## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

#### Information Mathematics Seminar

16:50-18:35 Online

From machine learning to deep learning (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)From machine learning to deep learning (Japanese)

[ Abstract ]

Explanation on machine learning and deep learning

[ Reference URL ]Explanation on machine learning and deep learning

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

### 2021/06/16

#### Number Theory Seminar

17:00-18:00 Online

Hecke eigensystems of automorphic forms (mod p) of Hodge type and algebraic modular forms (Japanese)

**Yasuhiro Terakado**(National Center for Theoretical Sciences)Hecke eigensystems of automorphic forms (mod p) of Hodge type and algebraic modular forms (Japanese)

[ Abstract ]

In a 1987 letter to Tate, Serre showed that the prime-to-p Hecke eigensystems arising in the space of mod p modular forms are the same as those appearing in the space of automorphic forms on a quaternion algebra. This result is regarded as a mod p analogue of the Jacquet-Langlands correspondence. In this talk, we give a generalization of Serre's result to the Hecke eigensystems of mod p automorphic forms on a Shimura variety of Hodge type with good reduction at p. This is joint work with Chia-Fu Yu.

In a 1987 letter to Tate, Serre showed that the prime-to-p Hecke eigensystems arising in the space of mod p modular forms are the same as those appearing in the space of automorphic forms on a quaternion algebra. This result is regarded as a mod p analogue of the Jacquet-Langlands correspondence. In this talk, we give a generalization of Serre's result to the Hecke eigensystems of mod p automorphic forms on a Shimura variety of Hodge type with good reduction at p. This is joint work with Chia-Fu Yu.

#### Seminar on Probability and Statistics

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

Levy-Ornstein-Uhlenbeck Regression

https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform

**Hiroki Masuda**(Kyushu University)Levy-Ornstein-Uhlenbeck Regression

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

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

We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the

covariate process. Also discussed will be model-selection issues and some possible model extensions.

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

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

We will present some of recent developments in parametric inference for a linear regression model driven by a non-Gaussian stable Levy process, when the process is observed at high frequency over a fixed time period. The model depends on a covariate process and the finite-dimensional parameter: the stability index (activity index) and the scale in the noise term, and the (auto)regression coefficients in the trend term, all being unknown. The maximum-likelihood estimator is shown to be asymptotically mixed-normally distributed with maximum concentration property. In order to bypass possible multiple-root problem and heavy numerical optimization, we also consider some easily computable initial estimator with which the one-step improvement does work. The asymptotic properties hold true in a unified manner regardless of whether the model is stationary and/or ergodic, almost without taking care of character of the

covariate process. Also discussed will be model-selection issues and some possible model extensions.

https://docs.google.com/forms/d/e/1FAIpQLSfkHbmXT_3kHkBIUedzNSFqQ6QxuZzUQ9_qOgc8HqtZsKHTPQ/viewform

### 2021/06/15

#### Operator Algebra Seminars

16:45-18:15 Online

$C^*$-simplicity has no local obstruction

[ Reference URL ]

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

**Yuhei Suzuki**(Hokkaido Univ.)$C^*$-simplicity has no local obstruction

[ 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.

Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Takamichi Sato**(Waseda University)Direct decompositions of groups of piecewise linear homeomorphisms of the unit interval (JAPANESE)

[ Abstract ]

In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.

[ Reference URL ]In this talk, we consider subgroups of the group PLo(I) of piecewise linear orientation-preserving homeomorphisms of the unit interval I = [0, 1] that are differentiable everywhere except at finitely many real numbers, under the operation of composition. We provide a criterion for any two subgroups of PLo(I) which are direct products of finitely many indecomposable non-commutative groups to be non-isomorphic. As its application we give a necessary and sufficient condition for any two subgroups of the R. Thompson group F that are stabilizers of finite sets of numbers in the interval (0, 1) to be isomorphic.

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

#### Lie Groups and Representation Theory

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

Limit algebras and tempered representations (Japanese)

**Toshiyuki KOBAYASHI**(The University of Tokyo)Limit algebras and tempered representations (Japanese)

[ Abstract ]

I plan to discuss the new connection between the following four (apparently unrelated) topics:

1. (analysis) Tempered unitary representations on homogeneous spaces

2. (combinatorics) Convex polyhedral cones

3. (topology) Limit algebras

4. (symplectic geometry) Quantization of coadjoint orbits

based on a series of joint papers with Y. Benoist "Tempered homogeneous spaces I-IV".

