## Seminar information archive

Seminar information archive ～04/12｜Today's seminar 04/13 | Future seminars 04/14～

### 2022/07/20

#### Number Theory Seminar

15:30-18:00 Hybrid

Completed prismatic F-crystals and crystalline local systems (ENGLISH)

Twisted differential operators in several variables (ENGLISH)

**Koji Shimizu**(UC Berkeley) 15:30-16:30Completed prismatic F-crystals and crystalline local systems (ENGLISH)

[ Abstract ]

Bhatt and Scholze introduced the absolute prismatic site of a p-adic ring and proved the equivalence of categories between prismatic F-crystals and lattices in crystalline representations in the CDVR case with perfect residue field. We will define a wider category of completed prismatic F-crystals in the relative case and explain its relation to the category of crystalline local systems. This is joint work with Heng Du, Tong Liu, and Yong Suk Moon.

Bhatt and Scholze introduced the absolute prismatic site of a p-adic ring and proved the equivalence of categories between prismatic F-crystals and lattices in crystalline representations in the CDVR case with perfect residue field. We will define a wider category of completed prismatic F-crystals in the relative case and explain its relation to the category of crystalline local systems. This is joint work with Heng Du, Tong Liu, and Yong Suk Moon.

**Pierre Houedry**(Université de Caen) 17:00-18:00Twisted differential operators in several variables (ENGLISH)

[ Abstract ]

The aim of my presentation is to give an overview of the results I obtained during the first year of my PhD. The theory of $q$-differences equations appeared a long time ago with the Birkhoff's work. It is well understood in the complex setting. In 2004, Lucia Di Vizio and Yves André, in the paper $q$-differences and p-adic local monodromy, gave an equivalence between certain type of $q$-differences equations and a certain type of classical differential equations in the p-adic setting. Recently, Adolfo Quiros, Bernard Le Stum and Michel Gros have been working on a generalization of this result not looking only for $q$-differences equations but also twisted equations in general. The framework that they develop is working for equations in one variable. The goal of my thesis is to generalize those results in several variables.

The aim of my presentation is to give an overview of the results I obtained during the first year of my PhD. The theory of $q$-differences equations appeared a long time ago with the Birkhoff's work. It is well understood in the complex setting. In 2004, Lucia Di Vizio and Yves André, in the paper $q$-differences and p-adic local monodromy, gave an equivalence between certain type of $q$-differences equations and a certain type of classical differential equations in the p-adic setting. Recently, Adolfo Quiros, Bernard Le Stum and Michel Gros have been working on a generalization of this result not looking only for $q$-differences equations but also twisted equations in general. The framework that they develop is working for equations in one variable. The goal of my thesis is to generalize those results in several variables.

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

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

Grothendieck enriched categories (Japanese)

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

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

**Yuki Imamura**(Osaka University)Grothendieck enriched categories (Japanese)

[ Abstract ]

Grothendieck圏は、入射的余生成子の存在や随伴関手定理の成立など、アーベル圏の中でも特に良い性質を持つことで知られる。通常Grothendieck圏は、生成子を持つ余完備なアーベル圏であって、フィルター余極限を取る関手が完全関手になるような圏として内在的な性質で以て定義されるが、加群圏の"良い部分圏"として実現できるという外在的な特徴づけ(Gabriel-Popescuの定理)も存在する。アーベル圏が自然なプレ加法圏(アーベル群の圏Ab上の豊穣圏)の構造を持つことから、Gabriel-Popescuの定理はAb-豊穣圏に対する定理だと思うことができる。本講演では、より一般のGrothendieckモノイダル圏V上の豊穣圏に対してGabriel-Popescuの定理の一般化を定式化し証明する。特にVとしてアーベル群の複体の圏Chを取ることによりGrothendieck圏のdg圏類似とそのGabriel-Popescuの定理が得られることも確認する。

