Slice regular functions over the quaternions. Geometric function theory, function spaces of slice-regular functions and operators, Carleson measures. *-Exponential of a slice regular function, slice regular functions preserving one or several slices.
Quaternionic differential geometry. Geometry of the unit ball of the quaternions and of other alternative algebras. Zeros and ideals of slice regular polynomials in several variables, slice algebraic varieties.
Complex geometry of hyperbolic manifolds and bounded and unbounded domains of C^n. Automorphism groups of bounded domains of C^n. Hilbert spaces of holomorphic functions of one and several complex variables and operators acting on them, Carleson measures, discrete potential theory. Complex and CR structures on flag configuration spaces.
