Xiaodong Cao

Xiaodong Cao is a Professor in the Department of Mathematics at Cornell University. His research interests include Analysis and Geometry. He has contributed to various areas within these fields, including the study of Ricci flow and related equations. His work has been published in journals such as Geometry & Topology, Communications in Analysis and Geometry, and Advances in Mathematics. Cao teaches courses such as Introduction to Differential Geometry, Manifolds and Differential Forms, and Supervised Research. His personal web page provides additional information about his research and teaching.

Xiaodong Cao is a Professor of Mathematics at Cornell University, specializing in Geometric Analysis. His research focuses on the interplay between geometric flows and partial differential equations, particularly the Ricci flow and its applications. He has extensively studied differential Harnack estimates, conjugate heat equations, and curvature properties of manifolds under geometric evolution. His work explores eigenvalues of geometric operators, ancient solutions of Ricci flow, and curvature pinching estimates. Cao's contributions have advanced understanding of gradient shrinking Ricci solitons and the behavior of geometric quantities under Ricci and cross curvature flows.