnetic potential in a dynamical Schroedinger equation in a magnetic field from the observations made at the boundary.

### 2013年12月19日(木)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 270号室
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
[ 講演概要 ]
In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.

#### FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 270号室
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
[ 講演概要 ]
In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf

### 2013年12月18日(水)

#### 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
いつもと場所が異なりますのでご注意ください

Heights of motives (ENGLISH)
[ 講演概要 ]
The height of a rational number a/b (a, b integers which are coprime) is defined as max(|a|, |b|). A rational number with small (resp. big) height is a simple (resp. complicated)  number. Though the notion height is so naive, height has played fundamental roles in number theory. There are important variants of this notion. In 1983, when Faltings proved Mordell conjecture, Faltings first proved Tate conjecture for abelian variaties by defining heights of abelian varieties, and then he deduced Mordell conjecture from the latter conjecture. I explain that his height of an abelian variety is generalized to the height of a motive. This generalization of height is related to open problems in number theory. If we can prove finiteness of the number of motives of bounded heights, we can prove important conjectures in number theory such as general Tate conjecture and Mordell-Weil type conjectures in many cases.
(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.)

### 2013年12月17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

Satellites of an oriented surface link and their local moves (JAPANESE)
[ 講演概要 ]
For an oriented surface link $F$ in $\\mathbb{R}^4$,
we consider a satellite construction of a surface link, called a
2-dimensional braid over $F$, which is in the form of a covering over
$F$. We introduce the notion of an $m$-chart on a surface diagram
$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$
satisfying certain conditions and is an extended notion of an
$m$-chart on a 2-disk presenting a surface braid.
A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.
It is known that two surface links are equivalent if and only if their
surface diagrams are related by a finite sequence of ambient isotopies
of $\\mathbb{R}^3$ and local moves called Roseman moves.
We show that Roseman moves for surface diagrams with $m$-charts can be
well-defined. Further, we give some applications.

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Dispersion and observability for completely integrable Schrödinger flows (ENGLISH)
[ 講演概要 ]
I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger
equations that are obtained as the quantization of a completely integrable Hamiltonian system.
The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus.
Our results are obtained through a detailed analysis of semiclassical measures corresponding to
sequences of solutions, which is performed using a two-microlocal approach.
This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.

#### Lie群論・表現論セミナー

16:30-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
Characterizations of the joint eigenspaces of invariant
differential operators in terms of the Poisson transform have been one of the central problems in harmonic analysis on symmetric spaces.
From the point of view of spectral theory, Strichartz (J. Funct.
Anal.(1989)) formulated a conjecture concerning a certain image
characterization of the Poisson transform of the $L^{2}$-space on the boundary on symmetric spaces of noncompact type. In this talk, we employ techniques in scattering theory to present a positive answer to the Strichartz conjecture.

### 2013年12月16日(月)

#### FMSPレクチャーズ

15:30-16:30   数理科学研究科棟(駒場) 056号室
Jon Nimmo 氏 (Univ. of Glasgow)
The discrete Schrodinger equation for compact support potentials (ENGLISH)
[ 講演概要 ]
We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.
Applications of this approach to the udKdV are also discussed.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

#### 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

Shilov boundaries of the pluricomplex Green function's level sets (JAPANESE)
[ 講演概要 ]
In this talk, we study a relation between the Shilov boundaries of the pluricomplex Green function's level sets and supports of Monge-Ampére type currents.

### 2013年12月12日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

くりこみ群の方法による大気重力波の自発的放射メカニズムの解明 (JAPANESE)
[ 講演概要 ]

### 2013年12月10日(火)

#### FMSPレクチャーズ

13:00-14:30   数理科学研究科棟(駒場) 126号室

Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

#### 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

Corks, plugs, and local moves of 4-manifolds. (JAPANESE)
[ 講演概要 ]
Akbulut and Yasui defined cork, and plug
to produce many exotic pairs.
In this talk, we introduce a plug
with respect to Fintushel-Stern's knot surgery
or more 4-dimensional local moves and
and argue by using Heegaard Fleor theory.

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Abel Klein 氏 (UC Irvine)
Quantitative unique continuation principle, local behavior of solutions, and bounds on the density of states for Schr\\"odinger operators (ENGLISH)
[ 講演概要 ]
We establish bounds on the density of states measure for Schr\\"odinger operators. These are deterministic results that do not require the existence of the density of states measure, or, equivalently, of the integrated density of states. The results are stated in terms of a density of states outer-measure'' that always exists, and provides an upper bound for the density of states measure when it exists. We prove log-H\\"older continuity for this density of states outer-measure in one, two, and three dimensions for Schr\\"odinger operators, and in any dimension for discrete Schr\\"odinger operators. Our proofs use a quantitative unique continuation principle and the local behavior of approximate solutions of the stationary Schr\\"odinger equation.
(Joint work with Jean Bourgain.)
References: Jean Bourgain and Abel Klein: Bounds on the density of states for Schr\\"odinger operators. Invent. Math. 194, 41-72 (2013).

### 2013年12月09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

Donaldson-Tian-Yau 予想と K-安定性について (JAPANESE)
[ 講演概要 ]

#### 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

On birationally tririgid Q-Fano threefolds (JAPANESE)
[ 講演概要 ]
I will talk about birational geometry of Q-Fano threefolds. A Mori
fiber space birational to a given Q-Fano threefold is called a birational Mori fiber structure of the threefold. The existence of Q-Fano threefolds with a unique birational Mori fiber structure (resp. with two birational Mori fiber structures) is known. In this talk I will give an example of Q-Fano threefolds with three birational Mori fiber structures and also discuss about the behavior of birational Mori fiber structures in a family.

### 2013年12月06日(金)

#### 幾何コロキウム

17:00-18:00   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

#### FMSPレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 118号室
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (II) (ENGLISH)
[ 講演概要 ]
About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]
GL(n) に対する局所 Langlands 対応とその幾何学的実現は,Harris-Taylor によって,保型表現の大域的な議論を用いて証明された.しかし,対応が実現される幾何学的な仕組みについては,未だ十分に理解されているとは言い難い.