The scientific topics discussed during this research school approved by CIMPA were Complex Geometry and their Applications. The objective was an introduction to recent developments in complex multi-variable geometry (with analytical concepts such as positivity, currents, pluri-sub-harmonicity and operators of Lelong-Poincaré and Monge-Ampère, etc.) in various directions: the holomorphic dynamics into several complex variables, the deformation of complex geometrical structures into "tropical" structures, the toric geometry and its relation to the real convex geometry, and finally the transposition to the real framework of concepts until then inherent in the complex framework (pluri-sub-harmonicity, operator of Monge-Ampere, positive currents, Lelong-Poincaré or Monge-Ampère equations); the questions of diophantine geometry (heights of schemes or arithmetic cycles, theory of the arithmetic intersection or Arakelov, the theory of pluri-potential in the framework non-Archimedean) were also be mentioned.

The report (in French) can be found here.