Symplectic geometry and Khovanov homology

Khovanov homology is a power tool in the study of knots and links. There are many different approaches of Khovanov homology. As for this talk, we will mainly be interested in a version from symplectic geometry, called symplectic Khovanov homology. It is conjecturally isomorphic to Khovanov homology. In 2020, Abouzaid and Smith proved this conjecture over characteristic-zero fields, while the more general cases remain open. In this talk, we will discuss some recent progress on the conjecture.