4 problems

Let $P\subset\mathbb F_q^d$ be the paraboloid. Suppose that $d=4k-1$ for some $k\in\mathbb N$ and that $-1\in\mathbb F_q$ is not a square. Sharp paraboloid extension conjecture. On…

Let $q=|\mathbb F_q|$, and let $P\subset\mathbb F_q^d$ be the paraboloid … Write $R_P^*(p\to r)\lesssim1$ for the uniform finite-field extension estimate. Critical endpoint conject…

Let $q=|\mathbb F_q|$, and let $P\subset \mathbb F_q^d$ be the paraboloid … Write $R_P^*(p\to r)\lesssim 1$ when the finite-field extension operator for $P$ is bounded from…

Let $n\ge 3$, and let $S_1$ and $S_2$ be smooth compact non-empty subsets of the paraboloid in ${\mathbf{R}}\times{\mathbf{R}}^{n-1}$ whose unit normals are separated by at least a…