The 2007 theme semester "Recent Advances in Combinatorics" taking place at the Centre de recherches mathématiques in Montréal, from January to June 2007, will focus on three main areas:
Interactions between Algebraic Combinatorics, Algebraic Geometry and Representation Theory, with an emphasis on the study of subjects such as the Cohomology of Schubert Varieties, Hilbert Schemes, Gromov-Witten Invariants, and their ties with Symmetric Functions such as Macdonald Polynomials, as well as problems of enumerative geometry in the real, complex and tropical contexts.
Algebraic Aspects of Combinatorics on Words, focussing on their natural links to the study of Free Groups, Free Fields, Free Lie Algebras or to fine properties of Continued Fractions in relation to the study of Artin's Billiards and Real Quadratic Fields.
Relations between Enumerative Combinatorics and Statistical Physics, particularly the use of enumeration techniques for the study of gas models, Ising and Potts models, etc., with the specific purpose of computing phase transitions or thermodynamic limits.
There will be a total of five main workshops and four major schools to introduce junior mathematicians to the most recent developments in these areas. A mini-workshop will inaugurate the semester in mid January. The schedule is then organized to have two more intensive periods of activities, one from mid February to mid March, and one from early May to mid June.