## Seminar information archive

Seminar information archive ～09/14｜Today's seminar 09/15 | Future seminars 09/16～

### 2020/10/27

#### Numerical Analysis Seminar

16:30-18:00 Online

Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)

https://forms.gle/HeuUxWLGa696KPvz8

**Buyang Li**(The Hong Kong Polytechnic University)Convergent evolving finite element algorithms for mean curvature flow and Willmore flow of closed surfaces (English)

[ Abstract ]

We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.

[1] https://doi.org/10.1007/s00211-019-01074-2

[2] https://arxiv.org/abs/2007.15257

[ Reference URL ]We construct evolving surface finite element methods for the mean curvature and Willmore flow through equivalently reformulating the original equations into coupled systems governing the evolution of surface position, velocity, normal vector and mean curvature. Then we prove $H^1$-norm convergence of the proposed evolving surface finite element methods for the reformulated systems, by combining stability estimates and consistency estimates. The stability analysis is based on the matrix–vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.

[1] https://doi.org/10.1007/s00211-019-01074-2

[2] https://arxiv.org/abs/2007.15257

https://forms.gle/HeuUxWLGa696KPvz8

#### PDE Real Analysis Seminar

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

Vanishing discount problems for Hamilton-Jacobi equations on changing domains (English)

**Son Tu**(University of Wisconsin Madison)Vanishing discount problems for Hamilton-Jacobi equations on changing domains (English)

[ Abstract ]

We study the asymptotic behavior, as the discount factor vanishes, of the Hamilton-Jacobi equation with state-constraint on changing domains. Surprisingly, we can obtain both convergence results and non-convergence results in this convex setting. Moreover, we provide a very first result on the asymptotic expansion of the additive eigenvalue of the Hamiltonian with respect to the changing domains. The main tool we use is a duality representation of solution with viscosity Mather measures.

We study the asymptotic behavior, as the discount factor vanishes, of the Hamilton-Jacobi equation with state-constraint on changing domains. Surprisingly, we can obtain both convergence results and non-convergence results in this convex setting. Moreover, we provide a very first result on the asymptotic expansion of the additive eigenvalue of the Hamiltonian with respect to the changing domains. The main tool we use is a duality representation of solution with viscosity Mather measures.

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Vassiliev derivatives of Khovanov homology and its application (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Jun Yoshida**(The University of Tokyo)Vassiliev derivatives of Khovanov homology and its application (JAPANESE)

[ Abstract ]

Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.

[ Reference URL ]Khovanov homology is a categorification of the Jones polynomial. It is known that Khovanov homology also arises from a categorical representation of braid groups, so we can regard it as a kind of quantum knot invariant. However, in contrast to the case of classical quantum invariants, its relation to Vassiliev invariants remains unclear. In this talk, aiming at the problem, we discuss a categorified version of Vassiliev skein relation on Khovanov homology. Namely, we extend Khovanov homology to singular links so that extended ones can be seen as "derivatives" in view of Vassiliev theory. As an application, we compute first derivatives to determine Khovanov homologies of twist knots. This talk is based on papers arXiv:2005.12664 (joint work with N.Ito) and arXiv:2007.15867.

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

#### Tokyo-Nagoya Algebra Seminar

16:30-18:00 Online

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

Positive cluster complex and $\tau$-tilting complex (Japanese)

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

**Yasuaki Gyoda**(Nagoya University)Positive cluster complex and $\tau$-tilting complex (Japanese)

[ Abstract ]

In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.

In cluster algebra theory, cluster complexes are actively studied as simplicial complexes, which represent the structure of a seed and its mutations. In this talk, I will discuss a certain subcomplex, called positive cluster complex, of a cluster complex. This is a subcomplex whose vertex set consists of all cluster variables except for those in the initial seed. I will also introduce another simplicial complex in this talk - the tau-tilting complex, which has vertices given by all indecomposable tau-rigid modules, and simplices given by basic tau-rigid modules. In the case of a cluster-tilted algebra, it turns out that a tau-tilting complex corresponds to some positive cluster complex. Due to this fact, we can investigate the structure of a tau-tilting complex of tau-tilting finite type by using the tools of cluster algebra theory. This is joint work with Haruhisa Enomoto.

### 2020/10/26

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Spectral convergence in geometric quantization

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**HATTORI Kota**(Keio University)Spectral convergence in geometric quantization

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2020/10/22

#### Operator Algebra Seminars

16:45-18:15 Online

$C^*$-algebras generated by multiplication operators and composition operators by functions with self-similar branches

[ Reference URL ]

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

**Hiroyasu Hamada**(National Institute of Technology, Sasebo College)$C^*$-algebras generated by multiplication operators and composition operators by functions with self-similar branches

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Room #オンライン(Zoom) (Graduate School of Math. Sci. Bldg.)

Think about a zero trust from information security 10 size menace 2020 (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Think about a zero trust from information security 10 size menace 2020 (Japanese)

[ Abstract ]

In this talk, we think about a zero trust from information security 10 size menace 2020.

[ Reference URL ]In this talk, we think about a zero trust from information security 10 size menace 2020.

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/10/20

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Poincaré duality for free loop spaces (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Alexandru Oancea**(Sorbonne Université)Poincaré duality for free loop spaces (ENGLISH)

[ Abstract ]

A certain number of dualities between homological and cohomological invariants of free loop spaces have been observed over the years, having the flavour of Poincaré duality but nevertheless holding in an infinite dimensional setting. The goal of the talk will be to explain these through a new duality theorem, whose proof uses symplectic methods. The talk will report on joint work with Kai Cieliebak and Nancy Hingston.

