## 過去の記録

#### 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

Allen-Cahn方程式における角錐型進行波の一意性と安定性
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)

[ 講演概要 ]
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.

#### 講演会

16:20-17:50   数理科学研究科棟(駒場) 052号室

インターネットにおける数理科学的手法と実際「DNSとWebアクセス」
[ 講演概要 ]
テーマごとに個別の企業活動を紹介し、第一線で活躍する企業研究者を招聘し、現場レポートを聴き、議論を行うことで、インターネット数理科学の原理とその応用の実際を紹介する。
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html

### 2008年06月18日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 117号室

On a ramification bound of semi-stable torsion representations over a local field

Beilinson-Tate予想と楕円曲面のK_1の不分解元
[ 講演概要 ]
(佐藤周友氏との共同研究)

これは、p進レギュレーターの非消滅と関係しており、

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 122号室

+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)

### 2008年06月17日(火)

#### 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

Multiplier ideal sheaves and Futaki invariant on toric Fano manifolds.
[ 講演概要 ]
I would like to discuss the subvarieties cut off by the multiplier
ideal sheaves (MIS) and Futaki invariant on toric Fano manifolds.
Futaki invariant is one of the necessary conditions for the existence
of Kahler-Einstein metrics on Fano manifolds,
on the other hand MIS is one of the sufficient conditions introduced by Nadel.
Especially I would like to focus on the MIS related to the Monge-Ampere equation
for Kahler-Einstein metrics on non-KE toric Fano manifolds.
The motivation of this work comes from the investigation of the
relationship with slope stability
of polarized manifolds introduced by Ross and Thomas.
This talk will be based on a part of the joint work with Akito Futaki
(arXiv:0711.0614).

### 2008年06月16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

### 2008年06月14日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation
[ 講演概要 ]
We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Paul A. Pearce 氏 (Univ. of Melbourne) 15:00-16:00
Exact Solution and Physical Combinatorics of Critical Dense
Polymers
[ 講演概要 ]
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\\Delta_{1,s}=\\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\\ldots$ where $s-1$ is
the number
of defects.

### 2008年06月12日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 156号室

On Lubotzky's property $(\\tau)$ and expander graphs

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/03.html

### 2008年06月09日(月)

#### 数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

ような効果(たとえば希釈効果)などがある。、たとえば幼生は成体に比べて一般に

である。

めぐる競争が激しい場合、上位の捕食者による捕食リスクが増えるにつれて

よって明らかにした。

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 470号室
W. Rundell 氏 (Texas A&M Univ.)
Some Unsolved Inverse Spectral Problems
[ 講演概要 ]
Perhaps the first well-studied inverse problem
was the determination of the potential $q(x)$ in
$-u'' + q(x) u = \\lambda_n u$ given the eigenvalues
$\\{\\lambda_n\\}$. Despite its venerable age and
the fact that a considerable literature is still being published,
there are several major outstanding problems;
some are quite simple to state.
This seminar will outline some of these.
We will try to show why the problems are hard,
but leave it to the audience to attempt solutions.

#### 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

Deficiencies of holomorphic curves in algebraic manifolds

### 2008年06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) 056号室

Another analogue of the Borel-Weil theory on loop groups

#### 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

Keller-Segel系に対する離散化手法
[ 講演概要 ]

### 2008年06月04日(水)

#### 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

$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)

