SFB-Sondervortrag: V-filtration and vanishing cycles

Abstract: Vanishing cycles capture the topology of singularities. V-filtrations are the algebraic counterpart of vanishing cycles. In the first part of the talk we will present a survey on these two related topics, with applications ranging from birational geometry, Hodge theory, arithmetic, and Donaldson-Thomas theory. In the second part, we will present a recent conjectural extension of the relation between vanishing cycles and V-filtration based on the geometry of local systems.