In this seminar we present some new results about Yang-Mills connections proved in collaboration with Aaron Naber. In particular, we prove that given a stationary Yang Mills connection with finite energy, there is a uniform $L^1$ bound for its hessian in the interior of the domain. In turn, we also prove the energy quantization conjecture.
The results are based on the quantitative stratification technique and summability estimates for the hessian on annular regions carried out using harmonic gauges. The results are available at arXiv:1610.02898.