个人简介
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 Phd students (NO MASTER STUDENT POSITIONS ARE AVAILABLE):
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 Spring 2019, and the previous lectures: Fall 2018, Spring 2018, Fall 2017.
Working seminar：
Spring 2019: Every Saturday 2 pm-5 pm, Room 1105 Minwei Meng Building.
Fall 2018: Every Saturday 2 pm-5 pm, 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
26th Jan. 2019 — 1st Feb. 2019 Visiting scholar, Department of Mathematics, Rutgers University, USA
1st Feb. 2019 — 21st Feb. 2019 Visiting scholar, Department of Mathematics, Princeton University, USA
7th July 2019 — 14th July 2019 Visiting scholar, Department of Mathematics, The Hong Kong University of Science and Technology
1st Aug. 2019 — 16th Aug. 2019 Visiting scholar, Department of Mathematics, Rutgers University, USA
主要课程：
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.
研究领域：
Geometric Analysis and Partial Differential Equations
联系方式：
xuezhangchen@nju.edu.cn