## Seminar information archive

Seminar information archive ～04/15｜Today's seminar 04/16 | Future seminars 04/17～

### 2022/05/12

#### Information Mathematics Seminar

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

Design and control of quantum computers V (Japanese)

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

### 2022/05/11

#### Number Theory Seminar

17:00-18:00 Hybrid

Cohomology of the unramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$ (ENGLISH)

**Joseph Muller**(University of Tokyo)Cohomology of the unramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$ (ENGLISH)

[ Abstract ]

Rapoport-Zink (RZ) spaces are moduli spaces which classify the deformations of a $p$-divisible group with additional structures. It is equipped with compatible actions of $p$-adic and Galois groups, and their cohomology is believed to play a role in the local Langlands program. So far, the cohomology of RZ spaces is entirely known only in the cases of the Lubin-Tate tower and of the Drinfeld space ; in particular both of them are RZ spaces of EL type. In this talk, we consider the unramified PEL unitary RZ space with signature $(1,n-1)$. In 2011, Vollaard and Wedhorn proved that it is stratified by generalized Deligne-Lusztig varieties, whose incidence relations mimic the combinatorics of the Bruhat-Tits building of a unitary group. We compute the cohomology of these strata and we draw some consequences on the cohomology of the RZ space. When $n = 3, 4$ we deduce

an automorphic description of the cohomology of the basic stratum in the corresponding Shimura variety via p-adic uniformization.

Rapoport-Zink (RZ) spaces are moduli spaces which classify the deformations of a $p$-divisible group with additional structures. It is equipped with compatible actions of $p$-adic and Galois groups, and their cohomology is believed to play a role in the local Langlands program. So far, the cohomology of RZ spaces is entirely known only in the cases of the Lubin-Tate tower and of the Drinfeld space ; in particular both of them are RZ spaces of EL type. In this talk, we consider the unramified PEL unitary RZ space with signature $(1,n-1)$. In 2011, Vollaard and Wedhorn proved that it is stratified by generalized Deligne-Lusztig varieties, whose incidence relations mimic the combinatorics of the Bruhat-Tits building of a unitary group. We compute the cohomology of these strata and we draw some consequences on the cohomology of the RZ space. When $n = 3, 4$ we deduce

an automorphic description of the cohomology of the basic stratum in the corresponding Shimura variety via p-adic uniformization.

### 2022/05/10

#### Operator Algebra Seminars

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

Reflection positive representations - the case of the integers $\mathbb{Z}$ and the real line $\mathbb{R}$ (English)

[ Reference URL ]

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

**Maria Stella Adamo**(Univ. Tokyo)Reflection positive representations - the case of the integers $\mathbb{Z}$ and the real line $\mathbb{R}$ (English)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Nielsen realization, knots, and Seiberg-Witten (Floer) homotopy theory (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Hokuto Konno**(The Univesity of Tokyo)Nielsen realization, knots, and Seiberg-Witten (Floer) homotopy theory (JAPANESE)

[ Abstract ]

I will discuss two different kinds of applications of Seiberg-Witten (Floer) homotopy theory involving involutions. The first application is about the Nielsen realization problem, which asks whether a given finite subgroup of the mapping class group of a manifold lifts to a subgroup of the diffeomorphism group. Although every finite subgroup is known to lift in dimension 2, there are manifolds of dimension greater than 2 for which the Nielsen realization fails. However, only few examples have been known in dimension 4. I will show that "4-dimensional Dehn twists" yield a large class of new examples. The second application is about 4-dimensional invariants of knots. I will introduce a version of "Floer K-theory for knots", and will explain that this framework gives the first comparison result for the smooth and topological versions of a certain knot invariant, called stabilizing number. Although the above two topics (Nielsen realization and knots) may seem to have different flavors, they are derived from a common idea. The first one is proved using a constraint on smooth involutions on a closed 4-manifold from Seiberg-Witten homotopy theory by Yuya Kato, and the second one is derived from a generalization of Kato's result to 4-manifolds with boundary using Seiberg-Witten Floer homotopy theory. This talk is partially based on joint work with Jin Miyazawa and Masaki Taniguchi.

