## Seminar information archive

Seminar information archive ～08/07｜Today's seminar 08/08 | Future seminars 08/09～

#### Information Mathematics Seminar

16:50-18:35 Room #128 (Graduate School of Math. Sci. Bldg.)

The role of cryptography (Japanese)

**Tatsuaki Okamoto**(NTT)The role of cryptography (Japanese)

[ Abstract ]

Explanation of the theory of cryptography

Explanation of the theory of cryptography

### 2023/03/28

#### Algebraic Geometry Seminar

10:00-11:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

On the canonical bundle formula in positive characteristic (English)

**Paolo Cascini**(Imperial College London)On the canonical bundle formula in positive characteristic (English)

[ Abstract ]

In a previous work in collaboration with F. Ambro, V. Shokurov and C. Spicer, we show that algebraically integrable foliations can be used to study the canonical bundle formula for fibrations which are not necessarily lc trivial.

I will discuss a work in progress by M. Benozzo on a generalisation of these results in positive characteristic.

In a previous work in collaboration with F. Ambro, V. Shokurov and C. Spicer, we show that algebraically integrable foliations can be used to study the canonical bundle formula for fibrations which are not necessarily lc trivial.

I will discuss a work in progress by M. Benozzo on a generalisation of these results in positive characteristic.

### 2023/03/24

#### Mathematical Biology Seminar

10:00-11:00 Online

Unexpected coexistence and extinction in an intraguild predation system (Japanese)

**Toshiyuki Namba**(Osaka Metropolitan University)Unexpected coexistence and extinction in an intraguild predation system (Japanese)

### 2023/03/14

#### Tuesday Seminar of Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Parameter reconstruction for degenerate parabolic equations (English)

https://forms.gle/nejpQS824vFKRbMQ6

**Piermarco Cannarsa**(University of Rome "Tor Vergata")Parameter reconstruction for degenerate parabolic equations (English)

[ Abstract ]

First, we study degenerate parabolic equations arising in climate dynamics, providing uniqueness and stability estimates for the determination of the insolation function. Then, we address several aspects of the reconstruction of the degenerate diffusion coefficient. Finally, we discuss systems of two equations including a vertical component into the model.

[ Reference URL ]First, we study degenerate parabolic equations arising in climate dynamics, providing uniqueness and stability estimates for the determination of the insolation function. Then, we address several aspects of the reconstruction of the degenerate diffusion coefficient. Finally, we discuss systems of two equations including a vertical component into the model.

https://forms.gle/nejpQS824vFKRbMQ6

### 2023/03/13

#### Colloquium

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

### 2023/03/10

#### Algebraic Geometry Seminar

13:15-14:45 Room #ハイブリッド開催/123 (Graduate School of Math. Sci. Bldg.)

On existence of flips for algebraically integrable foliations. (English)

**Paolo Cascini**(Imperical College London)On existence of flips for algebraically integrable foliations. (English)

[ Abstract ]

Assuming termination of (classical) flips in dimension r, we show that flips exist for any algebraically integrable foliation of rank r with log canonical singularities. Joint work with C. Spicer.

Assuming termination of (classical) flips in dimension r, we show that flips exist for any algebraically integrable foliation of rank r with log canonical singularities. Joint work with C. Spicer.

### 2023/03/08

#### Operator Algebra Seminars

16:45-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Structure and Inclusions of Twisted Araki-Woods Algebras (English)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Ricardo Correa da Silva**(Friedrich-Alexander-Universität Erlangen-Nürnberg)Structure and Inclusions of Twisted Araki-Woods Algebras (English)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Seminar on Probability and Statistics

14:00- Room # (Graduate School of Math. Sci. Bldg.)

Non-ergodic statistics for hamonizable stable processes (English)

https://docs.google.com/forms/d/e/1FAIpQLSet6w12XsqdCGQ8yEe4sOqRlCOhhrJXeKl5H7lMaRy4LZhmqQ/viewform

**Evgeny Spodarev**( Ulm University, Germany)Non-ergodic statistics for hamonizable stable processes (English)

[ Abstract ]

We consider stationary real harmonizable symmetric α-stable processes X={X(t):t∈ℝ} with a finite control measure. Assuming the control measure is symmetric and absolutely continuous with respect to the Lebesgue measure on the real line, we refer to its density function as the spectral density of X. Standard methods for statistical inference on stable processes cannot be applied as harmonizable stable processes are non-ergodic.

A stationary real harmonizable symmetric α-stable process X admits a LePage series representation and is conditionally Gaussian which allows us to derive the non-ergodic limit of sample functions on X. In particular, we give an explicit expression for the non-ergodic limits of the empirical characteristic function of X and the lag process {X(t+h)−X(t):t∈ℝ} with h>0, respectively.

