# Opening workshop of the ANR project HighAGT @ Institut Henri Poincaré (IHP)

Koszul duality is a powerful theory that can be used – among other things – to produce resolutions of algebras. Usual Koszul duality applies to quadratic algebras, i.e., algebras equipped with a presentation where relations are all quadratic. As soon as relations involve linear and especially constant terms, the theory becomes more involved: the Koszul dual of an algebra is not a mere coalgebra anymore, but a curved coalgebra. In this talk, I will explain how curved Koszul duality can be generalized to algebras over unital binary quadratic operads, based on ideas developed by Millès and Hirsh–Millès. I will then apply this theory of n-Poisson algebras in order to compute factorization homology of universal enveloping n-algebras of Lie algebras.