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Speaker: Anne Shepler, University of North Texas

Title: Invariant Theory Mod p: Matrix Groups Acting on Polynomials

Abstract: Weyl states that Invariant Theory came into existence in the middle of the nineteenth century "like Minerva: a grown-up virgin, mailed in the shining armor of algebra, she sprang forth from Cayley's Jovian head". Invariant theory has since fallen in and out of fashion, and momentum now swings toward modular invariant theory: the study of polynomials invariant under a finite subgroup of GL(V) over a field of nonzero characteristic. We will discuss the differences between modular and classical invariant theory and then present some new results using the underlying arrangement of "reflecting" hyperplanes.

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