The topic of the conference is words, i.e. finite or infinite sequences of symbols taken from a finite alphabet. Both combinatorial, algebraic and algorithmic aspects are looked for, as well as applications. The applications can be motivated by practice (e.g. biocomputing, cryptography) or by theory (e.g. tools for other fields of mathematics).
Combinatorics on words is a relatively new field in mathematics. It is active, pushed forward by challenging open questions and links with several fields of applications.
How to trace back its origins? We have tried with Jean Berstel to do it (The origins of Combinatorics on Words, European J. Combinatorics, 28, 2007, 996-1022). The most accurately identified ancester is certainly Axel Thue, in the sense that he was probably the first one to be interested in words for their own, independently of any interpretation of the symbols or their sequences. He wrote in the introduction of his second paper in 1912 "For the development of logical sciences it will be important, without consideration forpossible applications, to find large domains for speculations about difficult problems. In this paper, we present some investigations in the theory of sequences of symbols, a theory which has some connections with number theory."
Earlier occurrences of properties of words can of course be found in algebra, number theory and topology. To name a few, the coding of closed curves by words was studied by Gauss in 18th century (the so-called Gauss codes) and is now used as a representation of knots. As another example, the Thue-Morse sequence is today considered to have been discovered in 19th century by Eugène Prouhet in connexion with a problem in number theory. More recently, the solution by Adjan of Burnside conjecture on periodic groups uses cube-free words. So perhaps the question could be formulated differently: why are words so ubiquitous? The reason is probably that words are nothing else than sequences and that taking sequences of elements from a given set is certainly the most elementary thing to do. It actually reflects the linear nature of speech itself, as put forward by Saussure as a fundamental aspect of natural language.
So the Words conference has good object of study. It was M.P. Schützenberger's opinion that the problems on words were reminiscent of the beginning of number theory: they are often very simple to formulate and extremely difficult to solve. The solution in the last years of Dejean's conjecture is a good example of the truth of this assertion.
Previous WORDS conferences have taken place as follows: