## Seminar information archive

Seminar information archive ～11/07｜Today's seminar 11/08 | Future seminars 11/09～

#### Operator Algebra Seminars

16:45-18:15 Online

On regular $*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras

[ Reference URL ]

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

**Michiya Mori**(RIKEN)On regular $*$-algebras of bounded linear operators: A new approach towards a theory of noncommutative Boolean algebras

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)

**Ryosuke Nakahama**(Kyushu University)Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)

[ Abstract ]

Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.

Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).

In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.

Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.

Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.

Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.

Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).

In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.

Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.

Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.

### 2021/11/15

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals (Japanese)

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

**Katsusuke Nabeshima**(Tokyo University of Science)Computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals (Japanese)

[ Abstract ]

The concept of logarithmic vector fields along a hypersurface, introduced by K. Saito (1980), is of considerable importance in singularity theory.

Logarithmic vector fields have been extensively studied and utilized by several researchers. A. G. Aleksandrov (1986) and J. Wahl (1983) considered quasihomogeneous complete intersection cases and gave independently, among other things, a closed formula of generators of logarithmic vector fields. However, there is no closed formula for generators of logarithmic vector fields, even for semi-quasihomogeneous hypersurface isolated singularity cases. Many problems related with logarithmic vector fields remain still unsolved, especially for non-quasihomogeneous cases.

Bruce-Roberts Milnor number was introduced in 1988 by J. W. Bruce and R. M. Roberts as a generalization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety in terms of logarithmic vector fields. Recently, Bruce-Robert Milnor numbers are investigated by several researchers. However, many problems related with Bruce-Roberts Milnor numbers remain unsolved.

In this talk, we consider logarithmic vector fields along a hypersurface with an isolated singularity. We present methods to study complex analytic properties of logarithmic vector fields and illustrate an algorithm for computing logarithmic vector fields. As an application of logarithmic vector fields, we consider Bruce-Roberts Milnor numbers in the context of symbolic computation.

[ Reference URL ]The concept of logarithmic vector fields along a hypersurface, introduced by K. Saito (1980), is of considerable importance in singularity theory.

Logarithmic vector fields have been extensively studied and utilized by several researchers. A. G. Aleksandrov (1986) and J. Wahl (1983) considered quasihomogeneous complete intersection cases and gave independently, among other things, a closed formula of generators of logarithmic vector fields. However, there is no closed formula for generators of logarithmic vector fields, even for semi-quasihomogeneous hypersurface isolated singularity cases. Many problems related with logarithmic vector fields remain still unsolved, especially for non-quasihomogeneous cases.

Bruce-Roberts Milnor number was introduced in 1988 by J. W. Bruce and R. M. Roberts as a generalization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety in terms of logarithmic vector fields. Recently, Bruce-Robert Milnor numbers are investigated by several researchers. However, many problems related with Bruce-Roberts Milnor numbers remain unsolved.

In this talk, we consider logarithmic vector fields along a hypersurface with an isolated singularity. We present methods to study complex analytic properties of logarithmic vector fields and illustrate an algorithm for computing logarithmic vector fields. As an application of logarithmic vector fields, we consider Bruce-Roberts Milnor numbers in the context of symbolic computation.

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

### 2021/11/11

#### Information Mathematics Seminar

16:50-18:35 Online

Supervised/Unsupervised Learning and Reinforcement learning for Deep Learning (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Supervised/Unsupervised Learning and Reinforcement learning for Deep Learning (Japanese)

[ Abstract ]

Explanation on supervised/unsupervised learning and reinforcement learning for deep learning

[ Reference URL ]Explanation on supervised/unsupervised learning and reinforcement learning for deep learning

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

### 2021/11/09

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

The spaces of non-descendible quasimorphisms and bounded characteristic classes (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Shuhei Maruyama**(Nagoya University)The spaces of non-descendible quasimorphisms and bounded characteristic classes (JAPANESE)

[ Abstract ]

A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.

[ Reference URL ]A quasimorphism is a real-valued function on a group which is a homomorphism up to bounded error. In this talk, we discuss the (non-)descendibility of quasimorphisms. In particular, we consider the space of non-descendible quasimorphisms on universal covering groups and explain its relation to the space of bounded characteristic classes of foliated bundles. This talk is based on a joint work with Morimichi Kawasaki.

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

#### Operator Algebra Seminars

16:45-18:15 Online

Construction of Haag-Kastler nets for factorizing S-matrices with bound states

[ Reference URL ]

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

**Yoh Tanimoto**(University of Rome, Tor Vergata)Construction of Haag-Kastler nets for factorizing S-matrices with bound states

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

On the support of Plancherel measures and the image of moment map

(Japanese)

**Yoshiki Oshima**(Osaka University)On the support of Plancherel measures and the image of moment map

(Japanese)

[ Abstract ]

We see a relationship between the support of Plancherel measures for homogeneous spaces and the image of moment maps from cotangent bundles based on a joint work with Benjamin Harris.

Moreover, we discuss related problems and conjectures about inductions and restrictions for representations of Lie groups in general settings.

We see a relationship between the support of Plancherel measures for homogeneous spaces and the image of moment maps from cotangent bundles based on a joint work with Benjamin Harris.

Moreover, we discuss related problems and conjectures about inductions and restrictions for representations of Lie groups in general settings.

