## Seminar information archive

Seminar information archive ～09/22｜Today's seminar 09/23 | Future seminars 09/24～

#### Operator Algebra Seminars

16:45-18:15 Online

A characterization of the Razak-Jacelon algebra

[ Reference URL ]

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

**Norio Nawata**(Osaka Univ.)A characterization of the Razak-Jacelon algebra

[ Reference URL ]

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

### 2020/09/29

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)

https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

Pre-registration required. See our seminar webpage.

**Kohei Iwaki**(The University of Tokyo)Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds (JAPANESE)

[ Abstract ]

In 1998, Lawrence-Zagier introduced a certain q-series and proved that its limit value at root of unity q=exp(2π i / K) coincides with the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant of the Poincare homology sphere Σ(2,3,5) at the level K. Employing the idea of Gukov-Marino-Putrov based on resurgent analysis, we generalize the result of Lawrence-Zagier for the Seifert loops (Seifert manifolds with a single loop inside). That is, for each Seifert loop, we introduce an explicit q-series (WRT function) and show that its limit value at the root of unity coincides with the WRT invariant of the Seifert loop. We will also discuss a q-difference equation satisfied by the WRT function. This talk is based on a joint work with H. Fuji, H. Murakami and Y. Terashima which is available on arXiv:2007.15872.

[ Reference URL ]In 1998, Lawrence-Zagier introduced a certain q-series and proved that its limit value at root of unity q=exp(2π i / K) coincides with the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant of the Poincare homology sphere Σ(2,3,5) at the level K. Employing the idea of Gukov-Marino-Putrov based on resurgent analysis, we generalize the result of Lawrence-Zagier for the Seifert loops (Seifert manifolds with a single loop inside). That is, for each Seifert loop, we introduce an explicit q-series (WRT function) and show that its limit value at the root of unity coincides with the WRT invariant of the Seifert loop. We will also discuss a q-difference equation satisfied by the WRT function. This talk is based on a joint work with H. Fuji, H. Murakami and Y. Terashima which is available on arXiv:2007.15872.

https://zoom.us/meeting/register/tJcqdO6pqz0pGNbwpZOpG-o2h4xJwmpma3zL

### 2020/08/26

#### thesis presentations

16:00-17:15 Online

Irregular Riemann–Hilbert correspondence and its applications to Fourier transforms of holonomic D-modules

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**ITO Yohei**(Graduate Scool of Mathematical Sciences University of tokyo)Irregular Riemann–Hilbert correspondence and its applications to Fourier transforms of holonomic D-modules

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/31

#### thesis presentations

10:30-11:45 Online

Theory on Kähler metrics with constant exponentially weighted scalar curvature and exponentially weighted K-stability including Kähler-Ricci solitons

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**INOUE Eiji**(Graduate Scool of Mathematical Sciences University of tokyo)Theory on Kähler metrics with constant exponentially weighted scalar curvature and exponentially weighted K-stability including Kähler-Ricci solitons

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

#### thesis presentations

13:15-14:30 Online

Studies on singular Hermitian metrics on holomorphic vector bundles via L² estimates and L² extension theorems

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**INAYAMA Takahiro**(Graduate Scool of Mathematical Sciences University of tokyo)Studies on singular Hermitian metrics on holomorphic vector bundles via L² estimates and L² extension theorems

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/30

#### thesis presentations

10:30-11:45 Online

Monopole Floer homology for codimension-3 Riemannian foliation

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**LIN Dexie**(Graduate Scool of Mathematical Sciences University of tokyo)Monopole Floer homology for codimension-3 Riemannian foliation

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/28

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

A double filtration for the mapping class group and the Goeritz group of the sphere (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Anderson Vera**(RIMS, Kyoto University)A double filtration for the mapping class group and the Goeritz group of the sphere (ENGLISH)

[ Abstract ]

I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of $S^3$. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)

