## Seminar information archive

Seminar information archive ～04/12｜Today's seminar 04/13 | Future seminars 04/14～

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Combinatorial preprocessing methods for differential-algebraic equations (Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

**Taihei Oki**(The University of Tokyo)Combinatorial preprocessing methods for differential-algebraic equations (Japanese)

[ Reference URL ]

https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/

### 2023/04/24

#### Seminar on Geometric Complex Analysis

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

On site+Zoom

Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

On site+Zoom

**Takeo Ohsawa**(Nogoya Universiry)Guan's theorems on optimal strong openness and concavity of minimal $L^2$ integrals (日本語)

[ Abstract ]

Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.

THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$

\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},

$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.

This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.

[ Reference URL ]Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.

THEOREM. Let $\Omega$ be a pseudoconvex domain in $\mathbb{C}^n$ and let $\varphi$ be a negative psh function on $\Omega$ such that $\int_\Omega{e^{-\varphi}}<\infty$. Then, $e^{-p\varphi}\in L^1_{\text{loc}}$ around $x$ for any $x\in\Omega$ and $p>1$ satisfying the inequality $$

\frac{p}{p-1}>\frac{\int_\Omega{e^{-\varphi}}}{K_\Omega(x)},

$$ where $K_\Omega$ denotes the diagonalized Bergman kernel of $\Omega$.

This remarkable result is a consequence of a basic property of the minimal $L^2$ integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A

#### Tokyo Probability Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)

**Charles Bordenave**(Institut de Mathématiques de Marseille)Mobility edge, the Poisson Infinite weighted tree of Aldous and Lévy Matrices (English)

[ Abstract ]

Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).

Anderson's 1958 paper on wave scattering in disordered media is still of central importance in contemporary mathematical physics. In this talk, we will present recent progress in understanding the phenomena of localization / delocalization of eigenwaves for some random operators. These operators are built on random trees introduced by Aldous and these are the scaling limits of heavy-tailed random matrices, the Lévy matrices. The focus will be put on the existence of a mobility edge, that is to say of かn abrupt transition between localization and delocalization of eigenwaves. It is a work in collaboration with Amol Aggarwal (Columbia) and Patrick Lopatto (NYU).

#### Infinite Analysis Seminar Tokyo

16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Euler type integral formulas and hypergeometric solutions for

variants of the $q$ hypergeometric equations.

(Japanese)

**Takahiko Nobukawa**(Kobe University )Euler type integral formulas and hypergeometric solutions for

variants of the $q$ hypergeometric equations.

(Japanese)

[ Abstract ]

We know that Papperitz's differential equation is essentially obtained from

Gauss' hypergeometric equation by applying a Moebius transformation,

implying that we have Euler type integral formulas or hypergeometric solutions.

The variants of the $q$ hypergeometric equations, introduced by

Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order

$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.

This motivates us for deriving Euler type integral formulas and hypergeometric solutions

for the pertinent $q$-difference systems. If time admits, I explain

the relation with $q$-analogues of Kummer's 24 solutions,

or the variants of multivariate $q$-hypergeometric functions.

This talk is based on the collaboration with Taikei Fujii.

We know that Papperitz's differential equation is essentially obtained from

Gauss' hypergeometric equation by applying a Moebius transformation,

implying that we have Euler type integral formulas or hypergeometric solutions.

The variants of the $q$ hypergeometric equations, introduced by

Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order

$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.

This motivates us for deriving Euler type integral formulas and hypergeometric solutions

for the pertinent $q$-difference systems. If time admits, I explain

the relation with $q$-analogues of Kummer's 24 solutions,

or the variants of multivariate $q$-hypergeometric functions.

This talk is based on the collaboration with Taikei Fujii.

### 2023/04/21

#### Tokyo-Nagoya Algebra Seminar

13:00-14:30 Online

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

Categorifications of deformed Cartan matrices (Japanese)

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

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

**Kota Murakami**(University of Tokyo)Categorifications of deformed Cartan matrices (Japanese)

[ Abstract ]

In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.

In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).

[ Reference URL ]In a series of works of Gei\ss-Leclerc-Schr\″oer, they introduced a version of preprojective algebra associated with a symmetrizable generalized Cartan matrix and its symmetrizer. For finite type, it can be regarded as an un-graded analogue of Jacobian algebra of certain quiver with potential appeared in the theory of (monoidal) categorification of cluster algebras.

In this talk, we will present an interpretation of graded structures of the preprojective algebra of general type, in terms of a multi-parameter deformation of generalized Cartan matrix and relevant combinatorics motivated from several contexts in the theory of quantum loop algebras or quiver $\mathcal{W}$-algebras. From the vantage point of the representation theory of preprojective algebra, we will prove several purely combinatorial properties of these concepts. This talk is based on a joint work with Ryo Fujita (RIMS).

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

#### Algebraic Geometry Seminar

14:00-15:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Endomorphisms of varieties and Bott vanishing (Japanese)

**Tatsuro Kawakami**(Kyoto University)Endomorphisms of varieties and Bott vanishing (Japanese)

[ Abstract ]

In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.

In this talk, we show that a projective variety with an int-amplified endomorphism of degree invertible in the base field satisfies Bott vanishing. This is a new way to analyze which varieties have nontrivial endomorphisms. In particular, we extend some classification results on varieties admitting endomorphisms (for Fano threefolds of Picard number one and several other cases) to any characteristic. This talk is based on joint work with Burt Totaro.

