Topological Quantum Field Theory
Noah Snyder
Indiana University, Bloomington
Abstract: Topological quantum field theories are algebraic invariants of n-manifolds which can be computed via cutting-and-gluing. This can be formalized a symmetric monoidal functor of higher categories from a bordism category to an algebraic category. First we will introduce ordinary TQFTs and their classification in 1 and 2 dimensions. Next we will discuss extended TFTs and discuss 210 and 321 field theories and their relationship to modular tensor categories and Reshetikhin-Turaev field theories following Bartlett–Douglas–Schommer-Pries–Vicary. Finally, we will discuss the Baez–Dolan–Hopkins–Lurie cobordism hypothesis and its relationship to Turaev–Viro 3-2-1-0 topological field theories in joint work with Douglas–Schommer-Pries.
Problem session
In charge of Nicolás Escobar
Indiana University, Bloomington