5 problems

Weyl-law conjecture. A version of Weyl’s law should also apply to non-selfadjoint black-hole operators.

Consider problem and the transcendental complex-valued functions $\gamma_{\ell}(a,b,c,\lambda)$ associated with it. Suppose that parameters have been chosen so that…

Large-parameter positivity conjecture. There exists $y_1>0$ such that $\delta^T(y)>0$ on $[y_1,+\infty)$. The conjecture concerns the eventual monotonicity of the real part of the…

Let $D_m(b,V)$ be the Dirac operator from Assumption 1.1, with $V=\Phi W$, where $W$ is Hermitian of definite sign and…

Frank et al.'s conjecture. The restriction $\kappa\geq 1$ is superfluous, and the displayed estimate should hold for $\kappa$ satisfying the selfadjoint restrictions:…