## Colloquium

Seminar information archive ～12/04｜Next seminar｜Future seminars 12/05～

Organizer(s) | KATO Akishi, KITAYAMA Takahiro, MITAKE Yoshihiro, TSUJI Takeshi (chair) |
---|---|

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

**Seminar information archive**

### 2022/11/25

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

Motivic cohomology: theory and applications (ENGLISH)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

**Shane Kelly**(Graduate School of Mathematical Sciences, the University of Tokyo)Motivic cohomology: theory and applications (ENGLISH)

[ Abstract ]

The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).

One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.

In this talk I will give an introduction to the classical theory and discuss some current and future research directions.

[ Reference URL ]The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).

One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.

In this talk I will give an introduction to the classical theory and discuss some current and future research directions.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb

### 2022/10/21

15:30-16:30 Room #オンライン (Graduate School of Math. Sci. Bldg.)

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

The Fourier restriction conjecture (English)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

**Neal Bez**(Graduate School of Science and Engineering, Saitama University)The Fourier restriction conjecture (English)

[ Abstract ]

The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.

[ Reference URL ]The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2

### 2022/07/22

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

**Ryo Takada**(Graduate School of Mathematical Sciences, the University of Tokyo)Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

[ Abstract ]

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

[ Reference URL ]In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t

### 2022/06/24

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

**Yoshiki Oshima**(Graduate School of Mathematical Sciences, the University of Tokyo)Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)

[ Abstract ]

The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.

[ Reference URL ]The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR

### 2022/05/20

15:30-16:30 Hybrid

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

**Ryo Takada**(Graduate School of Mathematical Sciences, the University of Tokyo)Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

[ Abstract ]

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

### 2022/04/22

15:30-16:30 Online

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

Curve counting theories and categorification

(JAPANESE)

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

**Yukinobu Toda**(Kavli IPMU, The University of Tokyo)Curve counting theories and categorification

(JAPANESE)

[ Abstract ]

There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.

There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.

### 2022/03/26

16:00-17:00 Online

Registration is closed.

Registration is closed.

**Masahiko Kanai**(Graduate School of Mathematical Sciences, The University of Tokyo) -**Tetsuji Tokihiro**(Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00### 2022/01/21

15:30-16:30 Online

Registration is closed (12:00, January 21).

Classification of gapped ground state phases in quantum spin systems (JAPANESE)

Registration is closed (12:00, January 21).

**Yoshiko Ogata**(Graduate School of Mathematical Sciences, The University of Tokyo)Classification of gapped ground state phases in quantum spin systems (JAPANESE)

### 2021/12/17

15:30-16:30 Online

Registration is closed (12:00, December 17).

Growth vectors of distributions and lines on projective hypersurfaces (ENGLISH)

Registration is closed (12:00, December 17).

**Jun-Muk Hwang**(Center for Complex Geometry, IBS, Korea)Growth vectors of distributions and lines on projective hypersurfaces (ENGLISH)

[ Abstract ]

For a distribution on a manifold, its growth vector is a finite sequence of integers measuring the dimensions of the directions spanned by successive Lie brackets of local vector fields belonging to the distribution. The growth vector is the most basic invariant of a distribution, but it is sometimes hard to compute. As an example, we discuss natural distributions on the spaces of lines covering hypersurfaces of low degrees in the complex projective space. We explain the ideas in a joint work with Qifeng Li where the growth vector is determined for lines on a general hypersurface of degree 4 and dimension 5.

For a distribution on a manifold, its growth vector is a finite sequence of integers measuring the dimensions of the directions spanned by successive Lie brackets of local vector fields belonging to the distribution. The growth vector is the most basic invariant of a distribution, but it is sometimes hard to compute. As an example, we discuss natural distributions on the spaces of lines covering hypersurfaces of low degrees in the complex projective space. We explain the ideas in a joint work with Qifeng Li where the growth vector is determined for lines on a general hypersurface of degree 4 and dimension 5.

### 2021/11/26

15:30-16:30 Online

Registration is closed (12:00, November 26).

Ricci flow on Fano manifolds (ENGLISH)

Registration is closed (12:00, November 26).

**Gang Tian**(BICMR, Peking University)Ricci flow on Fano manifolds (ENGLISH)

[ Abstract ]

Ricci flow was introduced by Hamilton in early 80s. It preserves the Kahlerian structure and has found many applications in Kahler geometry. In this expository talk, I will focus on Ricci flow on Fano manifolds. I will first survey some results in recent years, then I will discuss my joint work with Li and Zhu. I will also discuss the connection between the long time behavior of Ricci flow and some algebraic geometric problems for Fano manifolds.

Ricci flow was introduced by Hamilton in early 80s. It preserves the Kahlerian structure and has found many applications in Kahler geometry. In this expository talk, I will focus on Ricci flow on Fano manifolds. I will first survey some results in recent years, then I will discuss my joint work with Li and Zhu. I will also discuss the connection between the long time behavior of Ricci flow and some algebraic geometric problems for Fano manifolds.

### 2021/10/29

15:30-16:30 Online

Registration was closed

Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)

Registration was closed

**Takahito Kashiwabara**(Graduate School of Mathematical Sciences, University of Tokyo)Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)

### 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.