## 過去の記録

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 128号室

Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性) (JAPANESE)

### 2011年02月02日(水)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
Yong Jung Kim 氏 (Korea Advanced Institute of Science and Technology (KAIST))
Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)
[ 講演概要 ]
The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

#### 講演会

15:15-16:15   数理科学研究科棟(駒場) 002号室
Guanghui ZHANG (張光輝) 氏 (東京大学大学院数理科学研究科)
Regularity of two dimensional capillary gravity water waves (ENGLISH)
[ 講演概要 ]
We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 006号室

An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data (JAPANESE)
[ 講演概要 ]

ファンドリターンデータ、確率過程の軌跡の順位統計量などである。さらに、テクニカル
トレーディングなど、市場の様子を見てタイミングを見て売買する戦略の定式化の試みも

とです。

: (1).weakly dependent caseの経験分布関数とVon Mises Functional.

これをもとにして、軌跡を直接扱う統計分析。

:(2)One Sample Problem.

Signed Rank Statistics. (Shibata/Miura’s decomposition?).

:(3)Two Sample Problem.

:Rankを使った軌跡の比較。順位相関係数。

:Time-Map Scattered Plot と順位相関との比較同等性?

:Two Sample Wilcoxon
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html

### 2011年01月31日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Sukmoon Huh 氏 (KIAS)
Restriction maps to the Coble quartic (ENGLISH)
[ 講演概要 ]
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Kwok-Wai Chan 氏 (IPMU, the University of Tokyo)
Mirror symmetry for toric Calabi-Yau manifolds from the SYZ viewpoint (ENGLISH)
[ 講演概要 ]
In this talk, I will discuss mirror symmetry for toric
Calabi-Yau (CY) manifolds from the viewpoint of the SYZ program. I will
start with a special Lagrangian torus fibration on a toric CY manifold,
and then construct its instanton-corrected mirror by a T-duality modified
by quantum corrections. A remarkable feature of this construction is that
the mirror family is inherently written in canonical flat coordinates. As
a consequence, we get a conjectural enumerative meaning for the inverse
mirror maps. If time permits, I will explain the verification of this
conjecture in several examples via a formula which computes open
Gromov-Witten invariants for toric manifolds.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Damian Brotbek 氏 (Rennes Univ.)
Varieties with ample cotangent bundle and hyperbolicity (ENGLISH)
[ 講演概要 ]
Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.

### 2011年01月28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) 117号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]
「2次元ブラウン運動のパスの(定数でない)正則関数による像は,また2次元ブラウン運動である」.このブラウン運動の共形不変性が,確率論においてあらわれる共形不変性でもっとも基本的なものである.2000年以降,ブラウン運動とは異なる確率モデルで共形不変性をキーワードに注目されているのが,Werner(2006年)とSmirnov(2010年)のフィールズ賞受賞業績とも密接に関係するSLE(Schramm-Loewner Evolution)である.本講演では,SLEとランダム解析関数の零点分布を、共形不変性があらわれるモデルとしてその背景や関連の結果などとあわせて紹介する

#### 作用素環セミナー

14:45-16:15   数理科学研究科棟(駒場) 122号室

Semiprojectivity of graph algebras (ENGLISH)

### 2011年01月27日(木)

#### 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

Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)

#### 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
Nitsan Ben-Gal 氏 (The Weizmann Institute of Science)
Attraction at infinity: Constructing non-compact global attractors in the slowly non-dissipative realm (ENGLISH)
[ 講演概要 ]
One of the primary tools for understanding the much-studied realm of reaction-diffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to non-dissipative reaction-diffusion equations.
In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the ‘completed inertial manifold’ and ‘non-compact global attractor’, and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.

### 2011年01月26日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
p進Gross-Zagier公式は, 楕円曲線のp進L関数の微分値をHeegner点のp進高さで記述する公式である. 楕円曲線がpで通常還元をもつときは, 20年以上前にPerrin-Riouによって証明されていた. 最近, pで超特異還元をもつときにも証明できたのでそれを紹介する. この講演では特に証明の解説に重点をおいて話したい.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jong-Shenq Guo 氏 (Department of Mathematics, Tamkang University
)
Quenching Problem Arising in Micro-electro Mechanical Systems

(JAPANESE)
[ 講演概要 ]
In this talk, we shall present some recent results on quenching problems which arise in Micro-electro Mechanical Systems.
We shall also give some open problems in this research area.

