6 problems

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.…

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

Let $\mathcal{B}(\mathbb{R}^2)$ be the state space, let $\mathcal{N}$ be the set of pairs $\alpha=(\widehat{u},\widehat{v})$, and let $\widehat{H}^{(\alpha)}$ be the corresponding…

Let $D_\epsilon$ be an $epsilon$-dependent family of density matrices, with Husimi function…

Mustard's conjecture. In the case of $R^2$, Mustard conjectured that