## Seminar information archive

Seminar information archive ～10/10｜Today's seminar 10/11 | Future seminars 10/12～

### 2022/10/11

#### Operator Algebra Seminars

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

Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras

[ Reference URL ]

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

**Takuya Takeishi**(Kyoto Inst. Tech.)Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras

[ 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.

Magnitude homology of graphs (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yasuhiko Asao**(Fukuoka University)Magnitude homology of graphs (JAPANESE)

[ Abstract ]

Magnitude is introduced by Leinster in 00’s as an ``Euler characteristic of metric spaces”. It is defined for the metric structure itself rather than the topology induced from the metric. Magnitude homology is a categorification of magnitude in a sense that ordinary homology categorifies the Euler characteristic. The speaker’s interest is in geometric meaning of this theory. In this talk, after an introduction to basic ideas, I will explain that magnitude truly extends the Euler characteristic. From this perspective, magnitude homology can be seen as one of the categorification of the Euler characteristic, and the path homology (Grigor’yan—Muranov—Lin—S-T. Yau et.al) appears as a part of another one. These structures are aggregated in a spectral sequence obtained from the classifying space of "filtered set enriched categories" which includes ordinary small categories and metric spaces.

[ Reference URL ]Magnitude is introduced by Leinster in 00’s as an ``Euler characteristic of metric spaces”. It is defined for the metric structure itself rather than the topology induced from the metric. Magnitude homology is a categorification of magnitude in a sense that ordinary homology categorifies the Euler characteristic. The speaker’s interest is in geometric meaning of this theory. In this talk, after an introduction to basic ideas, I will explain that magnitude truly extends the Euler characteristic. From this perspective, magnitude homology can be seen as one of the categorification of the Euler characteristic, and the path homology (Grigor’yan—Muranov—Lin—S-T. Yau et.al) appears as a part of another one. These structures are aggregated in a spectral sequence obtained from the classifying space of "filtered set enriched categories" which includes ordinary small categories and metric spaces.

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

### 2022/10/06

#### Information Mathematics Seminar

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

On a New Quantitative Definition of the Complexity of Organized Matters (Japanese)

**Tatsuaki Okamoto**(NTT)On a New Quantitative Definition of the Complexity of Organized Matters (Japanese)

[ Abstract ]

Scientific problems are classified into three classes: problems of simplicity, problems of disorganized complexity, and problems of organized complexity. For example, classical dynamics can be used to analyze and predict the motion of a few ivory balls as they move about on a billiard table. This is a typical problem of simplicity. Imagine a large billiard table with millions of balls rolling over its surface, colliding with one another and with the side rails. This is a typical problem of disorganized complexity. Problems of organized complexity, however, deal with features of an organization such as living things, ecosystems, and human societies. The quantitative definition of complexity is the most fundamental and important notion in problems of (organized and disorganized) complexity. The quantitative definition of disorganized complexity has been established to be entropy. In contrast, there is no agreed-upon quantitative definition for organized complexity, although many definitions have been proposed for this aim. In this talk, first, I will show the shortcomings of the existing definitions for organized complexity. I will then introduce a new definition and present that the new definition has solved all problems with the existing definitions. Finally, I will show some applications. This talk is based on the following paper.

Tatsuaki Okamoto, ‘‘A New Quantitative Definition of the Complexity of Organized Matters,’’ Complexity, Volume 2022, Article ID 1889348 (2022)

https://www.hindawi.com/journals/complexity/2022/1889348/

Scientific problems are classified into three classes: problems of simplicity, problems of disorganized complexity, and problems of organized complexity. For example, classical dynamics can be used to analyze and predict the motion of a few ivory balls as they move about on a billiard table. This is a typical problem of simplicity. Imagine a large billiard table with millions of balls rolling over its surface, colliding with one another and with the side rails. This is a typical problem of disorganized complexity. Problems of organized complexity, however, deal with features of an organization such as living things, ecosystems, and human societies. The quantitative definition of complexity is the most fundamental and important notion in problems of (organized and disorganized) complexity. The quantitative definition of disorganized complexity has been established to be entropy. In contrast, there is no agreed-upon quantitative definition for organized complexity, although many definitions have been proposed for this aim. In this talk, first, I will show the shortcomings of the existing definitions for organized complexity. I will then introduce a new definition and present that the new definition has solved all problems with the existing definitions. Finally, I will show some applications. This talk is based on the following paper.

