__NOTOC__ The Oswald Veblen Prize in Geometry is an award granted by the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

for notable research in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. It was founded in 1961 in memory of

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...

. The Veblen Prize is now worth US$5000, and is awarded every three years. The first seven prize winners were awarded for works in topology. James Harris Simons and William Thurston were the first ones to receive it for works in geometry (for some distinctions, see

geometry and topology In mathematics, geometry and topology is an umbrella term for the historically distinct disciplines of geometry and topology, as general frameworks allow both disciplines to be manipulated uniformly, most visibly in local to global theorems in Ri ...

). As of 2020, there have been thirty-four prize recipients.

List of recipients

* 1964 Christos Papakyriakopoulos * 1964

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous basic contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions whi ...

* 1966 Stephen Smale * 1966

Morton Brown Morton Brown (born August 12, 1931, in New York City, New York) is an American mathematician, who specializes in geometric topology. In 1958 Brown earned his Ph.D. from the University of Wisconsin-Madison under R. H. Bing. From 1960 to 1962 he w ...

and Barry Mazur * 1971

Robion Kirby Robion Cromwell Kirby (born February 25, 1938) is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he invented the Kirby–Siebenmann invariant f ...

* 1971

Dennis Sullivan Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate ...

* 1976 William Thurston * 1976 James Harris Simons * 1981 Mikhail Gromov for: ::''Manifolds of negative curvature.'' Journal of Differential Geometry 13 (1978), no. 2, 223–230. ::''Almost flat manifolds.'' Journal of Differential Geometry 13 (1978), no. 2, 231–241. ::''Curvature, diameter and Betti numbers.'' Comment. Math. Helv. 56 (1981), no. 2, 179–195. ::''Groups of polynomial growth and expanding maps.'' Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. ::''Volume and bounded cohomology.'' Inst. Hautes Études Sci. Publ. Math. 56 (1982), 5–99 * 1981

Shing-Tung Yau Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau announced retirement from Harvard to become Chair Professor of mathem ...

for: ::''On the regularity of the solution of the n-dimensional Minkowski problem.'' Comm. Pure Appl. Math. 29 (1976), no. 5, 495–516. (with

Shiu-Yuen Cheng Shiu-Yuen Cheng (鄭紹遠) is a Hong Kong mathematician. He is currently the Chair Professor of Mathematics at the Hong Kong University of Science and Technology. Cheng received his Ph.D. in 1974, under the supervision of Shiing-Shen Chern, from ...

) ::''On the regularity of the Monge-Ampère equation'' . Comm. Pure Appl. Math. 30 (1977), no. 1, 41–68. (with

) ::''Calabi's conjecture and some new results in algebraic geometry.'' Proc. Natl. Acad. Sci. U.S.A. 74 (1977), no. 5, 1798–1799. ::''On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I.'' Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411. ::''On the proof of the positive mass conjecture in general relativity.'' Comm. Math. Phys. 65 (1979), no. 1, 45–76. (with

Richard Schoen Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984. Career Born in Celina, Ohio, and a ...

) ::''Topology of three-dimensional manifolds and the embedding problems in minimal surface theory.'' Ann. of Math. (2) 112 (1980), no. 3, 441–484. (with William Meeks) * 1986

Michael Freedman Michael Hartley Freedman (born April 21, 1951) is an American mathematician, at Microsoft Station Q, a research group at the University of California, Santa Barbara. In 1986, he was awarded a Fields Medal for his work on the 4-dimensional gene ...

for: ::''The topology of four-dimensional manifolds.'' Journal of Differential Geometry 17 (1982), no. 3, 357–453. * 1991 Andrew Casson for: ::his work on the topology of low dimensional manifolds and specifically for the discovery of an integer valued invariant of homology three spheres whose reduction mod(2) is the invariant of Rohlin. * 1991

Clifford Taubes Clifford Henry Taubes (born February 21, 1954) is the William Petschek Professor of Mathematics at Harvard University and works in gauge field theory, differential geometry, and low-dimensional topology. His brother is the journalist Gary Taube ...

