## Seminar information archive

Seminar information archive ～07/14｜Today's seminar 07/15 | Future seminars 07/16～

### 2020/07/14

#### Tuesday Seminar on Topology

17:30-18:30 Online

Joint with Lie Groups and Representation Theory Seminar. Pre-registration required. See our seminar webpage.

Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (JAPANESE)

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

Joint with Lie Groups and Representation Theory Seminar. Pre-registration required. See our seminar webpage.

**Takayuki Okuda**(Hiroshima University)Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (JAPANESE)

[ Abstract ]

Let G be a Lie group and X a homogeneous G-space. A discrete subgroup of G acting on X properly is called a discontinuous group for X. We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly. However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive. In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)]

gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry. In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.

[ Reference URL ]Let G be a Lie group and X a homogeneous G-space. A discrete subgroup of G acting on X properly is called a discontinuous group for X. We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly. However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive. In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)]

gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces. As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry. In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.

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

#### Lie Groups and Representation Theory

17:30-18:30 Room ## (Graduate School of Math. Sci. Bldg.)

Joint with Tuesday Seminar on Topology. Online.

Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (Japanese)

Joint with Tuesday Seminar on Topology. Online.

**Takayuki Okuda**(Hiroshima University)Kobayashi's properness criterion and totally geodesic submanifolds in locally symmetric spaces (Japanese)

[ Abstract ]

Let G be a Lie group and X a homogeneous G-space.

A discrete subgroup of G acting on X properly is called a discontinuous group for X.

We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly.

However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive.

In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)] gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces.

As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry.

In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.

Let G be a Lie group and X a homogeneous G-space.

A discrete subgroup of G acting on X properly is called a discontinuous group for X.

We are interested in constructions and classifications of discontinuous groups for a given X.

It is well-known that if the isotropies of G on X are compact, any closed subgroup acts on X properly.

However, the cases where the isotropies are non-compact, the same claim does not hold in general.

Let us consider the case where G is a linear reductive.

In this situation, T. Kobayashi [Math. Ann. (1989)], [J. Lie Theory (1996)] gave a criterion for the properness of the action on a homogeneous G-space X of closed subgroups in G.

In this talk, we consider homogeneous G-spaces of reductive types realized as families of totally geodesic submanifolds in non-compact Riemannian symmetric spaces.

As a main result, we give a translation of Kobayashi's criterion within the framework of Riemannian geometry.

In particular, for a torsion-free discrete subgroup of G, the criterion can be stated in terms of totally geodesic submanifolds in the Riemannian locally symmetric space corresponding to the subgroup in G.

### 2020/07/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

$\mu$-cscK metrics and $\mu$K-stability of polarized manifolds

[ Reference URL ]

https://forms.gle/vSFPoVR6ugrkTGhX7

**INOUE Eiji**(University of Tokyo)$\mu$-cscK metrics and $\mu$K-stability of polarized manifolds

[ Reference URL ]

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/07/09

#### Operator Algebra Seminars

16:45-18:15 Online

Affine isometric actions of groups on $L_p$-spaces : dependence on the value of $p$ (English)

[ Reference URL ]

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

**Amine Marrakchi**(ENS Lyon)Affine isometric actions of groups on $L_p$-spaces : dependence on the value of $p$ (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

Ways from machine learning to deep learning (Japanese)

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Ways from machine learning to deep learning (Japanese)

[ Abstract ]

Explanation of ways from machine learning to deep learning

[ Reference URL ]Explanation of ways from machine learning to deep learning

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

### 2020/07/07

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor (JAPANESE)

https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

Pre-registration required. See our seminar webpage.

**Yuta Nozaki**(Hiroshima University)Abelian quotients of the Y-filtration on the homology cylinders via the LMO functor (JAPANESE)

[ Abstract ]

We construct a series of homomorphisms on the Y-filtration on the homology cylinders via the mod $\mathbb{Z}$ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of the Torelli group does not factor through Morita's refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. This is the joint work with Masatoshi Sato and Masaaki Suzuki.

[ Reference URL ]We construct a series of homomorphisms on the Y-filtration on the homology cylinders via the mod $\mathbb{Z}$ reduction of the LMO functor. The restriction of our homomorphism to the lower central series of the Torelli group does not factor through Morita's refinement of the Johnson homomorphism. We use it to show that the abelianization of the Johnson kernel of a closed surface has torsion elements. This is the joint work with Masatoshi Sato and Masaaki Suzuki.

https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

### 2020/07/06

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type (Japanese?)

https://forms.gle/vSFPoVR6ugrkTGhX7

**INAYAMA Takahiro**(University of Tokyo)Nakano positivity of singular Hermitian metrics and vanishing theorems of Demailly-Nadel-Nakano type (Japanese?)

