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過去の記録
過去の記録 ～07/26｜本日 07/27 | 今後の予定 07/28～
統計数学セミナー
13:40-14:50 数理科学研究科棟(駒場) 128号室
Stefano Maria Iacus 氏 (Universita degli Studi di Milano)
Applications of Iterated Function Systems to Inference and Simulation
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html
Stefano Maria Iacus 氏 (Universita degli Studi di Milano)
Applications of Iterated Function Systems to Inference and Simulation
[ 講演概要 ]
The Iterated Function Systems (IFSs) were born in mid eighties as applications of the theory of discrete dynamical systems and as useful tools for buildings fractals and other similar sets or to produce image compression algorithms. The fundamental result on which the IFS method is based is the Banach contraction theorem because IFSs are defined as operators with some contractive property. In practical applications the crucial point is to solve the inverse problem: given an element f in some metric space (S,d), find a contraction T:S -> S that admits a unique fixed point p such that d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the fixed point p can be identified with the operator T, but in most cases T is an approximation of the target f and T takes linear forms. We present applications of the IFS technique to the problem of estimation of distribution and density functions and to the simulation of L2 stochastic processes.
[ 参考URL ]The Iterated Function Systems (IFSs) were born in mid eighties as applications of the theory of discrete dynamical systems and as useful tools for buildings fractals and other similar sets or to produce image compression algorithms. The fundamental result on which the IFS method is based is the Banach contraction theorem because IFSs are defined as operators with some contractive property. In practical applications the crucial point is to solve the inverse problem: given an element f in some metric space (S,d), find a contraction T:S -> S that admits a unique fixed point p such that d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the fixed point p can be identified with the operator T, but in most cases T is an approximation of the target f and T takes linear forms. We present applications of the IFS technique to the problem of estimation of distribution and density functions and to the simulation of L2 stochastic processes.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html
2009年02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
Gombodorj Bayarmagnai 氏 (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Gombodorj Bayarmagnai 氏 (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
[ 講演概要 ]
In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
[ 参考URL ]In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009年02月02日(月)
講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich)
On a perceptron version of the Generalized Random Energy Model
Erwin Bolthausen 氏 (University of Zurich)
On a perceptron version of the Generalized Random Energy Model
2009年01月30日(金)
GCOEセミナー
16:15-17:15 数理科学研究科棟(駒場) 370号室
F. Cakoni 氏 (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
F. Cakoni 氏 (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
[ 講演概要 ]
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.
GCOEセミナー
15:10-16:10 数理科学研究科棟(駒場) 370号室
Lucie Baudouin 氏 (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
Lucie Baudouin 氏 (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
[ 講演概要 ]
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).
2009年01月29日(木)
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
千葉 逸人 氏 (京都大学 情報学研究科)
Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method
千葉 逸人 氏 (京都大学 情報学研究科)
Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method
[ 講演概要 ]
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.
2009年01月28日(水)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 122号室
講演曜日・場所が通常と異なりますのでご注意ください
吉野 伸 氏 (東京電力)
電場による配管損傷評価法について
講演曜日・場所が通常と異なりますのでご注意ください
吉野 伸 氏 (東京電力)
電場による配管損傷評価法について
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 056号室
Pierre Colmez 氏 (École polytechnique)
On the p-adic local Langlands correspondence
Pierre Colmez 氏 (École polytechnique)
On the p-adic local Langlands correspondence
2009年01月27日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
深谷 賢治 氏 (京都大学大学院理学研究科)
Lagrangian Floer homology and quasi homomorphism
from the group of Hamiltonian diffeomorphism
Tea: 16:40 - 17:00 コモンルーム
深谷 賢治 氏 (京都大学大学院理学研究科)
Lagrangian Floer homology and quasi homomorphism
from the group of Hamiltonian diffeomorphism
[ 講演概要 ]
Entov-Polterovich constructed quasi homomorphism
from the group of Hamiltonian diffeomorphisms using
spectral invariant due to Oh etc.
