Chao Li@Princeton University

I am an instructor at Department of Mathematics, Princeton University. In fall 2021, I will join New York University, the Courant Institute as an assistant professor. I got my Ph.D. at Stanford University. My dissertation advisors are Rick Schoen and Brian White. Before that I was an undergraduate student at Peking University, where I got my Bachelor's degree in Mathematics, mentored by Huijun Fan.

My research interests include differential geometry, partial differential equations, and geometric measure theory. Specifically, my recent work concerns minimal surfaces, scalar curvature and mathematical general relativity.

I am currently co-organizing the Differential Geometry and Geometric Analysis Seminar in Princeton, and the Joint Princeton-Rutgers Seminar on Geometric PDE's.

Teaching

I am teaching Princeton MAT 201, Multivariable Cacalculus. If you want to attend the class or you have any questions on the course, please refer to the info on Canvas Page.

Preiously, taught Princeton MAT 355 in spring 2020. I also taught MAT 201, MAT 103 and MAT 300 (Multivariable Analysis I). My office is located at Fine 704. Please write me an email if you have any questions.

Research

Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions, joint with Otis Chodosh and Yevgeny Liokumovich, submitted. arXiv.org
Generalized soap bubbles and the topology of manifolds with positive scalar curvature, joint with Otis Chodosh, submitted. arXiv.org
Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces, SIGMA 16 (2020), 099. Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday. arXiv.org
Regularity of free boundary minimal surfaces in locally polyhedral domains, joint with Nick Edelen, accepted by Comm. Purl. Appl. Math. arXiv.org
The dihedral rigidity conjecture for n-prisms , submitted. arXiv.org
Constrained deformations of positive scalar curvature metrics , joint with A. Carlotto, submitted. arXiv.org
Singularity and comparison theorems for metrics with positive scalar curvature , Ph.D. Thesis, Stanford University. PDF file. Video of a talk at the Institute for Advanced Study.
A polyhedron comparison theorem for three-manifolds with positive scalar curvature, Invent. Math. 219, 1-37 (2020) arXiv.org
Positive scalar curvature and skeleton singularities, joint with C. Mantoulidis, Math. Ann. (2019) 374: 99. arXiv.org

(A note fixing some imprecisions in Lemma 6.1. Thank Luen-Fai Tam for pointing out!)

Index and topology of minimal hypersurfaces in Rⁿ, Calc. Var. (2017) 56:180. arXiv.org

Notes

Nachdiplom Lectures - Topics in scalar curvature, lectures by Rick Schoen (Spring 2017, FIM-ETH). We encourage the readers to wait FIM-ETH for the publication of the lecture notes.
Lectures on mean curvature flow by Or Hershkovits. Joint with Evangelie Zachos. (Winter 2017, Stanford) PDF
Lectures on minimal submanifolds by Rick Schoen. Joint with C. Mantoulidis and D. Cheng. (Spring 2015, Stanford) PDF
Non-existence of metric on Tⁿ with positive scalar curvature. Notes for a talk given at Stanford and University of California, Irvine in 2014. PDF

Chao Li

Instructor, Princeton University, USA

Friends

Teaching

Research

Notes