Tatsuaki Okamoto, ‘‘A New Quantitative Definition of the Complexity of Organized Matters,’’ Complexity, Volume 2022, Article ID 1889348 (2022)

https://www.hindawi.com/journals/complexity/2022/1889348/

### 2022/10/05

#### Algebraic Geometry Seminar

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

Equivariant birational geometry (joint with A. Kresch) (English)

**Yuri Tschinkel**(Mathematics and Physical Sciences Division, Simons Foundation/ Courant Institute, New York University)Equivariant birational geometry (joint with A. Kresch) (English)

[ Abstract ]

Ideas from motivic integration led to the introduction of new invariants in equivariant birational geometry, the study of actions of finite groups on algebraic varieties, up to equivariant birational transformations.

These invariants allow us to distinguish actions in many new cases, shedding light on the structure of the Cremona group. The structure of the invariants themselves is also interesting: there are unexpected connections to modular curves and cohomology of arithmetic groups.

Ideas from motivic integration led to the introduction of new invariants in equivariant birational geometry, the study of actions of finite groups on algebraic varieties, up to equivariant birational transformations.

These invariants allow us to distinguish actions in many new cases, shedding light on the structure of the Cremona group. The structure of the invariants themselves is also interesting: there are unexpected connections to modular curves and cohomology of arithmetic groups.

### 2022/10/04

#### Tuesday Seminar on Topology

17:00-18:30 Online

Pre-registration required. See our seminar webpage.

Orientable rho-Q-manifolds and their modular classes (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shuichi Harako**(The Univesity of Tokyo)Orientable rho-Q-manifolds and their modular classes (JAPANESE)

[ Abstract ]

A rho-commutative algebra, or an almost commutative algebra, is a graded algebra whose commutativity is given by a function called a commutation factor. It is one generalization of a commutative algebra or a superalgebra. We obtain a rho-Lie algebra, or an epsilon-Lie algebra, by a similar generalization of a Lie algebra. On the other hand, we have the modular class of an orientable Q-manifold. Here, a Q-manifold is a supermanifold with an odd vector field whose Lie bracket with itself vanishes, and its orientability is described in terms of the Berezinian bundle. In this talk, we introduce the concept of a rho-manifold, which is a graded manifold whose functional algebra is a rho-commutative algebra, then we show that we can define Q-structures, Berezinian bundle, volume forms, and modular classes of a rho-manifold with some examples.

[ Reference URL ]A rho-commutative algebra, or an almost commutative algebra, is a graded algebra whose commutativity is given by a function called a commutation factor. It is one generalization of a commutative algebra or a superalgebra. We obtain a rho-Lie algebra, or an epsilon-Lie algebra, by a similar generalization of a Lie algebra. On the other hand, we have the modular class of an orientable Q-manifold. Here, a Q-manifold is a supermanifold with an odd vector field whose Lie bracket with itself vanishes, and its orientability is described in terms of the Berezinian bundle. In this talk, we introduce the concept of a rho-manifold, which is a graded manifold whose functional algebra is a rho-commutative algebra, then we show that we can define Q-structures, Berezinian bundle, volume forms, and modular classes of a rho-manifold with some examples.

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

#### Tuesday Seminar of Analysis

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

The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity (Japanese)

[ Reference URL ]

https://forms.gle/nPfEgKUX2tfUrg5LA

**FUKAO Takeshi**(Kyoto University of Education)The Cahn-Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity (Japanese)

[ Reference URL ]

https://forms.gle/nPfEgKUX2tfUrg5LA

### 2022/09/29

#### Classical Analysis

11:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 6 (JAPANESE)

Difference module and Homology 7 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 11:30-12:00Difference module and Homology 6 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 14:00-17:00Difference module and Homology 7 (JAPANESE)

### 2022/09/28

#### Classical Analysis

11:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 4 (JAPANESE)