In this talk I will explain a way to study this
quasi homomorphism by using Lagrangian Floer homology.
I will also explain its generalization to use quantum
cohomology with bulk deformation.
When applied to the case of toric manifold, it
gives an example where (infinitely) many quasi homomorphism
exists.
(Joint work with Oh-Ohta-Ono).
Entov-Polterovich constructed quasi homomorphism
from the group of Hamiltonian diffeomorphisms using
spectral invariant due to Oh etc.
In this talk I will explain a way to study this
quasi homomorphism by using Lagrangian Floer homology.
I will also explain its generalization to use quantum
cohomology with bulk deformation.
When applied to the case of toric manifold, it
gives an example where (infinitely) many quasi homomorphism
exists.
(Joint work with Oh-Ohta-Ono).
2009年01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
高山 茂晴 氏 (東大数理)
高次順像層のホッジ計量の正値性
高山 茂晴 氏 (東大数理)
高次順像層のホッジ計量の正値性
GCOEレクチャーズ
17:15-18:15 数理科学研究科棟(駒場) 470号室
大学院生を対象に、3回の講演を実施します。講演ごとに曜日、時間、場所が異なりますのでご注意ください。
又、各回ともなるべく独立になるようにします。
Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講
大学院生を対象に、3回の講演を実施します。講演ごとに曜日、時間、場所が異なりますのでご注意ください。
又、各回ともなるべく独立になるようにします。
Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講
[ 講演概要 ]
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セミナー
16:00-17:00 数理科学研究科棟(駒場) 470号室
Vilmos Komornik 氏 (University of Strasbourg)
Ingham-Beurling type inequalities
Vilmos Komornik 氏 (University of Strasbourg)
Ingham-Beurling type inequalities
[ 講演概要 ]
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.
2009年01月24日(土)
東京無限可積分系セミナー
11:00-16:00 数理科学研究科棟(駒場) 117号室
仲田 研登 氏 (京大数研) 11:00-12:00
一般化されたヤング図形の q-Hook formula
Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$
On a dimer model with impurities
仲田 研登 氏 (京大数研) 11:00-12:00
一般化されたヤング図形の q-Hook formula
[ 講演概要 ]
Young図形における hook formula は、組合せ論的には、その Young 図形の standar
d tableau の総数を数え上げる公式である。R. P. Stanley は reverse plane parti
tion のなす母関数を考えることにより、この公式をq-hook formula に拡張し、E. R
. Gansner はそれをさらに多変数に一般化した。
本講演では、この(多変数)q-Hook formula が(D. Peterson、R. A. Proctor の意
味の)一般化されたYoung図形においても成り立つこと紹介する。特にこれはPeterso
n の hook formula の証明も与える。
土岡 俊介 氏 (京大数研) 13:30-14:30Young図形における hook formula は、組合せ論的には、その Young 図形の standar
d tableau の総数を数え上げる公式である。R. P. Stanley は reverse plane parti
tion のなす母関数を考えることにより、この公式をq-hook formula に拡張し、E. R
. Gansner はそれをさらに多変数に一般化した。
本講演では、この(多変数)q-Hook formula が(D. Peterson、R. A. Proctor の意
味の)一般化されたYoung図形においても成り立つこと紹介する。特にこれはPeterso
n の hook formula の証明も与える。
Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$
[ 講演概要 ]
Motivated by a connection between representation theory of
the degenerate affine Hecke algebra of type A and
Lie theory associated with $A^{(1)}_{p-1}$, we determine the complete
set of representatives of the orbits for the Weyl group action on
the set of weights of level 2 integrable highest weight representations of $\\widehat{\\mathfrak{sl}}_p$.
Applying a crystal technique, we show that Catalan numbers appear in their weight multiplicities.
