Geometric representations of graded and rational Cherednik algebras

From the Weyl group of a complex reductive algebraic group one can construct the graded Cherednik algebra and the rational Cherednik algebra, which were first introduced by Etingof and Ginzburg in 2002 as degenerations of Cherednik's double affine Hecke algebras. The representation theory of these algebras is very rich and has links to many different areas of mathematics. I will discuss the geometric methods used by Oblomkov and Yun to construct certain families of finite-dimensional representations of graded and rational Cherednik algebras, building on a well-known result from Springer theory.