Past lectures

Abstract

We begin by reviewing generalities on classical and quantum integrable systems and Hamiltonian reduction. Then we consider Calogero-Moser systems. In particular, we prove their classical and quantum integrability for any root system using Dunkl operators, and also show how to obtain them by Hamiltonian reduction in type A. We then consider the representation theoretic side of the story - rational Cherednik algebras (more generally, symplectic reflection algebras) and the deformed Harish-Chandra homomorphism. We discuss representation theory of rational Cherednik algebras.

Then we consider "relativistic" versions of the above - Ruijsenaars-Schneider (Macdonald) integrable systems, Macdonald polynomials, Dunkl-Cherednik-operators, Cherednik's double affine Hecke algebras, relation between Macdonald polynomials and quantum groups. Finally, we look at the connection between Cherednik algebras and algebraic geometry of Calogero-Moser spaces and Hilbert schemes.

The first three lectures will be given by G. Felder.