## Seminar information archive

Seminar information archive ～05/23｜Today's seminar 05/24 | Future seminars 05/25～

#### Lie Groups and Representation Theory

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

Extensions between finite-dimensional simple modules over a generalized current Lie algebra

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**小寺諒介**(東京大学)Extensions between finite-dimensional simple modules over a generalized current Lie algebra

[ Abstract ]

$\\mathfrak{g}$を$\\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\\mathbb {C}$代数とする.

テンソル積$A \\otimes \\mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.

一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.

[ Reference URL ]$\\mathfrak{g}$を$\\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\\mathbb {C}$代数とする.

テンソル積$A \\otimes \\mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.

一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009/10/09

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)

暗号の実践編

**岡本龍明**(NTT 情報流通プラットフォーム研究所 岡本特別研究室長)暗号の実践編

#### GCOE lecture series

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Associated varieties for Representations of classical Lie

super-algebras

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michel Duflo**(Paris 7)Associated varieties for Representations of classical Lie

super-algebras

[ Abstract ]

In this lecture, I'll discuss the notion of "Associated

varieties for Representations of classical Lie super-algebras (joint work with Vera Serganova)" and the relation with the degree of atypicality. This is related to a conjecture of Kac and Wakimoto.

[ Reference URL ]In this lecture, I'll discuss the notion of "Associated

varieties for Representations of classical Lie super-algebras (joint work with Vera Serganova)" and the relation with the degree of atypicality. This is related to a conjecture of Kac and Wakimoto.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009/10/07

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Wiener measure and Feynman-Kac formula on the Heisenberg group

**劉和平(Liu Heping)**(Beijing University)Wiener measure and Feynman-Kac formula on the Heisenberg group

[ Abstract ]

It is well known that the Feynman-Kac formula on the Euclidean space gives the solution of Schrodinger equation by the Wiener integral. We will discuss the Wiener measure and Feynman-Kac formula on the Heisenberg group. The results hold on the H-type groups.

It is well known that the Feynman-Kac formula on the Euclidean space gives the solution of Schrodinger equation by the Wiener integral. We will discuss the Wiener measure and Feynman-Kac formula on the Heisenberg group. The results hold on the H-type groups.

#### GCOE lecture series

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Representations of classical Lie super-algebras

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michel Duflo**(Paris 7)Representations of classical Lie super-algebras

[ Abstract ]

In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie super-algebras, in particular the notion of the degree of atypicality.

[ Reference URL ]In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie super-algebras, in particular the notion of the degree of atypicality.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On GAGA theorems for the rigide-étale topology

**Ahmed Abbes**(Université de Rennes 1)On GAGA theorems for the rigide-étale topology

[ Abstract ]

Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.

Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.

### 2009/10/05

#### GCOE lecture series

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅲ

**Claudio Landim**(IMPA, Brazil)Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅲ

#### GCOE lecture series

13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Mini course on the gradient models, I: Effective gradient models, definitions and examples

**Jean-Dominique Deuschel**(TU Berlin)Mini course on the gradient models, I: Effective gradient models, definitions and examples

[ Abstract ]

We describe a phase separation in $R^{d+1}$ by an effective interface model with basis in $Z^d$ and height in $R$. We assume that the interaction potential depends only on the discrete gradient and that the a priori measure is the product Lebesgue measure. Note that this is an unbounded massless model with continuous symmetry and this implies that the interface is delocalized for the infinite model in lower lattice dimensions $d=1,2$. Instead of looking at the distribution of the height of the interface itself, we consider the measure on the height differences the so called gradient Gibbs measure, which exists in any dimensions. The gradient field must satisfy the loop condition, that is the sum of the gradient along any closed loop is zero, this implies a long range interaction with a slow decay of the correlations. We are interested in characterizing the ergodic components of this gradient field, in the decay of correlations, large deviations and continuous scaling limits. As an example we consider the harmonic or discrete gaussian free field with quadratic interactions.

