Title: Extended Topological Quantum Field Theories and Turaev--Viro invariants.

Abstract: We will give an overview of recent developments in TQFT, namely extending the theory from cobordisms to manifolds with corners of arbitrary codimension, following works of Baez and Lurie. We will also give an illustration of such an extended theory for 3-manifolds, called Turaev--Viro theory.