## Seminar information archive

### 2020/10/06

#### Tuesday Seminar on Topology

17:30-18:30   Online
Pre-registration required. See our seminar webpage.
Shinichiroh Matsuo (Nagoya University)
The Atiyah-Patodi-Singer index of manifolds with boundary and domain-wall fermions (JAPANESE)
[ Abstract ]
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index.

In a previous work, motivated by the study of lattice gauge theory, we derived a formula expressing the Atiyah-Patodi-Singer index in terms of the eta invariant of “domain-wall fermion Dirac operators” when the base manifold is a flat 4-dimensional torus. Now we generalise this formula to any even dimensional closed Riemannian manifolds, and prove it mathematically rigorously. Our proof uses a Witten localisation argument combined with a devised embedding into a cylinder of one dimension higher. Our viewpoint sheds some new light on the interplay among the Atiyah-Patodi-Singer boundary condition, domain-wall fermions, and edge modes.

This talk is based on a joint paper arXiv:1910.01987, to appear in CMP, with H. Fukaya, M. Furuta, T. Onogi, S. Yamaguchi, and M. Yamashita.
[ Reference URL ]
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

### 2020/10/01

#### Information Mathematics Seminar

16:50-18:35   Online
From the Cyber Attack by the malware to the Zero Trust Network (Japanese)
[ Abstract ]
I explain the Cyber Attack by the malware and the Zero Trust Network.
[ Reference URL ]
https://forms.gle/Uhy8uBujZatjNMsGA

#### Operator Algebra Seminars

16:45-18:15   Online
Norio Nawata (Osaka Univ.)
A characterization of the Razak-Jacelon algebra
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2020/09/29

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Kohei Iwaki (The University of Tokyo)
Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)
[ Abstract ]
In 1998, Lawrence-Zagier introduced a certain q-series and proved that its limit value at root of unity q=exp(2π i / K) coincides with the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant of the Poincare homology sphere Σ(2,3,5) at the level K. Employing the idea of Gukov-Marino-Putrov based on resurgent analysis, we generalize the result of Lawrence-Zagier for the Seifert loops (Seifert manifolds with a single loop inside). That is, for each Seifert loop, we introduce an explicit q-series (WRT function) and show that its limit value at the root of unity coincides with the WRT invariant of the Seifert loop. We will also discuss a q-difference equation satisfied by the WRT function. This talk is based on a joint work with H. Fuji, H. Murakami and Y. Terashima which is available on arXiv:2007.15872.
[ Reference URL ]
https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

### 2020/08/26

#### thesis presentations

16:00-17:15   Online
ITO Yohei (Graduate Scool of Mathematical Sciences University of tokyo)
Irregular Riemann–Hilbert correspondence and its applications to Fourier transforms of holonomic D-modules
[ Reference URL ]
https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/31

#### thesis presentations

10:30-11:45   Online
INOUE Eiji (Graduate Scool of Mathematical Sciences University of tokyo)
Theory on Kähler metrics with constant exponentially weighted scalar curvature and exponentially weighted K-stability including Kähler-Ricci solitons
[ Reference URL ]
https://forms.gle/jfh9Hpyt3XZXXcft6

#### thesis presentations

13:15-14:30   Online
INAYAMA Takahiro (Graduate Scool of Mathematical Sciences University of tokyo)
Studies on singular Hermitian metrics on holomorphic vector bundles via L² estimates and L² extension theorems
[ Reference URL ]
https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/30

#### thesis presentations

10:30-11:45   Online
LIN Dexie (Graduate Scool of Mathematical Sciences University of tokyo)
Monopole Floer homology for codimension-3 Riemannian foliation
[ Reference URL ]
https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/28

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Anderson Vera (RIMS, Kyoto University)
A double filtration for the mapping class group and the Goeritz group of the sphere (ENGLISH)
[ Abstract ]
I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of $S^3$. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)
[ Reference URL ]
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

#### thesis presentations

10:30-11:45   Online
Twisted arrow categories of operads and Segal conditions
[ Reference URL ]
https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/21

#### Numerical Analysis Seminar

16:30-18:00   Online
Tomoya Kemmochi (Nagoya University)
Structure-preserving numerical schemes for constrained gradient flows of planar curves (Japanese)
[ Reference URL ]
https://forms.gle/3JiNEjWnrWLW8cFA9

