Current Developments in Mathematics
Hecke algebras and $p$-adic groups
Pages: 73 – 135
This survey article, is written as an extended note and supplement of my lectures at the Current Developments in Mathematics conference in 2015. We discuss some recent developments on the conjugacy classes of affine Weyl groups and $p$-adic groups, and some applications to Shimura varieties and to representations of affine Hecke algebras.