Regular functions of a quaternionic variable with applications

The recent notion of quaternionic slice regularity has identified a new class of functions which can play the role of holomorphic (and meromorphic) functions in the quaternionic setting. The talk will present the main basic features of slice regular functions over the quaternions, as well as some of their most curious applications, including those concerning the study of orthogonal complex structures on subsets of the quaternionic space H.