Hypergraph list coloring and Euclidean Ramsey Theory
Hypergraph list coloring and Euclidean Ramsey Theory

Noga Alon, TelAviv University and IAS
Fine Hall 224
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 $s$listcolorable. This extends a similar result for graphs, and has some geometric Ramseytype consequences.