## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

### 2016/04/04

#### Numerical Analysis Seminar

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

Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)

**Eric Chung**(Chinese University of Hong Kong)Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations (English)

[ Abstract ]

In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.

In this talk, we present a staggered discontinuous Galerkin method for the approximation of the incompressible Navier-Stokes equations. Our new method combines the advantages of discontinuous Galerkin methods and staggered meshes, and results in many good properties, namely local and global conservations, optimal convergence and superconvergence through the use of a local postprocessing technique. Another key feature is that our method provides a skew-symmetric discretization of the convection term, with the aim of giving a better conservation property compared with existing discretizations. We also analyze the stability and convergence of the method. In addition, we will present some numerical results to show the performance of the proposed method.

### 2016/03/29

#### Number Theory Seminar

17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Motivic cohomology of formal schemes in characteristic p

(English)

**Matthew Morrow**(Universität Bonn)Motivic cohomology of formal schemes in characteristic p

(English)

[ Abstract ]

The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I will explain an analogous theory for formal schemes, as well as applications to algebraic cycles, such as a weak Lefschetz theorem for formal Chow groups.

### 2016/03/22

#### Colloquium

16:50-17:50 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Singularities and Jet schemes (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~shihoko/

**Shihoko Ishii**(Graduate School of Mathematical Sciences, University of Tokyo)Singularities and Jet schemes (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~shihoko/

#### FMSP Lectures

10:00-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Control and stabilization of degenerate wave equations (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Alabau.pdf

**Fatiha Alabau**(Université de Lorraine)Control and stabilization of degenerate wave equations (ENGLISH)

[ Abstract ]

The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.

For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.

This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).

[ Reference URL ]The control of degenerate PDE's arise in many applications such as cloaking, climatology, population genetics, and vision.

For such models, the diffusion operator degenerates on some subset of the spatial domain. We present some recent results on observability, control and stabilization of these equations.

This is a joint work with Piermarco Cannarsa (University di Roma Tor Vergata, Italy) and G\"unter Leugering (Friedrich-Alexander-Universit\"at Erlangen-N\"urnberg, Erlangen, Germany).

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Alabau.pdf

#### FMSP Lectures

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

Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bellassoued.pdf

**Mourad Bellassoued**(Université de Tunis El Manar)Stable determination of coefficients in the dynamical Schrödinger equation in a magnetic field (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bellassoued.pdf

### 2016/03/19

#### FMSP Lectures

11:00-12:00 Room #370 (Graduate School of Math. Sci. Bldg.)

About the Landis conjecture (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf

**Oleg Emanouilov**(Colorado State Univ.)About the Landis conjecture (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov160319.pdf

### 2016/03/18

#### FMSP Lectures

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

Control of degenerate parabolic equations: old and new (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa.pdf

**Piermarco Cannarsa**(Università degli Studi di Roma Tor Vergata)Control of degenerate parabolic equations: old and new (ENGLISH)

[ Abstract ]

This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.

We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.

[ Reference URL ]This talk will survey the main results obtained in the last fifteen years or so for the null controllability of degenerate parabolic operators.

We shall describe the state of the art for operators which degenerate at the boundary as well as for certain classes of interior degeneracy of hypoelliptic type.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cannarsa.pdf

### 2016/03/16

#### PDE Real Analysis Seminar

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

Fluids, vortex membranes, and skew-mean-curvature flows (English)

**Boris Khesin**(University of Toronto)Fluids, vortex membranes, and skew-mean-curvature flows (English)

[ Abstract ]

We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.

We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.

### 2016/03/11

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Convergence to the boundary for random walks on discrete quantum groups

(English)

**Bas Jordans**(Univ. Oslo)Convergence to the boundary for random walks on discrete quantum groups

(English)

### 2016/03/08

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Equilibrium and non-equilibrium states in Conformal Field Theory (英語)

**Roberto Longo**(Univ. Rome "Tor Vergata")Equilibrium and non-equilibrium states in Conformal Field Theory (英語)

### 2016/02/22

#### FMSP Lectures

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

Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf

**Michel Cristofol**(Aix-Marseille Univ.)Inverse problems for parabolic operators : comparison of three different approaches (ENGLISH)

[ Abstract ]

Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a diﬀerent and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.

