9 problems

Let an instance of the Unique Games Problem consist of a graph, a set of colors, and a matching of the colors for each edge. The value of an instance is the largest fraction of edg…

Consider the dynamical systems constructed from instances of the unique games conjecture, with alphabet size $k$, and let the invariant measure assign weight to neighborhoods of op…

Assume the unique games conjecture and consider the dynamical systems associated with unique games instances, together with their invariant-measure scaling properties. Turing-machi…

Sharp hardness consequence. For every $\varepsilon>0$, it is NP-hard to approximate MAX-3-CUT within a multiplicative factor of $\alpha_{3}+\varepsilon$.

A Unique-Games instance is a 1-to-1 Games instance: a 2-Prover-1-Round Games instance in which the two alphabets have equal size and every constraint is a bijection between them. F…

Strong Parallel Repetition Conjecture. The value of the repeated game should be

Let $X^{\alpha}$ be an $r$-fold cover of a graph $X$, where $\xi(X^{\alpha},t)$ is the transversal polynomial and $\deg(\xi(X^{\alpha},t))$ is the maximum number of edges satisfied…

Let $\Omega\subseteq\mathbb{R}^{n}$ be a periodic set, meaning that $\Omega+v=\Omega^{c}$ for every standard basis vector $v$ and $-\Omega=\Omega^{c}$. A periodic half space is a s…

Let $0<s<c<1$ and let $p>1$ be a prime. For fixed $a_{2},a_{4},\ldots,a_{2n}\in\mathbb{Z}/p\mathbb{Z}$, consider a system of $n$ two-term linear equations over…