28. Okt 2021
On the geometric P = W conjecture
ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR
Datum: 28. Oktober 2021 |
Sprecher: Mirko Mauri, University of Michigan
The geometric P = W conjecture is a conjectural description of the asymptotic behavior 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.