11 problems

For compact Lagrangians $L,L'$ in a symplectic manifold $(M,\omega)$, let $B(L,L')$ be the supremum of the numbers $r a 0$ for which there exists a symplectic embedding … satisfyin…

Two-set p-capacity factorisation conjecture.

IIC hitting conjecture.

Let $A$subseteq$\mathbb Z^d$ be finite, and let the p-capacity of $A$, denoted by $\operatorname{pCap}(A)$, be the capacity introduced in the paper. Let…

Let $\Theta$ be a finite frame, and let $\mathcal{M}^2$ denote the space of 2-monotone capacities on $\Theta$. This space is embedded in a Cartesian space of the same dimension as…

Let $\{Y_n;n\ge1\}$ be independent and identically distributed random variables in a sub-linear expectation space, and let $T_n=\sum_{i=1}^nY_i$ and $d_n=\sqrt{2n\log\log n}$. Writ…

Let $\{X_{n,i};i=1,\ldots,k_n\}$ be an array of independent random variables in the sub-linear expectation space $(\Omega,\mathscr{H},\widehat{\mathbb E})$ with … Let $x_n$ be a se…

Nonpositivity conjecture. At least for all pseudo-polarised toric surfaces,

Algebraic Weyl law.

Let $d\geq 2$, let $0<s<d$ with $s\notin\mathbf{N}$, and let $E\subset\mathbf{R}^d$ be compact. For a gauge $\Phi$, let $\operatorname{cap}_{\Phi,s}(E)$ denote the associated nonli…

Let $d$ be the ambient dimension, let $s$ be an integer with $1\leq s\leq d$, and let $\Sigma_\varphi$ be the class of nonnegative Borel measures $\mu$ on $\mathbb R^d$ satisfying…