## Seminar information archive

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

#### 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

### 2020/05/28

#### Operator Algebra Seminars

16:45-18:15 Online

Index theorem of lattice Wilson-Dirac operators and almost-commuting matrices (English)

[ Reference URL ]

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

**Yosuke Kubota**(Shinshu Univ.)Index theorem of lattice Wilson-Dirac operators and almost-commuting matrices (English)

[ Reference URL ]

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

### 2020/05/27

#### Number Theory Seminar

17:30-18:30 Online

Shintani generating class and the p-adic polylogarithm for totally real fields (ENGLISH)

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

**Kenichi Bannai**(Keio University/RIKEN)Shintani generating class and the p-adic polylogarithm for totally real fields (ENGLISH)

[ Abstract ]

In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke $L$-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke $L$-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto.

[ Reference URL ]In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke $L$-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke $L$-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto.

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

### 2020/05/25

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Characteristic forms of Cheng-Yau metric and CR invariants

[ Reference URL ]

https://forms.gle/vSFPoVR6ugrkTGhX7

**MARUGAME Taiji**(Riken AIP - Osaka University)Characteristic forms of Cheng-Yau metric and CR invariants

[ Reference URL ]

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/05/21

#### Information Mathematics Seminar

16:50-18:35 Online

From the birth of the computer to further speedup of the calculation speed

(Japanese)

https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)From the birth of the computer to further speedup of the calculation speed

(Japanese)

[ Abstract ]

Explanation of the birth of computer and the further speedup of calculation speed

[ Reference URL ]Explanation of the birth of computer and the further speedup of calculation speed

https://docs.google.com/forms/d/1d1RWvV8j1TzXg8eF93zMZeIzJeIvdq9zY8htO8w2St0/

#### Operator Algebra Seminars

16:45-18:15 Online

Partition functions as $C^*$-dynamical invariants and actions of congruence monoids (English)

**Takuya Takeishi**(Kyoto Institute of Technology)Partition functions as $C^*$-dynamical invariants and actions of congruence monoids (English)

### 2020/05/18

#### Seminar on Geometric Complex Analysis

10:30-12:00 Online

Higgs bundles and flat connections over compact Sasakian manifolds

https://forms.gle/vSFPoVR6ugrkTGhX7

**KASUYA Hisashi**(Osaka University)Higgs bundles and flat connections over compact Sasakian manifolds

[ Abstract ]

It is known that on a compact Kähler manifold, there is a correspondence between semisimple flat vector bundles and polystable higgs bundles with vanishing Chern classes via harmonic metrics (Simpson-Corlette). The purpose of this talk is to give the Sasakian (odd dimensional analogue of Kähler geometry) version of this correspondence. We prove that on a compact Sasakian manifold, there is an correspondence between semisimple flat vector bundles and the polystable basic Higgs bundles with vanishing basic Chern classes. (Joint work with Indranil Biswas, arXiv:1905.06178)

[ Reference URL ]It is known that on a compact Kähler manifold, there is a correspondence between semisimple flat vector bundles and polystable higgs bundles with vanishing Chern classes via harmonic metrics (Simpson-Corlette). The purpose of this talk is to give the Sasakian (odd dimensional analogue of Kähler geometry) version of this correspondence. We prove that on a compact Sasakian manifold, there is an correspondence between semisimple flat vector bundles and the polystable basic Higgs bundles with vanishing basic Chern classes. (Joint work with Indranil Biswas, arXiv:1905.06178)

https://forms.gle/vSFPoVR6ugrkTGhX7

### 2020/05/14

#### Operator Algebra Seminars

16:45-18:15 Online

Connes' bicentralizer problem for q-deformed Araki-Woods algebras (English)

[ Reference URL ]

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

**Yusuke Isono**(RIMS, Kyoto Univ.)Connes' bicentralizer problem for q-deformed Araki-Woods algebras (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

The past, the present, the future of the AI that a practical use stage began (Japanese)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)The past, the present, the future of the AI that a practical use stage began (Japanese)

[ Abstract ]

The explanation on the past, the present, the future of the AI that a practical use stage began

The explanation on the past, the present, the future of the AI that a practical use stage began

### 2020/05/13

#### Number Theory Seminar

17:30-18:30 Online

On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives (ENGLISH)

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

**Yifeng Liu**(Yale University)On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives (ENGLISH)

[ Abstract ]

In this talk, we will explain the final outcome on the Beilinson-Bloch-Kato conjecture for motives coming from certain automorphic representations of GL(n) x GL(n+1), of our recent project with Yichao Tian, Liang Xiao, Wei Zhang, and Xinwen Zhu. In particular, we show that the nonvanishing of the central L-value of the motive implies the vanishing of the corresponding Bloch-Kato Selmer group. We will also explain the main ideas and ingredients of the proof.

[ Reference URL ]In this talk, we will explain the final outcome on the Beilinson-Bloch-Kato conjecture for motives coming from certain automorphic representations of GL(n) x GL(n+1), of our recent project with Yichao Tian, Liang Xiao, Wei Zhang, and Xinwen Zhu. In particular, we show that the nonvanishing of the central L-value of the motive implies the vanishing of the corresponding Bloch-Kato Selmer group. We will also explain the main ideas and ingredients of the proof.

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

### 2020/05/07

#### Information Mathematics Seminar

16:50-18:35 Room #Zoom（詳細は講演概要に記載） (Graduate School of Math. Sci. Bldg.)

"Who are we? Where have we come from? Where are we?

Where will we go? What is the role of the mathematical science?"

～To establish of the new academic system by the basic theory regression

type approach and the social problem solving type approach～

(Japanese)

**Hiroshi Fujiwara**(BroadBand Tower, Inc.)"Who are we? Where have we come from? Where are we?

Where will we go? What is the role of the mathematical science?"

～To establish of the new academic system by the basic theory regression

type approach and the social problem solving type approach～

(Japanese)

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