A geometric realization of affine hecke algebras - lecture 1

The goal of these lectures is to explain a geometric realization of affine Hecke algebras using equivariant K-theory of Steinberg variety discovered by Kazhdan-Lusztig and Ginzburg. We will start by basic properties of the Springer resolution and Steinberg varieties as well as a brief introduction of equivariant K-theory. Then we will explain the geometric realisation of affine Hecke algebras. Finally, we will explain how this was used to obtain the Deligne-Langlands classification of irreducible modules for affine Hecke algebras.