### Italian Representation Theory Seminar

**Lucien Hennecart, Université de Paris-Saclay**

*Perverse sheaves with nilpotent singular support for curves and quivers*

Organizer's time: 2021-06-11 15:00 Europe/Rome

Duration: 1 hour

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Perverse sheaves on the representation stacks of quivers are fundamental in the categorification of quantum groups. I will explain how to prove that semisimple perverse sheaves with nilpotent singular support on the stack of representations of an affine quiver form Lusztig category and how to extend this question to quivers with loops. The analogous question for curves is to determine perverse sheaves on the stack of coherent sheaves whose singular support is a union of irreducible components of the global nilpotent cone. We solve this problem for elliptic curves, for which we also show that the characteristic cycle map induces a bijection between simple Eisenstein spherical perverse sheaves and irreducible components of the global nilpotent cone. This constitutes a step towards the understanding of the degree zero part of the cohomological Hall algebra of a curve.

Submitted by: Andrea Appel