## Seminar information archive

Seminar information archive ～09/15｜Today's seminar 09/16 | Future seminars 09/17～

#### Tuesday Seminar on Topology

17:00-18:00 Online

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

On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (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.

**Keiichi Maeta**(The Univesity of Tokyo)On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (JAPANESE)

[ Abstract ]

For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford—Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s. We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).

[ Reference URL ]For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford—Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s. We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).

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

#### Lie Groups and Representation Theory

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

Joint with Tuesday Seminar on Topology.

On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (Japanese)

Joint with Tuesday Seminar on Topology.

**Keiichi Maeta**(The University of Tokyo)On the existence problem of Compact Clifford-Klein forms of indecomposable pseudo-Riemannian symmetric spaces with signature (n,2) (Japanese)

[ Abstract ]

For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford-Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s.

We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).

For a homogeneous space $G/H$ and its discontinuous group $\Gamma\subset G$, the double coset space $\Gamma\backslash G/H$ is called a Clifford-Klein form of $G/H$. In the study of Clifford-Klein forms, the classification of homogeneous spaces which admit compact Clifford-Klein forms is one of the important open problems, which was introduced by Toshiyuki Kobayashi in 1980s.

We consider this problem for indecomposable and reducible pseudo-Riemannian symmetric spaces with signature (n,2). We show the non-existence of compact Clifford-Klein forms for some series of symmetric spaces, and construct new compact Clifford-Klein forms of countably infinite five-dimensional pseudo-Riemannian symmetric spaces with signature (3,2).

### 2022/01/06

#### Information Mathematics Seminar

16:50-18:35 Online

Next cyber security strategy of the Japanese Government (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Next cyber security strategy of the Japanese Government (Japanese)

[ Abstract ]

Explanation on next cyber security strategy of the Japanese government

[ Reference URL ]Explanation on next cyber security strategy of the Japanese government

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/12/23

#### Information Mathematics Seminar

16:50-18:35 Online

The cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google (Japanese)

[ Abstract ]

Explanation on the cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google

[ Reference URL ]Explanation on the cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/12/22

#### Number Theory Seminar

17:00-18:00 Online

Some properties of the Hecke eigenclasses of the mod p-cohomology of Shimura curves (English)

**Stefano Morra**(Paris 8 University)Some properties of the Hecke eigenclasses of the mod p-cohomology of Shimura curves (English)

[ Abstract ]

The mod p local Langlands program, foreseen by Serre and proposed in precise terms by C. Breuil after his p-divisible groups computations in the Breuil-Conrad-Diamond-Taylor proof of the Shimura-Taiyama-Weil conjecture, was realized in the particular case of GL_2(\mathbf{Q}_p) thanks to a vast convergence of new tools: classification of mod p-representations of GL_2(\mathbf{Q}_p), local Galois deformation techniques, local-global compatibility arguments.

When trying to extend these conjectures to more general groups, multiple problems arise (lack of classification results for smooth mod p-representations of p-adic groups, absence of explicit integral models for Galois representations with the relevant p-adic Hodge theory conditions), and the only way to formulate, and test, conjectures on a mod p local Langlands correspondence relies on its expected realization in Hecke eigenclasses of Shimura varieties (or, in other words, the expectation of a local-global compatibility of the Langlands correspondence).

In this talk we describe some properties of Hecke isotypical spaces of the mod p-cohomology of Shimura curves with infinite level at p, when the reflex field F is unramified at p and the Shimura curve arises from a quaternion algebra which is split at p. These Hecke isotypical spaces are expected to be the “good” smooth mod p-representations of GL_2(F_{\mathfrak{p}}) attached to mod p Galois representations of Gal(\overline{\mathbf{Q}_p}/F_{\mathfrak{p}}) via the expected local Langlands correspondence mod p. We will in particular comment on their Gelfand-Kirillov dimension, and their irreducibility (in particular, the finite length of these Hecke eigenspaces as GL_2(F_{\mathfrak{p}})-representations).