[ Abstract ]

We propose a general definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems.

[ Reference URL ]We propose a general definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems.

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/07/02

#### Operator Algebra Seminars

16:45-18:15 Online

Outer actions ($\mathcal{G}$-kernels) of discrete amenable groupoids on injective factors (English)

[ Reference URL ]

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

**Toshihiko Masuda**(Kyushu Univ.)Outer actions ($\mathcal{G}$-kernels) of discrete amenable groupoids on injective factors (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

Telework society and menace of the cyber attack (Japanese)

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Telework society and menace of the cyber attack (Japanese)

[ Abstract ]

Explanation on the menace of the cyber attack in telework society.

[ Reference URL ]Explanation on the menace of the cyber attack in telework society.

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

### 2020/06/30

#### Numerical Analysis Seminar

16:30-18:00 Online

Structure-preserving numerical methods for interface problems (Japanese)

[ Reference URL ]

https://forms.gle/ztK741vNdBT7hfGSA

**Koya Sakakibara**(Okayama University of Science)Structure-preserving numerical methods for interface problems (Japanese)

[ Reference URL ]

https://forms.gle/ztK741vNdBT7hfGSA

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Homology of right-angled Artin kernels (ENGLISH)

https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

Pre-registration required. See our seminar webpage.

**Daniel Matei**(IMAR Bucharest)Homology of right-angled Artin kernels (ENGLISH)

[ Abstract ]

The right-angled Artin groups A(G) are the finitely presented groups associated to a finite simplicial graph G=(V,E), which are generated by the vertices V satisfying commutator relations vw=wv for every edge vw in E. An Artin kernel

N

[ Reference URL ]The right-angled Artin groups A(G) are the finitely presented groups associated to a finite simplicial graph G=(V,E), which are generated by the vertices V satisfying commutator relations vw=wv for every edge vw in E. An Artin kernel

N

_{h}(G) is defined by an epimorphism h of A(G) onto the integers. In this talk, we discuss the module structure over the Laurent polynomial ring of the homology groups of N_{h}(G).https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

### 2020/06/29

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Oka properties of complements of holomorphically convex sets

https://forms.gle/vSFPoVR6ugrkTGhX7

**KUSAKABE Yuta**(Osaka University)Oka properties of complements of holomorphically convex sets

[ Abstract ]

A complex manifold is called an Oka manifold if the Oka principle for maps from Stein spaces holds. In this talk, we consider the question of when a holomorphically convex set in an Oka manifold has an Oka complement. Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold.

This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in $\mathbb{C}^{n}$ $(n>1)$ is Oka. The relative version of the main theorem can also be proved.

As an application, we show that the complement $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ of a totally real affine subspace is Oka if $n>1$ and $(n,k)\neq(2,1),(2,2),(3,3)$.

[ Reference URL ]A complex manifold is called an Oka manifold if the Oka principle for maps from Stein spaces holds. In this talk, we consider the question of when a holomorphically convex set in an Oka manifold has an Oka complement. Our main theorem states that the complement of a compact holomorphically convex set in a Stein manifold with the density property is an Oka manifold.

This gives a positive answer to the well-known long-standing problem in Oka theory whether the complement of a compact polynomially convex set in $\mathbb{C}^{n}$ $(n>1)$ is Oka. The relative version of the main theorem can also be proved.

As an application, we show that the complement $\mathbb{C}^{n}\setminus\mathbb{R}^{k}$ of a totally real affine subspace is Oka if $n>1$ and $(n,k)\neq(2,1),(2,2),(3,3)$.

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/06/25

#### Operator Algebra Seminars

16:45-18:15 Online

Properly proximal groups and their von Neumann algebras (English)

[ Reference URL ]

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

**Remi Boutonnet**(Univ. Bordeaux)Properly proximal groups and their von Neumann algebras (English)

[ Reference URL ]

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

### 2020/06/24

#### Discrete mathematical modelling seminar

15:00-16:30 Online

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

Combinatorial and Asymptotical Results on the Neighborhood Grid Data Structure (English)

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

**Martin Skrodzki**(RIKEN iTHEMS)Combinatorial and Asymptotical Results on the Neighborhood Grid Data Structure (English)

[ Abstract ]

In 2009, Joselli et al. introduced the Neighborhood Grid data structure for fast computation of neighborhood estimates in point clouds. Even though the data structure has been used in several applications and shown to be practically relevant, it is theoretically not yet well understood. The purpose of this talk is to present a polynomial-time algorithm to build the data structure. Furthermore, we establish the presented algorithm to be time-optimal. This investigations leads to several combinatorial questions for which partial results are given.

