Undergraduate Colloquium: Envy Free Division

How can a group of friends cut up a cake, so that no one is envious of another person's portion? How can three people who've just leased a three-bedroom apartment assign rooms and rent, so that no one feels like someone else has gotten a better deal? In both cases, there are many hard-to-quantify factors, such as the desirability of frosting on a slice of cake or a bay window in a bedroom. Forest Simmons and Francis Su discovered a way of using Sperner's lemma, an 80-year-old result in topology, to answer these questions. On Monday, October 26th, Dr. David Galvin (Notre Dame) described their solution at the Undergraduate Colloquium.

 

UPDATE: Missed the lecture? Dr. Galvin suggests you visit the New York Times for a nice exposition on the Simmons-Su solution, To Divide the Rent, Start With a Triangle. (article | interactive feature)

About the Speaker: David Galvin is Associate Professor of Mathematics at the University of Notre Dame. Before Notre Dame, he worked at UPenn, IAS in Princeton, and Microsoft Research, and before that he was a graduate student at Rutgers in New Jersey. He researches questions in graph theory, combinatorics and discrete probability.