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 using mathematical models for topological quantum field theory (such as the functorial axioms of Atiyah-Segal or the theory of E_n -algebras) is not always possible. In this talk Ill 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 with Pavel Safronov.

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