I plan to discuss the new connection between the following four (apparently unrelated) topics:

1. (analysis) Tempered unitary representations on homogeneous spaces

2. (combinatorics) Convex polyhedral cones

3. (topology) Limit algebras

4. (symplectic geometry) Quantization of coadjoint orbits

based on a series of joint papers with Y. Benoist "Tempered homogeneous spaces I-IV".

### 2021/06/14

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Projective K3 surfaces containing Levi-flat hypersurfaces (Japanese)

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

**Takayuki Koike**(Osaka City University)Projective K3 surfaces containing Levi-flat hypersurfaces (Japanese)

[ Abstract ]

In May 2017, I reported on the gluing construction of a K3 surface at Seminar on Geometric Complex Analysis.

Here, by the gluing construction of a K3 surface, I mean the construction of a K3 surface by holomorphically gluing two open complex surfaces which are the complements of tubular neighborhoods of elliptic curves included in the blow-ups of the projective planes by nine points.

As of 2017, it was an open problem whether a projective K3 surface can be obtained by the gluing construction. Recently, I and Takato Uehara found a very concrete way to construct a projective K3 surface by the gluing method. As a corollary, we obtained the existence of non-Kummer projective K3 surface with compact Levi-flat hypersurfaces.

In this talk, I will explain the detail of the concrete gluing construction of such a K3 surface.

[ Reference URL ]In May 2017, I reported on the gluing construction of a K3 surface at Seminar on Geometric Complex Analysis.

Here, by the gluing construction of a K3 surface, I mean the construction of a K3 surface by holomorphically gluing two open complex surfaces which are the complements of tubular neighborhoods of elliptic curves included in the blow-ups of the projective planes by nine points.

As of 2017, it was an open problem whether a projective K3 surface can be obtained by the gluing construction. Recently, I and Takato Uehara found a very concrete way to construct a projective K3 surface by the gluing method. As a corollary, we obtained the existence of non-Kummer projective K3 surface with compact Levi-flat hypersurfaces.

In this talk, I will explain the detail of the concrete gluing construction of such a K3 surface.

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

#### Algebraic Geometry Seminar

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

Rank two weak Fano bundles on del Pezzo threefolds of degree 5 (日本語)

Zoom

**Wahei Hara**(University of Glasgow)Rank two weak Fano bundles on del Pezzo threefolds of degree 5 (日本語)

[ Abstract ]

None

[ Reference URL ]None

Zoom

### 2021/06/10

#### Information Mathematics Seminar

16:50-18:35 Online

A technical base of the AI and machine learning as the basis (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)A technical base of the AI and machine learning as the basis (Japanese)

[ Abstract ]

Explanation on a technical base of the AI and machine learning as the basis

[ Reference URL ]Explanation on a technical base of the AI and machine learning as the basis

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

### 2021/06/09

#### Algebraic Geometry Seminar

15:00-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Rational simple connectedness and Fano threefolds (English)

Zoom

**Andrea Fanelli**(Bordeaux)Rational simple connectedness and Fano threefolds (English)

[ Abstract ]

The notion of rational simple connectedness can be seen as an algebro-geometric analogue of simple connectedness in topology. The work of de Jong, He and Starr has already produced several recent studies to understand this notion.

In this talk I will discuss the joint project with Laurent Gruson and Nicolas Perrin to study rational simple connectedness for Fano threefolds via explicit methods from birational geometry.

[ Reference URL ]The notion of rational simple connectedness can be seen as an algebro-geometric analogue of simple connectedness in topology. The work of de Jong, He and Starr has already produced several recent studies to understand this notion.

In this talk I will discuss the joint project with Laurent Gruson and Nicolas Perrin to study rational simple connectedness for Fano threefolds via explicit methods from birational geometry.

Zoom

### 2021/06/08

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Local well-posedness for the Landau-Lifshitz equation with helicity term (Japanese)

https://forms.gle/nc85Mw9Jd6NgJzT98

**SHIMIZU Ikkei**(Osaka University)Local well-posedness for the Landau-Lifshitz equation with helicity term (Japanese)

[ Abstract ]

We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We show that it is locally well-posed in Sobolev spaces $H^s$ when $s>2$. The key idea is to reduce the problem to a system of semi-linear Schr\"odinger equations, called modified Schr\"odinger map equation. The problem here is that the helicity term appears as quadratic derivative nonlinearities, which is known to be difficult to treat as perturbation of the free evolution. To overcome that, we consider them as magnetic terms, then apply the energy method by introducing the differential operator associated with magnetic potentials.