[ Reference URL ]I will discuss two different kinds of applications of Seiberg-Witten (Floer) homotopy theory involving involutions. The first application is about the Nielsen realization problem, which asks whether a given finite subgroup of the mapping class group of a manifold lifts to a subgroup of the diffeomorphism group. Although every finite subgroup is known to lift in dimension 2, there are manifolds of dimension greater than 2 for which the Nielsen realization fails. However, only few examples have been known in dimension 4. I will show that "4-dimensional Dehn twists" yield a large class of new examples. The second application is about 4-dimensional invariants of knots. I will introduce a version of "Floer K-theory for knots", and will explain that this framework gives the first comparison result for the smooth and topological versions of a certain knot invariant, called stabilizing number. Although the above two topics (Nielsen realization and knots) may seem to have different flavors, they are derived from a common idea. The first one is proved using a constraint on smooth involutions on a closed 4-manifold from Seiberg-Witten homotopy theory by Yuya Kato, and the second one is derived from a generalization of Kato's result to 4-manifolds with boundary using Seiberg-Witten Floer homotopy theory. This talk is partially based on joint work with Jin Miyazawa and Masaki Taniguchi.

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.)

Holomorphic multiplier representations over bounded homogeneous domains (Japanese)

**Koichi Arashi**(Nagoya University)Holomorphic multiplier representations over bounded homogeneous domains (Japanese)

[ Abstract ]

I will talk about unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over bounded homogeneous domains. We consider the identity components of algebraic groups acting transitively on the domains. The main part of this talk is a classification of such unitary representations.

We discuss an explicit description of the classification for a specific five-dimensional non-symmetric bounded homogeneous domain to illustrate the method of the classification (K. Arashi, "Holomorphic multiplier representations for bounded homogeneous domains", Journal of Lie Theory 30, 1091-1116 (2020)).

I will talk about unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over bounded homogeneous domains. We consider the identity components of algebraic groups acting transitively on the domains. The main part of this talk is a classification of such unitary representations.

We discuss an explicit description of the classification for a specific five-dimensional non-symmetric bounded homogeneous domain to illustrate the method of the classification (K. Arashi, "Holomorphic multiplier representations for bounded homogeneous domains", Journal of Lie Theory 30, 1091-1116 (2020)).

### 2022/04/28

#### Information Mathematics Seminar

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

量子計算機の制御 IV (Japanese)

**Yasunari Suzuki**(NTT)量子計算機の制御 IV (Japanese)

[ Abstract ]

Control of quantum computer I

Control of quantum computer I

### 2022/04/27

#### Number Theory Seminar

17:00-18:00 Hybrid

The Kaneko-Zagier conjecture on finite and symmetric multiple zeta values for general integer indices (JAPANESE)

**Shuji Yamamoto**(University of Tokyo)The Kaneko-Zagier conjecture on finite and symmetric multiple zeta values for general integer indices (JAPANESE)

[ Abstract ]

Kaneko and Zagier introduced two variants of multiple zeta values, which we call A-MZVs and S-MZVs, and conjectured that the algebraic structures of them are isomorphic. While these values were originally defined for positive integer (multi-)indices, recently, Komori extended the definition of S-MZVs to general integer indices. Since A-MZVs can also be defined for general integers, Komori's work suggests a generalization of the Kaneko-Zagier conjecture, from positive to general integers. In this talk, we will show how this generalization is reduced to the original conjecture. This is a joint work with Masataka Ono.

Kaneko and Zagier introduced two variants of multiple zeta values, which we call A-MZVs and S-MZVs, and conjectured that the algebraic structures of them are isomorphic. While these values were originally defined for positive integer (multi-)indices, recently, Komori extended the definition of S-MZVs to general integer indices. Since A-MZVs can also be defined for general integers, Komori's work suggests a generalization of the Kaneko-Zagier conjecture, from positive to general integers. In this talk, we will show how this generalization is reduced to the original conjecture. This is a joint work with Masataka Ono.

### 2022/04/26

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #Zoomによるオンライン開催 (Graduate School of Math. Sci. Bldg.)

PDE Optimization for Problems in Theoretical and Computational Turbulence (English)

**Pritpal Matharu**(McMaster University)PDE Optimization for Problems in Theoretical and Computational Turbulence (English)

[ Abstract ]

Turbulent flows occur in various fields and are a central, yet extremely complex topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircrafts. In this talk, we will introduce PDE optimization techniques to obtain solutions to problems utilizing adjoint-based analysis with an "optimize-then-discretize" approach, Sobolev gradients, and computationally flexible gradient-based techniques. Then, we will discuss how these techniques and their modifications, to deal with optimization problems with nonstandard structure, have been employed for problems in both theoretical and computational turbulence problems, concerning the "zeroth law of turbulence" and the turbulence closure problem.

