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FMSPレクチャーズ
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 担当者 | 河野俊丈 |
|---|
過去の記録
2013年12月19日(木)
17:00-18:00 数理科学研究科棟(駒場) 270号室
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf
Guanghui Hu 氏 (WIAS, Germany)
Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)
[ 講演概要 ]
In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.
[ 参考URL ]In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.
Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.
In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely
determined from the near-field data corresponding to a finite number of incident elastic plane waves.
This is a joint work with J. Elschner and M. Yamamoto.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf
2013年12月16日(月)
15:30-16:30 数理科学研究科棟(駒場) 056号室
Jon Nimmo 氏 (Univ. of Glasgow)
The discrete Schrodinger equation for compact support potentials (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf
Jon Nimmo 氏 (Univ. of Glasgow)
The discrete Schrodinger equation for compact support potentials (ENGLISH)
[ 講演概要 ]
We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.
Applications of this approach to the udKdV are also discussed.
[ 参考URL ]We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.
Applications of this approach to the udKdV are also discussed.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf
2013年12月10日(火)
13:00-14:30 数理科学研究科棟(駒場) 126号室
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
2013年12月06日(金)
16:30-18:00 数理科学研究科棟(駒場) 118号室
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (II) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (II) (ENGLISH)
[ 講演概要 ]
About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
[ 参考URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf
2013年12月04日(水)
15:00-16:30 数理科学研究科棟(駒場) 128号室
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (I) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf
Simon Gindikin 氏 (Rutgers University)
Horospheres: geometry and analysis (I) (ENGLISH)
[ 講演概要 ]
About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
[ 参考URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf
2013年12月03日(火)
13:00-14:30 数理科学研究科棟(駒場) 126号室
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
2013年11月29日(金)
10:40-12:10 数理科学研究科棟(駒場) 126号室
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
2013年11月29日(金)
14:50-16:20 数理科学研究科棟(駒場) 126号室
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
全4回講演
Erwin Bolthausen 氏 (University of Zurich)
Random walks in random environments (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf
2013年11月22日(金)
10:40-11:40 数理科学研究科棟(駒場) 123号室
Alfred RAMANI 氏 (École polytechnique)
Integrable discrete systems, an introduction Pt. 2 (ENGLISH)
Alfred RAMANI 氏 (École polytechnique)
Integrable discrete systems, an introduction Pt. 2 (ENGLISH)
[ 講演概要 ]
The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.
The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.
2013年11月18日(月)
15:30-16:30 数理科学研究科棟(駒場) 056号室
Alfred RAMANI 氏 (École polytechnique)
Integrable discrete systems, an introduction Pt.1 (ENGLISH)
Alfred RAMANI 氏 (École polytechnique)
Integrable discrete systems, an introduction Pt.1 (ENGLISH)
[ 講演概要 ]
The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.
The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.
2013年09月07日(土)
15:00-16:30 数理科学研究科棟(駒場) 123号室
Bertrand Deroin 氏 (University of Paris-Sud)
Dominating representations by Fuchsian ones (ENGLISH)
Bertrand Deroin 氏 (University of Paris-Sud)
Dominating representations by Fuchsian ones (ENGLISH)
[ 講演概要 ]
We will focus on the problem of dominating the translation lengths of a representation from a surface group to the isometries of a CAT(-1) space by the lengths induced by a hyperbolic structure on the surface. This is related to the construction of 3-dimensional anti-de-Sitter compact manifolds. This is a collaboration with Nicolas Tholozan.
We will focus on the problem of dominating the translation lengths of a representation from a surface group to the isometries of a CAT(-1) space by the lengths induced by a hyperbolic structure on the surface. This is related to the construction of 3-dimensional anti-de-Sitter compact manifolds. This is a collaboration with Nicolas Tholozan.
2013年08月12日(月)
16:30-18:00 数理科学研究科棟(駒場) 118号室
Roberto Longo 氏 (Univ. Roma, Tor Vergata)
Operator Algebraic Construction of Quantum Field Theory Models (ENGLISH)
Roberto Longo 氏 (Univ. Roma, Tor Vergata)
Operator Algebraic Construction of Quantum Field Theory Models (ENGLISH)
2013年08月07日(水)
16:00-17:00 数理科学研究科棟(駒場) 370号室
Philippe Guyenne 氏 (Univ. of Delaware)
Water waves over a random bottom (ENGLISH)
Philippe Guyenne 氏 (Univ. of Delaware)
Water waves over a random bottom (ENGLISH)
[ 講演概要 ]
We present a Hamiltonian formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to a lower-dimensional system involving boundary variables alone. To accomplish this, we express the Dirichlet-to-Neumann operator as a Taylor series in terms of the surface and bottom variations. This expansion is convenient for both asymptotic calculations and numerical simulations. First we apply this formulation to the asymptotic description of long waves over random topography. We show that the principal component of the solution can be described by a Korteweg-de Vries equation plus random phase corrections. We also derive an asymptotic expression for the scattered component. Finally numerical simulations will be shown to illustrate the theoretical results. This is joint work with Walter Craig and Catherine Sulem.
