Quasiconformal mappings, elliptic PDE's and Beltrami operators

Quasiconformal mappings are closely connected to elliptic PDE's. In the plane the Beltrami operators provide an efficient and systematic tool to study and apply these relations. I will describe the basic aspects of Beltrami operators with recent applications to PDE's. The applications include solution to a question of Pucci on equations of nondivergence type, QC Young measures, regularity of isotropic equations (work of Faraco). If time permits also recent applications to inverse problems are discussed.