Orateur
Martin Ulirsch
Description
Let X be a complex abelian variety. In this talk we will explain and prove an analogue of both the (cohomological) P=W conjecture and the geometric P=W conjecture relating the topology of the Dolbeault moduli space of topologically trivial semistable Higgs bundles on X and the Betti moduli space of characters of the fundamental group of X. The geometric heart of our approach is a new kind of Hitchin fibration for Dolbeault moduli spaces on abelian varieties whose target is not an affine space of pluricanonical sections, but a suitable symmetric product. This is based on ongoing joint work with B. Bolognese and A. Küronya
