## Colloquium

Seminar information archive ～06/09｜Next seminar｜Future seminars 06/10～

Organizer(s) | ABE Noriyuki, IWAKI Kohei, KAWAZUMI Nariya (chair), KOIKE Yuta |
---|---|

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

**Seminar information archive**

### 2020/06/05

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Exact WKB analysis and related topics

https://zoom.us/webinar/register/WN_ezXY3HjIQcCK2G9V-2CYrw

Please register at the link below to attend this online colloquium

**Kohei Iwaki**(Graduate School of Mathematical Sciences, University of Tokyo)Exact WKB analysis and related topics

[ Abstract ]

Exact WKB analysis, developed by Voros et.al., is an effective method for global study of (singularly perturbed) ordinary differential equations defined on a complex domain. After recalling several fundamental facts on exact WKB analysis, I'll talk about relationships to other research topics, such as cluster algebras, topological recursion, integrable systems of Painlevé type, etc.

[ Reference URL ]Exact WKB analysis, developed by Voros et.al., is an effective method for global study of (singularly perturbed) ordinary differential equations defined on a complex domain. After recalling several fundamental facts on exact WKB analysis, I'll talk about relationships to other research topics, such as cluster algebras, topological recursion, integrable systems of Painlevé type, etc.

https://zoom.us/webinar/register/WN_ezXY3HjIQcCK2G9V-2CYrw

### 2020/03/26

16:00-17:00 Room #117 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**KOHNO Toshitake**(Graduate School of Mathematical Sciences, The University of Tokyo)(JAPANESE)

### 2019/12/20

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

### 2019/11/08

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

### 2019/10/25

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

Arithmeticity of discrete subgroups (英語)

**Yves Benoist**( CNRS, Paris-Sud)Arithmeticity of discrete subgroups (英語)

[ Abstract ]

By a theorem of Borel and Harish-Chandra,

an arithmetic group in a semisimple Lie group is a lattice.

Conversely, by a celebrated theorem of Margulis,

in a higher rank semisimple Lie group G

any irreducible lattice is an arithmetic group.

The aim of this lecture is to survey an

arithmeticity criterium for discrete subgroups

which are not assumed to be lattices.

This criterium, obtained with Miquel,

generalizes works of Selberg and Hee Oh

and solves a conjecture of Margulis. It says:

a discrete irreducible Zariski-dense subgroup

of G that intersects cocompactly at least one

horospherical subgroup of G is an arithmetic group.

By a theorem of Borel and Harish-Chandra,

an arithmetic group in a semisimple Lie group is a lattice.

Conversely, by a celebrated theorem of Margulis,

in a higher rank semisimple Lie group G

any irreducible lattice is an arithmetic group.

The aim of this lecture is to survey an

arithmeticity criterium for discrete subgroups

which are not assumed to be lattices.

This criterium, obtained with Miquel,

generalizes works of Selberg and Hee Oh

and solves a conjecture of Margulis. It says:

a discrete irreducible Zariski-dense subgroup

of G that intersects cocompactly at least one

horospherical subgroup of G is an arithmetic group.

### 2019/06/28

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

### 2019/05/24

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

### 2019/04/26

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

### 2019/03/22

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

Mathematical structures of quantum mechanics and classical mechanics (日本語)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~shu/

Algebraic cyles, Periods and Motives (日本語)

[ Reference URL ]

http://gauss.ms.u-tokyo.ac.jp/index-j.html

Research on groups of homeomorphisms (日本語)

https://www.ms.u-tokyo.ac.jp/~tsuboi/

**Shu NAKAMURA**(The University of Tokyo) 13：00-14：00Mathematical structures of quantum mechanics and classical mechanics (日本語)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~shu/

**Tomohide TERASOMA**(The University of Tokyo) 14:30-15:30Algebraic cyles, Periods and Motives (日本語)

[ Reference URL ]

http://gauss.ms.u-tokyo.ac.jp/index-j.html

**Takashi TSUBOI**(The University of Tokyo) 16:00-17:00Research on groups of homeomorphisms (日本語)

[ Abstract ]

The homeomorphisms of a topological space form a group. The group seems to be too wild to be considered. In some cases it becomes a countable group but it is usually uncountable group. I have studied groups of homeomorphisms of topological spaces or groups of diffeomorphisms of manifolds which are related to invariants of foliations. I found several relationship between dynamical properties of group actions and homology of groups. There are many unsolved problems on the group of

homeomorphisms. I also intend to investigate more on the shape of groups. I would like to talk on such topics around groups of homeomorphisms.

[ Reference URL ]The homeomorphisms of a topological space form a group. The group seems to be too wild to be considered. In some cases it becomes a countable group but it is usually uncountable group. I have studied groups of homeomorphisms of topological spaces or groups of diffeomorphisms of manifolds which are related to invariants of foliations. I found several relationship between dynamical properties of group actions and homology of groups. There are many unsolved problems on the group of

homeomorphisms. I also intend to investigate more on the shape of groups. I would like to talk on such topics around groups of homeomorphisms.

https://www.ms.u-tokyo.ac.jp/~tsuboi/

### 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/