This is a report on a series of work joint with C. Breuil, F. Herzig, Y. Hu et B. Schraen.

The mod p local Langlands program, foreseen by Serre and proposed in precise terms by C. Breuil after his p-divisible groups computations in the Breuil-Conrad-Diamond-Taylor proof of the Shimura-Taiyama-Weil conjecture, was realized in the particular case of GL_2(\mathbf{Q}_p) thanks to a vast convergence of new tools: classification of mod p-representations of GL_2(\mathbf{Q}_p), local Galois deformation techniques, local-global compatibility arguments.

When trying to extend these conjectures to more general groups, multiple problems arise (lack of classification results for smooth mod p-representations of p-adic groups, absence of explicit integral models for Galois representations with the relevant p-adic Hodge theory conditions), and the only way to formulate, and test, conjectures on a mod p local Langlands correspondence relies on its expected realization in Hecke eigenclasses of Shimura varieties (or, in other words, the expectation of a local-global compatibility of the Langlands correspondence).

In this talk we describe some properties of Hecke isotypical spaces of the mod p-cohomology of Shimura curves with infinite level at p, when the reflex field F is unramified at p and the Shimura curve arises from a quaternion algebra which is split at p. These Hecke isotypical spaces are expected to be the “good” smooth mod p-representations of GL_2(F_{\mathfrak{p}}) attached to mod p Galois representations of Gal(\overline{\mathbf{Q}_p}/F_{\mathfrak{p}}) via the expected local Langlands correspondence mod p. We will in particular comment on their Gelfand-Kirillov dimension, and their irreducibility (in particular, the finite length of these Hecke eigenspaces as GL_2(F_{\mathfrak{p}})-representations).

This is a report on a series of work joint with C. Breuil, F. Herzig, Y. Hu et B. Schraen.

### 2021/12/21

#### Tuesday Seminar on Topology

17:30-18:30 Online

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

Classification of holomorphic vertex operator algebras of central charge 24 (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.

**Hiroki Shimakura**(Tohoku University)Classification of holomorphic vertex operator algebras of central charge 24 (JAPANESE)

[ Abstract ]

Holomorphic vertex operator algebras are imporant in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic. One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras. I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.

[ Reference URL ]Holomorphic vertex operator algebras are imporant in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic. One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras. I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.

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

#### Operator Algebra Seminars

16:45-18:15 Online

Interacting massless infraparticles in 1+1 dimensions

(English)

[ Reference URL ]

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

**Wojciech Dybalski**(Adam Mickiewicz University in Poznan)Interacting massless infraparticles in 1+1 dimensions

(English)

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Joint with Tuesday Seminar on Topology.

Classification of holomorphic vertex operator algebras of central charge 24

(Japanese)

Joint with Tuesday Seminar on Topology.

**Hiroki Shimakura**(Tohoku University)Classification of holomorphic vertex operator algebras of central charge 24

(Japanese)

[ Abstract ]

Holomorphic vertex operator algebras are important in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic.

One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras.

I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.

Holomorphic vertex operator algebras are important in vertex operator algebra theory. For example, the famous moonshine vertex operator algebra is holomorphic.

One of the fundamental problems is to classify holomorphic vertex operator algebras. It is known that holomorphic vertex operator algebras of central charge 8 and 16 are lattice vertex operator algebras.

I will talk about recent progress on the classification of holomorphic vertex operator algebras of central charge 24.

### 2021/12/17

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, December 17).

Growth vectors of distributions and lines on projective hypersurfaces (ENGLISH)

Registration is closed (12:00, December 17).