Turbulent flows occur in various fields and are a central, yet extremely complex topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircrafts. In this talk, we will introduce PDE optimization techniques to obtain solutions to problems utilizing adjoint-based analysis with an "optimize-then-discretize" approach, Sobolev gradients, and computationally flexible gradient-based techniques. Then, we will discuss how these techniques and their modifications, to deal with optimization problems with nonstandard structure, have been employed for problems in both theoretical and computational turbulence problems, concerning the "zeroth law of turbulence" and the turbulence closure problem.

#### Tuesday Seminar of Analysis

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

Existence of a bounded forward self-similar solution to a minimal Keller-Segel model (Japanese)

https://forms.gle/mrXnjsgctSJJ1WSF6

**WAKUI Hiroshi**(Tokyo University of Science)Existence of a bounded forward self-similar solution to a minimal Keller-Segel model (Japanese)

[ Abstract ]

In this talk, we consider existence of a bounded forward self-similar solution to the initial value problem of a minimal Keller-Segel model. It is well known that the mass conservation law plays an important role to classify its large time behavior of solutions to Keller-Segel models. On the other hand, we could not expect existence of self-similar solutions to our problem with the mass conservation law except for the two dimensional case due to the scaling invariance of our problem. We will show existence of a forward self-similar solution to our problem. The key idea to guarantee boundedness of its self-similar solution is to choose a concrete upper barrier function using the hypergeometric function.

[ Reference URL ]In this talk, we consider existence of a bounded forward self-similar solution to the initial value problem of a minimal Keller-Segel model. It is well known that the mass conservation law plays an important role to classify its large time behavior of solutions to Keller-Segel models. On the other hand, we could not expect existence of self-similar solutions to our problem with the mass conservation law except for the two dimensional case due to the scaling invariance of our problem. We will show existence of a forward self-similar solution to our problem. The key idea to guarantee boundedness of its self-similar solution is to choose a concrete upper barrier function using the hypergeometric function.

https://forms.gle/mrXnjsgctSJJ1WSF6

#### Tuesday Seminar on Topology

17:00-18:00 Online

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

On the existence of discrete series for homogeneous spaces (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.

**Yoshiki Oshima**(The Univesity of Tokyo)On the existence of discrete series for homogeneous spaces (JAPANESE)

[ Abstract ]

When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.

[ Reference URL ]When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.

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.)

Joint with Tuesday Seminar on Topology

On the existence of discrete series for homogeneous spaces (Japanese)

Joint with Tuesday Seminar on Topology

**Yoshiki Oshima**(The University of Tokyo)On the existence of discrete series for homogeneous spaces (Japanese)

[ Abstract ]

When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to

see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.

When a Lie group $G$ acts transitively on a manifold $X$, an irreducible subrepresentation of $L^2(X)$ is called a discrete series representation of $X$. One may ask which homogeneous space $X$ has a discrete series representation. For reductive symmetric spaces, it is known that the existence of discrete series is equivalent to a rank condition by works of Flensted-Jensen, T.Matsuki, and T.Oshima. The problem for general reductive homogeneous spaces was considered by T.Kobayashi and a sufficient condition for the existence of discrete series was obtained by using his theory of admissible restriction. In this talk, we would like to

see another sufficient condition for general homogeneous spaces and also the case of their line bundles in terms of the orbit method.

### 2022/04/22

#### Colloquium

15:30-16:30 Online

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

Curve counting theories and categorification

(JAPANESE)

If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.

**Yukinobu Toda**(Kavli IPMU, The University of Tokyo)Curve counting theories and categorification

(JAPANESE)

[ Abstract ]

There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.

There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.

