URegina Topology Seminar: Martin Frankland

Topological quantum field theories (TQFTs) are one of several mathematical approaches to quantum field theory in physics. They were introduced by Atiyah in the 1980s. The cobordism hypothesis, proposed by Baez and Dolan in the 1990s, is a statement about a classification of TQFTs. It was proved by Hopkins and Lurie, with contributions from others.

I will present an overview of the cobordism hypothesis and related notions: cobordisms, TQFTs, low-dimensional examples, higher categories of cobordisms, and extended TQFTs. After the overview, I will introduce Atiyah's axioms for a TQFT.