## Seminar information archive

Seminar information archive ～02/18｜Today's seminar 02/19 | Future seminars 02/20～

#### thesis presentations

14:30-15:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Combinatorics of jet schemes and its applications（ジェットスキームの組み合わせ論とその応用） (ENGLISH)

**Nguyen Duc Tam**(ベトナム科学技術アカデミー数学研究所)Combinatorics of jet schemes and its applications（ジェットスキームの組み合わせ論とその応用） (ENGLISH)

#### thesis presentations

16:00-17:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Rational singularities,ω-multiplier ideals and core of ideals（有理特異点、ω-乗数イデアルとイデアルのコア） (JAPANESE)

**柴田 康介**(東京大学大学院数理科学研究科)Rational singularities,ω-multiplier ideals and core of ideals（有理特異点、ω-乗数イデアルとイデアルのコア） (JAPANESE)

#### thesis presentations

14:30-15:45 Room #122 (Graduate School of Math. Sci. Bldg.)

Volume renormalization for the Blaschke metric on strictly convex domains （強凸領域上のブラシュケ計量の体積繰り込みについて） (JAPANESE)

**丸亀 泰二**(東京大学大学院数理科学研究科)Volume renormalization for the Blaschke metric on strictly convex domains （強凸領域上のブラシュケ計量の体積繰り込みについて） (JAPANESE)

### 2016/01/27

#### Seminar on Probability and Statistics

13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)

Multilevel SMC Samplers

**Ajay Jasra**(National University of Singapore)Multilevel SMC Samplers

[ Abstract ]

The approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs) is considered herein; this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with step-size level h_L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multi-level Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels \infty>h_0>h_1\cdots>h_L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained in the SMC context. The approach is numerically illustrated on a Bayesian inverse problem. This is a joint work with Kody Law (ORNL), Yan Zhou (NUS), Raul Tempone (KAUST) and Alex Beskos (UCL).

The approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs) is considered herein; this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with step-size level h_L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multi-level Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels \infty>h_0>h_1\cdots>h_L. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained in the SMC context. The approach is numerically illustrated on a Bayesian inverse problem. This is a joint work with Kody Law (ORNL), Yan Zhou (NUS), Raul Tempone (KAUST) and Alex Beskos (UCL).

#### Mathematical Biology Seminar

13:30-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematical analysis for HIV infection dynamics in lymphoid tissue network (JAPANESE)

On approximation of stability radius for an infinite-dimensional closed-loop control system

(JAPANESE)

Prediction of the increase or decrease of infected population based on the backstepping method

(JAPANESE)

Mathematical model of malaria spread for a village network

**Shinji Nakaoka**(Graduate School of Medicine, The University of Tokyo) 15:10-15:50Mathematical analysis for HIV infection dynamics in lymphoid tissue network (JAPANESE)

**Hideki Sano**(Graduate School of System Informatics, Kobe University) 13:30-14:10On approximation of stability radius for an infinite-dimensional closed-loop control system

(JAPANESE)

[ Abstract ]

We discuss the problem of approximating stability radius appearing

in the design procedure of finite-dimensional stabilizing controllers

for an infinite-dimensional dynamical system. The calculation of

stability radius needs the value of the H-infinity norm of a transfer

function whose realization is described by infinite-dimensional

operators in a Hilbert space. From the practical point of view, we

need to prepare a family of approximate finite-dimensional operators

and then to calculate the H-infinity norm of their transfer functions.

However, it is not assured that they converge to the value of the

H-infinity norm of the original transfer function. The purpose of

this study is to justify the convergence. In a numerical example,

we treat parabolic distributed parameter systems with distributed

control and distributed/boundary observation.

We discuss the problem of approximating stability radius appearing

in the design procedure of finite-dimensional stabilizing controllers

for an infinite-dimensional dynamical system. The calculation of

stability radius needs the value of the H-infinity norm of a transfer

function whose realization is described by infinite-dimensional

operators in a Hilbert space. From the practical point of view, we

need to prepare a family of approximate finite-dimensional operators

and then to calculate the H-infinity norm of their transfer functions.

However, it is not assured that they converge to the value of the

H-infinity norm of the original transfer function. The purpose of

this study is to justify the convergence. In a numerical example,

we treat parabolic distributed parameter systems with distributed

control and distributed/boundary observation.

**Toshikazu Kiniya**(Graduate School of System Informatics, Kobe University) 14:10-14:50Prediction of the increase or decrease of infected population based on the backstepping method

(JAPANESE)

**Takaaki Funo**(Faculty of science, Kyushu University) 15:50-16:30Mathematical model of malaria spread for a village network

### 2016/01/26

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Hamilton-Jacobi equations for optimal control on 2-dimensional junction (English)

**Salomé Oudet**(University of Tokyo)Hamilton-Jacobi equations for optimal control on 2-dimensional junction (English)

[ Abstract ]

We are interested in infinite horizon optimal control problems on 2-dimensional junctions (namely a union of half-planes sharing a common straight line) where different dynamics and different running costs are allowed in each half-plane. As for more classical optimal control problems, ones wishes to determine the Hamilton-Jacobi equation which characterizes the value function. However, the geometric singularities of the 2-dimensional junction and discontinuities of data do not allow us to apply the classical results of the theory of the viscosity solutions.

