Speaker
Alexia Yavicoli, University of British Columbia
Abstract
Let \(E\subset \mathbb{R}\) be a measurable set of positive Lebesgue measure. A simple argument using a density point shows that \(E\) contains a translated and rescaled copy of every finite subset of \(\mathbb R\). What happens if we replace a finite set by an infinite one? Erdős conjectured that the answer changes completely: for every infinite set \(A\subset\mathbb{R}\), there should be a measurable set \(E\) of positive measure that contains no translated and rescaled copy of \(A\). I will introduce this conjecture, explain some of the ideas surrounding it, and discuss recent progress toward its resolution.