Speaker: Deping Ye (Memorial University of Newfoundland)
Time: 2025-11-11 09:00-11:00
Location: 710, SIMIS
Abstract: In this talk, I will discuss the Riesz $\alpha$-energy, a concept that plays a fundamental role in various fields, including mathematics, physics, and related areas. I will present the first-order variational formula for the Riesz $\alpha$-energy of a log-concave function with respect to the Asplund sum, which gives rise to the Riesz $\alpha$-energy measure of the log-concave function. I will also discuss the related Riesz $\alpha$-energy Minkowski problem. Assuming sufficient smoothness, this problem reduces to a new Monge-Ampère-type equation involving the Riesz $\alpha$-potential. This Minkowski problem can be viewed as a functional counterpart of the recent Minkowski problem for chord measures in integral geometry, posed by Lutwak, Xi, Yang, and Zhang. I will also present our solutions to the Riesz $\alpha$-energy Minkowski problem under certain mild conditions on the pregiven measure $\mu$.
About Speaker: Deping Ye is a tenured full professor at Memorial University of Newfoundland. He obtained his B.S. degree from Shandong University in 2000, was a graduate student at Zhejiang University from 2000 to 2003, and received his Ph.D. from Case Western Reserve University (USA) in 2009. Professor Ye currently serves as an Associate Editor for the Canadian Journal of Mathematics, Canadian Mathematical Bulletin, and the newly established Canadian Mathematical Communications. He is the principal investigator of a research project funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and was the recipient of the JMAA Ames Award in 2017. His research interests span convex geometric analysis, geometric and functional inequalities, random matrices, quantum information theory, and statistics. He has published nearly 50 papers in Communications on Pure and Applied Mathematics, Advances in Mathematics, Journal of Functional Analysis, Mathematische Annalen, and Calculus of Variations and Partial Differential Equations (CVPDE), etc.
简体中文 
English