Pure Maths Colloquium: Orit Raz

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

Where: Zoom 862 5811 6194
When: Apr 22 2021 @ 16.00
Video: Not recorded
Speaker: Orit Raz The Hebrew University of Jerusalem
Title: Expanding polynomials and the discretized Elekes-Rónyai theorem

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 \(delta\)-covering number of a set, or its Hausdorff dimension.