Eduard J. Zehnder is a

Swiss Swiss may refer to: * the adjectival form of Switzerland * Swiss people Places * Swiss, Missouri * Swiss, North Carolina *Swiss, West Virginia * Swiss, Wisconsin Other uses *Swiss-system tournament, in various games and sports *Swiss Internation ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, considered one of the founders of

symplectic topology Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the H ...

Biography

Zehnder studied

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , ac ...

from 1960 to 1965, where he also did his Ph.D. in theoretical physics, defending his thesis on the

three-body problem In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...

in 1971 under the direction of

Res Jost Res Jost (10 January 1918 – 3 October 1990) was a Swiss theoretical physicist, who worked mainly in constructive quantum field theory. Biography Res Jost was born on January 10, 1918, in Bern. He is the son of the physics teacher Wilhelm ...

. He was a visiting professor at

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...

(invited by

Jürgen Moser Jürgen Kurt Moser (July 4, 1928 – December 17, 1999) was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations. Life Moser's mother Ilse Strehl ...

), visiting member of

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine ...

from 1972 to 1974. He passed his habilitation in mathematics in 1974 at the

University of Erlangen-Nuremberg A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...

. He had appointments at the

University of Bochum The Ruhr University Bochum (, ) is a public research university located in the southern hills of the central Ruhr area, Bochum, Germany. It was founded in 1962 as the first new public university in Germany after World War II. Instruction began in ...

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

, where he became

emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

in 2006. He was plenary speaker at the International Congress of Mathematicians (ICM) in 1986 at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-09-01. He has made fundamental contributions to the field of

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a ...

s. In particular, in one of his groundbreaking works with

Charles C. Conley Charles Cameron Conley (26 September 1933 – 20 November 1984) was an American mathematician who worked on dynamical systems. The Conley index theory and the Conley–Zehnder theorem are named after him. Early life and education Conley was born ...

, he established the celebrated

Arnold conjecture The Arnold conjecture, named after mathematician Vladimir Arnold, is a mathematical conjecture in the field of symplectic geometry, a branch of differential geometry. Statement Let (M, \omega) be a compact symplectic manifold. For any smooth func ...

for fixed points of Hamiltonian

diffeomorphism In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Definition Given two m ...

s, and paved the way for the development of the new field of

. He directed the thesis of several mathematicians. His first student was

Andreas Floer Andreas Floer (; 23 August 1956 – 15 May 1991) was a German mathematician who made seminal contributions to symplectic topology, and mathematical physics, in particular the invention of Floer homology. Floer's first pivotal contribution was a so ...

, who defended his thesis in 1984.

Major publications

Textbooks. *

and Eduard J. Zehnder. Notes on dynamical systems. Courant Lecture Notes in Mathematics, 12. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2005. viii+256 pp. * Eduard Zehnder. Lectures on dynamical systems. Hamiltonian vector fields and symplectic capacities. EMS Textbooks in Mathematics. European Mathematical Society, Zürich, 2010. x+353 pp. *

Helmut Hofer Helmut Hermann W. Hofer (born February 28, 1956) is a German-American mathematician, one of the founders of the area of symplectic topology. He is a member of the National Academy of Sciences, and the recipient of the 1999 Ostrowski Prize and ...

and Eduard Zehnder. Symplectic invariants and Hamiltonian dynamics. Reprint of the 1994 edition. Modern Birkhäuser Classics. Birkhäuser Verlag, Basel, 2011. xiv+341 pp. Research articles. * E. Zehnder. Generalized implicit function theorems with applications to some small divisor problems. I. Comm. Pure Appl. Math. 28 (1975), 91–140. * H. Amann and E. Zehnder. Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), no. 4, 539–603. * C.C. Conley and E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnolʹd. Invent. Math. 73 (1983), no. 1, 33–49. * Charles Conley and Eduard Zehnder. Morse-type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure Appl. Math. 37 (1984), no. 2, 207–253. * Dietmar Salamon and Eduard Zehnder. Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure Appl. Math. 45 (1992), no. 10, 1303–1360. * H. Hofer, K. Wysocki, and E. Zehnder. The dynamics on three-dimensional strictly convex energy surfaces. Ann. of Math. (2) 148 (1998), no. 1, 197–289. * F. Bourgeois, Y. Eliashberg, H. Hofer, K. Wysocki, and E. Zehnder. Compactness results in symplectic field theory. Geom. Topol. 7 (2003), 799–888.

References

External links

Oberwolfach photos of Eduard Zehnder
{{DEFAULTSORT:Zehnder, Eduard Geometers 21st-century Swiss mathematicians Living people 20th-century Swiss mathematicians ETH Zurich faculty Fellows of the American Mathematical Society Courant Institute of Mathematical Sciences faculty 1940 births