👋 Hi there, I’m Jingbo, who is passionate about Geometric Analysis and General Relativity!
🧑🎓 I am a fifth-year graduate student at Columbia University, supervised by Professor Mu-Tao Wang and Professor Elena Giorgi.
🗼 I am graduating from Columbia Univeristy and will be at Sorbonne University starting from 2025 fall.
🏫 I completed my undergraduate studies at the Hong Kong University of Science and Technology, where I was supervised by Professor Frederick Fong.
More About Me
✨ My research interests include differential geometry, partial differential equations, general relativity, and more, with a particular focus on various aspects of black holes.
📃 My published works cover topics such as positively curved manifolds, parabolic geometric/heat flows, and hyperbolic equations on black holes:
- (Joint with Dawei Shen) “Formation of Trapped Surfaces for the Einstein-Maxwell-Charged Scalar Field System”, arXiv:2504.19976, 28 Apr 2025.
- (Joint with Sergiu Klainerman and Dawei Shen) “A Canonical Foliation on Null Infinity in Perturbations of Kerr”, arXiv:2412.20119, 28 Dec 2024, submitted.
- (Joint with Elena Giorgi) “Boundedness and Decay for the Teukolsky System in Kerr-Newman Spacetime II: The Case ( a \ll M, Q < M ) in Axial Symmetry”, Adv. Theor. Math. Phys., to appear.
- “Sharp Interior Gradient Estimate for Area Decreasing Graphical Mean Curvature Flow in Arbitrary Codimension,” submitted.
- (Joint with Man-Chun Lee and Luen-Fai Tam) “Rigidity of Area Non-Increasing Maps”, Trans. Amer. Math. Soc. 378 (2025), no. 4, 2797-2827.
- (Joint with Man-Chun Lee) “Rigidity of Contracting Maps Using Harmonic Map Heat Flow”, Proc. Amer. Math. Soc., to appear.
- (Joint with Elena Giorgi) “Physical-Space Estimates for Axisymmetric Waves on Extremal Kerr Spacetime”, J. Funct. Anal. 287 (12), 110668.
- (Joint with Florian Johne and Tsz-Kiu Aaron Chow) “Preserving Positive Intermediate Curvature”, J. Geom. Anal. 33, 366 (2023).
- (Joint with Nicholas Cheng-Hoong Chin and Frederick Tsz-Ho Fong) “Uniqueness Theorems of Self-Conformal Solutions to Inverse Curvature Flows”, Proc. Amer. Math. Soc. 148 (2020), 4967-4982.
See my PUBLICATIONS LIST for more details.
Seminars and Talks
🧑🏫 I have co-organized several student seminars at Columbia University:
- Fall 2021: Informal student GR seminar (via Zoom)
- Fall 2022: Scalar Curvature and Topology
- Spring 2023: Scalar Curvature and Dihedral Rigidity
- Fall 2023: Geometric Flows and Their Applications
- Spring 2024: Regularity Theory of the Monge-Ampère Equation
- Fall 2024: BV Functions & Regularity of Minimal Surfaces
🗣️ For invited talks, here is a list of upcoming and recent events:
- Mathematical GR and Hyperbolic PDE Seminar - Virtual, Sep 2024
- Harmonic Analysis and Differential Equations Seminar - UC Berkeley, Sep 2024
- Mini-workshop in Geometric Analysis - SUSTech, Aug 2024
- Seminar on Pure Mathematics - HKUST, Aug 2024
- Topics in General Relativity at Mathematics Münster - Münster University, Jul 2024
- Westlake University Geometric Analysis Seminar - Westlake University (online), Apr 2024
- BIMCR Geometric Analysis Seminar - BIMCR (online), Mar 2024
- CUNY Geometric Analysis Seminar - CUNY Graduate Center, Sep 2023
- Geometric Analysis Seminar - CUHK, Aug 2023
- Seminar on Pure Mathematics - HKUST, Aug 2023
- MIST 2023 Workshop on Geometry - CUHK, Aug 2023
- Joint Geometric Analysis Seminar - CUHK, Jun 2023
- Columbia General Relativity & Geometric Analysis Seminar - Columbia University, Oct 2022
Invited Lectures:
- Short Course: Semi-linear Wave Equation on Black Holes - CUHK, Aug 2023
For more details on my seminars and invited talks, see my TALKS LIST.