[ Reference URL ]Grothendieck圏は、入射的余生成子の存在や随伴関手定理の成立など、アーベル圏の中でも特に良い性質を持つことで知られる。通常Grothendieck圏は、生成子を持つ余完備なアーベル圏であって、フィルター余極限を取る関手が完全関手になるような圏として内在的な性質で以て定義されるが、加群圏の"良い部分圏"として実現できるという外在的な特徴づけ(Gabriel-Popescuの定理)も存在する。アーベル圏が自然なプレ加法圏(アーベル群の圏Ab上の豊穣圏)の構造を持つことから、Gabriel-Popescuの定理はAb-豊穣圏に対する定理だと思うことができる。本講演では、より一般のGrothendieckモノイダル圏V上の豊穣圏に対してGabriel-Popescuの定理の一般化を定式化し証明する。特にVとしてアーベル群の複体の圏Chを取ることによりGrothendieck圏のdg圏類似とそのGabriel-Popescuの定理が得られることも確認する。

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

### 2022/07/12

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Cable knots and involutive Heegaard Floer homology (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Sungkyung Kang**(Center for Geometry and Physics, Institute of Basic Science)Cable knots and involutive Heegaard Floer homology (ENGLISH)

[ Abstract ]

Heegaard Floer homology (and its variants) carries an intrinsic symmetry, which conjecturally corresponds to the Pin(2)-equivariance in Seiberg-Witten Floer homology. By exploiting the symmetry, we prove that (odd,1)-cables of the figure-eight knots are linearly independent in the concordance group of rationally slice knots, and present a first example of rationally slice knots of complexity 1 which are not slice. Furthermore, we establish an explicit connection between involutive knot Floer theory and involutive bordered Floer theory of knot complements, and use it to prove a similar result for iterated cables of figure-eight knots. A part of this talk is based on a joint work with J. Hom, M. Stoffregen, and J. Park.

[ Reference URL ]Heegaard Floer homology (and its variants) carries an intrinsic symmetry, which conjecturally corresponds to the Pin(2)-equivariance in Seiberg-Witten Floer homology. By exploiting the symmetry, we prove that (odd,1)-cables of the figure-eight knots are linearly independent in the concordance group of rationally slice knots, and present a first example of rationally slice knots of complexity 1 which are not slice. Furthermore, we establish an explicit connection between involutive knot Floer theory and involutive bordered Floer theory of knot complements, and use it to prove a similar result for iterated cables of figure-eight knots. A part of this talk is based on a joint work with J. Hom, M. Stoffregen, and J. Park.

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

#### Operator Algebra Seminars

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

Relative Drinfeld centers associated to monoidal functors

[ Reference URL ]

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

**Mao Hoshino**(Univ. Tokyo)Relative Drinfeld centers associated to monoidal functors

[ Reference URL ]

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

### 2022/07/11

#### Seminar on Geometric Complex Analysis

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

The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Yoshihiko Matsumoto**(Osaka University)The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry (Japanese)

[ Abstract ]

In this talk, I introduce the CR Killing operator associated with compatible almost CR structures on contact manifolds, which describes trivial infinitesimal deformations generated by contact Hamiltonian vector fields, and discuss how it can also be reconstructed by the Bernstein-Gelfand-Gelfand construction in the general theory of parabolic geometries. The “modified” adjoint tractor connection defined by Cap (2008) plays a crucial role. If time permits, I’d also like to discuss what this observation might mean in relation to asymptotically complex hyperbolic Einstein metrics, which are bulk geometric structures for compatible almost CR structures at infinity.

[ Reference URL ]In this talk, I introduce the CR Killing operator associated with compatible almost CR structures on contact manifolds, which describes trivial infinitesimal deformations generated by contact Hamiltonian vector fields, and discuss how it can also be reconstructed by the Bernstein-Gelfand-Gelfand construction in the general theory of parabolic geometries. The “modified” adjoint tractor connection defined by Cap (2008) plays a crucial role. If time permits, I’d also like to discuss what this observation might mean in relation to asymptotically complex hyperbolic Einstein metrics, which are bulk geometric structures for compatible almost CR structures at infinity.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/07/07

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers XIII (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers XIII (Japanese)

[ Abstract ]

How to use quantum computer II

How to use quantum computer II

### 2022/07/06

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

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

Cyclic polytopes and higher Auslander--Reiten theory 3 (English)

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

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

**Nicholas Williams**(The University of Tokyo)Cyclic polytopes and higher Auslander--Reiten theory 3 (English)

[ Abstract ]

This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.

