## Seminar information archive

Seminar information archive ～02/21｜Today's seminar 02/22 | Future seminars 02/23～

#### GCOE Seminars

11:10-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Inverse problems with fractional derivatives in the space variable (ENGLISH)

**W. Rundell**(Texas A&M Univ.)Inverse problems with fractional derivatives in the space variable (ENGLISH)

[ Abstract ]

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.

#### GCOE Seminars

14:30-15:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

**Y. Luchko**(Beuth Technical University of Applied Sciences)Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)

[ Abstract ]

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.

In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.

In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.

#### GCOE Seminars

16:20-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

New kind of observations in an inverse parabolic problem (ENGLISH)

**M. Cristofol**(Aix-Marseille Univ.)New kind of observations in an inverse parabolic problem (ENGLISH)

[ Abstract ]

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.

### 2014/02/28

#### GCOE Seminars

13:00-14:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

**Patricia Gaitan**(Aix-Marseille University)Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)

[ Abstract ]

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.

For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).

#### GCOE Seminars

11:00-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

**Assia Benabdallah**(Aix-Marseille University)Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)

### 2014/02/27

#### GCOE Seminars

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

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

**Yves Dermenjian**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)

### 2014/02/18

#### GCOE Seminars

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

A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

**Yves Dermenjian**(Univ. of Marseille)A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)

### 2014/02/17

#### Lectures

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

Canceled!! (ENGLISH)

**Ratnasingham Shivaji**(The University of North Carolina at Greensboro)Canceled!! (ENGLISH)

[ Abstract ]

Canceled!!

Canceled!!

### 2014/02/15

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)

Uniform boundedness of conditinal expectation operators (JAPANESE)

**Batbold Tserendorj**(National University of Mongolia) 13:30-15:00Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)

**Masato Kikuchi**(University of Toyama) 15:30-17:00Uniform boundedness of conditinal expectation operators (JAPANESE)

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

**Yoshihiro Oonishi**(Yamanashi Univ.) 13:30-14:30Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

**Atsuko Kogie**(Toyama Univ.) 15:00-16:00Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

### 2014/02/13

#### Numerical Analysis Seminar

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

Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)

http://www.infsup.jp/utnas/

**Mitchell Luskin**(University of Minnesota)Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)

[ Abstract ]

The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.

[ Reference URL ]The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.

Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.

http://www.infsup.jp/utnas/

### 2014/02/12

#### Algebraic Geometry Seminar

14:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)

Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)

**Shin-ichi Matsumura**(Kagoshima University) 14:00-15:30An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)

[ Abstract ]

In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.

This theorem is a powerful generalization of various injectivity and vanishing theorems.

The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.

To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.

Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.

As an application, we obtain a Nadel type vanishing theorem.

In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.

This theorem is a powerful generalization of various injectivity and vanishing theorems.

The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.

To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.

Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.

As an application, we obtain a Nadel type vanishing theorem.

**Junyan Cao**(KIAS) 16:00-17:30Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)

[ Abstract ]

In this talk, we first prove a version of the Ohsawa-Takegoshi

extension theorem valid for on arbitrary K\\"ahler manifolds, and for

holomorphic line bundles equipped with possibly singular metrics. As an

application, we generalise Berndtsson and Paun 's result about the

pseudo-effectivity of the relative canonical bundles to arbitrary

compact K\\"ahler families.

In this talk, we first prove a version of the Ohsawa-Takegoshi

extension theorem valid for on arbitrary K\\"ahler manifolds, and for

holomorphic line bundles equipped with possibly singular metrics. As an

application, we generalise Berndtsson and Paun 's result about the

pseudo-effectivity of the relative canonical bundles to arbitrary

compact K\\"ahler families.

#### thesis presentations

09:30-10:45 Room #118 (Graduate School of Math. Sci. Bldg.)

A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)

**清水 達郎**(東京大学大学院数理科学研究科)A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)

**平野 雄一**(東京大学大学院数理科学研究科)Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)

**粕谷 直彦**(東京大学大学院数理科学研究科)On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)

#### thesis presentations

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

特異値間隔分布によるセルオートマトンの分類 (JAPANESE)

**金子 勇治**(東京大学大学院数理科学研究科)特異値間隔分布によるセルオートマトンの分類 (JAPANESE)

### 2014/02/10

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

**許 本源**(東京大学大学院数理科学研究科)Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

**柏原 崇人**(東京大学大学院数理科学研究科)Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)

#### thesis presentations

08:00-09:15 Room #128 (Graduate School of Math. Sci. Bldg.)

A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)

**森 真樹**(東京大学大学院数理科学研究科)A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)

#### thesis presentations

09:30-10:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)

(JAPANESE)

**柗本 雄也**(東京大学大学院数理科学研究科)Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Spaces of stability conditions on Calabi-Yau categories associated with quivers(箙に付随するCalabi-Yau圏の安定性条件の空間について)

(JAPANESE)

**池田 暁志**(東京大学大学院数理科学研究科)Spaces of stability conditions on Calabi-Yau categories associated with quivers(箙に付随するCalabi-Yau圏の安定性条件の空間について)

(JAPANESE)

### 2014/02/05

#### Number Theory Seminar

17:10-18:10 Room #002 (Graduate School of Math. Sci. Bldg.)

The Franke filtration of spaces of automorphic forms (ENGLISH)

**Neven Grbac**(University of Rijeka)The Franke filtration of spaces of automorphic forms (ENGLISH)

[ Abstract ]

The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.

The Franke filtration is a filtration of the space of all adelic automorphic forms on a reductive group defined over a number field. The filtration steps can be described as certain induced representations, which has applications to the study of Eisenstein cohomology. In this talk, we shall describe the Franke filtration in general, give several examples, and explain its connection to cohomology.

### 2014/02/03

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Classification of log del Pezzo surfaces of index three (JAPANESE)

**Kento Fujita**(RIMS)Classification of log del Pezzo surfaces of index three (JAPANESE)

[ Abstract ]

Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.

Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.

#### GCOE Seminars

16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

**Fatiha Alabau**(University of Lorraine)On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)

[ Abstract ]

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.

#### GCOE Seminars

17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

**Piermarco Cannarsa**(University of Rome Tor Vergata)Compactness estimates for Hamilton-Jacobi equations (ENGLISH)

[ Abstract ]

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.

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