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講演会
過去の記録 ～05/01｜次回の予定｜今後の予定 05/02～
過去の記録
2007年11月22日(木)
10:40-12:10 数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007年11月13日(火)
16:00-17:30 数理科学研究科棟(駒場) 052号室
Jens Starke 氏 (Technical University of Denmark)
Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb
Jens Starke 氏 (Technical University of Denmark)
Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb
[ 講演概要 ]
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.
(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.
(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.
(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.
This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.
(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.
(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.
(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.
This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.
2007年10月17日(水)
16:00-17:00 数理科学研究科棟(駒場) 470号室
J. Fritz 氏 (TU Budapest)
The method of compensated compactness for
microscopic systems
J. Fritz 氏 (TU Budapest)
The method of compensated compactness for
microscopic systems
2007年06月20日(水)
15:00-16:00 数理科学研究科棟(駒場) 470号室
Y.S. Chow 氏 (台湾中央研究院数学研究所)
On evolution games with local interaction and mutation
Y.S. Chow 氏 (台湾中央研究院数学研究所)
On evolution games with local interaction and mutation
2007年04月16日(月)
16:30-17:30 数理科学研究科棟(駒場) 056号室
Francois Hamel 氏 (エクス・マルセーユ第3大学 (Universite Aix-Marseille III))
Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators
Francois Hamel 氏 (エクス・マルセーユ第3大学 (Universite Aix-Marseille III))
Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators
[ 講演概要 ]
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.
The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.
The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
2007年04月10日(火)
15:00-16:00 数理科学研究科棟(駒場) 370号室
Thomas DURT 氏 (ブリユッセル自由大学・VUB)
Applications of the Generalised Pauli Group in Quantum Information
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf
Thomas DURT 氏 (ブリユッセル自由大学・VUB)
Applications of the Generalised Pauli Group in Quantum Information
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf
2007年03月09日(金)
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
魅力ある大学院教育イニシアティブ特別講演会
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007年03月08日(木)
15:30-17:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
魅力ある大学院教育イニシアティブ特別講演
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007年02月22日(木)
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
2007年02月22日(木)
13:00-15:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007年02月21日(水)
10:30-12:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
魅力ある大学院教育イニシアティブ特別講演会
※Osher先生の講演は中止になりました。
Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
2007年02月21日(水)
13:30-15:00 数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007年02月20日(火)
10:30-17:20 数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen 氏 (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments
田村要造 氏 (慶応大理工) 15:50-16:30
Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)
長田博文 氏 (九大数理) 16:40-17:20
Interacting Brownian motions related to Ginibre random point field
Erwin Bolthausen 氏 (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen 氏 (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments
田村要造 氏 (慶応大理工) 15:50-16:30
Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)
長田博文 氏 (九大数理) 16:40-17:20
Interacting Brownian motions related to Ginibre random point field
2007年02月01日(木)
15:00-16:00 数理科学研究科棟(駒場) 118号室
連絡先:山本昌宏
Lassi Paivarinta 氏 (Helsinki University of Technology, Finland)
On Calderon's inverse conductivity problem in the plane.
連絡先:山本昌宏
Lassi Paivarinta 氏 (Helsinki University of Technology, Finland)
On Calderon's inverse conductivity problem in the plane.
2007年02月01日(木)
16:15-17:15 数理科学研究科棟(駒場) 118号室
連絡先:山本昌宏
Nuuti Huyvonen 氏 (Helsinki University of Technology,
Finland)
Locating transparent cavities in optical absorption and scattering
tomography
連絡先:山本昌宏
Nuuti Huyvonen 氏 (Helsinki University of Technology,
Finland)
Locating transparent cavities in optical absorption and scattering
tomography
2007年01月31日(水)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
2007年01月30日(火)
16:30-18:00 数理科学研究科棟(駒場) 118号室
連絡先:山本昌宏
Jerome Le Rousseau 氏 (Laboratoire d'Analyse Topologie Probabilit\'es
Universit\'e de Provence / CNRS)
Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates
連絡先:山本昌宏
Jerome Le Rousseau 氏 (Laboratoire d'Analyse Topologie Probabilit\'es
Universit\'e de Provence / CNRS)
Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates
[ 講演概要 ]
We shall review the different concepts of controllability for parabolic equations and a fix-point method to achieve null-controllability of classes of semilinear equations. It is mainly based on observability inequalities and a precise knowledge of the observability constant. These inequalities are obtained by means of global Carleman estimates. We shall review their derivations and how they can be obtained in the case of non-smooth coefficients. We shall also present some open questions.
