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
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.
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.
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.
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.
Introduction to Symplectic Field Theory
Yakov Eliashberg;Alexander Givental;Helmut Hofer.
arXiv: Symplectic Geometry (2000)
Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three.
Inventiones Mathematicae (1993)
Compactness results in Symplectic Field Theory
Frédéric Bourgeois;Yakov Eliashberg;Helmut Hofer;Krzysztof Wysocki.
Geometry & Topology (2003)
On the topological properties of symplectic maps
Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (1990)
Transversality in elliptic Morse theory for the symplectic action
Andreas Floer;Helmut Hofer;Dietmar Salamon.
Duke Mathematical Journal (1995)
Floer homology and Novikov rings
Helmut Hofer;Dietmar A. Salamon.
The dynamics on three-dimensional strictly convex energy surfaces
Helmut Hofer;Krzysztof Wysocki;Eduard Zehnder.
Annals of Mathematics (1998)
Symplectic topology and Hamiltonian dynamics
Ivar Ekeland;Helmut Hofer.
Mathematische Zeitschrift (1989)
Coherent orientations for periodic orbit problems in symplectic geometry
A. Floer;H. Hofer.
Mathematische Zeitschrift (1993)
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