**Jun-Muk Hwang**(Center for Complex Geometry, IBS, Korea)Growth vectors of distributions and lines on projective hypersurfaces (ENGLISH)

[ Abstract ]

For a distribution on a manifold, its growth vector is a finite sequence of integers measuring the dimensions of the directions spanned by successive Lie brackets of local vector fields belonging to the distribution. The growth vector is the most basic invariant of a distribution, but it is sometimes hard to compute. As an example, we discuss natural distributions on the spaces of lines covering hypersurfaces of low degrees in the complex projective space. We explain the ideas in a joint work with Qifeng Li where the growth vector is determined for lines on a general hypersurface of degree 4 and dimension 5.

For a distribution on a manifold, its growth vector is a finite sequence of integers measuring the dimensions of the directions spanned by successive Lie brackets of local vector fields belonging to the distribution. The growth vector is the most basic invariant of a distribution, but it is sometimes hard to compute. As an example, we discuss natural distributions on the spaces of lines covering hypersurfaces of low degrees in the complex projective space. We explain the ideas in a joint work with Qifeng Li where the growth vector is determined for lines on a general hypersurface of degree 4 and dimension 5.

### 2021/12/16

#### Applied Analysis

16:00-17:00 Online

Existence of solutions for fractional semilinear parabolic equations in Besov-Morrey spaces (Japanese)

[ Reference URL ]

https://forms.gle/whpkgAwYvyQKQMzM8

**Zhanpeisov Erbol**( )Existence of solutions for fractional semilinear parabolic equations in Besov-Morrey spaces (Japanese)

[ Reference URL ]

https://forms.gle/whpkgAwYvyQKQMzM8

#### Tokyo-Nagoya Algebra Seminar

16:45-18:15 Online

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

Cyclic polytopes and higher Auslander-Reiten theory (English)

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

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

**Nicholas Williams**(University of Cologne)Cyclic polytopes and higher Auslander-Reiten theory (English)

[ Abstract ]

Oppermann and Thomas show that tilting modules over Iyama’s higher Auslander algebras of type A are in bijection with triangulations of even-dimensional cyclic polytopes. Triangulations of cyclic polytopes are partially ordered in two natural ways known as the higher Stasheff-Tamari orders, which were introduced in the 1990s by Kapranov, Voevodsky, Edelman, and Reiner as higher-dimensional generalisations of the Tamari lattice. These two partial orders were conjectured to be equal in 1996 by Edelman and Reiner, and we prove that this conjecture is true. We further show how the higher Stasheff-Tamari orders correspond in even dimensions to natural orders on tilting modules which were studied by Riedtmann, Schofield, Happel, and Unger. This then allows us to complete the picture of Oppermann and Thomas by showing that triangulations of odd-dimensional cyclic polytopes correspond to equivalence classes of d-maximal green sequences, which we introduce as higher-dimensional analogues of Keller’s maximal green sequences. We show that the higher Stasheff-Tamari orders correspond to natural orders on equivalence classes of d-maximal green sequences, which relate to the no-gap conjecture of Brustle, Dupont, and Perotin. The equality of the higher Stasheff-Tamari orders then implies that these algebraic orders on tilting modules and d-maximal green sequences are equal. If time permits, we will also discuss some results on mutation of cluster-tilting objects and triangulations.

[ Reference URL ]Oppermann and Thomas show that tilting modules over Iyama’s higher Auslander algebras of type A are in bijection with triangulations of even-dimensional cyclic polytopes. Triangulations of cyclic polytopes are partially ordered in two natural ways known as the higher Stasheff-Tamari orders, which were introduced in the 1990s by Kapranov, Voevodsky, Edelman, and Reiner as higher-dimensional generalisations of the Tamari lattice. These two partial orders were conjectured to be equal in 1996 by Edelman and Reiner, and we prove that this conjecture is true. We further show how the higher Stasheff-Tamari orders correspond in even dimensions to natural orders on tilting modules which were studied by Riedtmann, Schofield, Happel, and Unger. This then allows us to complete the picture of Oppermann and Thomas by showing that triangulations of odd-dimensional cyclic polytopes correspond to equivalence classes of d-maximal green sequences, which we introduce as higher-dimensional analogues of Keller’s maximal green sequences. We show that the higher Stasheff-Tamari orders correspond to natural orders on equivalence classes of d-maximal green sequences, which relate to the no-gap conjecture of Brustle, Dupont, and Perotin. The equality of the higher Stasheff-Tamari orders then implies that these algebraic orders on tilting modules and d-maximal green sequences are equal. If time permits, we will also discuss some results on mutation of cluster-tilting objects and triangulations.

