6 problems

Laptev–Safronov conjecture. The estimate should remain valid throughout the larger range $q\le d$, rather than only for $\frac d2<q\le\frac12(d+1)$.

Let $Phi\in\mathfrak{h}\wedge\mathfrak{h}$ be normalized with canonical form … Write $\lambda_{\max}=\sup_{k}\lambda_k$. Highly correlated regime conjecture. There exists a constan…

Let … where the positive-semidefinite random matrices $\bm{W}_i$ are independent, and let … where the independent random matrices $\bm{X}_i$ satisfy … Here $\mathsf{Mom}[\bm{W}_i]$…

Let $\Omega\subset\mathbb{R}^2$ be an open domain, and let $H_0^\Omega$ be its non-magnetic Dirichlet Laplacian. Write … for the eigenvalue counting function and let $|\Omega|$ den…

Let $\mathcal{G}$ be any connected, compact graph with total length $L$ and diameter $D$, and let $\mu_k(\mathcal{G})$ denote its $k$-th eigenvalue. Assume that $L/k>D/2$. Strict d…

Let $m$ be a positive integer and let ${\cal A}_{m;c}$ denote the matrix pencil defined in the paper, with $c>0$. An eigenvalue is non-real when $\lambda\notin\mathbb{R}$. Real-par…