#### Algebraic Geometry Seminar

12:45-13:45 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)

ACC of plc thresholds (English)

**Sung Rak Choi**(Yonsei University )ACC of plc thresholds (English)

[ Abstract ]

The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.

We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.

The notion of potential pairs was developed as a means to bound the singularities while running the anti-MMP. They behave similarly with the usual klt, lc pairs.

We introduce potential log canonical threshold and prove that the set of these thresholds also satisfies the ascending chain condition (ACC). We also study the relation with the complements. This is a joint work with Sungwook Jang.

### 2023/04/20

#### Information Mathematics Seminar

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

The basics of cryptography (Japanese)

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

[ Abstract ]

Explanation of the basics of cryptography

Explanation of the basics of cryptography

### 2023/04/19

#### Number Theory Seminar

17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

The conjugate uniformization in the semistable case (English)

https://sites.google.com/site/nclmzzr/

**Nicola Mazzari**(University of Padua)The conjugate uniformization in the semistable case (English)

[ Abstract ]

We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.

We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.

[ Reference URL ]We will review some recent results by Iovita-Morrow-Zaharescu about p-adic uniformization of abelian varieties with good reduction. Most of it relies on the theory developed by Fontaine especially about almost Cp-representations. These results were recently generalised by Howe-Morrow-Wear, via p-divisible groups.

We will explain how to treat the semistable case with focus on some really basic example, like the Tate elliptic curve.

https://sites.google.com/site/nclmzzr/

### 2023/04/18

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Representation theory of subregular W-algebras and principal W-superalgebras (English)

[ Reference URL ]

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

**Naoki Genra**(Univ. Tokyo)Representation theory of subregular W-algebras and principal W-superalgebras (English)

[ Reference URL ]

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

#### Operator Algebra Seminars

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Representation theory of subregular W-algebras and principal W-superalgebras

[ Reference URL ]

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

**Naoki Genra**(Univ. Tokyo)Representation theory of subregular W-algebras and principal W-superalgebras

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

A crossed homomorphism on a big mapping class group (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Shuhei Maruyama**(Chuo University)A crossed homomorphism on a big mapping class group (JAPANESE)

[ Abstract ]

Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.

[ Reference URL ]Big mapping class groups are mapping class groups of surfaces of infinite type. Calegari and Chen determined the second (co)homology group of the mapping class group of the sphere minus a Cantor set. They also raised related questions: one of the questions asks an explicit form of certain crossed homomorphisms on the big mapping class group. In this talk, we provide a construction of crossed homomorphisms via group actions on the circle, which answers the question of Calegari and Chen.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023/04/17

#### Tokyo Probability Seminar

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)

**清水良輔**(早稲田大学)Construction of Sobolev spaces and energies on the Sierpinski carpet (Japanese)

### 2023/04/13

#### Information Mathematics Seminar

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

Certification and signature

------Foundation of cryptography (Japanese)

**Tatsuaki Okamoto**(NTT)Certification and signature

------Foundation of cryptography (Japanese)

[ Abstract ]

Explanation on certification and signature.

Explanation on certification and signature.

### 2023/04/11

#### Tuesday Seminar on Topology

17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)

Pre-registration required. See our seminar webpage.

On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

Pre-registration required. See our seminar webpage.

**Kazuo Habiro**(The Univesity of Tokyo)On the stable cohomology of the (IA-)automorphism groups of free groups (JAPANESE)

[ Abstract ]

By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.

[ Reference URL ]By combining Borel's stability and vanishing theorem for the stable cohomology of GL(n,Z) with coefficients in algebraic GL(n,Z)-representations and the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group Aut(F_n) of the free group F_n of rank n. This method is used also in the study of the stable rational cohomology of the IA-automorphism group IA_n of F_n. We propose a conjectural algebraic structure of the stable rational cohomology of IA_n, and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces. This is a joint work with Mai Katada.

https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2023/04/06

#### Applied Analysis

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

Blowup solutions to the Keller-Segel system (English)

https://forms.gle/7ogZKyh1oXKkPbN56

**Van Tien Nguyen**(National Taiwan University)Blowup solutions to the Keller-Segel system (English)

[ Abstract ]

I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.

[ Reference URL ]I will present constructive examples of finite-time blowup solutions to the Keller-Segel system in $\mathbb{R}^d$. For $d = 2$ ($L^1$-critical), there are finite time blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized according to a discrete spectrum of a linearized operator around the rescaled stationary solution in the self-similar setting. There is a stable blowup mechanism which is expected to be generic among others. For $d \geq 3$ ($L^1$-supercritical), we construct finite time blowup solutions that are completely unrelated to the self-similar scale, in particular, they are of Type II with finite mass. Interestingly, the radial blowup profile is linked to the traveling-wave of the 1D viscous Burgers equation. Our constructed solution actually has the form of collapsing-ring which consists of an imploding, smoothed-out shock wave moving towards the origin to form a Dirac mass at the singularity. I will also discuss other blowup patterns that possibly occur in the cases $d = 2,3,4$.

https://forms.gle/7ogZKyh1oXKkPbN56

#### 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

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