Title: Dualities and pivotality in categorical Morita theory
Abstract: Topological field theories (TFT's) assign invariants to manifolds in a coherent manner. These are of interest in areas such as representation theory and topological quantum computing. The theory of tensor categories is the natural mathematical framework for the study of TFT's. It turns out that under certain equivalence relation (Morita equivalence) tensor categories produce isomorphic state sum topological field theories. However, the construction of these invariants for oriented manifolds relies on a choice of pivotal structure (trivialization of the double-dual) and thus it is desirable to have a consistent Morita theory for pivotal categories. The goal of the talk is to present some recent results about the interaction of dualities and pivotal structures with the notion of Morita equivalence.