UBC Algebra and Algebraic Geometry Seminar: Tom Graber

I will discuss how to formulate and prove a localization theorem for the virtual fundamental class of a moduli space with a relative perfect obstruction theory over a singular base. In the motivating example of the moduli space of stable log maps, I will explain how this leads to sums over types of tropical curves of cycle classes on moduli spaces of curves. Time permitting I will discuss some work in progress with Hu and Zaslow doing computations of counts on toric log K3 surfaces where we find agreement between these invariants and counts of constructible sheaves.