Topological Twists of Factorization Algebras

The idea of topologically twisting a supersymmetric field theory was introduced in the physics literature in order to generate interesting new examples of topological field theories.  The idea is very general, but systematically realising the examples it produces is not always possible using mathematical models for topological field theory (such as Atiyah-Segal's functorial field theory, or the theory of E_n-algebras).  In this talk I'll explain what it means to twist a supersymmetric field theory in the factorization algebra framework developed by Costello and Gwilliam, and address the question of just how topological these topologically twisted theories really are.  This is based on joint work in progress with Pavel Safronov.