[ Reference URL ]This continues part 2. In the third talk, we consider the relationship between the objects from the first two talks. We explain how triangulations of even-dimensional cyclic polytopes may be interpreted in terms of tilting modules, cluster-tilting objects, or d-silting complexes. We then proceed in the d-silting framework, and show how the higher Stasheff--Tamari orders may be interpreted algebraically for even dimensions. We explain how this allows one to interpret odd-dimensional triangulations algebraically, namely, as equivalence classes of d-maximal green sequences. We briefly digress to consider the issue of equivalence of maximal green sequences itself. We then show how one can interpret the higher Stasheff--Tamari orders on equivalence classes of d-maximal green sequences. We finish by drawing out some consequences of this algebraic interpretation of the higher Stasheff--Tamari orders.

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

#### Number Theory Seminar

17:00-18:00 Hybrid

The characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves (ENGLISH)

**Peijiang Liu**(University of Tokyo)The characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves (ENGLISH)

[ Abstract ]

$\ell$-adic GKZ hypergeometric sheaves are defined to be étale analogues of GKZ hypergeometric $\mathcal{D}$-modules. We introduce an algorithm of computing the characteristic cycles of certain type of $\ell$-adic GKZ hypergeometric sheaves. We compute the irreducible components by a push-forward formula for characteristic cycles of étale sheaves, and compute the multiplicities by considering a comparison theorem between the characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves and those of non-confluent GKZ hypergeometric $\mathcal{D}$-modules. We also explain the limitation of our algorithm by an example.

$\ell$-adic GKZ hypergeometric sheaves are defined to be étale analogues of GKZ hypergeometric $\mathcal{D}$-modules. We introduce an algorithm of computing the characteristic cycles of certain type of $\ell$-adic GKZ hypergeometric sheaves. We compute the irreducible components by a push-forward formula for characteristic cycles of étale sheaves, and compute the multiplicities by considering a comparison theorem between the characteristic cycles of non-confluent $\ell$-adic GKZ hypergeometric sheaves and those of non-confluent GKZ hypergeometric $\mathcal{D}$-modules. We also explain the limitation of our algorithm by an example.

### 2022/07/05

#### Operator Algebra Seminars

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

Frobenius algebras associated with the $\alpha$-induction for twisted modules of conformal nets

[ Reference URL ]

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

**Mizuki Oikawa**(Univ. Tokyo)Frobenius algebras associated with the $\alpha$-induction for twisted modules of conformal nets

[ 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.

Non-existence of Lyapunov exponents for homoclinic bifurcations of surface diffeomorphisms (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yushi Nakano**(Tokai University)Non-existence of Lyapunov exponents for homoclinic bifurcations of surface diffeomorphisms (JAPANESE)

[ Abstract ]

Lyapunov exponent is widely used in natural science including mathematics, such as a tool to find chaotic signal or a foundation of non-uniformly hyperbolic systems theory. However, its existence (outside of the supports of invariant probability measures) is seldom discussed. In this talk, I consider the problem of whether the Lyapunov irregular set, i.e. the set of points at which Lyapunov exponent fails to exist, has positive Lebesgue measure. I will show that surface diffeomorphisms with a robust homoclinic tangency given by Colli and Vargas, as well as other several known nonhyperbolic dynamics, has the Lyapunov irregular set of positive Lebesgue measure. This is a joint work with S. Kiriki, X. Li and T. Soma.

[ Reference URL ]Lyapunov exponent is widely used in natural science including mathematics, such as a tool to find chaotic signal or a foundation of non-uniformly hyperbolic systems theory. However, its existence (outside of the supports of invariant probability measures) is seldom discussed. In this talk, I consider the problem of whether the Lyapunov irregular set, i.e. the set of points at which Lyapunov exponent fails to exist, has positive Lebesgue measure. I will show that surface diffeomorphisms with a robust homoclinic tangency given by Colli and Vargas, as well as other several known nonhyperbolic dynamics, has the Lyapunov irregular set of positive Lebesgue measure. This is a joint work with S. Kiriki, X. Li and T. Soma.