We present a Hamiltonian formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to a lower-dimensional system involving boundary variables alone. To accomplish this, we express the Dirichlet-to-Neumann operator as a Taylor series in terms of the surface and bottom variations. This expansion is convenient for both asymptotic calculations and numerical simulations. First we apply this formulation to the asymptotic description of long waves over random topography. We show that the principal component of the solution can be described by a Korteweg-de Vries equation plus random phase corrections. We also derive an asymptotic expression for the scattered component. Finally numerical simulations will be shown to illustrate the theoretical results. This is joint work with Walter Craig and Catherine Sulem.
2013年07月26日(金)
10:30-12:00 数理科学研究科棟(駒場) 118号室
Birgit Speh 氏 (Cornell University)
Representations of reductive groups and L-functions (II) (ENGLISH)
Birgit Speh 氏 (Cornell University)
Representations of reductive groups and L-functions (II) (ENGLISH)
[ 講演概要 ]
In the second lecture we will quickly discuss Rankin Selberg integral approach to L-factors and then Shahidi's method of constructing L-functions by relating them to intertwining operators, leading to the definition of the the L-factors of tempered non degenerate representations. The lecture closes with a discussion of L-factors for nontempered representations.
In the second lecture we will quickly discuss Rankin Selberg integral approach to L-factors and then Shahidi's method of constructing L-functions by relating them to intertwining operators, leading to the definition of the the L-factors of tempered non degenerate representations. The lecture closes with a discussion of L-factors for nontempered representations.
2013年07月18日(木)
16:30-18:00 数理科学研究科棟(駒場) 117号室
Birgit Speh 氏 (Cornell University)
Representations of reductive groups and L-functions (I) (ENGLISH)
Birgit Speh 氏 (Cornell University)
Representations of reductive groups and L-functions (I) (ENGLISH)
[ 講演概要 ]
This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).
This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).
2013年07月08日(月)
16:15-17:15 数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)
Oleg Emanouilov 氏 (Colorado State Univ.)
Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)
[ 講演概要 ]
We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.
Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.
We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.
Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.
2013年07月05日(金)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (IV) Applications to differential geometry and foliations (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (IV) Applications to differential geometry and foliations (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
2013年06月28日(金)
16:00-17:30 数理科学研究科棟(駒場) 122号室
森 洋一朗 氏 (University of Minnesota)
イオンの電気拡散とその数理モデル 第二話 (JAPANESE)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf
森 洋一朗 氏 (University of Minnesota)
イオンの電気拡散とその数理モデル 第二話 (JAPANESE)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf
2013年06月27日(木)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (III) Curvature of metric measure spaces II
(ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (III) Curvature of metric measure spaces II
(ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
2013年06月27日(木)
16:00-17:30 数理科学研究科棟(駒場) 128号室
森 洋一朗 氏 (University of Minnesota)
イオンの電気拡散とその数理モデル 第一話 (JAPANESE)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf
森 洋一朗 氏 (University of Minnesota)
イオンの電気拡散とその数理モデル 第一話 (JAPANESE)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf
2013年06月20日(木)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (II) Curvature of metric measure spaces I (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (II) Curvature of metric measure spaces I (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
2013年06月19日(水)
14:40-16:10 数理科学研究科棟(駒場) 002号室
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (I) Wasserstein distance and optimal transportation
(ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
Szymon M. Walczak 氏 (University of Lodz, Poland)
Geometric applications of Wasserstein distance,
Lecture (I) Wasserstein distance and optimal transportation
(ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf
2013年06月13日(木)
17:00-18:00 数理科学研究科棟(駒場) 370号室
Fikret Golgeleyen 氏 (Bulent Ecevit University)
Boundary Rigidity for Riemannian Manifolds (ENGLISH)
Fikret Golgeleyen 氏 (Bulent Ecevit University)
Boundary Rigidity for Riemannian Manifolds (ENGLISH)
2013年06月06日(木)
16:00-17:30 数理科学研究科棟(駒場) 056号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Real-valued and circle-valued Morse theory:
an introduction
(ENGLISH)
Andrei Pajitnov 氏 (Univ. de Nantes)
Real-valued and circle-valued Morse theory:
an introduction
(ENGLISH)
[ 講演概要 ]
Classical Morse theory relates the number of critical points of a Morse
function f on a manifold M to the topology of M. The main technical
ingredient of this theory is a chain complex generated by the critical points
of the function. In 1981 S.P. Novikov generalized this theory to the case of
circle-valued Morse functions. In this talk we describe the construction of
both chain complexes, based on the idea of E. Witten (1982), which allows, in
particular, to compute the boundary operators in the Morse complex from
the count of flow lines of the gradient of f. We discuss geometric applications
of these constructions.
Classical Morse theory relates the number of critical points of a Morse
function f on a manifold M to the topology of M. The main technical
ingredient of this theory is a chain complex generated by the critical points
of the function. In 1981 S.P. Novikov generalized this theory to the case of
circle-valued Morse functions. In this talk we describe the construction of
both chain complexes, based on the idea of E. Witten (1982), which allows, in
particular, to compute the boundary operators in the Morse complex from
the count of flow lines of the gradient of f. We discuss geometric applications
of these constructions.
2013年05月30日(木)
13:00-14:30 数理科学研究科棟(駒場) 122号室
Mustafa Korkmaz 氏 (Middle East Technical University)
Low-dimensional linear representations of mapping class groups (III) (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf
Mustafa Korkmaz 氏 (Middle East Technical University)
Low-dimensional linear representations of mapping class groups (III) (ENGLISH)
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf
