## Seminar information archive

Seminar information archive ～09/14｜Today's seminar 09/15 | Future seminars 09/16～

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Homoclinic and heteroclinic orbits for a semilinear parabolic equation (ENGLISH)

**Marek FILA**(Comenius University (Slovakia))Homoclinic and heteroclinic orbits for a semilinear parabolic equation (ENGLISH)

[ Abstract ]

We study the existence of connecting orbits for the Fujita equation

u_t=\\Delta u+u^p

with a critical or supercritical exponent $p$. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and the existence of a homoclinic orbit with respect to zero. This is a joint work with Eiji Yanagida.

We study the existence of connecting orbits for the Fujita equation

u_t=\\Delta u+u^p

with a critical or supercritical exponent $p$. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and the existence of a homoclinic orbit with respect to zero. This is a joint work with Eiji Yanagida.

### 2011/04/13

#### Functional Analysis Seminar

15:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Spectral theory for functions of self-adjoint operators (ENGLISH)

**Alexander Pushnitski**(King's College, London)Spectral theory for functions of self-adjoint operators (ENGLISH)

[ Abstract ]

Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.

### 2011/04/12

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On diffeomorphisms over non-orientable surfaces embedded in the 4-sphere (JAPANESE)

**Susumu Hirose**(Tokyo University of Science)On diffeomorphisms over non-orientable surfaces embedded in the 4-sphere (JAPANESE)

[ Abstract ]

For a closed orientable surface standardly embedded in the 4-sphere,

it was known that a diffeomorphism over this surface is extendable to

the 4-sphere if and only if this diffeomorphism preserves

the Rokhlin quadratic form of this surafce.

In this talk, we will explain an approach to the same kind of problem for

closed non-orientable surfaces.

For a closed orientable surface standardly embedded in the 4-sphere,

it was known that a diffeomorphism over this surface is extendable to

the 4-sphere if and only if this diffeomorphism preserves

the Rokhlin quadratic form of this surafce.

In this talk, we will explain an approach to the same kind of problem for

closed non-orientable surfaces.

### 2011/04/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Algebraic analysis of resolvents and an exact algorithm for computing Spectral decomposition matrices (JAPANESE)

**Shinichi Tajima**(University of Tsukuba)Algebraic analysis of resolvents and an exact algorithm for computing Spectral decomposition matrices (JAPANESE)

### 2011/03/31

#### Lectures

13:00-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Dynamical localization for unitary Anderson models (JAPANESE)

**Alain Joye**(Univ. Grenoble)Dynamical localization for unitary Anderson models (JAPANESE)

#### Lectures

14:30-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Stable limits for biased random walks on random trees (JAPANESE)

**Gerard Ben Arous**(Courant Institute, New York Univ.)Stable limits for biased random walks on random trees (JAPANESE)

[ Abstract ]

It is well know that transport in random media can be hampered by dead-end regions and that the velocity can even vanish for strong drifts. We study this phenomenon in great detail for random trees. That is, we study the behavior of biased random walks on supercritical random trees with leaves, in the sub-ballistic regime. When the drift is strong enough it is well known that trapping in the dead-ends of the tree, causes the velocity to vanish. We study the behavior of the walk in this regime, and in particular find the exponents for the mean displacement and the time to reach a given large distance. We also establish a scaling limit result in the case where the drift are random and a non-lattice condition is satisfied. (Joint work with Alexander Fribergh, Alan Hammond, Nina Gantert)

It is well know that transport in random media can be hampered by dead-end regions and that the velocity can even vanish for strong drifts. We study this phenomenon in great detail for random trees. That is, we study the behavior of biased random walks on supercritical random trees with leaves, in the sub-ballistic regime. When the drift is strong enough it is well known that trapping in the dead-ends of the tree, causes the velocity to vanish. We study the behavior of the walk in this regime, and in particular find the exponents for the mean displacement and the time to reach a given large distance. We also establish a scaling limit result in the case where the drift are random and a non-lattice condition is satisfied. (Joint work with Alexander Fribergh, Alan Hammond, Nina Gantert)

