### Italian Representation Theory Seminar

**Giovanna Carnovale, University of Padova**

*Approximations of a Nichols algebra from a geometric point of view*

Organizer's time: 2021-04-09 15:00 Europe/Rome

Duration: 1 hour

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The talk is based on work in progress with Francesco Esposito and Lleonard Rubio y Degrassi. Recently Kapranov and Schechtman have settled an equivalence between the category of graded connected co-connected bialgebras in a braided monoidal category and the category of factorizable systems of perverse sheaves on all symmetric products with values in . The Nichols (shuffle) algebra associated with an object corresponds to the system of intersection cohomology extensions of a precise local system on the open strata. Motivated by the study of Fomin-Kirillov algebras and their relation with Nichols algebras, we describe the factorizable perverse sheaves counterpart of some algebraic constructions, including the n-th approximation of a graded bialgebra, and we translate into geometric statements when a Nichols algebra is quadratic.

Submitted by: Andrea Appel