11 problems

Non-expanding links conjecture. There is no sequence of bounded-degree finite graphs, with size growing to infinity, such that all links in all the graphs form an expander family.

Giant strongly connected component size conjecture. Under the assumption of local convergence of $G_n$ in probability, $\frac{1}{n}|SCC_1|$ converges in probability to

Polynomial dependence conjecture. The same conclusion should hold with

Let $G$ be a Cayley graph rooted at $o$, and consider the sequence of balls … Call this sequence an expander family if it forms an expander family in the usual graph-theoretic sens…

Let $A\subset\mathbb{R}$ be a finite set, and for a positive integer $k$ write … Here $X\gg_{k,l}Y$ means that $X\geq c_{k,l}Y$ for a positive constant depending only on $k$ and…

Balog–Roche-Newton conjecture. For every $\epsilon>0$,

Probability conjecture for random regular graphs to be Ramanujan. The probability that $\Gamma$ is Ramanujan is conjectured, based on experimental evidence, to tend to a nonzero li…

A normed space has the uniform decay property when the nonlinear spectral-gap quantities under discussion satisfy the uniform decay estimate established in the surrounding section.…

Let $X$ be a normed space. Say that a graph family has the relevant property when it is a family of bounded-degree graphs satisfying the graph Poincaré inequality for $X$; the sour…

Finite width conjecture. The abstract group-theoretic description of the groups $G_k=G/(G\cap H_k)$ is given by

Let $p$ be prime, let $F$ be a generating subset of $GL_2(\mathbb{F}_p)$, and let $N_0,N\in\mathbb{N}$ be the constants from the large-girth statement for fixed $d=2$ and $k=|F|$.…