### 2011/03/22

#### Lectures

14:00-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Potts models and Bethe states on sparse random graphs (JAPANESE)

**Amir Dembo**(Stanford Univ.)Potts models and Bethe states on sparse random graphs (JAPANESE)

[ Abstract ]

Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying mathematical structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on ferromagnetic Potts measures on random finite graphs that converge locally to trees we validate the `cavity' prediction for the limiting free energy per spin and show that local marginals are approximated well by the belief propagation algorithm. This is a concrete example of the more general approximation by Bethe measures, namely, the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on an appropriate infinite random tree (this talk is based on a joint work with Andrea Montanari and Nike Sun).

Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying mathematical structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on ferromagnetic Potts measures on random finite graphs that converge locally to trees we validate the `cavity' prediction for the limiting free energy per spin and show that local marginals are approximated well by the belief propagation algorithm. This is a concrete example of the more general approximation by Bethe measures, namely, the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on an appropriate infinite random tree (this talk is based on a joint work with Andrea Montanari and Nike Sun).

### 2011/03/08

#### GCOE Seminars

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Diagonal singularities of the scattering matrix and the inverse problem at a fixed energy (ENGLISH)

**Dimitri Yafaev**(Univ. Rennes 1)Diagonal singularities of the scattering matrix and the inverse problem at a fixed energy (ENGLISH)

### 2011/03/04

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets (ENGLISH)

[ Abstract ]

We discuss the inverse boundary value problem of determining the conductivity in two dimensions from the pair of all input Dirichlet data supported on an open subset S1 and all the corresponding Neumann data measured on an open subset S2.

We prove the global uniqueness under some additional geometric condition, in the case where the intersection of S_1 and S_2 has no interior points, and we prove also the uniqueness for a similar inverse problem for the stationary Schr"odinger equation.

The key of the proof isthe construction of appropriate complex geometrical optics solutions using Carleman estimates with a singular weight.

We discuss the inverse boundary value problem of determining the conductivity in two dimensions from the pair of all input Dirichlet data supported on an open subset S1 and all the corresponding Neumann data measured on an open subset S2.

We prove the global uniqueness under some additional geometric condition, in the case where the intersection of S_1 and S_2 has no interior points, and we prove also the uniqueness for a similar inverse problem for the stationary Schr"odinger equation.

The key of the proof isthe construction of appropriate complex geometrical optics solutions using Carleman estimates with a singular weight.

### 2011/03/03

#### Lectures

13:30-14:30 Room #270 (Graduate School of Math. Sci. Bldg.)

Energy Diffusion: hydrodynamic, weak coupling, kinetic limits (ENGLISH)

**Stefano Olla**(Univ. Paris Dauphine)Energy Diffusion: hydrodynamic, weak coupling, kinetic limits (ENGLISH)

[ Abstract ]

I will review recent results about weak coupling and kinetic limits for the energy diffusive evolution in hamiltonian systems perturbed by energy-conservating noise. Two universality classes of diffusion are obtained: Ginzburg-Landau dynamics that arise from weak coupling limit of anharmonic oscillators, and exclusion type processes that arise from kinetic limit (rarefied collisions) of interacting billiards. Works in collaboration with Carlangelo Liverani (weak coupling) and Francois Huveneers (kinetic limits).

I will review recent results about weak coupling and kinetic limits for the energy diffusive evolution in hamiltonian systems perturbed by energy-conservating noise. Two universality classes of diffusion are obtained: Ginzburg-Landau dynamics that arise from weak coupling limit of anharmonic oscillators, and exclusion type processes that arise from kinetic limit (rarefied collisions) of interacting billiards. Works in collaboration with Carlangelo Liverani (weak coupling) and Francois Huveneers (kinetic limits).

#### Lectures

14:45-15:45 Room #270 (Graduate School of Math. Sci. Bldg.)

