5 problems

The restriction conjecture for the sphere. This estimate should hold when

Let $\mathcal E(n)$ be the projected lattice points on $S^2$, and let $N_n$ denote their number. The covering radius $M(P_1,\dots,P_N)$ of a configuration on $S^2$ is the least…

Let $\mathcal E(n)$ be the projected lattice points on $S^2$, let $N_n$ be their number, and let $\sigma$ denote normalized spherical area. For a spherical cap or annulus…

Let $S^{2n+1}$ denote the $(2n+1)$-dimensional sphere, with $n$ a positive integer. Sasaki–Einstein metric abundance conjecture. There are infinitely many families of Sasaki–Einste…

Let $(S^n,g,\operatorname{vol}_g)$ satisfy $\operatorname{Ric}_g\geq\rho g$ with $\rho>0$, and let $g^\rho_{\mathrm{can}}$ be the canonical metric on $S^n$ rescaled so that…