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- Helmut Hofer

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
50
Citations
11,006
115
World Ranking
785
National Ranking
391

2020 - Fellow of the American Academy of Arts and Sciences

2013 - Fellow of the American Mathematical Society

2008 - Member of Academia Europaea

2008 - Member of the National Academy of Sciences

- Mathematical analysis
- Geometry
- Topology

The scientist’s investigation covers issues in Mathematical analysis, Symplectic geometry, Pure mathematics, Pseudoholomorphic curve and Symplectic manifold. His work on Mathematical analysis deals in particular with Holomorphic function, Weinstein conjecture, Periodic orbits, Differential geometry and Manifold. His Symplectic geometry research is multidisciplinary, incorporating perspectives in Hamiltonian system and Topology.

His work in Hamiltonian system tackles topics such as Diffeomorphism which are related to areas like Fixed-point theorem and Metric. Pure mathematics is closely attributed to Hamiltonian mechanics in his research. Many of his research projects under Moment map are closely connected to Fredholm operator with Fredholm operator, tying the diverse disciplines of science together.

- Symplectic Invariants and Hamiltonian Dynamics (657 citations)
- Introduction to Symplectic Field Theory (501 citations)
- Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three. (442 citations)

His primary areas of study are Pure mathematics, Symplectic geometry, Mathematical analysis, Symplectic manifold and Hamiltonian system. His Pure mathematics research focuses on Weinstein conjecture, Floer homology, Symplectic vector space, Compact space and Pseudoholomorphic curve. The study incorporates disciplines such as Transversal and Dimension, Combinatorics in addition to Weinstein conjecture.

His Symplectomorphism and Moment map study in the realm of Symplectic geometry interacts with subjects such as Fredholm theory. His Symplectic manifold study frequently draws connections between related disciplines such as Vector field. His biological study deals with issues like Hamiltonian mechanics, which deal with fields such as Fixed-point theorem and Diffeomorphism.

- Pure mathematics (46.15%)
- Symplectic geometry (46.15%)
- Mathematical analysis (35.90%)

- Pure mathematics (46.15%)
- Manifold (5.13%)
- Symplectic geometry (46.15%)

His scientific interests lie mostly in Pure mathematics, Manifold, Symplectic geometry, Geometry and Structure. In the field of Pure mathematics, his study on Compact space and Holomorphic function overlaps with subjects such as Fredholm theory and Intersection theory. His Compact space research incorporates themes from Hamiltonian mechanics, Conjecture, Pseudoholomorphic curve, Curvature and Symplectization.

His Symplectic geometry study combines topics in areas such as Transversality, Theoretical physics and Field theory. His study in the fields of Section and Vector field under the domain of Geometry overlaps with other disciplines such as Slope field. His study with Reeb vector field involves better knowledge in Mathematical analysis.

- Polyfold and Fredholm Theory (32 citations)
- Applications of Polyfold Theory I: The Polyfolds of Gromov-witten Theory (15 citations)
- Lectures on Polyfolds and Symplectic Field Theory (7 citations)

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.

Symplectic Invariants and Hamiltonian Dynamics

Helmut Hofer;Eduard Zehnder.

**(1994)**

1053 Citations

Introduction to Symplectic Field Theory

Yakov Eliashberg;Alexander Givental;Helmut Hofer.

arXiv: Symplectic Geometry **(2000)**

807 Citations

Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three.

H. Hofer.

Inventiones Mathematicae **(1993)**

709 Citations

Compactness results in Symplectic Field Theory

Frédéric Bourgeois;Yakov Eliashberg;Helmut Hofer;Krzysztof Wysocki.

Geometry & Topology **(2003)**

626 Citations

On the topological properties of symplectic maps

H. Hofer.

Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences **(1990)**

520 Citations

Transversality in elliptic Morse theory for the symplectic action

Andreas Floer;Helmut Hofer;Dietmar Salamon.

Duke Mathematical Journal **(1995)**

416 Citations

Floer homology and Novikov rings

Helmut Hofer;Dietmar A. Salamon.

**(1995)**

403 Citations

The dynamics on three-dimensional strictly convex energy surfaces

Helmut Hofer;Krzysztof Wysocki;Eduard Zehnder.

Annals of Mathematics **(1998)**

365 Citations

Symplectic topology and Hamiltonian dynamics

Ivar Ekeland;Helmut Hofer.

Mathematische Zeitschrift **(1989)**

350 Citations

Coherent orientations for periodic orbit problems in symplectic geometry

A. Floer;H. Hofer.

Mathematische Zeitschrift **(1993)**

328 Citations

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