## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

### 2022/11/02

#### Number Theory Seminar

17:00-18:00 Hybrid

Some compact generators of D_{lis} (Bun_G,\Lambda) (English)

**Laurent Fargues**(Mathematics Institute of Jussieu–Paris Rive Gauche, University of Tokyo)Some compact generators of D_{lis} (Bun_G,\Lambda) (English)

[ Abstract ]

I will speak about some aspect of my joint work with Scholze on the geomerization of the local Langlands correspondence. More precisely, I will explain how to construct explicitly some compact generators of the derived category of étale sheaves on Bun_G, the Artin v-stack of G-bundles on the curve. Those compact generators generalize the classical compactly induced representations in the classical local Langlands program. For this we construct some particular charts on Bun_G and this will be the occasion to review some geometric constructions in our joint work.

I will speak about some aspect of my joint work with Scholze on the geomerization of the local Langlands correspondence. More precisely, I will explain how to construct explicitly some compact generators of the derived category of étale sheaves on Bun_G, the Artin v-stack of G-bundles on the curve. Those compact generators generalize the classical compactly induced representations in the classical local Langlands program. For this we construct some particular charts on Bun_G and this will be the occasion to review some geometric constructions in our joint work.

### 2022/11/01

#### Operator Algebra Seminars

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

Permutation stability of finitely generated free metabelian groups

[ Reference URL ]

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

**Hiroki Ishikura**(Univ. Tokyo)Permutation stability of finitely generated free metabelian groups

[ 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.

An obstruction problem associated with finite path-integral (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Minkyu Kim**(The Univesity of Tokyo)An obstruction problem associated with finite path-integral (JAPANESE)

[ Abstract ]

Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.

[ Reference URL ]Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.

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

#### Algebraic Geometry Seminar

10:30-12:00 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

Extendability of differential forms via Cartier operators (Japanese)

**Tatsuro Kawakami**(Kyoto)Extendability of differential forms via Cartier operators (Japanese)

[ Abstract ]

For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.

In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.

For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.

For a normal variety X, we say X satisfies the extension theorem if, for every proper birational morphism from Y, every differential form on the regular locus of X extends to Y. This is a basic property relating differential forms and singularities, and many results are known over the field of complex numbers.

In this talk, we discuss the extension theorem in positive characteristic. Existing studies depend on geometric tools such as log resolutions, (mixed) Hodge theory, the minimal model program, and vanishing theorems, which are not expected to be true or are not known for higher-dimensional varieties in positive characteristic.

For this reason, I introduce a new algebraic approach to the extension theorem using Cartier operators. I also talk about an application of the theory of quasi-F-splitting, which is studied in joint work with Takamatsu-Tanaka-Witaszek-Yobuko-Yoshikawa, to the extension problem.

### 2022/10/31

#### Seminar on Geometric Complex Analysis

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

The non-archimedean μ-entropy in toric case (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Eiji Inoue**(RIKEN)The non-archimedean μ-entropy in toric case (Japanese)

[ Abstract ]

The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.

In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.

[ Reference URL ]The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.

In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/10/27

#### Information Mathematics Seminar

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

Recent Progress in Post-Quantum Cryptography (Japanese)

**Katsuyuki Takashima**(Waseda Univ.)Recent Progress in Post-Quantum Cryptography (Japanese)

[ Abstract ]

I will explain recent progress in post-quantum cryptography, particularly, in lattice cryptography.

I will explain recent progress in post-quantum cryptography, particularly, in lattice cryptography.

#### Lectures

11:00-12:30 Online

Seminars by Professor O. Emanouilov (Colorado State Univ.)

Inverse problems for partial differential equations: past and future works (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

Seminars by Professor O. Emanouilov (Colorado State Univ.)

**Professor O. Emanouilov**(Colorado State Univ.)Inverse problems for partial differential equations: past and future works (English)

[ Reference URL ]

https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

### 2022/10/25

#### Algebraic Geometry Seminar

10:30-11:45 Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)

Projective normality of general polarized abelian varieties (Japanese)

**Atsushi Ito**(Okayama)Projective normality of general polarized abelian varieties (Japanese)

[ Abstract ]

Projective normality is an important property of polarized varieties. Hwang and To prove that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $\chi(X,L) \geq (8g)^g/2g!$. In this talk, I will explain that their bound can be weaken as $\chi(X,L) > 2^{2g-1}$, which is sharp. A key tool in the proof is an invariant introduced by Jiang and Pareschi, which measures the basepoint freeness of $\mathbb{Q}$-divisors on abelian varieties.

