|Date: Wednesday, April 11, 2018
Location: 4096 East Hall (4:10 PM to 5:30 PM)
Title: Simpson correspondence and the P=W conjecture
Abstract: Given a compact complex curve, Simpson correspondence asserts that there exists a canonical diffeomorphism between the moduli space of representations of the fundamental group of the curve and the moduli space of Higgs bundles over the curve.The P=W conjecture predicts that via this (non-algebraic) diffeomorphism, the mixed Hodge structure and the perverse filtration correspond. In this talk, I will discuss how the multiplicativity of perverse filtrations and curious hard Lefschetz are related to the P=W conjecture. As concrete examples, 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.
Speaker: Zili Zhang