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

Posted in

- Talk [1]

Speaker:

Andrey Lazarev
Affiliation:

University of Lancaster/MPIM, Bonn
Date:

Tue, 2020-01-28 14:00 - 15:00 Koszul duality is a phenomenon that shows up in rational homotopy theory, deformation theory and other subfields of algebra and topology. Its modern formulation is due to the works of Hinich, Keller-Lefevre and Positselski. It is a certain correspondence between categories of differential graded (dg) algebras and conilpotent dg coalgebras; there is also a module-comodule level version of it. In this talk I explain what happens if one drops the condition of conilpotency on the coalgebra side; the consequences turn out to be quite dramatic. I will show how this non-conilpotent (or global) version of Koszul duality comes up naturally in the study of derived categories of complex algebraic manifolds and infinity local systems on topological spaces. Time permitting, I will also explain how one can construct a global version of deformation theory for certain deformation problems based on this approach. This is joint work with Ai Guan.

**Links:**

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

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

[3] https://www.mpim-bonn.mpg.de/node/5312