Title: Arithmetic field theories

Abstract:
In a series of recent papers, Minhyong Kim defined an arithmetic analogue of topological Chern-Simons theory. In this talk, I will give an introduction to arithmetic field theories, focusing at first on arithmetic Chern-Simons theory. I will then proceed by defining a new arithmetic field theory, developed in joint work with Minhyong Kim, and give some ideas on why this construction could be arithmetically interesting.