[ Reference URL ]We consider the initial value problem for the Landau-Lifshitz equation with helicity term (chiral interaction term), which arises from the Dzyaloshinskii-Moriya interaction. We show that it is locally well-posed in Sobolev spaces $H^s$ when $s>2$. The key idea is to reduce the problem to a system of semi-linear Schr\"odinger equations, called modified Schr\"odinger map equation. The problem here is that the helicity term appears as quadratic derivative nonlinearities, which is known to be difficult to treat as perturbation of the free evolution. To overcome that, we consider them as magnetic terms, then apply the energy method by introducing the differential operator associated with magnetic potentials.

https://forms.gle/nc85Mw9Jd6NgJzT98

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Takahiro Matsusita**(University of the Ryukyus)Graphs whose Kronecker coverings are bipartite Kneser graphs (JAPANESE)

[ Abstract ]

Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.

In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.

In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.

[ Reference URL ]Kronecker coverings are bipartite double coverings of graphs which are canonically determined. If a graph G is non-bipartite and connected, then there is a unique bipartite double covering of G, and the Kronecker covering of G coincides with it.

In general, there are non-isomorphic graphs although they have the same Kronecker coverings. Therefore, for a given bipartite graph X, it is a natural problem to classify the graphs whose Kronecker coverings are isomorphic to X. Such a classification problem was actually suggested by Imrich and Pisanski, and has been settled in some cases.

In this lecture, we classify the graphs whose Kronecker coverings are bipartite Kneser graphs H(n, k). The Kneser graph K(n, k) is the graph whose vertex set is the family of k-subsets of the n-point set {1, …, n}, and two vertices are adjacent if and only if they are disjoint. The bipartite Kneser graph H(n, k) is the Kronecker covering of K(n, k). We show that there are exactly k graphs whose Kronecker coverings are H(n, k) when n is greater than 2k. Moreover, we determine their automorphism groups and chromatic numbers.

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

#### Operator Algebra Seminars

16:45-18:15 Online

The generator rank of $C^*$-algebras (English)

[ Reference URL ]

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

**Hannes Thiel**(TU Dresden)The generator rank of $C^*$-algebras (English)

[ Reference URL ]

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

#### Numerical Analysis Seminar

16:30-18:00 Online

Action minimizing random walks and numerical analysis of Hamilton-Jacobi equations (Japanese)

[ Reference URL ]

https://forms.gle/kjhqne4nV6fqEFWB8

**Kohei Soga**(Keio University)Action minimizing random walks and numerical analysis of Hamilton-Jacobi equations (Japanese)

[ Reference URL ]

https://forms.gle/kjhqne4nV6fqEFWB8

#### Lie Groups and Representation Theory

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

The multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds (Japanese)

**Kazuki KANNAKA**(RIKEN iTHEMS)The multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds (Japanese)

[ Abstract ]

A \textit{pseudo-Riemannian locally symmetric space} is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$.

Toshiyuki Kobayashi initiated the study of spectral analysis of \textit{intrinsic differential operators} (such as the Laplacian) of a pseudo-Rimannian locally symmetric space. Unlike the classical Riemannian setting,

the Laplacian of a pseudo-Rimannian locally symmetric space is no longer an elliptic differential operator.

In its spectral analysis, new phenomena different from those in the Riemannian setting have been discovered in recent years, following pioneering works by Kassel-Kobayashi.

For instance, they studied the behavior of eigenvalues of intrinsic differential operators of $\Gamma\backslash G/H$ when deforming a discontinuous group $\Gamma$. As a special case, they found infinitely many \textit{stable

eigenvalues} of the (hyperbolic) Laplacian of a compact anti-de Sitter $3$-manifold $\Gamma\backslash

\mathrm{SO}(2,2)/\mathrm{SO}(2,1)$ ([Adv.\ Math.\ 2016]).

In this talk, I would like to explain recent results about the \textit{multiplicities} of stable eigenvalues in the anti-de Sitter setting.

A \textit{pseudo-Riemannian locally symmetric space} is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$.

