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Perverse filtrations and the P=W conjecture

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Speaker: 
Zili Zhang
Affiliation: 
Stony Brook U./MPIM
Date: 
Thu, 2017-06-08 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar
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 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.

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