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

### 2022/07/04

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Bloch's principle for holomorphic maps into subvarieties of semi-abelian varieties (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Katsutoshi Yamanoi**(Osaka University)Bloch's principle for holomorphic maps into subvarieties of semi-abelian varieties (Japanese)

[ Abstract ]

We discuss a generalization of the logarithmic Bloch-Ochiai theorem about entire curves in subvarieties of semi-abelian varieties, in terms of sequences of holomorphic maps from the unit disc.

This generalization implies, among other things, that subvarieties of log general type in semi-abelian varieties are pseudo-Kobayashi hyperbolic.

As another application, we discuss an improvement of a classical theorem due to Cartan in 1920's about the system of nowhere vanishing holomorphic functions on the unit disc satisfying Borel's identity.

[ Reference URL ]We discuss a generalization of the logarithmic Bloch-Ochiai theorem about entire curves in subvarieties of semi-abelian varieties, in terms of sequences of holomorphic maps from the unit disc.

This generalization implies, among other things, that subvarieties of log general type in semi-abelian varieties are pseudo-Kobayashi hyperbolic.

As another application, we discuss an improvement of a classical theorem due to Cartan in 1920's about the system of nowhere vanishing holomorphic functions on the unit disc satisfying Borel's identity.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/06/30

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computersXII (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computersXII (Japanese)

[ Abstract ]

How to use quantum computer I

How to use quantum computer I

#### Applied Analysis

16:00-17:00 Online

A brief introduction to a class of new phase field models (English)

https://forms.gle/esc7Y6KGASwbFro97

**Xingzhi Bian**(Shanghai University)A brief introduction to a class of new phase field models (English)

[ Abstract ]

Existence of weak solutions for a type of new phase field models, which are the system consisting of a degenerate parabolic equation of order parameter coupled to a linear elasticity sub-system. The models are applied to describe the phase transitions in elastically deformable solids.

[ Reference URL ]Existence of weak solutions for a type of new phase field models, which are the system consisting of a degenerate parabolic equation of order parameter coupled to a linear elasticity sub-system. The models are applied to describe the phase transitions in elastically deformable solids.

https://forms.gle/esc7Y6KGASwbFro97

### 2022/06/29

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

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

Cyclic polytopes and higher Auslander--Reiten theory 2 (English)

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

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

**Nicholas Williams**(The University of Tokyo)Cyclic polytopes and higher Auslander--Reiten theory 2 (English)

[ Abstract ]

This continues part 1. In the second talk, we focus on higher Auslander--Reiten theory. We survey the basic setting of this theory, starting with d-cluster-tilting subcategories of module categories. We then move on to d-cluster-tilting subcategories of derived categories in the case of d-representation-finite d-hereditary algebras. We explain how one can construct (d + 2)-angulated cluster categories for such algebras, generalising classical cluster categories. We finally consider the d-almost positive category, which is the higher generalisation of the category of two-term complexes. Throughout, we illustrate the results using the higher Auslander algebras of type A, and explain how the different categories can be interpreted combinatorially for these algebras.

[ Reference URL ]This continues part 1. In the second talk, we focus on higher Auslander--Reiten theory. We survey the basic setting of this theory, starting with d-cluster-tilting subcategories of module categories. We then move on to d-cluster-tilting subcategories of derived categories in the case of d-representation-finite d-hereditary algebras. We explain how one can construct (d + 2)-angulated cluster categories for such algebras, generalising classical cluster categories. We finally consider the d-almost positive category, which is the higher generalisation of the category of two-term complexes. Throughout, we illustrate the results using the higher Auslander algebras of type A, and explain how the different categories can be interpreted combinatorially for these algebras.