Projective normality is an important property of polarized varieties. Hwang and To prove that a general polarized abelian variety $(X,L)$ of dimension $g$ is projectively normal if $\chi(X,L) \geq (8g)^g/2g!$. In this talk, I will explain that their bound can be weaken as $\chi(X,L) > 2^{2g-1}$, which is sharp. A key tool in the proof is an invariant introduced by Jiang and Pareschi, which measures the basepoint freeness of $\mathbb{Q}$-divisors on abelian varieties.

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Stabilized convex symplectic manifolds are Weinstein (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Noboru Ogawa**(Tokai University)Stabilized convex symplectic manifolds are Weinstein (JAPANESE)

[ Abstract ]

There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.

[ Reference URL ]There are two important classes of convexity in symplectic geometry: Liouville and Weinstein structures. Basic objects such as cotangent bundles and Stein manifolds have these structures. In 90s, Eliashberg and Gromov formulated them as symplectic counterparts of Stein manifolds, since then, they have played a significant role in the study of symplectic topology. By definition, a Weinstein structure is a Liouville structure, but the converse is not true in general; McDuff gave the first example which is a Liouville manifold without any Weinstein structures. The purpose of this talk is to present the recent advances on the difference of both structures, up to homotopy. In particular, I will show that the stabilization of the McDuff’s example admits a flexible Weinstein structure. The main part is based on a joint work with Yakov Eliashberg (Stanford University) and Toru Yoshiyasu (Kyoto University of Education). If time permits, I would like to discuss some open questions and progress.

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

### 2022/10/24

#### Seminar on Geometric Complex Analysis

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

A new approach to the nilpotent orbit theorem via the $L^2$ extension theorem of Ohsawa-Takegoshi type (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Taro Fujisawa**(Tokyo Denki University)A new approach to the nilpotent orbit theorem via the $L^2$ extension theorem of Ohsawa-Takegoshi type (Japanese)

[ Abstract ]

I will talk about a new proof of (a part of) the nilpotent orbit theorem for unipotent variations of Hodge structure. This approach is largely inspired by the recent works of Deng and of Sabbah-Schnell. In my proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays essential roles.

[ Reference URL ]I will talk about a new proof of (a part of) the nilpotent orbit theorem for unipotent variations of Hodge structure. This approach is largely inspired by the recent works of Deng and of Sabbah-Schnell. In my proof, the $L^2$ extension theorem of Ohsawa-Takegoshi type plays essential roles.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/10/21

#### Colloquium

15:30-16:30 Room #オンライン (Graduate School of Math. Sci. Bldg.)

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

The Fourier restriction conjecture (English)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

**Neal Bez**(Graduate School of Science and Engineering, Saitama University)The Fourier restriction conjecture (English)

[ Abstract ]

The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.

[ Reference URL ]The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2

#### Seminar on Probability and Statistics

①14:30-15:40- ②16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

On the theory of distribution free testing of statistical hypothesis

①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.

②Further testing problems: parametric regression and Markov chains. (ENGLISH)

https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link

**Estate Khmaladze**(Victoria University of Wellington)On the theory of distribution free testing of statistical hypothesis

①Empirical processes for discrete and continuous observations: structure, difficulties and resolution.

②Further testing problems: parametric regression and Markov chains. (ENGLISH)

[ Abstract ]

The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.

Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.

In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.

Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.

[ Reference URL ]The concept of distribution free testing is familiar to all. Everybody, who heard about rank statistics, knows that the distribution of ranks is independent from the distribution of underlying random variables, provided this later is a continuous distribution on the real line. Everybody, who ever used classical goodness of fit tests like Kolmogorov - Smirnov test or Cram\'er-von Mises test, knows that the distribution of statistics of these tests is independent from the distribution of the underlying random variables, again, provided this distribution is a continuous distribution on the real line.

Development in subsequent decades revealed many cracks in existing theory and difficulties in extending the concept of distribution free testing to majority of interesting models. It gradually became clear that the new starting point is needed to expand the theory to these models.

In our lectures we first describe the current situation in empirical and related processes. Then we describe how the new approaches have been developed and what progress has been made.

Then we hope to show how the new approach can be naturally extended to the domain of stochastic processes, and how the important probabilistic models of the processes can be tested in distribution free way. In discrete time, results for Markov chains have been published in 2021. Extension to continuous time will be explored during the current visit to University of Tokyo.

https://docs.google.com/forms/d/e/1FAIpQLScxh_wNRs3WbMUG4S3cGlGAu1ZkP4trLbc08CBrvUDO66hwNg/viewform?usp=sf_link

### 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

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