Antoine Song

Antoine Y. Song is a French mathematician whose research concerns differential geometry and geometric analysis. He is a professor at Caltech. In 2018, he proved Yau's conjecture.

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 Pierre and [Marie Curie University|Université Pierre et Marie Curie]. He obtained his Ph.D. from Princeton University in 2019 under the supervision of Fernando Codá Marques.

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 and later Song proved it in full generality.
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.

He was a Clay Research Fellow.
He is a Sloan Fellow.
He delivered the 2021–2022 Peccot Lectures.
In 2024, he received the Frontiers of Science Award.