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

### 2022/06/28

#### Tuesday Seminar of Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Mourre inequality for non-local Schödinger operators (Japanese)

https://forms.gle/sBSeNH9AYFNypNBk9

**ISHIDA Atsuhide**(Tokyo University of Science)Mourre inequality for non-local Schödinger operators (Japanese)

[ Abstract ]

We consider the Mourre inequality for the following self-adjoint operator $H=\Psi(-\Delta/2)+V$ acting on $L^2(\mathbb{R}^d)$, where $\Psi: [0,\infty)\rightarrow\mathbb{R}$ is an increasing function, $\Delta$ is Laplacian and $V: \mathbb{R}^d\rightarrow\mathbb{R}$ is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, Mourre inequality has the application to the absence of the singular continuous spectrum by combining the limiting absorption principle and, in addition, Mourre inequality is also used for proof of the minimal velocity estimate that plays an important role in the scattering theory. In this talk, we report that Mourre inequality holds under the general $\Psi$ and $V$ by choosing the conjugate operator $A=(p\cdot x+x\cdot p)/2$ with $p=-\sqrt{-1}\nabla$, and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Hungarian Academy of Sciences) and I. Sasaki (Shinshu University).

[ Reference URL ]We consider the Mourre inequality for the following self-adjoint operator $H=\Psi(-\Delta/2)+V$ acting on $L^2(\mathbb{R}^d)$, where $\Psi: [0,\infty)\rightarrow\mathbb{R}$ is an increasing function, $\Delta$ is Laplacian and $V: \mathbb{R}^d\rightarrow\mathbb{R}$ is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, Mourre inequality has the application to the absence of the singular continuous spectrum by combining the limiting absorption principle and, in addition, Mourre inequality is also used for proof of the minimal velocity estimate that plays an important role in the scattering theory. In this talk, we report that Mourre inequality holds under the general $\Psi$ and $V$ by choosing the conjugate operator $A=(p\cdot x+x\cdot p)/2$ with $p=-\sqrt{-1}\nabla$, and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Hungarian Academy of Sciences) and I. Sasaki (Shinshu University).

https://forms.gle/sBSeNH9AYFNypNBk9

#### Lie Groups and Representation Theory

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

Computation of weighted Bergman inner products on bounded symmetric domains and Plancherel-type formulas for $(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$ (Japanese)

**Ryosuke Nakahama**(Kyushu University)Computation of weighted Bergman inner products on bounded symmetric domains and Plancherel-type formulas for $(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$ (Japanese)

[ Abstract ]

Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1:=(\mathfrak{p}^+)^\sigma\subset\mathfrak{p}^+$ respectively. Then the universal covering group $\widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space $\mathcal{H}_\lambda(D)\subset\mathcal{O}(D)=\mathcal{O}_\lambda(D)$ on $D$ for sufficiently large $\lambda$. Its restriction to the subgroup $\widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua--Kostant--Schmid--Kobayashi's formula in terms of the $\widetilde{K}_1$-decomposition of the space $\mathcal{P}(\mathfrak{p}^+_2)$ of polynomials on $\mathfrak{p}^+_2:=(\mathfrak{p}^+)^{-\sigma}\subset\mathfrak{p}^+$. Our goal is to understand the decomposition of the restriction $\mathcal{H}_\lambda(D)|_{\widetilde{G}_1}$ by studying the weighted Bergman inner product on each $\widetilde{K}_1$-type in $\mathcal{P}(\mathfrak{p}^+_2)\subset\mathcal{H}_\lambda(D)$.

Today we mainly deal with the symmetric pair $(G,G_1)=(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$.

Let $(G,G_1)=(G,(G^\sigma)_0)$ be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces $D_1=G_1/K_1\subset D=G/K$, realized as bounded symmetric domains in complex vector spaces $\mathfrak{p}^+_1:=(\mathfrak{p}^+)^\sigma\subset\mathfrak{p}^+$ respectively. Then the universal covering group $\widetilde{G}$ of $G$ acts unitarily on the weighted Bergman space $\mathcal{H}_\lambda(D)\subset\mathcal{O}(D)=\mathcal{O}_\lambda(D)$ on $D$ for sufficiently large $\lambda$. Its restriction to the subgroup $\widetilde{G}_1$ decomposes discretely and multiplicity-freely, and its branching law is given explicitly by Hua--Kostant--Schmid--Kobayashi's formula in terms of the $\widetilde{K}_1$-decomposition of the space $\mathcal{P}(\mathfrak{p}^+_2)$ of polynomials on $\mathfrak{p}^+_2:=(\mathfrak{p}^+)^{-\sigma}\subset\mathfrak{p}^+$. Our goal is to understand the decomposition of the restriction $\mathcal{H}_\lambda(D)|_{\widetilde{G}_1}$ by studying the weighted Bergman inner product on each $\widetilde{K}_1$-type in $\mathcal{P}(\mathfrak{p}^+_2)\subset\mathcal{H}_\lambda(D)$.

