The Nilpotence Growth Theorem, and applications to dimensions of mod-p Hecke algebras

We will discuss a theorem about the annihilating behavior of certain
operators defined by linear recursions on the polynomial algebra
F_p[x]. Such operators capture algebraic properties of Hecke operators,
and this theorem has applications to dimensions of big mod-p Hecke
algebras, generalizing recent work of Nicolas and Serre on the case p= 2.