Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Description

The perverse filtration plays a crucial role in the study of the topology of the Hitchin system; for example, in the (now proven) P=W conjecture, the perverse filtration for the Hitchin system describes the weight filtration of the character variety of the surface group via the non-abelian Hodge theory. For an algebraic curve with locally planar singularities, the perverse filtration for the compactified Jacobian of this curve is more mysterious. It was conjectured (by Oblomkov, Rasmussen, Shende, Gorsky …) that this “local” perverse filtration behaves similar to that of a Hitchin system, and is related to knot invariants. In this talk I will discuss some recent progress on structures of the perverse filtration associated with compactified Jacobians, where a Fourier transform plays a key role. I will discuss both the local case (the compactified Jacobian associated with a locally planar singularity), and the global case (the universal fine compactified Jacobians over the moduli space of stable curves). Applications and open questions will be discussed. Based on joint work with Davesh Maulik and Qizheng Yin.