## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

### 2021/01/22

#### Colloquium

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Convolution algebras and a new proof of Kazhdan-Lusztig formula (JAPANESE)

[ Reference URL ]

https://forms.gle/AAVzoCGPyLmzDJHf7

Please register at the link below to attend this online colloquium

**Hiraku Nakajima**(Kavli IPMU)Convolution algebras and a new proof of Kazhdan-Lusztig formula (JAPANESE)

[ Reference URL ]

https://forms.gle/AAVzoCGPyLmzDJHf7

### 2021/01/21

#### Information Mathematics Seminar

16:50-18:35 Online

Topological quantum error-correcting codes and fault-tolerant quantum computing (Japanese)

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

**Yasunari Suzuki**(NTT)Topological quantum error-correcting codes and fault-tolerant quantum computing (Japanese)

[ Abstract ]

Explanation on topological quantum error-correcting codes and fault-tolerant quantum computing

[ Reference URL ]Explanation on topological quantum error-correcting codes and fault-tolerant quantum computing

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

#### Tokyo-Nagoya Algebra Seminar

17:00-18:30 Online

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

Based modules over the i-quantum group of type AI (Japanese)

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

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

**Hideya Watanabe**(Kyoto University)Based modules over the i-quantum group of type AI (Japanese)

[ Abstract ]

In recent years, i-quantum groups are intensively studied because of their importance in various branches of mathematics and physics. Although i-quantum groups are thought of as generalizations of Drinfeld-Jimbo quantum groups, their representation theory is much more difficult than that of quantum groups. In this talk, I will focus on the i-quantum group of type AI. It is a non-standard quantization of the special orthogonal Lie algebra so_n. I will report my recent research on based modules, which are modules equipped with distinguished bases, called the i-canonical bases. The first main result is a new combinatorial formula describing the branching rule from sl_n to so_n. The second one is the irreducibility of cell modules associated with the i-canonical bases.

[ Reference URL ]In recent years, i-quantum groups are intensively studied because of their importance in various branches of mathematics and physics. Although i-quantum groups are thought of as generalizations of Drinfeld-Jimbo quantum groups, their representation theory is much more difficult than that of quantum groups. In this talk, I will focus on the i-quantum group of type AI. It is a non-standard quantization of the special orthogonal Lie algebra so_n. I will report my recent research on based modules, which are modules equipped with distinguished bases, called the i-canonical bases. The first main result is a new combinatorial formula describing the branching rule from sl_n to so_n. The second one is the irreducibility of cell modules associated with the i-canonical bases.

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

#### Operator Algebra Seminars

16:45-18:15 Online

On induction along a homomorphism of compact quantum groups

[ Reference URL ]

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

**Kan Kitamura**(Univ. Tokyo)On induction along a homomorphism of compact quantum groups

[ Reference URL ]

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

### 2021/01/20

#### Number Theory Seminar

17:00-18:00 Online

Overconvergent Lubin-Tate $(\varphi, \Gamma)$-modules for different uniformizers (Japanese)

**Yuta Saito**(University of Tokyo)Overconvergent Lubin-Tate $(\varphi, \Gamma)$-modules for different uniformizers (Japanese)

[ Abstract ]

$(\varphi, \Gamma)$-modules are used for investigating p-adic Galois representations, which has an important role in constructing the p-adic local Langlands correspondence for GL_2(Q_p). When we try to construct the p-adic local correspondence for GL_2(F) for a general local field F, we want more useful and more suitable $(\varphi, \Gamma)$-modules. Lubin-Tate $(\varphi, \Gamma)$-modules are the candidates for such $(\varphi, \Gamma)$-modules. Lubin-Tate extensions are used for defining Lubin-Tate $(\varphi, \Gamma)$-modules. However, these extensions depend on the choice of uniformizers and the behavior of Lubin-Tate $(\varphi, \Gamma)$-modules for different uniformizers has not been discussed so much. We focus on overconvergency and discuss the coincidence for 2-dimensional triangulable $(\varphi, \Gamma)$-modules for different uniformizers.

