Laboratory of Algebraic Geometry Weekly Seminar: Ben Tighe (online)

Abstract: The Hodge theory of singular symplectic varieties has been studied over the past few years by Fu-Menet and Bakker-Lehn.  In particular, local Torelli makes it interesting to understand bounds on the 2nd Betti numbers. In this talk, we will investigate these uniform bounds for symplectic orbifolds using stringy Hodge theory.  We will also show that for a general symplectic 4-fold, $b_2$ is bounded by a number depending only on the singularities.  Time permitting, I will discuss some further work dealing with the intersection cohomology of primitive symplectic varieties.