## 過去の記録

#### 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

http://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 ]
http://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)

### 2011年11月22日(火)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

Spyridon Michalakis 氏
( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ 講演概要 ]
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.

#### 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

Quantum and homological representations of braid groups (JAPANESE)
[ 講演概要 ]
Homological representations of braid groups are defined as
the action of homeomorphisms of a punctured disk on
the homology of an abelian covering of its configuration space.
These representations were extensively studied by Lawrence,
Krammer and Bigelow. In this talk we show that specializations
of the homological representations of braid groups
are equivalent to the monodromy of the KZ equation with
values in the space of null vectors in the tensor product
of Verma modules when the parameters are generic.
To prove this we use representations of the solutions of the
KZ equation by hypergeometric integrals due to Schechtman,
Varchenko and others.

In the case of special parameters these representations
are extended to quantum representations of mapping
class groups. We describe the images of such representations
and show that the images of any Johnson subgroups
contain non-abelian free groups if the genus and the
level are sufficiently large. The last part is a joint
work with Louis Funar.

#### 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

Smallest complex nilpotent orbit with real points (JAPANESE)
[ 講演概要 ]
Let $\\mathfrak{g}$ be a non-compact simple Lie algebra with no complex
structures.
In this talk, we show that there exists a complex nilpotent orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ in
$\\mathfrak{g}_\\mathbb{C}$ ($:=\\mathfrak{g} \\otimes \\mathbb{C}$)
containing all of real nilpotent orbits in $\\mathfrak{g}$ of minimal
positive dimension.
For many $\\mathfrak{g}$, the orbit
$\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is just the
complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
However, for the cases where $\\mathfrak{g}$ is isomorphic to
$\\mathfrak{su}^*(2k)$, $\\mathfrak{so}(n-1,1)$, $\\mathfrak{sp}(p,q)$,
$\\mathfrak{e}_{6(-26)}$ or $\\mathfrak{f}_{4(-20)}$,
the orbit $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$ is not
the complex minimal nilpotent orbit in $\\mathfrak{g}_\\mathbb{C}$.
We also determine $\\mathcal{O}^{G_\\mathbb{C}}_{\\text{min},\\mathfrak{g}}$
by describing the weighted Dynkin diagrams of these for such cases.

### 2011年11月21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

Techniques of computations of Dolbeault cohomology of solvmanifolds (JAPANESE)

#### 諸分野のための数学研究会

13:30-14:30   数理科学研究科棟(駒場) 056号室

Ernie Esser 氏 (University of California, Irvine)
A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)
[ 講演概要 ]
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
This talk is based on joint work with Michael Moeller, Stanley Osher, Guillermo Sapiro and Jack Xin.

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Siu-Cheong Lau 氏 (IPMU)
Enuemerative meaning of mirror maps for toric Calabi-Yau manifolds (ENGLISH)
[ 講演概要 ]
For a mirror pair of smooth manifolds X and Y, mirror symmetry associates a complex structure on Y to each Kaehler structure on X, and this association is called the mirror map. Traditionally mirror maps are defined by solving Picard-Fuchs equations and its geometric meaning was unclear. In this talk I explain a recent joint work with K.W. Chan, N.C. Leung and H.H. Tseng which proves that mirror maps can be obtained by taking torus duality (the SYZ approach) and disk-counting for a class of toric Calabi-Yau manifolds in any dimensions. As a consequence we can compute disk-counting invariants by solving Picard-Fuchs equations.

### 2011年11月19日(土)

#### 保型形式の整数論月例セミナー

10:15-12:30   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

この微分方程式の基本解が超楕円積分と超幾何関数を使って表示できることを示しさらに関連した話題を説明する。

[ 講演概要 ]

### 2011年11月18日(金)

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 052号室

Inverse problems for heat equations with discontinuous conductivities
(JAPANESE)
[ 講演概要 ]
In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat
equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat
conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on
$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on
$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results
for the inverse problems of reconstructing $\\gamma(t,x)$ from the
Dirichlet-to-Neumann map :
$u(t)|_{\\partial\\Omega} \\to$\\partial_{\\nu}u|_{\\partial\\Omega}$for a time interval$(0,T)\$. These are the joint works with P.Gaitan, O.Poisson,
S.Siltanen, J.Tamminen.