## Seminar information archive

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

#### 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

### 2020/12/14

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

On Levi flat hypersurfaces with transversely affine foliation

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

**ADACHI Masanori**(Shizuoka University)On Levi flat hypersurfaces with transversely affine foliation

[ Abstract ]

In this talk, we discuss the classification problem of Levi flat hypersurfaces in complex surfaces by restricting ourselves to the case that the Levi foliation is transversely affine. After presenting known examples, we give a proof for the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and Levi foliation is transversely affine in a compact Kähler surface. This is a joint work with Severine Biard (arXiv:2011.06379).

[ Reference URL ]In this talk, we discuss the classification problem of Levi flat hypersurfaces in complex surfaces by restricting ourselves to the case that the Levi foliation is transversely affine. After presenting known examples, we give a proof for the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and Levi foliation is transversely affine in a compact Kähler surface. This is a joint work with Severine Biard (arXiv:2011.06379).

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

### 2020/12/10

#### Operator Algebra Seminars

16:45-18:15 Online

Towards an equivariant Kirchberg-Phillips theorem (English)

[ Reference URL ]

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

**Gabor Szabo**(KU Leuven)Towards an equivariant Kirchberg-Phillips theorem (English)

[ Reference URL ]

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

#### Tokyo-Nagoya Algebra Seminar

16:30-18:00 Online

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

Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)

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

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

**Hiroki Matsui**(University of Tokyo)Subcategories of module/derived categories and subsets of Zariski spectra (Japanese)

[ Abstract ]

The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.

[ Reference URL ]The classification problem of subcategories has been well considered in many areas. This problem is initiated by Gabriel in 1962 by giving a classification of localizing subcategories of the module category Mod R via specialization-closed subsets of the Zariski spectrum Spec R for a commutative noetherian ring. After that several authors tried to generalize this result in many ways. For example, four decades later, Krause introduced the notion of coherent subsets of Spec R and used it to classify wide subcategories of Mod R. In this talk, I will introduce the notions of n-wide subcategories of Mod R and n-coherent subsets of Spec R for a (possibly infinite) non-negative integer n. I will also introduce the notion of n-uniform subcategories of the derived category D(Mod R) and prove the correspondences among these classes. This result unifies/generalizes many known results such as the classification given by Gabriel, Krause, Neeman, Takahashi, Angeleri Hugel-Marks-Stovicek-Takahashi-Vitoria. This talk is based on joint work with Ryo Takahashi.

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

#### Information Mathematics Seminar

16:50-18:35 Online

The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The cyber attack to a car company supply chain network and Zero trust by the Cisco Systems (Japanese)

[ Abstract ]

Explanation on the cyber attack to a car company supply chain network and zero trust by the Cisco Systems

[ Reference URL ]Explanation on the cyber attack to a car company supply chain network and zero trust by the Cisco Systems

https://forms.gle/Uhy8uBujZatjNMsGA

### 2020/12/09

#### Discrete mathematical modelling seminar

17:00-18:30 Online

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

Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations (English)

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

**Anton DZHAMAY**(University of Northern Colorado)Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations (English)

[ Abstract ]

We use Sakai’s geometric theory of discrete Painlevé equations to study a recurrence relation that can be used to generate ladder operators for the Laguerre unitary ensemble. Using a recently proposed identification procedure for discrete Painlevé equations we show how this recurrence can be transformed into one of the standard equations on the affine D5-algebraic surface. This is a joint work with Yang Chen and Jie Hu.

We use Sakai’s geometric theory of discrete Painlevé equations to study a recurrence relation that can be used to generate ladder operators for the Laguerre unitary ensemble. Using a recently proposed identification procedure for discrete Painlevé equations we show how this recurrence can be transformed into one of the standard equations on the affine D5-algebraic surface. This is a joint work with Yang Chen and Jie Hu.

### 2020/12/08

#### Tuesday Seminar on Topology

17:30-18:30 Online

Pre-registration required. See our seminar webpage.

The intersection polynomials of a virtual knot (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shin Satoh**(Kobe University)The intersection polynomials of a virtual knot (JAPANESE)

[ Abstract ]

We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.

