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, Gian-Carlo 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.

Coordinator:

Christian KRATTENTHALER Tel : (43)-1-427750643 Fax : (43)-1-427750620 e-mail :

Institut Girard Desargues Université Claude Bernard Lyon-I 21, avenue Claude Bernard F-69622 Villeurbanne Cedex FRANCE

Work programme

The main themes of research of the network are:

Post- and pre-doctoral 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 pre-doctoral 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.

Activities of the network

Contract : HPRN-CT-2001-00272.