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Eduard Zehnder | |
|---|---|
 Zehnder in Oberwolfach, 2005 | |
| Born | 10 November 1940 Lausanne, Switzerland |
| Nationality | Swiss |
| Alma mater | ETH Zurich |
| Known for | Conley–Zehnder theorem Hofer–Zehnder capacity |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Res Jost |
| Doctoral students | Andreas Floer |
Eduard J. Zehnder is a Swiss mathematician, considered one of the founders of symplectic topology.
Zehnder studied mathematics and physics at ETH Zurich from 1960 to 1965, where he also did his Ph.D. in theoretical physics, defending his thesis on the three-body problem in 1971 under the direction of Res Jost. [1] He was a visiting professor at Courant Institute of Mathematical Sciences (invited by Jürgen Moser), visiting member of Institute for Advanced Study in Princeton from 1972 to 1974. He passed his habilitation in mathematics in 1974 at the University of Erlangen-Nuremberg. He had appointments at the University of Bochum from 1976 to 1986; at the University of Aix-la-Chapelle during the academic year 1987–88, where he was director of the Mathematical Institute. From 1988, he had a chair at ETH Zurich, where he became emeritus in 2006. He was plenary speaker at the International Congress of Mathematicians (ICM) in 1986 at the University of California, Berkeley. In 2012 he became a fellow of the American Mathematical Society. [2]
He has made fundamental contributions to the field of dynamical systems. In particular, in one of his groundbreaking works with Charles C. Conley, he established the celebrated Arnold conjecture for fixed points of Hamiltonian diffeomorphisms, and paved the way for the development of the new field of symplectic topology.
He directed the thesis of several mathematicians. His first student was Andreas Floer, who defended his thesis in 1984.
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Research articles.
Vladimir Igorevich Arnold was a Soviet and Russian mathematician. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made revolutionary and deep contributions in several areas including geometrical theory of dynamical systems theory, algebra, catastrophe theory, topology, algebraic geometry, symplectic geometry, symplectic topology, differential equations, classical mechanics, differential geometric approach to hydrodynamics, geometric analysis and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. He co-founded two new branches of mathematics—KAM theory, and topological Galois theory. He is widely regarded as one of greatest mathematicians of all time.
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In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as (smooth) three- and four-dimensional manifolds.
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In mathematics, the Conley–Zehnder theorem, named after Charles C. Conley and Eduard Zehnder, provides a lower bound for the number of fixed points of Hamiltonian diffeomorphisms of standard symplectic tori in terms of the topology of the underlying tori. The lower bound is one plus the cup-length of the torus (thus 2n+1, where 2n is the dimension of the considered torus), and it can be strengthen to the rank of the homology of the torus (which is 22n) provided all the fixed points are non-degenerate, this latter condition being generic in the C1-topology.
Alexander Nikolaevich Varchenko is a Soviet and Russian mathematician working in geometry, topology, combinatorics and mathematical physics.
Viktor L. Ginzburg is a Russian-American mathematician who has worked on Hamiltonian dynamics and symplectic and Poisson geometry. As of 2017, Ginzburg is Professor of Mathematics at the University of California, Santa Cruz.
Ana M. L. G. Cannas da Silva is a Portuguese mathematician specializing in symplectic geometry and geometric topology. She works in Switzerland as an adjunct professor in mathematics at ETH Zurich.
Dietmar Arno Salamon is a German mathematician.
The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry.
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