Matthew Gursky, University of Notre Dame

Title: Gap and index estimates for some conformally invariant problems in dimensions 2 and 4

Abstract: In this talk I want to discuss sharp 'gap' estimates for the energy of Yang-Mills
connections in 4-d, and the related question of the energy of harmonic two-spheres.
I will also talk about index estimates for Yang-Mills connections and Einstein metrics in 4-d.