## Seminar information archive

Seminar information archive ～05/25｜Today's seminar 05/26 | Future seminars 05/27～

#### Discrete mathematical modelling seminar

19:00-20:00 Online

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

Deformations of cluster mutations and invariant presymplectic forms

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

**Andrew Hone**(University of Kent)Deformations of cluster mutations and invariant presymplectic forms

[ Abstract ]

We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5-cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4 we find suitable conditions such that the deformation produces a two-parameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higher-dimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to four-dimensional symplectic maps arising as reductions of the discrete sine-Gordon equation.

We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by the exchange matrix. The simplest example is the Lyness 5-cycle, arising from the cluster algebra of type A_2: this deforms to the Lyness family of integrable symplectic maps in the plane. For types A_3 and A_4 we find suitable conditions such that the deformation produces a two-parameter family of Liouville integrable maps (in dimensions two and four, respectively). We also perform Laurentification for these maps, by lifting them to a higher-dimensional space of tau functions with a cluster algebra structure, where the Laurent property is restored. More general types of deformed mutations associated with affine Dynkin quivers are shown to correspond to four-dimensional symplectic maps arising as reductions of the discrete sine-Gordon equation.

#### Information Mathematics Seminar

16:50-18:35 Online

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

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Internet Business Appearance/The basics of GPU/2Iinput Quantum Gates (Japanese)

[ Abstract ]

Explanation on internet business appearance, the basics of GPU and 2Iinput quantum gates.

[ Reference URL ]Explanation on internet business appearance, the basics of GPU and 2Iinput quantum gates.

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/10/26

#### Operator Algebra Seminars

16:45-18:15 Online

A modern point of view on Antony Wassermann's paper "Operator Algebras and Conformal Field Theory III" (English)

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

**Bin Gui**(Tsinghua University)A modern point of view on Antony Wassermann's paper "Operator Algebras and Conformal Field Theory III" (English)

[ Abstract ]

In 1998, Antony Wassermann's groundbreaking paper "Operator Algebras and Conformal Field Theory III" was published. This paper calculated Connes fusion rules for the representations of type A WZW conformal nets and was essential to many subsequent works on conformal nets. In this talk, I will try to convince the audience that many of Wassermann's ideas are powerful for understanding VOA/Conformal net correspondence in the framework of Carpi-Kawahigashi-Longo-Weiner and Tener.

[ Reference URL ]In 1998, Antony Wassermann's groundbreaking paper "Operator Algebras and Conformal Field Theory III" was published. This paper calculated Connes fusion rules for the representations of type A WZW conformal nets and was essential to many subsequent works on conformal nets. In this talk, I will try to convince the audience that many of Wassermann's ideas are powerful for understanding VOA/Conformal net correspondence in the framework of Carpi-Kawahigashi-Longo-Weiner and Tener.

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

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

On the strongly pseudoconcave boundary of a compact complex surface (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Naohiko Kasuya**(Hokkaido University)On the strongly pseudoconcave boundary of a compact complex surface (JAPANESE)

[ Abstract ]

On the strongly pseudoconvex (resp. pseudoconcave) boundary of a complex surface, the complex

tangency defines a positive (resp. negative) contact structure. Bogomolov and De Oliveira proved

that the boundary contact structure of a strongly pseudoconvex surface is Stein fillable.

Therefore, for a closed contact 3-manifold, Stein fillability and holomorphic fillability are

equivalent. Then what about the boundary of a strongly pseudoconcave surface? We prove that any

closed negative contact 3-manifold can be realized as the boundary of a strongly pseudoconcave

surface. The proof is done by establishing holomorphic handle attaching method to the strongly

pseudoconcave boundary of a complex surface, based on Eliashberg's handlebody construction of Stein

manifolds. This is a joint work with Daniele Zuddas (University of Trieste).

[ Reference URL ]On the strongly pseudoconvex (resp. pseudoconcave) boundary of a complex surface, the complex

tangency defines a positive (resp. negative) contact structure. Bogomolov and De Oliveira proved

that the boundary contact structure of a strongly pseudoconvex surface is Stein fillable.

