5 problems

Near-quadratic energy conjecture. If $A\subset\mathbb{R}$ is convex, then

Let $A\subset\mathbb{R}$ be a finite convex set, meaning that if $A=\{a_1<a_2<\cdots<a_k\}$, then … for every $1<i<k$. Erdős's conjecture. For every $\epsilon>0$, … This conjecture…

Let a state space be a convex set whose states admit spectral decompositions, and call it symmetric when any $n$-frame can be transformed into any other $n$-frame by an affine map…

Let $S$ be a finite-dimensional convex compact set that is spectral, meaning that all of its states have orthogonal decompositions with a common spectrum, and suppose that the symm…

Let $D$ be a convex set in the plane, and call a scaled and translated copy of $D$ without rotation a homothetic copy of $D$. Let $S$ be a finite set of points. The three-color hom…