for: ::''Self-dual Yang-Mills connections on non-self-dual 4-manifolds.'' Journal of Differential Geometry 17 (1982), no. 1, 139–170. ::''Gauge theory on asymptotically periodic 4-manifolds.'' J. Differential Geom. 25 (1987), no. 3, 363–430. ::''Casson's invariant and gauge theory.'' J. Differential Geom. 31 (1990), no. 2, 547–599. * 1996 Richard S. Hamilton. for: ::''The formation of singularities in the Ricci flow.'' Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 7–136, Int. Press, Cambridge, MA, 1995. ::''Four-manifolds with positive isotropic curvature.'' Comm. Anal. Geom. 5 (1997), no. 1, 1–92. * 1996 Gang Tian for: ::''On Calabi's conjecture for complex surfaces with positive first Chern class.'' Invent. Math. 101 (1990), no. 1, 101–172. ::''Compactness theorems for Kähler-Einstein manifolds of dimension 3 and up.'' J. Differential Geom. 35 (1992), no. 3, 535–558. ::''A mathematical theory of quantum cohomology.'' J. Differential Geom. 42 (1995), no. 2, 259–367. (with Yongbin Ruan) ::''Kähler-Einstein metrics with positive scalar curvature.'' Invent. Math. 130 (1997), no. 1, 1–37. * 2001 Jeff Cheeger. for: ::''Families index for manifolds with boundary, superconnections, and cones. I. Families of manifolds with boundary and Dirac operators.'' J. Funct. Anal. 89 (1990), no. 2, 313–363. (with Jean-Michel Bismut) ::''Families index for manifolds with boundary, superconnections and cones. II. The Chern character.'' J. Funct. Anal. 90 (1990), no. 2, 306–354. (with Jean-Michel Bismut) ::''Lower bounds on Ricci curvature and the almost rigidity of warped products.'' Ann. of Math. (2) 144 (1996), no. 1, 189–237. (with Tobias Colding) ::''On the structure of spaces with Ricci curvature bounded below. I.'' J. Differential Geom. 46 (1997), no. 3, 406–480. (with Tobias Colding) * 2001 Yakov Eliashberg for: ::''Combinatorial methods in symplectic geometry.'' Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 531–539, Amer. Math. Soc., Providence, RI, 1987. ::''Classification of overtwisted contact structures on 3-manifolds.'' Invent. Math. 98 (1989), no. 3, 623–637. * 2001 Michael J. Hopkins for: ::''Nilpotence and stable homotopy theory. I.'' Ann. of Math. (2) 128 (1988), no. 2, 207–241. (with Ethan Devinatz and Jeffrey Smith) ::''The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory.'' Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 1, 76–86. (with Benedict Gross) ::''Equivariant vector bundles on the Lubin-Tate moduli space.'' Topology and representation theory (Evanston, IL, 1992), 23–88, Contemp. Math., 158, Amer. Math. Soc., Providence, RI, 1994. (with Benedict Gross) ::''Elliptic spectra, the Witten genus and the theorem of the cube.'' Invent. Math. 146 (2001), no. 3, 595–687. (with Matthew Ando and

Neil Strickland Neil is a masculine name of Gaelic and Irish origin. The name is an anglicisation of the Irish ''Niall'' which is of disputed derivation. The Irish name may be derived from words meaning "cloud", "passionate", "victory", "honour" or "champion".. A ...

) ::''Nilpotence and stable homotopy theory. II.'' Ann. of Math. (2) 148 (1998), no. 1, 1–49. (with Jeffrey Smith) * 2004

David Gabai David Gabai is an American mathematician and the Hughes-Rogers Professor of Mathematics at Princeton University. Focused on low-dimensional topology and hyperbolic geometry, he is a leading researcher in those subjects. Biography David Ga ...

* 2007 Peter Kronheimer and Tomasz Mrowka. for: ::''The genus of embedded surfaces in the projective plane.'' Math. Res. Lett. 1 (1994), no. 6, 797–808. ::''Embedded surfaces and the structure of Donaldson's polynomial invariants.'' J. Differential Geom. 41 (1995), no. 3, 573–734. ::''Witten's conjecture and property P.'' Geom. Topol. 8 (2004), 295–310. * 2007 Peter Ozsváth and Zoltán Szabó for: ::''Holomorphic disks and topological invariants for closed three-manifolds.'' Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. ::''Holomorphic disks and three-manifold invariants: properties and applications.'' Ann. of Math. (2) 159 (2004), no. 3, 1159–1245. ::''Holomorphic disks and genus bounds.'' Geom. Topol. 8 (2004), 311–334. * 2010 Tobias Colding and

William Minicozzi II William Philip Minicozzi II is an American mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967. Career Minicozzi graduated from Princeton University in 1990 and received his Ph.D. from Stanford University in 1994 under the direction o ...