Part of this work is in collaboration with Assia Benabdallah and Yves Dermenjian (also from Universit\\'e de Provence).
We shall review the different concepts of controllability for parabolic equations and a fix-point method to achieve null-controllability of classes of semilinear equations. It is mainly based on observability inequalities and a precise knowledge of the observability constant. These inequalities are obtained by means of global Carleman estimates. We shall review their derivations and how they can be obtained in the case of non-smooth coefficients. We shall also present some open questions.
Part of this work is in collaboration with Assia Benabdallah and Yves Dermenjian (also from Universit\\'e de Provence).
2007年01月29日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
2007年01月26日(金)
16:30-18:00 数理科学研究科棟(駒場) 126号室
「魅力ある大学院教育」イニシアティブにより以下の3回の講演を行います。
1月26日(金),1月29日(月),31日(水)
連絡先:俣野博、山本昌宏
Li Daqian 氏 (復旦大学)
Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems
「魅力ある大学院教育」イニシアティブにより以下の3回の講演を行います。
1月26日(金),1月29日(月),31日(水)
連絡先:俣野博、山本昌宏
Li Daqian 氏 (復旦大学)
Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems
2007年01月19日(金)
10:30-12:00 数理科学研究科棟(駒場) 056号室
Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
2007年01月18日(木)
13:00-14:30 数理科学研究科棟(駒場) 056号室
連続講演 1月18日, 19日
連絡先: 儀我美一
Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
連続講演 1月18日, 19日
連絡先: 儀我美一
Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
[ 講演概要 ]
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold. The global existence is proven using techniques of fast singular oscillating limits, Lemmas on restricted convolutions and the Littlewood-Paley dyadic decomposition. In the second part of the talk, we analyze regularity and dynamics of the 3D Euler equations in cylindrical domains with weakly aligned large initial vorticity.
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold. The global existence is proven using techniques of fast singular oscillating limits, Lemmas on restricted convolutions and the Littlewood-Paley dyadic decomposition. In the second part of the talk, we analyze regularity and dynamics of the 3D Euler equations in cylindrical domains with weakly aligned large initial vorticity.
2007年01月17日(水)
15:30-17:00 数理科学研究科棟(駒場) 470号室
確率論特別セミナー
担当 舟木直久
市原直幸 氏 氏 (大阪大学基礎工学研究科)
Hamilton-Jacobi方程式の漸近解とその周辺の話題
確率論特別セミナー
担当 舟木直久
市原直幸 氏 氏 (大阪大学基礎工学研究科)
Hamilton-Jacobi方程式の漸近解とその周辺の話題
2007年01月17日(水)
16:30-18:00 数理科学研究科棟(駒場) 122号室
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential in the wave equation via Dirichlet-to-Neumann map.
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential in the wave equation via Dirichlet-to-Neumann map.
2007年01月16日(火)
16:30-18:00 数理科学研究科棟(駒場) 122号室
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from partial Cauchy data for the Schrödinger equation.
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from partial Cauchy data for the Schrödinger equation.
2007年01月15日(月)
16:30-18:00 数理科学研究科棟(駒場) 122号室
連続講演1月15日(月),16日(火)、17日(水)
「魅力ある大学院教育」イニシアティブにより以下の講演を行います。
担当 山本昌宏
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from full Cauchy data for the Schrödinger equation.
連続講演1月15日(月),16日(火)、17日(水)
「魅力ある大学院教育」イニシアティブにより以下の講演を行います。
担当 山本昌宏
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from full Cauchy data for the Schrödinger equation.
[ 講演概要 ]
In this lectures we survey recent progress on the problem of determining a potential by measuring the Dirichlet to Neumann map
for the associated Schr\\"odinger equation or wave equation. We make emphasis on the new results obtained with M.Yamamoto which is concerned with the case that the measurements are made on a strict
subset of the boundary for the wave equation.
In this lectures we survey recent progress on the problem of determining a potential by measuring the Dirichlet to Neumann map
for the associated Schr\\"odinger equation or wave equation. We make emphasis on the new results obtained with M.Yamamoto which is concerned with the case that the measurements are made on a strict
subset of the boundary for the wave equation.