Singularity and absolute continuity of Palm measures of Ginibre random fields

(ENGLISH)

**Hirofumi Osada**(Kyushu Univ.)Singularity and absolute continuity of Palm measures of Ginibre random fields

(ENGLISH)

[ Abstract ]

The Ginibre random point field is a probability measure on the configuration space over the complex plane $\\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\\beta = 2 $. This fact is justified by the integration by parts formula.

Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \\in \\mathbb{C}$ are mutually absolutely continuous.

The Ginibre random point field is a probability measure on the configuration space over the complex plane $\\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\\beta = 2 $. This fact is justified by the integration by parts formula.

Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \\in \\mathbb{C}$ are mutually absolutely continuous.

#### Lectures

16:00-16:30 Room #270 (Graduate School of Math. Sci. Bldg.)

A proof of the Brascamp-Lieb inequality based on Skorokhod embedding (ENGLISH)

**Yuu Hariya**(Tohoku Univ.)A proof of the Brascamp-Lieb inequality based on Skorokhod embedding (ENGLISH)

[ Abstract ]

In this talk, we provide a probabilistic approach to the Brascamp-Lieb inequality based on Skorokhod embedding. An extension of the inequality to non-convex potentials will also be discussed.

In this talk, we provide a probabilistic approach to the Brascamp-Lieb inequality based on Skorokhod embedding. An extension of the inequality to non-convex potentials will also be discussed.

### 2011/02/28

#### Lectures

17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Extremum Seeking Control: history and recent developments (ENGLISH)

**Ying Tan**(The University of Melbourne)Extremum Seeking Control: history and recent developments (ENGLISH)

[ Abstract ]

A control system which is to determine and maintain the extremum value of a function is called extremum seeking control. The first extremum seeking control application appeared in 1922, in which the extremum seeking control was applied to electric railways. The first rigorous local stability analysis for an ESC scheme was recently proved in 2000 and later extended to semi-global stability analysis 2006.. This has spurred a renewed interest in this research area, leading to numerous practical implementations of the scheme. This talk will first revisit the history of extremum seeking control. It is followed by an explanation how the extremum seeking works. Finally, it will focus on the latest unifying framework that combines arbitrary continuous optimization algorithms with an estimator for derivatives of the unknown reference-to-output steady state map that contains an extremum.

A control system which is to determine and maintain the extremum value of a function is called extremum seeking control. The first extremum seeking control application appeared in 1922, in which the extremum seeking control was applied to electric railways. The first rigorous local stability analysis for an ESC scheme was recently proved in 2000 and later extended to semi-global stability analysis 2006.. This has spurred a renewed interest in this research area, leading to numerous practical implementations of the scheme. This talk will first revisit the history of extremum seeking control. It is followed by an explanation how the extremum seeking works. Finally, it will focus on the latest unifying framework that combines arbitrary continuous optimization algorithms with an estimator for derivatives of the unknown reference-to-output steady state map that contains an extremum.

### 2011/02/24

#### Applied Analysis

16:00-18:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections (ENGLISH)

Some open problems in PDE control (ENGLISH)

**Arnaud Ducrot**(University of Bordeaux 2) 16:00-17:00Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections (ENGLISH)

[ Abstract ]

This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.

This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.

**Enrique Zuazua**(Basque Center for Applied Mathematics) 17:10-18:10Some open problems in PDE control (ENGLISH)

[ Abstract ]

The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.

From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location

of the controller, nonlinearity in the equation,...)

In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:

1.- Semilinear wave equations and their control properties.

2.- Microlocal optimal design of wave processes

3.- Sharp observability estimates for heat processes.

4.- Robustness on the control of finite-dimensional systems.

5.- Unique continuation for discrete elliptic models

6.- Control of Kolmogorov equations and other hypoelliptic models.

The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.

From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location

of the controller, nonlinearity in the equation,...)

In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:

1.- Semilinear wave equations and their control properties.