$(\varphi, \Gamma)$-modules are used for investigating p-adic Galois representations, which has an important role in constructing the p-adic local Langlands correspondence for GL_2(Q_p). When we try to construct the p-adic local correspondence for GL_2(F) for a general local field F, we want more useful and more suitable $(\varphi, \Gamma)$-modules. Lubin-Tate $(\varphi, \Gamma)$-modules are the candidates for such $(\varphi, \Gamma)$-modules. Lubin-Tate extensions are used for defining Lubin-Tate $(\varphi, \Gamma)$-modules. However, these extensions depend on the choice of uniformizers and the behavior of Lubin-Tate $(\varphi, \Gamma)$-modules for different uniformizers has not been discussed so much. We focus on overconvergency and discuss the coincidence for 2-dimensional triangulable $(\varphi, \Gamma)$-modules for different uniformizers.

### 2021/01/18

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

The hydrodynamic period matrices and closings of an open Riemann surface of finite genus

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

**HAMANO Sachiko**(Osaka City University)The hydrodynamic period matrices and closings of an open Riemann surface of finite genus

[ Abstract ]

A closing of an open Riemann srface $R$ of finite genus is a shorter name of a closed Riemann surface of the same genus into which $R$ can be embedded by a homology type preserving conformal mapping. We observe the Riemann period matrices of all closings of $R$ in the Siegel upper half space. It is known that every hydrodynamic differential on $R$ yields a closing of $R$ called a hydrodynamic closing. (A hydrodynamic differential is a holomorphic which describes a steady flow on $R$ of an ideal fluid.) We study the period matices induced by hydrodynamic closings of $R$. This is a joint work with Masakazu Shiba.

[ Reference URL ]A closing of an open Riemann srface $R$ of finite genus is a shorter name of a closed Riemann surface of the same genus into which $R$ can be embedded by a homology type preserving conformal mapping. We observe the Riemann period matrices of all closings of $R$ in the Siegel upper half space. It is known that every hydrodynamic differential on $R$ yields a closing of $R$ called a hydrodynamic closing. (A hydrodynamic differential is a holomorphic which describes a steady flow on $R$ of an ideal fluid.) We study the period matices induced by hydrodynamic closings of $R$. This is a joint work with Masakazu Shiba.

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

### 2021/01/14

#### Information Mathematics Seminar

16:50-18:35 Online

Introduction to quantum computation and quantum error-correcting codes (Japanese)

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

**Yasunari Suzuki**(NTT)Introduction to quantum computation and quantum error-correcting codes (Japanese)

[ Abstract ]

Introduction to quantum computation and quantum error-correcting codes

[ Reference URL ]Introduction to quantum computation and quantum error-correcting codes

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

$(-2)$ blow-up formula (Japanese)

[ Reference URL ]

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

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

**Ryo Ohkawa**(Kobe University)$(-2)$ blow-up formula (Japanese)

[ Reference URL ]

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

#### Operator Algebra Seminars

16:45-18:15 Online

The Green-Tao theorem for number fields

[ Reference URL ]

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

**Masato Mimura**(Tohoku Univ.)The Green-Tao theorem for number fields

[ Reference URL ]

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

#### Mathematical Biology Seminar

15:00-16:00 Room # (Graduate School of Math. Sci. Bldg.)

Estimation of the evacuation effect from Wuhan, China, during COVID-19 outbreak

**Yusuke Asai**(National Center for Global Health and Medicine)Estimation of the evacuation effect from Wuhan, China, during COVID-19 outbreak

### 2021/01/13

#### Discrete mathematical modelling seminar

17:00-18:00 Online

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras (in Japanese)

This seminar will be held using Zoom. If you wish to participate, please contact R. Willox by email.

**Akihito Yoneyama**(Institute of Physics, Graduate School of Arts and Sciences, the University of Tokyo)Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras (in Japanese)

[ Abstract ]

We study transition matrices of PBW bases of the nilpotent subalgebra of quantum superalgebras associated with all possible Dynkin diagrams of type A and B in the case of rank 2 and 3, and examine relationships with three-dimensional (3D) integrability. We obtain new solutions to the Zamolodchikov tetrahedron equation via type A and the 3D reflection equation via type B, where the latter equation was proposed by Isaev and Kulish as a 3D analog of the reflection equation of Cherednik. As a by-product of our approach, the Bazhanov-Sergeev solution to the Zamolodchikov tetrahedron equation is characterized as the transition matrix for a particular case of type A, which clarifies an algebraic origin of it. Our work is inspired by the recent developments connecting transition matrices for quantum non-super algebras with intertwiners of irreducible representations of quantum coordinate rings. We also discuss the crystal limit of transition matrices, which gives a super analog of transition maps of Lusztig's parametrizations of the canonical basis.

