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]
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]
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]
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]