Antoine Song

Antoine Song
Born	(1992-07-18) July 18, 1992 (age 32)
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

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

• "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

1. Song's CV
2. "Antoine Song | Clay Mathematics Institute". www.claymath.org.
3. Antoine Song at the Mathematics Genealogy Project
4. "Antoine Song | the Division of Physics, Mathematics and Astronomy".
5. "Caltech Professors Win 2024 Sloan Fellowships". 20 February 2024.
6. "2024 Fellows | Alfred P. Sloan Foundation".
7. Nadis, Steve (30 November 2023), "A Century Later, New Math Smooths Out General Relativity", Quanta Magazine
8. "Cours Peccot 2021-2022 | CNRS Mathématiques". 27 September 2021.
9. "Density of minimal hypersurfaces for generic metrics | Annals of Mathematics".
10. Song, Antoine (2018). "Existence of infinitely many minimal hypersurfaces in closed manifolds". arXiv:1806.08816 [math.DG].
11. "Math Duo Maps the Infinite Terrain of Minimal Surfaces". 12 March 2019.
12. "A Century Later, New Math Smooths Out General Relativity". 30 November 2023.

External link

• The Geometry of Minimal Surfaces: An Interview with Antoine Song (October 13, 2023)