Complex geometry of hyperbolic manifolds and bounded domains in Cn. Groups of automorfisms of bounded domains in Cn. One-parameter semigroups of holomorphic endomorphisms of the unit ball, thel polydisk, the Cartan domains of di type IV.
Complex geometry of unbounded domains in Cn. One-parameter groups of holomorphic automorphisms of C2. Spaces of square-integrable entire functions with respect to a given weight in C, Cn and C*. Multiplication operators on generalized Bergman spaces.
Quaternionic geometry. S-regular functions of quaternionic variable. Hardy spaces of s-regular functions. *-Exponential of an s-regular function. S-regular functions which preserve one or several slices.
Applications of geometry to technology and art. Multifield theories for complex bodies with microstructure. Analysis of art works (paintings, poems) by means of geometry techniques as a tool for the composition of musical pieces.