5 problems

Higher-order differentiability conjecture. The spectral function $f\circ\lambda$ is $k$ times continuously differentiable at $X$ if and only if $f$ is $k$ times continuously differ…

Let $\Phi(\omega)$ be a spectral function with finite, positive zero-frequency value, $0<\Phi(0)<\infty$. Suppose that hydrodynamic tails make $\Phi(\omega)$ nonanalytic at…

Let $\Phi(\omega)$ be the spectral function of a chaotic quantum system. Operator Growth Hypothesis. The high-frequency spectral function $\Phi(\omega\to\infty)$ generically decays…

Let $\Phi(\omega)$ be a spectral function associated with an autocorrelation function $C(t)$, and suppose that $C(t)$ decays algebraically faster than $1/t$. Semicircle-persistence…

Let $X$ be a rectangular matrix with repeated singular values, and let the directional derivative refer to the formula established in Theorem for the relevant matrix-valued spectra…