## Seminar information archive

#### Lie Groups and Representation Theory

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Toshihisa Kubo (Ryukoku University)
On the classification of the $K$-type formulas for the Heisenberg ultrahyperbolic equation (Japanese)
[ Abstract ]
About ten years ago, Kable constructed a one-parameter family $\square^{(n)}_s$ ($s\in \mathbb{C}$) of differential operators for $\mathfrak{sl}(n,\mathbb{C})$. He referred to $\square^{(n)}_s$ as the Heisenberg ultrahyperbolic operator. In the viewpoint of intertwining operators, $\square^{(n)}_s$ can be thought of as an intertwining differential operator between certain parabolically induced representations for $\widetilde{SL}(n,\mathbb{R})$. In this talk we discuss about the classification of the $K$-type formulas of the space of $K$-finite solutions to the differential equation $\square^{(3)}_sf=0$ for $\widetilde{SL}(3,\mathbb{R})$ and some related topics. This is joint work with Bent {\O}rsted.

### 2021/12/02

#### Information Mathematics Seminar

16:50-18:35   Online
The whole summary and other machine learning technique in the AI
～ LSTM/GAN/Unsupervised learning /Auto Encoder～ (Japanese)
[ Abstract ]
The whole summary and the explanation on other machine learning techniques in the AI (LSTM/GAN/Unsupervised learning /Auto Encoder).
[ Reference URL ]

#### Applied Analysis

16:00-17:00   Online

( )

[ Reference URL ]
https://forms.gle/6cKyu9meCxSv72N19

### 2021/11/30

#### Operator Algebra Seminars

16:45-18:15   Online
Yosuke Kubota (Shinshu Univ.)
Crystallographic $T$-duality in twisted equivariant $K$-theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Masatoshi Sato (Tokyo Denki University)
A non-commutative Reidemeister-Turaev torsion of homology cylinders (JAPANESE)
[ Abstract ]
The Reidemeister-Turaev torsion of homology cylinders takes values in the integral group ring of the first homology of a surface. We lift it to a torsion valued in the $K_1$-group of the completed rational group ring of the fundamental group of the surface. We show that it induces a finite type invariant of homology cylinders, and describe the induced map on the graded quotient of the Y-filtration of homology cylinders via the 1-loop part of the LMO functor and the Enomoto-Satoh trace. This talk is based on joint work with Yuta Nozaki and Masaaki Suzuki.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Mathematical Biology Seminar

15:30-17:00   Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)
Takeshi OJIMA (Fukushima University)
Endogenous Waves in a SIR Model with Risk Heterogeneity
(Japanese)
[ Reference URL ]
オンライン開催です．参加希望者は　inaba@ms.u-tokyo.ac.jp までご連絡ください．

#### Lie Groups and Representation Theory

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Quentin Labriet (Reims University)
Branching problems for conformal Lie groups and orthogonal polynomials (English)
[ Abstract ]
In this talk, I will present some results obtained during my PhD about a link between branching problems for conformal Lie groups and orthogonal polynomials. More precisely, I am going to look at some examples of branching problems for representations in the scalar-valued holomorphic discrete series of some conformal Lie groups. Using the geometry of symmetric cone, I will explain how the theory of orthogonal polynomials can be related to branching problems and to the construction of symmetry breaking and holographic operators.

### 2021/11/29

#### Seminar on Geometric Complex Analysis

10:30-12:00   Online
Akira Kitaoka (The University of Tokyo)
レンズ空間上のRay-Singer捩率とRumin複体のラプラシアン (Japanese)
[ Abstract ]
Rumin複体は、接触多様体に関するBernstein-Gelfand-Gelfand複体(BGG複体)である。BGG複体は、放物型幾何やフィルター付き多様体に対して構成される複体であり、BGG複体のコホモロジーはde Rhamコホモロジーに一致するという事が挙げられる。また、Rumin複体はsub-Riemmann極限を考えた際に自然に現れるという性質を持つ。

De Rham複体を使って定義した概念をRumin複体に置き換えるとどうなるのか、ということを考える。本講演では、この考えを解析的捩率に適応した場合を話す。レンズ空間上のユニモジュラーなホロのミーから誘導される平坦ベクトル束に対して、Rumin複体の解析的捩率の値が、Betti数とRay-Singer捩率を用いて表されることを報告する。
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/11/26

#### Colloquium

15:30-16:30   Online
Registration is closed (12:00, November 26).
Gang Tian (BICMR, Peking University)
Ricci flow on Fano manifolds (ENGLISH)
[ Abstract ]
Ricci flow was introduced by Hamilton in early 80s. It preserves the Kahlerian structure and has found many applications in Kahler geometry. In this expository talk, I will focus on Ricci flow on Fano manifolds. I will first survey some results in recent years, then I will discuss my joint work with Li and Zhu. I will also discuss the connection between the long time behavior of Ricci flow and some algebraic geometric problems for Fano manifolds.

#### Mathematical Biology Seminar

15:00-16:30   Online
Shinji NAKAOKA (Faculty of Advanced Life Science, Hokkaido University)
Derivation of structured population models of cellular proliferation on an
energy landscape
[ Reference URL ]
オンライン参加希望の方は，inaba@ms.u-tokyo.ac.jp　までご連絡ください．

### 2021/11/25

#### Applied Analysis

16:00-17:30   Online
( )
(日本語)
[ Reference URL ]
https://forms.gle/xBAgncTERzYfauJE6

#### Information Mathematics Seminar

16:50-18:35   Online
Classification and Clustering in the Machine Learning (Japanese)
[ Abstract ]
Explanation on classification and clustering in the Machine Learning
[ Reference URL ]

### 2021/11/24

#### Number Theory Seminar

17:00-18:00   Online
Kazuma Ohara (University of Tokyo)
On the formal degree conjecture for non-singular supercuspidal representations (Japanese)
[ Abstract ]
We prove the formal degree conjecture for non-singular supercuspidal representations based on Schwein's work proving the formal degree conjecture for regular supercuspidal representations. The main difference between our work and Schwein's work is that in non-singular case, the Deligne--Lusztig representations can be reducible, and the $S$-groups are not necessarily abelian. Therefore, we have to compare the dimensions of irreducible constituents of the Deligne--Lusztig representations and the dimensions of irreducible representations of $S$-groups.

