3 problems

Let $M^n$ be a complete Riemannian manifold, let $\Omega\subset M^n$ be a bounded domain, and let $\lambda_k$ denote the Dirichlet eigenvalues of the operator $\mathcal{L}$ from Pr…

Let $\beta>0$, and let the Gaussian beta ensemble G$\beta$E have joint density … Let $t^n_{k,\beta}$ be its $k$-th smallest gap. Small-gap conjecture. There exists a constant…

Triangular fundamental-gap conjecture.