The EUROCORES (European Collaborative Research) scheme is a unique framework offered by the European Science Foundation (ESF) to promote collaborative research, networking and dissemination while targeting broad and complex topics of research across all scientific domains at the European level and in a global context. In 2009 Eurocores selected 7 topics, including EuroGIGA, out of 70 submissions, and in 2010 launched a call for proposals for collaborative research projects (CRP).

EuroGIGA, the first program to date on mathematics within the Eurocores program, focuses on graphs in Geometry and Algorithms. Geometric graph and hypergraph structures are at the core of Discrete and Computational Geometry, and simultaneously, they are a crucial tool in many applications. In June 2010 five CRPs have been selected to develop EuroGIGA, among them ComPoSe. It focuses on combinatorial properties of discrete sets of points and geometric graphs, and consists of coordinated projects in several countries, leaded by Oswin Aichholzer (Austria), Jean Cardinal (Belgium), Stefan Felsner (Germany), Ferran Hurtado (Spain), János Pach (Hungary), Pavel Valtr (Czech Republic), and Emo Welzl (Switzerland).

The goal at CIEM in May 2011 is to constitute a strong European group to attack in a joint effort one of the central topics of ComPoSe, the Erdős‐Szekeres problems on convex subsets. We will investigate specific variants of this famous class of problems, such as colored versions, and use newly developed techniques to advance on this topic. Recent progress on these and other Erdős‐Szekeres type problems has been made by ComPoSe members. Thus, by coordinating the scattered efforts, this activity will contribute to consolidate the existing and partially fragmentary knowledge on these structures. It possibly will bring back the fruits of this research to more applied algorithmic analysis and to other branches of mathematics which are based on these fundamental questions.