Time: 5:00PM – 6:30PM
Location: Wean 8220
Title: VC-density, dp-rank, and op-dimension.
Abstract: I talk about my recent work joint with Cameron Hill on various notions of rank and dimension in NIP theories. I begin with a discussion of dp-rank and it’s relation to VC-density. I show that dp-rank and VC-density over indiscernible sequences coincide in the natural way. Then, I talk about the notion of op-dimension, which is a new rank related to both dp-rank and Shelah’s 2-rank. I show that op-dimension bounds dp-rank, is subadditive, and generalizes dimension in o-minimal theories.