5 problems

Pointwise Weyl-law improvement conjecture. There exists a quantifiable constant $\kappa>0$ such that, for every $x\in K_\varepsilon$,

Sharp bandwidth conjecture. The main projector estimate should hold for

Let $S$ be a polynomial surface of revolution, and let $p(t)$ be its associated polynomial. A proper real polynomial parametrization is a real polynomial map that parametrizes $S$…

Grand uniqueness conjecture. The genus-$g=0$ or $1$ Canham problem with any isoperimetric ratio constraint $v_0\in(0,1)$ has a unique solution up to homothety. Moreover: (i) for…

Let $N\geq 2$, and let $p$ be a trigonometric polynomial of degree $N$ with coefficients $a_N,b_N$ satisfying $a_N\ne 0$ or $b_N\ne 0$. Let $f\in\mathbb{R}[x,y,z]$ be the defining…