In the first part of the talk I will motivate the Breuil--Mezard conjecture, which describes the geometry of moduli spaces of mod p Galois representations in terms of the representation theory of groups like GLn(Fq). In the second part I will explain how new cases of this conjecture can be proven by describing explicit subschemes inside the affine grassmannian whose geometry locally models the geometry of moduli spaces of Galois representations.