André Neves

Department of Mathematics and the College

André Neves is a geometer, whose goal is to understand which restrictions curvature imposes on space or on its submanifolds. With Fernando Marques, he proved that the least bended torus in space is the Clifford torus and, in doing so, solved the Willmore conjecture. The method of proof was revolutionary, in that it made use of the existence theory of unstable minimal surfaces (known as “min-max theory”), which a priori had nothing to do with the Willmore conjecture. Using the same method, jointly with Ian Agol and Marques, he also found the “best” representative for a non-trivial two-component link in space, the Hopf link. Last year, with Marques, he again used min-max theory to show that any compact manifold that is positively curved has an infinite number of minimal hypersurfaces. For this discovery, Neves and Marques were honored with the 2016 Oswald Veblen Prize in Geometry from the American Mathematical Society, the most prestigious award for geometers. In the same year, he was also awarded the New Horizons in Mathematics Prize, given by the Breakthrough Prize.

Neves is also the recipient of the Royal Society Wolfson Research Merit Award, the Leverhulme Prize in Mathematics, and the London Mathematical Society Whitehead Prize.

He received his PhD in mathematics from Stanford University and completed a postdoctoral fellowship at Princeton University, eventually joining its faculty. Most recently, he was a professor at Imperial College London.

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