## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

### 2022/05/30

#### Seminar on Geometric Complex Analysis

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

Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)

https://forms.gle/hYT2hVhDE3q1wDSh6

**Yusaku Tiba**(Ochanomizu University)Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)

[ Abstract ]

In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.

[ Reference URL ]In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.

https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022/05/26

#### Information Mathematics Seminar

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

Design and control of quantum computers VII (Japanese)

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

### 2022/05/25

#### Number Theory Seminar

17:00-18:00 Hybrid

Torsion points of elliptic curves over cyclotomic fields (JAPANESE)

**Koji Matsuda**(University of Tokyo)Torsion points of elliptic curves over cyclotomic fields (JAPANESE)

[ Abstract ]

By Mordell--Weil theorem, the Mordell--Weil groups of elliptic curves over number fields are finitely generated, and in particular their torsion subgroups are finite. For a fixed elliptic curve, it is easy to compute its torsion subgroups. Conversely using modular curves, we can study the possible torsion subgroups of elliptic curves. More precisely, the existence of an elliptic curve with certain torsion points is essentially equivalent to the existence of certain rational points of a modular curve. In this talk, in order to study the rational points of modular curves over cyclotomic fields, we compute the Mordell--Weil ranks of their Jacobian varieties over cyclotomic fields.

By Mordell--Weil theorem, the Mordell--Weil groups of elliptic curves over number fields are finitely generated, and in particular their torsion subgroups are finite. For a fixed elliptic curve, it is easy to compute its torsion subgroups. Conversely using modular curves, we can study the possible torsion subgroups of elliptic curves. More precisely, the existence of an elliptic curve with certain torsion points is essentially equivalent to the existence of certain rational points of a modular curve. In this talk, in order to study the rational points of modular curves over cyclotomic fields, we compute the Mordell--Weil ranks of their Jacobian varieties over cyclotomic fields.

### 2022/05/24

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Stability analysis for the surface diffusion flow on double bubbles using the Lojasiewicz-Simon (English)

https://forms.gle/Cam3mpSSEKKVppZr9

**Michael Goesswein**(The University of Tokyo/University of Regensburg)Stability analysis for the surface diffusion flow on double bubbles using the Lojasiewicz-Simon (English)

[ Abstract ]

Many strategies for stability analysis use precise knowledge of the set of equilibria. For example, Escher, Mayer, and Simonett used center manifold analysis to study the surface diffusion flow on closed manifolds. Especially in higher dimensional situations with boundaries, this can cause problems as the set of equilibria will have a lot of degrees of freedom. In such situations approaches with a Lojasiewicz-Simon inequality gives an elegant way to avoid this problem. In this talk, we will both explain the general tools and ideas for this strategy and use them to prove the stability of standard double bubbles with respect to the surface diffusion flow. The talk is based on joint work with H. Garcke.

[ Reference URL ]Many strategies for stability analysis use precise knowledge of the set of equilibria. For example, Escher, Mayer, and Simonett used center manifold analysis to study the surface diffusion flow on closed manifolds. Especially in higher dimensional situations with boundaries, this can cause problems as the set of equilibria will have a lot of degrees of freedom. In such situations approaches with a Lojasiewicz-Simon inequality gives an elegant way to avoid this problem. In this talk, we will both explain the general tools and ideas for this strategy and use them to prove the stability of standard double bubbles with respect to the surface diffusion flow. The talk is based on joint work with H. Garcke.

https://forms.gle/Cam3mpSSEKKVppZr9

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Polynomial functors associated with beaded open Jacobi diagrams (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Christine Vespa**(IRMA, Université de Strasbourg / JSPS)Polynomial functors associated with beaded open Jacobi diagrams (ENGLISH)

[ Abstract ]

The Kontsevich integral is a very powerful invariant of knots, taking values is the space of Jacobi diagrams. Using an extension of the Kontsevich integral to tangles in handlebodies, Habiro and Massuyeau construct a functor from the category of bottom tangles in handlebodies to the linear category A of Jacobi diagrams in handlebodies. The category A has a subcategory equivalent to the linearization of the opposite of the category of finitely generated free groups, denoted by $\textbf{gr}^{op}$. By restriction to this subcategory, morphisms in the linear category $\textbf{A}$ give rise to interesting contravariant functors on the category $\textbf{gr}$, encoding part of the composition structure of the category A.

In recent papers, Katada studies the functor given by the morphisms in the category A from 0. In particular, she obtains a family of polynomial functors on $\textbf{gr}^{op}$ which are outer functors, in the sense that inner automorphisms act trivially.

In this talk, I will explain these results and give extensions of Katada’s results concerning the functors given by the morphisms in the category A from any integer k. These functors give rise to families of polynomial functors on $\textbf{gr}^{op}$ which are no more outer functors. Our approach is based on an equivalence of categories given by Powell. Through this equivalence the previous polynomial functors correspond to functors given by beaded open Jacobi diagrams.

[ Reference URL ]The Kontsevich integral is a very powerful invariant of knots, taking values is the space of Jacobi diagrams. Using an extension of the Kontsevich integral to tangles in handlebodies, Habiro and Massuyeau construct a functor from the category of bottom tangles in handlebodies to the linear category A of Jacobi diagrams in handlebodies. The category A has a subcategory equivalent to the linearization of the opposite of the category of finitely generated free groups, denoted by $\textbf{gr}^{op}$. By restriction to this subcategory, morphisms in the linear category $\textbf{A}$ give rise to interesting contravariant functors on the category $\textbf{gr}$, encoding part of the composition structure of the category A.

