## 過去の記録

### 2014年01月22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

Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)
[ 講演概要 ]
The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.
(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.)

#### 代数幾何学セミナー

15:00-16:30   数理科学研究科棟(駒場) 122号室
いつもと曜日・時間が異なります
Thomas Ducat 氏 (University of Warwick)
Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)
[ 講演概要 ]
Consider a singular curve C contained in a smooth 3-fold X.
Assuming the existence of a Du Val general elephant S containing C,
I give a normal form for the equations of C in X and an outline of how to
construct a divisorial extraction from this curve. If the general S is
Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit
conditions for the existence of a terminal extraction. A treatment of
the D_{2k+1} case should be possible by similar means.

### 2014年01月21日(火)

#### 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

[ 講演概要 ]

その補助関数に対する偏微分方程式を解くことで曲面の動きを求める。 しかし

り出すことが困難となる。 そこで本講演では、方程式を適当に修正すること
で、 ゼロ等高面付近で傾きが小さくならない解が得られることを、 符号付き距

#### 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 コモンルーム

On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
[ 講演概要 ]
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.

#### トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室

ホモクリニック類における弱固有値:小さい角度を持つサドルからの摂動 (ENGLISH)
[ 講演概要 ]
For 3-dimensional homoclinic classes of saddles with index 2, a
new sufficient condition for creating weak contracting eigenvalues is
provided. Our perturbation makes use of small angles between stable and
unstable subspaces of saddles. In particular, by recovering the unstable
eigenvector, we can designate that the newly created weak eigenvalue is
contracting. As applications, we obtain C^1-generic non-trivial index-
intervals of homoclinic classes and the C^1-approximation of robust
heterodimensional cycles. In particular, this sufficient condition is
satisfied by a substantial class of saddles with homoclinic tangencies.

### 2014年01月20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

タイヒミュラー距離の幾何学とその応用 (JAPANESE)
[ 講演概要 ]
タイヒミュラー空間上にはタイヒミュラー距離と呼ばれるリーマン面の擬等角変形理論に関して自然な距離がある. タイヒミュラー距離はタイヒミュラー空間の複素構造に関する小林距離と一致する. この講演では, タイヒミュラー空間の一つのコンパクト化を用いて, タイヒミュラー距離に関する幾何学と曲面上の単純閉曲線の交点数関数による幾何学との関連を解説する. そして, このコンパクト化の性質を応用して得られる, 単位円板からタイヒミュラー空間への正則写像の剛性についても話す.

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 118号室
Victor Isakov 氏 (The Wichita State University)
Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)
[ 講演概要 ]
We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 126号室
いつもと部屋が異なります

Deforming elephants of Q-Fano 3-folds (ENGLISH)
[ 講演概要 ]
Shokurov and Reid proved that a Fano 3-fold with canonical
Gorenstein singularities has a Du Val elephant, that is,
a member of the anticanonical linear system with only Du Val singularities.
The classification of Fano 3-folds is based on this fact.
However, for a Fano 3-fold with non-Gorenstein terminal singularities,
the anticanonical system does not contain such a member in general.
Alt{\\i}nok--Brown--Reid conjectured that, if the anticanonical system is non-empty,
a Q-Fano 3-fold can be deformed to that with a Du Val elephant.
In this talk, I will explain how to deform an elephant with isolated
singularities to a Du Val elephant.

### 2014年01月15日(水)

#### 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 IV (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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

#### 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

Wedge-local fields in integrable models with bound states (JAPANESE)

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 370号室
Victor Isakov 氏 (The Wichita State University)
Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)
[ 講演概要 ]
We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Jin Cheng 氏 (Fudan University)
A numerical method for solving the inverse heat conduction problem without initial value (ENGLISH)
[ 講演概要 ]
In this talk, we will present some results for the inverse heat conduction problem for the heat equation of determining a boundary value at in an unreachable part of the boundary. The main difficulty for this problem is that the initial value is unknown by the practical reason. A new method is prposed to solve this problem and the nuemrical tests show the effective of this method. Some theoretic analysis will be presented. This is a joint work with J Nakagawa, YB Wang, M Yamamoto.

#### 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
Stephen Lichtenbaum 氏 (Brown University)
Special values of zeta-functions of schemes (ENGLISH)
[ 講演概要 ]
We will give conjectured formulas giving the behavior of the
seta-function of regular schemes projective and flat over Spec Z at
non-positive integers in terms of Weil-etale cohomology. We will also
explain the conjectured relationship of Weil-etale cohomology to etale
cohomology, which makes it possible to express these formulas also in terms
of etale cohomology.

### 2014年01月14日(火)

#### 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 III (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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム
Rinat Kashaev 氏 (University of Geneva)
State-integral partition functions on shaped triangulations (ENGLISH)
[ 講演概要 ]
Quantum Teichm\\"uller theory can be promoted to a
generalized TQFT within the combinatorial framework of shaped
triangulations with the tetrahedral weight functions given in
terms of the Weil-Gelfand-Zak transformation of Faddeev.FN"s
quantum dilogarithm. By using simple examples, I will
illustrate the connection of this theory with the hyperbolic
geometry in three dimensions.

#### 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

Threshold properties for one-dimensional discrete Schr\\"odinger operators (JAPANESE)
[ 講演概要 ]
We study the relation between the generalized eigenspace and the asymptotic expansion of the resolvent around the threshold $0$ for the one-dimensional discrete Schr\\"odinger operator on $\\mathbb Z$. We decompose the generalized eigenspace into the subspaces corresponding to the eigenstates and the resonance states only by their asymptotics at infinity, and classify the coefficient operators of the singlar part of resolvent expansion completely in terms of these eigenspaces. Here the generalized eigenspace we consider is largest possible. For an explicit computation of the resolvent expansion we apply the expansion scheme of Jensen-Nenciu (2001). This talk is based on the recent joint work with Arne Jensen (Aalborg University).

#### 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

セルラー代数の手法によるHecke-Cliffordスーパー代数の単純加群の分類
(JAPANESE)
[ 講演概要 ]
Hecke--Cliffordスーパー代数はA型岩堀--Hecke代数のスーパー版である。
その単純加群の分類は、Brundan, Kleshchevと土岡により
アフィンLie代数の圏論化の手法を用いて行われた。しかしこの構成は
とても抽象的であり実際に単純加群の構造を詳しく調べるのは難しい。
そこで本講演では、より具体的な単純加群の構成方法を紹介する。
これはGrahamとLehrerによるセルラー代数の理論を拡張した手法である。
ここではSpecht加群のスーパー類似にCliffordスーパー代数が

Hecke--Cliffordスーパー代数の単純加群を作ることができる。

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 118号室
Oleg Emanouilov 氏 (Colorado State University)
Calderon problem for Maxwell's equations in cylindrical domain (ENGLISH)
[ 講演概要 ]
We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations from partial Dirichlet-to-Neumann map.

### 2014年01月11日(土)

#### 保型形式の整数論月例セミナー

14:00-16:00   数理科学研究科棟(駒場) 123号室
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 14:00-14:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)
Dihua Jiang 氏 (School of Mathematics, University of Minnesota) 15:00-15:45
A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

### 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.
[ 講演参考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.
[ 講演参考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.