# Lie Theory for Complete Curved Strong Homotopy Associative Algebras

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Niek de Kleijn

created by lapastina on 11 Oct 2018

modified on 07 Jan 2019

23 oct 2018
-- 14:30

Sala Riunioni DipMat, Salerno

**Abstract.**

General deformation theory over a field of characteristic 0 has been formalized in terms of the Maurer-Cartan space of a strong homotopy Lie algebra (often a dgla). This was done through the works of many mathematicians, notably
Drinfeld, Kontsevich-Soibelman, Lurie, Manetti, Pridham, Deligne, Hinich and Getzler. The last three showed how to construct an infinity groupoid (Kan complex) modeling the moduli space of a deformation problem given a strong homotopy Lie algebra.
In this talk I will discuss the analogous case of constructing this moduli space in the case of a curved strong homotopy associative algebra. This is the first step in an attempt to generalize the work on deformation theory completely from characteristic 0 to arbitrary characteristic. As a specific example of such a deformation problem I will showcase the deformation theory of 1-morphisms over non-symmetric operads.