6 problems

Generic simplicity conjecture. We conjecture that the exceptional set $\mathcal{E}$ has measure zero in parameter space.

Resonance-order conjecture. It is conjectured that $p=(2j-1)/2$ first enters at order $k=2j-1$, one new resonance per two additional orders, consistent with the tongue widths…

Slow-dispersion conjecture. For every $\varepsilon>0$, there exists a choice of $\nu(t)$ such that the $L^1\to L^\infty$ decay rate is no faster than $t^{-\varepsilon}$; more preci…

Let $H^\varepsilon(t)$ be the time-periodic continuous Floquet Hamiltonian, and let its monodromy operator be the unitary operator obtained by evolving over one forcing period. Its…

Let $\Gamma$ be the Riemann surface associated with the periodic operator, and let $\phi(x;\lambda)$ be its normalized Floquet solution. If $\Gamma$ has finitely many ramification…

Let $T(\lambda)$ be the Floquet matrix associated with the periodic differential operator in (A3). A pathology of the first kind occurs when, at a ramification point of the spectra…