Toshiyuki Kobayashi initiated the study of spectral analysis of \textit{intrinsic differential operators} (such as the Laplacian) of a pseudo-Rimannian locally symmetric space. Unlike the classical Riemannian setting,

the Laplacian of a pseudo-Rimannian locally symmetric space is no longer an elliptic differential operator.

In its spectral analysis, new phenomena different from those in the Riemannian setting have been discovered in recent years, following pioneering works by Kassel-Kobayashi.

For instance, they studied the behavior of eigenvalues of intrinsic differential operators of $\Gamma\backslash G/H$ when deforming a discontinuous group $\Gamma$. As a special case, they found infinitely many \textit{stable

eigenvalues} of the (hyperbolic) Laplacian of a compact anti-de Sitter $3$-manifold $\Gamma\backslash

\mathrm{SO}(2,2)/\mathrm{SO}(2,1)$ ([Adv.\ Math.\ 2016]).

In this talk, I would like to explain recent results about the \textit{multiplicities} of stable eigenvalues in the anti-de Sitter setting.

### 2021/06/07

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane (Japanese)

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

**Kurando Baba**(Tokyo University of Science)Calabi-Yau structure and Bargmann type transformation on the Cayley projective plane (Japanese)

[ Abstract ]

In this talk, I would like to discuss a problem of the geometric quantization for the Cayley projective plane. Our purposes are to show the existence of a Calabi-Yau structure on the punctured cotangent bundle of the Cayley projective plane, and to construct a Bargmann type transformation between a space of holomorphic functions on the bundle and the $L_2$-space on the Cayley projective space. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators. This talk is based on a joint work with Kenro Furutani (Osaka City University Advanced Mathematical Institute): arXiv:2101.07505.

[ Reference URL ]In this talk, I would like to discuss a problem of the geometric quantization for the Cayley projective plane. Our purposes are to show the existence of a Calabi-Yau structure on the punctured cotangent bundle of the Cayley projective plane, and to construct a Bargmann type transformation between a space of holomorphic functions on the bundle and the $L_2$-space on the Cayley projective space. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators. This talk is based on a joint work with Kenro Furutani (Osaka City University Advanced Mathematical Institute): arXiv:2101.07505.

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

### 2021/06/03

#### Information Mathematics Seminar

16:50-18:35 Online

The past, the present, the future of the AI (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The past, the present, the future of the AI (Japanese)

[ Abstract ]

On the explanation of the past, the present, the future of the AI

[ Reference URL ]On the explanation of the past, the present, the future of the AI

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

### 2021/06/02

#### Algebraic Geometry Seminar

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

Quasiexcellence implies strong generation (日本語)

Zoom

**Ko Aoki**(Tokyo)Quasiexcellence implies strong generation (日本語)

[ Abstract ]

BondalとVan den Berghは（小さい）三角圏からの反変関手がいつ表現可能かという問題の考察の中で、対象が三角圏を強生成(strongly generate)することの定義を導入した。強生成する対象が存在するときは良い表現可能性定理が成立する。

どのような有限次元Noetherスキームに対してその連接層の導来圏が強生成であるかについてはBondal–Van den Bergh以降Rouquier, Keller–Van den Bergh, Aihara–Takahashi, Iyengar–Takahashiなどにより多くの結果が得られていたが、最近Neemanは別の手法を用いてそれをalterationが適用できる分離Noetherスキームに対して示した。それを講演者はGabberのweak local uniformizationを用いることでさらに分離的準優秀スキームにまで拡張した。講演ではこの結果およびその証明の手法を紹介する。

[ Reference URL ]BondalとVan den Berghは（小さい）三角圏からの反変関手がいつ表現可能かという問題の考察の中で、対象が三角圏を強生成(strongly generate)することの定義を導入した。強生成する対象が存在するときは良い表現可能性定理が成立する。

どのような有限次元Noetherスキームに対してその連接層の導来圏が強生成であるかについてはBondal–Van den Bergh以降Rouquier, Keller–Van den Bergh, Aihara–Takahashi, Iyengar–Takahashiなどにより多くの結果が得られていたが、最近Neemanは別の手法を用いてそれをalterationが適用できる分離Noetherスキームに対して示した。それを講演者はGabberのweak local uniformizationを用いることでさらに分離的準優秀スキームにまで拡張した。講演ではこの結果およびその証明の手法を紹介する。

Zoom

#### 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)

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