Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Andrey Lazarev
Affiliation:

Lancaster/MPIM
Date:

Fri, 2020-03-13 09:30 - 10:30 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/10152