Inequalities among sums of dilates

Abstract: Let $c \cdot A$ denote the dilate of the set $A$ by the scalar $c$. For which choices of complex numbers $\lambda_1, \ldots, \lambda_\ell, \mu_1, \ldots, \mu_m$ does the inequality $$|\lambda_1 \cdot A+\cdots+\lambda_\ell \cdot A| \leq |\mu_1 \cdot A+\cdots+\mu_m \cdot A|$$ hold for all finite sets $A \subseteq \mathbb{C}$? This question captures a vast generalization of the more-sums-than-differences sets phenomenon. We will discuss recent progress, with a particular focus on the setting where the dilates are integers.

commutative algebracombinatoricsnumber theory

Audience: researchers in the topic

New York Number Theory Seminar

Series comments: Meeting ID: 840 6618 4717 Passcode: 304403