Abstract Mirko Mauri

Mirko Mauri will speak on

P=W conjectures for singular character varieties

Abstract: Character varieties parametrise representations of the fundamental group of a curve. They are in general singular moduli spaces, and for this reason it is customary to shift attention to smooth analogues, called twisted character varieties. The P=W conjecture formulated by de Cataldo, Hausel and Migliorini posits a relation between the Hodge theory of twisted character varieties and the geometry of some holomorphic Lagrangian fibrations. We explore P=W phenomena in the untwisted and singular case. We show that the P=W conjecture holds for character varieties which admit a symplectic resolution, namely in genus 1 and arbitrary rank, and in genus 2 and rank 2. I will also discuss new numerical evidence of P=W phenomena in higher genus, when no symplectic resolution exists. This is in part a joint work with Camilla Felisetti.