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Koszul duality and deformation theory

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Andrey Lazarev
Fri, 2020-03-13 09:30 - 10:30
MPIM Lecture Hall

Koszul duality between Lie algebras and cocommutative coalgebras constructed by Hinich is the basis for formal deformation theory, at least in characteristic zero.  In this talk I explain, following Manetti, Pridham and Lurie, how Koszul duality, combined with Brown representability theorem from homotopy theory leads to representability of a formal deformation functor up to homotopy. Sometimes a formal deformation functor has a `noncommutative structure', meaning that it is defined on a suitable homotopy category of associative algebras. In this case there is a similar representability result, valid in an arbitrary characteristic. I will also discuss a generalization of this noncommutative representability theorem to the non-local case.

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