8 problems

Let ${\mathcal P}\subset\mathbb C^n$ be a product of discs or ${\mathcal P}\subset\mathbb R^n$ a product of intervals, and let $f_1,\ldots,f_N$ be analytic functions satisfying pol…

Let $\mathbb R_{\mathrm{LN},\mathrm{PF}}$ be the structure generated by the larger class of Noetherian and Pfaffian functions considered in the paper. Noetherian–Pfaffian counting…

Let $\mathbb R_{\mathrm{LN}}$ denote the structure generated by restricted Noetherian functions. Restricted-Noetherian counting o-minimality conjecture. The structure generated by…

Let ${\mathcal P}$ be the domain of a Noetherian chain and let $P_1,\ldots,P_n:{\mathcal P}\to\mathbb C$ be Noetherian functions of format ${\mathscr F}$. Khovanskii's format-bound…

Let $P_1({\mathbf z},\varepsilon),\ldots,P_n({\mathbf z},\varepsilon):({\mathbb C}^{n+1},0)\to\mathbb C$ be holomorphic functions depending analytically on $\varepsilon$. For each…

Sharp o-minimality conjecture. The structures

Let $f_1,\ldots,f_n:\Omega\to{\mathbb C}$ be Noetherian functions over ${\mathbb C}(t)$, with $t$-degree $(\alpha,\beta)$ over a common Pfaffian chain of order $\ell$, and let…

Let $V\subset\mathbb{C}^n$ be an algebraic curve, let $F:\Omega\to\mathbb{C}$ be a Noetherian function, and let $B\subset\Omega$ be a Euclidean ball. The paper proves that, for…