## Lectures

Seminar information archive ～12/01｜Next seminar｜Future seminars 12/02～

**Seminar information archive**

### 2012/06/13

17:00-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

A KPZ equation for zero-range interactions (ENGLISH)

**Sunder Sethuraman**(University of Arizona)A KPZ equation for zero-range interactions (ENGLISH)

[ Abstract ]

We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

We derive a type of KPZ equation, in terms of a martingale problem, as a scaling limit of fluctuation fields in weakly asymmetric zero-range processes. Joint work (in progress) with Milton Jara and Patricia Goncalves.

### 2012/06/13

11:00-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

**S. Harase, et. al.**(Tokyo Institute of Technology/JSPS)Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

### 2012/06/12

09:50-17:10 Room #118 (Graduate School of Math. Sci. Bldg.)

Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

**Josef Dick, et. al.**(Univ. New South Wales)Workshop for Quasi-Monte Carlo and Pseudo Random Number Generation (ENGLISH)

[ Reference URL ]

http://sites.google.com/a/craft.titech.ac.jp/workshop-on-qmc-and-prng-2012-utms/

### 2012/05/30

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (III) (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/29

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (II) (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/28

14:50-16:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

**Harald Niederreiter**(RICAM, Austrian Academy of Sciences)Low-discrepancy sequences and algebraic curves over finite fields (I) (ENGLISH)

[ Abstract ]

This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:

Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo

methods in computational mathematics. QMC methods employ evenly distributed

low-discrepancy sequences instead of the random samples used in Monte Carlo methods.

For many types of computational problems, QMC methods are more efficient than

Monte Carlo methods. After a general introduction to QMC methods, the talk focuses

on the problem of constructing low-discrepancy sequences which has fascinating links

with subjects such as finite fields, error-correcting codes, and algebraic curves.

[ Reference URL ]This is the second of the four lectures. The first one is Colloquium talk on May 25th 16:30--17:30 at 002.

Abstract from Colloquium:

Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo

methods in computational mathematics. QMC methods employ evenly distributed

low-discrepancy sequences instead of the random samples used in Monte Carlo methods.

For many types of computational problems, QMC methods are more efficient than

Monte Carlo methods. After a general introduction to QMC methods, the talk focuses

on the problem of constructing low-discrepancy sequences which has fascinating links

with subjects such as finite fields, error-correcting codes, and algebraic curves.

https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html

### 2012/05/08

14:40-16:10 Room #470 (Graduate School of Math. Sci. Bldg.)

Embedding spaces and string topology (JAPANESE)

**Keiichi Sakai**(Shishu University)Embedding spaces and string topology (JAPANESE)

[ Abstract ]

There are several similarities between the topology of embedding spaces and that of (free) loop space.

In this talk I will review the similarities, with a focus on "string topology" for embedding spaces.

There are several similarities between the topology of embedding spaces and that of (free) loop space.

In this talk I will review the similarities, with a focus on "string topology" for embedding spaces.

### 2012/03/23

10:30-11:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)

**R. Penner**(Aarhus/Caltech)Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)

[ Abstract ]

A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.

A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.

### 2012/03/21

10:15-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Geochemical structure of biological macromolecules (ENGLISH)

**R. Penner**(Aarhus/Caltech)Geochemical structure of biological macromolecules (ENGLISH)

[ Abstract ]

This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.

This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.

### 2012/03/21

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

Moduli space techniques in computational biology

(ENGLISH)

**R. Penner**(Aarhus/Caltech)Moduli space techniques in computational biology

(ENGLISH)

[ Abstract ]

Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of

3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.

Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of

3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.

### 2011/12/09

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

### 2011/12/09

10:40-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An iterative construction of solutions of the TAP equation (ENGLISH)

**Erwin Bolthausen**(University of Zurich)An iterative construction of solutions of the TAP equation (ENGLISH)

[ Abstract ]

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.

### 2011/12/07

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

"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

"Hautus test for the approximate controllability of linear systems" (ENGLISH)

**Michel Cristofol**(マルセイユ大学) 16:00-17:00"Inverse problems associated with linear and non-linear parabolic systems " (ENGLISH)

[ Abstract ]

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.

**Guillaume Olive**(マルセイユ大学) 17:00-18:00"Hautus test for the approximate controllability of linear systems" (ENGLISH)

[ Abstract ]

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.

### 2011/12/01

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

### 2011/11/29

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

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

### 2011/11/24

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Stability of topological phases of matter (ENGLISH)

**Spyridon Michalakis**(Caltech)Stability of topological phases of matter (ENGLISH)

### 2011/11/18

15:00-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)

Inverse problems for heat equations with discontinuous conductivities

(JAPANESE)

**Hiroshi Isozaki**(University of Tsukuba)Inverse problems for heat equations with discontinuous conductivities

(JAPANESE)

[ Abstract ]

In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat

equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat

conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on

$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on

$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results

for the inverse problems of reconstructing $\\gamma(t,x)$ from the

Dirichlet-to-Neumann map :

$u(t)|_{\\partial\\Omega} \\to $\\partial_{\\nu}u|_{\\partial\\Omega}$ for a time

interval $(0,T)$. These are the joint works with P.Gaitan, O.Poisson,

S.Siltanen, J.Tamminen.

In a bounded domain $\\Omega \\subset {\\bf R}^n$, consider the heat

equation $\\partial_tu = \\nabla(\\gamma(t,x)\\nabla u)$. The heat

conductivity is assumed to be piecewise constant : $\\gamma = k^2$ on

$\\Omaga_1(t) \\subset\\subset \\Omega$, $\\gamma(t,x) = 1$ on

$\\Omega\\setminus\\Omega_1(t)$. In this talk, we present recent results

for the inverse problems of reconstructing $\\gamma(t,x)$ from the

Dirichlet-to-Neumann map :

$u(t)|_{\\partial\\Omega} \\to $\\partial_{\\nu}u|_{\\partial\\Omega}$ for a time

interval $(0,T)$. These are the joint works with P.Gaitan, O.Poisson,

S.Siltanen, J.Tamminen.

### 2011/06/13

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

Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)

**CHEN Hua**(Wuhan University)Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)

[ Abstract ]

In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including

(1) generalized Kolmogorov equations,

(2) Fokker-Planck equations,

(3) Landau equations and

(4) sub-elliptic Monge-Ampere equations.

In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including

(1) generalized Kolmogorov equations,

(2) Fokker-Planck equations,

(3) Landau equations and

(4) sub-elliptic Monge-Ampere equations.

### 2011/03/31

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)

### 2011/03/31

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

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).

### 2011/03/03

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).

### 2011/03/03

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.

### 2011/03/03

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

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.