## Seminar information archive

Seminar information archive ～10/09｜Today's seminar 10/10 | Future seminars 10/11～

### 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)

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)

[ 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.

#### 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)

#### thesis presentations

13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Refinement of Young’s convolution inequality on locally compact groups and generalizations of related inequalities

(局所コンパクト群上のYoung の畳み込み不等式の精密化と関連の不等式の拡張)

**SATOMI Takashi**(Graduate School of Mathematical Sciences University of Tokyo)Refinement of Young’s convolution inequality on locally compact groups and generalizations of related inequalities

(局所コンパクト群上のYoung の畳み込み不等式の精密化と関連の不等式の拡張)

### 2023/01/26

#### thesis presentations

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

Fourier-Mukai transforms for non-commutative complex tori

(非可換複素トーラスのフーリエ・向井変換)

**OKUDA Nobuki**(Graduate School of Mathematical Sciences University of Tokyo)Fourier-Mukai transforms for non-commutative complex tori

(非可換複素トーラスのフーリエ・向井変換)

#### thesis presentations

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

Earthquake theorem and cluster algebras

(地震定理とクラスター代数)

**ASAKA Takeru**(Graduate School of Mathematical Sciences University of Tokyo)Earthquake theorem and cluster algebras

(地震定理とクラスター代数)

#### thesis presentations

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

On universality of the Kardar-Parisi-Zhang equation in high temperature regime

(高温相におけるKardar-Parisi-Zhang 方程式の普遍性について)

**HAYASHI Kohei**(Graduate School of Mathematical Sciences University of Tokyo)On universality of the Kardar-Parisi-Zhang equation in high temperature regime

(高温相におけるKardar-Parisi-Zhang 方程式の普遍性について)

#### thesis presentations

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

Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees

(錐予想, 自己同型と算術次数の研究)

**WANG LONG**(Graduate School of Mathematical Sciences University of Tokyo)Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees

(錐予想, 自己同型と算術次数の研究)

#### thesis presentations

13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Finite path integral model and toric code based on homological algebra

(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)

**KIM Minkyu**(Graduate School of Mathematical Sciences University of Tokyo)Finite path integral model and toric code based on homological algebra

(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)

#### thesis presentations

14:45-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras

(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)

**TSURUSAKI Hisanori**(Graduate School of Mathematical Sciences University of Tokyo)Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras

(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)

### 2023/01/20

#### Colloquium

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

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

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

Tropical cluster transformations and train track splittings (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.

**Shunsuke Kano**(Tohoku University)Tropical cluster transformations and train track splittings (Japanese)

[ Reference URL ]

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

### 2023/01/19

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Code-based cryptography and its decoding algorithm (Japanese)

**Shintaro Narisada**(KDDI Research, Inc.)Code-based cryptography and its decoding algorithm (Japanese)

[ Abstract ]

This talk overviews code-based cryptography and its decoding algorithm called Information Set Decoding (ISD). All lectures will be given in Japanese.

This talk overviews code-based cryptography and its decoding algorithm called Information Set Decoding (ISD). All lectures will be given in Japanese.

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