복소곡면 특이점의 변형의 기하와 위상

• 김준태 _ 서강대학교

Lagrangian surfaces in symplectic manifolds

We give an overview of the embedding and isotopy problems of Lagrangian surfaces in symplectic manifolds. Based on holomorphic curves, we explore the exoticness of monotone/real Lagrangian 2-tori in closed monotone symplectic four-manifolds (also known as symplectic del Pezzo surfaces). In particular, we explain the uniqueness of real Lagrangian tori in a monotone symplectic quadric surface.

• 김호성 _ IBS-CCG

Lagrangian fibration structure on the cotangent bundle of a del Pezzo surface of degree 4

The cotangent bundle of a complex projective manifold carries a natural holomorphic symplectic 2-form. The existence of a natural Lagrangian fibration structure of these non-compact complex manifolds has not been studied very much. In this talk, we are going to talk on a natural Lagrangian fibration structure on the map Φ from the cotangent bundle of a del Pezzo surface X of degree 4. This is a joint work with Prof. Yongnam Lee.

• 신동수 _ 충남대학교

Deformations of complex surface singularities

I will introduce three theories on deformations of complex surface singularities and their relations: Picture deformations by de Jong and van Straten, P-modifications by Kollár, and smoothings of negative weights by Pinkham.

• 이상진 _ IBS-CGP

Symplectic Lefschetz fibrations on cotangent bundles

Symplectic Lefschetz fibration is a powerful tool for studying symplectic topology. Thus, it is natural to ask how to find it. This talk will give an algorithmic construction of Lefschetz fibrations of cotangent bundles from their symplectic handle decompositions.

• 전재관 _ 충남대학교

Correspondence between P-resolutions and Picture deformations of weighted homogeneous surface singularities with big central node

For a weighted homogeneous surface singularity $X$, we have two descriptions of components of Def($X$). One way is a P-resolution introduced by J. Koll\'{a}r and N.I. Shepherd-Barron. Roughly speaking, it is a resolution with some mild singularities. They conjectured that P-resolutions describe all components of the deformation space of rational singularities(Koll\'{a}r conjecture). The other way is a Picture deformation of a sandwiched singularity introduced by T. de. Jong and D. van Straten. They restrict a deformation of a sandwiched singularity to a deformation of plane curves and prove that Picture deformations describe all components of deformations of sandwiched singularities. If we can show a correspondence between P-resolutions and picture deformations of a given singularity, than it means that the conjecture holds for the singularity. H. Park and D. Shin prove that we can induce a picture deformation from a P-resolution of a sandwiched singularity by using the minimal model program for threefolds. In this talk, we show that we can induce a P-resolution from a picture deformation of a weighted homogeneous surface singularity by using combinatorial constraints of picture deformations. This is a joint work with D. Shin.

• 최학호 _ 서울대학교

On symplectic fillings of Seifert 3-manifolds

One way to understand the topology of symplectic manifolds is to study techniques for constructing symplectic manifolds. When we try to get a new symplectic manifold by gluing together local pieces, the symplectic structure on each piece should be compatible with each other along the pasting region. This search for symplectic cut-and-paste techniques has led us to the study of symplectic 4-manifolds with convex boundaries, which we call symplectic fillings. In this series of talks, we discuss minimal symplectic fillings of a Seifert 3-manifold $Y$ with a canonical contact structure. After a review of the classification scheme for minimal symplectic fillings of $Y$, I’ll explain surgery descriptions of the fillings together with relations between the fillings and Milnor fibers of the normal complex surface singularity corresponding to $Y$.

• Laura Starkston _ University of California, Davis

Symplectic fillings for links of rational singularities with reduced fundamental cycle

De Jong and van Straten developed an equivalence between classifications of deformations of certain (sandwiched) normal surface singularities and picture deformations of curve singularities. We will discuss an analogue in the symplectic setting in the case of rational singularities with reduced fundamental cycle. This is a joint work with Olga Plamenevskaya.