We describe a phase separation in $R^{d+1}$ by an effective interface model with basis in $Z^d$ and height in $R$. We assume that the interaction potential depends only on the discrete gradient and that the a priori measure is the product Lebesgue measure. Note that this is an unbounded massless model with continuous symmetry and this implies that the interface is delocalized for the infinite model in lower lattice dimensions $d=1,2$. Instead of looking at the distribution of the height of the interface itself, we consider the measure on the height differences the so called gradient Gibbs measure, which exists in any dimensions. The gradient field must satisfy the loop condition, that is the sum of the gradient along any closed loop is zero, this implies a long range interaction with a slow decay of the correlations. We are interested in characterizing the ergodic components of this gradient field, in the decay of correlations, large deviations and continuous scaling limits. As an example we consider the harmonic or discrete gaussian free field with quadratic interactions.

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

代数曲面上の随伴束の基底点集合について

**伊藤 敦**(東大数理)代数曲面上の随伴束の基底点集合について

[ Abstract ]

偏極付き代数多様体上(X,L)は、Lに数値的な条件を付け加えると

その随伴束が自由になったり、基底点集合が具体的にかけることがある。しかし

、曲線の場合は簡単であるが高次元の場合は難しい。今回の講演では主に代数曲

面の場合について解説する。

偏極付き代数多様体上(X,L)は、Lに数値的な条件を付け加えると

その随伴束が自由になったり、基底点集合が具体的にかけることがある。しかし

、曲線の場合は簡単であるが高次元の場合は難しい。今回の講演では主に代数曲

面の場合について解説する。

### 2009/10/02

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)

暗号の基礎編

**岡本龍明**(NTT 情報流通プラットフォーム研究所 岡本特別研究室長)暗号の基礎編

### 2009/09/30

#### GCOE lecture series

15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅱ

**Claudio Landim**(IMPA, Brazil)Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅱ

#### Seminar on Probability and Statistics

15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)

HDLSSデータにおけるPCAについて

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html

**矢田 和善**(筑波大学大学院数理物質科学研究科)HDLSSデータにおけるPCAについて

[ Abstract ]

マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.

HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.

当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.

[ Reference URL ]マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.

HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.

当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html

### 2009/09/29

#### Tuesday Seminar on Topology

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

Symbol of the Conway polynomial and Drinfeld associator

**Sergei Duzhin**(Steklov Mathematical Institute, Petersburg Division)Symbol of the Conway polynomial and Drinfeld associator

[ Abstract ]

The Magnus expansion is a universal finite type invariant of pure braids

with values in the space of horizontal chord diagrams. The Conway polynomial

composed with the short circuit map from braids to knots gives rise to a

series of finite type invariants of pure braids and thus factors through

the Magnus map. We describe explicitly the resulting mapping from horizontal

chord diagrams on 3 strands to univariante polynomials and evaluate it on

the Drinfeld associator obtaining a beautiful generating function whose

coefficients are integer combinations of multple zeta values.

The Magnus expansion is a universal finite type invariant of pure braids

with values in the space of horizontal chord diagrams. The Conway polynomial

composed with the short circuit map from braids to knots gives rise to a

series of finite type invariants of pure braids and thus factors through

the Magnus map. We describe explicitly the resulting mapping from horizontal

chord diagrams on 3 strands to univariante polynomials and evaluate it on

the Drinfeld associator obtaining a beautiful generating function whose

coefficients are integer combinations of multple zeta values.

### 2009/09/28

#### GCOE lecture series

15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Macroscopic fluctuation theory for nonequilibrium stationary states, I

**Claudio Landim**(IMPA, Brazil)Macroscopic fluctuation theory for nonequilibrium stationary states, I

[ Abstract ]

We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.

We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.

### 2009/09/17

#### Applied Analysis

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

On a parabolic free boundary problem modelling price formation

**Norayr MATEVOSYAN**(ケンブリッジ大学・数理)On a parabolic free boundary problem modelling price formation

[ Abstract ]

We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.

We also present numerical results.

We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.

We also present numerical results.

### 2009/09/15

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

渦層の超局所解析

**打越 敬祐**(防衛大学校数学教育室)渦層の超局所解析

[ Abstract ]

渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,

界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.

渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,

界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.

