3 problems

Guth–Zahl conjecture. Let $p\geqslant\frac{n}{n-1}$. For every $\varepsilon>0$, there are a complexity $D=D_{\varepsilon,n}\in\mathbb{N}$ and a constant $C_{\varepsilon,n}>0$ such…

Let $F$ be a finitely generated free group, and let $w\mapsto T_w$ be an ergodic action of $F$ on a probability space $(X,\mathscr B,\mu)$. For $n\geq1$, let…

Return Times conjecture. For every function $g\in L^q(X)$ there is a universal set $X_0\subseteq X$ with $\mu(X_0)=1$ such that, for every second dynamical system…