Peter Ozsváth

Peter Steven Ozsváth ( born October 20, 1967 in Dallas ) is an American mathematician.

Ozsváth studied at Stanford University ( BA 1989) and his PhD in 1994 with John Morgan at Princeton University (On Blowup Formulas For SU (2) Donaldson Polynomials ). After that, he was a post-doc at the California Institute of Technology (Caltech ), at the Max Planck Institute for Mathematics in Bonn, at the Mathematical Sciences Research Institute ( MSRI ) in Berkeley, and the Institute for Advanced Study. After positions at the University of California, Berkeley, Princeton University and Michigan State University, he is at Columbia University, where he is currently a professor since 2002.

With Zoltán Szabó, he developed the Heegaard Floer homology. Both received for the 2007 Oswald Veblen Prize -.

Ozsváth was Sloan Fellow and Szabo Invited Speaker at the International Congress of Mathematicians (ICM ) 2006 in Madrid ( Heegaard Floer homology and diagrams ). In 2004 he held a plenary lecture Szabo with the 4th European Congress of Mathematicians (On Heegard diagrams and holomorphic discs).

Works

• Tomasz Mrowka, Baozhen Yu: Seiberg - Witten monopoles on Seifert fibered spaces. Comm. Anal. Geom 5 (1997 ), no 4, 685-791.
• The symplectic Thom conjecture: with Szabó. Ann. of Math ( 2) 151 (2000 ), no 1, 93-124.
• With Szabó: Absolutely graded Floer homo logies and intersection forms for four - manifolds with boundary. Adv Math 173 (2003), no 2, 179-261.
• With Szabó: Knot Floer homology and the four- ball genus. Geom Topol. 7 (2003), 615-639.
• With Szabó: holomorphic disks and genus bounds. Geom Topol. 8 (2004), 311-334.
• With Szabó: holomorphic disks and knot invariants. Adv Math 186 (2004), no 1, 58-116.
• With Szabó: holomorphic disks and topological invariants for closed three- manifolds. Ann. of Math ( 2) 159 (2004 ), no 3, 1027-1158.
• With Szabó: holomorphic disks and three -manifold invariants: properties and applications. Ann. of Math ( 2) 159 (2004 ), no 3, 1159-1245.
• With Szabó: Heegaard Floer homology and contact structures. Duke Math J. 129 (2005), no 1, 39-61.
• With Szabó: On knot Floer homology and lens space surgeries. Topology 44 (2005 ), no 6, 1281-1300.
• With Szabó: holomorphic triangles and invariants for smooth four- manifolds. Adv Math 202 (2006), no 2, 326-400.
• With Peter Kronheimer, Mrowka, Szabó: monopole and lens space surgeries. Ann. of Math (2 ) 165 (2007 ), no 2, 457-546.
• Ciprian Manolescu with, Sucharit Sankar: A combinatorial description of knot Floer homology. Ann. of Math ( 2) 169 (2009 ), no 2, 633-660.