Abstract: Mod p Hecke algebras play an important role in the mod p Langlands program. We will explain a mod p version of the geometric Satake isomorphism which gives a sheaf-theoretic description of the unramified mod p Hecke algebra. We will also construct central elements in the Iwahori mod p Hecke algebra by adapting a method due to Gaitsgory. Our methods give geometric proofs of identities in mod p Hecke algebras originally due to Henniart, Herzig, Vignéras, and Ollivier. Time permitting, we will also mention further results in the unramified case in joint work with Pépin. We will begin by reviewing background material on affine flag varieties and the function-sheaf dictionary.