Title: Approximation of Sobolev mappings into metric spaces

Abstract: The theory of Sobolev mappings between manifolds and metric spaces has been a subject of an intense research for the past two decades. In the talk I will review the classical results and the recent development about approximation of Sobolev mappings by smooth and Lipschitz mappings and I will show how it applies to calculus of variations, geometry of sub-Riemannian manifolds and algebraic topology. The talk will not be technical and should be of interest to anyone familiar with the basic theory of manifolds.