### 2022/04/21

#### Applied Analysis

16:00-17:30 Online

Effect of decay rates of initial data on the sign of solutions to Cauchy problems of some higher order parabolic equations (Japanese)

[ Reference URL ]

https://forms.gle/96bBNEAEHrsdXfH57

**( )**Effect of decay rates of initial data on the sign of solutions to Cauchy problems of some higher order parabolic equations (Japanese)

[ Reference URL ]

https://forms.gle/96bBNEAEHrsdXfH57

#### Information Mathematics Seminar

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

Design and control of quantum computers III (Japanese)

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

[ Abstract ]

Explanation on the Pauli group and its properties.

Explanation on the Pauli group and its properties.

### 2022/04/20

#### Number Theory Seminar

17:00-18:00 Hybrid

On generalized Fuchs theorem over p-adic polyannuli (ENGLISH)

**Peiduo Wang**(University of Tokyo)On generalized Fuchs theorem over p-adic polyannuli (ENGLISH)

[ Abstract ]

In this talk, we study finite projective differential modules on p-adic polyannuli satisfying the Robba condition. Christol and Mebkhout proved the decomposition theorem (the p-adic Fuchs theorem) of such differential modules on one dimensional p-adic annuli under certain non-Liouvilleness assumption and Gachets generalized it to higher dimensional cases. On the other hand, Kedlaya proved a generalization of the p-adic Fuchs theorem in one dimensional case. We prove Kedlaya's generalized version of p-adic Fuchs theorem in higher dimensional cases.

In this talk, we study finite projective differential modules on p-adic polyannuli satisfying the Robba condition. Christol and Mebkhout proved the decomposition theorem (the p-adic Fuchs theorem) of such differential modules on one dimensional p-adic annuli under certain non-Liouvilleness assumption and Gachets generalized it to higher dimensional cases. On the other hand, Kedlaya proved a generalization of the p-adic Fuchs theorem in one dimensional case. We prove Kedlaya's generalized version of p-adic Fuchs theorem in higher dimensional cases.

### 2022/04/19

#### Operator Algebra Seminars

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

Cartan subalgebras of $C^*$-algebras associated to dynamical systems

[ Reference URL ]

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

**Kei Ito**(Univ. Tokyo)Cartan subalgebras of $C^*$-algebras associated to dynamical systems

[ Reference URL ]

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

#### Tuesday Seminar on Topology

17:30-18:30 Online

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

On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces (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.

**Toshihisa Kubo**(Ryukoku University)On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces (JAPANESE)

[ Abstract ]

Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a

In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$. In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.

[ Reference URL ]Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a

**differential symmetry breaking operator**(differential SBO for short) ([T.~Kobayashi, Differential Geom. Appl. (2014)]).In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$. In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.

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

On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces

(Japanese)

Joint with Tuesday Seminar on Topology

**Toshihisa Kubo**(Ryukoku University)On the classification and construction of conformal symmetry breaking operators for anti-de Sitter spaces

(Japanese)

[ Abstract ]

Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a \emph{differential symmetry breaking operator} (differential SBO for short)

([T. Kobayashi, Differential Geom. Appl. (2014)]).

In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard

Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$.

In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.

Let $X$ be a smooth manifold and $Y$ a smooth submanifold of $X$. Take $G' \subset G$ to be a pair of Lie groups that act on $Y \subset X$, respectively. Consider a $G'$-intertwining differential operator $\mathcal{D}$ from the space of smooth sections for a $G$-equivariant vector bundle over $X$ to that for a $G'$-equivariant vector bundle over $Y$. Toshiyuki Kobayashi called such a differential operator $\mathcal{D}$ a \emph{differential symmetry breaking operator} (differential SBO for short)

([T. Kobayashi, Differential Geom. Appl. (2014)]).

In [Kobayashi-K-Pevzner, Lecture Notes in Math. 2170 (2016)], we explicitly constructed and classified all the differential SBOs from the space of differential $i$-forms $\mathcal{E}^i(S^n)$ over the standard

Riemann sphere $S^n$ to that of differential $j$-forms $\mathcal{E}^j(S^{n-1})$ over the totally geodesic hypersphere $S^{n-1}$.

In this talk, by extending the results in a Riemannian setting, we discuss about the classification and construction of differential SBOs in a pseudo-Riemannian setting such as anti-de Sitter spaces and hyperbolic spaces. This is a joint work with Toshiyuki Kobayashi and Michael Pevzner.

