Robert Fraser

Large Sets Avoiding Polynomial Configurations

A 2017 result of Andr\'as M\'ath\'e states that, given any degree $latex d$ polynomial $latex p : \mathbb{R}^{nv} \to \mathbb{R}$ with rational coefficients, there is a subset $latex E \subset \mathbb{R}^n$ of Hausdorff dimension $latex \frac{n}{d}$ that does not contain any $latex v$ distinct points $latex x_1, \ldots, x_v$ such that $latex p(x_1, \ldots, x_v) = 0$. We discuss a version of this result that applies when the coefficients of $latex p$ are assumed only to be algebraic over the rational numbers.

Robert Fraser is a postdoc at the University of Edinburgh. He did his PhD at the University of British Columbia.