Character theory of fusion systems

Fusion systems are a generalisation of finite groups designed in a way to capture local structure at a prime motivated by the existence of "exotic" fusion systems; local structures that do not appear in any finite group. In this talk I will give a brief introduction to fusion systems with emphasis on how they relate to groups. I will then discuss recent work done on fusion invariant character theory, concluding with a short excursion into biset functor theory to state a character value formula for "induction" between fusion systems and a Frobenius reciprocity analogue.