Alex Bullivant, Univ. Leeds, UK
A categorification of the tube algebra
Starting from the data of an $(n+1)$-dimensional state-sum TQFT, to each $(n-1)$-manifold we can associate a so-called tube algebra whose modules admit a physical interpretation as topological excitations in the theory. In this talk I will first introduce the tube algebra before describing an appropriate categorification. Such categorified tube algebras associate to each $(n-2)$-manifold a $2$-algebra and we propose an interpretation of the module theory in terms of excitations in the theory pinned to gapped boundaries.