Chen Xuezhang (Associate Professor )

BIO

COURSES:

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.

RESEARCH FIELD

Geometric Analysis and Partial Differential Equations

CONTACT