## 過去の記録

### 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.

### 2011年12月06日(火)

#### 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

https://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/saito/

### 2011年12月05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

Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)
[ 講演概要 ]
In this talk, I review some results from a joint work with Mukai:
1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and
2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.
As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.

### 2011年12月01日(木)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 117号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Mathematics Institute/ KIAS)
Cyclic K-theory (ENGLISH)
[ 講演概要 ]
Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.

### 2011年11月30日(水)

#### 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

Information criteria for parametric and semi-parametric models (JAPANESE)
[ 講演概要 ]
Since Akaike proposed an Information Criteria, this approach to
model selection has been important part of Statistical data analysis.
Since then many Information Criteria have been proposed and it is still
an active field of research. Despite there are many contributors in this
topic, we have not have proper Information Criteria for semiparametric
models. In this talk, we give ideas to develop an Information Criteria
for semiparametric models.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html

### 2011年11月29日(火)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 126号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)

#### 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: 16:40 - 17:00 コモンルーム
Athanase Papadopoulos 氏 (IRMA, Univ. de Strasbourg)
Mapping class group actions (ENGLISH)
[ 講演概要 ]
I will describe and present some rigidity results on mapping
class group actions on spaces of foliations on surfaces, equipped with various topologies.

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
Daniel Sternheimer 氏 (Rikkyo Univertiry and Université de Bourgogne)
Symmetries, (their) deformations, and physics: some perspectives and open problems from half a century of personal experience (ENGLISH)
[ 講演概要 ]
This is a flexible general framework, based on quite a number of papers, some of which are reviewed in:
MR2285047 (2008c:53079) Sternheimer, Daniel. The geometry of space-time and its deformations from a physical perspective. From geometry to quantum mechanics, 287–301, Progr. Math., 252, Birkhäuser Boston, Boston, MA, 2007
http://monge.u-bourgogne.fr/d.sternh/papers/PiMOmori-DS.pdf

### 2011年11月28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

Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)
[ 講演概要 ]
In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.

#### 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

An ampleness criterion with the extendability of singular positive metrics (JAPANESE)
[ 講演概要 ]
Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this talk, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.

### 2011年11月25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) 002号室

お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

[ 講演概要 ]

### 2011年11月24日(木)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 117号室
Spyridon Michalakis 氏 (Caltech)
Stability of topological phases of matter (ENGLISH)