Time: 3:30pm – 4:30 pm
Room: Wean Hall 8220
Speaker: Jing Zhang
Department of Mathematical Sciences
Title: How to get the brightest rainbows from the darkest colorings
We will discuss the rainbow (sometimes called polychromatic) variation of the Ramsey theorem on uncountable cardinals. It roughly says if a given coloring on n-tuples satisfies that each color is not used too many times, we can always find a rainbow subset, that is a set in which no two n-tuples from the set get the same color. We will use problems in different settings (inaccessible cardinals, successors of singular cardinals, small uncountable cardinals etc) to demonstrate that the rainbow variation is a “strict combinatorial weakening” of Ramsey theory.