2026 CRM-Fields-PIMS Prize Lecture: Robert McCann

Robert McCann of the University of Toronto has been awarded the 2026 CRM-Fields-PIMS Prize and will deliver the prize lecture on March 20 at 12:30 PM PT / 3:30 PM ET. 

In the words of the selection committee, Professor McCann “was awarded the CRM-Fields-PIMS prize for his unparalleled contributions to the foundations and applications of the theory of optimal transportation and the impact of his work on the development of mathematics, physics, and economics, as well as his leadership in the mathematical sciences community.”

Abstract:

The principal-agent problem is an important paradigm in economic theory for studying the value of private information: the nonlinear pricing problem faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products, Rochet and Chone (1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences are bilinear in the product and agent parameters. This optimization corresponds mathematically to a convexity-constrained obstacle problem. The solution is divided into multiple regions, according to the rank of the Hessian of the optimizer. Apart from four possible pathologies, if the monopolists costs grow quadratically with the product type we show that a smooth free boundary delineates the region where it becomes efficient to customize products for individual buyers. We give the first complete solution of the problem on square domains, and discover new transitions from unbunched to targeted and from targeted to blunt bunching as market conditions become more and more favorable to the seller. Based on work such as https://arxiv.org/abs/2412.15505 with Cale Rankin (Monash and University of New South Wales at Canberra), Kelvin Shuangjian Zhang (Fudan University), and more recently Lucas O'Brien (MIT).