## Colloquium

Seminar information archive ～06/23｜Next seminar｜Future seminars 06/24～

Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
---|---|

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

**Seminar information archive**

### 2021/10/01

14:30-17:00 Online

Registration is closed (12:00, October 1).

Research Ethics in Computer Aided Mathematics (JAPANESE)

What's keeping back female mathematicians & physicists? (JAPANESE)

Registration is closed (12:00, October 1).

**Sadayoshi Kojima**(Waseda University) 14:30-15:30Research Ethics in Computer Aided Mathematics (JAPANESE)

[ Abstract ]

Since the solution of the four colored problem, a computer aided method has been expanding its base in mathematical research based on quite rapid development of Information Technology. Since then, it has been asked what the proof is, which is fundamental in mathematical research ethics. In this talk, I would like to present a history of discussions on this matter until now and to discuss some future aspect.

Since the solution of the four colored problem, a computer aided method has been expanding its base in mathematical research based on quite rapid development of Information Technology. Since then, it has been asked what the proof is, which is fundamental in mathematical research ethics. In this talk, I would like to present a history of discussions on this matter until now and to discuss some future aspect.

**Hiromi Yokoyama**(Kavli IPMU) 16:00-17:00What's keeping back female mathematicians & physicists? (JAPANESE)

[ Abstract ]

In Japan, female students' rate is low in mathematics and physics. The American Educational Psychology group pointed out there are three factors. We extended the model and added gender inequality social climate factors. We confirmed that the new factors influenced the male image of mathematics and physics in Japan and England. I would like to Introduce interdisciplinary research on science and technology society.

In Japan, female students' rate is low in mathematics and physics. The American Educational Psychology group pointed out there are three factors. We extended the model and added gender inequality social climate factors. We confirmed that the new factors influenced the male image of mathematics and physics in Japan and England. I would like to Introduce interdisciplinary research on science and technology society.

### 2021/07/30

15:30-16:30 Online

Registration is closed (12:00, July 30).

Toda equations and harmonic bundles (JAPANESE)

Registration is closed (12:00, July 30).

**Takuro Mochizuki**(RIMS, Kyoto University)Toda equations and harmonic bundles (JAPANESE)

### 2021/06/25

15:30-16:30 Online

Registration is closed (12:00, June 25).

The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)

Registration is closed (12:00, June 25).

**Hisashi Okamoto**(Gakushuin University)The Prandtl-Batchelor theory and its applications to Kolmogorov's problem (JAPANESE)

### 2021/05/28

15:30-16:30 Online

Registration is closed (12:00, May 28).

Physics and algebraic topology (ENGLISH)

Registration is closed (12:00, May 28).

**Yuji Tachikawa**(Kavli IPMU)Physics and algebraic topology (ENGLISH)

[ Abstract ]

Although we often talk about the "unreasonable effectiveness of mathematics in the natural sciences", there are great disparities in the relevance of various subbranches of mathematics to individual fields of natural sciences. Algebraic topology was a subject whose influence to physics remained relatively minor for a long time, but in the last several years, theoretical physicists started to appreciate the effectiveness of algebraic topology more seriously. For example, there is now a general consensus that the classification of the symmetry-protected topological phases, which form a class of phases of matter with a certain particularly simple property, is done in terms of generalized cohomology theories.

In this talk, I would like to provide a historical overview of the use of algebraic topology in physics, emphasizing a few highlights along the way. If the time allows, I would also like to report my struggle to understand the anomaly of heterotic strings, using the theory of topological modular forms.

Although we often talk about the "unreasonable effectiveness of mathematics in the natural sciences", there are great disparities in the relevance of various subbranches of mathematics to individual fields of natural sciences. Algebraic topology was a subject whose influence to physics remained relatively minor for a long time, but in the last several years, theoretical physicists started to appreciate the effectiveness of algebraic topology more seriously. For example, there is now a general consensus that the classification of the symmetry-protected topological phases, which form a class of phases of matter with a certain particularly simple property, is done in terms of generalized cohomology theories.

In this talk, I would like to provide a historical overview of the use of algebraic topology in physics, emphasizing a few highlights along the way. If the time allows, I would also like to report my struggle to understand the anomaly of heterotic strings, using the theory of topological modular forms.

### 2021/04/30

15:30-16:30 Online

Registration is closed (12:00, April 30).

Uniform bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds (Talk in Japanese, Slide in English)

Registration is closed (12:00, April 30).

**Shihoko Ishii**(The University of Tokyo)Uniform bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds (Talk in Japanese, Slide in English)

[ Abstract ]

In the talk I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obtained by at most two weighted blow ups. Our proof suggests the following conjecture:

Every pair consisting of a smooth N-fold and a "general" real ideal is computed by a divisor obtained by at most N-1 weighted blow ups.

This is regarded as a weighted blow up version of Mustata-Nakamura's conjecture. The condition "general" is slightly weakened from the version presented in ZAG Seminar.

In the talk I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obtained by at most two weighted blow ups. Our proof suggests the following conjecture:

Every pair consisting of a smooth N-fold and a "general" real ideal is computed by a divisor obtained by at most N-1 weighted blow ups.

This is regarded as a weighted blow up version of Mustata-Nakamura's conjecture. The condition "general" is slightly weakened from the version presented in ZAG Seminar.

### 2021/03/19

15:00-17:30 Online

Effects of viscosity and diffusion described by differential equations (JAPANESE)

Monodromy representations in higher categories and iterated integrals (JAPANESE)

**Yoshikazu Giga**(University of Tokyo) 15:00-16:00Effects of viscosity and diffusion described by differential equations (JAPANESE)

**Toshitake Kohno**(Meiji University/University of Tokyo) 16:30-17:30Monodromy representations in higher categories and iterated integrals (JAPANESE)

### 2021/01/22

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Convolution algebras and a new proof of Kazhdan-Lusztig formula (JAPANESE)

[ Reference URL ]

https://forms.gle/AAVzoCGPyLmzDJHf7

Please register at the link below to attend this online colloquium

**Hiraku Nakajima**(Kavli IPMU)Convolution algebras and a new proof of Kazhdan-Lusztig formula (JAPANESE)

[ Reference URL ]

https://forms.gle/AAVzoCGPyLmzDJHf7

### 2020/12/18

15:30-16:30 Online

Please register at the link below to attend this online colloquium

On Hilbert's proof theory (JAPANESE)

[ Reference URL ]

https://forms.gle/Nmi1KieFDjhchdU69

Please register at the link below to attend this online colloquium

**Toshiyasu Arai**(University of Tokyo)On Hilbert's proof theory (JAPANESE)

[ Reference URL ]

https://forms.gle/Nmi1KieFDjhchdU69

### 2020/11/20

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Tilting theory and its companions (JAPANESE)

[ Reference URL ]

https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K

Please register at the link below to attend this online colloquium

**Osamu Iyama**(University of Tokyo)Tilting theory and its companions (JAPANESE)

[ Reference URL ]

https://zoom.us/meeting/register/tJIrcu-prjoiGdNRSs0z3a5rl1SiuVgk0W8K

### 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.)