The goal of the special research period is to bring together experts of different Universities in order to achieve strong synergetic effects in training young Ph.D and PostDoc, focusing on fundamental problems in Complex and Real Geometry. The period will be characterized by a series of miniconferences, basic and advanced lectures and seminars.

The subjects that will be focused during the research period are:

** Trascendental methods in algebraic geometry: vanishing theorems for positive bundles, Hodge conjecture by L2 methods, positive currents
** Geometry and analysis of convexity in complex analysis
** Almost complex manifolds, generalizations, CR-structure
** Variations of the Levi problem on singular spaces
** Kobayashi hyperbolicity
** Real and complex dynamics
** Geometric and differential properties of subanalytic sets, global semianalytic sets, metric properties of semialgebraic sets
** Isotopy types of real algebraic curves and surfaces; algebraic invariants, Betti numbers, algebraic cycles in surfaces
** Rings of analytic functions, sums of squares, positive functions. The 17 th Hilbert problem for noncompact analytic manifolds
** Real algebraic structures on polyhedra, finiteness of the number of algebraic structures on a complex variety
** Real holomorphy ring and Schmüdgen's theorem, cones of positive polynomials Pythagora's numbers, complexity
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