The purpose of this CIME summer school was to present current areas of research arising both in
the theoretical and applied setting that involve fully nonlinear partial different equations.
The equations presented in the school stem from the fields of Conformal Mapping Theory
Differential Geometry Optics and Geometric Theory of Several Complex Variables. The school
consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca
Capogna Fully nonlinear equations in geometry by Pengfei Guan Monge-Ampere type equations and
geometric optics by Cristian E. Gutiérrez and On the Levi Monge Ampere equation by Annamaria
Montanari.
