8 problems

Let $\mathcal C$ be a proper closed convex subset of $\mathbb R^2$ with positive Lebesgue measure. Assume that $\operatorname{Op}^w(\mathbf 1_{\mathcal C})$ is a bounded self-adjoi…

Bounded spectrum conjecture for convex bodies. One has

Logarithmic polygon-spectrum conjecture. The sequence $(\mu_N^+)_{N\ge2}$ is increasing, and there exists $\alpha>0$ such that

Let $E$ be an anisotropic paraboloid in $\mathbb R^{2n}$ equipped with its canonical symplectic structure, and let $\mathbf 1_E$ denote its indicator function. Anisotropic-parabolo…

Let $E$ be an ellipsoid in $\mathbb R^{2n}$ equipped with its canonical symplectic structure, and let $\mathbf 1_E$ denote its indicator function. Flandrin's ellipsoid conjecture.…

Let $n\ge1$, $\alpha=(\alpha_1,\dots,\alpha_n)\in\mathbb N^n$, and $a=(a_1,\dots,a_n)\in(0,+\infty)^n$ be as in the Laguerre-integral conjecture, and let $K_\alpha(a)$ denote the c…

Laguerre-integral lower-bound conjecture. Assuming $0<a_{1}\le\dots\le a_{n}$, one has

Let $C$ be a convex subset of the plane, and let $\mathbf 1_C^w$ denote the Weyl quantization of its characteristic function. Uniform spectral-bound problem. Does there exist a con…