Peter Kronheimer, Tomasz Mrowka, Peter Ozsváth, and Zoltán Szabó Receive 2007 Veblen Prize in Geometry

January 8, 2007

Providence, RI:

The AMS Oswald Veblen Prize in Geometry has been awarded to two pairs of mathematical collaborators: to Peter Kronheimer of Harvard University and Tomasz Mrowka of the Massachusetts Institute of Technology, and to Peter Ozsváth of Columbia University and Zoltán Szabó of Princeton University. Awarded every three years, the Veblen Prize is one of the field's highest honors for work in geometry or topology. The prize was awarded on Saturday, January 6, 2007, at the Joint Mathematics Meetings in New Orleans, Louisiana.

The prize citation states that Kronheimer and Mrowka are being honored "for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications." The citation pointed in particular to three seminal papers by Kronheimer and Mrowka:

"Embedded surfaces and the structure of Donaldson's polynomial invariants," Journal of Differential Geometry, 41 (1995), no. 3, 573--734;

"The genus of embedded surfaces in the projective plane," Mathematical Research Letters, 1 (1994), no. 6, 797--808; and

"Witten's conjecture and property P," Geometry and Topology, 8 (2004), 295--310.

Ozsváth and Szabó are honored for "the contributions they have made to 3- and 4-dimensional topology through their Heegaard Floer homology theory." This theory was developed in a highly influential series of over 20 papers in the last 5 years. The citation specifically mentions three of their papers:

"Holomorphic disks and topological invariants for closed three-manifolds," Annals of Mathematics, (2) 159 (2004), 1027-1158;

"Holomorphic disks and three-manifold invariants: properties and applications", Annals of Mathematics, (2) 159 (2004), 1159-1245;

"Holomorphic disks and genus bounds", Geometry and Topology, 8 (2004), 311-334.

Find out more about AMS prizes at http://www.ams.org/prizes-awards.

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