Peter S. Ozsvath
Princeton University
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2018)
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Biosketch
Peter Ozsváth is a mathematician working on the interface between symplectic geometry and low-dimensional topology. Ozsváth was born and raised in Dallas, Texas. He graduated from Stanford University in 1989 with a degree in Mathematics, and went on to write his PhD at Princeton University in 1994. His honors include a Sloan Fellowship, a Guggenheim Fellowship, and the 2007 Osvald Veblen Prize in Geometry (shared with Peter Kronheimer, Tomasz Mrowka, and Zoltan Szabo). Ozsváth is a professor at Princeton University's mathematics department.
Research Interests
Peter Ozsváth's work has focused on applications of techniques from symplectic geometry to low-dimensional topology. In 2000, in joint work with Zoltan Szabo, he introduced "Heegaard Floer homology", an invariant for three-and four-dimensional manifolds, defined using a suitable version of Lagrangian Floer homology in a symmetric product of a Riemann surface. Heegaard Floer homology was born in an attempt to give a more geometric formulation of the gauge-theoretic invariants introduced by Andreas Floer and Simon Donaldson; but owing to its concrete, geometric description, Heegaard Floer homology has become a useful tool for studying topological problems in its own right. A version of Heegaard Floer homology, introduced jointly with Szabo and independently by Jacob Rasmussen, gives an invariant for knots in three-space. Another version, introduced jointly with Robert Lipshitz and Dylan Thurston, gives invariants for three-manifolds with parameterized boundary. Heegaard Floer homology has been used to study classical questions in low-dimensional topology; especially ones that relate to four-dimensional aspects. It has also opened new directions for further research.
