The Cauchy problem for the Yang-Mills equations on the Minkowski spacetime

Abstract: 

In this talk I aim to give a brief introduction to the Yang-Mills equations, which can be viewed as the counterpart of the Maxwell equations for a non-abelian transformation group. Unlike the Maxwell equations, however, the Yang-Mills equations are non-linear, and non-trivial to solve. I will talk about the Cauchy problem, which presents some subtleties due to the gauge invariance of the equations, and in particular I will focus on the global regularity question.