## Seminar information archive

### 2008/07/16

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
On p-adic differential equation on semi-stable varieties

### 2008/07/15

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

One-step Markov Theorem on exchange classes
[ Abstract ]
The main theorem in this talk claims the following.
Let L_A and L_B denote a closed a-braid and a closed b-braid,
respectively, that represent one link type.
After at most (a^2 b^2)/4 exchange moves on L_A,
we can 'see' the pair of closed braids."
In this talk, we explain the main theorem in details, and
we present some applications.
In particular, we propose a strategy to construct an algorithm
that determines whether two links are ambient isotopic.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

GL(4,R)の退化主系列表現の一般Whittaker関数
[ Abstract ]
$GL(n,R)$の退化球主系列表現の一般Whittaker模型の空間は,対称空間$GL(n,R)/O(n)$上の$C^\\infty$級関数の中で,ある微分作用素達のkernelとして特徴付けられる.この微分作用素達は,大島利雄氏による退化主系列表現に対するPoisson変換の像の特徴付けに用いられたものであり,その明示的な表示が氏によって得られている.また,こうしたkernel定理は山下博氏のユニタリ最低ウエイト加群の一般Whittaker模型に対する定理の類似にあたる.こういった背景の下,$GL(4,R)$の退化主系列表現に対し、いくつかの具体例を考えたい.そこでは一般Whittaker模型は一変数変形Bessel関数、Hornの二変数合流型超幾何関数によって実現される.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/07/12

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

) 13:30-14:30
On certain types and the Hecke algebras for unramified p-adic unitary groups

The $(\\mathfrak{g},K)$-module structures of the principal series resentations for $SL(4,R)$

[ Abstract ]
$SL(4,R)$ の主系列表現 $H$ の $(\\mathfrak{g},K)$-module としての構造を

### 2008/07/10

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

The Structure of a Hyponormal Operator (a joint work with Kotaro
Tanahashi)

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

Two positive solutions for an inhomogeneous scalar field equation
[ Abstract ]
We consider the following nonlinear elliptic equation:
$$-\\Delta u+u=g(u)+f(x), x \\in R^N,$$
where $N\\ge 3$. When $f(x)\\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \\not\\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\\| f\\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

Bayesian learning of biological pathways on genomic data assimilation
[ Abstract ]
States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html

### 2008/07/08

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Otto van Koert (北海道大学大学院理学研究科, JSPS)
Contact homology of left-handed stabilizations and connected sums
[ Abstract ]
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

construction of extended affine Lie algebras from multiloop Lie algebras
[ Abstract ]
affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/07/07

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Henon 写像の複素力学系

### 2008/07/03

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

http://www.ism.ac.jp/~nisiyama/pism080626.pdf
にまとめてある。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/05.html

### 2008/07/02

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

(安田正大氏との共同研究)

### 2008/07/01

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
MacWilliams変換と呼ばれる変換で不変な複素2変数斉次多項式に対して、zeta多項式と呼ばれる複素1変数多項式を定義する。
TypeIV extremal と呼ばれる不変式の無限列に対し、deg = 0 (mod 6) の場合には、対応する全ての zeta多項式の零点が同一円周上に乗るという事が証明されているが、deg = 2,4 (mod 6) の場合は未解決であった。
この講演では、不変式に対する微分作用素を用いて、deg = 4 (mod6) の場合にも全てのzeta多項式の零点が同一円周上に乗るということを示したい。

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

On the Johnson homomorphisms of the automorphism group of
a free metabelian group
[ Abstract ]
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.

### 2008/06/30

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
J.Manuel Garcia-Islas (National Autonomous University of Mexico)
Quantum topological invariants and black hole entropy
[ Abstract ]
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.

### 2008/06/26

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Solid groups and orbit equivalence rigidity

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

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 -
[ Abstract ]
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。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/04.html

### 2008/06/24

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Kenneth Shackleton (東京工業大学, JSPS)
On computing distances in the pants complex
[ Abstract ]
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.
[ Reference URL ]
http://www.is.titech.ac.jp/~kjshack5/FYEO.pdf

### 2008/06/23

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

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

### 2008/06/20

#### Colloquium

16:30-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

IPMU, Mathematics, Physics, and me
[ Abstract ]
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.

### 2008/06/19

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
David Kerr (Texas A&M University)
Turbulence, representations, and trace-preserving actions

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

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)

[ Abstract ]
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.

#### Lectures

16:20-17:50   Room #052 (Graduate School of Math. Sci. Bldg.)

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」
[ Abstract ]
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。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html

### 2008/06/18

#### Number Theory Seminar

16:30-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)

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
[ Abstract ]
(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、