In recent papers, Katada studies the functor given by the morphisms in the category A from 0. In particular, she obtains a family of polynomial functors on $\textbf{gr}^{op}$ which are outer functors, in the sense that inner automorphisms act trivially.

In this talk, I will explain these results and give extensions of Katada’s results concerning the functors given by the morphisms in the category A from any integer k. These functors give rise to families of polynomial functors on $\textbf{gr}^{op}$ which are no more outer functors. Our approach is based on an equivalence of categories given by Powell. Through this equivalence the previous polynomial functors correspond to functors given by beaded open Jacobi diagrams.

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

### 2022/05/20

#### Colloquium

15:30-16:30 Hybrid

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.

**Ryo Takada**(Graduate School of Mathematical Sciences, the University of Tokyo)Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)

[ Abstract ]

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.

### 2022/05/19

#### Information Mathematics Seminar

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

Design and control of quantum computersVI (Japanese)

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

### 2022/05/18

#### Number Theory Seminar

17:00-18:00 Hybrid

Local Langlands correspondence for non-quasi-split odd special orthogonal groups (JAPANESE)

**Hiroshi Ishimoto**(University of Tokyo)Local Langlands correspondence for non-quasi-split odd special orthogonal groups (JAPANESE)

[ Abstract ]

In 2013, Arthur established the endoscopic classification of representations of quasi-split symplectic and orthogonal groups, and Mok analogously proved the similar classification for quasi-split unitary groups. In 2014, Kaletha-Minguez-Shin-White established the classification for non-quasi-spilt unitary groups assuming Mok's results. Similarly, we can prove that for non-quasi-split odd orthogonal groups assuming Arthur's results. In this talk, I will explain the local Langlands correspondence for non-quasi-split odd special orthogonal groups, which is a part of the classification of representations.

In 2013, Arthur established the endoscopic classification of representations of quasi-split symplectic and orthogonal groups, and Mok analogously proved the similar classification for quasi-split unitary groups. In 2014, Kaletha-Minguez-Shin-White established the classification for non-quasi-spilt unitary groups assuming Mok's results. Similarly, we can prove that for non-quasi-split odd orthogonal groups assuming Arthur's results. In this talk, I will explain the local Langlands correspondence for non-quasi-split odd special orthogonal groups, which is a part of the classification of representations.

### 2022/05/17

#### Operator Algebra Seminars

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

Towards integral perturbation of two-dimensional CFT (English)

[ Reference URL ]

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

**Yoh Tanimoto**(Univ. Rome, "Tor Vergata")Towards integral perturbation of two-dimensional CFT (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.

Contribution of simple loops to the configuration space integral (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Tatsuro Shimizu**(Tokyo Denki University)Contribution of simple loops to the configuration space integral (JAPANESE)

[ Abstract ]

For a manifold with a representation of the fundamental group, the configuration space integral associated with a graph (Feynman diagram) gives a real number. An appropriate linear combination of graphs gives an invariant of the manifold with the representation. In this talk, we discuss the contribution of simple loops to the configuration space integral. Hutchings, Lee and Kitayama give geometric descriptions of the Reidemeister torsion by using circle valued Morse functions. By using these descriptions and a Morse theoretical description of the configuration space integral, we have equations among the Reidemeister torsion and the contributions of simple loops in some cases. In this talk, we extend the equations for some other cases and give a computational example of the configuration space integrals by using Morse function.

[ Reference URL ]For a manifold with a representation of the fundamental group, the configuration space integral associated with a graph (Feynman diagram) gives a real number. An appropriate linear combination of graphs gives an invariant of the manifold with the representation. In this talk, we discuss the contribution of simple loops to the configuration space integral. Hutchings, Lee and Kitayama give geometric descriptions of the Reidemeister torsion by using circle valued Morse functions. By using these descriptions and a Morse theoretical description of the configuration space integral, we have equations among the Reidemeister torsion and the contributions of simple loops in some cases. In this talk, we extend the equations for some other cases and give a computational example of the configuration space integrals by using Morse function.

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.)

Estimate of the optimal constant of convolution inequalities on unimodular

locally compact groups

(Japanese)

**Takashi Satomi**(The University of Tokyo)Estimate of the optimal constant of convolution inequalities on unimodular

locally compact groups

(Japanese)

[ Abstract ]

Some convolution inequalities (Young's inequality, the reverse Young's inequality, the Hausdorff--Young inequality) known for a long time on $\mathbb{R}$ can be generalized for any unimodular locally compact group.

In this seminar, we estimate the optimal constants (the ratio of both sides such that these inequalities are optimal) of these inequalities from above and below, and discuss that these estimates are the best for $G=\mathbb{R}$.

Some convolution inequalities (Young's inequality, the reverse Young's inequality, the Hausdorff--Young inequality) known for a long time on $\mathbb{R}$ can be generalized for any unimodular locally compact group.

In this seminar, we estimate the optimal constants (the ratio of both sides such that these inequalities are optimal) of these inequalities from above and below, and discuss that these estimates are the best for $G=\mathbb{R}$.

### 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.

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