Unitary topological field theory

Hybrid. Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)

I will start by reviewing the original definition of a topological field theory by Atiyah and his ideas on incorporating unitarity. This leads us to the notion of a dagger category, which is notorious for being 'evil', i.e. ill-behaved under equivalences. I will explain my joint work with Jan Steinebrunner giving us a 'non-evil' way to understand what dagger categories are in terms of an abstract notion of a 'Hermitian pairing on an object of a category'. Returning to the world of differential geometry, I will highlight some subtleties that arise when defining Hermitian pairings on objects of bordism categories of spin manifolds.