Therefore, for a closed contact 3-manifold, Stein fillability and holomorphic fillability are

equivalent. Then what about the boundary of a strongly pseudoconcave surface? We prove that any

closed negative contact 3-manifold can be realized as the boundary of a strongly pseudoconcave

surface. The proof is done by establishing holomorphic handle attaching method to the strongly

pseudoconcave boundary of a complex surface, based on Eliashberg's handlebody construction of Stein

manifolds. This is a joint work with Daniele Zuddas (University of Trieste).

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

#### Lie Groups and Representation Theory

17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)

Applications of uniform bounded families of g-modules to branching problems (Japanese)

**Masatoshi KITAGAWA**(Waseda University)Applications of uniform bounded families of g-modules to branching problems (Japanese)

[ Abstract ]

Using the notion of uniformly bounded families of g-modules introduced in arXiv:2109.05556, we can prove several finiteness and uniform boundedness results of multiplicities in branching laws and induced representations.

After the introduction of such results, I will explain how to obtain the necessary and sufficient condition for the uniform boundedness of multiplicities in branching laws given in arXiv:2109.05555.

Using the notion of uniformly bounded families of g-modules introduced in arXiv:2109.05556, we can prove several finiteness and uniform boundedness results of multiplicities in branching laws and induced representations.

After the introduction of such results, I will explain how to obtain the necessary and sufficient condition for the uniform boundedness of multiplicities in branching laws given in arXiv:2109.05555.

### 2021/10/21

#### 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://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

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

(Japanese)

[ Abstract ]

Explanation on history of PC-LAN offense and defense, classification of Flynn, quantum gate and actual quantum gate

[ Reference URL ]Explanation on history of PC-LAN offense and defense, classification of Flynn, quantum gate and actual quantum gate

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/10/20

#### Number Theory Seminar

17:00-18:00 Online

Geometric arc fundamental group (English)

**Alex Youcis**(University of Tokyo)Geometric arc fundamental group (English)

[ Abstract ]

Unlike algebraic geometry, the correct notion for a ‘covering space’ of a rigid analytic variety is non-obvious to define. In particular, the class of finite etale covering spaces doesn’t encompass many real world examples of ‘covering space’-like maps (e.g. Tate’s uniformization of elliptic curves, or period mappings of Rapoport—Zink spaces). In de Jong’s seminal work on the topic he made great strides forward by studying a notion of covering space, suggested by work of Berkovich, which includes many previous ‘covering spaces’ which are not finite etale and is rich enough to support a theory of a fundamental group.

Unfortunately, de Jong’s notion of covering space lacks many of the natural properties one would expect from the notion of a ‘covering space’. In this talk we discuss recent work of Achinger, Lara, and myself which proposes a larger class of ‘covering spaces’ than those considered by de Jong which enjoys the geometric properties missing from de Jong’s picture. In addition, we mention how this larger category is related to work of Scholze on pro-etale local systems as well as work of Bhatt and Scholze on the pro-etale fundamental group of a scheme.

Unlike algebraic geometry, the correct notion for a ‘covering space’ of a rigid analytic variety is non-obvious to define. In particular, the class of finite etale covering spaces doesn’t encompass many real world examples of ‘covering space’-like maps (e.g. Tate’s uniformization of elliptic curves, or period mappings of Rapoport—Zink spaces). In de Jong’s seminal work on the topic he made great strides forward by studying a notion of covering space, suggested by work of Berkovich, which includes many previous ‘covering spaces’ which are not finite etale and is rich enough to support a theory of a fundamental group.

Unfortunately, de Jong’s notion of covering space lacks many of the natural properties one would expect from the notion of a ‘covering space’. In this talk we discuss recent work of Achinger, Lara, and myself which proposes a larger class of ‘covering spaces’ than those considered by de Jong which enjoys the geometric properties missing from de Jong’s picture. In addition, we mention how this larger category is related to work of Scholze on pro-etale local systems as well as work of Bhatt and Scholze on the pro-etale fundamental group of a scheme.

