## Colloquium

Seminar information archive ～01/18｜Next seminar｜Future seminars 01/19～

Organizer(s) | Tomohide Terasoma |
---|---|

URL | http://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html |

**Seminar information archive**

### 2018/11/30

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

The theory of viscosity solutions and Aubry-Mather theory

(日本語)

**Hiroyoshi Mitake**(The University of Tokyo)The theory of viscosity solutions and Aubry-Mather theory

(日本語)

[ Abstract ]

In this talk, we give two topics of my recent results.

(i) Asymptotic analysis based on the nonlinear adjoint method: Wepresent two results on the large-time behavior for the Cauchy problem, and the vanishing discount problem for degenerate Hamilton-Jacobiequations.

(ii) Rate of convergence in homogenization of Hamilton-Jacobi equations: The convergence appearing in the homogenization was proved in a famous unpublished paper by Lions, Papanicolaou, Varadhan (1987). In this talk, we present some recent progress in obtaining the optimal rate of convergence $O(¥epsilon)$ in periodic homogenization of Hamilton-Jacobi equations. Our method is completely different from previous pure PDE approaches which only provides $O(¥epsilon^{1/3})$. We have discovered a natural connection between the convergence rate and the underlying Hamiltonian system.

In this talk, we give two topics of my recent results.

(i) Asymptotic analysis based on the nonlinear adjoint method: Wepresent two results on the large-time behavior for the Cauchy problem, and the vanishing discount problem for degenerate Hamilton-Jacobiequations.

(ii) Rate of convergence in homogenization of Hamilton-Jacobi equations: The convergence appearing in the homogenization was proved in a famous unpublished paper by Lions, Papanicolaou, Varadhan (1987). In this talk, we present some recent progress in obtaining the optimal rate of convergence $O(¥epsilon)$ in periodic homogenization of Hamilton-Jacobi equations. Our method is completely different from previous pure PDE approaches which only provides $O(¥epsilon^{1/3})$. We have discovered a natural connection between the convergence rate and the underlying Hamiltonian system.

### 2018/10/26

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Asymptotic behavior of generalized eigenfunctions and scattering theory

(JAPANESE)

**Kenichi ITO**(The University of Tokyo)Asymptotic behavior of generalized eigenfunctions and scattering theory

(JAPANESE)

### 2018/07/13

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Pluripotential theory and complex dynamics in higher dimension

**DINH Tien Cuong**(National University of Singapore )Pluripotential theory and complex dynamics in higher dimension

[ Abstract ]

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

Positive closed currents, the analytic counterpart of effective cycles in algebraic geometry, are central objects in pluripotential theory. They were introduced in complex dynamics in the 1990s and become now a powerful tool in the field. Challenging dynamical problems involve currents of any dimension. We will report recent developments on positive closed currents of arbitrary dimension, including the solutions to the regularization problem, the theory of super-potentials and the theory of densities. Applications to dynamics such as properties of dynamical invariants (e.g. dynamical degrees, entropies, currents, measures), solutions to equidistribution problems, and properties of periodic points will be discussed.

### 2018/06/29

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Power concavity for parabolic equations (日本語)

**Kazuhiro Ishige**(The University of Tokyo)Power concavity for parabolic equations (日本語)

### 2018/05/25

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Mod p representation theory of p-adic reductive groups

(日本語)

**Noriyuki ABE**(The University of Tokyo)Mod p representation theory of p-adic reductive groups

(日本語)

### 2018/05/11

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Generic density theorems for periodic Reeb orbits and minimal hypersurfaces (日本語)

**Kei IRIE**(The University of Tokyo)Generic density theorems for periodic Reeb orbits and minimal hypersurfaces (日本語)

### 2018/04/06

15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

### 2018/03/10

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

(JAPANESE)

**Hitoshi ARAI**(Univ. Tokyo)(JAPANESE)

### 2018/03/10

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

(JAPANESE)

**Akito FUTAKI**(Univ. Tokyo)(JAPANESE)

### 2018/03/10

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

(JAPANESE)

**Yujiro KAWAMATA**(Univ. Tokyo)(JAPANESE)

### 2018/03/10

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

(JAPANESE)

**Hiroshi MATANO**(Univ. Tokyo)(JAPANESE)

### 2018/02/23

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Hiromu Tanaka**(Univ. Tokyo)(JAPANESE)

### 2018/01/26

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yuta Koike**(Univ. Tokyo)(JAPANESE)

### 2017/11/24

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Yukari Ito**(IPMU, Nagoya University)(JAPANESE)

### 2017/10/06

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)

[ Reference URL ]

http://lab.twcu.ac.jp/miyachi/English.html

**Akihiko Miyachi**(Tokyo Woman's Christian University)Singular Integrals and Real Variable Methods in Harmonic Analysis (JAPANESE)

[ Reference URL ]

http://lab.twcu.ac.jp/miyachi/English.html

### 2017/07/07

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Smith Normal Form and Combinatorics (English)

http://www-math.mit.edu/~rstan/

**Richard Stanley**(MIT)Smith Normal Form and Combinatorics (English)

[ Abstract ]

Let R be a commutative ring (with identity) and A an n x n matrix over R. Suppose there exist n x n matrices P,Q invertible over $R$ for which PAQ is a diagonal matrix

diag(e_1,...,e_r,0,...,0), where e_i divides e_{i+1} in R. We then call PAQ a Smith normal form (SNF) of $A$. If R is a PID then an SNF always exists and is unique up to multiplication by units. Moreover if A is invertible then det A=ua_1\cdots a_n, where u is a unit, so SNF gives a

canonical factorization of det A.

