Lili He's Homepage
Department of Mathematics
Johns Hopkins University
404 Krieger Hall
3400 N. Charles Street
Baltimore, MD 21218
Office: Krieger 201
Email: lhe31 at jhu dot edu
I am a graduate student at Johns Hopkins University.
My advisor is Professor
Hans Lindblad.
For more details, you can find my CV here.
Research
My research interests are general relativity and nonlinear wave
equations, with focus on the stability problems of solutions to the
Einstein(-Maxwell) equations. I am also
interested in microlocal analysis and scattering theory. My work involves
the vectorfield method and the techniques of microlocal analysis.
Publications and preprints
- The linear stability of weakly charged and slowly rotating Kerr-Newman family of charged black holes,
arXiv:2301.08557
[arXiv]
- Masses at null infinity for Einstein's equations in harmonic coordinates (joint with Hans Lindblad),
To appear in Pure and Appl. Math. Quarterly.
[arXiv]
- Scattering from the infinity of the Maxwell Klein Gordon
equations in Lorenz gauge, Commun. Math. Phys. 386, 1747–1801 (2021).
[journal
|arXiv]
Invited talks
-
PDE Seminar, Vanderbilt University, April 2023.
- PDE mini-school: geometric singular analysis and black holes,
UNC Chapel Hill, March 2023.
-
PDE Seminar, Georgia Tech, March 2023.
-
Analysis and PDE Seminar, UC Berkeley, November 2022.
- Advances in Nonlinear differential equations : Analysis, Numerics and Applications,
Tianjin University, August 2022.
- Analysis and PDE Seminar, University of Kentucky, October 2021.
- PDE Seminar, University of Science and Technology of China, March 2021.
Teaching
- Teaching assistant for Math 202: Calculus III (Spring 2022)
- Grader for Math 607: Complex variables (Spring 2022)
- Teaching assistant for Math 637: Functional Analysis (Fall 2020, Fall 2021, Fall 2022)
- Teaching assistant for Math 405: Real Analysis I (Fall 2020, Fall 2021, Fall 2022)
- Teaching assistant for Math 201: Linear Algebra (Summer 2021)
- Teaching assistant for Math 107: Calculus II (Biology and Social Science) (Spring 2020)
- Instructor for Math 302: Differential Equations and Applications (Summer 2019)
- Teaching assistant for Math 302: Differential Equations and Applications (Spring 2019, Summer 2020, Summer 2021, Summer 2022)
- Teaching assistant for Math 106: Calculus I (Biology and Social Science) (Fall 2018)
- Teaching assistant for Math 109: Calculus II (Engineering and Physical Science) (Summer 2018)
- Teaching assistant for Math 108: Calculus I (Engineering and Physical Science) (Summer 2018, Fall 2019)
- Grader for Math 311: Methods of Complex Analysis (Spring 2018)
- Grader for Math 443: Fourier Analysis (Fall 2017)