Time: 16:00-17:00, August 16

Venue: Lecture Hall

Abstract: Perverse filtrations emerge naturally in the context of the relative Hard Lefschetz theorem which concerns the relative Hodge theory associated with a proper map. Over recent years, they have played a crucial role in the study of integrable systems, enumerative geometry, knot invariants, and geometric representation theory. In this talk I will discuss two conjectures where perverse filtrations come into play surprisingly. The first is the P=W conjecture by de Cataldo, Hausel, and Migliorini, which concerns cohomological aspects of non-abelian Hodge theory. The second is the Oblomkov-Rasmussen-Shende conjecture which relates algebraic geometry of a planar singularity and the topological invariants of the corresponding link. I will discuss recent developments and new techniques in these stories.