6 problems

Let $k\geq 2$. Let $S_1,\ldots,S_k\subseteq\mathbb{R}^{d}$ be smooth hypersurfaces equipped with measures $\sigma_1,\ldots,\sigma_k$, respectively. They are transversal if there is…

Let $U_{1},U_{2},U_{3}\subset U$ be a $\nu$-disjoint triple of squares, meaning that each has side length comparable to $\nu$ and distinct squares are separated by at least $\nu$.…

Let $0<\delta\leq\nu<1$. Three families $\mathbb{T}_{1},\mathbb{T}_{2},\mathbb{T}_{3}$ of $\delta$-tubes are $\nu$-disjoint when their orientations lie in spherical patches of diam…

Multilinear restriction conjecture. Under these assumptions, there is a constant $C$, depending on finitely many derivatives of the $\Sigma_i$, the sets $U_i$, $\nu$, and $n$, such…

Let $(\mathbf{L},\mathbf{p})$ be a Brascamp–Lieb datum with finite Brascamp–Lieb constant $\mathbf{BL}(\mathbf{L},\mathbf{p})$. For each $1\leq j\leq k$, let…

Let $S_1,\ldots,S_d$ be transversal smooth codimension-one submanifolds of $\mathbb{R}^d$, with induced measures $d\sigma_j$. Let $p'$ be the Hölder conjugate of $p$. Strengthened…