5 problems

Let $d\geq n$, let $\Sigma\subset\mathbb{R}^{d+n}$ be a smooth $d$-dimensional submanifold, and let $\mathcal{T}(\Sigma)$ be its Fourier restriction trapezoid. Let $\mathcal{T}_0$…

Let $\mathbf{Q}$ be a quadratic manifold, and let “well-curved” and “best Stein–Tomas” denote the geometric and Fourier-analytic conditions defined in the paper. Best Stein–Tomas c…

Let $F_1(\xi),\dots,F_{d-n}(\xi)$ be quadratic homogeneous polynomials on $\mathbb{R}^n$, and let their graphs over an open ball $\Omega\subset\mathbb{R}^n$ define an $n$-dimension…

Let $fbf{Q}(fxi)=(Q_1(fxi),\ldots,Q_n(fxi))$ be an $n$-tuple of real quadratic forms in $d$ variables, and let … For a rectangle $B\subset[0,1]^d$, call $f$ adapted to $B$ if…

Let $X\subset {\mathbb P}^N$ be a quadratic manifold of dimension $n$. Small-degree complete-intersection conjecture. If … then $X$ is a complete intersection, unless it is project…