3 problems

Uniform expansion conjecture. If $G$ is $\varepsilon$-quasirandom, then all connected Cayley graphs of $G$ are $\varepsilon$-uniform expanders.

Let $H$ be a group, let $t$ be a positive integer, and let $X,Y$ be independent random variables that are 2-wise uniform over $H^{t}$, meaning that every pair of coordinates of eac…

Pyber's conjecture. The class of perfect groups with commutator width at most $n$ is Q.U.P.