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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
2009/03/12
Colloquium
15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
菊地文雄 (東京大学大学院数理科学研究科) 15:00-16:00
数値解析:得られた成果と残された課題
正標数の世界に40年
菊地文雄 (東京大学大学院数理科学研究科) 15:00-16:00
数値解析:得られた成果と残された課題
[ Abstract ]
有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
桂 利行 (東京大学大学院数理科学研究科) 16:30-17:30有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
正標数の世界に40年
[ Abstract ]
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。
GCOE lecture series
09:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Roger Zierau (Oklahoma State University) 09:30-10:30
Dirac Cohomology
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz (Max Planck) 11:00-12:00
Harish-Chandra modules
Special unipotent representations of real reductive groups
Roger Zierau (Oklahoma State University) 09:30-10:30
Dirac Cohomology
[ Abstract ]
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.
[ Reference URL ]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.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz (Max Planck) 11:00-12:00
Harish-Chandra modules
[ Abstract ]
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 (Utah大学) 13:30-14:30We 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.
Special unipotent representations of real reductive groups
[ Abstract ]
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.
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.
2009/03/05
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Shicheng Wang (Peking University)
Extending surface automorphisms over 4-space
Shicheng Wang (Peking University)
Extending surface automorphisms over 4-space
[ Abstract ]
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.
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 Seminars
10:15-11:15 Room #270 (Graduate School of Math. Sci. Bldg.)
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
V. Isakov (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
[ Abstract ]
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.
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 Seminars
11:15-12:15 Room #270 (Graduate School of Math. Sci. Bldg.)
J. Ralston (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
J. Ralston (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
[ Abstract ]
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.
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.
2009/03/04
GCOE Seminars
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
P. Gaitan (with H. Isozaki and O. Poisson) (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
P. Gaitan (with H. Isozaki and O. Poisson) (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves
GCOE Seminars
16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
M. Cristofol (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
M. Cristofol (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
2009/03/03
GCOE Seminars
16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
O. Poisson (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
O. Poisson (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
[ Abstract ]
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.
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 Seminars
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Y. Dermenjian (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf
Y. Dermenjian (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf
2009/03/02
GCOE Seminars
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Bernd Hofmann (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf
Bernd Hofmann (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
[ Abstract ]
Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
[ Reference URL ]Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf
2009/02/26
Lectures
17:00-18:30 Room #270 (Graduate School of Math. Sci. Bldg.)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
GCOE Seminars
15:00-16:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Jijun Liu (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
Jijun Liu (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
[ Abstract ]
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.
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.
2009/02/24
Colloquium
16:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
神保道夫 (東京大学大学院数理科学研究科)
相関関数の構成要素
神保道夫 (東京大学大学院数理科学研究科)
相関関数の構成要素
[ Abstract ]
2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。
講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。
2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。
講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。
2009/02/23
Lectures
13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
長田 博文 (九大数理)
TBA
長田 博文 (九大数理)
TBA
Lectures
14:40-16:10 Room #123 (Graduate School of Math. Sci. Bldg.)
Herbert Spohn (ミュンヘン工科大学)
Some problems from Statistical Mechanics linked to matrix-valued
Brownian motion
Herbert Spohn (ミュンヘン工科大学)
Some problems from Statistical Mechanics linked to matrix-valued
Brownian motion
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
Stefano Olla (パリ第9大学)
Macroscopic energy transport: a weak coupling approach
Stefano Olla (パリ第9大学)
Macroscopic energy transport: a weak coupling approach
2009/02/19
Lectures
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
Algebraic Geometry Seminar
15:50-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
O. F. Pasarescu (Romanian Academy)
・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)
・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)
O. F. Pasarescu (Romanian Academy)
・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)
・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)
2009/02/18
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
野原勉 (武蔵工業大学)
Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system
野原勉 (武蔵工業大学)
Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system
[ Abstract ]
We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.
We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.
thesis presentations
17:00-18:10 Room #122 (Graduate School of Math. Sci. Bldg.)
清野和彦 (東京大学大学院数理科学研究科)
Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)
清野和彦 (東京大学大学院数理科学研究科)
Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)
2009/02/14
Infinite Analysis Seminar Tokyo
10:30-14:00 Room #117 (Graduate School of Math. Sci. Bldg.)
藤健太 (神戸理) 10:30-11:30
野海・山田系におけるタウ関数の関係式
ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式
藤健太 (神戸理) 10:30-11:30
野海・山田系におけるタウ関数の関係式
[ Abstract ]
野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階
の常微分方程式系である.
本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ
て, 野海・山田系のタウ関数の双線形方程式を求める.
鈴木貴雄 (神戸理) 13:00-14:00野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階
の常微分方程式系である.
本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ
て, 野海・山田系のタウ関数の双線形方程式を求める.
ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式
[ Abstract ]
ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ
ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で
ある.
本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ
に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik
uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.
また, パンルヴェ型微分方程式との関連についても述べる.
ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ
ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で
ある.
本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ
に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik
uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.
また, パンルヴェ型微分方程式との関連についても述べる.
2009/02/13
GCOE lecture series
15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Vladimir Romanov (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講
Vladimir Romanov (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講
[ Abstract ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.
GCOE Seminars
14:00-14:45 Room #270 (Graduate School of Math. Sci. Bldg.)
Johannes Elschner (Weierstrass Institute)
Direct and inverse problems in fluid-solid interaction
Johannes Elschner (Weierstrass Institute)
Direct and inverse problems in fluid-solid interaction
[ Abstract ]
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.
GCOE Seminars
16:15-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Wenbin Chen (Fudan University)
New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations
Wenbin Chen (Fudan University)
New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations
[ Abstract ]
In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.
In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.
2009/02/12
Lectures
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure
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