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

#### Information Mathematics Seminar

16:50-18:35 Online

The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

[ Abstract ]

Explanation on the cyber attack to the supply chain network of car company and zero trust by the Cisco Systems

[ Reference URL ]Explanation on the cyber attack to the supply chain network of car company and zero trust by the Cisco Systems

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/12/15

#### Seminar on Probability and Statistics

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

Theory of Distribution-free Testing

https://docs.google.com/forms/d/e/1FAIpQLSdFj1XF8WJSPRmE0GFKY2QxscaGxC9msM6GkEsAf0TgD9yv2g/viewform

**Estate Khmaladze**(Victoria University of Wellington)Theory of Distribution-free Testing

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

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

The aim of the talk is to introduce transformations of empirical-type processes by a group of unitary operators. Recall that if v_{nP} is empirical process on real line, based on a sample from P, it can be mapped into empirical process v_{nQ} by appropriate change of time

v_{nP}(h(x))=v_{nQ}(x)

where h(x) is continuous and increasing. This is the basis for distribution-free theory of goodness of fit testing. If w(\phi) is a function-parametric “empirical-type” process (i.e. has functions \phi from a space L as a time) and if K* is a unitary operator on L, then transformed process Kw we define as

Kw(\phi) = w(K*\phi)

These two formulas have good similarity, but one transformation in on the real line, while the other transformation in on functional space.This later one turns out to be of very broad use, and allows to base distribution-free theory upon it. Examples, we have specific results for, are parametric empirical

processes in R^d, regression empirical processes, those in GLM, parametric models for point processes and for Markov processes in discrete time. Hopefully, further examples will follow.

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

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

The aim of the talk is to introduce transformations of empirical-type processes by a group of unitary operators. Recall that if v_{nP} is empirical process on real line, based on a sample from P, it can be mapped into empirical process v_{nQ} by appropriate change of time

v_{nP}(h(x))=v_{nQ}(x)

where h(x) is continuous and increasing. This is the basis for distribution-free theory of goodness of fit testing. If w(\phi) is a function-parametric “empirical-type” process (i.e. has functions \phi from a space L as a time) and if K* is a unitary operator on L, then transformed process Kw we define as

Kw(\phi) = w(K*\phi)

These two formulas have good similarity, but one transformation in on the real line, while the other transformation in on functional space.This later one turns out to be of very broad use, and allows to base distribution-free theory upon it. Examples, we have specific results for, are parametric empirical

processes in R^d, regression empirical processes, those in GLM, parametric models for point processes and for Markov processes in discrete time. Hopefully, further examples will follow.

https://docs.google.com/forms/d/e/1FAIpQLSdFj1XF8WJSPRmE0GFKY2QxscaGxC9msM6GkEsAf0TgD9yv2g/viewform

### 2021/12/14

#### Operator Algebra Seminars

16:45-18:15 Online

Constructions in minimal amenable dynamics and applications to classification of $C^*$-algebras

[ Reference URL ]

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

**Karen Strung**(Czech Academy of Science)Constructions in minimal amenable dynamics and applications to classification of $C^*$-algebras

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

On the definition of Conley indices (Japanese)

**Yosuke Morita**(Kyoto University)On the definition of Conley indices (Japanese)

[ Abstract ]

Conley indices are used to describe local behaviour of topological dynamical systems. In this talk, I will explain a new framework for Conley index theory. Our approach is very elementary, and uses only general topology and some computations of inclusion relations of subsets.

