
Algebraic Combinatorics in Europe(ACE)(September 1, 2002  August 31, 2005) 





Project overview When a variety of fields meets combinatorics The origins of Algebraic Combinatorics lie in the desire to advance combinatorial theory from the state as a ``bag of various, isolated tricks" (as it is often seen) to an organised body of algebraic theories that bring order into seemingly disorder. Of course, GianCarlo Rota's name has to be mentioned here. He started this development by the introduction of the theory of Möbius functions, and the systematical use and development of umbral calculus in the 60's and 70's. Since then many more algebraic theories have evolved and are still being developed, e.g., theory of "species" and "generatingfunctionology", combinatorial representation theory, symmetric functions and tableau calculus, combinatorial topology (to mention just a few), bringing increasing insight in and understanding of combinatorial structures. Today, Algebraic Combinatorics concerns itself with the study of combinatorial problems arising from other branches of mathematics and, on the other hand, with the application and use of techniques coming from other parts of mathematics to combinatorial problems. At the heart of the subject there is the development of algebraic theories for the solution of such problems. The implied interactions with other fields are mutually beneficial and concern particularly Coxeter Groups, Group Representations, Commutative Algebra, Algebraic Geometry, Topology, Computer Science, and Statistical Mechanics. Partnership 8 working groups from 6 countries with a wealth of expertise across many fields It is the aim of the project to develop tools for attacking and solving various intriguing problems at the interface of Combinatorics, Algebra, Geometry, Computer Science, and Statistical Mechanics, by linking different working groups in some european and associated countries.
Work programme The main themes of research of the network are:
Post and predoctoral positions The "Algebraic Combinatorics in Europe" network is sponsored by the European Commission's current programme for "Research Training Networks". In this framework, it is offering post and predoctoral positions at each of its associated nodes, as part of its initiative to foster research in central subjects of this active domain of mathematical research. The network organizes or cosponsors the 15th International Conference on "Formal Power Series and Algebraic Combinatorics" and several summer schools. The famous Séminaire Lotharingien de Combinatoire provides a basis for regular network meetings. 





This network is a Research Training
Network of the European Community, under the programme
Improving Human Potential and the SocioEconomic Knowledge BaseContract : HPRNCT200100272. 