[ Reference URL ]Basing my talk around a toy problem : reconstruction of the potential for a linear parabolic problem, I will recall the two main classical following methods : Dirichlet to Neumann map and Carleman estimates. Then I will present a diﬀerent and recent approach based on pointwise observations and I will underline some points to be improved for each method. Then, I will finish my talk by a review of some results related to this technic of pointwise observations.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf

### 2016/02/19

#### FMSP Lectures

10:30-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Poisson.pdf

**Olivier Poisson**(Aix-Marseille University)Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method (ENGLISH)

[ Abstract ]

Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:

- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,

- An energy estimate for x-multidimensional convex inclusions.

In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :

this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.

[ Reference URL ]Many articles solve a version of the Calder'on inverse problem for the heat equation. The biggest part of them assume that the unknown conductivity do not depend on time t. But they are very few results concerning the time de- pendent situation, and they are based on the computation of an ansatz for the parabolic equation:

- A reconstruction method of an unknown moving inclusion by a dynamical probe method was performed by Daido-Kang-Nakamura in 2007, but it works for the one dimensional spatial space only,

- An energy estimate for x-multidimensional convex inclusions.

In the talk I will present a dynamical probe method based on special fundamental solutions of the heat equation and basic inequalities :

this approach is very close to the probe method for the elliptic Calderon inverse problem, and does not require regularity of the inclusion.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Poisson.pdf

### 2016/02/18

#### FMSP Lectures

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

L^2 Extension and its applications: A survey (3) (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

**Dror Varolin**(Stony Brook)L^2 Extension and its applications: A survey (3) (ENGLISH)

[ Abstract ]

We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

[ Reference URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

#### FMSP Lectures

10:30-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf

**Michel Cristofol**(Aix-Marseille Univ.)Inverse boundary value problem for a hyperbolic equation in an infinite guide (ENGLISH)

[ Abstract ]

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.

[ Reference URL ]We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Holder stability with the aid of a Carleman estimate specially designed for hyperbolic waveguides. I will provide numerical simulations in multiple backgrounds.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Cristofol.pdf

### 2016/02/17

#### FMSP Lectures

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

L^2 Extension and its applications: A survey (2) (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

**Dror Varolin**(Stony Brook)L^2 Extension and its applications: A survey (2) (ENGLISH)

[ Abstract ]

We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

[ Reference URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

### 2016/02/16

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

String Topology, Euler Class and TNCZ free loop fibrations (ENGLISH)

**Luc Menichi**(University of Angers)String Topology, Euler Class and TNCZ free loop fibrations (ENGLISH)

[ Abstract ]

Let $M$ be a connected, closed oriented manifold.

Chas and Sullivan have defined a loop product and a loop coproduct on

$H_*(LM;¥mathbb{F})$, the homology of the

free loops on $M$ with coefficients in the field $¥mathbb{F}$.

By studying this loop coproduct, I will show that if the free loop

fibration

$¥Omega M¥buildrel{i}¥over¥hookrightarrow

LM¥buildrel{ev}¥over¥twoheadrightarrow M$

is homologically trivial, i.e. $i^*:H^*(LM;¥mathbb{F})¥twoheadrightarrow

H^*(¥Omega M;¥mathbb{F})$ is onto,

then the Euler characteristic of $M$ is divisible by the characteristic

of the field $¥mathbb{F}$

(or $M$ is a point).

Let $M$ be a connected, closed oriented manifold.

Chas and Sullivan have defined a loop product and a loop coproduct on

$H_*(LM;¥mathbb{F})$, the homology of the

free loops on $M$ with coefficients in the field $¥mathbb{F}$.

By studying this loop coproduct, I will show that if the free loop

fibration

$¥Omega M¥buildrel{i}¥over¥hookrightarrow

LM¥buildrel{ev}¥over¥twoheadrightarrow M$

is homologically trivial, i.e. $i^*:H^*(LM;¥mathbb{F})¥twoheadrightarrow

H^*(¥Omega M;¥mathbb{F})$ is onto,

then the Euler characteristic of $M$ is divisible by the characteristic

of the field $¥mathbb{F}$

(or $M$ is a point).

