Combinatorics Seminar

When: Monday, December 11, 10am
Where: Schreiber 209
Speaker: Shira Zerbib, University of Michigan and MSRI
Title: Colorful coverings of polytopes - the topological truth behind different colorful phenomena


We prove a colorful polytopal generalization of the topological KKMS theorem due to Shapley. Our theorem implies some seemingly unrelated results in discrete geometry and combinatorics involving colorful settings. For example, we apply our theorem to prove Barany's Colorful Caratheodory theorem, and to obtain an upper bound on the piercing numbers in families of colored d-intervals, extending results of Tardos, Kaiser and Alon. We further apply our theorem to questions regarding fair division. Joint with Florian Frick.