7 problems

Let $M$ be a closed $n$-manifold with nonpositive sectional curvature, negative Ricci curvature, and no local $\mathbb{R}$ factors. Let $N$ be any closed Riemannian manifold and le…

CC degree formula conjecture. For $d=4$ and $n\leq 12$, the CC degree of $V_{\{2\}}$ is

Let $m$ and $s$ be nonnegative integers, and consider the rational map … whose coordinates on $\mathbb P^m\setminus \operatorname{V}(z_0)$ are given by … where the $\gamma_i(z)$ ar…

Let $L\colon H\to G$ and $C\colon G\to H$ define the eigenvalue problem $Lx=\lambda Cx$, let $\psi$ be the oriented $\Phi_0$-map on the cylinder $\mathbb{R}\times\mathrm{S}$ of uni…

Let $L\colon\mathbb{R}^k\to\mathbb{R}^k$ be a linear operator, let $\mathbf{S}$ be the unit sphere in $\mathbb{R}^k$, and let $N\colon\mathbf{S}\to\mathbb{R}^k$ be continuous. For…

Let $\Omega\subset\mathbb R^2$ and let $N:\Omega\to\mathbb R^2$ be a map in $C^{\frac{1}{2}+\varepsilon}$. Assume that … for every open $V\Subset\Omega$ with Lipschitz boundary. Zü…

Let $\mathbb{H}$ be the halting problem for BSS computation on $\mathbb{R}$, and let a countable set mean a subset of $\mathbb{R}^\infty$ of cardinality at most $\omega$. For sets…