The process admits an equivalent representation as a series of sinusoidal waves with random frequencies whose probability density function is in fact the (normalized) spectral density of X. Using the strongly consistent frequency estimation via periodograms we present a strongly consistent estimator of the spectral density which is based only on one sampled path of X. The periodogram computation is fast and efficient, and our method is not affected by the non-ergodicity of X. Most notably no prior knowledge on parameters of the process such as its index of stability α is needed.

References:

[1] L.V. Hoang, E. Spodarev, "Inversion of alpha-sine and alpha-cosine transforms on R", Inverse Problems 37 (2021), 085008

[2] L.V. Hoang, E. Spodarev, "Non-ergodic statistics and spectral density estimation for stationary real harmonizable symmetric α-stable processes", Preprint arXiv:2209.04315, submitted, 2022.

[ Reference URL ]We consider stationary real harmonizable symmetric α-stable processes X={X(t):t∈ℝ} with a finite control measure. Assuming the control measure is symmetric and absolutely continuous with respect to the Lebesgue measure on the real line, we refer to its density function as the spectral density of X. Standard methods for statistical inference on stable processes cannot be applied as harmonizable stable processes are non-ergodic.

A stationary real harmonizable symmetric α-stable process X admits a LePage series representation and is conditionally Gaussian which allows us to derive the non-ergodic limit of sample functions on X. In particular, we give an explicit expression for the non-ergodic limits of the empirical characteristic function of X and the lag process {X(t+h)−X(t):t∈ℝ} with h>0, respectively.

The process admits an equivalent representation as a series of sinusoidal waves with random frequencies whose probability density function is in fact the (normalized) spectral density of X. Using the strongly consistent frequency estimation via periodograms we present a strongly consistent estimator of the spectral density which is based only on one sampled path of X. The periodogram computation is fast and efficient, and our method is not affected by the non-ergodicity of X. Most notably no prior knowledge on parameters of the process such as its index of stability α is needed.

References:

[1] L.V. Hoang, E. Spodarev, "Inversion of alpha-sine and alpha-cosine transforms on R", Inverse Problems 37 (2021), 085008

[2] L.V. Hoang, E. Spodarev, "Non-ergodic statistics and spectral density estimation for stationary real harmonizable symmetric α-stable processes", Preprint arXiv:2209.04315, submitted, 2022.

https://docs.google.com/forms/d/e/1FAIpQLSet6w12XsqdCGQ8yEe4sOqRlCOhhrJXeKl5H7lMaRy4LZhmqQ/viewform

### 2023/02/22

#### Applied Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Long time decay of Fokker-Planck equations with confining drift (ENGLISH)

https://forms.gle/SCyZWtfC5bNGadxE8

**Alessio Porretta**(University of Rome Tor Vergata)Long time decay of Fokker-Planck equations with confining drift (ENGLISH)

[ Abstract ]

The convergence to equilibrium of Fokker-Planck equations with confining drift is a classical issue, starting with the basic model of the Ornstein-Uhlenbeck process. I will discuss a new approach to obtain estimates on the time decay rate, which applies to both local and nonlocal diffusions. This is based on duality arguments and oscillation estimates for transport-diffusion equations, which are reminiscent of coupling methods used in probabilistic approaches.

[ Reference URL ]The convergence to equilibrium of Fokker-Planck equations with confining drift is a classical issue, starting with the basic model of the Ornstein-Uhlenbeck process. I will discuss a new approach to obtain estimates on the time decay rate, which applies to both local and nonlocal diffusions. This is based on duality arguments and oscillation estimates for transport-diffusion equations, which are reminiscent of coupling methods used in probabilistic approaches.

https://forms.gle/SCyZWtfC5bNGadxE8

### 2023/02/20

#### Algebraic Geometry Seminar

10:00-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The 4th lecture of series talks

K-stability of Fano varieties. (English)

The 4th lecture of series talks

**Chenyang Xu**(Princeton University)K-stability of Fano varieties. (English)

[ Abstract ]

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

### 2023/02/17

#### Algebraic Geometry Seminar

10:00-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

The 3rd lecture of series talks

K-stability of Fano varieties. ( English)

The 3rd lecture of series talks

**Chenyang Xu**(Princeton University)K-stability of Fano varieties. ( English)

[ Abstract ]

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

### 2023/02/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On a presentation to introduce function theory of several variables (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Junjiro Noguchi**(The University of Tokyo)On a presentation to introduce function theory of several variables (Japanese)

