## Seminar information archive

Seminar information archive ～09/10｜Today's seminar 09/11 | Future seminars 09/12～

#### 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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

The classification problem of non-topological invertible QFT's and a differential model for the Anderson duals (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Mayuko Yamashita**(RIMS, Kyoto University)The classification problem of non-topological invertible QFT's and a differential model for the Anderson duals (JAPANESE)

[ Abstract ]

Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. Actually this construction turns out to be mathematically interesting because of its relation with differential cohomology theories. I will start from basic motivations for the classification problem, reportthe progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Tohokku, physics).

[ Reference URL ]Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT's. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. Actually this construction turns out to be mathematically interesting because of its relation with differential cohomology theories. I will start from basic motivations for the classification problem, reportthe progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Tohokku, physics).

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

#### Numerical Analysis Seminar

16:30-18:00 Online

Topics on finite element error analysis on anisotropic meshes (Japanese)

[ Reference URL ]

https://forms.gle/CoaM4vSE1GvDRuDR6

**Takuya Tsuchiya**(Ehime University )Topics on finite element error analysis on anisotropic meshes (Japanese)

[ Reference URL ]

https://forms.gle/CoaM4vSE1GvDRuDR6

#### Lie Groups and Representation Theory

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

Online

Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups (Japanese)

Online

**Ryosuke NAKAHAMA**(Kyushu University)Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups (Japanese)

[ Abstract ]

Let $D¥subset M(r,¥mathbb{C})$ be the bounded symmetric domain, and we consider the weighted Bergman space $¥mathcal{H}_¥lambda(D)$ on $D$. Then $SU(r,r)$ acts unitarily on $¥mathcal{H}_¥lambda(D)$.

In this seminar, we compute explicitly the inner products for some polynomials on $¥operatorname{Alt}(r,¥mathbb{C})$, $¥operatorname{Sym}(r,¥mathbb{C})¥subset M(r,¥mathbb{C})$, and prove that the inner products are given by multivariate hypergeometric polynomials when the polynomials are some powers of the determinants or the Pfaffians.

As an application, we present the results on the construction of symmetry breaking operators from $SU(r,r)$ to $Sp(r,¥mathbb{R})$ or $SO^*(2r)$.

Let $D¥subset M(r,¥mathbb{C})$ be the bounded symmetric domain, and we consider the weighted Bergman space $¥mathcal{H}_¥lambda(D)$ on $D$. Then $SU(r,r)$ acts unitarily on $¥mathcal{H}_¥lambda(D)$.

In this seminar, we compute explicitly the inner products for some polynomials on $¥operatorname{Alt}(r,¥mathbb{C})$, $¥operatorname{Sym}(r,¥mathbb{C})¥subset M(r,¥mathbb{C})$, and prove that the inner products are given by multivariate hypergeometric polynomials when the polynomials are some powers of the determinants or the Pfaffians.

As an application, we present the results on the construction of symmetry breaking operators from $SU(r,r)$ to $Sp(r,¥mathbb{R})$ or $SO^*(2r)$.

### 2021/05/10

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

強擬凹複素曲面の境界に現れる接触構造 (Japanese)

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

**Naohiko Kasuya**(Hokkaido University)強擬凹複素曲面の境界に現れる接触構造 (Japanese)

[ Abstract ]

強擬凸複素曲面の境界は3次元強擬凸CR多様体であり、正の接触構造を誘導する。BogomolovとDe Oliveiraは強擬凸複素曲面の境界に現れる接触構造はStein fillableであること（CR構造としては、Stein fillableなものに変形同値であること）を示した。

一方、強擬凹複素曲面の境界には負の3次元接触構造が現れる。本講演では、任意の負の3次元閉接触多様体が強擬凹複素曲面の境界として実現可能であることを示す。証明は、EliashbergによるStein manifoldの構成法を参考にして強擬凹境界への正則ハンドルの接着手法を確立することによってなされる。

尚、本講演内容はDaniele Zuddas氏（トリエステ大学）との共同研究である。

[ Reference URL ]強擬凸複素曲面の境界は3次元強擬凸CR多様体であり、正の接触構造を誘導する。BogomolovとDe Oliveiraは強擬凸複素曲面の境界に現れる接触構造はStein fillableであること（CR構造としては、Stein fillableなものに変形同値であること）を示した。

一方、強擬凹複素曲面の境界には負の3次元接触構造が現れる。本講演では、任意の負の3次元閉接触多様体が強擬凹複素曲面の境界として実現可能であることを示す。証明は、EliashbergによるStein manifoldの構成法を参考にして強擬凹境界への正則ハンドルの接着手法を確立することによってなされる。

