Title: Geometric properties of nilpotent singularity types 

Abstract: In prime characteristic commutative algebra, the study of the Frobenius map dominates. In particular, the hierarchy of classical singularity types for prime characteristic local rings are universally given in terms of how ``nice" the Frobenius map and other maps induced by Frobenius can be, e.g. F-injective or F-pure rings. Of recent interest have been new singularity types where Frobenius can be particularly ``bad," and in this talk we will discuss recent work which helps explore the broader geometric context for F-nilpotent singularities