Zili Zhang will speak on

Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces

Abstract: Given a proper morphism between algebraic varieties, the rational cohomology groups of the source are endowed with the perverse filtration. In this talk, I will introduce five families of Hitchin systems which are Hilbert schemes of points on surfaces. I will discuss why the perverse filtrations associated with these five families of Hitchin maps are multiplicative. The same method works for Hilbert schemes of points of elliptic K3 surfaces. I will also discuss the connection between the multiplicativity of the perverse filtration and the P=W conjecture for reductive groups.