In 2009, Joselli et al. introduced the Neighborhood Grid data structure for fast computation of neighborhood estimates in point clouds. Even though the data structure has been used in several applications and shown to be practically relevant, it is theoretically not yet well understood. The purpose of this talk is to present a polynomial-time algorithm to build the data structure. Furthermore, we establish the presented algorithm to be time-optimal. This investigations leads to several combinatorial questions for which partial results are given.

### 2020/06/23

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Gauge theory and the diffeomorphism and homeomorphism groups of 4-manifolds (JAPANESE)

https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

Pre-registration required. See our seminar webpage.

**Hokuto Konno**(The University of Tokyo)Gauge theory and the diffeomorphism and homeomorphism groups of 4-manifolds (JAPANESE)

[ Abstract ]

I will explain my recent collaboration with several groups that develops gauge theory for families

to extract difference between the diffeomorphism groups and the homeomorphism groups of 4-manifolds.

After Donaldson’s celebrated diagonalization theorem, gauge theory has given strong constraints on the topology of smooth 4-manifolds. Combining such constraints with Freedman’s theory, one may find many non-smoothable topological 4-manifolds.

Recently, a family version of this argument was started by T. Kato, N. Nakamura and myself, and soon later it was developed also by D. Baraglia and his collaborating work with myself. More precisely, considering gauge theory for smooth fiber bundles of 4-manifolds, they obtained some constraints on the topology of smooth 4-manifold bundles. Using such constraints, they detected non-smoothable topological fiber bundles of smooth 4-manifolds. The existence of such bundles implies that there is homotopical difference between the diffeomorphism and homeomorphism groups of the 4-manifolds given as the fibers.

If time permits, I will also mention my collaboration with Baraglia which shows that a K3 surface gives a counterexample to the Nielsen realization problem in dimension 4. This example reveals also that there is difference between the Nielsen realization problems asked in the smooth category and the topological category.

[ Reference URL ]I will explain my recent collaboration with several groups that develops gauge theory for families

to extract difference between the diffeomorphism groups and the homeomorphism groups of 4-manifolds.

After Donaldson’s celebrated diagonalization theorem, gauge theory has given strong constraints on the topology of smooth 4-manifolds. Combining such constraints with Freedman’s theory, one may find many non-smoothable topological 4-manifolds.

Recently, a family version of this argument was started by T. Kato, N. Nakamura and myself, and soon later it was developed also by D. Baraglia and his collaborating work with myself. More precisely, considering gauge theory for smooth fiber bundles of 4-manifolds, they obtained some constraints on the topology of smooth 4-manifold bundles. Using such constraints, they detected non-smoothable topological fiber bundles of smooth 4-manifolds. The existence of such bundles implies that there is homotopical difference between the diffeomorphism and homeomorphism groups of the 4-manifolds given as the fibers.

If time permits, I will also mention my collaboration with Baraglia which shows that a K3 surface gives a counterexample to the Nielsen realization problem in dimension 4. This example reveals also that there is difference between the Nielsen realization problems asked in the smooth category and the topological category.

https://zoom.us/webinar/register/WN_oS594Z6BRyaKNCvlm3yCoQ

#### Numerical Analysis Seminar

16:30-18:00 Online

Linearly implicit and high-order conservative schemes for ordinary differential equations with a quadratic invariant (Japanese)

[ Reference URL ]

https://forms.gle/hvvvFLAhH1314UQK8

**Shun Sato**(The University of Tokyo)Linearly implicit and high-order conservative schemes for ordinary differential equations with a quadratic invariant (Japanese)

[ Reference URL ]

https://forms.gle/hvvvFLAhH1314UQK8

### 2020/06/18

#### Information Mathematics Seminar

16:50-18:35 Online

Ways from speedup of the classic computing to a quantum (Japanese)

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Ways from speedup of the classic computing to a quantum (Japanese)

[ Abstract ]

Explanation of ways from speedup of the classic computing to a quantum

[ Reference URL ]Explanation of ways from speedup of the classic computing to a quantum

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

#### Operator Algebra Seminars

16:45-18:15 Online

On Arveson's boundary theorem (English)

[ Reference URL ]

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

**Yoshimichi Ueda**(Nagoya Univ.)On Arveson's boundary theorem (English)

[ Reference URL ]

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

### 2020/06/17

#### Number Theory Seminar

17:30-18:30 Online

On modular representations of GL_2(L) for unramified L (ENGLISH)

https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html

**Christophe Breuil**(CNRS, Université Paris-Sud)On modular representations of GL_2(L) for unramified L (ENGLISH)

[ Abstract ]

Let p be a prime number and L a finite unramified extension of Q_p. We give a survey of past and new results on smooth admissible representations of GL_2(L) that appear in mod p cohomology. This is joint work with Florian Herzig, Yongquan Hu, Stefano Morra and Benjamin Schraen.