Here "a crystal technique" means a result based on a joint work with S.Ariki and V.Kreiman,
which (as an application of the Littelmann's path model) combinatorially characterize
the connected component (usually called Kleshchev bipartition in the representation theoretic context)
$B(\\Lambda_0+\\Lambda_s)\\subseteq B(\\Lambda_0)\\otimes B(\\Lambda_s)$ in the tensor product.
中野 史彦 氏 (高知大理学部数学) 15:00-16:00Motivated by a connection between representation theory of
the degenerate affine Hecke algebra of type A and
Lie theory associated with $A^{(1)}_{p-1}$, we determine the complete
set of representatives of the orbits for the Weyl group action on
the set of weights of level 2 integrable highest weight representations of $\\widehat{\\mathfrak{sl}}_p$.
Applying a crystal technique, we show that Catalan numbers appear in their weight multiplicities.
Here "a crystal technique" means a result based on a joint work with S.Ariki and V.Kreiman,
which (as an application of the Littelmann's path model) combinatorially characterize
the connected component (usually called Kleshchev bipartition in the representation theoretic context)
$B(\\Lambda_0+\\Lambda_s)\\subseteq B(\\Lambda_0)\\otimes B(\\Lambda_s)$ in the tensor product.
On a dimer model with impurities
[ 講演概要 ]
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the boundary, which we set as a conjecture. We first show that there is a bijection between the set of dimer coverings on
$G$ and the set of spanning forests on two graphs which are made from $G$, with configuration of impurities satisfying a pairing condition, and this bijection can be regarded as a extension of the Temperley bijection. We consider local move consisting of two operations, and by using the bijection mentioned above, we prove local move connectedness. Finally, we prove that the above conjecture is true,
in some spacial cases.
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the boundary, which we set as a conjecture. We first show that there is a bijection between the set of dimer coverings on
$G$ and the set of spanning forests on two graphs which are made from $G$, with configuration of impurities satisfying a pairing condition, and this bijection can be regarded as a extension of the Temperley bijection. We consider local move consisting of two operations, and by using the bijection mentioned above, we prove local move connectedness. Finally, we prove that the above conjecture is true,
in some spacial cases.
2009年01月23日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 128号室
渡辺 秀明 氏 (防衛省技術研究本部電子装備研究所)
防衛電子技術についてⅡ
渡辺 秀明 氏 (防衛省技術研究本部電子装備研究所)
防衛電子技術についてⅡ
GCOEレクチャーズ
17:00-18:00 数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam )
The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
Eric Opdam 氏 (University of Amsterdam )
The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009年01月22日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
関根良紹 氏 (東大数理)
On the electron-phonon interacting system
関根良紹 氏 (東大数理)
On the electron-phonon interacting system
GCOEレクチャーズ
17:00-18:00 数理科学研究科棟(駒場) 370号室
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
Eric Opdam 氏 (University of Amsterdam)
The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009年01月21日(水)
講演会
16:50-17:50 数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich)
The quenched critical point of a diluted disordered polymer model and the related question for the random copolymer
Erwin Bolthausen 氏 (University of Zurich)
The quenched critical point of a diluted disordered polymer model and the related question for the random copolymer
2009年01月20日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
吉野 邦生 氏 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
吉野 邦生 氏 (武蔵工業大学)
Generating function of eigenvalues of Daubechies Localization Operator
[ 講演概要 ]
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について
トポロジー火曜セミナー
16:30-17:30 数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム
野澤 啓 氏 (東京大学大学院数理科学研究科)
Five dimensional $K$-contact manifolds of rank 2
Tea: 16:00 - 16:30 コモンルーム
野澤 啓 氏 (東京大学大学院数理科学研究科)
Five dimensional $K$-contact manifolds of rank 2
[ 講演概要 ]
A $K$-contact manifold is an odd dimensional manifold $M$ with a contact form $\\alpha$ whose Reeb flow preserves a Riemannian metric on $M$. For examples, the underlying manifold with the underlying contact form of a Sasakian manifold is $K$-contact. In this talk, we will state our results on classification up to surgeries, the existence of compatible Sasakian metrics and a sufficient condition to be toric for closed $5$-dimensional $K$-contact manifolds with a $T^2$ action given by the closure of the Reeb flow, which are obtained by the application of Morse theory to the contact moment map for the $T^2$ action.
