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.