[ Reference URL ]Let p be a prime number and L a finite unramified extension of Q_p. We give a survey of past and new results on smooth admissible representations of GL_2(L) that appear in mod p cohomology. This is joint work with Florian Herzig, Yongquan Hu, Stefano Morra and Benjamin Schraen.

https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html

### 2020/06/11

#### Operator Algebra Seminars

16:45-18:15 Online

Homology and K-theory of torsion free ample groupoids and Smale spaces (English)

[ Reference URL ]

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

**Makoto Yamashita**(Univ. Oslo)Homology and K-theory of torsion free ample groupoids and Smale spaces (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

Big picture of the modern AI and Machine learning in the basics (Japanese)

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Big picture of the modern AI and Machine learning in the basics (Japanese)

[ Abstract ]

Explanation of the modern AI and Machine learning

[ Reference URL ]Explanation of the modern AI and Machine learning

[学外用] https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/ [学内用] https://bit.ly/2zCBj8x (g.ecc.u-tokyo.ac.jpアカウントでアクセスできます)

### 2020/06/08

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Applications of the Quot-scheme limit to variational aspects of the Hermitian-Einstein metric

https://forms.gle/vSFPoVR6ugrkTGhX7

**HASHIMOTO Yoshinori**(Tokyo Institute of Technology)Applications of the Quot-scheme limit to variational aspects of the Hermitian-Einstein metric

[ Abstract ]

The Kobayashi-Hitchin correspondence, proved by Donaldson and Uhlenbeck-Yau by using the nonlinear PDE theory, states that the existence of Hermitian-Einstein metrics on a holomorphic vector bundle is equivalent to an algebro-geometric stability condition. We present some results that exhibit an explicit link between differential and algebraic geometry in the above correspondence, from a variational point of view. The key to such results is an object called the Quot-scheme limit of Fubini-Study metrics, which is used to evaluate certain algebraic 1-parameter subgroups of Hermitian metrics by using the theory of Quot-schemes in algebraic geometry. This method also works for the proof of the correspondence between the balanced metrics and the Gieseker stability, as originally proved by X.W. Wang. Joint work with Julien Keller.

[ Reference URL ]The Kobayashi-Hitchin correspondence, proved by Donaldson and Uhlenbeck-Yau by using the nonlinear PDE theory, states that the existence of Hermitian-Einstein metrics on a holomorphic vector bundle is equivalent to an algebro-geometric stability condition. We present some results that exhibit an explicit link between differential and algebraic geometry in the above correspondence, from a variational point of view. The key to such results is an object called the Quot-scheme limit of Fubini-Study metrics, which is used to evaluate certain algebraic 1-parameter subgroups of Hermitian metrics by using the theory of Quot-schemes in algebraic geometry. This method also works for the proof of the correspondence between the balanced metrics and the Gieseker stability, as originally proved by X.W. Wang. Joint work with Julien Keller.

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/06/05

#### Colloquium

15:30-16:30 Online

Please register at the link below to attend this online colloquium

Exact WKB analysis and related topics

https://zoom.us/webinar/register/WN_ezXY3HjIQcCK2G9V-2CYrw

Please register at the link below to attend this online colloquium

**Kohei Iwaki**(Graduate School of Mathematical Sciences, University of Tokyo)Exact WKB analysis and related topics

[ Abstract ]

Exact WKB analysis, developed by Voros et.al., is an effective method for global study of (singularly perturbed) ordinary differential equations defined on a complex domain. After recalling several fundamental facts on exact WKB analysis, I'll talk about relationships to other research topics, such as cluster algebras, topological recursion, integrable systems of Painlevé type, etc.

[ Reference URL ]Exact WKB analysis, developed by Voros et.al., is an effective method for global study of (singularly perturbed) ordinary differential equations defined on a complex domain. After recalling several fundamental facts on exact WKB analysis, I'll talk about relationships to other research topics, such as cluster algebras, topological recursion, integrable systems of Painlevé type, etc.

https://zoom.us/webinar/register/WN_ezXY3HjIQcCK2G9V-2CYrw

### 2020/06/04

#### Operator Algebra Seminars

16:45-18:15 Online

Equivariant $O_2$-absorption theorem for exact groups

**Yuhei Suzuki**(Hokkaido Univ.)Equivariant $O_2$-absorption theorem for exact groups

#### Information Mathematics Seminar

16:50-18:35 Online

Telework society and importance of the cyber security to increase

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)Telework society and importance of the cyber security to increase

[ Abstract ]

Explanation on telework society and importance of the cyber security

Explanation on telework society and importance of the cyber security

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