3 problems

Let $p$ be prime, let $k\geq 3$, and let $A\subseteq\mathbb{F}_p^n$. Let $\mathrm{NFOP}_k$ denote the absence of the higher-order functional order property, and let a degree-$k$ fa…

Strength–analytic-rank conjecture. Strength is bounded by a constant multiple of analytic rank:

Let $f:\mathbb{F}_p^n\to\mathbb{C}$, and let $\|f\|_{U^3}$ be the Gowers uniformity norm of order three. A quadratic character here means a quadratic phase function of the form…