https://arxiv.org/abs/2012.13385

We study transition matrices of PBW bases of the nilpotent subalgebra of quantum superalgebras associated with all possible Dynkin diagrams of type A and B in the case of rank 2 and 3, and examine relationships with three-dimensional (3D) integrability. We obtain new solutions to the Zamolodchikov tetrahedron equation via type A and the 3D reflection equation via type B, where the latter equation was proposed by Isaev and Kulish as a 3D analog of the reflection equation of Cherednik. As a by-product of our approach, the Bazhanov-Sergeev solution to the Zamolodchikov tetrahedron equation is characterized as the transition matrix for a particular case of type A, which clarifies an algebraic origin of it. Our work is inspired by the recent developments connecting transition matrices for quantum non-super algebras with intertwiners of irreducible representations of quantum coordinate rings. We also discuss the crystal limit of transition matrices, which gives a super analog of transition maps of Lusztig's parametrizations of the canonical basis.

https://arxiv.org/abs/2012.13385

#### Seminar on Probability and Statistics

14:30-15:30 Room #Zoom (Graduate School of Math. Sci. Bldg.)

Depth of Curve Data and Applications (ENGLISH)

https://sites.google.com/view/apsps/previous-speakers

**Pierre Lafaye de Micheaux**(UNSW)Depth of Curve Data and Applications (ENGLISH)

[ Abstract ]

[ Reference URL ]https://sites.google.com/view/apsps/previous-speakers

### 2021/01/12

#### Numerical Analysis Seminar

16:30-18:00 Online

DGNet: Deep Energy-Based Modeling of Discrete-Time Physics and Related Topics (Japanese)

[ Reference URL ]

https://forms.gle/DpuhGupZ7NYbot5d7

**Takaharu Yaguchi**(Kobe University)DGNet: Deep Energy-Based Modeling of Discrete-Time Physics and Related Topics (Japanese)

[ Reference URL ]

https://forms.gle/DpuhGupZ7NYbot5d7

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Mitsuaki Kimura**(The University of Tokyo)Bounded cohomology of volume-preserving diffeomorphism groups (JAPANESE)

[ Abstract ]

Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.

(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.

(2) When the volume of M is infinite.

In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".

[ Reference URL ]Let M be a complete Riemannian manifold of finite volume. Brandenbursky and Marcinkowski proved that the third bounded cohomology of the volume-preserving diffeomorphism group of M is infinite dimensional when the fundamental group of M is "complicated enough". For example, if M is two-dimensional, the above condition is satisfied if the Euler characteristic is negative. Recently, we have extended this result in the following two directions.

(1) When M is two-dimensional and the Euler characteristic is greater than or equal to zero.

(2) When the volume of M is infinite.

In this talk, we will mainly discuss (1). The key idea is to use the fundamental group of the configuration space of M (i.e., the braid group), rather than the fundamental group of M. If time permits, we will also explain (2). For this extension, we introduce the notion of "norm controlled cohomology".

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

### 2021/01/07

#### Operator Algebra Seminars

16:45-18:15 Online

An extremely close look at the arithmetic-geometric inequality (English)

[ Reference URL ]

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

**Colin McSwiggen**(Univ. Tokyo)An extremely close look at the arithmetic-geometric inequality (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

The cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google (Japanese)

[ Abstract ]

Explanation on the cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google

[ Reference URL ]Explanation on the cyber attack to the Ministry of Defense-affiliated company and zero trust of Amazon/Google

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/12/24

#### Information Mathematics Seminar

14:55-16:40 Online

Mathematics and cryptographic applications of isogeny graphs (Japanese)

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

Internet Business Appearance/The basics of GPU/2Iinput Quantum Gates (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Katsuyuki Takashiam**(Mitsubishi Electric Co.) 14:55-16:40Mathematics and cryptographic applications of isogeny graphs (Japanese)

[ Abstract ]

We explain mathematics and cryptographic applications of isogeny graphs.

[ Reference URL ]We explain mathematics and cryptographic applications of isogeny graphs.