[ Abstract ]

微積分は，主に1変数の理論を講義するが，後半で多変数の内容を入れる．同じ様に，複素解析（函数論）でも，一変数の後につなぎよく，多変数の講義を段差なく行えるようにしたい．

モデルケースとして'リーマンの写像定理'がある．現在多くの教科書に書かれているモンテルの定理による初等的な証明(1922, Fejér--Riesz)まで，もとのリーマンの学位論文(1851)から約70年の歳月がかかている．

岡理論・多変数関数論基礎についてみると，Oka IX (1953)より本年でやはり70年たつが，あまり'初等化'の方面へは進展していないように思う．こここでは，学部の複素解析のコースで'リーマンの写像定理'の後に，段差無く完全証明付きで岡理論・多変数関数論基礎を講義する展開を考える．

初等化には，岡のオリジナル法(1943未発表, IX 1953)を第1連接定理に基づき展開するのが適当であることを紹介したい．学部講義の数学内容に日本人による成果が入ることで，学生のモチベーションに好効果を与えるであろうことも期待したい．

時間が許せば，擬凸問題解決の岡のオリジナル法と別証明とされるGrauertの証明との間のFredholm定理をめぐる類似性についても述べたい．

[ Reference URL ]微積分は，主に1変数の理論を講義するが，後半で多変数の内容を入れる．同じ様に，複素解析（函数論）でも，一変数の後につなぎよく，多変数の講義を段差なく行えるようにしたい．

モデルケースとして'リーマンの写像定理'がある．現在多くの教科書に書かれているモンテルの定理による初等的な証明(1922, Fejér--Riesz)まで，もとのリーマンの学位論文(1851)から約70年の歳月がかかている．

岡理論・多変数関数論基礎についてみると，Oka IX (1953)より本年でやはり70年たつが，あまり'初等化'の方面へは進展していないように思う．こここでは，学部の複素解析のコースで'リーマンの写像定理'の後に，段差無く完全証明付きで岡理論・多変数関数論基礎を講義する展開を考える．

初等化には，岡のオリジナル法(1943未発表, IX 1953)を第1連接定理に基づき展開するのが適当であることを紹介したい．学部講義の数学内容に日本人による成果が入ることで，学生のモチベーションに好効果を与えるであろうことも期待したい．

時間が許せば，擬凸問題解決の岡のオリジナル法と別証明とされるGrauertの証明との間のFredholm定理をめぐる類似性についても述べたい．

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2023/02/10

#### Tokyo-Nagoya Algebra Seminar

17:00-18:30 Online

Please see the reference URL for details on the online seminar.

Silting discrete代数上のsemibrick複体とspherical objects (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

Please see the reference URL for details on the online seminar.

**Wahei Hara**(University of Glasgow)Silting discrete代数上のsemibrick複体とspherical objects (Japanese)

[ Reference URL ]

http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

### 2023/02/09

#### Lectures

15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Diffusive behavior in completely integrable infinite dynamics (English)

**Stefano Olla**(Dauphine大学)Diffusive behavior in completely integrable infinite dynamics (English)

[ Abstract ]

We investigate the macroscopic behaviour of the density fluctuations of a one dimensional dynamics of hard rods with random length. After recentering on the effective velocity the density fluctuations of particles of a given velocity v will evolve on the diffusive scaling driven by a brownian motion with a diffusivity depending on v. This rigid evolution of fluctuations is expected in other completely integrable systems (Box-Ball, Toda Lattice,..), in contrast with the behavior in chaotic dynamics.

Joint work with Pablo Ferrari (U. Buenos Aires).

We investigate the macroscopic behaviour of the density fluctuations of a one dimensional dynamics of hard rods with random length. After recentering on the effective velocity the density fluctuations of particles of a given velocity v will evolve on the diffusive scaling driven by a brownian motion with a diffusivity depending on v. This rigid evolution of fluctuations is expected in other completely integrable systems (Box-Ball, Toda Lattice,..), in contrast with the behavior in chaotic dynamics.

Joint work with Pablo Ferrari (U. Buenos Aires).

### 2023/02/06

#### Applied Analysis

16:00-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)

Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)

https://forms.gle/nKa4XATuuGPwZWbUA

**Marek Fila**(Comenius University) 16:00-17:00Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)

[ Abstract ]

We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.

We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.

**Petra Mackova**(Comenius University) 17:10-18:10Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)

[ Abstract ]

This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions. This is a joint work with M. Fila.

[ Reference URL ]This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions. This is a joint work with M. Fila.

https://forms.gle/nKa4XATuuGPwZWbUA

#### Algebraic Geometry Seminar

13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

The 2nd lecture of series talks.