[ Reference URL ]A certain number of dualities between homological and cohomological invariants of free loop spaces have been observed over the years, having the flavour of Poincaré duality but nevertheless holding in an infinite dimensional setting. The goal of the talk will be to explain these through a new duality theorem, whose proof uses symplectic methods. The talk will report on joint work with Kai Cieliebak and Nancy Hingston.

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

### 2020/10/19

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

On projective manifolds with pseudo-effective tangent bundle

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**MATSUMURA, Shin-ichi**(Tohoku University)On projective manifolds with pseudo-effective tangent bundle

[ Abstract ]

In this talk, I would like to discuss projective manifolds whose tangent bundle is pseudo-effective or admits a positively curved singular metric. I will explain a structure theorem for such manifolds and the classification in the two-dimensional case, comparing our theory with classical results for nef tangent bundle or non-negative bisectional curvature. Related open problems will be discussed if time permits.

This is joint work with Genki Hosono (Tohoku University) and Masataka Iwai (Osaka City University).

[ Reference URL ]In this talk, I would like to discuss projective manifolds whose tangent bundle is pseudo-effective or admits a positively curved singular metric. I will explain a structure theorem for such manifolds and the classification in the two-dimensional case, comparing our theory with classical results for nef tangent bundle or non-negative bisectional curvature. Related open problems will be discussed if time permits.

This is joint work with Genki Hosono (Tohoku University) and Masataka Iwai (Osaka City University).

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

#### Seminar on Probability and Statistics

10:30-11:30 Room #Zoom (Graduate School of Math. Sci. Bldg.)

Development of high-dimensional CLTs arising from high-frequency data analysis (日本語)

[ Reference URL ]

https://docs.google.com/forms/d/e/1FAIpQLSfDhlzlC6haR8dsDn9_mCxi1s9RtXZxTi_U7Nb_Xl6q7Gw1dA/viewform

**Yuta Koike**(University of Tokyo)Development of high-dimensional CLTs arising from high-frequency data analysis (日本語)

[ Reference URL ]

https://docs.google.com/forms/d/e/1FAIpQLSfDhlzlC6haR8dsDn9_mCxi1s9RtXZxTi_U7Nb_Xl6q7Gw1dA/viewform

### 2020/10/15

#### Operator Algebra Seminars

16:45-18:15 Online

Structure of Hecke von Neumann algebras and applications to representation theory

[ Reference URL ]

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

**Sven Raum**(Stockholm Univ.)Structure of Hecke von Neumann algebras and applications to representation theory

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Room #オンライン(Zoom) (Graduate School of Math. Sci. Bldg.)

Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (Japanese)

[ Abstract ]

Explanation on the speedup technique of the classic computing and Innovation of causality in the root of the quantum computing

[ Reference URL ]Explanation on the speedup technique of the classic computing and Innovation of causality in the root of the quantum computing

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/10/12

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Two topics on psedoconvex domains (Japanese)

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**NOGUCHI Junjiro**(University of Tokyo)Two topics on psedoconvex domains (Japanese)

[ Reference URL ]

https://zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2020/10/08

#### Operator Algebra Seminars

16:45-18:15 Online

An entropic proof of cutoff on Ramanujan graphs

[ Reference URL ]

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

**Narutaka Ozawa**(RIMS, Kyoto Univ.)An entropic proof of cutoff on Ramanujan graphs

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

From a neural network to deep learning (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)From a neural network to deep learning (Japanese)

[ Abstract ]

Explanation on how to reach from a neural network to deep learning

[ Reference URL ]Explanation on how to reach from a neural network to deep learning

https://forms.gle/Uhy8uBujZatjNMsGA

#### Applied Analysis

16:00-17:30 Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)

(Japanese)

[ Reference URL ]

https://docs.google.com/forms/d/e/1FAIpQLSd7MT077191TeM4aQzeo2hK9Bqn6HQudr3pjLRdmEqND2heqQ/viewform?usp=sf_link

**( )**(Japanese)

[ Reference URL ]

https://docs.google.com/forms/d/e/1FAIpQLSd7MT077191TeM4aQzeo2hK9Bqn6HQudr3pjLRdmEqND2heqQ/viewform?usp=sf_link

### 2020/10/07

#### Mathematical Biology Seminar

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

The method of the third wave prediction of the infection by the Effective SIQR model (日本語)

**Masao Namiki**(Former Executive Vice President, Board of Directors and Representative Executive Officers)The method of the third wave prediction of the infection by the Effective SIQR model (日本語)

### 2020/10/06

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

The Atiyah-Patodi-Singer index of manifolds with boundary and domain-wall fermions (JAPANESE)

https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

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 ]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.

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)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)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 ]I explain the Cyber Attack by the malware and the Zero Trust Network.

https://forms.gle/Uhy8uBujZatjNMsGA

#### Operator Algebra Seminars

16:45-18:15 Online

A characterization of the Razak-Jacelon algebra

[ Reference URL ]

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

**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.

Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)

https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

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 ]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.

https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

### 2020/08/26

#### thesis presentations

16:00-17:15 Online

Irregular Riemann–Hilbert correspondence and its applications to Fourier transforms of holonomic D-modules

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**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

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

**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

Studies on singular Hermitian metrics on holomorphic vector bundles via L² estimates and L² extension theorems

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**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

Monopole Floer homology for codimension-3 Riemannian foliation

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**LIN Dexie**(Graduate Scool of Mathematical Sciences University of tokyo)Monopole Floer homology for codimension-3 Riemannian foliation

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

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