Sven Hirsch – Home
Sven Hirsch

I am a Ritt Assistant Professor at Columbia University working on geometric analysis and mathematical relativity. Previously, I was a member at the Institute for Advanced Study in Princeton, and in 2023 I obtained a PhD from Duke working with Hubert Bray. There I won the L.P. Smith Award for Teaching Excellence and the Rudin Prize for Outstanding PhD Dissertations.


Outside of math I enjoy climbing, surfing and mountaineering.


News: In June 2024, I will be teaching a mini-course on spinors, gravitational waves and black holes in Copenhagen. In January 2025, I am co-organizing a workshop at the Chennai Mathematical Institute.


Contact: sven.hirsch@columbia.edu

Publications

  1. Rigidity of Asymptotically Hyperboloidal Initial Data Sets with Vanishing Mass, joint with Hyun Chul Jang and Yiyue Zhang, 2024, arXiv
  2. Rigidity of spin fill-ins with non-negative scalar curvature, joint with Simone Cecchini and Rudolf Zeidler, 2024, arXiv
  3. Initial data sets with vanishing mass are contained in pp-wave spacetimes, joint with Yiyue Zhang, 2024, arXiv
  4. Stability of Llarull’s theorem in all dimensions, joint with Yiyue Zhang, 2023, Adv. Math., arXiv
  5. Uniqueness of blowups for forced mean curvature flow, joint with Jonathan Zhu, 2023, Int. Math. Res. Not., arXiv
  6. 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
  7. Monotone quantities of p-harmonic functions and their applications, joint with Pengzi Miao and Luen-Fai Tam, 2022, Pure Appl. Math. Q., arXiv
  8. Hawking mass monotonicity for initial data sets, 2022, arXiv
  9. Rigid comparison geometry for Riemannian bands and open incomplete manifolds, joint with Demetre Kazaras, Marcus Khuri and Yiyue Zhang, 2022, Math. Ann., arXiv
  10. A generalization of Geroch’s conjecture, joint with Simon Brendle and Florian Johne, 2023, Comm. Pure Appl. Math., arXiv
  11. The case of equality for the spacetime positive mass theorem, joint with Yiyue Zhang, J. Geom. Anal., 2022, arXiv
  12. 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
  13. On the Moduli Space of Asymptotically Flat Manifolds with Boundary and the Constraint Equations, joint with Martin Lesourd, Comm. Anal. Geom., 2021, arXiv
  14. Mass of asymptotically flat 3-manifolds with boundary, joint with Pengzi Miao and Tin-Yau Tsang, Comm. Anal. Geom., 2021, arXiv
  15. Spacetime Harmonic Functions and Applications to Mass, joint with Hubert Bray, Demetre Kazaras, Marcus Khuri and Yiyue Zhang, SIGMA, 2021, arXiv
  16. Contracting convex surfaces by mean curvature flow with free boundary on convex barriers, joint with Martin Li, Asian J. Math., 2023, arXiv
  17. Flatly Foliated Relativity, joint with Hubert Bray, Benjamin Hamm, James Wheeler and Yiyue Zhang, Pure Appl. Math. Q., 2019, arXiv
  18. A Positive Mass Theorem for Manifolds with Boundary, joint with Pengzi Miao, Pac. J. Math., 2019, arXiv