Factorization algebras in Representation theory

Factorization algebras, algebraic objects describing the observables of a field theory, can be used to construct TQFTs.

 

For example, some factorization algebras with values on categories can be used to the construct the (2,1)-part of the Turaev-Viro 3D theory, or the (3,2)-part of Crane-Yetter theory 4D theory.

 

In this talk we will discuss the first step into a "categorified" analogue of the previous results. Concretely, we consider the description of locally constant factorization algebras with values on bicategories, and discuss examples of such algebras arising from categorification in representation theory.