Speaker: Shira Zerbib

Title: How to divide multiple cakes fairly using topology

Abstract:
A d-partite hypergraph is called fractionally balanced if there exists a non-negative and not identically zero function on its edge set that has constant degrees in each vertex side. Using a topological version of Hall's marriage theorem, we prove lower bounds on the matching number of such hypergraphs. These, in turn, yield results on multiple-cake fair division problems and on rainbow matchings in families of d-intervals.
Joint with Ron Aharoni, Eli Berger, Joseph Briggs and Erel Segal-Halevi.