### 2021/10/19

#### Tuesday Seminar of Analysis

16:00-17:30 Online

Global structure of steady-states for a cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model (Japanese)

https://forms.gle/hkfCd3fSW5A77mwv5

**KUTO Kousuke**(Waseda University)Global structure of steady-states for a cross-diffusion limit in the Shigesada-Kawasaki-Teramoto model (Japanese)

[ Abstract ]

In 1979, Shigesada, Kawasaki and Teramoto proposed a Lotka-Volterra competition model with cross-diffusion terms in order to realize the segregation phenomena of two competing species. This talk concerns the asymptotic behavior of steady-states to the Shigesada-Kawasaki-Teramoto model in the full cross-diffusion limit where both coefficients of cross-diffusion terms tend to infinity at the same rate. In the former half of this talk, we derive a uniform estimate of all steady-states independent of the cross-diffusion terms. In the latter half, we show the global structure of steady-states of a shadow system in the full cross-diffusion limit.

[ Reference URL ]In 1979, Shigesada, Kawasaki and Teramoto proposed a Lotka-Volterra competition model with cross-diffusion terms in order to realize the segregation phenomena of two competing species. This talk concerns the asymptotic behavior of steady-states to the Shigesada-Kawasaki-Teramoto model in the full cross-diffusion limit where both coefficients of cross-diffusion terms tend to infinity at the same rate. In the former half of this talk, we derive a uniform estimate of all steady-states independent of the cross-diffusion terms. In the latter half, we show the global structure of steady-states of a shadow system in the full cross-diffusion limit.

https://forms.gle/hkfCd3fSW5A77mwv5

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Period matrices of some hyperelliptic Riemann surfaces (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Yoshihiko Shinomiya**(Shizuoka University)Period matrices of some hyperelliptic Riemann surfaces (JAPANESE)

[ Abstract ]

In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form $w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2) \cdots (z^2-a_{g-1}^2)$ ($1 < a_1< a_2< \cdots < a_{g-1}$). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.

[ Reference URL ]In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form $w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2) \cdots (z^2-a_{g-1}^2)$ ($1 < a_1< a_2< \cdots < a_{g-1}$). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.

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

#### Lie Groups and Representation Theory

17:00-18:00 Room #online (Graduate School of Math. Sci. Bldg.)

Classification of type A analogues of minimal representations

(Japanese)

**Hiroyoshi Tamori**(Hokkaido University)Classification of type A analogues of minimal representations

(Japanese)

[ Abstract ]

If $\mathfrak{g}$ is a simple Lie algebra not of type A, the enveloping algebra $U(\mathfrak{g})$ has a unique completely prime primitive ideal whose associated variety equals the closure of the minimal nilpotent orbit. The ideal is called the Joseph Ideal. An irreducible admissible representation of a simple Lie group is called minimal if the annihilator of the underlying $(\mathfrak{g},\mathfrak{k})$-modules is given by the Joseph ideal. Minimal representations are known to have simple $\mathfrak{k}$-type decompositions (called pencil), and a simple Lie group has at most two minimal representations up to complex conjugate. In this talk, we consider the type A analogues for the above statements.

If $\mathfrak{g}$ is a simple Lie algebra not of type A, the enveloping algebra $U(\mathfrak{g})$ has a unique completely prime primitive ideal whose associated variety equals the closure of the minimal nilpotent orbit. The ideal is called the Joseph Ideal. An irreducible admissible representation of a simple Lie group is called minimal if the annihilator of the underlying $(\mathfrak{g},\mathfrak{k})$-modules is given by the Joseph ideal. Minimal representations are known to have simple $\mathfrak{k}$-type decompositions (called pencil), and a simple Lie group has at most two minimal representations up to complex conjugate. In this talk, we consider the type A analogues for the above statements.

### 2021/10/14

#### Applied Analysis

#### Information Mathematics Seminar

16:50-18:35 Online

History of PC rise and fall history/What is a parallel processing? What is a quantum gate? (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)History of PC rise and fall history/What is a parallel processing? What is a quantum gate? (Japanese)

[ Abstract ]

Introduction to the history of PC, and the explanation on a parallel processing and a quantum gate.

[ Reference URL ]Introduction to the history of PC, and the explanation on a parallel processing and a quantum gate.