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

**Hiroshi Fujiwara**(株式会社ブロードバンドタワー) 16:50-18:35Internet Business Appearance/The basics of GPU/2Iinput Quantum Gates (Japanese)

[ Abstract ]

Explabnation on the internet business appearance, the basics of GPU and 2Iinput Quantum Gates

[ Reference URL ]Explabnation on the internet business appearance, the basics of GPU and 2Iinput Quantum Gates

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/12/21

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

On a mixed Monge-Ampère operator for quasiplurisubharmonic functions

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

**Martin Sera**(KUAS)On a mixed Monge-Ampère operator for quasiplurisubharmonic functions

[ Abstract ]

This reports on a joint work with R. Lärkäng and E. Wulcan. We consider mixed Monge-Ampère products of quasiplurisubharmonic functions with analytic singularities (introduced in a previous work with H. Raufi additionally). These products have the advantage that they preserve mass (a property which is missing for non-pluripolar products).

The main result of the work presented here is that such Monge-Ampère products can be regularized as explicit one parameter limits of mixed Monge-Ampère products of smooth functions, generalizing a result of Andersson-Błocki-Wulcan. We will explain how the theory of residue currents, going back to Coleff-Herrera, Passare and others, plays an important role in the proof.

As a consequence, we get an approximation of Chern and Segre currents of certain singular hermitian metrics on vector bundles by smooth forms in the corresponding Chern and Segre classes.

[ Reference URL ]This reports on a joint work with R. Lärkäng and E. Wulcan. We consider mixed Monge-Ampère products of quasiplurisubharmonic functions with analytic singularities (introduced in a previous work with H. Raufi additionally). These products have the advantage that they preserve mass (a property which is missing for non-pluripolar products).

The main result of the work presented here is that such Monge-Ampère products can be regularized as explicit one parameter limits of mixed Monge-Ampère products of smooth functions, generalizing a result of Andersson-Błocki-Wulcan. We will explain how the theory of residue currents, going back to Coleff-Herrera, Passare and others, plays an important role in the proof.

As a consequence, we get an approximation of Chern and Segre currents of certain singular hermitian metrics on vector bundles by smooth forms in the corresponding Chern and Segre classes.

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

### 2020/12/18

#### Colloquium

15:30-16:30 Online

Please register at the link below to attend this online colloquium

On Hilbert's proof theory (JAPANESE)

[ Reference URL ]

https://forms.gle/Nmi1KieFDjhchdU69

Please register at the link below to attend this online colloquium

**Toshiyasu Arai**(University of Tokyo)On Hilbert's proof theory (JAPANESE)

[ Reference URL ]

https://forms.gle/Nmi1KieFDjhchdU69

### 2020/12/17

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

The finite EI categories of Cartan type (English)

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

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

**Xiao-Wu Chen**(University of Science and Technology of China)The finite EI categories of Cartan type (English)

[ Abstract ]

We will recall the notion of a finite free EI category introduced by Li. To each Cartan triple, we associate a finite free EI category, called the finite EI category of Cartan type. The corresponding category algebra is isomorphic to the 1-Gorenstein algebra, introduced by Geiss-Leclerc-Schroer, that is associated to possibly another Cartan triple. The construction of the second Cartan triple is related to the well-known unfolding of valued graphs. We will apply the obtained algebra isomorphism to re-interpret some tau-locally free modules as induced modules over a certain skew group algebra. This project is joint with Ren Wang.

[ Reference URL ]We will recall the notion of a finite free EI category introduced by Li. To each Cartan triple, we associate a finite free EI category, called the finite EI category of Cartan type. The corresponding category algebra is isomorphic to the 1-Gorenstein algebra, introduced by Geiss-Leclerc-Schroer, that is associated to possibly another Cartan triple. The construction of the second Cartan triple is related to the well-known unfolding of valued graphs. We will apply the obtained algebra isomorphism to re-interpret some tau-locally free modules as induced modules over a certain skew group algebra. This project is joint with Ren Wang.

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

#### Information Mathematics Seminar

14:55-18:35 Online

Computationally hard problems for quantum computers and their cryptographic applications (Japanese)

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

Classification and Clustering in the Machine Learning (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Katsuyuki Takashima**(Mitsubishi Electric Co.) 14:55-16:40Computationally hard problems for quantum computers and their cryptographic applications (Japanese)

[ Abstract ]

We explain computationally hard problems for quantum computers and their cryptographic applications.

