香香腐宅

报告题目：Special Lagrangian and quadratic Hessian equations

报告人：袁域 教授（美国华盛顿大学）

会议时间：2026年3月23日 10:00开始  

会议地点：香香腐宅 113报告厅

摘要：We survey some new and old, positive and negative results on a priori estimate, regularity, rigidity, and constant rank results for special Lagrangian and quadratic Hessian equations. These equations originate in calibrated, convex, conformal, and complex geometries among other fields.

Unlike all other order Hessian equations such as the linear (Laplace) and top order (Monge-Ampere) equations, the regularity/irregularity and a priori Hessian estimates for these two equations have not been settled yet in five and higher dimensions. 

报告人简介：Yu YUAN, professor of University of Washington, Seattle, received his Bachelor, Master, and Ph.D. degrees respectively from Tsinghua University, Institute of Mathematics, Academia Sinica, University of Minnesota. His research concentrates on PDE and differential geometry, and he has made original contributions to the study of linear parabolic equations and fully nonlinear equations such as special Lagrangian and quadratic Hessian equations. His papers are published in Adv. Math., Amer. J. Math., Ann. of Math., Comm. Pure Appl. Math., Duke Math. J., and Invent. Math. among other journals. He has been awarded Sloan Research Fellowship and Simons Fellowship.