10 problems

Spectral radius extension conjecture. The spectral radius formulae of Theorem $$ are valid for all $\varphi\in\mathcal{S}_m$.

For a $g$-tuple of matrices $\mathcal X=(X_1,\dots,X_g)$, define its outer spectral radius by … where $\operatorname{rad}(X)$ is the ordinary spectral radius. Let…

Let $A=A_s+A_d\varepsilon$ be an $n\times n$ dual number matrix and let $k\in\mathbb{N}$. Here $O$ denotes the zero matrix, and $\rho(A_s)$ denotes the spectral radius of the stand…

Let $I=[0,1]$ be the domain, let $S$ be the vertical scaling function, and let $M_k$ and $M'_k$ be the matrices associated with the $k$-th subdivision, with spectral radii denoted…

Let $G$ be a connected graph and let $u,v\tnobreak$ be vertices with $d(u),d(v)\geq 2$. Suppose that $u$ and $v$ are joined by a path … where $d(w_i)=2$ for $1\leq i\leq s-1$.…

Bordenave–Caputo–Chafaï–Tikhomirov conjecture. The convergence in probability

Let $M_2(\mathbb{R})$ be the space of all $2\times2$ real matrices, and let … be the lower spectral radius as a function on pairs of matrices. Discontinuity-dimension conjecture. T…

Bochi–Fayad conjecture. The set of all resistant pairs $(H,R)\in\mathcal{H}\times\mathcal{R}$ has full Lebesgue measure. Partial results are known, and explicit resistant pairs can…

Strict exclusion conjecture. One has

For a finite set $A\subset\mathbb{R}^+$, define … For $k\geq 1$, define … A cubic minimum conjecture asserts … where $T(k)=k(k+1)/2$ is the $k$-th triangular number; moreover,…