Conley indices are used to describe local behaviour of topological dynamical systems. In this talk, I will explain a new framework for Conley index theory. Our approach is very elementary, and uses only general topology and some computations of inclusion relations of subsets.

### 2021/12/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

A generalized Hermitian curvature flow on almost Hermitian manifolds (Japanese)

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

**Masaya Kawamura**(National Institute of Technology)A generalized Hermitian curvature flow on almost Hermitian manifolds (Japanese)

[ Abstract ]

It is well-known that the Uniformization theorem (any Riemannian metric on a closed 2-manifold is conformal to one of constant curvature) can be proven by using the Ricci flow. J. Streets and G. Tian questioned whether or not a geometric flow can be used to classify non-Kähler complex surfaces as in the case of the Ricci flow. Also they asked if it is possible to prove classification results in higher dimensions by using geometric flows in non-Kähler Hermitian geometry. Streets and Tian considered that these flows should be close to the Kähler-Ricci flow as much as possible. From this point of view, they introduced a geometric flow called the Hermitian curvature flow (HCF) which evolves an initial Hermitian metric in the direction of a Ricci-type tensor of the Chern connection modified with some lower order torsion terms. Streets and Tian also introduced another geometric flow, which is called the pluriclosed flow (PCF), by choosing torsion terms to preserve the pluriclosed condition on Hermitian metrics. Y. Ustinovskiy studied a particular version of the HCF over a compact Hermitian manifold. Ustinovskiy proved that if the initial metric has Griffiths positive (non-negative) Chern curvature, then this property is preserved along the flow.

In recent years, some results concerning geometric flows on complex manifolds have been extended to the almost complex setting. For instance, L. Vezzoni defined a new Hermitian curvature flow on almost Hermitian manifolds for generalizing some studies on the HCF and the Hermitian Hilbert functional. And J. Chu, V. Tosatti and B. Weinkove considered parabolic Monge-Ampère equation on almost Hermitian manifolds, which is equivalent to the almost complex Chern-Ricci flow. T. Zheng characterized the maximal existence time for a solution to the almost complex Chern-Ricci flow.

In this talk, we consider a generalized Hermitian curvature flow in almost Hermitian geometry and introduce that it has some properties such as the long-time existence obstruction, the uniform equivalence between its solution and an almost Hermitian metric, and the preservation result along the flow.

[ Reference URL ]It is well-known that the Uniformization theorem (any Riemannian metric on a closed 2-manifold is conformal to one of constant curvature) can be proven by using the Ricci flow. J. Streets and G. Tian questioned whether or not a geometric flow can be used to classify non-Kähler complex surfaces as in the case of the Ricci flow. Also they asked if it is possible to prove classification results in higher dimensions by using geometric flows in non-Kähler Hermitian geometry. Streets and Tian considered that these flows should be close to the Kähler-Ricci flow as much as possible. From this point of view, they introduced a geometric flow called the Hermitian curvature flow (HCF) which evolves an initial Hermitian metric in the direction of a Ricci-type tensor of the Chern connection modified with some lower order torsion terms. Streets and Tian also introduced another geometric flow, which is called the pluriclosed flow (PCF), by choosing torsion terms to preserve the pluriclosed condition on Hermitian metrics. Y. Ustinovskiy studied a particular version of the HCF over a compact Hermitian manifold. Ustinovskiy proved that if the initial metric has Griffiths positive (non-negative) Chern curvature, then this property is preserved along the flow.

In recent years, some results concerning geometric flows on complex manifolds have been extended to the almost complex setting. For instance, L. Vezzoni defined a new Hermitian curvature flow on almost Hermitian manifolds for generalizing some studies on the HCF and the Hermitian Hilbert functional. And J. Chu, V. Tosatti and B. Weinkove considered parabolic Monge-Ampère equation on almost Hermitian manifolds, which is equivalent to the almost complex Chern-Ricci flow. T. Zheng characterized the maximal existence time for a solution to the almost complex Chern-Ricci flow.

