## 過去の記録

### 2012年01月05日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 117号室

Classification and amenability in theory of von Neumann algebras (ENGLISH)

### 2011年12月27日(火)

#### 作用素環セミナー

14:30-18:00   数理科学研究科棟(駒場) 117号室

Deformation of algebras associated to group cocycles (JAPANESE)

Construction of wedge-local nets through
Longo-Witten endomorphisms (JAPANESE)

#### GCOEセミナー

13:30-14:30   数理科学研究科棟(駒場) 370号室
Yichao Zhu 氏 (University of Oxford)
The Modelling of Dislocations in the Early Stage of the Metal Fatigue (ENGLISH)
[ 講演概要 ]
Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of
fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.

#### GCOEセミナー

14:30-15:30   数理科学研究科棟(駒場) 370号室
Manabu Machida 氏 (University of Michigan)
Wave Transport in Random Media and Inverse Problems (ENGLISH)
[ 講演概要 ]
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

### 2011年12月26日(月)

#### 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

Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)
[ 講演概要 ]
It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

### 2011年12月21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

Sharifi 予想について (JAPANESE)
[ 講演概要 ]

### 2011年12月20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
Gueorgui Raykov 氏 (Catholic University of Chile)
A trace formula for the perturbed Landau Hamiltonian (ENGLISH)
[ 講演概要 ]
The talk will be based on a joint work with A. Pushnitski
and C. Villegas-Blas, the preprint is available here:
http://arxiv.org/abs/1110.3098 .

#### 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

5次元球面上のLawson 葉層の葉向シンプレクティック構造について (JAPANESE)
[ 講演概要 ]
We are going to show that Lawson's foliation on the 5-sphere
admits a smooth leafwise symplectic sturcture. Historically, Lawson's
foliation is the first one among foliations of codimension one which are
constructed on the 5-sphere. It is obtained by modifying the Milnor
fibration associated with the Fermat type cubic polynominal in three
variables.
Alberto Verjovsky proposed a question whether if the Lawson's
foliation or slighty modified ones admit a leafwise smooth symplectic
structure and/or a leafwise complex structure. As Lawson's one has a
Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not
be solved simultaneously both for the symplectic and the complex cases.
The main part of the construction is to show that the Fermat type
cubic surface admits an `end-periodic' symplectic structure, while the
natural one as an affine surface is conic at the end. Even though for
the other two families of the simple elliptic hypersurface singularities
almost the same construction works, at present, it seems very limited
where a Stein manifold admits an end-periodic symplectic structure. If
the time allows, we also discuss the existence of such structures on
globally convex symplectic manifolds.

### 2011年12月19日(月)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
いつもと曜日と部屋が違います。ご注意ください。
Tamas Szamuely 氏 (Budapest)
Galois Theory: Past and Present (ENGLISH)

### 2011年12月17日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

$J_1(N)$ の位数有限の ${\\\\mathbb Q}$- 有理点について (JAPANESE)
[ 講演概要 ]
$N$ を 5 以上の素数とし、${\\mathbb Q}$ 上のモジュラー曲線$X_0(N)$, $X_1(N)$ の ${\\mathbb Q}$ 上定義されたヤコビ多様体を$J_0(N)$, $J_1(N)$ とする。($X_1(N)$ は 0- カスプが ${\\mathbb Q}$-有理的であるモデルとする。) $J_0(N)({\\mathbb Q})$ のねじれ部分は、Ogg が予想し Mazur が証明したように、$X_0(N)$ の二つのカスプの差の因子類で生成された。 $J_1(N)({\\mathbb Q})$ のねじれ部分については、$X_1(N)$ の二つの 0- カスプの差の因子類たちで生成されることが Conrad とEdixhoven および Stein によって予想されていた。この予想が 2- べきねじれ部分を除いて証明できたのでそれについて報告する。

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)
[ 講演概要 ]
この講演では、distinguished Deligne-Lusztig 多様体がアファインになるための判定条件を与える。特に $q$ が大きくなるとアファインになること、ランクが2以下であればすべてのdistinguished Deligne-Lusztig 多様体がアファインになることを紹介する。

### 2011年12月16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) 123号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]

### 2011年12月14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
いつもと時間が異なりますのでご注意ください.
Lucien Szpiro 氏 (City University of New York)
Good and bad reduction for algebraic dynamical systems (ENGLISH)
[ 講演概要 ]
We will report on a recent work with collaborators in New York on the
different ways to look at degenerations of a dynamical system in a one
parameter family. Resultants, conductors and isotriviality will be analyzed.

### 2011年12月13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
Wolfram Bauer 氏 (ゲッチンゲン大学)
Trivializable subriemannian structures and spectral analysis of associated operators (ENGLISH)

#### 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
Hung Yean Loke 氏 (National University of Singapore)
Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)
[ 講演概要 ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### 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
Hung Yean Loke 氏 (National University of Singapore)
Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups (ENGLISH)
[ 講演概要 ]

In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \\times O(m,n)$ lies in the stable range, ie. $2p \\leq \\min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.

#### 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
Mircea Voineagu 氏 (IPMU, The University of Tokyo)
Remarks on filtrations of the singular homology of real varieties. (ENGLISH)
[ 講演概要 ]
We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.

### 2011年12月12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

Brody曲線と平均次元 (JAPANESE)
[ 講演概要 ]
We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

#### 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

Robert Laterveer 氏 (CNRS, IRMA, Université de Strasbourg)
A version of Barth's theorem for singular varieties (中止になりました) (JAPANESE)

### 2011年12月09日(金)

#### 講演会

10:40-11:30   数理科学研究科棟(駒場) 122号室
Erwin Bolthausen 氏 (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
[ 講演概要 ]
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### 講演会

10:40-11:30   数理科学研究科棟(駒場) 122号室
Erwin Bolthausen 氏 (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
[ 講演概要 ]
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

#### GCOEセミナー

11:40-12:30   数理科学研究科棟(駒場) 122号室
Wolfgang Koenig 氏 (Weierstrass Institute Berlin)
Eigenvalue order statistics and mass concentration in the parabolic Anderson model (ENGLISH)
[ 講演概要 ]
We consider the random Schr\\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).

#### GCOEセミナー

14:00-14:50   数理科学研究科棟(駒場) 122号室
Roman Kotecky 氏 (Charles University Prague/University of Warwick)
Gradient Gibbs models with non-convex potentials (ENGLISH)
[ 講演概要 ]
A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.

#### GCOEセミナー

15:00-15:50   数理科学研究科棟(駒場) 122号室
Stefano Olla 氏 (University Paris - Dauphine)
Einstein relation and linear response for random walks in random environment (ENGLISH)

### 2011年12月08日(木)

#### 代数学コロキウム

18:30-19:30   数理科学研究科棟(駒場) 056号室

Gerd Faltings 氏 (Max Planck Institute for Mathematics, Bonn)
Nonabelian p-adic Hodge theory and Frobenius (ENGLISH)
[ 講演概要 ]
Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.

(本講演は「東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とIHESとの双方向同時中継で行います。)

### 2011年12月07日(水)

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 122号室
Michel Cristofol 氏 (マルセイユ大学) 16:00-17:00
"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)
[ 講演概要 ]
In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.
Guillaume Olive 氏 (マルセイユ大学) 17:00-18:00
"Hautus test for the approximate controllability of linear systems" (ENGLISH)
[ 講演概要 ]
We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.
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