MathOverflow

Given continuous maps of topological spaces $X\xrightarrow{f}Y\xrightarrow{g}Z$ such that the induced map of preimages $(g\circ f)^{-1}(z)\xrightarrow{\simeq}g^{-1}(z)$ is a (homotopy or weak) equivalence for each $z\in Z$, when one can guarantee that...

A projective structure $[\nabla]$ is an equivalence class of affine connections inducing the same unparametrized geodesics. It's metrizable if the equivalence class contains the Levi-Civita connection of some metric. A flat projective structure is equivalently...

Let $p$ be a prime, $S\subseteq \mathbb{F}_p$ be a subset satisfying $2^{\#S}>p$. By the Dirichlet Box Principle, there exist distinct subsets $S_1,S_2\subset S$ such that $\sum_{s\in S_1}s=\sum_{s\in S_2}s$. I am wondering what can be said about...

Let us say that a tiling of a square into rectangles is Mondrian if the rectangles (1) are pairwise non-congruent and (2) have the same area. It is an outstanding open problem whether there exists a Mondrian tiling of a square in which the side lengths...