### 2022/04/18

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Approximation and bundle convexity on complex manifolds of pseudo convex type (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Takeo Ohasawa**(Nagoya University)Approximation and bundle convexity on complex manifolds of pseudo convex type (Japanese)

[ Abstract ]

An approximation theorem will be proved for the space of holomorphic sections of vector bundles on certain Zariski open sets of weakly 1-complete manifolds. As an existence result on such manifolds, a solution of the bundle-valued version of the Levi problem will be given by a variant of a method of Hoermander.

[ Reference URL ]An approximation theorem will be proved for the space of holomorphic sections of vector bundles on certain Zariski open sets of weakly 1-complete manifolds. As an existence result on such manifolds, a solution of the bundle-valued version of the Levi problem will be given by a variant of a method of Hoermander.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/04/14

#### Information Mathematics Seminar

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

Design and control of quantum computers II (Japanese)

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

[ Abstract ]

Explanation on the fundamental notion of quantum calculation.

Explanation on the fundamental notion of quantum calculation.

### 2022/04/13

#### Tokyo-Nagoya Algebra Seminar

10:30-12:00 Online

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

Tilting ideals of deformed preprojective algebras

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

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

**Yuta Kimura**(Osaka Metropolitan University)Tilting ideals of deformed preprojective algebras

[ Abstract ]

Let $K$ be a field and $Q$ a finite quiver. For a weight $\lambda \in K^{|Q_0|}$, the deformed preprojective algebra $\Pi^{\lambda}$ was introduced by Crawley-Boevey and Holland to study deformations of Kleinian singularities. If $\lambda = 0$, then $\Pi^{0}$ is the preprojective algebra introduced by Gelfand-Ponomarev, and appears many areas of mathematics. Among interesting properties of $\Pi^{0}$, the classification of tilting ideals of $\Pi^{0}$, shown by Buan-Iyama-Reiten-Scott, is fundamental and important. They constructed a bijection between the set of tilting ideals of $\Pi^{0}$ and the Coxeter group $W_Q$ of $Q$.

In this talk, when $Q$ is non-Dynkin, we see that $\Pi^{\lambda}$ is a $2$-Calabi-Yau algebra, and show that there exists a bijection between tilting ideals and a Coxeter group. However $W_Q$ does not appear, since $\Pi^{\lambda}$ is not necessary basic. Instead of $W_Q$, we consider the Ext-quiver of rigid simple modules, and use its Coxeter group. When $Q$ is an extended Dynkin quiver, we see that the Ext-quiver is finite and this has an information of singularities of a representation space of semisimple modules.

This is joint work with William Crawley-Boevey.

[ Reference URL ]Let $K$ be a field and $Q$ a finite quiver. For a weight $\lambda \in K^{|Q_0|}$, the deformed preprojective algebra $\Pi^{\lambda}$ was introduced by Crawley-Boevey and Holland to study deformations of Kleinian singularities. If $\lambda = 0$, then $\Pi^{0}$ is the preprojective algebra introduced by Gelfand-Ponomarev, and appears many areas of mathematics. Among interesting properties of $\Pi^{0}$, the classification of tilting ideals of $\Pi^{0}$, shown by Buan-Iyama-Reiten-Scott, is fundamental and important. They constructed a bijection between the set of tilting ideals of $\Pi^{0}$ and the Coxeter group $W_Q$ of $Q$.

In this talk, when $Q$ is non-Dynkin, we see that $\Pi^{\lambda}$ is a $2$-Calabi-Yau algebra, and show that there exists a bijection between tilting ideals and a Coxeter group. However $W_Q$ does not appear, since $\Pi^{\lambda}$ is not necessary basic. Instead of $W_Q$, we consider the Ext-quiver of rigid simple modules, and use its Coxeter group. When $Q$ is an extended Dynkin quiver, we see that the Ext-quiver is finite and this has an information of singularities of a representation space of semisimple modules.

This is joint work with William Crawley-Boevey.

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

### 2022/04/12

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)

https://forms.gle/QbQKex12dbQrt2Lw6

**Amru Hussein**(Technische Universität Kaiserslautern)Maximal $L^p$-regularity and $H^{\infty}$-calculus for block operator matrices and applications (English)

[ Abstract ]

Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.

