Title: Dieudonné theory: from classical to modern

Abstract: Dieudonné theory gives a classification in terms of “semi-linear algebra” of finite flat commutative group schemes of p-power order over a perfect field of characteristic p > 0. Over the years, Dieudonné theory has evolved in many forms (crystalline, prismatic) and recently V. Drinfeld has proposed various “Shimurian” generalizations of the theory. I will give an introduction to and overview of some of this history and more recent developments.