Claudia Scheimbauer "Higher categories, factorization homology, and fully extended TFTs"

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.