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Antoine Song

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Antoine Song
Born (1992-07-18) July 18, 1992 (age 32)
Alma materPrinceton University
Known forYau's conjecture
Scientific career
FieldsDifferential geometry
InstitutionsCaltech
Doctoral advisorFernando Codá Marques

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]

He delivered the 2021–2022 Peccot Lectures (in 2022, due to the coronavirus pandemic).[8]

Existence of minimal surfaces

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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 claimed it in full generality.[10]

Selected publications

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  • "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)[12]

References

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  1. ^ Song's CV
  2. ^ "Antoine Song | Clay Mathematics Institute". www.claymath.org.
  3. ^ Antoine Song at the Mathematics Genealogy Project
  4. ^ https://pma.caltech.edu/people/antoine-song
  5. ^ https://www.caltech.edu/about/news/caltech-professors-win-2024-sloan-fellowships
  6. ^ https://sloan.org/fellowships/2024-Fellows
  7. ^ Nadis, Steve (30 November 2023), "A Century Later, New Math Smooths Out General Relativity", Quanta Magazine
  8. ^ https://www.insmi.cnrs.fr/fr/cnrsinfo/cours-peccot-2021-2022
  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. ^ https://www.quantamagazine.org/math-duo-maps-the-infinite-terrain-of-minimal-surfaces-20190312/
  12. ^ https://www.quantamagazine.org/a-century-later-new-math-smooths-out-general-relativity-20231130/
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