Type: Seminar

Modified: Thu 20 Feb 2020 1459

Distribution: World

Expiry: 28 Feb 2020

CalTitle1: Maxim - Vanishing cycles and applications, Part I

Calendar2: 28 Feb 2020 1500-1700

CalLoc2: Quad S224

CalTitle2: Maxim - Vanishing cycles and applications, Part II

Auth: romanova@10.17.126.222 (arom8272) in SMS-WASM

In the first part, I will introduce vanishing cycles from a topological perspective, using the topology of complex hypersurface singularity germs as a motivation. The second part will be devoted to applications: (a) I plan to show how vanishing cycles can be used to compute the Euler characteristic of a complex projective hypersurface with arbitrary singularities; (b) I will briefly explain Beilinsonâ€™s gluing of perverse sheaves via vanishing cycles; (c) I will indicate how vanishing cycles can be used to categorify Donaldson-Thomas invariants; (d) If time permits, I will explain how motivic characteristic classes for vanishing cycles can be used in birational geometry to detect jumping coefficients of multiplier ideal and to characterize rational or du Bois singularities.