In recent years new perspectives in valuation theory have begun to appear as well as unexpected applications. The two historical flows of valuation theory, namely the Henselian and the Zariskian, are merging like never before in the development of Berkovich geometry and the new approaches to resolution of singularities, which now extend to the singularities of vector fields. One begins to really be able to do analysis on spaces of of valuations, leading to important new results on complex analytic dynamical sytems stemming from a radically new point of view on the use of valuations of the ring of holomorphic functions. There is a new understanding of the structure of spaces of valuations with a given center, exemplified by the valuative tree of Favre-Jonsson, and also of the more global aspects for which tropical geometry gives useful hints. The purpose of the workshop is to gather experts who are contributing to this new perspective so that they can strengthen their common views and share problems and results.

Charles Favre, Mattias Jonsson, Daniel Panazzolo, Florian Pop, Mark Spivakovsky