Today we mainly deal with the symmetric pair $(G,G_1)=(Sp(2r,\mathbb{R}),Sp(r,\mathbb{R})\times Sp(r,\mathbb{R}))$.

### 2022/06/24

#### Colloquium

15:30-16:30 Hybrid

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR

If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].

**Yoshiki Oshima**(Graduate School of Mathematical Sciences, the University of Tokyo)Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)

[ Abstract ]

The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.

[ Reference URL ]The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR

### 2022/06/23

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computersXI (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computersXI (Japanese)

[ Abstract ]

On the error-correcting code of quantum computer.

On the error-correcting code of quantum computer.

### 2022/06/22

#### Number Theory Seminar

17:00-18:00 Hybrid

Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields (JAPANESE)

**Yugo Takanashi**(University of Tokyo)Parity of conjugate self-dual representations of inner forms of $\mathrm{GL}_n$ over $p$-adic fields (JAPANESE)

[ Abstract ]

There are two parametrizations of discrete series representations of $\mathrm{GL}_n$ over $p$-adic fields. One is the local Langlands correspondence, and the other is the local Jacquet-Langlands correspondence. The composite of these two maps the discrete series representations of an inner form of $\mathrm{GL}_n$ to Galois representations called discrete L-parameters. On the other hand, we can define the parity for each self-dual representation depending on whether the representation is orthogonal or symplectic. The composite preserves the notion of self-duality, and it transforms the parity in a nontrivial manner. Prasad and Ramakrishnan computed the transformation law, and Mieda proved its conjugate self-dual analog under some conditions on groups and representations. We will talk about the proof of the general case of this analog. We use the globalization method, as in the proof of Prasad and Ramakrishnan.

There are two parametrizations of discrete series representations of $\mathrm{GL}_n$ over $p$-adic fields. One is the local Langlands correspondence, and the other is the local Jacquet-Langlands correspondence. The composite of these two maps the discrete series representations of an inner form of $\mathrm{GL}_n$ to Galois representations called discrete L-parameters. On the other hand, we can define the parity for each self-dual representation depending on whether the representation is orthogonal or symplectic. The composite preserves the notion of self-duality, and it transforms the parity in a nontrivial manner. Prasad and Ramakrishnan computed the transformation law, and Mieda proved its conjugate self-dual analog under some conditions on groups and representations. We will talk about the proof of the general case of this analog. We use the globalization method, as in the proof of Prasad and Ramakrishnan.

#### Tokyo-Nagoya Algebra Seminar

17:00-18:30 Online

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

Update on singular equivalences between commutative rings (English)

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

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

**Martin Kalck**(Freiburg University)Update on singular equivalences between commutative rings (English)

[ Abstract ]

We will start with an introduction to singularity categories, which were first studied by Buchweitz and later rediscovered by Orlov. Then we will explain what is known about triangle equivalences between singularity categories of commutative rings, recalling results of Knörrer, D. Yang (based on our joint works on relative singularity categories. This result also follows from work of Kawamata and was generalized in a joint work with Karmazyn) and a new equivalence obtained in arXiv:2103.06584.

In the remainder of the talk, we will focus on the case of Gorenstein isolated singularities and especially hypersurfaces, where we give a complete description of quasi-equivalence classes of dg enhancements of singularity categories, answering a question of Keller & Shinder. This is based on arXiv:2108.03292.

