Courses

Fall 2019: Partial Differential Equations (undergraduate), see textbook and exercises.

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.

Bio

Born on 1st  Aug. 1980, citizen of China,

xuezhangchen@nju.edu.cn/chenxuezhang@sina.com

Office Address:

309-3 Meng Minwei Building, Math Department, Gulou Campus.

My recent research interests are rigidity theorems on compact manifolds with boundary; prescribed curvature problems and geometric flows in conformal geometry, such as, scalar curvature flow, Q-curvature flow,  scalar curvature plus mean curvature flow, on compact manifolds; and fractional Q-curvature flow on the unit sphere.

Prerequisites of my future master students:

First of all, you should be interested in geometry, explicitly differential geometry and Riemannian geometry. Definitely you will benefit from the following two courses:

1. Partial Differential Equations;  2. Differential Geometry/ Riemannian Geometry.

You should decide to pursue a Phd position in your near future before going to meet me. Be patient and keep working hard.

You are welcome to join the group of geometric analysis at Nanjing University.   

Geometric Analysis and Differential Geometry Seminar@NJU:

See here for invited lectures in Fall 2018, and the previous lectures: Spring 2018, Fall 2017.

Working seminar：

Fall 2018: Every Saturday 2 pm-5 pm from March 17, Room 1105 Minwei Meng Building.

Spring 2018: Every Saturday 2 pm-5 pm from March 17, Room 1105 Minwei Meng Building.

Fall 2017: Every Saturday 2 pm-5 pm from September 19 2017, Room 1105 Minwei Meng Building. 

Spring 2017: Every Saturday 2 pm-5 pm, Room 1105 Minwei Meng Building.   

Academic Visiting Experience:

20th  Feb. 2009 — 5th Apr. 2009     Visiting (Ph. D.) graduate student, Department of Mathematics, National University of Singapore, Singapore

5th Jan. 2011 — 8th Mar. 2011        Visiting scholar, Department of Mathematics, National University of Singapore, Singapore

19th  Jan. 2012 — 18th Feb. 2012   Visiting scholar, Simons Center of Geometry and Physics, Stony Brook University, New York, USA

1st Apr. 2012 —30th  April 2012      Visiting scholar, Department of Mathematics, National University of Singapore, Singapore

1st July 2012 —14th  July 2012       Participant, AMSI/ANU/UQ Winter School, School of Mathematics and Physics, The University of Queensland Brisbane, Australia

21st Aug. 2013 — 19th Sep. 2013   Visiting scholar, Department of Mathematics, National University of Singapore, Singapore

8th Jan. 2014 — 16th Feb. 2014      Visiting scholar, Morningside Center of Mathematics, Chinese Academy of Sciences, China

28th July 2014 — 25th Aug. 2014   Visiting scholar, Department of Mathematics, National University of Singapore, Singapore

24th Nov. 2014 — 20th Dec. 2014   Visiting scholar, Program on scalar curvature in manifold topology and conformal geometry, Institute of Mathematical Sciences, National University of Singapore, Singapore

4th Sep. 2015 — 29th Aug. 2016    Visiting scholar, Department of Mathematics, Rutgers University, USA

20th Jan. 2017 — 18th Feb. 2017    Visiting scholar, Department of Mathematics, Rutgers University, USA

27th May 2017 — 3rd June 2017    Visiting scholar, Department of Mathematics, Sogang University, Korea

30th Sep. 2017 — 7th Oct. 2017    Visiting scholar, Department of Mathematics, Sogang University, Korea

24th Jan. 2018 — 14th Feb. 2018    Visiting scholar, Department of Mathematics, Rutgers University, USA

29th Apr. 2018 — 6th May 2018    Visiting scholar, Department of Mathematics, Sogang University, Korea

15th July 2018 — 11th Aug. 2018    Visiting scholar, Department of Mathematics, Princeton University, USA