Georgia Institute of Technology College of Sciences

For the last four decades, mathematicians have used the Frobenius map to investigate phenomena in several fields of mathematics including Algebraic Geometry. The goal of this talk is twofold, first to give a brief introduction to the study of singularities in positive characteristic (aided by the Frobenius map). Second to define an explain the constancy regions for mixed test ideals in the case of a regular ambient; an invariant associated to a family of functions that shows a Fractal behavior.