[ Reference URL ]We explain computationally hard problems for quantum computers and their cryptographic applications.

https://docs.google.com/forms/d/1yIKNrwSLsdYt_rivZI8JxhIu3kWtJua5hG8nV5FYbCk/

**Hiroshi Fujiwara**(BroadBand Tower, Inc.) 16:50-18:35Classification and Clustering in the Machine Learning (Japanese)

[ Abstract ]

Explanation on the classification and clustering in the machine learning

[ Reference URL ]Explanation on the classification and clustering in the machine learning

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/12/16

#### Number Theory Seminar

17:00-18:00 Online

Rigid analytic Hyodo--Kato theory with syntomic coefficients (Japanese)

**Kazuki Yamada**(Keio University)Rigid analytic Hyodo--Kato theory with syntomic coefficients (Japanese)

[ Abstract ]

The Hyodo—Kato theory is the study of comparison between Hyodo—Kato cohomology and de Rham cohomology associated to semistable schemes over complete discrete valuation rings of mixed characteristic $(0,p)$.

In this talk, we will give a rigid analytic reconstruction of Hyodo—Kato theory and study coefficients of cohomology.

Our construction is useful for explicit computation and treatment of base extension, because it gives us a natural interpretation of the dependence of Hyodo—Kato theory on the choice of a branch of the $p$-adic logarithm.

The results of this talk are based on a joint work with Veronika Ertl, which deals with the case of trivial coefficient.

The Hyodo—Kato theory is the study of comparison between Hyodo—Kato cohomology and de Rham cohomology associated to semistable schemes over complete discrete valuation rings of mixed characteristic $(0,p)$.

In this talk, we will give a rigid analytic reconstruction of Hyodo—Kato theory and study coefficients of cohomology.

Our construction is useful for explicit computation and treatment of base extension, because it gives us a natural interpretation of the dependence of Hyodo—Kato theory on the choice of a branch of the $p$-adic logarithm.

The results of this talk are based on a joint work with Veronika Ertl, which deals with the case of trivial coefficient.

#### Seminar on Probability and Statistics

14:30-16:00 Room #Zoom (Graduate School of Math. Sci. Bldg.)

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

How to tell a tale of two tails? (ENGLISH)

https://docs.google.com/forms/d/e/1FAIpQLSf6XCBIUMnI9OJjNi6KP7QEixLnZVMsw8BVeNqiPFxlUC8rQQ/viewform

Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.

**Parthanil Roy**(Indian Statistical Institute, Bangalore)How to tell a tale of two tails? (ENGLISH)

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home

Branching random walk is a system of growing particles that starts with one particle. This particle branches into a random number of particles, and each new particle makes a random displacement independently of each other and of the branching mechanism. The same dynamics goes on and gives rise to a branching random walk. This model arises in statistical physics, and has connections to various probabilistic objects, mathematical biology, ecology, etc. In this overview talk, we shall discuss branching random walks and their long run behaviour. More precisely, we shall try to answer the following question: if we run a branching random walk for a very long time and take a snapshot of the particles, how would the system look like? We shall investigate how the tails of the progeny and displacement distributions change the answer to this question.

This talk is based on a series of joint papers with Ayan Bhattacharya, Rajat Subhra Hazra, Krishanu Maulik, Zbigniew Palmowski, Souvik Ray and Philippe Soulier.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics https://sites.google.com/view/apsps/home

Branching random walk is a system of growing particles that starts with one particle. This particle branches into a random number of particles, and each new particle makes a random displacement independently of each other and of the branching mechanism. The same dynamics goes on and gives rise to a branching random walk. This model arises in statistical physics, and has connections to various probabilistic objects, mathematical biology, ecology, etc. In this overview talk, we shall discuss branching random walks and their long run behaviour. More precisely, we shall try to answer the following question: if we run a branching random walk for a very long time and take a snapshot of the particles, how would the system look like? We shall investigate how the tails of the progeny and displacement distributions change the answer to this question.

