## Colloquium

Organizer(s) ABE Noriyuki, IWAKI Kohei, KAWAZUMI Nariya (chair), KOIKE Yuta https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html

Seminar information archive

### 2023/07/21

15:30-16:30   Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Masahito Yamazaki (Kavli Institute for the Physics and Mathematics of the Uniiverse, the University of Tokyo)
Quantum Field Theory in Mathematics (JAPANESE)
[ Abstract ]
While quantum field theory has primarily been a theory in physics, it has also been a source of new ideas in mathematics, and has facilitated interactions between different branches of mathematics. There have also been many attempts to formulate quantum field theories themselves rigorously in mathematics. In this lecture we will discuss some examples of research in knot invariants and integrable models, to illustrate the impact of quantum field theories and string theory in modern mathematics.
[ Reference URL ]
https://forms.gle/igR5ZB5AwginXBt49

### 2023/06/30

15:30-16:30   Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/z22nKn1NUrT41qiR7
Guy Henniart (Université Paris-Saclay)
Did you say $p$-adic? (English)
[ Abstract ]
I am a Number Theorist and $p$ is a prime number. The $p$-adic numbers are obtained by pushing to the limit a simple idea. Suppose that you want to know which integers are sums of two squares. If an integer $x$ is odd, its square has the form $8k+1$; if $x$ is even, its square is a multiple of $4$. So the sum of two squares has the form $4k$, $4k+1$ or $4k+2$, never $4k+3$ ! More generally if a polynomial equation with integer coefficients has no integer solution if you work «modulo $N$» that is you neglect all multiples of an integer $N$, then a fortiori it has no integer solution. By the Chinese Remainder Theorem, working modulo $N$ is the same as working modulo $p^r$ where $p$ runs through prime divisors of $N$ and $p^r$ is the highest power of $p$ dividing $N$. Now work modulo $p$, modulo $p^2$, modulo $p^3$, etc. You have invented the $p$-adic integers, which are, I claim, as real as the real numbers and (nearly) as useful!

### 2023/06/05

15:30-16:30   Online
Curtis T McMullen (Harvard University)
Billiards and Moduli Spaces (ENGLISH)
[ Abstract ]
The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.
In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.
A variety of open problems will be mentioned along the way.
[ Reference URL ]

### 2023/05/19

15:30-16:30   Room #大講義室 (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/J4Wo8N6CbLmYiprUA.
Hiroki Masuda (Graduate School of Mathematical Sciences, the University of Tokyo)
Locally stable regression (日本語)
[ Abstract ]
A non-ergodic model structure naturally emerges in estimating a stochastic process model observed at high frequency over a fixed period. The probability structure of the driving noise determines whether or not the characteristics of the model can be statistically estimated. However, it is difficult to describe the possible phenomena in general when the noise is non-Gaussian. Building on such backgrounds, we will present some recent results on non-ergodic regression modeling driven by a locally stable Lévy process: the construction of an explicit non-Gaussian quasi-maximum likelihood and the asymptotic distribution of the corresponding estimator. We will also present a method for relative model comparison and its theoretical property.

### 2023/04/28

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]
Kazuo Habiro (Graduate School of Mathematical Sciences, the University of Tokyo)
On quantum topology (日本語)
[ Abstract ]
I started my research from surgery theory of knots and 3-manifolds. This is related to finite type invariants, which was studied intensively at that time. I obtained a result which characterises the information that is carried by finite type invariants in terms of clasper surgery. After that, I have studied quantum invariants of integral homology spheres, Kirby calculus of framed links, quantum invariants of bottom tangles, functorialization of Le-Murakami-Ohtsuki invariants, quantum fundamental groups and quantum representation variety of 3-manifolds, traces of categorified quantum groups, etc. I would like to reflect on these studies and also discuss future prospects.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM

### 2023/03/13

13:00-17:00   Hybrid
Registration for online participation: [Reference URL], Application for onsite participation: https://forms.gle/2eDKDtNsTounyoXw6 (Update: Mar. 5)
Masahiko Kanai ( Graduate School of Mathematical Sciences, the University of Tokyo) 13:00-14:00
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZElcO2oqTgoG9a1JSawX0kFRMSFheEptcaA
Hisashi Inaba (Graduate School of Mathematical Sciences, the University of Tokyo) 14:30-15:30
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkceigrj4tEt0AydbnE8PVJmIS6xLanDAe
Shuji Saito ( Graduate School of Mathematical Sciences, the University of Tokyo) 16:00-17:00
From higher dimensional class field theory to a new theory of motives (ENGLISH)
[ Abstract ]
My first research was on Higher Dimensional Class Theory done in collaboration with Kazuya Kato. That was 40 years ago. The classical class field theory is a theory that controls the Galois group of the maximal abelian extension of a number field (a finite extension of the field of rational numbers) using only information intrinsic to the field (e.g., its ideal class group). Higher dimensional class field theory is an extension of this theory to the case of finitely generated fields over the field of rational numbers or a finite field. It is formulated as an arithmetic algebro-geometric problem using scheme theory.

In this talk, I will start with a review of the classical class field theory that can be understood by undergraduates and explain how higher dimensional class field theory is formulated in a way that is easy to understand even for non-specialists. I will also briefly explain an improvement of Kato-Saito's higher-dimensional class field theory that I made with Moritz Kerz in 2016, and how it triggered a recent new development of theory of motive. In particular, I will discuss the relationship between the new theory and ramification theory (of which Takeshi Saito is a world leader), which until now has had no interaction with theory of motives.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZAqf-ioqz8jG9BWefiIf_zTJ1t7R7VG1beV

### 2023/01/20

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].
Mikhail Bershtein (HSE University, Skoltech)
Kyiv formula and its applications (ENGLISH)
[ Abstract ]
The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P

### 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].
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 ]
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.
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 ]
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)
[ 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 ]
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].
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 ]
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)
[ 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.

### 2022/04/22

15:30-16:30   Online
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.

### 2022/03/26

16:00-17:00   Online
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).
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).
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.

### 2021/11/26

15:30-16:30   Online
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.

### 2021/10/29

15:30-16:30   Online
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)
[ 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.
Hiromi Yokoyama (Kavli IPMU) 16:00-17:00
What'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.

### 2021/07/30

15:30-16:30   Online
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).
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).
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.

### 2021/04/30

15:30-16:30   Online
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.

### 2021/03/19

15:00-17:30   Online
Yoshikazu Giga (University of Tokyo) 15:00-16:00
Effects of viscosity and diffusion described by differential equations (JAPANESE)
Toshitake Kohno (Meiji University/University of Tokyo) 16:30-17:30
Monodromy representations in higher categories and iterated integrals (JAPANESE)

### 2021/01/22

15:30-16:30   Online