. for: ::''The space of embedded minimal surfaces of fixed genus in a 3-manifold. I. Estimates off the axis for disks.'' Ann. of Math. (2) 160 (2004), no. 1, 27–68. ::''The space of embedded minimal surfaces of fixed genus in a 3-manifold. II. Multi-valued graphs in disks.'' Ann. of Math. (2) 160 (2004), no. 1, 69–92. ::''The space of embedded minimal surfaces of fixed genus in a 3-manifold. III. Planar domains.'' Ann. of Math. (2) 160 (2004), no. 2, 523–572. ::''The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV. Locally simply connected.'' Ann. of Math. (2) 160 (2004), no. 2, 573–615. ::''The Calabi-Yau conjectures for embedded surfaces.'' Ann. of Math. (2) 167 (2008), no. 1, 211–243. * 2010

Paul Seidel Paul Seidel (born December 30, 1970) is a Swiss-Italian mathematician. He is a faculty member at the Massachusetts Institute of Technology. Career Seidel attended Heidelberg University, where he received his Diplom under supervision of Albrecht ...

for: ::''A long exact sequence for symplectic Floer cohomology.'' Topology 42 (2003), no. 5, 1003–1063. ::''The symplectic topology of Ramanujam's surface.'' Comment. Math. Helv. 80 (2005), no. 4, 859–881. (with Ivan Smith) ::''Fukaya categories and Picard-Lefschetz theory.'' Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich, 2008. viii+326 pp. ::''Exact Lagrangian submanifolds in simply-connected cotangent bundles.'' Invent. Math. 172 (2008), no. 1, 1–27. (with Kenji Fukaya and Ivan Smith) * 2013

Ian Agol Ian Agol (born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Education and career Agol graduated with B.S. in mathematics from the California Institute of Technology in 1992 and ...

. for: ::''Lower bounds on volumes of hyperbolic Haken 3-manifolds.'' With an appendix by Nathan Dunfield. J. Amer. Math. Soc. 20 (2007), no. 4, 1053–1077. (with Daniel Storm and William Thurston) ::''Criteria for virtual fibering.'' J. Topol. 1 (2008), no. 2, 269–284. ::''Residual finiteness, QCERF and fillings of hyperbolic groups.'' Geom. Topol. 13 (2009), no. 2, 1043–1073. (with Daniel Groves and Jason Fox Manning) * 2013 Daniel Wise for: ::''Subgroup separability of graphs of free groups with cyclic edge groups.'' Q. J. Math. 51 (2000), no. 1, 107–129. ::''The residual finiteness of negatively curved polygons of finite groups.'' Invent. Math. 149 (2002), no. 3, 579–617. ::''Special cube complexes.'' Geom. Funct. Anal. 17 (2008), no. 5, 1551–1620. (with Frédéric Haglund) ::''A combination theorem for special cube complexes.'' Ann. of Math. (2) 176 (2012), no. 3, 1427–1482. (with Frédéric Haglund) * 2016

Fernando Codá Marques Fernando Codá dos Santos Cavalcanti Marques (born 8 October 1979) is a Brazilian mathematician working mainly in geometry, topology, partial differential equations and Morse theory. He is a professor at Princeton University. In 2012, together ...

and André Neves for: ::''Min-max theory and the Willmore conjecture.'' Ann. of Math. (2) 179 (2014), no. 2, 683–782. ::''Min-max theory and the energy of links.'' J. Amer. Math. Soc. 29 (2016), no. 2, 561–578. (with

) ::''Existence of infinitely many minimal hypersurfaces in positive Ricci curvature.'' Invent. Math. 209 (2017), no. 2, 577–616. * 2019 Xiuxiong Chen,

Simon Donaldson Sir Simon Kirwan Donaldson (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. H ...

and Song Sun for: ::''Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities.'' J. Amer. Math. Soc. 28 (2015), no. 1, 183–197. ::''Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2π.'' J. Amer. Math. Soc. 28 (2015), no. 1, 199–234. ::''Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof.'' J. Amer. Math. Soc. 28 (2015), no. 1, 235–278. * 2022 Michael A. Hill, Michael J. Hopkins, and Douglas Ravenel"2022 Oswald Veblen Prize in Geometry"
/ref> for: ::''On the nonexistence of elements of Kervaire invariant one.'' Annals of Mathematics SECOND SERIES, Vol. 184, No. 1 (July, 2016), pp. 1-262

References

External links

Veblen prize home page
{{DEFAULTSORT:Veblen Prize Awards of the American Mathematical Society Awards established in 1961 Triennial events Geometry Topology

List of recipients

See also

References

External links