Higher Categorical Structures from 3D Topological Field Theories

I will survey recent advances in the classication of extended topological eld
theories, with a particular focus on dimension three. I will describe recent work
(joint with B. Bartlett, C. Douglas, and J. Vicary) giving an explicit "generators
and relations" classication of partially extended 3D TFTS (assigning values
only to 3-manifolds, surfaces, and 1-manifolds) and the relationship between this
presentation and modular tensor categories. Time permitting, this will be compared
to the fully-local case (which has been considered in joint work with C. Douglas
and N. Snyder).