In this talk, we consider a generalized Hermitian curvature flow in almost Hermitian geometry and introduce that it has some properties such as the long-time existence obstruction, the uniform equivalence between its solution and an almost Hermitian metric, and the preservation result along the flow.

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

### 2021/12/09

#### Information Mathematics Seminar

16:50-18:35 Online

The consideration of the account injustice access case and zero trust by Microsoft (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The consideration of the account injustice access case and zero trust by Microsoft (Japanese)

[ Abstract ]

The explanation on the account injustice access case and zero trust by Microsoft

[ Reference URL ]The explanation on the account injustice access case and zero trust by Microsoft

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/12/07

#### Operator Algebra Seminars

16:45-18:15 Online

Classification of quantum graphs on $M_2$ and their quantum automorphism groups

[ Reference URL ]

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

**Junichiro Matsuda**(Kyoto Univ.)Classification of quantum graphs on $M_2$ and their quantum automorphism groups

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-1800 Online

Pre-registration required. See our seminar webpage.

A Bar-Natan homotopy type (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Taketo Sano**(The Univesity of Tokyo)A Bar-Natan homotopy type (JAPANESE)

[ Abstract ]

In year 2000, Khovanov introduced a categorification of the Jones polynomial, now known as Khovanov homology. In 2014, Lipshitz and Sarkar introduced a spatial refinement of Khovanov homology, called Khovanov homotopy type, which is a finite CW spectrum whose reduced cellular cohomology recovers Khovanov homology. On the algebraic level, there are several deformations of Khovanov homology, such as Lee homology and Bar-Natan homology. These variants are also important in that they give knot invariants such as Rasmussen’s $s$-invariant. Whether these variants admit spatial refinements have been open.

In 2021, the speaker constructed a spatial refinement of Bar-Natan homology and determined its stable homotopy type. The construction follows that of Lipshitz and Sarkar, which is based on the construction proposed by Cohen, Segal and Jones using the concept of flow categories. Also, we adopt techniques called “Morse moves in flow categories” introduced by Lobb et.al. to determine the stable homotopy type. Spacialy (or homotopically) refining the $s$-invariant is left as a future work.

[ Reference URL ]In year 2000, Khovanov introduced a categorification of the Jones polynomial, now known as Khovanov homology. In 2014, Lipshitz and Sarkar introduced a spatial refinement of Khovanov homology, called Khovanov homotopy type, which is a finite CW spectrum whose reduced cellular cohomology recovers Khovanov homology. On the algebraic level, there are several deformations of Khovanov homology, such as Lee homology and Bar-Natan homology. These variants are also important in that they give knot invariants such as Rasmussen’s $s$-invariant. Whether these variants admit spatial refinements have been open.

In 2021, the speaker constructed a spatial refinement of Bar-Natan homology and determined its stable homotopy type. The construction follows that of Lipshitz and Sarkar, which is based on the construction proposed by Cohen, Segal and Jones using the concept of flow categories. Also, we adopt techniques called “Morse moves in flow categories” introduced by Lobb et.al. to determine the stable homotopy type. Spacialy (or homotopically) refining the $s$-invariant is left as a future work.

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

#### Lie Groups and Representation Theory

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

On the classification of the $K$-type formulas for the Heisenberg ultrahyperbolic equation (Japanese)

**Toshihisa Kubo**(Ryukoku University)On the classification of the $K$-type formulas for the Heisenberg ultrahyperbolic equation (Japanese)

[ Abstract ]

About ten years ago, Kable constructed a one-parameter family $\square^{(n)}_s$ ($s\in \mathbb{C}$) of differential operators for $\mathfrak{sl}(n,\mathbb{C})$. He referred to $\square^{(n)}_s$ as the Heisenberg ultrahyperbolic operator. In the viewpoint of intertwining operators, $\square^{(n)}_s$ can be thought of as an intertwining differential operator between certain parabolically induced representations for $\widetilde{SL}(n,\mathbb{R})$. In this talk we discuss about the classification of the $K$-type formulas of the space of $K$-finite solutions to the differential equation $\square^{(3)}_sf=0$ for $\widetilde{SL}(3,\mathbb{R})$ and some related topics. This is joint work with Bent {\O}rsted.