This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962

[ Reference URL ]Many coupled evolution equations can be described via $2\times2$-block operator matrices of the form $\mathcal{A}=\begin{bmatrix}A & B \\ C & D \end{bmatrix}$ in a product space $X=X_1\times X_2$ with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator $\mathcal{A}$ can be seen as a relatively bounded perturbation of its diagonal part though with possibly large relative bound. For such operators, the properties of sectoriality, $\mathcal{R}$-sectoriality and the boundedness of the $H^\infty$-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time-dependent parabolic problem associated with $\mathcal{A}$ can be analyzed in maximal $L^p_t$-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model.

This talk is based on a joint work with Antonio Agresti, see https://arxiv.org/abs/2108.01962

https://forms.gle/QbQKex12dbQrt2Lw6

### 2022/04/07

#### Information Mathematics Seminar

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

Design and control of quantum computers (Japanese)

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

[ Abstract ]

Explanation on the design and control of quantum computers

Explanation on the design and control of quantum computers

### 2022/04/05

#### Lie Groups and Representation Theory

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

Note on the restriction of minimal representations with respect to reductive symmetric pairs (Japanese)

**Toshiyuki KOBAYASHI**(The University of Tokyo)Note on the restriction of minimal representations with respect to reductive symmetric pairs (Japanese)

[ Abstract ]

I discuss briefly some abstract feature of branching problems with focus on the restriction of minimal representations with respect to reductive symmetric pairs.

I discuss briefly some abstract feature of branching problems with focus on the restriction of minimal representations with respect to reductive symmetric pairs.

#### Lie Groups and Representation Theory

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

Estimate of the norm of the $L^p$-Fourier transform on compact extensions of locally compact groups

(Japanese)

**Junko INOUE**(Tottori University)Estimate of the norm of the $L^p$-Fourier transform on compact extensions of locally compact groups

(Japanese)

[ Abstract ]

The classical Hausdorff-Young theorem for locally compact abelian groups is generalized by Kunze for unimodular locally compact groups.

When the group $G$ is of type I, the abstract Plancherel theorem gives a decomposition of the regular representation into a direct integral of irreducible representations through the Fourier transform;

By the Hausdorff-Young theorem generalized by Kunze, for exponents $p$ $(1 < p \leq 2)$ and ${p'}=p/(p-1)$, the Fourier transform yields a bounded operator $\mathcal{F}^p:L^p(G)\to L^{p'}(\widehat{G})$, where $L^{p'}(\widehat{G})$ is the $L^{p'}$ space of measurable fields of the Schatten class operators on the unitary dual $\widehat{G}$ of $G$.

Under this setting, we are concerned with the norm $\|\mathcal{F}^p(G)\|$ of the $L^p$-Fourier transform $\mathcal{F}^p$.

Let $G$ be a separable unimodular locally compact group of type I,and $N$ be a type I, unimodular, closed normal subgroup of $G$. Suppose $G/N$ is compact. Then we show the inequality $\|\mathcal{F}^p(G)\|\leq\|\mathcal F^p(N)\|$ for $1< p \leq 2$.

This result is a joint work with Ali Baklouti

(J. Fourier Anal. Appl. 26 (2020), Paper No. 26).

The classical Hausdorff-Young theorem for locally compact abelian groups is generalized by Kunze for unimodular locally compact groups.

When the group $G$ is of type I, the abstract Plancherel theorem gives a decomposition of the regular representation into a direct integral of irreducible representations through the Fourier transform;

By the Hausdorff-Young theorem generalized by Kunze, for exponents $p$ $(1 < p \leq 2)$ and ${p'}=p/(p-1)$, the Fourier transform yields a bounded operator $\mathcal{F}^p:L^p(G)\to L^{p'}(\widehat{G})$, where $L^{p'}(\widehat{G})$ is the $L^{p'}$ space of measurable fields of the Schatten class operators on the unitary dual $\widehat{G}$ of $G$.

Under this setting, we are concerned with the norm $\|\mathcal{F}^p(G)\|$ of the $L^p$-Fourier transform $\mathcal{F}^p$.

Let $G$ be a separable unimodular locally compact group of type I,and $N$ be a type I, unimodular, closed normal subgroup of $G$. Suppose $G/N$ is compact. Then we show the inequality $\|\mathcal{F}^p(G)\|\leq\|\mathcal F^p(N)\|$ for $1< p \leq 2$.

This result is a joint work with Ali Baklouti

(J. Fourier Anal. Appl. 26 (2020), Paper No. 26).

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