## Lectures

Seminar information archive ～07/21｜Next seminar｜Future seminars 07/22～

**Seminar information archive**

### 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.

### 2011/02/02

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

Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

**Yong Jung Kim**(Korea Advanced Institute of Science and Technology (KAIST))Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

[ Abstract ]

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

### 2011/02/02

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

Regularity of two dimensional capillary gravity water waves (ENGLISH)

**Guanghui ZHANG**(Graduate School of Mathematical Sciences, the University of Tokyo)Regularity of two dimensional capillary gravity water waves (ENGLISH)

[ Abstract ]

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

### 2010/12/16

13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Credit Derivatives Modelling and the concept of Background Intensity I (ENGLISH)

**Sebastien Hitier**(BNP Paribas, Head of Quantitative Research, Credit Asia)Credit Derivatives Modelling and the concept of Background Intensity I (ENGLISH)

[ Abstract ]

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

### 2010/12/16

14:40-16:10 Room #123 (Graduate School of Math. Sci. Bldg.)

Credit Derivatives Modelling and the concept of Background Intensity II (ENGLISH)

**Sebastien Hitier**(BNP Paribas, Head of Quantitative Research, Credit Asia)Credit Derivatives Modelling and the concept of Background Intensity II (ENGLISH)

[ Abstract ]

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

### 2010/11/04

10:40-12:10 Room #123 (Graduate School of Math. Sci. Bldg.)

Market, Liquidity and Counterparty Risk (ENGLISH)

**Jean Meyer, Yasuko HISAMATSU**(Risk Capital Market Tokyo, BNP Paribas)Market, Liquidity and Counterparty Risk (ENGLISH)

[ Abstract ]

1. Introduction to the market risk

- Introduction to the Risk Management

in the Financial institutions

- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks

-Focus on volatility risk

-Focus on correlation risk

-Conclusion (common features of the market risks)

3. Risk measure

- Stress test

- Value at risk

- Risks measure for counterparty risk

1. Introduction to the market risk

- Introduction to the Risk Management

in the Financial institutions

- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks

-Focus on volatility risk

-Focus on correlation risk

-Conclusion (common features of the market risks)

3. Risk measure

- Stress test

- Value at risk

- Risks measure for counterparty risk

### 2010/11/02

13:00-16:10 Room #122 (Graduate School of Math. Sci. Bldg.)

The Malliavin calculus on configuration spaces and applications (ENGLISH)

**Vladimir Bogachev**(Moscow)The Malliavin calculus on configuration spaces and applications (ENGLISH)

[ Abstract ]

It is planned to discuss first a general scheme of the Malliavin

calculus on an abstract measurable

manifold with minimal assumptions about the manifold.

Then a practical realization of this scheme will be discussed in

several concrete examples with emphasis

on configuration spaces, i.e., spaces of locally finite configurations

in a given manifold (for example, just

a finite-dimensional Euclidean space), which can be alternatively

described as the spaces of integer-valued

discrete measures equipped with suitable differential structures.

No acquaintance with the Malliavin calculus and differential geometry

is assumed.

It is planned to discuss first a general scheme of the Malliavin

calculus on an abstract measurable

manifold with minimal assumptions about the manifold.

Then a practical realization of this scheme will be discussed in

several concrete examples with emphasis

on configuration spaces, i.e., spaces of locally finite configurations

in a given manifold (for example, just

a finite-dimensional Euclidean space), which can be alternatively

described as the spaces of integer-valued

discrete measures equipped with suitable differential structures.

No acquaintance with the Malliavin calculus and differential geometry

is assumed.

### 2010/11/01

16:00-18:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Inverse problems in non linear parabolic equations : Two differents approaches (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/abstractTokyo.pdf

Inverse Problems for parabolic System

(ENGLISH)

**Michel Cristofol**(マルセイユ大学) 16:00-17:00Inverse problems in non linear parabolic equations : Two differents approaches (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/abstractTokyo.pdf

**Patricia Gaitan**(マルセイユ大学) 17:15-18:15Inverse Problems for parabolic System

(ENGLISH)

[ Abstract ]

I will present a review of stability and controllability results for linear parabolic coupled systems with coupling of first and zeroth-order terms by data of reduced number of components. The key ingredients are global Carleman estimates.

I will present a review of stability and controllability results for linear parabolic coupled systems with coupling of first and zeroth-order terms by data of reduced number of components. The key ingredients are global Carleman estimates.

### 2010/10/28

10:40-12:10 Room #123 (Graduate School of Math. Sci. Bldg.)

Market, Liquidity and Counterparty Risk (ENGLISH)

**Jean Meyer, Yasuko HISAMATSU**(Risk Capital Market Tokyo, BNP Paribas)Market, Liquidity and Counterparty Risk (ENGLISH)

[ Abstract ]

1. Introduction to the market risk

- Introduction to the Risk Management

in the Financial institutions

- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks

-Focus on volatility risk

-Focus on correlation risk

-Conclusion (common features of the market risks)

3. Risk measure

- Stress test

- Value at risk

- Risks measure for counterparty risk

1. Introduction to the market risk

- Introduction to the Risk Management

in the Financial institutions

- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks

-Focus on volatility risk

-Focus on correlation risk

-Conclusion (common features of the market risks)

3. Risk measure

- Stress test

- Value at risk

- Risks measure for counterparty risk

### 2010/09/09

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

Mini-course on Buildings (3/3) (ENGLISH)

**Bernhard Mühlherr**(Justus-Liebig-Universität Gießen)Mini-course on Buildings (3/3) (ENGLISH)

[ Abstract ]

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

The third lecture will be then devoted to classification results,

mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.

