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SUMMARY:Joost Nuiten (Université de Montpellier)
DTSTART:20200811T114500Z
DTEND:20200811T124500Z
DTSTAMP:20260423T004139Z
UID:operad/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/operad/8/">M
 oduli problems for operadic algebras</a>\nby Joost Nuiten (Université de 
 Montpellier) as part of operad pop-up\n\n\nAbstract\nA classical principle
  in deformation theory asserts that any formal deformation problem over a 
 field of characteristic zero is classified by a differential graded Lie al
 gebra. This principle has been described more precisely by Lurie and Pridh
 am\, who establish an equivalence between dg-Lie algebras and formal modul
 i problems indexed by Artin commutative dg-algebras. I will discuss an ext
 ension of this result to more general pairs of Koszul dual operads over a 
 field of characteristic zero. For example\, there is an equivalence of inf
 inity-categories between pre-Lie algebras and formal moduli problems index
 ed by permutative algebras. Under this equivalence\, permutative deformati
 ons of a trivial algebra are classified by the usual pre-Lie structure on 
 its deformation complex. In the case of the coloured operad for nonunital 
 operads\, a relative version of Koszul duality yields an equivalence betwe
 en nonunital operads and certain kinds of operadic formal moduli problems.
  This is joint work with D. Calaque and R. Campos.\n
LOCATION:https://researchseminars.org/talk/operad/8/
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