Geometry Seminar: Morse index stability for Yang-Mills connections

Abstract
We investigate Morse index stability for a sequence of Yang-Mills connections on closed 4-manifolds under bubble-tree convergence. As critical points of a conformally invariant energy, Yang-Mills connections share close ties with harmonic maps in various aspects. Simultaneously, their analysis is simpler as long as we work in an appropriate gauge, the so-called Coulomb gauge. Motivated by applications in constructing non-stable solutions of the Yang-Mills equations, this work extends recent methods developed by Da Lio-Gianocca-Rivière for index stability to the Yang-Mills framework, using sharp decay estimates to prove that the neck regions account for a positive contribution to the second variation.