# Multiple zeta values (7th April to 24th April, 2011)

Very few results are known on the diophantine properties of the values of the Riemann zeta function at positive odd integers. It is generally expected that all these numbers are algebraically independent over the field $Q(\pi)$. To prove that there is no non--trivial algebraic dependence relation looks like a very hard problem. One may expect to attack this question by considering a more general situation, which amounts to linearize the problem: namely to study the linear relations among the so--called multiple zeta values. It turns out that these numbers satisfy many linear dependence relations, giving rise to a very rich algebraic structure, which has been studied extensively during the recent years. This course will be an introduction to this vast topic. Among the tools is the theory of algebraic combinatorics.