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Prize: Oswald Veblen Prize in Geometry

Oswald Veblen Prize in Geometry 2022 Dr. Michael A. Hill; Professor Michael J Hopkins; Professor Douglas C Ravenel

**Michael Hill**, **Michael Hopkins**, and **Douglas Ravenel **received the 2022 Veblen Prize for their paper "On the nonexistence of elements of Kervaire invariant one." This paper solved a 50-year-old problem in geometric topology by showing that framed manifolds with Kervaire invariant one can only exist in finitely many dimensions, introducing deeply influential new ideas and techniques in algebraic topology.

Oswald Veblen Prize in Geometry 2019 Xiuxiong Chen; Simon Donaldson; Song Sun

**Xiu Xiong Chen**, **Simon Donaldson**, and **Song Sun** received the 2019 Veblen Prize for their three-part series, "Kähler-Einstein metrics on Fano manifolds, I, II and III," published in 2015 in the Journal of the American Mathematical Society, in which they proved a long-standing conjecture in differential geometry.

Prize announcement as seen in *Notices of the AMS* and in the news release.

Oswald Veblen Prize in Geometry 2016 Fernando Codá Marques; André Neves

Nineteenth award: The 2016 Veblen Prize was awarded to Fernando Codá Marques and André Neves, for "their remarkable work on variational problems in differential geometry [including] the proof of the Willmore conjecture". This work resolved a longstanding question about the nature of surfaces.

Prize announcement as seen in *Notices of the AMS* and in the news release.

Oswald Veblen Prize in Geometry 2013 Ian Agol; Daniel Wise

Eighteenth award: The 2013 Veblen Prize was awarded to Ian Agol, for his many fundamental contributions to hyperbolic geometry, 3-manifold topology, and geometric group theory and to Daniel Wise, for his deep work establishing subgroup separability (LERF) for a wide class of groups and for introducing and developing with Frédéric Haglund the theory of special cube complexes which are of fundamental importance for the topology of three-dimensional manifolds.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 2010 Tobias H. Colding; William P. Minicozzi II; Paul Seidel

Seventeenth award: to Tobias H. Colding and William P. Minicozzi II for their profound work on minimal surfaces; and to Paul Seidel for his fundamental contributions to symplectic geometry.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 2007 Peter Kronheimer; Tomasz Mrowka; Zoltán Szabó; Peter Ozsvath

Sixteenth award: to Peter Kronheimer and Tomasz Mrowka for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications; and to Peter Ozsváth and Zoltán Szabó for their contributions to 3- and 4-dimensional topology through their Heegaard Floer homology theory.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 2004 David Gabai

Fifteenth award: to David Gabai for his work in geometric topology, in particular, the topology of 3-dimensional manifolds.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 2001 Jeff Cheeger; Yakov Eliashberg; Michael J. Hopkins

Fourteenth award: to Jeff Cheeger for his work in differential geometry, to Yakov Eliashberg for his work in symplectic and contact topology, and to Michael J. Hopkins for his work in homotopy theory.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 1996 Richard Hamilton; Gang Tian

Thirteenth award: to Richard Hamilton for his continuing study of the Ricci flow and related parabolic equations for a Riemannian metric, and to Gang Tian for his contributions to geometric analysis.

Prize announcement as seen in *Notices of the AMS*.

Oswald Veblen Prize in Geometry 1991 Andrew J. Casson; Clifford H. Taubes

Twelfth award: to Andrew J. Casson for his work on the topology of low-dimensional manifolds, and to Clifford H. Taubes for his foundational work in Yang-Mills theory.

Oswald Veblen Prize in Geometry 1986 Michael H. Freedman

Eleventh award: to Michael H. Freedman for his work in differential geometry and, in particular, the solution of the four-dimensional Poincaré conjecture.

Oswald Veblen Prize in Geometry 1981 Shing-Tung Yau; Mikhael Gromov

Ninth award: to Mikhael Gromov for his work relating topological and geometric properties of Riemannian manifolds.

Oswald Veblen Prize in Geometry 1976 James Simons; William P. Thurston

Seventh award: to William P. Thurston for his work on foliations.

Oswald Veblen Prize in Geometry 1971 Dennis P. Sullivan; Robion C. Kirby

Fifth award: to Robion C. Kirby for his paper, Stable homeomorphisms and the annulus conjecture, Annals of Mathematics, Series 2, volume 89 (1969), pp.575-582.

Oswald Veblen Prize in Geometry 1966 Morton Brown; Barry Mazur; Stephen Smale

Third award: to Stephen Smale for his contributions to various aspects of differential topology.

Oswald Veblen Prize in Geometry 1964 Raoul Bott; C. D. Papakyriakopoulos

First award: to C. D. Papakyriakopoulos for his papers, *On Solid Tori*, Annals of Mathematics, Series 2, volume 66 (1957), pp. 1-26, and *On Dehn's lemma and the asphericity of knots*, Proceedings of the National Academy of Sciences, volume 43 (1957), pp. 169-172.