K-stability of Fano varieties. (English)

The 2nd lecture of series talks.

**Chenyang Xu**(Princeton University)K-stability of Fano varieties. (English)

[ Abstract ]

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

### 2023/01/31

#### Algebraic Geometry Seminar

14:30-16:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

Some properties of splinters via ultrapower (English)

**Shiji Lyu**(Princeton University)Some properties of splinters via ultrapower (English)

[ Abstract ]

A Noetherian (reduced) ring is called a splinter if it is a direct summand of every finite ring extension of it. This notion is related to various interesting notions of singularities, but far less properties are known about splinters.

In this talk, we will discuss the question of "regular ascent"; in the simplest (but already essential) form, we ask, for a Noetherian splinter R, is the polynomial ring R[X] always a splinter. We will see how ultrapower, a construction mainly belonging to model theory, is involved.

A Noetherian (reduced) ring is called a splinter if it is a direct summand of every finite ring extension of it. This notion is related to various interesting notions of singularities, but far less properties are known about splinters.

In this talk, we will discuss the question of "regular ascent"; in the simplest (but already essential) form, we ask, for a Noetherian splinter R, is the polynomial ring R[X] always a splinter. We will see how ultrapower, a construction mainly belonging to model theory, is involved.

### 2023/01/27

#### Algebraic Geometry Seminar

13:00-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

4 lectures; 1/27: 13:00―14:30 Room056, 2/6: 13:00―14:30, Room 123, 2/17: 10:00―11:30,Room 123室 2/20 10:00ー11:30, Room:056室

K-stability of Fano varieties (English)

[ Abstract ]

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

4 lectures; 1/27: 13:00―14:30 Room056, 2/6: 13:00―14:30, Room 123, 2/17: 10:00―11:30,Room 123室 2/20 10:00ー11:30, Room:056室

**Chenyang Xu**(Princeton University)K-stability of Fano varieties (English)

The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

#### thesis presentations

9:15-10:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Integral Derived Invariants and Motives

(整数導来不変量とモチーフ)

**MATSUMOTO Keiho**(Graduate School of Mathematical Sciences University of Tokyo)Integral Derived Invariants and Motives

(整数導来不変量とモチーフ)

#### thesis presentations

9:15-10:30 Room #122 (Graduate School of Math. Sci. Bldg.)

On classification of 2-generated axial algebras of Jordan and Majorana type

(Jordan型及びMajorana型の二元生成軸代数の分類について)

**YABE Takahiro**(Graduate School of Mathematical Sciences University of Tokyo)On classification of 2-generated axial algebras of Jordan and Majorana type

(Jordan型及びMajorana型の二元生成軸代数の分類について)

#### thesis presentations

9:15-10:30 Room #126 (Graduate School of Math. Sci. Bldg.)

On microscopic interpretation for convex integration and self- similar structure of vortices in turbulence

(凸積分法に関する微視的表現と乱流渦の自己相似構造について)

**TSURUHASHI Tomonori**(Graduate School of Mathematical Sciences University of Tokyo)On microscopic interpretation for convex integration and self- similar structure of vortices in turbulence

(凸積分法に関する微視的表現と乱流渦の自己相似構造について)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

A group action on higher Chow cycles on a family of Kummer surfaces

(あるクンマー曲面族の上の高次チャウサイクルへの群作用について)

**SATO Ken**(Graduate School of Mathematical Sciences University of Tokyo)A group action on higher Chow cycles on a family of Kummer surfaces

(あるクンマー曲面族の上の高次チャウサイクルへの群作用について)

#### thesis presentations

11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Manifolds Graded by an Arbitrary Abelian Group

(任意のアーベル群で次数付けられた多様体)

**HARAKO Shuichi**(Graduate School of Mathematical Sciences University of Tokyo)Manifolds Graded by an Arbitrary Abelian Group

(任意のアーベル群で次数付けられた多様体)

#### thesis presentations

11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Various problems for properties of solutions to fractional partial differential equations

(非整数階偏微分方程式の解の性質に関する諸問題)

**SATO Shoichi**(Graduate School of Mathematical Sciences University of Tokyo)Various problems for properties of solutions to fractional partial differential equations

(非整数階偏微分方程式の解の性質に関する諸問題)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Integral Structures in the Local Algebra of a Singularity

(特異点の局所代数の整構造について)

**ZHA Chenghan**(Graduate School of Mathematical Sciences University of Tokyo)Integral Structures in the Local Algebra of a Singularity

(特異点の局所代数の整構造について)

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