Representations of $p$-adic groups and affine Hecke algebras

The representation theories of $p$-adic groups and affine Hecke algebras are closely related. In this talk, I will explore how the representation theory of affine Hecke algebras provides valuable tools for studying the representations of $p$-adic groups, with a particular emphasis on the case of $\mathrm{SL}_2$.