## 過去の記録

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室
Jean JACOD 氏 (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
[ 講演概要 ]
Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Jean JACOD 氏 (Universite Paris VI)
A survey on realized p-variations for semimartingales
[ 講演概要 ]
Let $X$ be a process which is observed at the times $i\\Delta_n$ for $i=0,1,\\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is

V^n(p)_t=\\sum_{i=1}^{[t/\\Delta_n]}|X_{i\\Delta_n}-X_{(i-1)\\Delta_n}|^p.

The behavior of these $p$-variations when $\\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html

### 2009年04月14日(火)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 056号室
Klaus Niederkruger 氏 (Ecole normale superieure de Lyon)
Resolution of symplectic orbifolds obtained from reduction
[ 講演概要 ]
We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.

### 2009年04月13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

A new method to generalize the Nevanlinna theory to several complex variables

### 2009年04月09日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Dietmar Bisch 氏 (Vanderbilt University)
Bimodules, planarity and freeness

### 2009年04月08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

Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station
[ 講演概要 ]
We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.

http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html

We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.

### 2009年03月25日(水)

#### GCOEレクチャーズ

16:00-17:30   数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II
[ 講演概要 ]
The second half of the lecture.

### 2009年03月24日(火)

#### GCOEレクチャーズ

16:00-17:30   数理科学研究科棟(駒場) 128号室
Mark Gross 氏 (University of California, San Diego)
The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I
[ 講演概要 ]
I will discuss the SYZ conjecture which attempts to explain mirror symmetry via the existence of dual torus fibrations on mirror pairs of Calabi-Yau manifolds. After reviewing some older work on this subject, I will explain how it leads to an algebro-geometric version of this conjecture and will discuss recent work with Bernd Siebert. This recent work gives a mirror construction along with far more detailed information about the B-model side of mirror symmetry, leading to new mirror symmetry predictions.

### 2009年03月21日(土)

#### 東京無限可積分系セミナー

11:00-14:30   数理科学研究科棟(駒場) 117号室

On classes of transformations for bilinear sum of
(basic) hypergeometric series and multivariate generalizations.
[ 講演概要 ]
In this talk, I will present classes of bilinear transformation
formulas for basic hypergeometric series and Milne's multivariate
basic hypergeometric series associated with the root system of
type $A$. Our construction is similar to one of elementary
proof of Sears-Whipple transformation formula for terminating
balanced ${}_4 \\phi_3$ series while we use multiple Euler
transformation formula with different dimensions which has
obtained in our previous work.

On explicit formulas for Whittaker functions on real semisimple Lie groups
[ 講演概要 ]
will report explicit formulas
for Whittaker functions related to principal series
reprensetations on real semisimple Lie groups $G$ of
classical type.
Our explicit formulas are recursive formulas with
respect to the real rank of $G$, and in some lower rank
cases they are related to generalized
hypergeometric series ${}_3F_2(1)$ and ${}_4F_3(1)$.

### 2009年03月17日(火)

#### GCOEレクチャーズ

10:00-17:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi 氏 (Metz University) 13:30-14:30
Bernhard Krötz
(Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa 氏 (Utah) 16:30-17:30
Special unipotent representations of real reductive groups

### 2009年03月16日(月)

#### GCOEレクチャーズ

10:00-16:20   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Bernhard Krötz
(Max Planck Institute) 10:00-11:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa 氏 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
[ 講演概要 ]
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.

3. Geometric definition of special unipotent representations.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau 氏 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi 氏 (Metz University) 15:20-16:20
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory.
Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi

### 2009年03月14日(土)

#### GCOEレクチャーズ

09:00-14:00   数理科学研究科棟(駒場) 123号室
Roger Zierau 氏 (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi 氏 (Metz University) 10:15-11:15
Bernhard Krötz 氏 (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa 氏 (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups

### 2009年03月13日(金)

#### GCOEレクチャーズ

09:30-16:30   数理科学研究科棟(駒場) 123号室
Salah Mehdi 氏 (Metz) 09:30-10:30
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Peter Trapa 氏 (Utah) 11:00-12:00
Special unipotent representations of real reductive groups
Bernhard Krötz
(Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau 氏 (Oklahoma State University) 15:00-16:00
Dirac Cohomology

### 2009年03月12日(木)

#### 談話会・数理科学講演会

15:00-17:30   数理科学研究科棟(駒場) 050号室
お茶&Coffee&お菓子: 16:00～16:30

[ 講演概要 ]

[ 講演概要 ]

#### GCOEレクチャーズ

09:30-14:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 09:30-10:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz 氏 (Max Planck) 11:00-12:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
Peter Trapa 氏 (Utah大学) 13:30-14:30
Special unipotent representations of real reductive groups
[ 講演概要 ]
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.

### 2009年03月05日(木)

#### 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
いつもと曜日が異なります. Tea: 16:00 - 16:30 コモンルーム
Shicheng Wang 氏 (Peking University)
Extending surface automorphisms over 4-space
[ 講演概要 ]
Let $e: M^p\\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\\tau \\in E_e$.

Some applications: (1) the index $[{\\cal M}_{F_g}:E_e]\\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\\cal M}_{T^p}:E_e]\\geq 2^p-1$ for any unknotted embedding
$e:T^p\\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.

This is a joint work of Ding-Liu-Wang-Yao.

#### GCOEセミナー

10:15-11:15   数理科学研究科棟(駒場) 270号室
V. Isakov 氏 (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
[ 講演概要 ]
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.

#### GCOEセミナー

11:15-12:15   数理科学研究科棟(駒場) 270号室
J. Ralston 氏 (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
[ 講演概要 ]
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.

### 2009年03月04日(水)

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
P. Gaitan (with H. Isozaki and O. Poisson) 氏 (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves

#### GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室
M. Cristofol 氏 (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf

### 2009年03月03日(火)

#### GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室
O. Poisson 氏 (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
[ 講演概要 ]
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
Y. Dermenjian 氏 (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf

### 2009年03月02日(月)

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
Bernd Hofmann 氏 (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
[ 講演概要 ]
Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf

### 2009年02月26日(木)

#### 講演会

17:00-18:30   数理科学研究科棟(駒場) 270号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 470号室

Jijun Liu 氏 (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
[ 講演概要 ]
Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.