Elekes and Rónyai have characterized real bivariate polynomials which have a small image over large Cartesian products. Besides being an interesting problem in itself, the Elekes-Rónyai setup, and certain generalizations thereof (such as those considered by Elekes and Szabó), arise in many Erdős-type problems in combinatorial geometry and additive combinatorics. In the talk I will give some overview of this topic, and then tell about a recent result (joint with J. Zahl) in which cardinality of a finite set is replaced by either the δ-covering number of a set, or its Hausdorff dimension.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
