4 problems

Let $\widehat{\mathcal{Z}}$ be the space of even and odd polynomial and Laurent-polynomial $\infty$-cycles considered in the paper, equipped with its…

Let $d=1,2$, and let $u$ satisfy the bounds referred to in the source, with $2<\eta_2\leq\eta_1<4$, and suppose that $u(x)<0$ whenever $|x|>R$. Write $\zeta_c(\rho,\beta)$ for the…

Cycle-structure conjecture. At all temperatures, a typical permutation decomposes into finite cycles when $d=1$ or $d=2$, whereas for $d\geq 3$ there exists a critical value…

Angel's sharp transition conjecture. If $\mathscr{T}^G$ is non-empty, then