Equivariant hermitian K-theory and a periodicity result for C_2-L-theory

Hermitian K-theory is the subject pertaining to studying the moduli space of modules equipped with quadratic forms and has many deep relations to, for instance, number theory and manifold theory. Recently, this theory has been given a very flexible and powerful unified treatment by a set of nine authors, building on ideas of Ranicki and Lurie, among many others. In this talk, I would like to give a brief introduction to this work and then discuss an enhancement to the equivariant setting for finite groups G. As an application, I will indicate how one can use said enhancement to deduce a new periodicity result for L-theory when G is the cyclic group of order 2.