In this seminar we will familiarise ourselves with the ideas and several results in the mathematical field of topological quantum field theories (TQFTs). These are an active field of research in mathematics and physics, and ideally participants would get to a point where they can understand and appreciate current problems in this area. We will start by reviewing the mathematical basics (manifolds, monoidal categories) and the physical motivation for TQFTs (the path integral), before studying TQFTs formally. Generally, TQFTs translate gluing relations between manifolds into algebraic data, and one of our main goals will be to understand and classify various flavours of TQFTs. We will thereby learn more about both sides of this translation. Finally, at the end of the semester we will have one or two talks surveying advanced topics that lead on to current research topics. Our main reference are the lecture notes by Pavel Safronov.
Please contact me by email if you might be interested.
Organisational
Prerequisits
Having taken a course on "Topology" and "Algebra" is recommended.
Familiarity with the notions of a manifold and their smooth maps, as well as with the notions of a category, functor, and natural transformation would be beneficial.
(If necessary, you could read up on these before the semester start.)