Claudia Scheimbauer (ETH)
Higher categories, factorization homology, and fully extended TFTs
Factorization algebras, first introduced by Beilinson and Drinfeld in an algebro-geometric context, are algebraic structures encoding the structure of observables of a quantum field theory. (Homotopy) algebras and (pointed) bimodules over them can be viewed as factorization algebras on the real line $\mathbb R$ which are locally constant with respect to a certain stratification. Moreover, drawing upon tools from higher algebra, Lurie proved that locally constant factorization algebras on $R^n$ are equivalent to $E_n$-algebras. Starting from these two facts I will explain how to model the Morita category of $E_n$-algebras as an $(\infty, n)$-category. Every object in this category, i.e. any $E_n$-algebra $A$, is "fully dualizable" in the sense of Lurie and thus gives rise to a fully extended TFT by the cobordism hypothesis of Baez-Dolan-Lurie. I will explain how this TFT can be explicitly constructed by (essentially) taking factorization homology with coefficients in the $E_n$-algebra A.