4 problems

Bessis–Itzykson–Zuber conjecture. The logarithm of the normalized partition function has an asymptotic expansion

Let $d\mu_\textbf{t}$ be a unitary-ensemble measure with partition function $\widetilde{Z}_N(\textbf{t})$, and let $\textbf{t}$ denote the coefficients of the external potential. T…

Genus expansion conjecture. In the large-$n$ limit, $\mathcal G_N^{(n)}$ should have, in some sense, an asymptotic expansion in inverse powers of $n^2$ of the form

Good-basis conjecture. Given a generic potential $V$ and a generalized path $\gamma$, such a good basis always exists, although it may not be unique.