[ Reference URL ]We define two kinds of invariants of a virtual knot called the first and second intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. We study several properties of the polynomials. By introducing invariants of long virtual knots, we give connected sum formulae of the intersection polynomials, and prove that there are infinitely many connected sums of any two virtual knots as an application. Furthermore, by studying the behavior under a crossing change, we show that the intersection polynomials are finite type invariants of order two, and find an invariant of a flat virtual knot derived from the the intersection polynomials. This is a joint work with R. Higa, T. Nakamura, and Y. Nakanishi.

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

### 2020/12/03

#### Tokyo-Nagoya Algebra Seminar

16:00-17:30 Online

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

Full strong exceptional collections for invertible polynomials of chain type

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

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

**Yuki Hirano**(Kyoto University)Full strong exceptional collections for invertible polynomials of chain type

[ Abstract ]

Constructing a tilting object in the stable category of graded maximal Cohen-Macaulay modules over a given graded Gorenstein ring is an important problem in the representation theory of graded Gorenstein rings. For a hypersurface S/f in a graded regular ring S, this problem is equivalent to constructing a tilting object in the homotopy category of graded matrix factorizations of f. In this talk, we discuss this problem in the case when S is a polynomial ring, f is an invertible polynomial of chain type and S has a rank one abelian group grading (called the maximal grading of f), and in this case we show the existence of a tilting object arising from a full strong exceptional collection. This is a joint work with Genki Ouchi.

[ Reference URL ]Constructing a tilting object in the stable category of graded maximal Cohen-Macaulay modules over a given graded Gorenstein ring is an important problem in the representation theory of graded Gorenstein rings. For a hypersurface S/f in a graded regular ring S, this problem is equivalent to constructing a tilting object in the homotopy category of graded matrix factorizations of f. In this talk, we discuss this problem in the case when S is a polynomial ring, f is an invertible polynomial of chain type and S has a rank one abelian group grading (called the maximal grading of f), and in this case we show the existence of a tilting object arising from a full strong exceptional collection. This is a joint work with Genki Ouchi.

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

#### Information Mathematics Seminar

16:50-18:35 Online

History of PC-LAN offense and defense/Classification of Flynn/Quantum gate, Actual Quantum Gate (Japanese)

https://forms.gle/Uhy8uBujZatjNMsGA

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)History of PC-LAN offense and defense/Classification of Flynn/Quantum gate, Actual Quantum Gate (Japanese)

[ Abstract ]

Explanation on the history of PC-LAN offense and defense/Classification of Flynn/Quantum Gate, Actual Quantum Gate

[ Reference URL ]Explanation on the history of PC-LAN offense and defense/Classification of Flynn/Quantum Gate, Actual Quantum Gate

https://forms.gle/Uhy8uBujZatjNMsGA

#### Operator Algebra Seminars

16:45-18:15 Online

Generalized strong asymptotic freeness (English)

[ Reference URL ]

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

**Benoit Collins**(Kyoto Univ.)Generalized strong asymptotic freeness (English)

[ Reference URL ]

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

### 2020/12/01

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Goeritz groups of bridge decompositions (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yuya Koda**(Hiroshima University)Goeritz groups of bridge decompositions (JAPANESE)

[ Abstract ]

For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.

[ Reference URL ]For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. The Birman-Hilden theory tells us that this is a $\mathbb{Z} / 2 \mathbb{Z}$-quotient of a "hyperelliptic Goeritz group". In this talk, we discuss properties, mainly of dynamical nature, of this group using a measure of complexity called the distance of the decomposition. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings. This talk is based on a joint work with Susumu Hirose, Daiki Iguchi and Eiko Kin.

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

#### Numerical Analysis Seminar

16:30-18:00 Online

Conjugate gradient methods for optimization problems on manifolds (Japanese)

[ Reference URL ]

https://forms.gle/Ubeccm8neLkacjbk8

**Hiroyuki Sato**(Kyoto University)Conjugate gradient methods for optimization problems on manifolds (Japanese)

[ Reference URL ]

https://forms.gle/Ubeccm8neLkacjbk8

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