This is Part 3 of a 3-part lecture.

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

The third lecture will be then devoted to classification results,

mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.

This is Part 3 of a 3-part lecture.

### 2010/09/04

09:30-11:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Mini-course on Buildings (1/3) (ENGLISH)

**Bernhard Mühlherr**(Justus-Liebig-Universität Gießen)Mini-course on Buildings (1/3) (ENGLISH)

[ Abstract ]

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.

This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.

This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.

### 2010/09/04

11:10-12:40 Room #126 (Graduate School of Math. Sci. Bldg.)

Mini-course on Buildings (2/3) (ENGLISH)

**Bernhard Mühlherr**(Justus-Liebig-Universität Gießen)Mini-course on Buildings (2/3) (ENGLISH)

[ Abstract ]

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my second lecture I will start with chamber systems and coset

geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.

This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.

The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.

In my second lecture I will start with chamber systems and coset

geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.

This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.

### 2010/09/03

14:30-15:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Carleman estimates and boundary problems. (JAPANESE)

**Luc Robbiano**(University of Versailles)Carleman estimates and boundary problems. (JAPANESE)

[ Abstract ]

In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.

One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.

If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.

In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.

One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.

If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.

### 2010/08/06

15:30-17:45 Room #370 (Graduate School of Math. Sci. Bldg.)

A Spectral Method for Space--

Time Fractional Diffusion Equation (ENGLISH)

A multidimensional Borg-Levinson theorem (ENGLISH)

**Leevan Ling**(Hong Kong Baptist University) 15:30-16:30A Spectral Method for Space--

Time Fractional Diffusion Equation (ENGLISH)

**Mourad Choulli**(University of Metz) 16:45-17:45A multidimensional Borg-Levinson theorem (ENGLISH)

### 2010/08/05

16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Radiation Conditions for Wave in Stratified Medium and Related Inverse

Problems (ENGLISH)

**Yongzhi Steve Xu**(University of Louisville, USA)Radiation Conditions for Wave in Stratified Medium and Related Inverse

Problems (ENGLISH)

### 2010/08/05

16:30-17:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)

**Yongzhi Steve Xu**(University of Louisville, USA)Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems (ENGLISH)

### 2010/06/26

10:00-16:10 Room #056 (Graduate School of Math. Sci. Bldg.)

On the predual of non-commutative $H^\\infty$ (ENGLISH)

${\\mathbf Z}^N$-actions on UHF algebras of infinite type (ENGLISH)

On a subfactor generalization of Wall's conjecture (ENGLISH)

Group actions on Kirchberg algebras (ENGLISH)

**Yoshimichi Ueda**(Kyushu Univ.) 10:00-11:00On the predual of non-commutative $H^\\infty$ (ENGLISH)

**Hiroki Matui**(Chiba Univ.) 11:20-12:20${\\mathbf Z}^N$-actions on UHF algebras of infinite type (ENGLISH)

**Feng Xu**(UC Riverside) 13:50-14:50On a subfactor generalization of Wall's conjecture (ENGLISH)

**Masaki Izumi**(Kyoto Univ.) 15:10-16:10Group actions on Kirchberg algebras (ENGLISH)

### 2010/06/25

15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)

Ruelle-Lanford functions for quantum spin systems (ENGLISH)

**Narutaka Ozawa**(Univ. Tokyo) 15:00-16:00Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)

**Yoshiko Ogata**(Univ. Tokyo) 16:30-17:30Ruelle-Lanford functions for quantum spin systems (ENGLISH)

### 2010/05/12

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

Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)

**Luc Illusie**(東京大学/Paris南大学)Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)

[ Abstract ]

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

### 2010/05/07

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

Independence of families of $\\ell$-adic representations and uniform constructibility

**Luc Illusie**(東京大学/Paris南大学)Independence of families of $\\ell$-adic representations and uniform constructibility

[ Abstract ]

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

### 2010/04/28

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

Independence of families of $\\ell$-adic representations and uniform constructibility

**Luc Illusie**(東京大学/Paris南大学)Independence of families of $\\ell$-adic representations and uniform constructibility

[ Abstract ]

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

### 2010/04/19

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

**Cyrill Muratov**(New Jersey Institute of Technology)Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

[ Abstract ]

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

### 2010/03/25

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

Heuristic Choice Rules for Convex Variational Regularization

**Dr Bangti Jin**(Center for Industrial Mathematics University of Bremen, Germany)Heuristic Choice Rules for Convex Variational Regularization

[ Abstract ]

In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.

In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.

### 2010/03/25

16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Modern computer architectures for tsunami simulation

**M.M. Lavrentiev, Jr.**(Sobolev Institute of Mathematics, Novosibirsk, Russia)Modern computer architectures for tsunami simulation

[ Abstract ]

Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.

Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.

### 2010/03/19

11:00-12:00 Room #366 (Graduate School of Math. Sci. Bldg.)

A Regularization Parameter for Nonsmooth Tikhonov Regularization

**竹内 知哉**(North Carolina State University, USA)A Regularization Parameter for Nonsmooth Tikhonov Regularization

[ Abstract ]

We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.

We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.