PIMS/UBC Distinguished Lecture Series: Robert McCann
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Economists are interested in studying who matches with whom (and why) in the educational, labour, and marriage sectors. With Aloysius Siow, Xianwen Shi, and Ronald Wolthoff, we propose a toy model for this process, which is based on the assumption that production in any sector requires completion of two complementary tasks. Individuals are assumed to have both social and cognitive skills, which can be modified through education, and which determine what they choose to specialize in and with whom they choose to partner.
Our model predicts variable, endogenous, many-to-one matching. Given a fixed initial distribution of characteristics, the steady state equilibrium of this model is the solution to an (infinite dimensional) linear program, for which we develop a duality theory which exhibits a phase transition depending on the number of students who can be mentored. If this number is two or more, then a continuous distributions of skills leads to formation of a pyramid in the education market with a few gurus having unbounded wage gradients. One preprint is on the arXiv; a sequel is in progress.
Additional Information
Robert McCann
Robert McCann has been a Professor of Mathematics at the University of Toronto since 1998.
He grew up in Windsor Ontario, and studied engineering and physics at Queen's University before completing his doctorate in mathematics at Princeton in 1994. In the subsequent years, McCann has emerged as a leading figure in the development of the theory of optimal transportation. His work balances very pure contributions to deep mathematics with the discovery of new applications to image processing, atmospheric circulation patterns, and to optimizing economic decisions.
Before accepting a position at the University of Toronto, McCann was Tamarkin Assistant Professor of Mathematics at Brown University in Providence, Rhode Island.
His past awards include an American Mathematical Society Centennial Fellowship, the Monroe Martin Prize in Applied Mathematics, and the Coxeter-James Prize of the Canadian Mathematical Society. He currently serves as Editor-in-Chief of the Canadian Journal of Mathematics.
