The Arnold conjecture for fixed points of Hamiltonian diffeomorphisms found a structural solution through the research of Eduard Zehnder, a move that fundamentally altered the trajectory of symplectic topology. Born in Leuggern in 1940, Zehnder emerged as a significant figure in geometry, theoretical physics, and mathematics, shaping the discipline through decades of rigorous academic inquiry.
Academic Formation and Early Research
Zehnder pursued his higher education at ETH Zurich between 1960 and 1965, eventually earning a PhD in theoretical physics in 1971. His doctoral thesis focused on the three-body problem under the supervision of Res Jost. Following this, he spent time at the Institute for Advanced Study in Princeton from 1972 to 1974. He completed his habilitation at the University of Erlangen-Nuremberg in 1974, marking his formal transition into the broader mathematical community.
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His primary research interests lay in dynamical systems and symplectic topology. Collaborating with Charles C. Conley, Zehnder addressed the Arnold conjecture, a critical development that laid the groundwork for modern symplectic topology. His body of work includes numerous publications, such as his 2005 collaboration with Jürgen Moser, Notes on dynamical systems, and his 2010 text, Lectures on dynamical systems: Hamiltonian vector fields and symplectic capacities. In 1994, he published Symplectic invariants and Hamiltonian dynamics alongside Helmut Hofer, a work later reprinted in 2011.
Professional Appointments and Mentorship
Zehnder held faculty positions at Ruhr University Bochum from 1976 to 1986. During the 1987-88 academic year, he served as the director of the Mathematical Institute at the University of Aix-la-Chapelle. In 1988, he accepted a chair at ETH Zurich, maintaining this appointment until his retirement in 2006. Beyond his research, he was an active educator who guided multiple PhD students, including Andreas Floer, who completed his thesis in 1984.
Professional Recognition
The mathematical community recognized his work through various international invitations and memberships. He served as a plenary speaker at the 1986 International Congress of Mathematicians held at the University of California, Berkeley. Later honors included becoming a fellow of the American Mathematical Society in 2012 and an elected member of the Academia Europaea in 2021. He was also a member of the German Academy of Sciences Leopoldina. Zehnder passed away in Greifensee on 22 November 2024.
Fast facts
- Born: 1940, Leuggern, Switzerland
- Died: 22 November 2024, Greifensee
- Education: ETH Zurich, University of Erlangen-Nuremberg
- Key Field: Symplectic topology
- Notable Role: Chair at ETH Zurich
- Professional Society: Academia Europaea, American Mathematical Society
- PhD Advisor: Res Jost
Questions readers ask
What were Eduard Zehnder's primary fields of research?
He focused on mathematics, specifically geometry, topology, and theoretical physics.
Where did Zehnder hold major academic positions?
He served on the faculty at Ruhr University Bochum and ETH Zurich.
Achievements
- Held posts at Ruhr University Bochum and ETH Zurich
- Fields: geometry, topology and mathematics
