Publications

1. Stable 2-systoles, scalar curvature and spin^c comass bounds, joint with Simone Cecchini and Rudolf Zeidler, 2026, arXiv
2. On a Variant of the Penrose Conjecture, joint with Yipeng Wang, 2026, arXiv
3. The Hyperboloidal and Spacetime Positive Mass Theorem in all dimensions, joint with Marcus Khuri, Martin Lesourd and Yiyue Zhang, 2026, arXiv
4. The Spacetime Positive Mass Theorem with Multiple Time Dimensions, joint with Alec Payne and Yiyue Zhang, 2026, arXiv
5. The lock principle for scalar curvature, joint with Georg Frenck and Bernhard Hanke, 2026, arXiv
6. Surgery and total mean curvature, joint with Georg Frenck and Bernhard Hanke, 2026, arXiv
7. A universal Bochner formula for scalar curvature, 2026, arXiv
8. Causal character of imaginary Killing spinors and spinorial slicings, joint with Yiyue Zhang, 2025, arXiv
9. Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers, joint with Lan-Hsuan Huang, 2025, arXiv
10. Rigidity of Asymptotically Hyperboloidal Initial Data Sets with Vanishing Mass, joint with Hyun Chul Jang and Yiyue Zhang, 2025, Comm. Math. Phys., arXiv
11. Rigidity of spin fill-ins with non-negative scalar curvature, joint with Simone Cecchini and Rudolf Zeidler, 2024, arXiv
12. Initial data sets with vanishing mass are contained in pp-wave spacetimes, joint with Yiyue Zhang, 2025, J. Eur. Math. Soc., arXiv
13. Stability of Llarull’s theorem in all dimensions, joint with Yiyue Zhang, 2024, Adv. Math., arXiv
14. Uniqueness of blowups for forced mean curvature flow, joint with Jonathan Zhu, 2023, Int. Math. Res. Not., arXiv
15. Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem, joint with Demetre Kazaras, Marcus Khuri and Yiyue Zhang, 2023, Int. Math. Res. Not., arXiv
16. Hawking mass monotonicity for initial data sets, 2025, Asian J. Math., arXiv
17. Rigid comparison geometry for Riemannian bands and open incomplete manifolds, joint with Demetre Kazaras, Marcus Khuri and Yiyue Zhang, 2022, Math. Ann., arXiv
18. A generalization of Geroch’s conjecture, joint with Simon Brendle and Florian Johne, 2023, Comm. Pure Appl. Math., arXiv
19. Monotone quantities of p-harmonic functions and their applications, joint with Pengzi Miao and Luen-Fai Tam, 2022, Pure Appl. Math. Q., arXiv
20. The case of equality for the spacetime positive mass theorem, joint with Yiyue Zhang, J. Geom. Anal., 2022, arXiv
21. Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations, joint with Demetre Kazaras and Marcus Khuri, J. Differential Geom., 2021, arXiv
22. On the Moduli Space of Asymptotically Flat Manifolds with Boundary and the Constraint Equations, joint with Martin Lesourd, Comm. Anal. Geom., 2021, arXiv
23. Mass of asymptotically flat 3-manifolds with boundary, joint with Pengzi Miao and Tin-Yau Tsang, Comm. Anal. Geom., 2021, arXiv
24. Spacetime Harmonic Functions and Applications to Mass, joint with Hubert Bray, Demetre Kazaras, Marcus Khuri and Yiyue Zhang, SIGMA, 2021, arXiv
25. Contracting convex surfaces by mean curvature flow with free boundary on convex barriers, joint with Martin Li, Asian J. Math., 2023, arXiv
26. Flatly Foliated Relativity, joint with Hubert Bray, Benjamin Hamm, James Wheeler and Yiyue Zhang, Pure Appl. Math. Q., 2019, arXiv
27. A Positive Mass Theorem for Manifolds with Boundary, joint with Pengzi Miao, Pac. J. Math., 2019, arXiv

Professional Activities

Seminars and conferences organized

• I organized the first Lonavala Geometry Festival .
• I co-organized a workshop at the Chennai Mathematical Institute.
• I am co-organizing a learning seminar on String Theory.

Teaching

• I am currently teaching Modern Analysis (Math 4061). Information about the course can be found here.
• I taught a minicourse on spinors, gravitational waves and black holes in Copenhagen. The lecture notes can be found here: Spinors and Spacetime Harmonic Functions (PDF) .
• I am organizing an undergraduate geometry and mathematical relativity reading course. If you would like to participate, please send me an email.

Outreach

• My research was featured in Quanta and appeared on The Late Show with Stephen Colbert .
• Sofya Kovalevskaya Day

Upcoming events and talks

• April: Banff; Duke
• May: Tsinghua; BIMSA; Zhejiang
• June: Oberwolfach; KTH Stockholm

Geometric Analysis Seminar

The seminar takes place on Fridays from 3 to 4 pm in Math 507.