Research topics

The main research areas are in the field of Algebraic Geometry, and there are some researches in the area of Complex Analysis.
We summarize their topics in the following:

  • Classification problems for projective varieties. It deals with the three main classes of projective varieties, namely curves, surfaces and higher dimensional varieties. In the last case special emphasis is on the so called Mori theory (or Minimal Model Program) with important results for the cases of dimension 4 and 5. In the case of surfaces the main object of study is the moduli spaces of minimal surfaces of general type. Finally, the geometry of algebraic curves is investigated both from the perspective of Brill-Noether theory and from the point of view of moduli theory.
  • Special algebraic varieties (e.g. Fano manifolds, Moishezon manifolds, almost homogeneous manifolds, symplectic manifolds).
  • Vector bundles and related problems.
  • Real algebraic geometry: topology of real algebraic sets, algebraic structures on manifolds and on Nash sets (existence and moduli)
  • Complex and Hypercomplex analysis: quaternionic functions and Clifford analysis, theory of slice-regular functions on real alternative algebras, applications of the theory of slice-regular functions to functional analysis on quaternionic Hilbert spaces and on hypercomplex Banach spaces.