We will survey some connections between SNF and combinatorics. Topics will include (1) the general theory of SNF, (2) a close connection between SNF and chip firing in graphs, (3) the SNF of a random matrix of integers (joint work with Yinghui Wang), (4) SNF of special classes of matrices, including some arising in the theory of symmetric functions, hyperplane arrangements, and lattice paths.

[ Reference URL ]Let R be a commutative ring (with identity) and A an n x n matrix over R. Suppose there exist n x n matrices P,Q invertible over $R$ for which PAQ is a diagonal matrix

diag(e_1,...,e_r,0,...,0), where e_i divides e_{i+1} in R. We then call PAQ a Smith normal form (SNF) of $A$. If R is a PID then an SNF always exists and is unique up to multiplication by units. Moreover if A is invertible then det A=ua_1\cdots a_n, where u is a unit, so SNF gives a

canonical factorization of det A.

We will survey some connections between SNF and combinatorics. Topics will include (1) the general theory of SNF, (2) a close connection between SNF and chip firing in graphs, (3) the SNF of a random matrix of integers (joint work with Yinghui Wang), (4) SNF of special classes of matrices, including some arising in the theory of symmetric functions, hyperplane arrangements, and lattice paths.

http://www-math.mit.edu/~rstan/

### 2017/06/20

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Some stochastic population models in a random environment (English)

http://www.ummisco.ird.fr/perso/bacaer/

**Nicolas Bacaër**(Institute de Resherrche pour le Developpement, the University of Tokyo)Some stochastic population models in a random environment (English)

[ Abstract ]

Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.

[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)

[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)

[ Reference URL ]Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.

[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)

[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)

http://www.ummisco.ird.fr/perso/bacaer/

### 2017/05/26

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)

**Shigeki Aida**(Graduate School of Mathematical Sciences, The University of Tokyo)ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)

### 2017/04/28

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

可積分量子スピン鎖における隠れた超対称性 (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matsui/index.html

**Chihiro Matsui**(Graduate School of Mathematical Sciences, the University of Tokyo)可積分量子スピン鎖における隠れた超対称性 (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~matsui/index.html

### 2017/03/21

14:40-15:40 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

A tour around microlocal analysis and algebraic analysis (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

**Kiyoomi Kataoka**(Graduate School of Mathematical Sciences, The University of Tokyo)A tour around microlocal analysis and algebraic analysis (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

### 2017/03/21

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

40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~funaki/

**Tadahisa Funaki**(Graduate School of Mathematical Sciences, The University of Tokyo)40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~funaki/

### 2016/12/07

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On a conjecture of Bloch and Kato, and a local analogue.

**Uwe Jannsen**On a conjecture of Bloch and Kato, and a local analogue.

[ Abstract ]

In their seminal paper on Tamagawa Numbers of motives,

Bloch and Kato introduced a notion of motivic pairs, without

loss of generality over the rational numbers, which should

satisfy certain properties (P1) to (P4). The last property

postulates the existence of a Galois stable lattice T in the

associated adelic Galois representation V such that for each

prime p the fixed module of the inertia group of Q_p of

V/T is l-divisible for almost all primes l different from p.

I postulate an analogous local conjecture and show that it

implies the global conjecture.

In their seminal paper on Tamagawa Numbers of motives,

Bloch and Kato introduced a notion of motivic pairs, without

loss of generality over the rational numbers, which should

satisfy certain properties (P1) to (P4). The last property

postulates the existence of a Galois stable lattice T in the

associated adelic Galois representation V such that for each

prime p the fixed module of the inertia group of Q_p of

V/T is l-divisible for almost all primes l different from p.

I postulate an analogous local conjecture and show that it

implies the global conjecture.

### 2016/11/25

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yoneda/index.html

**Tsuyoshi Yoneda**(Graduate School of Mathematical Sciences, The University of Tokyo)An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yoneda/index.html

### 2016/10/04

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Waning and boosting : on the dynamics of immune status (ENGLISH)

http://www.uu.nl/staff/ODiekmann

**Odo Diekmann**(Utrecht University)Waning and boosting : on the dynamics of immune status (ENGLISH)

[ Abstract ]

A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.

[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis

of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388

[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259

[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7

[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47

[ Reference URL ]A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.

[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis

of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388

[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259

[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7

[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47

http://www.uu.nl/staff/ODiekmann

### 2016/06/24

15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Recent developments of MMP and around (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/teacher/gongyo.html

**GONGYO Yoshinori**(Graduate School of Mathematical Sciences, The University of Tokyo)Recent developments of MMP and around (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/teacher/gongyo.html