Speaker: Xueqing Wen (Chongqing University of Technology)
Time: 14:30-15:30, Oct 15, 2026
Venue: room 1329, Building 1 (Section A), New Campus of USTC Shanghai Institute for Advanced Studies & Tencent Meeting ID: 942 663 0176, password: 202501
The Hitchin fibration equips the cohomology of Higgs bundle moduli spaces with a perverse filtration. TheP=W conjecture predicts that this filtration is compatible with cup product, a property that does not hold for general projective morphisms. In this talk, I will present a proof of multiplicativity for the canonical SL_n Hitchin system in arbitrary rank, over a smooth projective complex curve of genus at least two, with fixed determinant of degree coprime to the rank. I will begin by reviewing the Fourier-transform approach of Maulik–Shen–Yin to the perverse filtration for compactified Jacobian fibrations. I will then explain how to adapt this approach to compactified Pryms, highlighting the new ingredients required in the SL_n setting. Two difficulties arise: the dual fibration is naturally a quotient stack, and the Hitchin direct image has contributions supported on proper endoscopic loci. Addressing these requires a Fourier-correspondence formalism for quotient stacks and a comparison between Fourier projectors and the endoscopic correspondence. This comparison replaces the full-support argument in the compactified Jacobian case and identifies the Fourier filtration with the perverse filtration over the elliptic locus of an auxiliary twisted Hitchin system.