Difference module and Homology 5 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 11:30-12:00Difference module and Homology 4 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 14:00-17:00Difference module and Homology 5 (JAPANESE)

#### Number Theory Seminar

17:00-18:00 Hybrid

A K-theoretic approach to geometric representation theory (ENGLISH)

**Jens Eberhardt**(University of Wuppertal)A K-theoretic approach to geometric representation theory (ENGLISH)

[ Abstract ]

Perverse sheaves and intersection cohomology are central objects in geometric representation theory. This talk is about their long-lost K-theoretic cousins, called K-motives. We will discuss definitions and basic properties of K-motives and explore potential applications to geometric representation theory. For example, K-motives shed a new light on Beilinson--Ginzburg--Soergel's Koszul duality -- a remarkable symmetry in the representation theory and geometry of two Langlands dual reductive groups. We will see that this new form of Koszul duality does not involve any gradings or mixed geometry which are as essential as mysterious in the classical approaches.

Perverse sheaves and intersection cohomology are central objects in geometric representation theory. This talk is about their long-lost K-theoretic cousins, called K-motives. We will discuss definitions and basic properties of K-motives and explore potential applications to geometric representation theory. For example, K-motives shed a new light on Beilinson--Ginzburg--Soergel's Koszul duality -- a remarkable symmetry in the representation theory and geometry of two Langlands dual reductive groups. We will see that this new form of Koszul duality does not involve any gradings or mixed geometry which are as essential as mysterious in the classical approaches.

### 2022/09/27

#### Classical Analysis

11:30-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 2 (JAPANESE)

Difference module and Homology 3 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 11:30-12:00Difference module and Homology 2 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University) 14:00-17:00Difference module and Homology 3 (JAPANESE)

### 2022/09/26

#### Classical Analysis

14:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Difference module and Homology 1 (JAPANESE)

**Koki Ito**(Osaka Electro-Communication University)Difference module and Homology 1 (JAPANESE)

### 2022/09/20

#### Operator Algebra Seminars

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

Honeycombs, polytopes, and representation theory (English)

[ Reference URL ]

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

**Robert Coquereaux**(CNRS/CPT)Honeycombs, polytopes, and representation theory (English)

[ Reference URL ]

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

### 2022/09/16

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Prospects

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Prospects

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

### 2022/09/15

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse problems for fluid dynamics

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse problems for fluid dynamics

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81167784080?pwd=VE94RnNYcmJZUXJ4QTIvZUhEQmVJZz09

### 2022/09/09

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/08

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)Inverse parabolic problems: recent results

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/02

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/09/01

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State Univ.)DN map for hyperbolic inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/83144151309?pwd=NEIwbzdGNU5xcFR2UTFWbnZlOW5pUT09

### 2022/08/26

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Recent researches on inverse problems by Carleman estimatesPart II + discussions on new aspects of mathematical analysis for inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State University)Recent researches on inverse problems by Carleman estimatesPart II + discussions on new aspects of mathematical analysis for inverse problems

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

### 2022/08/25

#### Lectures

16:00-17:30 Online

Seminars by Professor Emanouilov

Recent researches on inverse problems by Carleman estimates Part I

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

Seminars by Professor Emanouilov

**Professor O. Emanouilov**(Colorado State University )Recent researches on inverse problems by Carleman estimates Part I

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/81424491417?pwd=T1BOMWtmZkhtY0pjUEs1NFZUZEYzQT09

### 2022/08/23

#### Tuesday Seminar of Analysis

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

Quantitative homogenization for monotone, uniformly elliptic systems with random coefficients (English)

https://forms.gle/V1wxbYhT4mkPF4gY9

**Stefan Neukamm**(Dresden University/RIMS)Quantitative homogenization for monotone, uniformly elliptic systems with random coefficients (English)

[ Abstract ]

Motivated by homogenization of nonlinearly elastic composite materials, we study homogenization rates for elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. Under the assumption of a fast decay of correlations on scales larger than the microscale $\varepsilon$, we establish estimates of optimal order for the approximation of the homogenized operator by the method of representative volumes. Moreover, we discuss applications to nonlinear elasticity random laminates.