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

### 2021/10/13

#### Seminar on Probability and Statistics

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

Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models

https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform

**Li Cheng**(National University of Singapore (NUS))Bayesian Fixed-domain Asymptotics for Covariance Parameters in Gaussian Random Field Models

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Gaussian random field models are commonly used for modeling spatial processes. In this work we focus on the Gaussian process with isotropic Matern covariance functions. Under fixed-domain asymptotics,it is well known that when the dimension of data is less than or equal to three, the microergodic parameter can be consistently estimated with asymptotic normality while the range (or length-scale) parameter cannot. Motivated by this frequentist result, we prove that under a Bayesian fixed-domain framework, the posterior distribution of the microergodic parameter converges in total variation norm to a normal distribution with shrinking variance, while the posterior of the range parameter does not necessarily converge. Built on this new theory, we further show that the Bayesian kriging predictor satisfies the posterior asymptotic efficiency in linear prediction. We illustrate these asymptotic results in numerical examples.

https://docs.google.com/forms/d/e/1FAIpQLSfEWrpkVavWEELx93dPxd0g2thhkC8NtA_8We4cDeiCKI6mZg/viewform

### 2021/10/12

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Seiberg-Witten Floer homotopy and contact structures (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Nobuo Iida**(The Univesity of Tokyo)Seiberg-Witten Floer homotopy and contact structures (JAPANESE)

[ Abstract ]

Seiberg-Witten theory has been an efficient tool to study 4-dimensional symplectic and 3-dimensional contact geometry. In this talk, we introduce new homotopical invariants related to these structures using Seiberg-Witten theory and explain their properties and applications. These invariants have two main origins:

1. Kronheimer-Mrowka's invariant for 4-manifold with contact boundary, whose construction is based on Seiberg-Witten equation on 4-manifolds with conical end.

2. Bauer-Furuta and Manolescu's homotopical method called finite dimensional approximation in Seiberg-Witten theory.

This talk includes joint works with Masaki Taniguchi(RIKEN) and Anubhav Mukherjee(Georgia tech).

[ Reference URL ]Seiberg-Witten theory has been an efficient tool to study 4-dimensional symplectic and 3-dimensional contact geometry. In this talk, we introduce new homotopical invariants related to these structures using Seiberg-Witten theory and explain their properties and applications. These invariants have two main origins:

1. Kronheimer-Mrowka's invariant for 4-manifold with contact boundary, whose construction is based on Seiberg-Witten equation on 4-manifolds with conical end.

2. Bauer-Furuta and Manolescu's homotopical method called finite dimensional approximation in Seiberg-Witten theory.

This talk includes joint works with Masaki Taniguchi(RIKEN) and Anubhav Mukherjee(Georgia tech).

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

#### Operator Algebra Seminars

16:45-18:15 Online

Lifts of completely positive (equivariant) maps

(English)

[ Reference URL ]

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

**Eusebio Gardella**(G\"oteborgs Universitet)Lifts of completely positive (equivariant) maps

(English)

[ Reference URL ]

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

### 2021/10/11

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

cscK計量に付随する完備スカラー平坦Kähler計量について (Japanese)

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

**Takahiro Aoi**(Abuno High School)cscK計量に付随する完備スカラー平坦Kähler計量について (Japanese)

[ Abstract ]

複素多様体上のKähler計量であって, そのスカラー曲率が定数となるもの(cscK計量)が存在するか, という問題は非自明であり，極めて重要である．ここでは正則ベクトル場などに対して適当な条件を満たす偏極多様体と, 滑らかな超曲面を考える. 本講演では,この超曲面を無限遠と見做し, それが適当な偏極類にcscK計量を持つ, という境界条件を満たせば,その補集合は漸近錐的完備なスカラー平坦Kähler計量を許容する, という結果について紹介を行い,時間が許す限り関連する問題についても紹介する.

[ Reference URL ]複素多様体上のKähler計量であって, そのスカラー曲率が定数となるもの(cscK計量)が存在するか, という問題は非自明であり，極めて重要である．ここでは正則ベクトル場などに対して適当な条件を満たす偏極多様体と, 滑らかな超曲面を考える. 本講演では,この超曲面を無限遠と見做し, それが適当な偏極類にcscK計量を持つ, という境界条件を満たせば,その補集合は漸近錐的完備なスカラー平坦Kähler計量を許容する, という結果について紹介を行い,時間が許す限り関連する問題についても紹介する.

https://u-tokyo-ac-jp.zoom.us/meeting/register/tJ0vcu2rrDIqG9Rv5AT0Mpi37urIkJ1IRldB

### 2021/10/07

#### Information Mathematics Seminar

16:50-18:35 Online

Essence of DX

- History of Industrial Revolution and role of the mathematics - (Japanese)

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Essence of DX

- History of Industrial Revolution and role of the mathematics - (Japanese)

[ Abstract ]

Explanation on the essence of DX.