尚、本講演内容はDaniele Zuddas氏（トリエステ大学）との共同研究である。

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

### 2021/05/06

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

Derived quotients of Cohen-Macaulay rings (English)

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

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

**Liran Shaul**(Charles University)Derived quotients of Cohen-Macaulay rings (English)

[ Abstract ]

It is well known that if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is an $A$-regular sequence, then the quotient ring $A/(a_1,\dots,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by deriving the quotient operation, if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is any sequence of elements in $A$, the derived quotient of $A$ with respect to $(a_1,\dots,a_n)$ is Cohen-Macaulay. Several applications of this result are given, including a generalization of Hironaka's miracle flatness theorem to derived algebraic geometry.

[ Reference URL ]It is well known that if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is an $A$-regular sequence, then the quotient ring $A/(a_1,\dots,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by deriving the quotient operation, if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is any sequence of elements in $A$, the derived quotient of $A$ with respect to $(a_1,\dots,a_n)$ is Cohen-Macaulay. Several applications of this result are given, including a generalization of Hironaka's miracle flatness theorem to derived algebraic geometry.

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

#### Information Mathematics Seminar

16:50-18:35 Online

From the birth of the computer to high-speed computing (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)From the birth of the computer to high-speed computing (Japanese)

[ Abstract ]

Explanation on the birth of the computer and the development of high-speed computing

[ Reference URL ]Explanation on the birth of the computer and the development of high-speed computing

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

### 2021/04/30

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, April 30).

Uniform bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds (Talk in Japanese, Slide in English)

Registration is closed (12:00, April 30).

**Shihoko Ishii**(The University of Tokyo)Uniform bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds (Talk in Japanese, Slide in English)

[ Abstract ]

In the talk I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obtained by at most two weighted blow ups. Our proof suggests the following conjecture:

Every pair consisting of a smooth N-fold and a "general" real ideal is computed by a divisor obtained by at most N-1 weighted blow ups.

This is regarded as a weighted blow up version of Mustata-Nakamura's conjecture. The condition "general" is slightly weakened from the version presented in ZAG Seminar.

In the talk I will show that the minimal log discrepancy of every pair consisting of a smooth 3-fold and a "general" real ideal is computed by the divisor obtained by at most two weighted blow ups. Our proof suggests the following conjecture:

Every pair consisting of a smooth N-fold and a "general" real ideal is computed by a divisor obtained by at most N-1 weighted blow ups.

This is regarded as a weighted blow up version of Mustata-Nakamura's conjecture. The condition "general" is slightly weakened from the version presented in ZAG Seminar.

### 2021/04/28

#### Algebraic Geometry Seminar

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

Dimensional reduction in cohomological Donaldson-Thomas theory (日本語)

**Tasuki Kinjo**(Tokyo/IPMU)Dimensional reduction in cohomological Donaldson-Thomas theory (日本語)

[ Abstract ]

None

None

### 2021/04/27

#### Numerical Analysis Seminar

16:30-18:00 Online

Rigorous numerics for nonlinear heat equations in the complex plane of time (Japanese)

[ Reference URL ]

https://forms.gle/qW5ktphBB6dsh8Np7

**Akitoshi Takayasu**(University of Tsukuba)Rigorous numerics for nonlinear heat equations in the complex plane of time (Japanese)

[ Reference URL ]

https://forms.gle/qW5ktphBB6dsh8Np7

#### Operator Algebra Seminars

16:45-18:15 Online

The bulk-boundary correspondence for topological insulators on lattices with screw dislocation

[ Reference URL ]

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

**Yosuke Kubota**(Shinshu Univ.)The bulk-boundary correspondence for topological insulators on lattices with screw dislocation

[ 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 a singular de Rham complex in diffeology (JAPANESE)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj

Pre-registration required. See our seminar webpage.

**Katsuhiko Kuribayashi**(Shinshu University)On a singular de Rham complex in diffeology (JAPANESE)

[ Abstract ]

Diffeology gives a complete, co-complete, cartesian closed category into which the category of manifolds embeds. In the framework of diffeology, the de Rham complex in the sense of Souriau enables us to develop de Rham calculus. Moreover,Iglesias-Zemmour has been introduced homotopical concepts such as homotopy groups, cubic homology groups and fibrations in diffeology. Thus one might expect `differential homotopy theory'. However, the de Rham theorem does not hold for Souriau's cochain

complex in general. In this talk, I will introduce a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space.