This talk is based on a series of joint papers with Ayan Bhattacharya, Rajat Subhra Hazra, Krishanu Maulik, Zbigniew Palmowski, Souvik Ray and Philippe Soulier.

https://docs.google.com/forms/d/e/1FAIpQLSf6XCBIUMnI9OJjNi6KP7QEixLnZVMsw8BVeNqiPFxlUC8rQQ/viewform

### 2020/12/15

#### Numerical Analysis Seminar

16:30-18:00 Online

Iterated pressure-correction projection methods for the 2d Navier-Stokes equations based on the scalar auxiliary variable approach (English)

https://forms.gle/y7w2nmaYtHNeoDSn8

**Ming-Cheng Shiue**(National Chiao Tung University)Iterated pressure-correction projection methods for the 2d Navier-Stokes equations based on the scalar auxiliary variable approach (English)

[ Abstract ]

In this talk, the first-order iterated pressure-correction projection methods based on the scalar auxiliary variable approach is proposed and studied for the 2d Navier-Stokes equations and Boussinesq equations.

In the literature, enormous amounts of work have contributed to the study of numerical schemes for computing the Navier-Stokes equations. In general, two of the main numerical difficulties for solving Navier-Stokes equations are the incompressible condition and the nonlinear term. One of the approaches to deal with the incompressible condition is the so-called projection. The typical projection method only needs to solve the Poisson type of equations depending on the nonlinear term's treatment, which is efficient. However, the pressure-correction projection methods suffer from the splitting error, leading to spurious numerical boundary layers and the limitation of accuracy in time. In the literature, an iterated pressure-correction projection method has been proposed to overcome the difficulty.

As for the nonlinear term treatment, it is better to treat the nonlinear term explicitly so that one only requires to solve the corresponding linear system with constant coefficients at each time step. However, such treatment often results in a restricted time step due to the stable issue. Recently, the scalar auxiliary variable approach has been constructed to have an unconditional energy stable numerical scheme.

In this work, a new iterated pressure-correction projection method based on the scalar auxiliary variable's simple choice is proposed. We find that this new scheme can enjoy two properties, including reducing the splitting errors and having unconditional energy stability. The proofs of the energy stability and error convergence are provided and analyzed. Finally, numerical examples are provided to illustrate the theoretical work. This is joint work with Tony Chang.

[ Reference URL ]In this talk, the first-order iterated pressure-correction projection methods based on the scalar auxiliary variable approach is proposed and studied for the 2d Navier-Stokes equations and Boussinesq equations.

In the literature, enormous amounts of work have contributed to the study of numerical schemes for computing the Navier-Stokes equations. In general, two of the main numerical difficulties for solving Navier-Stokes equations are the incompressible condition and the nonlinear term. One of the approaches to deal with the incompressible condition is the so-called projection. The typical projection method only needs to solve the Poisson type of equations depending on the nonlinear term's treatment, which is efficient. However, the pressure-correction projection methods suffer from the splitting error, leading to spurious numerical boundary layers and the limitation of accuracy in time. In the literature, an iterated pressure-correction projection method has been proposed to overcome the difficulty.

As for the nonlinear term treatment, it is better to treat the nonlinear term explicitly so that one only requires to solve the corresponding linear system with constant coefficients at each time step. However, such treatment often results in a restricted time step due to the stable issue. Recently, the scalar auxiliary variable approach has been constructed to have an unconditional energy stable numerical scheme.

In this work, a new iterated pressure-correction projection method based on the scalar auxiliary variable's simple choice is proposed. We find that this new scheme can enjoy two properties, including reducing the splitting errors and having unconditional energy stability. The proofs of the energy stability and error convergence are provided and analyzed. Finally, numerical examples are provided to illustrate the theoretical work. This is joint work with Tony Chang.

https://forms.gle/y7w2nmaYtHNeoDSn8

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Braids, triangles and Lissajous curve (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Eiko Kin**(Osaka University)Braids, triangles and Lissajous curve (JAPANESE)

[ Abstract ]

The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.

[ Reference URL ]The purpose of this talk is to introduce Lissajous 3-braids. Suppose we have a closed curve on the plane, and we consider the periodic motion of n points along the closed curve. If the motion is collision-free, then we get a braid obtained from the trajectory of the set of n points in question. In this talk, we consider 3-braids coming from the periodic motion of 3 points on Lissajous curves. We classify Lissajous 3-braids and present a parametrization in terms of natural numbers together with slopes. We also discuss some properties of pseudo-Anosov stretch factors for Lissajous 3-braids. The main tool is the shape sphere --- the configuration space of the oriented similarity classes of triangles. This is a joint work with Hiroaki Nakamura and Hiroyuki Ogawa.

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

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