时间：2025年6月6日（周五）14:40-15:40
地点：E10-212 & ZOOM
ZOOM ID: 941 7323 5553
PASSCODE: 425562
主讲人：Robert McCann, University of Toronto
主讲人简介：Robert McCann received his Bachelors degree from Queen's University at Kingston, Ontario and his Doctorate from Princeton. Following a Tamarkin appointment at Brown University and a postdoctoral fellowship at Institut des Hautes Études Scientifiques (in Paris), he became a professor of mathematics at the University of Toronto, where he now holds a Canada Research Chair in Mathematics, Economics, and Physics. He is an authority on optimal transportation and has played a pioneering role in its rapid development since the 1990s. The notion of displacement convexity introduced in his 1994 PhD thesis lies behind many of the area's myriad applications. He serves on the editorial board of various journals, and as editor-in-chief of the Canadian Journal of Mathematics since 2007 (with a hiatus from 2017-21). His research has been recognized by awards such as an invitation to lecture at the 2014 International Congress of Mathematicians in Seoul; fellowship in the American Mathematical Society (AMS) since 2012, the Royal Society of Canada since 2014, the Fields Institute since 2015 and the Canadian Mathematical Society since 2020. He has won the CMS 2017 Jeffery-Williams Prize; the 2023 W.T. and Idalia Reid Prize of the Society for Industrial and Applied Mathematics (SIAM) and the 2025 Norbert Wiener Prize in Applied Mathematics co-sponsored by the AMS and SIAM. His former students and postdocs have achieved acclaim as faculty member at distinguished institutions throughout the world, including two here in China.
讲座主题：The monopolist's free boundary problem in the plane: an excursion into the economic value of private information
讲座摘要: 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 with Cale Rankin (Monash University) and Kelvin Shuangjian Zhang (Fudan University) https://arxiv.org/abs/2412.15505
