Antoine Song

Antoine Y. Song (born 18 July 1992 in Paris) is a French^[1] mathematician whose research concerns differential geometry and geometric analysis. He is a professor at Caltech.^[2] In 2018, he proved Yau's conjecture.

Antoine Song
Born	(1992-07-18) July 18, 1992 (age 33)
Alma mater	Princeton University (PhD) Université Pierre et Marie Curie (BS and MS) École Normale Supérieure de Paris
Known for	Yau's conjecture Huisken–Ilmanen conjecture Equidistribution of minimal hypersurfaces
Scientific career
Fields	Differential geometry Geometric analysis
Institutions	Caltech
Doctoral advisor	Fernando Codá Marques
Website	sites.google.com/view/antoinesong/home

Education

Antoine Song was a student at the École Normale Supérieure de Paris from 2012 to 2015. He obtained a bachelor's and a master's degree in mathematics from the Université Pierre et Marie Curie (Paris 6).^[1] He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando Codá Marques.^[3]

Mathematical work

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 Codá Marques, and André Neves solved this problem in the generic case ^[4] and later, in 2018, Antoine Song proved it in full generality.^[5]

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.^[6]

Honours and awards

He was a Clay Research Fellow (2019–2024).^[7]

He is a Sloan Fellow.^[8][9]

He delivered the 2021–2022 Peccot Lectures (in 2022, due to the coronavirus pandemic).^[10]

In 2024, he received the Frontiers of Science Award.^[11]

Selected publications

• "Existence of infinitely many minimal hypersurfaces in closed manifolds" (2018), Annals of Mathematics https://arxiv.org/abs/1806.08816
• Joint with Marques and Neves: "Equidistribution of minimal hypersurfaces for generic metrics" (2019), Inventiones mathematicae https://arxiv.org/abs/1712.06238 ^[12]
• Joint with Conghan Dong: "Stability of Euclidean 3-space for the positive mass theorem" (2023), Inventiones mathematicae https://arxiv.org/abs/2302.07414 ^[13]