6 problems

Let a random-matrix ensemble have a complex eigenvalue spectrum, and consider its bulk spectral statistics after local rescaling. Haldane–Kausch–Kieburg–Urbina's second conjecture.…

Partial-screening conjecture. A positive impurity contribution to the spinon density of states corresponds to partial screening of the impurity.

A photonic system is described by a Hamiltonian $H$ with local gap $\mu_{(x,y,\omega)}^{\textrm{C}}$ at position $(x,y)$ and frequency $\omega$. Let $\delta H$ be a perturbation, a…

Semicontinuity conjecture. The spectrum of diagonalizable operators should be both inner and outer semicontinuous with respect to diagonalizable perturbations.

In a non-Hermitian model exhibiting conventional bulk-boundary correspondence (cBBC), consider a domain-wall geometry formed by coupling it to another model in a different topologi…

Let $p(s)$ denote the nearest-level-spacing distribution after unfolding the spectrum of a non-Hermitian random matrix. The symmetry classes are A, AI, AII, D, C, AIII, AIII$^\dag$…