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)
[ 講演概要 ]
The object of talk is the differentiability of implicitly defined functions which we
encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild
(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly
defined functions by reparametrizing parameters in the profile likelihood and using an approximate least
favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach
developed in Hirose (2010) which uses the differentiability of implicitly defined functions.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

### 2011年01月25日(火)

#### 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

シート数が小さい曲面結び目の自明化について (JAPANESE)
[ 講演概要 ]
A connected surface smoothly embedded in ${\\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot $F$ is homeomorphic to the $2$-sphere or the torus, then it is called an $S^2$-knot or a $T^2$-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a $1$-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an $S^2$-knot. In particular, it is known that an $S^2$-knot is trivial if and only if its sheet number is $1$, and there is no $S^2$-knot whose sheet number is $2$. In this talk, we show that there is no $S^2$-knot whose sheet number is $3$, and a $T^2$-knot is trivial if and only if its sheet number is $1$.

### 2011年01月24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) 128号室

Toward a complex analytic 3-dimensional Kleinian group theory (JAPANESE)
[ 講演概要 ]
1次元射影変換群の離散部分群はクライン群理論として複素解析的にも微分幾何学的にも長く深く研究されてきた。この理論の高次元化は、微分幾何学的には発展したが、複素解析的にはあまり進んでいないように思う。複素2次元ではうまくいかないが、ここでは複素3次元の複素解析的なクライン群理論の試みについて述べたいと思う。

### 2011年01月20日(木)

#### 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

Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)
[ 講演概要 ]

「$G$を普遍格子SL$_m(Z[x_1,...,x_k])$ ($m$は3以上)または斜交普遍格子Sp$_{2m}(Z[x_1,...,x_k])$ ($m$は2以上)の指数有限の部分群とする ($k$は任意の自然数). このとき, $G$から曲面(コンパクトで向きづけ可能)の写像類群への; または, 有限生成自由群の(外部)自己同型群への準同型は有限の像をもつ.」

### 2011年01月19日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Mullins方程式の本質への探求 (JAPANESE)
[ 講演概要 ]
1957年にMullinsは、蒸発-凝縮機構による固体表面の発展方程式を提案した。その方程式の定性的本質を探る事によって、どのような知見が得られるかについて議論する。具体的には、曲率と駆動力との間の関係が形態に与える影響について明らかにする。

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

Notes on estimating the probability of ruin and some generalization (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

### 2011年01月18日(火)

#### 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
Claude-Alain Pillet 氏 (Univ. de Toulon et du Var)
Scattering induced current in a tight binding band (ENGLISH)

#### 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
いつもと開始時刻がことなります
Pierre Clare 氏 (Universite Orleans and the University of Tokyo)
Connections between Noncommutative Geometry and Lie groups
representations (ENGLISH)
[ 講演概要 ]
One of the principles of Noncommutative Geometry is to study singular spaces that the tools of classical analysis like algebras of continuous functions fail to describe, replacing them by more general C*-algebras. After recalling fundamental facts about C*-algebras, Hilbert modules and group C*-algebras, we will present constructions and results aiming to understand principal series representations and Knapp-Stein theory in the noncommutative geometrical framework. Eventually we will explain the relationship between the analysis of reduced group C*-algebras and the computation of the Connes-Kasparov isomorphisms.

### 2011年01月17日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Dano Kim 氏 (KIAS)
L^2 methods and Skoda division theorems (ENGLISH)
[ 講演概要 ]
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)
[ 講演概要 ]
In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

### 2011年01月13日(木)

#### 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
Robert Coquereaux 氏 (CNRS/CPT)
Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)

### 2011年01月12日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 056号室
Zhonghua Li 氏 (東京大学大学院数理科学研究科) 16:30-17:30
On regularized double shuffle relation for multiple zeta values (ENGLISH)
[ 講演概要 ]
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki 氏 (North Carolina University) 17:45-18:45
Spines with View Toward Modular Forms (ENGLISH)
[ 講演概要 ]
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.