10 problems

D'Angelo's degree conjecture. The degree bound can be taken to be

Fix an integer $n\geq 2$. For each $k\in\mathbb N^+$ such that $k(k+1)/2<n$, define … The gap phenomenon concerns rational proper maps from the unit ball $\mathbb B^n$ to…

Dimension bound conjecture. One has

Juxtaposition conjecture. All proper holomorphic maps between annuli are juxtapositions of homogeneous maps.

Let $X$ be a noncompact generalized continuum. Let $T$ be an infinite tree and let … be a proper embedding. Assume that the induced map on end spaces … is injective. Existence of a…

Let $Q$ be any class of morphisms of topological spaces, and write $Q^{lr}$ for its double Quillen orthogonal. The proper-map maximality conjecture. If … then … The paper proves th…

Let $f$ be a map of finite topological spaces. Say that a fibre has two points bounded above but not below when its two points have a common upper bound but no common lower bound,…

Let $\{o\}\to\{o\to c\}$ be the indicated map of finite topological spaces, and let the subscript $<5$ denote the subclass consisting of maps between spaces with fewer than $5$ poi…

Conjecture C. The set $\mathcal{P}$ is constructible, and it is defined by the algebraic conditions given in part 2 of Theorem 2 bis.

Properness conjecture. The map $F_A(x)$ is non-proper if and only if this system has a non-zero solution.