Myeonggi Kwon - Rigidity aspects of symplectic fillings

Abstract: Given a contact manifold, it is a fundamental question in symplectic topology in how many ways the contact manifold can be written as the boundary of a symplectic manifold. In this lecture, we discuss notable rigidity results on symplectic fillings of the standard contact spheres and their generalizations. In the first part, we mainly deal with a theorem by Eliashberg—Floer—McDuff asserting that exact symplectic fillings of the standard contact sphere are unique up to diffeomorphism type. The proof uses J-holomorphic curve theory manipulating a symplectic capping foliated by J-holomorphic spheres. In the second part, we discuss a Floer theoretic analogue due to Seidel—Smith: every Liouville filling of the standard contact sphere has trivial symplectic homology. A proof largely relies on index-positivity of contact manifolds and invariance of positive symplectic homology.

Sukjoo Lee - Sheaf theoretic property of wrapped Fukaya categories

Abstract: In a series of works, Ganatra, Pardon, and Shende establish a well-behaved theory of wrapped Fukaya categories for a certain class

of Liouville manifolds. Notably, these sheaf-theoretic properties highlight their effectiveness as computational tools, especially in higher-dimensional cases. In this lecture, I will introduce their work, with a focus on these sheaf-theoretic properties, and illustrate how they can be applied by computing a higher-dimensional example: the complement of a complexified hyperplane arrangement.

Youngjin Bae - Lagrangian fillings for Legendrian links

We introduce Legendrian links and their invariants of DGA and sheaf theoretic types. We discuss the relationship between Lagrangian fillings for Legendrian links and the above invariants. We also review how the cluster structure appears on the space of Lagrangian fillings.

Yoosik Kim - Geometric invariant theory quotient and symplectic reduction 

I will explain geometric invariant theory quotient, symplectic reduction, stability, and their connections between them.