4 problems

Dynkin's conjecture. Every compact set $S\subset {\bf R}^{n}$ carries a non-trivial doubling measure $\mu$.

Let $E^n$ be $n$-dimensional Euclidean space, and consider superintegrable systems whose integrals of motion are differential operators of order at most two. The Montreal conjectur…

Let $E^n$ denote $n$-dimensional Euclidean space, and consider quantum superintegrable systems on $E^n$ whose integrals of motion have differential order at most two. The Montreal…

Critical-volume conjecture. For $m\leq m_{*}$, the ball of volume $m$ uniquely minimizes $\mathcal{E}(\cdot)$ among measurable sets $F\subset\mathbb{R}^n$ with $|F|=m$, and for…