#### FMSP Lectures

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

L^2 Extension and its applications: A survey (1) (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

**Dror Varolin**(Stony Brook)L^2 Extension and its applications: A survey (1) (ENGLISH)

[ Abstract ]

We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

[ Reference URL ]We discuss certain aspects of the theory of L^2 extension, going back to the famous and fundamental work of Ohsawa and Takegoshi, and even further back to work of Donnelly and Fefferman.

The first of three lectures will recall a number of L^2 extension theorems, to some extent following an incomplete history (as I see it), and ending with a sketch of a proof of one of these theorems.

The second lecture will discuss a number of my favorite applications of L^2 extension, from Bergman kernels to deformation invariance of plurigenera.

The third lecture will discuss a new proof of the extension theorem, due to Berndtsson and Lempert. The key tool is a theorem of Berndtsson on the positivity of direct images, which we will review. Berndtsson's theorem permits the introduction of degeneration techniques, whose surprising application to L^2 extension represents one of the most beautiful and fundamental recent breakthroughs in the subject.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Varolin.pdf

#### FMSP Lectures

16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Inverse Problem for an Hyperbolic-Parabolic System and Perspectives (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan160216.pdf

**Patricia Gaitan**(Aix-Marseille University)Inverse Problem for an Hyperbolic-Parabolic System and Perspectives (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan160216.pdf

### 2016/02/15

#### FMSP Lectures

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

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

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan.pdf

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

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gaitan.pdf

### 2016/02/08

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Dynamical rigidity of stochastic Coulomb systems

**Hirofumi Osada**(Graduate School of Mathematics, Kyushu University)Dynamical rigidity of stochastic Coulomb systems

#### Infinite Analysis Seminar Tokyo

13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)

q-Bosons, Toda lattice and Baxter Q-Operator (ENGLISH)

**Vincent Pasquier**(IPhT Saclay)q-Bosons, Toda lattice and Baxter Q-Operator (ENGLISH)

[ Abstract ]

I will use the Pieri rules of the Hall Littlewood polynomials to construct some

lattice models, namely the q-Boson model and the Toda Lattice Q matrix.

I will identify the semi infinite chain transfer matrix of these models with well known

half vertex operators. Finally, I will explain how the Gaudin determinant appears in the evaluation

of the semi infine chain scalar products for an arbitrary spin and is related to the Macdonald polynomials.

I will use the Pieri rules of the Hall Littlewood polynomials to construct some

lattice models, namely the q-Boson model and the Toda Lattice Q matrix.

I will identify the semi infinite chain transfer matrix of these models with well known

half vertex operators. Finally, I will explain how the Gaudin determinant appears in the evaluation

of the semi infine chain scalar products for an arbitrary spin and is related to the Macdonald polynomials.

### 2016/02/01

#### Tokyo Probability Seminar

16:50-18:20 Room #270 (Graduate School of Math. Sci. Bldg.)

**Kohei Soga**(Faculty of Science and Technology, Keio University)### 2016/01/29

#### thesis presentations

9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Algebraic structure on the space of intertwining operators（絡作用素の空間上の代数構造） (JAPANESE)

**北川 宜稔**(東京大学大学院数理科学研究科)Algebraic structure on the space of intertwining operators（絡作用素の空間上の代数構造） (JAPANESE)

#### thesis presentations

10:45-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Some topics on analysis of holomorphic discrete series representations（正則離散系列表現の解析に関するいくつかの話題） (JAPANESE)

**中濱 良祐**(東京大学大学院数理科学研究科)Some topics on analysis of holomorphic discrete series representations（正則離散系列表現の解析に関するいくつかの話題） (JAPANESE)

#### thesis presentations

12:45-14:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On codimension two contact embeddings in the standard spheres（標準接触球面への余次元2の接触埋め込みについて）

**古川 遼**(東京大学大学院数理科学研究科)On codimension two contact embeddings in the standard spheres（標準接触球面への余次元2の接触埋め込みについて）

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