3 problems

Log-optimal configurations conjecture. For all $k$ such that $2\leq k\leq d$, the set of all relative minima of $E_h$ consists of $k$ mutually orthogonal regular $d_i$-simplexes…

Universal optimality conjecture for lifted ETFs. The following configurations minimize the $p$-frame potential $\operatorname{FP}_{p,d+1,d}$: when $p\in(p_{k-1},p_k]$, the $L_k^d$…

Let $d$ be a positive integer, and let $[x]$ denote the greatest integer function. Consider configurations of $d+2$ points on the unit sphere $\mathbb{S}^{d-1}$, and let…