Research Interest:
My research field is differential geometry and geometric analysis. The subject is closely related with partial differential equations, topology, Lie groups and general relativity.
My research effort has been concentrated on global Riemannian geometry --- interaction of curvature with the underlying geometry and topology. Topics include the study of the fundamental groups, comparison geometry, manifolds with integral curvature bounds,
spaces with weak curvature bounds, the eigenvalue of Laplacian, etc..
Teaching:
All courses materials are avialable to the students who have enrolled or been on the waitlist of the class via
UCSB Canvas .
Current Ph.D. Students: Jihye Lee, Fabio Ricci, Malik Tuerkoen, Yusen Xia
Former Ph.D. Students: See Math Genealogy
Editorial Service:
- Editorial Board, Proceedings of the American Mathematical Society Feb. 1 2014 --- Jan. 31 2022
- Editorial Board, Journal of Topology and Analysis 2019--
- Editorial Board, Annals of Global Analysis and Geometry 2020--
