9 problems

Let $A\subset\mathbb{F}_p^3$ satisfy … Recall the exceptional set $E_s(A)$ for projection to lines or planes. Let $t(a,s)$ be the lower bound for $T(a,s)$ given by Proposition 1 fo…

Let $T(a,s)$ denote the exponent governing the exceptional-set estimate, and let the lower bounds for $T(a,s)$ be those established in Propositions 1 and 2. Sharp bounds conjecture…

Let $A\subset \mathbb{F}_p^2$ satisfy … For $0<s<\max\{1,a\}$, let $E_s(A)$ be the exceptional set defined for projection to lines, with $n=1$ and $k=1$. The finite-field exception…

The exceptional-set projection conjecture. Then

Let $E\subset\mathbb{R}^d$ be a Borel set with $\dim_{\mathcal{H}} E\in(k-1,k]$, where $k=0,1,\dots,d-1$. For $y\in\mathbb{R}^d$, let $\pi^y(x)=(x-y)/|x-y|$ be the radial projectio…

Let $X$ be a smooth projective geometrically integral Fano variety over a number field, and set $L=-K_X$. For a thin map $f:Y\to X$ from a smooth projective geometrically integral…

Let $K\subset\mathbb{R}^{2}$ be a Borel set, and let $\pi_e\colon\mathbb{R}^{2}\to\mathbb{R}$ be the orthogonal projection $\pi_e(x)=x\cdot e$ for $e\in S^{1}$. Assume that…

Let $\Lambda=(\lambda_n)$ be the frequency sequence and let $L$ and $L^{-}$ denote the classes of auxiliary functions used in the paper. For $\varphi\in L$, define … Let $h$ be the…

Let ${\mathcal A},{\mathcal B}\subseteq {\mathbb N}$. Write $\overline{{\mathcal A}+{\mathcal B}}$ for the exceptional set associated with the sumset ${\mathcal A}+{\mathcal B}$, l…