Victor Roca i Lucio: A new approach to formal moduli problems

Abstract:

The celebrated Lurie—Pridham theorem states that infinitesimal deformations are encoded by dg Lie algebras, over a characteristic zero field. “Infitesimal deformations” are here made precise via the notion of a formal moduli problem. Since then, this theorem has been generalized in many directions. Nevertheless, these generalizations rely on variations of the initial arguments proposed by Lurie. The goal of this talk is to explain a new framework for formal moduli problems, using methods coming from operadic calculus. This allows us to fully characterize when formal moduli problems of some type of algebras are equivalent to their Koszul dual algebras, over a field of any characteristic. And it will give us a new proof of the celebrated Lurie—Pridham theorem, as well as of many of its generalizations. This is joint work with Brice Le Grignou.