A $K$-contact manifold is an odd dimensional manifold $M$ with a contact form $\\alpha$ whose Reeb flow preserves a Riemannian metric on $M$. For examples, the underlying manifold with the underlying contact form of a Sasakian manifold is $K$-contact. In this talk, we will state our results on classification up to surgeries, the existence of compatible Sasakian metrics and a sufficient condition to be toric for closed $5$-dimensional $K$-contact manifolds with a $T^2$ action given by the closure of the Reeb flow, which are obtained by the application of Morse theory to the contact moment map for the $T^2$ action.
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 002号室
Tea: 16:00 - 16:30 コモンルーム
中村 伊南沙 氏 (東京大学大学院数理科学研究科)
Surface links which are coverings of a trivial torus knot (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
中村 伊南沙 氏 (東京大学大学院数理科学研究科)
Surface links which are coverings of a trivial torus knot (JAPANESE)
[ 講演概要 ]
We consider surface links which are in the form of coverings of a
trivial torus knot, which we will call torus-covering-links.
By definition, torus-covering-links include
spun $T^2$-knots, turned spun $T^2$-knots, and symmetry-spun tori.
We see some properties of torus-covering-links.
We consider surface links which are in the form of coverings of a
trivial torus knot, which we will call torus-covering-links.
By definition, torus-covering-links include
spun $T^2$-knots, turned spun $T^2$-knots, and symmetry-spun tori.
We see some properties of torus-covering-links.
2009年01月19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
金子 宏 氏 (東京理科大理)
確率論的視点による単位円周の双対としてのp進整数環の考察
金子 宏 氏 (東京理科大理)
確率論的視点による単位円周の双対としてのp進整数環の考察
2009年01月16日(金)
GCOE社会数理講演シリーズ
16:20-17:50 数理科学研究科棟(駒場) 128号室
渡辺 秀明 氏 (防衛省技術研究本部電子装備研究所)
防衛電子技術についてⅠ
渡辺 秀明 氏 (防衛省技術研究本部電子装備研究所)
防衛電子技術についてⅠ
2009年01月15日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Alin Ciuperca 氏 (Univ. Toronto)
Isomorphism of Hilbert modules over stably finite $C^*$-algebras
Alin Ciuperca 氏 (Univ. Toronto)
Isomorphism of Hilbert modules over stably finite $C^*$-algebras
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
木村 正人 氏 (九州大学・大学院数理学研究院)
On a phase field model for mode III crack growth
木村 正人 氏 (九州大学・大学院数理学研究院)
On a phase field model for mode III crack growth
[ 講演概要 ]
2次元弾性体の面外変形による亀裂の進展を記述する,ある
フェイズ・フィールド・モデルについて考える.モデルの
導出は,Francfort-Marigoによる拡張された意味での
Griffithの破壊基準をもとに,Ambrosio-Tortorelliに
よるエネルギー正則化のアイデアを用いてなされる.
現状で得られている数学的な結果と,適合型メッシュを
用いた有限要素シミュレーション例についての紹介も行う.
本研究は高石武史(広島国際学院大学)との共同研究である.
2次元弾性体の面外変形による亀裂の進展を記述する,ある
フェイズ・フィールド・モデルについて考える.モデルの
導出は,Francfort-Marigoによる拡張された意味での
Griffithの破壊基準をもとに,Ambrosio-Tortorelliに
よるエネルギー正則化のアイデアを用いてなされる.
現状で得られている数学的な結果と,適合型メッシュを
用いた有限要素シミュレーション例についての紹介も行う.
本研究は高石武史(広島国際学院大学)との共同研究である.
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