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
Abstract:
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.