[ 講演概要 ]
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and

#### PDE実解析研究会

16:00-18:15   数理科学研究科棟(駒場) 056号室
William Rundell 氏 (Department of Mathematics, Texas A&M University) 16:00-17:00
Inverse Obstacle Recovery when the boundary condition is also unknown
[ 講演概要 ]
We consider the inverse problem of recovering the shape, location
and surface properties of an object where the surrounding medium
is both conductive and homogeneous. It is assumed that the physical situation is modeled by either harmonic functions or solutions of the Helmholtz equation and that the boundary condition on the obstacle is one of impedance type. We measure either Cauchy data, on an accessible part of the exterior boundary or the far field pattern resulting from a plane wave. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance.
It turns out this adds considerable complexity to the analysis. We give a local injectivity result and use two different algorithms
to investigate numerical reconstructions. The setting is in two space dimensions, but indications of possible extensions (and difficulties) to three dimensions are provided. We also look at the case of a nonlinear impedance function.
David Colton 氏 (Department of Mathematical Sciences, University of Delaware) 17:15-18:15
The Inverse Scattering Problem for an Isotropic Medium
[ 講演概要 ]
This talk is concerned with the inverse electromagnetic scattering problem for an isotropic inhomogeneous infinite cylinder. After formulating the direct scattering problem we proceed to the inverse scattering problem which is the main theme of this lecture. After discussing what is known about uniqueness for the inverse problem,we will proceed to the definition and properties of the far field operator. This leads to the study of a rather unusual spectral problem for partial differential equations called the interior transmission problem. We will state what is known about this problem including its role in determining lower bounds for the index of refraction from a knowledge of the far field pattern of the scattered wave, The talk is concluded by briefly considering the case of limited aperture data,in particular the use of the gap reciprocity method to determine the shape and location of buried objects. Numerical examples will be given as well as a number of open problems.

### 2008年06月03日(火)

#### 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

Matrix valued commuting differential operators with B2 symmetry
[ 講演概要 ]
B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。

[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

#### 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

On the geometry of certain slices of the character variety of a knot group
[ 講演概要 ]
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.

### 2008年06月02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

A new series of compact minitwistor spaces and Moishezon twistor spaces over them

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Shinobu Hikami 氏 (The University of Tokyo)
Intersection theory from duality and replica
[ 講演概要 ]
Kontsevich's work on Airy matrix integrals has led to explicit results for the
intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).

### 2008年05月29日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Rolf Dyre Svegstrup 氏 (東大数理)
2D models in AQFT from wedge algebras

### 2008年05月27日(火)

#### 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

Visible actions on multiplicity-free spaces
[ 講演概要 ]
The holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a real submanifold S such that D':=G・S is open in D and an anti-holomorphic diffeomorphism σ which is an identity map on S and preserves each G-orbit in D'.
In this talk, we treat the case where D is a multiplicity-free space V of a connected complex reductive Lie group G(C), and show that the action of a compact real form of G(C) on V is strongly visible.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008年05月26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

### 2008年05月24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
Raimandus Vidunas
(神戸大学理学部
) 13:30-14:30
Identities between Appell's and univariate hyeprgeometric functions

[ 講演概要 ]
We look for univariate specializations of Appell'd bivariante hypergeometric functions that can be expressed in terms of univaraite ${}_{i+1} F_{i} ~(i=1,2,3)$ HGF's. The method is identifying cases when the partial differential equations for Appell's functions imply hypegeometric ordinary differential equations for their univariate specializations. In general, ordinary differential equations for univariate specializations of Apell's functions have order at moast 4.

Whittaker functions with one-dimensional $K$-type on a semisimple Lie group of Hermitian type
[ 講演概要 ]

### 2008年05月23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)
Jean-Michel Bismut 氏 (Univ. Paris-Sud, Orsay)
Functional integration and index theory

[ 講演概要 ]
The heat equation proof of the Atiyah-Singer index theorem involves a local `fantastic cancellation' mechanism, which has long been unexplained conceptually.

In this lecture, I will show how the supersymmetric formalism introduced by physicists has ultimately led to a new understanding of this cancellation mechanism. Ideas of Witten and Atiyah relating the index theorem to the localization formulas of Duistermaat-Heckman in equivariant cohomology have ultimately led to a renewed understanding of the cancellation mechanism as being of geometric nature (albeit in infinite dimensions). The key fact is that when interpreting the heat equation method for the proof of the index theorem, integrals of measures on the loop space of the given manifold, which one obtains via Ito stochastic calculus, should be properly interpreted as integrals of differential forms on the loop space.

I will then explain how this new understanding of the local index theorem has naturally led to a better understanding of spectral invariants, and often to the proof of certain key properties.