Discoveries / combinatorics

The Near-Quadratic Elekes-Ronyai Expander Conjecture

The near-quadratic Elekes-Ronyai expander conjecture over $\mathbb{R}$ predicts that a nonspecial polynomial expands any finite set to near-quadratic size. False: a fixed nonspecial quadratic polynomial, together with arbitrarily large finite sets of real algebraic integers, has image with a fixed power saving from quadratic size.