Antoine Song
Antoine Song | |
|---|---|
| Born | July 18, 1992 |
| Alma mater | Princeton University |
| Known for | Yau's conjecture |
| Scientific career | |
| Fields | Differential geometry |
| Institutions | Caltech |
| Doctoral advisor | Fernando Codá Marques |
| Website | https://sites.google.com/view/antoinesong/home |
Antoine Song (born 18 July 1992 in Paris) is a French[1] mathematician whose research concerns differential geometry. In 2018, he proved Yau's conjecture.
He was a Clay Research Fellow (2019–2024).[2] He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando Codá Marques.[3] He is an assistant professor of mathematics at Caltech.[4] He is a Sloan Fellow.[5][6]
In 2023, together with Conghan Dong, he proved a conjecture from 2001 by G. Huisken and T. Ilmanen on the mathematics of general relativity, about the curvature in spaces with very little mass.[7]
He delivered the 2021–2022 Peccot Lectures (in 2022, due to the coronavirus pandemic).[8]
Existence of minimal surfaces
[edit]It is known that any closed surface possesses infinitely many closed geodesics. The first problem in the minimal submanifolds section of Yau's list asks whether any closed three-manifold has infinitely many closed smooth immersed minimal surfaces. At the time it was known from Almgren–Pitts min-max theory the existence of at least one minimal surface. Kei Irie, Fernando Codá Marques, and André Neves solved this problem in the generic case [9] and later Antoine Song proved it in full generality.[10]
Selected publications
[edit]- "Existence of infinitely many minimal hypersurfaces in closed manifolds" (2018), Annals of Mathematics
- Joint with Marques and Neves: "Equidistribution of minimal hypersurfaces for generic metrics" (2019), Inventiones mathematicae[11]
- Joint with Conghan Dong: "Stability of Euclidean 3-space for the positive mass theorem" (2023), Inventiones mathematicae[12]
References
[edit]- ^ Song's CV
- ^ "Antoine Song | Clay Mathematics Institute". www.claymath.org.
- ^ Antoine Song at the Mathematics Genealogy Project
- ^ "Antoine Song | the Division of Physics, Mathematics and Astronomy".
- ^ "Caltech Professors Win 2024 Sloan Fellowships". 20 February 2024.
- ^ "2024 Fellows | Alfred P. Sloan Foundation".
- ^ Nadis, Steve (30 November 2023), "A Century Later, New Math Smooths Out General Relativity", Quanta Magazine
- ^ "Cours Peccot 2021-2022 | CNRS Mathématiques". 27 September 2021.
- ^ "Density of minimal hypersurfaces for generic metrics | Annals of Mathematics".
- ^ Song, Antoine (2018). "Existence of infinitely many minimal hypersurfaces in closed manifolds". arXiv:1806.08816 [math.DG].
- ^ "Math Duo Maps the Infinite Terrain of Minimal Surfaces". 12 March 2019.
- ^ "A Century Later, New Math Smooths Out General Relativity". 30 November 2023.
External link
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