## Colloquium

Seminar information archive ～09/15｜Next seminar｜Future seminars 09/16～

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**

### 2024/07/26

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

Mean value expansions for solutions to general elliptic and parabolic equations (English)

https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

**Juan Manfredi**(University of Pittsburgh)Mean value expansions for solutions to general elliptic and parabolic equations (English)

[ Abstract ]

Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.

The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.

I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.

[ Reference URL ]Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.

The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.

I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.

https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url

### 2024/06/21

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

The minimal exponent of hypersurface singularities (English)

https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing

In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.

**Mircea Mustaţă**(The University of Michigan)The minimal exponent of hypersurface singularities (English)

[ Abstract ]

The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.

[ Reference URL ]The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.

https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing

### 2024/05/31

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].

Introduction to large cardinals (JAPANESE)

https://forms.gle/ZmHhZW6bxUyKewro8

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Hiroshi Sakai**(Graduate School of Mathematical Sciences, The University of Tokyo)Introduction to large cardinals (JAPANESE)

[ Abstract ]

Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.

[ Reference URL ]Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.

https://forms.gle/ZmHhZW6bxUyKewro8

### 2024/04/26

15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)

Riemannian manifolds and their limit spaces (JAPANESE)

**Shouhei Honda**(Graduate School of Mathematical Sciences, University of Tokyo)Riemannian manifolds and their limit spaces (JAPANESE)

[ Abstract ]

The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.

The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.

### 2024/03/14

14:30-17:00 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].

Many years from now (JAPANESE)

https://forms.gle/m38f1KRi67ECuA7MA

Mathematics, which I eventually found that I like: from the viewpoint of some marginal areas (JAPANESE)

https://forms.gle/m38f1KRi67ECuA7MA

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Toshiyasu Arai**(Graduate School of Mathematical Sciences, The University of Tokyo) 14:30-15:30Many years from now (JAPANESE)

[ Abstract ]

I have been studying proof theory since the 1980's. In this talk I will talk about what happened to me in these 40 years, and let me report the latest result on ordinal analysis.

[ Reference URL ]I have been studying proof theory since the 1980's. In this talk I will talk about what happened to me in these 40 years, and let me report the latest result on ordinal analysis.

https://forms.gle/m38f1KRi67ECuA7MA

**Masahiro Yamamoto**(Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00Mathematics, which I eventually found that I like: from the viewpoint of some marginal areas (JAPANESE)

[ Abstract ]

Looking back on my experiences over 40 years, I have been convinced that I have been loving my own mathematics among others.

After all, I can sum up as that all my mathematics are concerned with the three topics: control theories, inverse problems and time-fractional partial differential equations. Some of these research fields has already developed to major topics, while others keep still minor interests.

When I started studies on inverse problems in 1980's, there were very few population of mathematicians as specialists in Japan. In particular, inverse problems did not call great attention of mathematicians and were understood as marginal mathematical topics in spite of practical significance and demands On the other hand, possibly available methodologies and ideas have been exploited and integrated gradually. As consequence, main research partners have been outside Japan.

I have been enjoying not only the research contents, but also such wider collaboration.

Aiming at non-meaningless reference for the youngers, and trying not to be too retrospective, I will describe how I have done in mathematics as well as my research contents.

[ Reference URL ]Looking back on my experiences over 40 years, I have been convinced that I have been loving my own mathematics among others.

After all, I can sum up as that all my mathematics are concerned with the three topics: control theories, inverse problems and time-fractional partial differential equations. Some of these research fields has already developed to major topics, while others keep still minor interests.

When I started studies on inverse problems in 1980's, there were very few population of mathematicians as specialists in Japan. In particular, inverse problems did not call great attention of mathematicians and were understood as marginal mathematical topics in spite of practical significance and demands On the other hand, possibly available methodologies and ideas have been exploited and integrated gradually. As consequence, main research partners have been outside Japan.

I have been enjoying not only the research contents, but also such wider collaboration.

Aiming at non-meaningless reference for the youngers, and trying not to be too retrospective, I will describe how I have done in mathematics as well as my research contents.

https://forms.gle/m38f1KRi67ECuA7MA

### 2024/01/19

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].

Lagrangian correspondence and Floer theory (JAPANESE)

https://forms.gle/7T6ewXWtrVEKM9dY7

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Kenji Fukaya**(Simons Center for Geometry and Physics)Lagrangian correspondence and Floer theory (JAPANESE)

[ Abstract ]

It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).

Gromov-Witten invariant is not functorial for this functor.

However Lagrangian Floer theory is functorial.

I will explain present status of the study of this functoriality and a few of its applications.

[ Reference URL ]It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).

Gromov-Witten invariant is not functorial for this functor.

However Lagrangian Floer theory is functorial.

I will explain present status of the study of this functoriality and a few of its applications.

https://forms.gle/7T6ewXWtrVEKM9dY7

### 2023/12/15

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].

Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

https://forms.gle/42wEF5c2pqsqrHqR7

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Mikiya Masuda**(Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)

[ Abstract ]

Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

[ Reference URL ]Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.

https://forms.gle/42wEF5c2pqsqrHqR7

### 2023/10/27

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].

Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)

https://forms.gle/9xDcHfHXFFHPfsKW6

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].

**Jenn-Nan Wang**(National Taiwan University)Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)

[ Abstract ]

According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.

[ Reference URL ]According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.

https://forms.gle/9xDcHfHXFFHPfsKW6

### 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].

Quantum Field Theory in Mathematics (JAPANESE)

https://forms.gle/igR5ZB5AwginXBt49

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 ]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.

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

Did you say $p$-adic? (English)

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!

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

Billiards and Moduli Spaces (ENGLISH)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD

**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 ]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.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD

### 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.

Locally stable regression (日本語)

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.

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]

On quantum topology (日本語)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM

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 ]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.

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)

(JAPANESE)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZElcO2oqTgoG9a1JSawX0kFRMSFheEptcaA

(JAPANESE)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkceigrj4tEt0AydbnE8PVJmIS6xLanDAe

From higher dimensional class field theory to a new theory of motives (ENGLISH)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZAqf-ioqz8jG9BWefiIf_zTJ1t7R7VG1beV

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) 16:00-17:00From 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 ]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.

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].

Kyiv formula and its applications (ENGLISH)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P

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 ]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.

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].

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.