[ Reference URL ]Diffeology gives a complete, co-complete, cartesian closed category into which the category of manifolds embeds. In the framework of diffeology, the de Rham complex in the sense of Souriau enables us to develop de Rham calculus. Moreover,Iglesias-Zemmour has been introduced homotopical concepts such as homotopy groups, cubic homology groups and fibrations in diffeology. Thus one might expect `differential homotopy theory'. However, the de Rham theorem does not hold for Souriau's cochain

complex in general. In this talk, I will introduce a singular de Rham complex endowed with an integration map into the singular cochain complex which gives the de Rham theorem for every diffeological space.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJUpcOCppzwpGd3r_XqdszQ1XN6FvXpNURbj

### 2021/04/26

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

多様体の留数 (Japanese)

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

**Jun O'Hara**(Chiba University)多様体の留数 (Japanese)

[ Abstract ]

$M$を多様体、$z$を複素数とし、$M$の二点間の距離の$z$乗を積空間$M\times M$上積分したものを考えると、$z$の実部が大きいところで$z$の正則関数になる。解析接続により複素平面上の有理関数で1位の極のみ持つものが得られる。この有理型関数、特にその留数の性質を紹介する。具体的には、メビウス不変性、留数と似た量（曲面のWillmoreエネルギー、4次元多様体のGraham-Wittenエネルギー、積分幾何で出てくる内在的体積、ラプラシアンのスペクトルなど）との比較、有理型関数・留数による多様体の同定問題などを扱う。

参考資料：https://sites.google.com/site/junohara/ ダウンロード 「多様体のエネルギーと留数」（少し古い）, arXiv:2012.01713

[ Reference URL ]$M$を多様体、$z$を複素数とし、$M$の二点間の距離の$z$乗を積空間$M\times M$上積分したものを考えると、$z$の実部が大きいところで$z$の正則関数になる。解析接続により複素平面上の有理関数で1位の極のみ持つものが得られる。この有理型関数、特にその留数の性質を紹介する。具体的には、メビウス不変性、留数と似た量（曲面のWillmoreエネルギー、4次元多様体のGraham-Wittenエネルギー、積分幾何で出てくる内在的体積、ラプラシアンのスペクトルなど）との比較、有理型関数・留数による多様体の同定問題などを扱う。

参考資料：https://sites.google.com/site/junohara/ ダウンロード 「多様体のエネルギーと留数」（少し古い）, arXiv:2012.01713

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

### 2021/04/22

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

Exact categories via A-infinity algebras (English)

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

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

**Julian Külshammer**(Uppsala University)Exact categories via A-infinity algebras (English)

[ Abstract ]

Many instances of extension closed subcategories appear throughout representation theory, e.g. filtered modules, Gorenstein projectives, as well as modules of finite projective dimension. In the first part of the talk, I will outline a general strategy to realise such subcategories as categories of induced modules from a subalgebra using A-infinity algebras. In the second part, I will describe how this strategy has been successfully applied for the exact category of filtered modules over a quasihereditary algebra. In particular I will present compatibility results of this approach with heredity ideals in a quasihereditary algebra from joint work with Teresa Conde.

[ Reference URL ]Many instances of extension closed subcategories appear throughout representation theory, e.g. filtered modules, Gorenstein projectives, as well as modules of finite projective dimension. In the first part of the talk, I will outline a general strategy to realise such subcategories as categories of induced modules from a subalgebra using A-infinity algebras. In the second part, I will describe how this strategy has been successfully applied for the exact category of filtered modules over a quasihereditary algebra. In particular I will present compatibility results of this approach with heredity ideals in a quasihereditary algebra from joint work with Teresa Conde.

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

#### Applied Analysis

16:30-18:00 Online

Relaxation of Optimal Transport problem on finite state space via Bregman divergence (Japanese)

[ Reference URL ]

https://forms.gle/yg9XZDVdxYG6qMos8

**( )**Relaxation of Optimal Transport problem on finite state space via Bregman divergence (Japanese)

[ Reference URL ]

https://forms.gle/yg9XZDVdxYG6qMos8

#### Information Mathematics Seminar

16:50-18:35 Online

Look back on the half life of a challenge to Digital technology and Entrepreneurship (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Look back on the half life of a challenge to Digital technology and Entrepreneurship (Japanese)

[ Abstract ]

Recollection on the half life of a challenge to Digital technology and Entrepreneurship

[ Reference URL ]Recollection on the half life of a challenge to Digital technology and Entrepreneurship

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

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