Irina Markina: On geometrical background of the Yang-Mills theory

In the talk we present a geometric viewpoint on the Yang - Mills theory. Yang - Mills theory is a generalization of classical electromagnetism. Yang-Mills equations is a generalization of Maxwell's equations (in vacuum). The circle group which embodies the phase factor in Maxwell theory is generalized to a non-abelian compact Lie group G such as SU(2) or SU(n), in general. The non-abelian nature of G leads to non-linearity for the Yang-Mills equations. We will describe links between this theory and principal G-bundles. We also discuss geodesic equations and the structure of geodesics viewed as geodesics on non-holonomic manifolds.