9 problems

Let $P_n(z)$ be the orthonormal polynomials associated with the Jacobi operator, and let the asymptotic formulas for $P_n(z)$ have coefficients as in the complex spectral asymptoti…

Critical energy conjecture.

Osserman's conjecture. If $(M,g)$ is an Osserman metric, then the group of local isometries acts transitively on $S(M)$; equivalently, $(M,g)$ is flat or locally rank-one symmetric…

Let $V$ be a finite-dimensional real vector space, let $\langle\cdot,\cdot\rangle$ be a non-degenerate symmetric bilinear form on $V$, and let $A$ be an algebraic curvature tensor.…

Assume that $a_n=1/2$ for all $n$ and, up to sufficiently rapidly decaying terms, $b_n=\kappa n^{-\varrho}$, where $\varrho<2$ and $\kappa>0$. Let $\tau(\lambda)$ denote the spectr…

Hansmann–Katriel conjecture. The inequality above is no longer true when the assumption that $J$ is self-adjoint is dropped. The conjecture concerns the extension of Lieb–Thirring…

Kullback–Leibler divergence conjecture. The Kullback–Leibler divergence is related to weak properties of the connection coefficient matrix $C$, in a manner suggested by the regular…

Let $(\beta,A_\epsilon^E)$ be an analytic almost periodic Jacobi cocycle, and suppose that its determinant is bounded away from zero. Almost reducibility conjecture for Jacobi cocy…

Failure conjecture. The displayed inequality is not true for non-selfadjoint Jacobi operators.