3 problems

Let $A_\ell$ denote the weighted adjacency matrix of the supersingular $\ell$-isogeny graph $\mathcal{G}(p,\ell)$ for all $\ell\neq p$. Let $v$ be an $L^2$-normalized simultaneous…

Let $p\ge 5$ and let $\ell\ne p$ be prime. Let $\mathcal{G}^{SS}_{2}(\ell,p)$ be the superspecial isogeny graph, with normalized adjacency eigenvalues … where $m=|SS_2(p)|$, and se…

Maximal-order containment conjecture. For every $\epsilon>0$, the number of maximal orders containing $\Lambda$ is