On the geometric P=W conjecture
Organizers
Pengfei Huang
,
Tao Su
, Hao Sun
Speaker
Mirko Mauri
Time
Wednesday, May 8, 2024 3:30 PM - 4:30 PM
Venue
A3-2-303
Online
Zoom 242 742 6089
(BIMSA)
Abstract
The geometric P = W conjecture is a conjectural description of the asymptotic behaviour of a celebrated correspondence in non-abelian Hodge theory. In a joint work with Enrica Mazzon and Matthew Stevenson, we establish the full geometric conjecture for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus: this is the first non-trivial evidence of the conjecture for compact Riemann surfaces. To this end, we employ non-Archimedean, birational and degeneration techniques to study the topology of the dual boundary complex of certain character varieties.