A topological field theory (TFT) with particles exhibits distinguished state spaces, where the incoming and outgoing particles match. These "endo-state spaces" occur naturally in physical applications and possess interesting mathematical structures: There is a natural gauge action by conjugation and a natural stabilization map. We will show that the gauge action has a non-trivial orbit structure, leading to quiver moduli spaces, and the stabilization map leads to a treatment of infinite particle content and AF-algebras.

The talk will be rather introductory and assumes no knowledge of quivers or AF-algebras.