Preface: Volume 81

Abstract

ForewordThe main mathematical disciplines that have been used in theoretical computer science are discrete mathematics (especially, graph theory and ordered structures), logics (mostly proof theory for all kinds of logics, classical, intuitionistic, modal etc.) and category theory (cartesian closed categories, topoi etc.). General Topology has also been used for instance in denotational semantics, with relations to ordered structures in particular.Recently, ideas and notions from mainstream "geometric" topology and algebraic topology have entered the scene in Concurrency Theory and Distributed Systems Theory (some of them based on older ideas). They have been applied in particular to problems dealing with coordination of multi-processor and distributed systems. Among those are techniques borrowed from algebraic and geometric topology: Simplicial techniques have led to new theoretical bounds for coordination problems. Higher dimensional automata have been modelled as cubical sets with a partial order reflecting the time flows, and their homotopy properties allow to reason about a system's global behaviour.This workshop aims at bringing together researchers from both the mathematical (geometry, topology, algebraic topology etc.) and computer scientific side (concurrency theorists, semanticians, researchers in distributed systems etc.) with an active interest in these or related developments.It follows the first workshop on the subject "Geometric and Topological Methods in Concurrency Theory" which has been held in Aalborg, Denmark, in June 1999. Then came GETCO'00 in Pennstate, USA, GETCO'01 in Aalborg, Denmark, all associated with CONCUR. This time, GETCO'02 was associated with DISC'02 in Toulouse, as these geometric methods are also applied successfully in the realm of distributed systems.The Workshop has been financially supported by GdR CNRS "Algorithmique, Langage et Programmation" and "Architecture, Réseaux et Systèmes, Parallélisme" and the Basic Research Institute in Computer Science (Aarhus, Denmark), and I thank these institutions for this, and more specifically Christiane Frougny and Luc Bougé. I also wish to thank the referees, the authors and the programme committee members for their very precise and timely job. Many thanks are also due to Michael Mislove who kindly supported the workshop by letting us submit the papers through the Electronic Notes in Theoretical Computer Science. Last but not least, I wish to thank the DISC organizers, in particular Gérard Padiou and Anne-Marie Zerr, for making this possible.