### 2021/11/04

#### Information Mathematics Seminar

16:50-18:35 Online

Internet business establishment/GPU application/Quantum computer design (Japanese)

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

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Internet business establishment/GPU application/Quantum computer design (Japanese)

[ Abstract ]

Explanation on Internet business establishment, GPU application and quantum computer design

[ Reference URL ]Explanation on Internet business establishment, GPU application and quantum computer design

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

### 2021/11/02

#### Operator Algebra Seminars

16:45-18:15 Online

Magnetic properties of ground states in many-electron systems

[ Reference URL ]

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

**Tarahiro Miyao**(Hokkaido Univ.)Magnetic properties of ground states in many-electron systems

[ Reference URL ]

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.

Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups (JAPANESE)

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

Pre-registration required. See our seminar webpage.

**Takefumi Nosaka**(Tokyo Institute of Technolog)Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups (JAPANESE)

[ Abstract ]

There are many developments of fibered knots and homology cylinders from topological and algebraic viewpoints. In a converse sense, we discuss meta-nilpotent localization of knot groups,

which can deal with any knot like fibered knots. The monodoromy can be regarded as a symplectic automorphism of free nilpotent group, and the conjugacy classes in the outer automorphism groups produce knot invariants in terms of Johnson homomorphisms. In this talk, I show the construction of the monodoromies, and some results on the knot invariants. I also talk approaches from Fox pairings.

[ Reference URL ]There are many developments of fibered knots and homology cylinders from topological and algebraic viewpoints. In a converse sense, we discuss meta-nilpotent localization of knot groups,

which can deal with any knot like fibered knots. The monodoromy can be regarded as a symplectic automorphism of free nilpotent group, and the conjugacy classes in the outer automorphism groups produce knot invariants in terms of Johnson homomorphisms. In this talk, I show the construction of the monodoromies, and some results on the knot invariants. I also talk approaches from Fox pairings.

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.)

Difference between the distribution and hyperfunction solution spaces of an irregular holonomic D-module (Japanese)

**Taito TAUCHI**(Kyushu University)Difference between the distribution and hyperfunction solution spaces of an irregular holonomic D-module (Japanese)

[ Abstract ]

Let M be a holonomic D-module. Then the distribution and hyperfunction solution spaces of M coincide if M is regular. However, there is a difference between them in general if M is irregular. In this talk, we explain this phenomena taking a Whittaker functional of the principal series representation of SL(2, R) as a concrete example.

Let M be a holonomic D-module. Then the distribution and hyperfunction solution spaces of M coincide if M is regular. However, there is a difference between them in general if M is irregular. In this talk, we explain this phenomena taking a Whittaker functional of the principal series representation of SL(2, R) as a concrete example.

### 2021/10/29

#### Colloquium

15:30-16:30 Online

Registration was closed

Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)

Registration was closed

**Takahito Kashiwabara**(Graduate School of Mathematical Sciences, University of Tokyo)Well-posedness of friction- or Signorini-type boundary value problems in the non-stationary case (JAPANESE)

### 2021/10/28

#### Applied Analysis

16:00-17:00 Online

Quasiconformal and Sobolev mappings on metric measure

https://forms.gle/QATECqmwmWGvXoU56

**Xiaodan Zhou**(OIST)Quasiconformal and Sobolev mappings on metric measure

[ Abstract ]

The study of quasiconformal mappings has been an important and active topic since its introduction in the 1930s and the theory has been widely applied to different fields including differential geometry, harmonic analysis, PDEs, etc. In the Euclidean space, it is a fundamental result that three definitions (metric, geometric and analytic) of quasiconformality are equivalent. The theory of quasiconformal mappings has been extended to metric measure spaces by Heinonen and Koskela in the 1990s and their work laid the foundation of analysis on metric spaces. In general, the equivalence of the three characterizations will no longer hold without appropriate assumptions on the spaces and mappings. It is a question of general interest to find minimal assumptions on the metric spaces and on the mapping to guarantee the metric definition implies the analytic characterization or geometric characterization. In this talk, we will give an brief review of the above mentioned classical theory and present some recent results we achieved in obtaining the analytic property, in particular, the Sobolev regularity of a metric quasiconformal mapping with relaxed spaces and mapping conditions. Unexpectedly, we can apply this to prove results that are new even in the classical Euclidean setting. This is joint work with Panu Lahti (Chinese Academy of Sciences).

[ Reference URL ]The study of quasiconformal mappings has been an important and active topic since its introduction in the 1930s and the theory has been widely applied to different fields including differential geometry, harmonic analysis, PDEs, etc. In the Euclidean space, it is a fundamental result that three definitions (metric, geometric and analytic) of quasiconformality are equivalent. The theory of quasiconformal mappings has been extended to metric measure spaces by Heinonen and Koskela in the 1990s and their work laid the foundation of analysis on metric spaces. In general, the equivalence of the three characterizations will no longer hold without appropriate assumptions on the spaces and mappings. It is a question of general interest to find minimal assumptions on the metric spaces and on the mapping to guarantee the metric definition implies the analytic characterization or geometric characterization. In this talk, we will give an brief review of the above mentioned classical theory and present some recent results we achieved in obtaining the analytic property, in particular, the Sobolev regularity of a metric quasiconformal mapping with relaxed spaces and mapping conditions. Unexpectedly, we can apply this to prove results that are new even in the classical Euclidean setting. This is joint work with Panu Lahti (Chinese Academy of Sciences).

https://forms.gle/QATECqmwmWGvXoU56

#### 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

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