Logic Seminar: Sum product phenomenon in fields with dimension, by Yuyan He
March 3, 2026
3:00 PM - 3:50 PM
Yuyan He (University of Notre Dame): Sum product phenomenon in fields with dimension
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.
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Date posted
Mar 9, 2026
Date updated
Mar 9, 2026
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