### Abstract

Rational Cherednik algebras were introduced five years ago as degenerations of Cherednik's double affine Hecke algebras. They have a very rich representation theory which has found applications in many areas including combinatorics, invariant theory, algebraic integrable systems, algebraic symplectic geometry, Lie theory.

In this talk we will discuss new connections between representations of Cherednik algebras (category O), the combinatorics Hecke algebras of finite Coxeter groups, and the geometry of Nakajima quiver varieties. This is a small first step towards a (noncommutative) geometric picture of the representation theory of these algebras.