The PIs are organizing a workshop at the Centre International de Rencontres Mathematiques in Luminy, September 1-5, 2008 on the subject of Representations of fundamental groups of surfaces. The conference will be organized around minicourses, covering the following topics:
(1) Hitchin's connection over Teichmueller spaces, conformal field theory, and the finite dimensional unitary representations of the mapping class group;
(2) Positive and tropical geometry of Teichmueller theory, higher Teichmueller-Thurston theory in the sense of Fock and Goncharov;
(3) Infinite-dimensional representations of mapping class groups arising through cluster algebras;
(4) Translation surfaces and moduli spaces of holomorphic quadratic differentials;
(5) Hyperbolic geometry and 3-dimensional Lorentzian conformal geometry.
This subject has been extremely active in recent years, with many connections opening up with mathematical physics, low-dimensional topology, dynamical systems, representation theory and algebraic geometry. This conference follows several conferences in related fields, although this one has a somewhat different focus. The PIs hope to bring together researchers from different fields, and many different parts of the world. The format of this conference will be inspired by that of the American Institute of Mathematics where a related workshop was held last year.