2.- Microlocal optimal design of wave processes

3.- Sharp observability estimates for heat processes.

4.- Robustness on the control of finite-dimensional systems.

5.- Unique continuation for discrete elliptic models

6.- Control of Kolmogorov equations and other hypoelliptic models.

### 2011/02/23

#### Functional Analysis Seminar

14:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)

Uniform localization (ENGLISH)

Global solutions to the eikonal equation (ENGLISH)

Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

**Dimitri Yafaev**(Univ. Rennes 1) 14:00-14:45The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)

**David Damanik**(Rice University) 15:00-15:45Uniform localization (ENGLISH)

**Erik Skibsted**(Aarhus University) 16:15-17:00Global solutions to the eikonal equation (ENGLISH)

**Christian Gerard**(Univ. Paris Sud 11) 17:15-18:00Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

### 2011/02/18

#### Operator Algebra Seminars

10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Dirac families and 1-cocycles (ENGLISH)

**Pedram Hekmati**(Univ. Adelaide)Dirac families and 1-cocycles (ENGLISH)

[ Abstract ]

Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.

Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.

#### Classical Analysis

11:00-15:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)

Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)

(ENGLISH)

Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)

(ENGLISH)

**T. Morita**(Osaka University) 11:00-12:00Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)

**M. Yamaguchi**(University of Tokyo) 13:30-14:30Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)

(ENGLISH)

**L. Di Vizio**(Universite Paris 7) 14:45-15:45Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)

(ENGLISH)

#### Classical Analysis

10:15-10:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

**Y. Ohyama**(Osaka University)Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

### 2011/02/17

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)

**Thomas Giletti**(University of Paul Cezanne (Marseilles))Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)

[ Abstract ]

This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.

This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.

#### Classical Analysis

11:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Overview of local theory of $q$-difference equations and summation, 1

(ENGLISH)

Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)

Blow-up of solutions for a nonlinear difference equation (ENGLISH)

Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

**L. Di Vizio**(Universite Paris 7) 11:00-12:00Overview of local theory of $q$-difference equations and summation, 1

(ENGLISH)

**Y. Katsushima**(University of Tokyo) 13:30-14:30Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)

**K. Matsuya**(University of Tokyo) 14:45-15:45Blow-up of solutions for a nonlinear difference equation (ENGLISH)

**L. Di Vizio**(Universite Paris 7) 16:00-17:00Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

### 2011/02/16

#### Classical Analysis

13:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)

Degeneration scheme of 4-dimensional Painlev¥'e type equations

(Joint work with H. Sakai and A. Nakamura)

(ENGLISH)

Solvability of difference Riccati equations (ENGLISH)

**H. Sakai**(University of Tokyo) 13:30-14:30Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)

**H. Kawakami**(University of Tokyo) 14:45-15:45Degeneration scheme of 4-dimensional Painlev¥'e type equations

(Joint work with H. Sakai and A. Nakamura)

(ENGLISH)

**S. Nishioka**(University of Tokyo) 16:00-17:00Solvability of difference Riccati equations (ENGLISH)

### 2011/02/14

#### GCOE Seminars

13:00-14:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)

**Jin Cheng**(Fudan University)Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)

[ Abstract ]

The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

### 2011/02/10

#### Operator Algebra Seminars

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

Symplectic and quantum categories (ENGLISH)

**Alan Weinstein**(UC Berkeley)Symplectic and quantum categories (ENGLISH)

#### Applied Analysis

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Control and nonlinearity (ENGLISH)

**Jean-Michel Coron**(University of Paris 6)Control and nonlinearity (ENGLISH)

[ Abstract ]

We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.

We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).

We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.

We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).

#### Number Theory Seminar

11:00-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The motivic Galois group and periods of algebraic varieties (ENGLISH)

**Joseph Ayoub**(University of Zurich)The motivic Galois group and periods of algebraic varieties (ENGLISH)

[ Abstract ]

We give a construction of the motivic Galois group of $\\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.

We give a construction of the motivic Galois group of $\\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.

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