EVENT DETAILS AND ABSTRACT

Title: Algebraic invariants in symplectic geometry (pre-talk)
Speaker: Nate Bottman
Speaker Info: USC
Brief Description:
Special Note:
Abstract:

Over the past three decades, symplectic geometers have constructed rich curve-counting invariants of symplectic manifolds. The chief example is the Fukaya category, which revealed a deep connection with algebraic geometry via Kontsevich's Homological Mirror Symmetry conjecture. I will begin by introducing the Fukaya category, as well as its precursor, Floer cohomology. Next, I will describe quilted Floer theory, which is a technology that relates curve-counting invariants of different symplectic manifolds. I will conclude by introducing witch balls, which are a type of quilted map that I use to systemically endow the Fukaya category with a functoriality property.