김신영 (이화여대)

Title: Minimal rational curves on complete symmetric varieties

Abstract: 

We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents. In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves, and hence a unique variety of minimal rational tangents. This talk is based on a work with M. Brion and N. Perrin.

서동휘 (서울대학교)

Title: On the first Steklov-Dirichlet eigenvalue for eccentric annuli

Abstract: 

The Steklov eigenvalue problem is an eigenvalue problem for an operator which is defined in the boundary of a domain. Since the operator is nonlocal, the eigenvalues depend on both the geometries of the interior and the boundary of the domain. In this talk, we consider the Steklov-Dirichlet eigenvalue problem in eccentric annuli and related problems. We obtain a lower bound of the first Steklov-Dirichlet eigenvalues of the eccentric annuli by analyzing the first eigenvalues if the distance between the boundary components are sufficiently close. This is based on joint work with Jiho Hong and Mikyoung Lim.

서호섭 (IBS-CCG)

TBA

설석봉 (KIAS)

TBA

염지훈 (IBS-CCG)

Title: Bergman Geometry

Abstract: 

이상훈 (부산대학교)

Title: Rigidity for weighted area-minimizing hypersurface via weighted scalar curvature

Abstract: 

In this talk, we study rigidity for weighted area-minimizing hypersurface. First, we review previous rigidity results in three dimensional manifold. We also review higher dimensional results. Second, we consider weighted manifold and define curvature related to weighted manifold. Finally, we introduce our results for weighted scalar curvature rigidity.

이승재 (IBS-CCG)

Title: Complex geometry of holomorphic ball bundles over complex manifolds

Abstract: 

A holomorphic ball bundle over a compact manifold is a locally
trivial holomorphic fiber bundle with the complex unit ball as its frame. This
bundle can be regarded as a relatively compact open set in the associated bundle
whose fiber is the complex projective space. Thus, we can investigate the Levi
geometry on the bundles such as the Steiness of such bundles.
Interestingly, it turns out that the Levi geometry such a bundle depends on
Kahlerness of the base manifold or a given representation of the holomorphic
automorphisms on the universal cover of the bundle onto the complex unit ball.
In this context, we will explore several relations between the Levi geometry
and complex geometry of such a bundle. This presentation is partially based on
joint work with Aeryeong Seo of Kyungpook National University.
 

이재훈 (KIAS)

Title: Geometry of Costa-Hoffman-Meeks surfaces

Abstract:

The discovery of Costa-Hoffman-Meeks surfaces proved the existence of complete embedded minimal surfaces with arbitrary genus in three-dimensional Euclidean space, and it has played a crucial role in constructing various additional examples. In this talk, we will discuss two distinct approaches to understanding Costa-Hoffman-Meeks surfaces and explore whether these methods can be used to obtain new examples of minimal surfaces in other spaces.

이태훈 (KIAS)

TBA

조예원 (부산대학교)

Title: Singular Kahler-Einstein metrics on compact Kahler spaces 

Abstract: 

In this talk, I shall discuss the development of the notion of canonical metrics on Kahler manifolds and Kahler spaces.

I will also present my recent result on the regularity of solutions of the degenerate complex Monge-Ampere equation on compact Kahler spaces.

This in particular implies that any singular Kahler-Einstein potential on a compact klt pair is globally continuous.