Carə tuttə,
Vi scrivo per annunciarvi che questo giovedì 9 Dicembre 2021 vi sarà un seminario in presenza per il ciclo di seminari "Seminario di Combinatoria, Teoria di Lie e Topologia” di Pisa. Il seminario si svolgerà in Aula Seminari dalle 15 alle 16. L'oratrice è Giovanna Carnovale (Università di Padova).
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Titolo: Approximations of a Nichols algebra from a geometric point of view
Abstract: The talk is based on an ongoing joint project with Francesco Esposito and Lleonard Rubio y Degrassi.
Nichols (shuffle) algebras are a family of graded Hopf algebras (in a braided monoidal category) which includes symmetric algebras, exterior algebras and the positive part of quantized enveloping algebras. They are crucial in the classification of (pointed) Hopf algebras. However, it is very difficult to describe their relations or to estimate their dimensions in general and new tools are very welcome. We will exploit an equivalence due to Kapranov and Schechtman between a category of graded bialgebras in a braided monoidal category V and the category of factorizable systems of perverse sheaves on all symmetric products Sym^n(C) with values in V. I will describe the factorizable perverse sheaves counterpart of some algebraic constructions, including the n-th approximation of a graded bialgebra. Since the image of Nichols algebras through Kapranov and Schechtman equivalence is very precise, we can translate into geometric statements when a Nichols algebra is finitely presented, or coincides with any of its approximations. —
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Sperando di vedervi numerosi, vi mando i miei saluti,
Francesco