## Seminar information archive

Seminar information archive ～06/14｜Today's seminar 06/15 | Future seminars 06/16～

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

An equivariant Hochster's formula for $S_n$-invariant monomial ideals (Japanese)

[ Reference URL ]

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

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

**Satoshi Murai**(Waseda University)An equivariant Hochster's formula for $S_n$-invariant monomial ideals (Japanese)

[ Reference URL ]

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

### 2021/06/01

#### Tuesday Seminar on Topology

17:30-18:30 Online

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)

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

Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.

**Masatoshi Kitagawa**(Waseda University)On the discrete decomposability and invariants of representations of real reductive Lie groups (JAPANESE)

[ Abstract ]

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form,

can be obtained as intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J. Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98). The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

[ Reference URL ]A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form,

can be obtained as intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J. Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98). The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

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

#### Lie Groups and Representation Theory

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

Joint with Tuesday Seminar on Topology. Online.

On the discrete decomposability and invariants of representations of real reductive Lie groups (Japanese)

Joint with Tuesday Seminar on Topology. Online.

**Masatoshi KITAGAWA**(Waseda University)On the discrete decomposability and invariants of representations of real reductive Lie groups (Japanese)

[ Abstract ]

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form, can be obtained as

intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J.

Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98).

The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

A problem to determine the behavior of the restriction of an irreducible group representation to a subgroup is called the branching problem. The restriction of an irreducible representation is not irreducible in general, and if the representation is unitary, the restriction has an irreducible decomposition described by a direct integral. The decomposition can be regarded as a generalization of spectral decomposition of unitary operators, and has continuous spectrum and discrete spectrum in general. If the decomposition has no continuous spectrum, the representation is said to be discretely decomposable.

Discretely decomposable branching laws are technically easy to deal with, and in the setting, it is relatively easy to extract information about representations of a small subgroup from that of a large group. The following applications are known. It is known that the operators, called the Rankin--Cohen brackets which make a new automorphic form from a automorphic form, can be obtained as

intertwiner from discretely decomposable representations to irreducible representations. Many generalizations of the operators are obtained recently. The discrete decomposability is used to construct discrete spectrum of the space of L^2 functions on homogeneous spaces (T. Kobayashi, J.

Funct. Anal. ('98)).

In this talk, I will give several criterion about the discrete decomposability and G'-admissibility based on the general theory and criterion given by T. Kobayashi (Invent. math. '94, Annals of Math. '98, Invent. math. '98).

The criterion are written by associated varieties (algebraic invariants), wave front sets (analytic invariants) and topological structure of representations.

#### Operator Algebra Seminars

16:45-18:15 Online

KMS states of Toeplitz algebras of graphs

[ Reference URL ]

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

**Takuya Takeishi**(Kyoto Institute of Technology)KMS states of Toeplitz algebras of graphs

[ Reference URL ]

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

### 2021/05/31

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Nonnegativity of the CR Paneitz operator for embeddable CR manifolds (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Yuya Takeuchi**(Tsukuba University)Nonnegativity of the CR Paneitz operator for embeddable CR manifolds (Japanese)

[ Abstract ]

The CR Paneitz operator, which is a fourth-order CR invariant differential operator, plays a crucial role in three-dimensional CR geometry; it is deeply connected to global embeddability and the CR positive mass theorem. In this talk, I will show that the CR Paneitz operator is nonnegative for embeddable CR manifolds. I will also apply this result to some problems in CR geometry. In particular, I will give an affirmative solution to the CR Yamabe problem for embeddable CR manifolds.

[ Reference URL ]The CR Paneitz operator, which is a fourth-order CR invariant differential operator, plays a crucial role in three-dimensional CR geometry; it is deeply connected to global embeddability and the CR positive mass theorem. In this talk, I will show that the CR Paneitz operator is nonnegative for embeddable CR manifolds. I will also apply this result to some problems in CR geometry. In particular, I will give an affirmative solution to the CR Yamabe problem for embeddable CR manifolds.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/05/28

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, May 28).

