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Abstract: At its most elementary level, algebraic geometry deals with the geometry of zero sets of polynomials. The work of Hilbert, Zariski, Weil and Grothendieck laid the foundation for an elegant theory that treats both geometric and number theoretic questions. In the last ten years, a collection of prime characteristic techniques have been developed in order to study questions geometric questions. I'll describe some recent applications of these techniques to two important areas of research in algebraic geometry: invariant theory and Mori's programme.