3 problems

Finiteness conjecture. There are at most finitely many discrete spectra in the branching law $\varpi^{p,q}|_{G'}$.

Let $(X,T)$ be an invertible topological dynamical system and let $bc$ be an invariant measure on $(X,T)$. Say that $bc$ has bounded complexity with respect to the sequence of aver…

Let $V_0$ and $V_1$ be potentials supported on $[0,a]$, and let $H(t)=-\frac{d^2}{dx^2}+V_0+tV_1$, with $H(0)$ self-adjoint. Suppose that $V_1>0$ on $[0,a]$ or $V_1<0$ on $[0,a]$.…