Biography
I am Warren Li, a Stanford Science Fellow affiated with the Department of Mathematics in the School of Humanities and Sciences, mentored by Jonathan Luk. My research concerns the analysis of partial differential equations, particularly those arising in mathematical physics such as Einstein's equations of General Relativity. I received my Ph.D. in Mathematics from Princeton University in 2025.
My current research interests include the study of nonlinear wave equations including the Einstein equations, the Euler equations of gas dynamics, and other model nonlinear waves arising from particle physics (e.g. Yang-Mills). I am particularly interested in the study of singularities, which arise naturally in General Relativity either in the interior of black holes or at the Big Bang.
I am also currently a Junior Research Fellow at Trinity College, University of Cambridge. Starting in 2026, I will be a Chapman Fellow at Imperial College London, mentored by Martin Taylor.
Publications
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BKL bounces outside homogeneity: Einstein–Maxwell–scalar field in surface symmetryPreprint available at arxiv:2408.12434.
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BKL bounces outside homogeneity: Gowdy symmetric spacetimesPreprint available at arxiv:2408.12427.
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Scattering towards the singularity for the wave equation and the linearized Einstein–scalar field system in Kasner spacetimesPreprint available at arxiv:2401.08427.
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Kasner-like description of spacelike singularities in spherically symmetric spacetimes with scalar matterAnnals of PDE, Vol 11, article number 5, 2025, link here.
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Kasner inversions and fluctuation collapse inside hairy black holes with charged matter(with M. Van de Moortel) Annals of PDE, Vol 11, article number 3, 2025, link here.
Recent and Upcoming Talks
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Joint Online Mathematical Relativity Colloquium, October 2 2025
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Workshop at Cook's Branch (organized by Texas A&M), April 1 2025
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PDE Seminar, Brown University, February 28 2025
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CMSA General Relativity Seminar, Harvard University, February 25 2025
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Workshop on "Black Holes, Singularities, Shocks and Implosions", National University of Singapore, January 9 2025
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Seminar on Mathematical General Relativity, Laboratoire Jacques-Louis Lions, (Universit\'e Pierre et Marie Curie), November 21 2024
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Geometry, Analysis and Gravitation Seminar, Queen Mary University of London, November 12 2024
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DAMTP General Relativity Seminar, University of Cambridge, November 1 2024
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Analysis & PDE Seminar, Stanford University, September 17 2024
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Analysis & PDE Seminar, UC Berkeley, September 16 2024
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Analysis Seminar, Columbia University, September 13 2024
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Analysis Seminar, Princeton University, September 9 2024
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Workshop on "Mathematical Aspects of General Relativity", Oberwolfach, Aug 7 2024
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ESI Thematic Programme on "Nonlinear Waves and Relativity'', Vienna, June 20 2024
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PDE Seminar, Vanderbilt University, February 16 2024
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PDE Seminar, University of Cambridge, January 22 2024
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PDE/Analysis Seminar, BICMR, Peking University, December 19 2023
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Analysis Seminar, Toronto, November 3 2023.
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Cretan Waves Workshop, University of Crete, October 11 2023
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London PDE Seminar, University College London, June 23 2023
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Mathematical GR and Hyperbolic PDE Seminar, Online, June 16 2023
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Seminar of Differential Equations and Numerical Analysis, University of Crete, May 9 2023
Teaching
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MATH 256A: Intro to Partial Differential EquationsGraduate Level | Winter Quarter 2026
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Introductory lecture at SLMath Summer School on "Mathematics of General Relativity and Fluids"Gave preparatory lecture and problem session, notes available here. See also the following problem sheet.
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Teaching experience at PrincetonTeaching assistant, involving grading, office hours and precepts in various undergraduate courses.