The Caloron Correspondence: Instantons, Monopoles, and String Classes

The instanton is a solution to the self-dual Yang-Mills equation on a 4 dimensional manifold.  The Caloron Correspondence refers to the observation that when these solutions are periodic with respect to time, then they are related to monopoles on a related 3 manifold.  More recently, a relation between the string classes of these manifolds through the Caloron Correspondence was discovered.  In this talk, I will discuss some of the historical background for the Caloron Correspondence as well as its relation with string structures.  I will also discuss potential extensions of this correspondence to higher structures and differential cohomology.