turkmath.org

In this talk, we outline a general framework for geometric field theories formulated by Ludewig and Stoffel. In brief, functorial field theories (FFTs) can be formalized as certain functors from an appropriate bordism category Bord to a suitable target category. Atiyah's topological field theories and Segal's conformal field theories are the two important examples of such formulation. Given an FFT, one can also require the source category to endow with a ''geometric structure''. Of course, the meaning of ''geometry'' must be clarified in this new context. To introduce geometric field theories in an appropriate way, therefore, we first explain how to define ''geometries'' using the language of stacks, and then we provide the so-called geometric bordism category GBord. Finally, we give the definition of a geometric field theory as a suitable functor on GBord.