Title: Ideal Closure Operations in Prime Characteristic Rings
Abstract: In Noetherian rings of prime characteristic, the Frobenius endomorphism seems to control most of the data about the ring. In this talk, I will define several ideal closure operations in terms of Frobenius and discuss singularity types associated to them. Time permitting, I will discuss some recent joint work with Lance Edward Miller regarding F-nilpotent singularities in the graded setting. Only a background level of algebra at the undergraduate level will be assumed (e.g., the definition of rings, fields, ideals).