Generalized Springer theory and harmonic analysis of $p$-adic groups

The classical Springer theory and the generalized Springer theory initiated by Lusztig have an application in describing the characters of finite reductive groups in terms of (perverse) sheaves. We shall give a quick introduction to Springer theory from this point of view. After that, we discuss a possible upgrade to $p$-adic groups using recent generalization of generalized Springer theory by Lusztig and Yun.