Algebra/topology seminar

Speaker: Claudia Scheimbauer  (MPIM Bonn)

Title: (Twisted) field theories and factorization algebras

Abstract: After giving an introduction to functorial field theories I will explain a generalization thereof, called "twisted" field theories by Stolz-Teichner and closely related to Freed-Teleman's "relative" boundary field theories. Segal's weakly conformal field theories are examples thereof. A natural target for such a twisted field theory is the higher Morita category of algebras, bimodules, and intertwiners, and generalizations thereof. I will use this example to explain the concept of a higher category. The main tool will be the notion of a factorization algebra, which can be thought of as a multiplicative version of a cosheaf and which is an algebraic structure encoding the structure of the observables of a perturbative quantum field theory. Examples include (homotopy) algebras and (pointed) bimodules, but also braided monoidal categories such as the category of finite dimensional representations of a reductive algebraic group Rep G or of the associated quantum group Rep U_q(g), and, coming from topology, E_n-algebras, which are algebras for the little disks operad. Finally, I will sketch how twisted field theories and factorization algebras are related in the case of topological field theories.