How to divide multiple cakes fairly using topology

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

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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.