The main theme of most of our objectives is analytic convexity.
We want to study convexity properties of coverings of 1-convex complex manifolds. The Shafarevich conjecture asks to decide if the universal covering of a projective manifold is holomorphically convex. We will consider an analogue of Shafarevich conjecture for coverings of 1-convex quasi-projective surfaces. We would like to decide if a covering of a 1-convex surface has the discrete disk property.
We intend also to study the separation of the cohomology groups with coefficients in a coherent sheaf of coverings of 1-convex manifolds. We would like to produce a series of examples in this framework.
We plan to consider complex manifolds on which global holomorphic functions separate points and give local coordinates and decide if they are open subsets of Stein singular spaces.
We will study the dynamics of holomorphic endomorphisms of the n-dimensional complex projective space and also the ergodic properties of measures obtained as limits of sequences of certain distributions with dynamical significance or with certain good invariance properties.
Expected results: we expect to obtain results regarding the above mentioned problems. We would like to publish at least 6 papers in well-known journals.