6 problems

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

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…

Let $k$ be a positive integer, and consider an instance of the two-variable linear system $2$-Lin-$k$ over $\mathbb{Z}_k$, with equations … An assignment is a map…

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…

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…