A glimpse into Koszul duality for factorization algebras

A fundamental technique in mathematics is to start with an object we understand and deform it to produce a new object with more interesting behavior. Trying to formalize this process leads to the rich fields of deformation theory and Koszul duality. A natural place to apply this technique is to study QFTs, in particular the factorization algebra formalism. Deformation theory and Koszul duality of locally constant factorization algebras is well understood and has remarkable geometric interpretations in terms of configuration spaces of manifolds and Poincaré duality. In this talk, we extend some of the known results on Koszul duality for locally constant factorization algebras to general factorization algebras in an attempt to develop a setting to study deformations of factorization algebras.