[ Reference URL ]Explanation on the essence of DX.

https://docs.google.com/forms/d/1I3XD63V937BT_IoqRWBVN67goQAtbkSoIKs-6hfLUAM

#### Mathematical Biology Seminar

15:00-16:30 Online

The role of mathematical model in the practice of infectious disease control (Japanese)

**Ryosuke Omori**(International Institute for Zoonosis Control, Hokkaido University)The role of mathematical model in the practice of infectious disease control (Japanese)

### 2021/10/05

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Hiroshi Goda**(Tokyo University of Agriculture and Technology)Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds (JAPANESE)

[ Abstract ]

We discuss a relationship between the chirality of knots and higher dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic $3$-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic $3$-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations. (This is a joint work with Takayuki Morifuji.)

[ Reference URL ]We discuss a relationship between the chirality of knots and higher dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic $3$-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic $3$-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations. (This is a joint work with Takayuki Morifuji.)

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

#### Lie Groups and Representation Theory

17:00-18:00 Room #Online (Graduate School of Math. Sci. Bldg.)

Bounded multiplicity in the branching problems of "small" infinite-dimensional representations (Japanese)

**Toshiyuki KOBAYASHI**(The University of Tokyo)Bounded multiplicity in the branching problems of "small" infinite-dimensional representations (Japanese)

[ Abstract ]

I plan to explain a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional

representations of real reductive Lie groups in branching problems.

Applying the criterion to symmetric pairs, we give a full description of the triples H ⊂ G ⊃ G' such that any irreducible admissible representations of G with H-distinguished vectors have the bounded multiplicity property when restricted to the subgroup G'.

The precise results are available in [Adv. Math. 2021, Section 7] and arXiv:2109.14424, and I plan to give some flavor.

I plan to explain a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional

representations of real reductive Lie groups in branching problems.

Applying the criterion to symmetric pairs, we give a full description of the triples H ⊂ G ⊃ G' such that any irreducible admissible representations of G with H-distinguished vectors have the bounded multiplicity property when restricted to the subgroup G'.

The precise results are available in [Adv. Math. 2021, Section 7] and arXiv:2109.14424, and I plan to give some flavor.

### 2021/10/01

#### Colloquium

14:30-17:00 Online

Registration is closed (12:00, October 1).

Research Ethics in Computer Aided Mathematics (JAPANESE)

What's keeping back female mathematicians & physicists? (JAPANESE)

Registration is closed (12:00, October 1).

**Sadayoshi Kojima**(Waseda University) 14:30-15:30Research Ethics in Computer Aided Mathematics (JAPANESE)

[ Abstract ]

Since the solution of the four colored problem, a computer aided method has been expanding its base in mathematical research based on quite rapid development of Information Technology. Since then, it has been asked what the proof is, which is fundamental in mathematical research ethics. In this talk, I would like to present a history of discussions on this matter until now and to discuss some future aspect.

Since the solution of the four colored problem, a computer aided method has been expanding its base in mathematical research based on quite rapid development of Information Technology. Since then, it has been asked what the proof is, which is fundamental in mathematical research ethics. In this talk, I would like to present a history of discussions on this matter until now and to discuss some future aspect.

**Hiromi Yokoyama**(Kavli IPMU) 16:00-17:00What's keeping back female mathematicians & physicists? (JAPANESE)

[ Abstract ]

In Japan, female students' rate is low in mathematics and physics. The American Educational Psychology group pointed out there are three factors. We extended the model and added gender inequality social climate factors. We confirmed that the new factors influenced the male image of mathematics and physics in Japan and England. I would like to Introduce interdisciplinary research on science and technology society.

In Japan, female students' rate is low in mathematics and physics. The American Educational Psychology group pointed out there are three factors. We extended the model and added gender inequality social climate factors. We confirmed that the new factors influenced the male image of mathematics and physics in Japan and England. I would like to Introduce interdisciplinary research on science and technology society.

