Fall 2019: Partial Differential Equations (undergraduate), see textbook.
Spring 2019: Differential Geometry (undergraduate), see textbook.
Fall 2018: Partial Differential Equations (undergraduate), see textbook.
Spring 2018: Differential Geometry (undergraduate), see textbook.
Fall 2017: Geometric Analysis ( We mainly focus on the recent developments on the existence of a conformal metric with positive constant Q-curvature. The contents include the derivation of Q-curvature as well as Paneitz operator, the existence results when the related conformal invariance are positive, etc. This topic is selected from a seriece of papers by Sun-Yung Alice Chang-Paul Yang, M. Gursky, A. Malchiodi, F. B. Hang, Y. J. Lin et al. )
The following topic has been left to some future semester:
(textbook: Sorin Dragomir and Giuseppe Tomassini, Differential Geometry and Analysis on CR Manifolds, Progress in Mathematics, Vol 246, 2006. This class is mainly concerned with the CR Yamabe problem and its resolution). Prerequisites of this class: Differential Geometry (Undergraduate) and something about Riemannian Geometry.
Spring 2017: (1) Differential Geometry (undergraduate), see textbook. (2) Discussion course (undergraduate, a little bit like a seminar): The compactness of the Yamabe problem.
Fall 2016: Geometric Analysis (plan to present relatively complete proofs of the existence of scalar-flat conformal metrics with constant boundary mean curvature on compact manifolds with boundary, including the formulation of this problem and motivation of the study on this problem).
Spring 2015: Partial Differential Equations II (the Yamabe problem and a brief introduction to the mean curvature problem on a compact manifold with boundary).
Spring 2014: Partial Differential Equations II (Geometric wave equations, focus on wave maps)
and Real Analysis, Calculus, etc.
Geometric Analysis and Partial Differential Equations