D-Index & Metrics Best Publications

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 43 Citations 13,002 91 World Ranking 1126 National Ranking 520

Research.com Recognitions

Awards & Achievements

2018 - Member of the National Academy of Sciences

2008 - Fellow of John Simon Guggenheim Memorial Foundation

2000 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Pure mathematics
  • Topology
  • Algebra

Peter Ozsvath mostly deals with Floer homology, Pure mathematics, Khovanov homology, Morse homology and Knot invariant. His Floer homology research is under the purview of Mathematical analysis. As part of his studies on Pure mathematics, Peter Ozsvath often connects relevant subjects like Algebra.

His Morse homology study is related to the wider topic of Homology. His Knot invariant research is mostly focused on the topic Knot polynomial. His work carried out in the field of Knot polynomial brings together such families of science as Quantum invariant and Combinatorics.

His most cited work include:

  • Holomorphic disks and knot invariants (760 citations)
  • Holomorphic disks and topological invariants for closed three-manifolds (714 citations)
  • Holomorphic disks and three-manifold invariants: Properties and applications (595 citations)

What are the main themes of his work throughout his whole career to date?

His primary areas of investigation include Floer homology, Pure mathematics, Combinatorics, Khovanov homology and Morse homology. The various areas that Peter Ozsvath examines in his Floer homology study include Heegaard splitting, Pseudoholomorphic curve, Knot and Knot invariant. His Pure mathematics study combines topics in areas such as Discrete mathematics, Mathematical analysis and Algebra.

His Algebra research is multidisciplinary, relying on both Gromov–Witten invariant and Riemann surface. His study explores the link between Combinatorics and topics such as Unknotting number that cross with problems in Slice genus. The study of Khovanov homology is intertwined with the study of Link in a number of ways.

He most often published in these fields:

  • Floer homology (76.35%)
  • Pure mathematics (52.03%)
  • Combinatorics (44.59%)

What were the highlights of his more recent work (between 2014-2020)?

  • Pure mathematics (52.03%)
  • Floer homology (76.35%)
  • Combinatorics (44.59%)

In recent papers he was focusing on the following fields of study:

His primary areas of investigation include Pure mathematics, Floer homology, Combinatorics, Knot and Knot invariant. In general Pure mathematics study, his work on Invariant, Noncommutative geometry and Casorati–Weierstrass theorem often relates to the realm of Computation and Transverse plane, thereby connecting several areas of interest. His studies in Floer homology integrate themes in fields like Low-dimensional topology, Dehn surgery and Homomorphism.

His Combinatorics research is multidisciplinary, incorporating elements of Skein and Knot theory, Unknotting number. The Knot theory study combines topics in areas such as Morse homology and Khovanov homology. His research investigates the connection with Knot invariant and areas like Alexander polynomial which intersect with concerns in Euler characteristic.

Between 2014 and 2020, his most popular works were:

  • Concordance homomorphisms from knot Floer homology (134 citations)
  • Bimodules in bordered Heegaard Floer homology (61 citations)
  • Bordered Heegaard Floer Homology (40 citations)

In his most recent research, the most cited papers focused on:

  • Topology
  • Pure mathematics
  • Geometry

Floer homology, Pure mathematics, Knot, Invariant and Knot invariant are his primary areas of study. His Floer homology study results in a more complete grasp of Combinatorics. His work in Combinatorics tackles topics such as Knot theory which are related to areas like Discrete mathematics.

His research in Pure mathematics is mostly concerned with Low-dimensional topology. His research integrates issues of Homomorphism, Crosscap number, Ball, Upper and lower bounds and Betti number in his study of Knot. In his research, Mapping class group and Alexander polynomial is intimately related to Homology, which falls under the overarching field of Invariant.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Holomorphic disks and three-manifold invariants: Properties and applications

Peter Steven Ozsvath;Zoltan Szabo.
Annals of Mathematics (2004)

959 Citations

Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary

Peter Steven Ozsvath;Zoltan Szabo.
Advances in Mathematics (2003)

918 Citations

Holomorphic disks and knot invariants

Peter Ozsváth;Zoltán Szabó.
Advances in Mathematics (2004)

820 Citations

Holomorphic disks and topological invariants for closed three-manifolds

Peter Ozsváth;Zoltán Szabó.
Annals of Mathematics (2004)

784 Citations

Holomorphic disks and genus bounds

Peter Ozsvath;Zoltan Szabo.
Geometry & Topology (2004)

736 Citations

On knot Floer homology and lens space surgeries

Peter Steven Ozsvath;Zoltan Szabo.
Topology (2005)

735 Citations

Knot Floer homology and the four-ball genus

Peter Steven Ozsvath;Zoltan Szabo.
Geometry & Topology (2003)

686 Citations

On the Heegaard Floer homology of branched double-covers

Peter Steven Ozsvath;Zoltan Szabo.
Advances in Mathematics (2005)

566 Citations

Holomorphic triangles and invariants for smooth four-manifolds

Peter S Ozsvath;Zoltan Szabo.
Advances in Mathematics (2006)

447 Citations

Heegaard Floer homology and contact structures

Peter Steven Ozsvath;Zoltan Szabo.
Duke Mathematical Journal (2005)

370 Citations

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