[ Reference URL ]I will talk about a double-indexed filtration of the mapping class group and of the Goeritz group of the sphere, the latter is the group of isotopy classes of self-homeomorphisms of the 3-sphere which preserves the standard Heegaard splitting of $S^3$. In particular I will explain how this double filtration allows to write the Torelli group as a product of some subgroups of the mapping class group. A similar study could be done for the group of automorphisms of a free group. (work in progress with K. Habiro)

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

#### thesis presentations

10:30-11:45 Online

Twisted arrow categories of operads and Segal conditions

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

**Brkin,Sergei Vladimirovich**(Graduate Scool of Mathematical Sciences University of tokyo)Twisted arrow categories of operads and Segal conditions

[ Reference URL ]

https://forms.gle/jfh9Hpyt3XZXXcft6

### 2020/07/21

#### Numerical Analysis Seminar

16:30-18:00 Online

Structure-preserving numerical schemes for constrained gradient flows of planar curves (Japanese)

[ Reference URL ]

https://forms.gle/3JiNEjWnrWLW8cFA9

**Tomoya Kemmochi**(Nagoya University)Structure-preserving numerical schemes for constrained gradient flows of planar curves (Japanese)

[ Reference URL ]

https://forms.gle/3JiNEjWnrWLW8cFA9

#### Tuesday Seminar on Topology

17:00-18:00 Online

Pre-registration required. See our seminar webpage.

Twisted arrow categories of operads and Segal conditions (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Sergei Burkin**(The University of Tokyo)Twisted arrow categories of operads and Segal conditions (ENGLISH)

[ Abstract ]

We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category $\Delta$, Segal's category $\Gamma$ and Moerdijk--Weiss category $\Omega$ are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.

[ Reference URL ]We generalize twisted arrow category construction from categories to operads, and show that several important categories, including the simplex category $\Delta$, Segal's category $\Gamma$ and Moerdijk--Weiss category $\Omega$ are twisted arrow categories of operads. Twisted arrow categories of operads are closely connected with Segal conditions, and the corresponding theory can be generalized from multi-object associative algebras (i.e. categories) to multi-object P-algebras for reasonably nice operads P.

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

#### Tuesday Seminar on Topology

18:00-19:00 Online

Pre-registration required. See our seminar webpage.

Monopole Floer homology for codimension-3 Riemannian foliation (ENGLISH)

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

Pre-registration required. See our seminar webpage.

**Dexie Lin**(The University of Tokyo)Monopole Floer homology for codimension-3 Riemannian foliation (ENGLISH)

[ Abstract ]

In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold with codimension-3 oriented Riemannian foliation. Under a certain topological condition, we construct the basic monopole Floer homologies for a transverse spinc structure with a bundle-like metric, generic perturbation and a complete local system. We will show that these homologies are independent of the bundle-like metric and generic perturbation. The major difference between the basic monopole Floer homologies and the ones on manifolds is the necessity to use the complete local system to construct the monopole Floer homologies.

[ Reference URL ]In this paper, we give a systematic study of Seiberg-Witten theory on closed oriented manifold with codimension-3 oriented Riemannian foliation. Under a certain topological condition, we construct the basic monopole Floer homologies for a transverse spinc structure with a bundle-like metric, generic perturbation and a complete local system. We will show that these homologies are independent of the bundle-like metric and generic perturbation. The major difference between the basic monopole Floer homologies and the ones on manifolds is the necessity to use the complete local system to construct the monopole Floer homologies.

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

### 2020/07/16

#### Operator Algebra Seminars

16:45-18:15 Online

Complex quantum groups and the Baum-Connes conjecture (English)

[ Reference URL ]

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

**Christian Voigt**(Univ. Glasgow)Complex quantum groups and the Baum-Connes conjecture (English)

[ Reference URL ]

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

#### Information Mathematics Seminar

16:50-18:35 Online

Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (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.)Basics of the speedup technique of the classic computing and Innovation of Causality in the root of the quantum computing (Japanese)

[ Abstract ]

Explanation of the speedup technique of the classic computing and innovation of causality in the root of the quantum computing

[ Reference URL ]Explanation of the speedup technique of the classic computing and innovation of causality in the root of the quantum computing

[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)

### 2020/07/14

#### 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

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