## Seminar information archive

Seminar information archive ～11/29｜Today's seminar 11/30 | Future seminars 12/01～

### 2022/10/20

#### Tokyo-Nagoya Algebra Seminar

16:40-18:10 Online

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

A surface and a threefold with equivalent singularity categories (English)

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

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

**Martin Kalck**(Freiburg University)A surface and a threefold with equivalent singularity categories (English)

[ Abstract ]

We discuss a triangle equivalence between singularity categories of an

affine surface and an affine threefold.

Both are isolated cyclic quotient singularities.

This seems to be the first (non-trivial) example of a singular

equivalence involving varieties of even and odd Krull dimension.

The same approach recovers a result of Dong Yang showing a singular

equivalence between certain cyclic quotient singularities in dimension

2 and certain finite dimensional commutative algebras.

This talk is based on https://arxiv.org/pdf/2103.06584.pdf

[ Reference URL ]We discuss a triangle equivalence between singularity categories of an

affine surface and an affine threefold.

Both are isolated cyclic quotient singularities.

This seems to be the first (non-trivial) example of a singular

equivalence involving varieties of even and odd Krull dimension.

The same approach recovers a result of Dong Yang showing a singular

equivalence between certain cyclic quotient singularities in dimension

2 and certain finite dimensional commutative algebras.

This talk is based on https://arxiv.org/pdf/2103.06584.pdf

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

### 2022/10/19

#### Seminar on Probability and Statistics

10:30-11:40 Room # (Graduate School of Math. Sci. Bldg.)

https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link

**Hayate Yamagishi**(Graduate School of Mathematical Sciences, The University of Tokyo)
[ Abstract ]

[ Reference URL ]https://docs.google.com/forms/d/e/1FAIpQLSd3i_gFci4Dc8T8gjtMigm08aIoQH6gM_Yfw0bHfppM1CNmag/viewform?usp=sf_link

#### Lectures

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

If you wish to participate online, please register by 17:00 on the 18th from the reference URL.

Probabilistic solutions of singular free boundary problems (English)

https://forms.gle/XXH2cAb18pQhC6w96

If you wish to participate online, please register by 17:00 on the 18th from the reference URL.

**Mykhaylo Shkolnikov**(Princeton University)Probabilistic solutions of singular free boundary problems (English)

[ Abstract ]

The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will discuss this new concept in the context of Stefan problems from mathematical physics that describe melting/solidification of a solid/liquid (e.g., ice/water) in the presence of supercooling. In particular, I will present new global existence, regularity and uniqueness results for the two geometrically simplest settings: flat and radial. Based on joint works with Sergey Nadtochiy, Francois Delarue and Yucheng Guo.

[ Reference URL ]The main focus of the talk will be on a new, probabilistic, concept of solution to singular free boundary problems, in which boundary points may move at infinite speed. I will discuss this new concept in the context of Stefan problems from mathematical physics that describe melting/solidification of a solid/liquid (e.g., ice/water) in the presence of supercooling. In particular, I will present new global existence, regularity and uniqueness results for the two geometrically simplest settings: flat and radial. Based on joint works with Sergey Nadtochiy, Francois Delarue and Yucheng Guo.

https://forms.gle/XXH2cAb18pQhC6w96

#### Number Theory Seminar

17:00-18:00 Hybrid

A nilpotent variant cdh-topology (English)

**Shane Kelly**(University of Tokyo)A nilpotent variant cdh-topology (English)

[ Abstract ]

I will speak about a version of the cdh-topology which can see nilpotents, and applications to algebraic K-theory. This is joint work in progress with Shuji Saito.

I will speak about a version of the cdh-topology which can see nilpotents, and applications to algebraic K-theory. This is joint work in progress with Shuji Saito.

### 2022/10/18

#### Operator Algebra Seminars

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

A geometric Elliott invariant and noncommutative rigidity of mapping tori (English)

[ Reference URL ]

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

**Valerio Proietti**(Univ. Tokyo)A geometric Elliott invariant and noncommutative rigidity of mapping tori (English)

[ Reference URL ]

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

### 2022/10/13

#### Information Mathematics Seminar

16:50-18:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Introduction to Attacks and Countermeasures for Cryptographic Implementation (Japanese)

**Yuichi Komano**(Toshiba Corporation)Introduction to Attacks and Countermeasures for Cryptographic Implementation (Japanese)

[ Abstract ]

Even if an encryption scheme is provably secure in some mathematical sense, against cryptographic products including a hardware/software implementation of the cryptographic scheme, it is possible to guess secret information operated in the product by analyzing observable information (side-channel information). Such guessing attack is called as side-channel attack, and lots of research have been reported on side-channel attacks using timing information or power consumption trace as observable information and on its countermeasures. In this talk, we will review the principles of side-channel attacks and countermeasures.

Even if an encryption scheme is provably secure in some mathematical sense, against cryptographic products including a hardware/software implementation of the cryptographic scheme, it is possible to guess secret information operated in the product by analyzing observable information (side-channel information). Such guessing attack is called as side-channel attack, and lots of research have been reported on side-channel attacks using timing information or power consumption trace as observable information and on its countermeasures. In this talk, we will review the principles of side-channel attacks and countermeasures.

### 2022/10/12

#### Number Theory Seminar

17:00-18:00 Hybrid

Syntomic complex with coefficients (English)

**Abhinandan**(University of Tokyo)Syntomic complex with coefficients (English)

[ Abstract ]

In the proof of $p$-adic crystalline comparison theorem, one of the most important steps in the approach of Fontaine and Messing is to establish a comparison between syntomic cohomology and p-adic étale cohomology via (Fontaine-Messing) period map. This approach was successfully generalized to the semistable case by Kato and a complete proof of crystalline and semistable comparison theorems for schemes was given by Tsuji. Few years ago, Colmez and Nizioł gave a new interpretation of the (local) Fontaine-Messing period map in terms of complexes of $(\varphi,\Gamma)$-modules and used it to prove semistable comparison theorem for $p$-adic formal schemes. We will present a generalisation (of crystalline version of this interpretation by Colmez and Nizioł) to coefficients arising from relative Fontaine-Laffaille modules of Faltings (on syntomic side) and relative Wach modules introduced by the speaker (on $(\varphi,\Gamma)$-module side).

In the proof of $p$-adic crystalline comparison theorem, one of the most important steps in the approach of Fontaine and Messing is to establish a comparison between syntomic cohomology and p-adic étale cohomology via (Fontaine-Messing) period map. This approach was successfully generalized to the semistable case by Kato and a complete proof of crystalline and semistable comparison theorems for schemes was given by Tsuji. Few years ago, Colmez and Nizioł gave a new interpretation of the (local) Fontaine-Messing period map in terms of complexes of $(\varphi,\Gamma)$-modules and used it to prove semistable comparison theorem for $p$-adic formal schemes. We will present a generalisation (of crystalline version of this interpretation by Colmez and Nizioł) to coefficients arising from relative Fontaine-Laffaille modules of Faltings (on syntomic side) and relative Wach modules introduced by the speaker (on $(\varphi,\Gamma)$-module side).

### 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

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