Antoine Song
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 is 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 Huisken and Ilmanen on the mathematics of general relativity, about the curvature in spaces with very little mass.[7]
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 [8] and later Antoine Song claimed it in full generality.[9]
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[10]
- Joint with Conghan Dong: "Stability of Euclidean 3-space for the positive mass theorem" (2023)[11]
References[edit]
- ^ Song's CV
- ^ "Antoine Song | Clay Mathematics Institute". www.claymath.org.
- ^ Antoine Song at the Mathematics Genealogy Project
- ^ https://pma.caltech.edu/people/antoine-song
- ^ https://www.caltech.edu/about/news/caltech-professors-win-2024-sloan-fellowships
- ^ https://sloan.org/fellowships/2024-Fellows
- ^ Nadis, Steve (30 November 2023), "A Century Later, New Math Smooths Out General Relativity", Quanta Magazine
- ^ "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].
- ^ https://www.quantamagazine.org/math-duo-maps-the-infinite-terrain-of-minimal-surfaces-20190312/
- ^ https://www.quantamagazine.org/a-century-later-new-math-smooths-out-general-relativity-20231130/
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