Abstract

The geometric P=W conjecture is a conjectural description of the asymptotic behaviour of acelebrated correspondence in non-abelian Hodge theory. in a joint work with Enrica Mazzon andMatthew Stevenson, we establish the full geometric conjecture for compact Riemann surfaces ofgenus one, and obtain partial results in arbitrary genus: this is the first non-trivial evidence of theconiecture for compact Riemann surfaces. To this end, we employ non-Archimedean, birational anddegeneration techniques to study the topology of the dual boundary complex of certain charactervarieties.