[ Reference URL ]We will start with an introduction to singularity categories, which were first studied by Buchweitz and later rediscovered by Orlov. Then we will explain what is known about triangle equivalences between singularity categories of commutative rings, recalling results of Knörrer, D. Yang (based on our joint works on relative singularity categories. This result also follows from work of Kawamata and was generalized in a joint work with Karmazyn) and a new equivalence obtained in arXiv:2103.06584.

In the remainder of the talk, we will focus on the case of Gorenstein isolated singularities and especially hypersurfaces, where we give a complete description of quasi-equivalence classes of dg enhancements of singularity categories, answering a question of Keller & Shinder. This is based on arXiv:2108.03292.

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

### 2022/06/21

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Cosmetic surgeries on knots in the 3-sphere (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Kazuhiro Ichihara**(Nihon University)Cosmetic surgeries on knots in the 3-sphere (JAPANESE)

[ Abstract ]

A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).

[ Reference URL ]A pair of Dehn surgeries on a knot is called purely (resp. chirally) cosmetic if the obtained manifolds are orientation-preservingly (resp. -reversingly) homeomorphic. It is conjectured that if a knot in the 3-sphere admits purely (resp. chirally) cosmetic surgeries, then the knot is a trivial knot (resp. a torus knot or an amphicheiral knot). In this talk, after giving a brief survey on the studies on these conjectures, I will explain recent progresses on the conjectures. This is based on joint works with Tetsuya Ito (Kyoto University), In Dae Jong (Kindai University), and Toshio Saito (Joetsu University of Education).

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

### 2022/06/20

#### Seminar on Geometric Complex Analysis

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

Constructions of CR GJMS operators in dimension three (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Taiji Marugame**(The University of Electro-Communications)Constructions of CR GJMS operators in dimension three (Japanese)

[ Abstract ]

CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.

[ Reference URL ]CR GJMS operators are invariant differential operators on CR manifolds whose leading parts are powers of the sublaplacian. Such operators can be constructed by Fefferman's ambient metric or the Cheng-Yau metric, but the construction is obstructed at a finite order due to the ambiguity of these metrics. Gover-Graham constructed some higher order CR GJMS operators by using tractor calculus and BGG constructions. In particular, they showed that three dimensional CR manifolds admit CR GJMS operators of all orders. In this talk, we give proofs to this fact in two different ways. One is by the use of self-dual Einstein ACH metric and the other is by the Graham-Hirachi inhomogeneous ambient metric adapted to the Fefferman conformal structure. We also state a conjecture on the relationship between these two metrics.

https://forms.gle/hYT2hVhDE3q1wDSh6

#### Number Theory Seminar

15:00-16:00 Hybrid

p-adic weight-monodromy conjecture for complete intersections (Japanese)

**Hiroki Kato**(Paris-Saclay University)p-adic weight-monodromy conjecture for complete intersections (Japanese)

### 2022/06/16

#### Information Mathematics Seminar

16:50-18:35 Room #123 (Graduate School of Math. Sci. Bldg.)

Design and control of quantum computers X (Japanese)

**Yasunari Suzuki**(NTT)Design and control of quantum computers X (Japanese)

[ Abstract ]

Error-correcting of quantum computer

Error-correcting of quantum computer

### 2022/06/15

#### Number Theory Seminar

17:00-18:00 Hybrid

Steinberg symbols and reciprocity sheaves (JAPANESE)

**Junnosuke Koizumi**(University of Tokyo)Steinberg symbols and reciprocity sheaves (JAPANESE)

[ Abstract ]

The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.

The norm residue symbol and the differential symbol are known to satisfy the common relation $(a,1-a)=0$ which is called the Steinberg relation. Hu-Kriz showed that the Steinberg relation can be understood as a relation between certain morphisms in the stable motivic homotopy category. On the other hand, there is also an “additive variant” of the Steinberg relation, namely $(a,a)+(1-a,1-a)=0$, for which the classical motivic theory is no longer applicable. In this talk we will explain how the theory of reciprocity sheaves due to Kahn-Saito-Yamazaki can be utilized to generalize the theory of Hu-Kriz to include the additive Steinberg relation.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185 Next >