## 過去の記録

#### 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 Johnson homomorphisms of the automorphism group of
a free metabelian group
[ 講演概要 ]
The main object of our research is the automorphism group of a
free group. To be brief, the Johnson homomorphisms are studied in order to
describe one by one approximations of the automorphism group of a free group
. They play important roles on the study of the homology groups of the autom
orphism group of a free group. In general, to determine their images are ver
y difficult problem. In this talk, we define the Johnson homomorphisms of th
e automorphism group of a free metabelian group, and determine their images.
Using these results, we can give a lower bound on the image of the Johnson
homomorphisms of the automorphism group of a free group.

### 2008年06月30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

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
J.Manuel Garcia-Islas 氏 (National Autonomous University of Mexico)
Quantum topological invariants and black hole entropy
[ 講演概要 ]
A type of topological invariants of three manifolds were
introduced by Turaev and Viro. We will define an invariant of graphs
embedded in a three dimensional manifold in a Turaev-Viro spirit.
The relation of these invariants to mathematical physics is
a really nice one. We will show how entropy of a three dimensional
black hole known as BTZ can be described using our formulation.

### 2008年06月26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

Solid groups and orbit equivalence rigidity

#### 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

アイテムの選好度のモデルとパラメタ推定法 - Plackett-Luceモデルの一般化 -
[ 講演概要 ]
アイテムの比較やランキングデータが多数与えられたとき、一つ一つのアイテムが潜在的に持つ 価値を決定する問題は、心理学、経済学、政治学などの分野で古くから研究が行われているが、 近年機械学習の分野でも注目されている。 Plackett-Luceモデルはアイテムへのランキングの確率モデルであり、アイテム一つ一つに 多項分布のパラメタを割り当ててアイテム選択のプロセスを説明する。 本発表では、映画評の生成プロセスに注目し、Plackett-Luceの一般化として グループ化ランキングモデルを提案する。このモデルの尤度関数を直接評価することは 困難であるため、尤度関数の下界を与え、emアルゴリズムを用いて近似的に下界の 最大化を行うことでパラメタ推定を行う。 Toy exampleに対する実験結果と、映画評データに対する適用結果を紹介する。 時間が許せば、個人の嗜好に基づくパラメタの推定と、協調フィルタリングへの 応用についても言及する。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/04.html

### 2008年06月24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
Kenneth Shackleton 氏 (東京工業大学, JSPS)
On computing distances in the pants complex
[ 講演概要 ]
The pants complex is an accurate combinatorial
model for the Weil-Petersson metric (WP) on Teichmueller space
(Brock). One hopes that many of the geometric properties
of WP are accurately replicated in the pants complex, and
this is the source of many open questions. We compare these
in general, and then focus on the 5-holed sphere and the
2-holed torus, the first non-trivial surfaces. We arrive at
an algorithm for computing distances in the (1-skeleton of the)
pants complex of either surface.
[ 参考URL ]
http://www.is.titech.ac.jp/~kjshack5/FYEO.pdf

### 2008年06月23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

5次対称群が作用するK3曲面のある1次元族の周期写像と逆写像

### 2008年06月20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)

IPMU, Mathematics, Physics, and me
[ 講演概要 ]
Institute for the Physics and Mathematics of the Universe (IPMU) was founded to promote synergy between mathematics and physics, and to address deep mysteries about the universe. In this colloquium, I will discuss the mysteries IPMU will address, and why the interaction between mathematicians and physicists are crucial for this purpose. I will also talk about my personal journey about mathematics and physics.

### 2008年06月19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
David Kerr 氏 (Texas A&M University)
Turbulence, representations, and trace-preserving actions

#### 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。
[ 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 ]

[ 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.