Jump to content

Antoine Song

From Wikipedia, the free encyclopedia
Antoine Song
Born (1992-07-18) July 18, 1992 (age 34)
EducationPrinceton University (PhD)
Université Pierre et Marie Curie (BS and MS)
École Normale SupĂ©rieure de Paris
Known forYau's conjecture
Huisken–Ilmanen conjecture
Equidistribution of minimal hypersurfaces
Talagrand's convexity conjecture[1]
Scientific career
FieldsDifferential geometry
Geometric analysis
WorkplacesCaltech
ThesisIn search of minimal hypersurfaces (2019)
Fernando CodĂĄ Marques
Websitesites.google.com/view/antoinesong/home

Antoine Y. Song (born 18 July 1992 in Paris) is a French[2] mathematician whose research concerns differential geometry and geometric analysis. He is a professor at Caltech.[3] In 2018, he proved Yau's conjecture. He holds the Alexzandria Figueroa & Robert Penner Chair for invited researchers at the Institut des Hautes Études Scientifiques.[4]

Contributions to mathematics

[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 (Yau's conjecture) 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 CodĂĄ Marques, and AndrĂ© Neves solved this problem in the generic case [5] and later Song proved it in full generality.[6]

Together with Conghan Dong,[7] 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.[8]

Education

[edit]

Antoine Song was a student at the École Normale SupĂ©rieure de Paris from 2012 to 2015. He obtained a bachelor's and a master's degree in mathematics from the UniversitĂ© Pierre et Marie Curie (Paris 6).[2] He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando CodĂĄ Marques, with the thesis In search of minimal hypersurfaces.[9]

Honours and awards

[edit]

He was a Clay Research Fellow (2019–2024).[10]

He is a Sloan Fellow.[11][12]

He delivered the 2021–2022 Peccot Lectures (in 2022, due to the coronavirus pandemic).[13]

In 2024, he received the Frontiers of Science Award.[14]

Selected publications

[edit]
  • Song, Antoine (2023). "Existence of infinitely many minimal hypersurfaces in closed manifolds". Annals of Mathematics. Second Series. 197 (3). arXiv:1806.08816. doi:10.4007/annals.2023.197.3.1. MR 4564260. Zbl 1526.53013.
  • Marques, Fernando C.; Neves, AndrĂ©; Song, Antoine (2019). "Equidistribution of minimal hypersurfaces for generic metrics". Inventiones Mathematicae. 216 (2): 421–443. arXiv:1712.06238. Bibcode:2019InMat.216..421M. doi:10.1007/s00222-018-00850-5.[15]
  • Dong, Conghan; Song, Antoine (2025). "Stability of Euclidean 3-space for the positive mass theorem". Inventiones Mathematicae. 239 (1): 287. arXiv:2302.07414. Bibcode:2025InMat.239..287D. doi:10.1007/s00222-024-01302-z.[16]

References

[edit]
[edit]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Antoine_Song&oldid=1382000077"