We will explain how to skirt these difficulties using arguments coming both from the viscosity theory and from optimal control theory. By this way we prove that the expected equation to characterize the value function is well posed. In particular we prove a comparison principle for this equation.

We are interested in infinite horizon optimal control problems on 2-dimensional junctions (namely a union of half-planes sharing a common straight line) where different dynamics and different running costs are allowed in each half-plane. As for more classical optimal control problems, ones wishes to determine the Hamilton-Jacobi equation which characterizes the value function. However, the geometric singularities of the 2-dimensional junction and discontinuities of data do not allow us to apply the classical results of the theory of the viscosity solutions.

We will explain how to skirt these difficulties using arguments coming both from the viscosity theory and from optimal control theory. By this way we prove that the expected equation to characterize the value function is well posed. In particular we prove a comparison principle for this equation.

### 2016/01/25

#### Tokyo Probability Seminar

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

Hamilton-Jacobi equations in metric spaces

**Atsushi Nakayasu**(Graduate School of Mathematical Sciences, The University of Tokyo)Hamilton-Jacobi equations in metric spaces

#### Seminar on Geometric Complex Analysis

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

(Japanese)

**Kunio Obitsu**(Kagoshima Univ.)(Japanese)

### 2016/01/22

#### FMSP Lectures

15:00 -16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Functor categories and stable homology of groups (8) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**(ENGLISH)Functor categories and stable homology of groups (8) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSP Lectures

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

Functor categories and stable homology of groups (9) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (9) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### Operator Algebra Seminars

15:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to $C^*$-tensor categories

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to $C^*$-tensor categories

### 2016/01/21

#### FMSP Lectures

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Functor categories and stable homology of groups (6) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (6) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSP Lectures

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

Functor categories and stable homology of groups (7) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (7) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### Operator Algebra Seminars

15:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to $C^*$-tensor categories

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to $C^*$-tensor categories

### 2016/01/20

#### FMSP Lectures

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

Functor categories and stable homology of groups (5) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (5) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### Operator Algebra Seminars

15:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to $C^*$-tensor categories

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to $C^*$-tensor categories

#### Seminar on Probability and Statistics

13:00-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Fractional calculus and some applications to stochastic processes

**Enzo Orsingher**(Sapienza University of Rome)Fractional calculus and some applications to stochastic processes

[ Abstract ]

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

1) Riemann-Liouville fractional integrals and derivatives

2) integrals of derivatives and derivatives of integrals

3) Dzerbayshan-Caputo fractional derivatives

4) Marchaud derivative

5) Riesz potential and fractional derivatives

6) Hadamard derivatives and also Erdelyi-Kober derivatives

7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives

8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)

9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)

10) Time-fractional telegraph Poisson process

11) Space fractional Poisson process

13) Other fractional point processes (birth and death processes)

14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.

In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.

### 2016/01/19

#### FMSP Lectures

13:30 -14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Functor categories and stable homology of groups (3) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (3) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSP Lectures

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

Functor categories and stable homology of groups (4) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (4) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### Operator Algebra Seminars

**Reiji Tomatsu**(Hokkaido Univ.)

Introduction to $C^*$-tensor categories

#### Tuesday Seminar on Topology

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)

**Hikaru Yamamoto**(The University of Tokyo)Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)

[ Abstract ]

A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean

curvature flow and a Ricci flow.

In this talk, we consider a Ricci-mean curvature flow in a gradient

shrinking Ricci soliton, and give a generalization of a well-known result

of Huisken which states that if a mean curvature flow in a Euclidean space

develops a singularity of type I, then its parabolic rescaling near the singular

point converges to a self-shrinker.

A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean

curvature flow and a Ricci flow.

In this talk, we consider a Ricci-mean curvature flow in a gradient

shrinking Ricci soliton, and give a generalization of a well-known result

of Huisken which states that if a mean curvature flow in a Euclidean space

develops a singularity of type I, then its parabolic rescaling near the singular

point converges to a self-shrinker.

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows

**Hao Wu**(Fudan University)Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows

[ Abstract ]

In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.

We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.

In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.

In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.

We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.

In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.

### 2016/01/18

#### Seminar on Geometric Complex Analysis

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

Holomorphic motions and the monodromy (Japanese)

**Hiroshige Shiga**(Tokyo Institute of Technology)Holomorphic motions and the monodromy (Japanese)

[ Abstract ]

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.

#### FMSP Lectures

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Functor categories and stable homology of groups (1) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (1) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

#### FMSP Lectures

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

Functor categories and stable homology of groups (2) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

**Aurelien Djament (Nantes/CNRS)(by video conference system) and Christine Vespa (Strasbourg)**Functor categories and stable homology of groups (2) (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf

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