Hypergraph list coloring and Euclidean Ramsey Theory A hypergraph is simple if it has no two edges sharing more than a single vertex. It is s-list colorable if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. I will discuss a recent result, obtained jointly with A. Kostochka, that asserts that for any r and s there is a finite d=d(r,s) so that any r-uniform simple hypergraph with average degree at least d(r,s) is not s-list-colorable. This extends a similar result for graphs, and has some geometric Ramsey-type consequences.