Andrew Roberts (University of Leeds) – An introduction to Harmonic Maps

Harmonic Maps between Riemannian Manifolds are some of the most widely studied maps in Geometric Analysis. They appear as critical points of the Dirichlet Energy Functional, perhaps the simplest functional between Manifolds one can write down. They can also be viewed as generalisations of Harmonic Functions which I will introduce and discuss some of their remarkable properties. Then I will go on to generalise to Harmonic Maps and discuss some of the problems that arise from them.