Physics and algebraic topology (ENGLISH)

Registration is closed (12:00, May 28).

**Yuji Tachikawa**(Kavli IPMU)Physics and algebraic topology (ENGLISH)

[ Abstract ]

Although we often talk about the "unreasonable effectiveness of mathematics in the natural sciences", there are great disparities in the relevance of various subbranches of mathematics to individual fields of natural sciences. Algebraic topology was a subject whose influence to physics remained relatively minor for a long time, but in the last several years, theoretical physicists started to appreciate the effectiveness of algebraic topology more seriously. For example, there is now a general consensus that the classification of the symmetry-protected topological phases, which form a class of phases of matter with a certain particularly simple property, is done in terms of generalized cohomology theories.

In this talk, I would like to provide a historical overview of the use of algebraic topology in physics, emphasizing a few highlights along the way. If the time allows, I would also like to report my struggle to understand the anomaly of heterotic strings, using the theory of topological modular forms.

Although we often talk about the "unreasonable effectiveness of mathematics in the natural sciences", there are great disparities in the relevance of various subbranches of mathematics to individual fields of natural sciences. Algebraic topology was a subject whose influence to physics remained relatively minor for a long time, but in the last several years, theoretical physicists started to appreciate the effectiveness of algebraic topology more seriously. For example, there is now a general consensus that the classification of the symmetry-protected topological phases, which form a class of phases of matter with a certain particularly simple property, is done in terms of generalized cohomology theories.

In this talk, I would like to provide a historical overview of the use of algebraic topology in physics, emphasizing a few highlights along the way. If the time allows, I would also like to report my struggle to understand the anomaly of heterotic strings, using the theory of topological modular forms.

### 2021/05/27

#### Mathematical Biology Seminar

15:00-16:00 Online

Modeling infective contact by point process (Japanese)

**Nariyuki Minami**(Keio University School of Medicine)Modeling infective contact by point process (Japanese)

#### Information Mathematics Seminar

16:50-18:35 Online

The practice of the speedup technique of the classic computing and quantum computing basics=superposition principle (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The practice of the speedup technique of the classic computing and quantum computing basics=superposition principle (Japanese)

[ Abstract ]

Explanation on the practice of the speedup technique of the classic computing and on quantum computing basics=superposition principle.

[ Reference URL ]Explanation on the practice of the speedup technique of the classic computing and on quantum computing basics=superposition principle.

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/05/26

#### Algebraic Geometry Seminar

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

Multiplier ideals via ultraproducts (日本語)

**Itsuki Yamaguchi**(Tokyo)Multiplier ideals via ultraproducts (日本語)

[ Abstract ]

正標数の可換環と複素数体上の可換環の性質を比較する方法の一つにultraproductを用いた手法がある. このultraproductは超準解析において超実数の構成などに用いられているものである. これを可換環論へ応用する研究としてSchoutensによるnon-standard hullがある. この手法は等標数0の局所環に対するbig Cohen-Macaulay 代数の構成などにも応用がある. 彼の研究の一つに川又対数端末特異点のultraproductを用いた特徴付けがある. 本講演では, この結果の一般化として乗数イデアルがultraproductを用いて記述できることを説明する.

正標数の可換環と複素数体上の可換環の性質を比較する方法の一つにultraproductを用いた手法がある. このultraproductは超準解析において超実数の構成などに用いられているものである. これを可換環論へ応用する研究としてSchoutensによるnon-standard hullがある. この手法は等標数0の局所環に対するbig Cohen-Macaulay 代数の構成などにも応用がある. 彼の研究の一つに川又対数端末特異点のultraproductを用いた特徴付けがある. 本講演では, この結果の一般化として乗数イデアルがultraproductを用いて記述できることを説明する.

#### Number Theory Seminar

17:00-18:00 Online

Geometric Structure of Affine Deligne-Lusztig Varieties for $\mathrm{GL}_3$ (Japanese)

**Ryosuke Shimada**(University of Tokyo)Geometric Structure of Affine Deligne-Lusztig Varieties for $\mathrm{GL}_3$ (Japanese)

[ Abstract ]

The Langlands correspondence, which contains class field theory as a special case, is one of the most important topics in number theory. Shimura varieties have been used, with great success, towards applications in the realm of the Langlands program. In this context, geometric and homological properties of affine Deligne-Lusztig varieties have been used to examine Shimura varieties and the local Langlands correspondence.