### 2009/09/14

#### Number Theory Seminar

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Modular forms and Calabi-Yau varieties

**Dinakar Ramakrishnan**(カリフォルニア工科大学)Modular forms and Calabi-Yau varieties

### 2009/09/10

#### Applied Analysis

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

A two phase free boundary problem with applications in potential theory

**Henrik SHAHGHOLIAN**(王立工科大学・ストックホルム)A two phase free boundary problem with applications in potential theory

[ Abstract ]

In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.

The most simple free boundary/potential problem that we can present is the following. Given constants $a_\\pm, \\lambda_\\pm >0$ and two points $x^\\pm$ in ${\\bf R}^n$. Find a function $u$ such that

$$\\Delta u = \\left( \\lambda_+ \\chi_{\\{u>0 \\}} - a_+\\delta_{x^+}\\right) - \\left( \\lambda_- \\chi_{\\{u<0 \\}} - a_-\\delta_{x^-}\\right),$$

where $\\delta$ is the Dirac mass.

In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).

In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.

In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.

The most simple free boundary/potential problem that we can present is the following. Given constants $a_\\pm, \\lambda_\\pm >0$ and two points $x^\\pm$ in ${\\bf R}^n$. Find a function $u$ such that

$$\\Delta u = \\left( \\lambda_+ \\chi_{\\{u>0 \\}} - a_+\\delta_{x^+}\\right) - \\left( \\lambda_- \\chi_{\\{u<0 \\}} - a_-\\delta_{x^-}\\right),$$

where $\\delta$ is the Dirac mass.

In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).

In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.

### 2009/09/08

#### GCOE Seminars

15:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Global compact attractors and their tripartition under persistence (ENGLISH)

**H.R.Thieme**(Arizona State University)Global compact attractors and their tripartition under persistence (ENGLISH)

[ Abstract ]

The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.

Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.

Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)

The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.

Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.

Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)

#### GCOE Seminars

16:15-17:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)

**Glenn Webb**(Vanderbilt University)Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)

[ Abstract ]

We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.

We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.

### 2009/09/07

#### Operator Algebra Seminars

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Generalized Gaussian field, theta function of Jacobi and functor of second quantization

**Marek Bozejko**(University of Wroclaw)Generalized Gaussian field, theta function of Jacobi and functor of second quantization

### 2009/09/01

#### Algebraic Geometry Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Arithmetic of K3 surfaces

**Matthias Schuett**(Leibniz University Hannover)Arithmetic of K3 surfaces

[ Abstract ]

This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.

We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.

This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.

We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.

### 2009/08/12

#### Lie Groups and Representation Theory

10:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Radon Transform and some Applications

Multitemporal Wave Equations: Mean Value Solutins

Analytic continuation of the resolvent of the Laplacian in the Euclidean settings

Decay of smooth vectors for regular representations

**Sigurdur Helgason**(MIT) 10:00-11:00Radon Transform and some Applications

**Fulton G. Gonzalez**(Tufts University) 11:20-12:20Multitemporal Wave Equations: Mean Value Solutins

**Angela Pasquale**(Universite Metz) 14:00-15:00Analytic continuation of the resolvent of the Laplacian in the Euclidean settings

[ Abstract ]

We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.

We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.

**Henrik Schlichtkrull**(University of Copenhagen) 15:30-16:30Decay of smooth vectors for regular representations

[ Abstract ]

Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)

Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)

### 2009/08/07

#### Number Theory Seminar

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

On the $p$-parity conjecture in the function field case

**Fabien Trihan**(Nottingham大学)On the $p$-parity conjecture in the function field case

[ Abstract ]

Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).

Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).

### 2009/07/30

#### GCOE lecture series

11:00-15:45 Room #002 (Graduate School of Math. Sci. Bldg.)

長波長近似モデルと孤立波の安定性Ⅱ

Dynamics of solitons in non-integrable systemsⅤ

Dynamics of solitons in non-integrable systemsⅥ

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html

**水町 徹**(九州大学) 11:00-12:00長波長近似モデルと孤立波の安定性Ⅱ

**Frank Merle**(Cergy Pontoise 大学/IHES) 13:30-14:30Dynamics of solitons in non-integrable systemsⅤ

**Frank Merle**(Cergy Pontoise 大学/IHES) 14:45-15:45Dynamics of solitons in non-integrable systemsⅥ

[ Reference URL ]

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