By the cobordism hypothesis, specfifying a (fully extended) Topological Field Theory (TFT) with target some higher category amounts to providing a sufficiently dualizable object therein. This paradigm allows one to recover, and generalize, many important TFTs of conceptual and physical significance (Crane-Yetter, Turaev-Viro, Reshetikhin-Turaev) whose construction previously relied on explicit combinatorics. The supply of such target higher categories is rather limited though; most examples either come as categories of categories, or as Morita categories of algebras (with bimodules as morphisms), and higher versions thereof. Thus understanding dualizability in these examples is of particular interest to field theorists. I will talk about work in progress with Claudia Scheimbauer and Will Stewart that resolves a conjecture of Lurie characterizing dualizability of an n-dimensional disk algebra, which is an object in the higher Morita (n+1)-category, in terms of factorization homology of that algebra over various handles. As I will explain, our results rely on a new framework of factorization/disk algebras over marked stratified manifolds, as recently developed by Eilind Karlsson in her thesis.