[ Reference URL ]Motivated by homogenization of nonlinearly elastic composite materials, we study homogenization rates for elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. Under the assumption of a fast decay of correlations on scales larger than the microscale $\varepsilon$, we establish estimates of optimal order for the approximation of the homogenized operator by the method of representative volumes. Moreover, we discuss applications to nonlinear elasticity random laminates.

https://forms.gle/V1wxbYhT4mkPF4gY9

### 2022/08/18

#### Discrete mathematical modelling seminar

15:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Different Hamiltonians for Painlevé Equations and their identification using geometry of the space of

initial conditions (English)

**Anton Dzhamay**(University of Northern Colorado)Different Hamiltonians for Painlevé Equations and their identification using geometry of the space of

initial conditions (English)

[ Abstract ]

It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique – there are many very different Hamiltonians that result in the same differential Painlevé equation. In this paper we describe a systematic procedure of finding

changes of coordinates transforming different Hamiltonian systems into some canonical form.

Our approach is based on the Okamoto-Sakai geometric approach to Painlevé equations. We explain this approach using the differential P-IV equation as an example, but the procedure is general and can be easily adapted to other Painlevé equations as well. (Joint work with Galina Filipuk, Adam Ligeza and Alexander Stokes.)

It is well-known that differential Painlevé equations can be written in a Hamiltonian form. However, a coordinate form of such representation is far from unique – there are many very different Hamiltonians that result in the same differential Painlevé equation. In this paper we describe a systematic procedure of finding

changes of coordinates transforming different Hamiltonian systems into some canonical form.

Our approach is based on the Okamoto-Sakai geometric approach to Painlevé equations. We explain this approach using the differential P-IV equation as an example, but the procedure is general and can be easily adapted to other Painlevé equations as well. (Joint work with Galina Filipuk, Adam Ligeza and Alexander Stokes.)

### 2022/08/17

#### thesis presentations

13:00-14:15 Online

A study on cohomological Donaldson-Thomas invariants

[ Reference URL ]

https://forms.gle/cGq4sCUFSLjJqPw97

**KINJO Tasuki**(Graduate School of Mathematical Sciences University of Tokyo)A study on cohomological Donaldson-Thomas invariants

[ Reference URL ]

https://forms.gle/cGq4sCUFSLjJqPw97

### 2022/07/26

#### Tuesday Seminar of Analysis

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

Periodic homogenization of non-symmetric jump-type processes with drifts (Japanese)

https://forms.gle/ewZEy1jAXrAhWx1Q8

**KUMAGAI Takashi**(Waseda University)Periodic homogenization of non-symmetric jump-type processes with drifts (Japanese)

[ Abstract ]

Homogenization problem is one of the classical problems in analysis and probability which is very actively studied recently. In this talk, we consider homogenization problem for non-symmetric Lévy-type processes with drifts in periodic media. Under a proper scaling, we show the scaled processes converge weakly to Lévy processes on ${\mathds R}^d$. In particular, we completely characterize the limiting processes when the coefficient function of the drift part is bounded continuous, and the decay rate of the jumping measure is comparable to $r^{-1-\alpha}$ for $r>1$ in the spherical coordinate with $\alpha \in (0,\infty)$. Different scaling limits appear depending on the values of $\alpha$.

This talk is based on joint work with Xin Chen, Zhen-Qing Chen and Jian Wang (Ann. Probab. 2021).

[ Reference URL ]Homogenization problem is one of the classical problems in analysis and probability which is very actively studied recently. In this talk, we consider homogenization problem for non-symmetric Lévy-type processes with drifts in periodic media. Under a proper scaling, we show the scaled processes converge weakly to Lévy processes on ${\mathds R}^d$. In particular, we completely characterize the limiting processes when the coefficient function of the drift part is bounded continuous, and the decay rate of the jumping measure is comparable to $r^{-1-\alpha}$ for $r>1$ in the spherical coordinate with $\alpha \in (0,\infty)$. Different scaling limits appear depending on the values of $\alpha$.

This talk is based on joint work with Xin Chen, Zhen-Qing Chen and Jian Wang (Ann. Probab. 2021).

https://forms.gle/ewZEy1jAXrAhWx1Q8

### 2022/07/22

#### 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].

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

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