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Sergei Burkin (The University of Tokyo)
Twisted arrow categories of operads and Segal conditions (ENGLISH)
[ Abstract ]
We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category $\Delta$, Segal's category $\Gamma$ and Moerdijk--Weiss category $\Omega$ are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.
[ Reference URL ]
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

#### Tuesday Seminar on Topology

18:00-19:00   Online
Pre-registration required. See our seminar webpage.
Dexie Lin (The University of Tokyo)
Monopole Floer homology for codimension-3 Riemannian foliation (ENGLISH)
[ Abstract ]
In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold with codimension-3 oriented Riemannian foliation. Under a certain topological condition, we construct the basic monopole Floer homologies for a transverse spinc structure with a bundle-like metric, generic perturbation and a complete local system. We will show that these homologies are independent of the bundle-like metric and generic perturbation. The major difference between the basic monopole Floer homologies and the ones on manifolds is the necessity to use the complete local system to construct the monopole Floer homologies.
[ Reference URL ]
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

### 2020/07/16

#### Operator Algebra Seminars

16:45-18:15   Online
Christian Voigt (Univ. Glasgow)
Complex quantum groups and the Baum-Connes conjecture (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Information Mathematics Seminar

16:50-18:35   Online
Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (Japanese)
[ Abstract ]
Explanation of the speedup technique of the classic computing and innovation of causality in the root of the quantum computing
[ Reference URL ]

### 2020/07/14

#### Tuesday Seminar on Topology

17:30-18:30   Online
Joint with Lie Groups and Representation Theory Seminar. Pre-registration required. See our seminar webpage.
Takayuki Okuda (Hiroshima University)
Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (JAPANESE)
[ Abstract ]
Let G be a Lie group and X a homogeneous G-space. A discrete subgroup of G acting on X properly is called a discontinuous group for X. We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly. However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive. In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)]
gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry. In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### Lie Groups and Representation Theory

17:30-18:30   Room ## (Graduate School of Math. Sci. Bldg.)
Joint with Tuesday Seminar on Topology. Online.
Takayuki Okuda (Hiroshima University)
Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (Japanese)
[ Abstract ]
Let G be a Lie group and X a homogeneous G-space.
A discrete subgroup of G acting on X properly is called a discontinuous group for X.
We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly.
However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive.
In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)] gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces.
As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry.
In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.

### 2020/07/13

#### Seminar on Geometric Complex Analysis

10:30-12:00   Online
INOUE Eiji (University of Tokyo)
$\mu$-cscK metrics and $\mu$K-stability of polarized manifolds
[ Reference URL ]
https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/07/09

#### Operator Algebra Seminars

16:45-18:15   Online
Amine Marrakchi (ENS Lyon)
Affine isometric actions of groups on $L_p$-spaces : dependence on the value of $p$ (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Information Mathematics Seminar

16:50-18:35   Online
Ways from machine learning to deep learning (Japanese)
[ Abstract ]
Explanation of ways from machine learning to deep learning
[ Reference URL ]

### 2020/07/07

#### Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Yuta Nozaki (Hiroshima University)
Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor (JAPANESE)
[ Abstract ]
We construct a series of homomorphisms on the Y-filtration on the homology cylinders via the mod $\mathbb{Z}$ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of the Torelli group does not factor through Morita's refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. This is the joint work with Masatoshi Sato and Masaaki Suzuki.
[ Reference URL ]
https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

### 2020/07/06

#### Seminar on Geometric Complex Analysis

10:30-12:00   Online
INAYAMA Takahiro (University of Tokyo)
Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type (Japanese?)
[ Abstract ]
We propose a general definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems.
[ Reference URL ]
https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/07/02

#### Operator Algebra Seminars

16:45-18:15   Online
Toshihiko Masuda (Kyushu Univ.)
Outer actions ($\mathcal{G}$-kernels) of discrete amenable groupoids on injective factors (English)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### Information Mathematics Seminar

16:50-18:35   Online
Telework society and menace of the cyber attack (Japanese)
[ Abstract ]
Explanation on the menace of the cyber attack in telework society.
[ Reference URL ]