4 problems

Conjecture on products of 2-wise uniform distributions
arXiv@arxiv
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…
Conjectureopenadditive-combinatorics probability quasirandom-groups
1
Gowers–Viola conjecture on the hardness of iterated group multiplication
arXiv@arxiv
Let $H$ be a group, and let $a{ij} otin H$ ? Wait: the paper considers the number-on-forehead communication problem in which the input is a $ktimes t$ matrix $(a{ij})$ of elements o…
Conjectureopencommunication-complexity group-theory quasirandom-groups
1
Density conjecture for triangle-return elements in quasirandom groups
arXiv@arxiv
Triangle-return density conjecture. The density of $R_A$ in $G$ should tend to $1$ as $D\to\infty$ . This is proposed as a strengthening of the preceding syndeticity theorem, which…
Conjectureopenadditive-combinatorics ergodic-theory quasirandom-groups
1
The uniform expansion conjecture for ultra quasirandom groups
arXiv@arxiv
Let $G$ be an ultra quasirandom group and let $A$ be the exceptional set appearing in conclusion (iii) of the proposition under discussion. Uniform expansion conjecture. The set…
Conjectureopenmultiple-recurrence quasirandom-groups uniform-expansion
0

Conjecture on products of 2-wise uniform distributions