About ten years ago, Kable constructed a one-parameter family $\square^{(n)}_s$ ($s\in \mathbb{C}$) of differential operators for $\mathfrak{sl}(n,\mathbb{C})$. He referred to $\square^{(n)}_s$ as the Heisenberg ultrahyperbolic operator. In the viewpoint of intertwining operators, $\square^{(n)}_s$ can be thought of as an intertwining differential operator between certain parabolically induced representations for $\widetilde{SL}(n,\mathbb{R})$. In this talk we discuss about the classification of the $K$-type formulas of the space of $K$-finite solutions to the differential equation $\square^{(3)}_sf=0$ for $\widetilde{SL}(3,\mathbb{R})$ and some related topics. This is joint work with Bent {\O}rsted.

### 2021/12/02

#### Information Mathematics Seminar

16:50-18:35 Online

The whole summary and other machine learning technique in the AI

～ LSTM/GAN/Unsupervised learning /Auto Encoder～ (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The whole summary and other machine learning technique in the AI

～ LSTM/GAN/Unsupervised learning /Auto Encoder～ (Japanese)

[ Abstract ]

The whole summary and the explanation on other machine learning techniques in the AI (LSTM/GAN/Unsupervised learning /Auto Encoder).

[ Reference URL ]The whole summary and the explanation on other machine learning techniques in the AI (LSTM/GAN/Unsupervised learning /Auto Encoder).

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

#### Applied Analysis

### 2021/11/30

#### Operator Algebra Seminars

16:45-18:15 Online

Crystallographic $T$-duality in twisted equivariant $K$-theory

[ Reference URL ]

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

**Yosuke Kubota**(Shinshu Univ.)Crystallographic $T$-duality in twisted equivariant $K$-theory

[ 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.

A non-commutative Reidemeister-Turaev torsion of homology cylinders (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Masatoshi Sato**(Tokyo Denki University)A non-commutative Reidemeister-Turaev torsion of homology cylinders (JAPANESE)

[ Abstract ]

The Reidemeister-Turaev torsion of homology cylinders takes values in the integral group ring of the first homology of a surface. We lift it to a torsion valued in the $K_1$-group of the completed rational group ring of the fundamental group of the surface. We show that it induces a finite type invariant of homology cylinders, and describe the induced map on the graded quotient of the Y-filtration of homology cylinders via the 1-loop part of the LMO functor and the Enomoto-Satoh trace. This talk is based on joint work with Yuta Nozaki and Masaaki Suzuki.

[ Reference URL ]The Reidemeister-Turaev torsion of homology cylinders takes values in the integral group ring of the first homology of a surface. We lift it to a torsion valued in the $K_1$-group of the completed rational group ring of the fundamental group of the surface. We show that it induces a finite type invariant of homology cylinders, and describe the induced map on the graded quotient of the Y-filtration of homology cylinders via the 1-loop part of the LMO functor and the Enomoto-Satoh trace. This talk is based on joint work with Yuta Nozaki and Masaaki Suzuki.

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

#### Mathematical Biology Seminar

15:30-17:00 Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)

Endogenous Waves in a SIR Model with Risk Heterogeneity

(Japanese)

[ Reference URL ]

オンライン開催です．参加希望者は inaba@ms.u-tokyo.ac.jp までご連絡ください．

**Takeshi OJIMA**(Fukushima University)Endogenous Waves in a SIR Model with Risk Heterogeneity

(Japanese)

[ Reference URL ]

オンライン開催です．参加希望者は inaba@ms.u-tokyo.ac.jp までご連絡ください．

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