In this talk we study the geometric structure of affine Deligne-Lusztig varieties $X_{\lambda}(b)$ for $\mathrm{GL}_3$ and $b$ basic.

We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.

The Langlands correspondence, which contains class field theory as a special case, is one of the most important topics in number theory. Shimura varieties have been used, with great success, towards applications in the realm of the Langlands program. In this context, geometric and homological properties of affine Deligne-Lusztig varieties have been used to examine Shimura varieties and the local Langlands correspondence.

In this talk we study the geometric structure of affine Deligne-Lusztig varieties $X_{\lambda}(b)$ for $\mathrm{GL}_3$ and $b$ basic.

We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.

### 2021/05/25

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer (Japanese)

https://forms.gle/wHpi7BSpppsiiguD6

**TAKADA Ryo**(Kyushu University)Asymptotic limit of fast rotation for the incompressible Navier-Stokes equations in a 3D layer (Japanese)

[ Abstract ]

In this talk, we consider the initial value problem for the Navier-Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation, and show that the global solution converges to that of 2D incompressible Navier-Stokes equations in some global in time space-time norms. This talk is based on the joint work with Hiroki Ohyama (Kyushu University).

[ Reference URL ]In this talk, we consider the initial value problem for the Navier-Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation, and show that the global solution converges to that of 2D incompressible Navier-Stokes equations in some global in time space-time norms. This talk is based on the joint work with Hiroki Ohyama (Kyushu University).

https://forms.gle/wHpi7BSpppsiiguD6

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

On a characteristic class associated with deformations of foliations (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Taro Asuke**(The University of Tokyo)On a characteristic class associated with deformations of foliations (JAPANESE)

[ Abstract ]

A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.

[ Reference URL ]A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is discussed. It seems unknown if there is a real foliation with non-trivial FLK class. In this talk, we show some conditions to assure the triviality of the FLK class. On the other hand, we show that the FLK class is easily to be non-trivial for transversely holomorphic foliations. We present an example and give a construction which generalizes it.

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

#### Operator Algebra Seminars

16:45-18:15 Online

Lattices of logmodular algebras

[ Reference URL ]

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

**Rajarama Bhat**(Indian Statistical Institute)Lattices of logmodular algebras

[ Reference URL ]

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

### 2021/05/24

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Cartan-Hartogs領域の固有正則写像 (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Atsushi Hayashimoto**(Nagano National College of Technology)Cartan-Hartogs領域の固有正則写像 (Japanese)

[ Abstract ]

2つの球の間の固有正則写像は自己同型写像である。球を別の領域にしたらどうなるかを調べたい。球の一般化として複素擬楕円体や有界対称領域が考えられる。これら2つの領域を合わせた領域としてHua領域がある。これは有界対称領域の上に複素擬楕円体が乗っているような領域である。Hua領域の一番簡単な場合としてCartan-Hartogs領域があり、これらの間の固有正則写像の分類問題を考える。分類すると本質的には１種類の写像しかないことが分かる。ここでは2つの多項式写像が自己同型写像の差を省いて一致すれば、Isotoropy写像の差を省いて一致することを使う。

[ Reference URL ]2つの球の間の固有正則写像は自己同型写像である。球を別の領域にしたらどうなるかを調べたい。球の一般化として複素擬楕円体や有界対称領域が考えられる。これら2つの領域を合わせた領域としてHua領域がある。これは有界対称領域の上に複素擬楕円体が乗っているような領域である。Hua領域の一番簡単な場合としてCartan-Hartogs領域があり、これらの間の固有正則写像の分類問題を考える。分類すると本質的には１種類の写像しかないことが分かる。ここでは2つの多項式写像が自己同型写像の差を省いて一致すれば、Isotoropy写像の差を省いて一致することを使う。

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/05/20

#### Information Mathematics Seminar

16:50-18:35 Online

Speedup principle of the classic computing and Innovation of the law of causation in the quantum computing (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Speedup principle of the classic computing and Innovation of the law of causation in the quantum computing (Japanese)

[ Abstract ]

Explanation on the speedup principle of the classic computing and innovation of the law of causation in the quantum computing.

