Abstract The Union Closed Set Conjecture states that if a set system X\subseteq\mathcal{P}([n]) is closed under pairwise unions, then there exists a\in[n] in at least half of the sets of X. We show that there is a very natural generalization of the union closed set conjecture which gives a lower ... more >>>

We show that the value of the $n$-fold repeated GHZ game is at most $2^{-\Omega(n)}$, improving upon the polynomial bound established by Holmgren and Raz. Our result is established via a reduction to approximate subgroup type questions from additive combinatorics.

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We study boolean constraint satisfaction problems (CSPs) $\mathrm{Max}\text{-}\mathrm{CSP}^f_n$ for all predicates $f: \{ 0, 1 \} ^k \to \{ 0, 1 \}$. In these problems, given an integer $v$ and a list of constraints over $n$ boolean variables, each obtained by applying $f$ to a sequence of literals, we wish ... more >>>