## Lectures

Seminar information archive ～10/10｜Next seminar｜Future seminars 10/11～

**Seminar information archive**

### 2007/10/17

16:00-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

The method of compensated compactness for

microscopic systems

**J. Fritz**(TU Budapest)The method of compensated compactness for

microscopic systems

### 2007/06/20

15:00-16:00 Room #470 (Graduate School of Math. Sci. Bldg.)

On evolution games with local interaction and mutation

**Y.S. Chow**(台湾中央研究院数学研究所)On evolution games with local interaction and mutation

### 2007/04/16

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

Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators

**Francois Hamel**(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

[ Abstract ]

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.

### 2007/04/10

15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Applications of the Generalised Pauli Group in Quantum Information

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf

**Thomas DURT**(ブリユッセル自由大学・VUB)Applications of the Generalised Pauli Group in Quantum Information

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf

### 2007/03/09

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Nonsmooth Optimization and Applications in PDEs

**Kazufumi Ito**(North Carolina State University)Nonsmooth Optimization and Applications in PDEs

[ Abstract ]

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.

### 2007/03/08

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

Nonsmooth Optimization and Applications in PDEs

**Kazufumi Ito**(North Carolina State University)Nonsmooth Optimization and Applications in PDEs

[ Abstract ]

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.

### 2007/02/22

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The level set method, multivalued solutions and image science

**Stan Osher**(UCLA)The level set method, multivalued solutions and image science

[ Abstract ]

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.

### 2007/02/22

13:00-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Optimal control of semilinear parabolic equations and an application to laser material treatments

**Dietmar Hoemberg**(Berlin Technical University)Optimal control of semilinear parabolic equations and an application to laser material treatments

[ Abstract ]

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.

### 2007/02/21

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The level set method, multivalued solutions and image science

**Stan Osher**(UCLA)The level set method, multivalued solutions and image science

[ Abstract ]

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.

### 2007/02/21

13:30-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Optimal control of semilinear parabolic equations and an application to laser material treatments

**Dietmar Hoemberg**(Berlin Technical University)Optimal control of semilinear parabolic equations and an application to laser material treatments

[ Abstract ]

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.

### 2007/02/20

10:30-17:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Exit distributions for random walks in random environments

Quasi one-dimensional random walks in random environments

Large deviation principle for currents generated by stochasticline integrals

on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)

Interacting Brownian motions related to Ginibre random point field

**Erwin Bolthausen**(University of Zurich) 10:30-12:00Exit distributions for random walks in random environments

**Erwin Bolthausen**(University of Zurich) 14:00-15:30Quasi one-dimensional random walks in random environments

**田村要造**(慶応大理工) 15:50-16:30Large deviation principle for currents generated by stochasticline integrals

on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)

**長田博文**(九大数理) 16:40-17:20Interacting Brownian motions related to Ginibre random point field

### 2007/02/01

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On Calderon's inverse conductivity problem in the plane.

**Lassi Paivarinta**(Helsinki University of Technology, Finland)On Calderon's inverse conductivity problem in the plane.

### 2007/02/01

16:15-17:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Finland)

Locating transparent cavities in optical absorption and scattering

tomography

**Nuuti Huyvonen**(Helsinki University of Technology,Finland)

Locating transparent cavities in optical absorption and scattering

tomography

### 2007/01/31

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

Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

**Li Daqian**(復旦大学)Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

### 2007/01/30

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Universit\'e de Provence / CNRS)

Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates

**Jerome Le Rousseau**(Laboratoire d'Analyse Topologie Probabilit\'esUniversit\'e de Provence / CNRS)

Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates

[ Abstract ]

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).

### 2007/01/29

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

Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

**Li Daqian**(復旦大学)Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

### 2007/01/26

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

Controllability and Observability:

from ODEs to Quasilinear Hyperbolic Systems

**Li Daqian**(復旦大学)Controllability and Observability:

from ODEs to Quasilinear Hyperbolic Systems

### 2007/01/19

10:30-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)

3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

**Alex Mahalov**(Arizona State University)3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

### 2007/01/18

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

**Alex Mahalov**(Arizona State University)3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

[ Abstract ]

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.

### 2007/01/17

15:30-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Hamilton-Jacobi方程式の漸近解とその周辺の話題

**市原直幸 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

### 2007/01/17

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Recovering a potential in the wave equation via Dirichlet-to-Neumann map.

**Mourad Bellassoued**(Faculte des Sciences de Bizerte)Recovering a potential in the wave equation via Dirichlet-to-Neumann map.

### 2007/01/16

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Recovering a potential from partial Cauchy data for the Schrödinger equation.

**Mourad Bellassoued**(Faculte des Sciences de Bizerte)Recovering a potential from partial Cauchy data for the Schrödinger equation.

### 2007/01/15

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Recovering a potential from full Cauchy data for the Schrödinger equation.

**Mourad Bellassoued**(Faculte des Sciences de Bizerte)Recovering a potential from full Cauchy data for the Schrödinger equation.

[ Abstract ]

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.

### 2007/01/15

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Analysis of physical systems involving multiple spatial scales: some case studies

**Antonio DeSimone**(SISSA (International School for Advanced Studies))Analysis of physical systems involving multiple spatial scales: some case studies

[ Abstract ]

Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.

We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.

Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.

The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.

Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.

We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.

Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.

The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.

### 2007/01/11

16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.

**Oleg Yu. Emanouilov**(Colorado State University)Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.