### 2021/09/15

#### Seminar on Probability and Statistics

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

Ergodic risk-sensitive control: history, new results and open problems

https://docs.google.com/forms/d/e/1FAIpQLSe-136jVBQwRDg3rgEGpgVtH2d4chXCvQuvnk_gE2fZqMGwBw/viewform

**Anup Biswas**(Indian Institute of Science Education and Research (IISER), Pune)Ergodic risk-sensitive control: history, new results and open problems

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Risk-sensitive control became popular because of the robustness it provides to the optimal control. Its connection to the theory of large deviation also made it a natural candidate of mathematical interest. In this talk, we shall give an overview of the history of risk-sensitive control problems and some of its applications. We shall then (informally) discuss the ways of tackling this problem and the main questions of interest. At the end, we shall see some important open problems.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Risk-sensitive control became popular because of the robustness it provides to the optimal control. Its connection to the theory of large deviation also made it a natural candidate of mathematical interest. In this talk, we shall give an overview of the history of risk-sensitive control problems and some of its applications. We shall then (informally) discuss the ways of tackling this problem and the main questions of interest. At the end, we shall see some important open problems.

https://docs.google.com/forms/d/e/1FAIpQLSe-136jVBQwRDg3rgEGpgVtH2d4chXCvQuvnk_gE2fZqMGwBw/viewform

### 2021/08/18

#### Seminar on Probability and Statistics

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

Dependence, Sklar's copulas and discreteness

https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform

**Gery Geenens**(The University of New South Wales (UNSW Sydney))Dependence, Sklar's copulas and discreteness

[ Abstract ]

Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.

[ Reference URL ]Asia-Pacific Seminar in Probability and Statistics (APSPS)

https://sites.google.com/view/apsps/home

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Yet the classical copula approach, building on Sklar’s theorem, cannot be legitimised if the variables of interest are not continuous. Indeed in the presence of discreteness, copula models are (i) unidentifiable, and (ii) not margin-free, and this by construction. In spite of the serious inconsistencies that this creates, downplaying statements are widespread in the literature, where copula methods are devised and used in discrete settings. In this work we call to reconsidering this current practice. To reconcile copulas with discreteness, we argued that they should be apprehended from a more fundamental perspective. Inspired by century-old ideas of Yule, we propose a novel construction which allows all the pleasant properties of copulas for modelling dependence (in particular:‘margin-freeness’) to smoothly carry over to the discrete setting.

https://docs.google.com/forms/d/e/1FAIpQLScU9_QHdHZ-JeVyUIJOKUFmYJvG697NBDFkNh735WK9Cov1Og/viewform

### 2021/07/30

#### Colloquium

15:30-16:30 Online

Registration is closed (12:00, July 30).

Toda equations and harmonic bundles (JAPANESE)

Registration is closed (12:00, July 30).

**Takuro Mochizuki**(RIMS, Kyoto University)Toda equations and harmonic bundles (JAPANESE)

### 2021/07/29

#### Applied Analysis

16:00-17:00 Online

Lotka-Volterra competition-diffusion system: the critical case

https://forms.gle/LHj5mVUdpQ3Jxkrd6

**Dongyuan Xiao**( )Lotka-Volterra competition-diffusion system: the critical case

[ Abstract ]

We consider the reaction-diffusion competition system u_t=u_{xx}+u(1-u-v), v_t=dv_{xx}+rv(1-v-u), which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the ''faster'' species excludes the ''slower'' species (with an identified ''spreading speed''), but also provide a sharp description of the profile of the solution, thus shedding light on a new ''bump phenomenon''.

[ Reference URL ]We consider the reaction-diffusion competition system u_t=u_{xx}+u(1-u-v), v_t=dv_{xx}+rv(1-v-u), which is the so-called critical case. The associated ODE system then admits infinitely many equilibria, which makes the analysis quite intricate. We first prove the non-existence of monotone traveling waves by applying the phase plane analysis. Next, we study the long time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the ''faster'' species excludes the ''slower'' species (with an identified ''spreading speed''), but also provide a sharp description of the profile of the solution, thus shedding light on a new ''bump phenomenon''.

https://forms.gle/LHj5mVUdpQ3Jxkrd6

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