[ Reference URL ]Explanation on the speedup principle of the classic computing and innovation of the law of causation in the quantum computing.

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

This talk is based on joint work with Tsutomu Nakamura. For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable flat cotorsion right modules and the isoclasses of indecomposable injective left modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality between Ziegler spectra.

[ Reference URL ]

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

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

**Ryo Kanda**(Osaka city University)This talk is based on joint work with Tsutomu Nakamura. For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable flat cotorsion right modules and the isoclasses of indecomposable injective left modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality between Ziegler spectra.

[ Reference URL ]

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

### 2021/05/19

#### Seminar on Probability and Statistics

14:30-16:00 Online

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

Limit Theorems and Random Fractal Curves in Statistical Mechanics (ENGLISH)

https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

**Federico Camia**(NYU Abu Dhabi)Limit Theorems and Random Fractal Curves in Statistical Mechanics (ENGLISH)

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.

https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform

#### Seminar on Probability and Statistics

14:30-16:00 Room # (Graduate School of Math. Sci. Bldg.)

Limit Theorems and Random Fractal Curves in Statistical Mechanics

https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform

**Federico Camia**(NYU Abu Dhabi)Limit Theorems and Random Fractal Curves in Statistical Mechanics

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Statistical mechanics deals with systems that have a large number of components whose behavior can often be considered random. For this reason, probability theory plays an essential role in the mathematical analysis of the subject. After a gentle introduction to statistical mechanics, I will give a nontechnical overview of recent, exciting developments that combine in a beautiful and unexpected way discrete probability, stochastic processes and complex analysis. For concreteness, I will discuss two specific models, percolation and the Ising model, which have a long history, have played an important part in the development of statistical mechanics, and occupy a central place in modern probability theory.

https://docs.google.com/forms/d/e/1FAIpQLSe2ObhY3dsFUUU4EaRyslLiAwfuA6chMmiw5uyfa1bvKMdyfg/viewform

### 2021/05/18

#### Operator Algebra Seminars

16:45-18:15 Online

Simplicity of $C^*$-algebras associated to some self-similar groups

[ Reference URL ]

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

**Keisuke Yoshida**(Hokkaido Univ.)Simplicity of $C^*$-algebras associated to some self-similar 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.

On derivations of free algebras over an operad and the generalized divergence (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Geoffrey Powell**(CNRS and University of Angers)On derivations of free algebras over an operad and the generalized divergence (ENGLISH)

[ Abstract ]

This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.

One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.

The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.

[ Reference URL ]This talk will first introduce the generalized divergence map from the Lie algebra of derivations of a free algebra over an operad to the trace space of the appropriate associative algebra. This encompasses the Satoh trace (for Lie algebras) and the double divergence of Alekseev, Kawazumi, Kuno and Naef (for associative algebras). The generalized divergence is a Lie 1-cocyle.

One restricts to considering the positive degree subalgebra with respect to the natural grading on the Lie algebra of derivations. The relationship of the positive subalgebra with its subalgebra generated in degree one is of particular interest. For example, this question arises in considering the Johnson morphism in the Lie case.

The talk will outline the structural results obtained by using the generalized divergence. These were inspired by Satoh's study of the kernel of the trace map in the Lie case. A new ingredient is the usage of naturality with respect to the category of free, finite-rank abelian groups and split monomorphisms. This allows global results to be formulated using 'torsion' for functors on this category and extends the usage of naturality with respect to the general linear groups.

