Topology Seminar (Main Talk): Fully extended twisted field theories

Seminar | March 1 | 4:10-5 p.m. | 3 Evans Hall

 Claudia Scheimbauer, Max Planck

 Department of Mathematics

After recalling functorial field theories I will explain a natural generalization thereof, called "twisted" field theories by Stolz-Teichner and closely related to Freed-Teleman's "relative" boundary field theories. A natural target for such a twisted field theory is the higher Morita category of algebras, bimodules, and intertwiners, and generalizations. Using the Cobordism Hypothesis, we will see some simple examples. Then I will explain a family of examples arising from "topological'' factorization algebras, which essentially are $E_n$-algebras (algebras for the little disks operad). Examples include (homotopy) algebras, but also braided monoidal categories such as the category of finite dimensional representations of a reductive algebraic group $\text {Rep}G$ or of the associated quantum group $\text {Rep} U_q(g)$. This is based on joint work with Calaque, Gwilliam, and Johnson-Freyd.