#### 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.)
Yosuke Hasegawa (Institute of Industrial Science, the University of Tokyo)

### 2021/11/23

#### Lie Groups and Representation Theory

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Yuichiro Tanaka (The University of Tokyo)
A Cartan decomposition for a reductive real spherical subgroup
(Japanese)
[ Abstract ]
A closed subgroup H of a real reductive Lie group G is real spherical if a minimal parabolic subgroup of G has an open orbit on G/H.
In this talk I would like to show a proof of a Cartan decomposition G=KAH when H is reductive.
This is a conjecture of T. Kobayashi, introduced in the 3rd Number Theory Summer School in 1995.

### 2021/11/19

#### Tokyo-Nagoya Algebra Seminar

17:00-18:30   Online
Please see the URL below for details on the online seminar.
Yuta Kozakai (Tokyo University of Science)

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

### 2021/11/18

#### Information Mathematics Seminar

16:50-18:35   Online
Reinforcement learning and  Regression algorithm to support AI (Japanese)
[ Abstract ]
Explanation on reinforcement learning and  regression algorithm to support AI
[ Reference URL ]

### 2021/11/17

#### Seminar on Probability and Statistics

15:30-17:00   Room # (Graduate School of Math. Sci. Bldg.)
Jean Bertoin (Institut of Mathematics, University of Zurich (UZH))
On the local times of noise reinforced Bessel processes
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics (APSPS)

Bessel processes form a one-parameter family of self-similar diffusion on $[0,\infty)$ with the same Hurst exponent 1/2 as Brownian motion. Loosely speaking, in this setting, linear noise reinforcement with reinforcement parameter $p$ consists of repeating (if $p>0$) or counterbalancing (if $p<0$)infinitesimal increments of the process, uniformly at random and at a fixed rate as time passes. In this talk, we will investigate the effect of noise reinforcement on the local time at level $0$, that is, informally, the time that the process spends at $0$. A connection with increasing self-similar Markov processes will play a key role.
[ Reference URL ]

### 2021/11/16

#### Tuesday Seminar of Analysis

16:00-17:30   Online
KUBO Hideo (Hokkaido University)
TBA (Japanese)
[ Reference URL ]
https://forms.gle/6ZCp8hQxKA3vq3DB9

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Wataru Yuasa (RIMS, Kyoto University)
Skein and cluster algebras of marked surfaces without punctures for sl(3) (JAPANESE)
[ Abstract ]
We consider a skein algebra consisting of sl(3)-webs with the boundary skein relations for a marked surface without punctures. We construct a quantum cluster algebra coming from the moduli space of decorated SL(3)-local systems of the surface inside the skew-field of fractions of the skein algebra. In this talk, we introduce the sticking trick and the cutting trick for sl(3)-webs. The sticking trick expands the boundary-localized skein algebra into the cluster algebra. The cutting trick gives Laurent expressions of "elevation-preserving" webs with positive coefficients in certain clusters. We can also apply these tricks in the case of sp(4). This talk is based on joint works with Tsukasa Ishibashi.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Operator Algebra Seminars

16:45-18:15   Online
Michiya Mori (RIKEN)
On regular $*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Lie Groups and Representation Theory

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)
[ Abstract ]
Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.
Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).
In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.
Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.
Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.

### 2021/11/15

#### Seminar on Geometric Complex Analysis

10:30-12:00   Online
Katsusuke Nabeshima (Tokyo University of Science)
Computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals (Japanese)
[ Abstract ]
The concept of logarithmic vector fields along a hypersurface, introduced by K. Saito (1980), is of considerable importance in singularity theory.
Logarithmic vector fields have been extensively studied and utilized by several researchers. A. G. Aleksandrov (1986) and J. Wahl (1983) considered quasihomogeneous complete intersection cases and gave independently, among other things, a closed formula of generators of logarithmic vector fields. However, there is no closed formula for generators of logarithmic vector fields, even for semi-quasihomogeneous hypersurface isolated singularity cases. Many problems related with logarithmic vector fields remain still unsolved, especially for non-quasihomogeneous cases.
Bruce-Roberts Milnor number was introduced in 1988 by J. W. Bruce and R. M. Roberts as a generalization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety in terms of logarithmic vector fields. Recently, Bruce-Robert Milnor numbers are investigated by several researchers. However, many problems related with Bruce-Roberts Milnor numbers remain unsolved.
In this talk, we consider logarithmic vector fields along a hypersurface with an isolated singularity. We present methods to study complex analytic properties of logarithmic vector fields and illustrate an algorithm for computing logarithmic vector fields. As an application of logarithmic vector fields, we consider Bruce-Roberts Milnor numbers in the context of symbolic computation.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/11/11

#### Information Mathematics Seminar

16:50-18:35   Online
Supervised/Unsupervised Learning and Reinforcement learning for Deep Learning (Japanese)
[ Abstract ]
Explanation on supervised/unsupervised learning and reinforcement learning for deep learning
[ Reference URL ]