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

#### Lie Groups and Representation Theory

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

Affine Yangians and rectangular W-algebras (Japanese)

**Mamoru UEDA**(Kyoto University)Affine Yangians and rectangular W-algebras (Japanese)

[ Abstract ]

Motivated by the generalized AGT conjecture, in this talk I will construct surjective homomorphisms from Guay's affine Yangians to the universal enveloping algebras of rectangular W-algebras of type A.

This result is a super affine analogue of a result of Ragoucy and Sorba, which gave surjective homomorphisms from finite Yangians of type A to rectangular finite W-algebras of type A.

Motivated by the generalized AGT conjecture, in this talk I will construct surjective homomorphisms from Guay's affine Yangians to the universal enveloping algebras of rectangular W-algebras of type A.

This result is a super affine analogue of a result of Ragoucy and Sorba, which gave surjective homomorphisms from finite Yangians of type A to rectangular finite W-algebras of type A.

### 2021/05/17

#### Algebraic Geometry Seminar

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

Calabi problem for smooth Fano threefolds (English)

**Ivan Cheltsov**(Edinburgh)Calabi problem for smooth Fano threefolds (English)

[ Abstract ]

In this talk I will explain which three-dimensional complex Fano manifolds admit Kahler-Einstein metrics.

In this talk I will explain which three-dimensional complex Fano manifolds admit Kahler-Einstein metrics.

### 2021/05/13

#### Algebraic Geometry Seminar

9:00-10:00 Room #zoom (Graduate School of Math. Sci. Bldg.)

いつもと日時が異なります。京大と共催

Relative vanishing theorems for schemes of equal characteristic zero (Englishg)

いつもと日時が異なります。京大と共催

**Takumi Murayama**(Princeton)Relative vanishing theorems for schemes of equal characteristic zero (Englishg)

[ Abstract ]

In 1953, Kodaira proved the Kodaira vanishing theorem, which states that if L is an ample divisor on a complex projective manifold X, then H^i(X,-L) = 0 for all i < dim(X). Since then, Kodaira's theorem and its generalizations have become indispensable tools in algebraic geometry over fields of characteristic zero. Even in this context, however, it is often necessary to work with schemes of finite type over power series rings, and a fundamental problem has been the lack of vanishing theorems in this setting.

We prove the analogue of the Kawamata-Viehweg vanishing theorem for proper morphisms of schemes of equal characteristic zero, which implies Kodaira's vanishing theorem in this context. This result resolves conjectures of Boutot and Kawakita, and is an important ingredient toward establishing the minimal model program for excellent schemes of equal characteristic zero.

In 1953, Kodaira proved the Kodaira vanishing theorem, which states that if L is an ample divisor on a complex projective manifold X, then H^i(X,-L) = 0 for all i < dim(X). Since then, Kodaira's theorem and its generalizations have become indispensable tools in algebraic geometry over fields of characteristic zero. Even in this context, however, it is often necessary to work with schemes of finite type over power series rings, and a fundamental problem has been the lack of vanishing theorems in this setting.

We prove the analogue of the Kawamata-Viehweg vanishing theorem for proper morphisms of schemes of equal characteristic zero, which implies Kodaira's vanishing theorem in this context. This result resolves conjectures of Boutot and Kawakita, and is an important ingredient toward establishing the minimal model program for excellent schemes of equal characteristic zero.

#### Information Mathematics Seminar

16:50-18:35 Online

Speedup of the classic computing and quantum computing (Japanese)

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Speedup of the classic computing and quantum computing (Japanese)

[ Abstract ]

Explanation on the speedup of classic computing and quantum computing

[ Reference URL ]Explanation on the speedup of classic computing and quantum computing

https://docs.google.com/forms/d/1zdmPdHWcVgH6Sn62nVHNp0ODVBJ7fyHKJHdABtDd_Tw

### 2021/05/11

#### Operator Algebra Seminars

17:15-18:45 Online

The time slot is different from usual.

The split property and absence of superselection sectors in 2D (English)

[ Reference URL ]

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

The time slot is different from usual.

**Pieter Naaijkens**(Cardiff Univ.)The split property and absence of superselection sectors in 2D (English)

[ Reference URL ]

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

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