Logic Seminar
Yuyan He
University of Notre Dame
Sum product phenomenon in fields with dimension
Abstract: A classical result of Ruzsa and Szemeredi shows that there is no subset A of the integers such that both the sumset A+A and the productset AA are small. Breuillard, Katz and Tao found a similar result for the subsets of finite prime fields of “medium size”. We show that under certain mild assumptions on a dimension theory , a “medium sized” subset of a field with small sumset and productset in the sense of not expanding in dimension indicates the existence of a subfield of the same dimension. This is joint work with Sergei Starchenko.
Tuesday March 3, 2026 at 3:00 PM in 636 SEO