# How to divide multiple cakes fairly using topology

Shira Zerbib, Iowa State University
Wednesday, January 13, 2021 - 3:30pm to 5:00pm
via Zoom

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting: https://washington.zoom.us/j/91547335974 (New link!)
Meeting ID: 915 4733 5974

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.
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