About this Event
Piotr Suwara -- Monopoles and Exotic 4-Manifolds
Abstract:
In early 80’s, Donaldson stunned the mathematical world by proving results about smooth manifolds that seemed out of reach at that time, for instance, the existence of topological 4-dimensional manifolds with no smooth structure. He did this by studying moduli spaces to certain PDEs, coming from gauge theory, to develop invariants of smooth 4-manifolds that were sensitive to the underlying smooth structure.
In ’94, Witten introduced what we now call the Seiberg-Witten invariants, coming from a different flavor of gauge theory. These turned out to be much more computable than Donaldson's invariants and led to new results in smooth 4-manifold topology. I will sketch how one can use them to prove the existence of families of 4-dimensional smooth manifolds which are homeomorphic but not diffeomorphic to each other (so-called “exotic” smooth manifolds).