11 problems

Maximal Hardy-field conjecture. If $H$ is maximal, then there is no $y\in\mathcal{C}^1$ such that

Let $k\in\mathbb{N}$ and let $a_1,\ldots,a_k\in\mathcal{H}$ be functions of polynomial growth. Assume that every non-trivial linear combination $a$ of $a_1,\ldots,a_k$ satisfies ……

Let $\mathcal{H}$ be the Hardy field under consideration, let $a\in\mathcal{H}$ have polynomial growth, and assume … for every $c\in\mathbb{R}$ and $p(t)\in\mathbb{Z}[t]$. Let…

Conjectured optimal convergence criterion. Under this assumption, the averages

Let $\mathcal{H}$ be a Hardy field, let $f_1,\ldots,f_k,W\in\mathcal{H}$, and define … Property (WP) is that, for every $f\in\operatorname{span}^*(f_1,\ldots,f_k)$ and…

Nilsequence structure conjecture. There exist a nilmanifold $Y=G/\Gamma$, a continuous function $F\in C(Y)$, a point $y\in Y$, elements $a_1,\ldots,a_k\in G$, and a sequence…

Let $f_1,\ldots,f_k$ be linearly independent functions of the form … Let $(X,\mathcal{B},\mu,T)$ be a totally ergodic measure-preserving system and let…

Let $f_1,\ldots,f_k$ be functions from a Hardy field, and define … Let $(X,\mathcal{B},\mu,T)$ be an ergodic measure-preserving system and let $h_1,\ldots,h_k\in L^\infty(X)$. Fran…

Let $\mathbb{T}^{\operatorname{da}}$ denote the field of accelero-summable transseries, and let $H$ be a Hardy field. In real accelero-summation, use the organic average whenever s…

Let $\mathcal{H}$ denote the Hardy field under consideration, let $[x]$ be the integer part of $x$, and let “the growth assumptions of Theorem A (or Conjecture A)” refer to the hyp…

Let $\mathcal{H}$ denote the Hardy field under consideration, let $[x]$ be the integer part of $x$, and let $\bar d(\Lambda)$ denote the upper density of $\Lambda\subset\mathbb{Z}$…