Mathematisches Kolloquium Relative Serre Functors and Some of Their Applications

We present the notion of a relative Serre functor and exhibit its usefulness in algebra, quantum topology and low-dimensional quantum field theory. Specifically, we describe how trivializations of relative Serre functors are a prolific source of Frobenius algebras. We also explain that relative Serre functors provide a conceptual understanding of “modified traces” which recently appeared in quantum topology.

The talk requires only basic familiarity with notions from category theory. We will describe some applications to low-dimensional quantum field theories, but do not assume any knowledge of quantum field theory.