4 problems

Generic non-optimality conjecture. The set of edge-length vectors and values $M>0$ for which the constant potential minimizes the spectral gap in $C_{T,M}$ is of the first Baire ca…

Lavine's conjecture. The constant potential minimizes the fundamental gap among all convex potentials, and

Cutoff conditional-expectation conjecture. Under these assumptions, something similar to the conditional-expectation theorem should hold, perhaps after restricting to a smaller ope…

Let $V(\mathbf{x})\in C^2(\mathbb{R}^n)$ satisfy … where $0<\gamma_1\le\gamma_2$, and let $I_n$ be the $n\times n$ identity matrix. Set $\gamma=\gamma_1$ and…