Manuel Araújo, Instituto Superior Técnico
Topological Field Theory in dimension $3$

I will give an overview of some aspects of $3d$ TFT, from the Turaev-Viro and Reshetikin-Turaev invariants of oriented $3$-manifolds, to the more recent classifications of fully extended theories in terms of fusion categories and once extended theories in terms of Modular Tensor Categories.