Mathematician Helmut Hofer Joins the Faculty of the Institute for Advanced Study

Helmut Hofer

Helmut Hofer has been appointed to the Faculty of the School of Mathematics at the Institute for Advanced Study, effective July 1, 2009.  Dr. Hofer comes to the Institute from the Courant Institute of Mathematical Sciences of New York University, where he serves as Silver Professor of Mathematics.

One of the founders of the area of symplectic topology, Dr. Hofer's research focuses on symplectic geometry, dynamical systems and partial differential equations. He was a Member in the School of Mathematics at the Institute in 1987, 2001-02, and 2005. 

"Helmut Hofer has taken a leading role in the development of symplectic geometry, one of the most exciting areas of mathematics today," commented Peter Goddard, Director of the Institute.  "His combination of geometric insight and deep analytical skills, together with his energy and enthusiasm, has provided inspiration for many other mathematicians. We are delighted that he will be joining the Faculty of our School of Mathematics."

Peter Sarnak, Professor in the School of Mathematics stated, "The fields of symplectic geometry, symplectic topology and related Hamiltonian dynamics have enjoyed dramatic advances in the last 20 years. Helmut Hofer is one of the main architects of these developments. Together with his engaging style, energy, record of collaborations and mentorship, his addition to the Faculty of the School of Mathematics will position the Institute as a center for these areas."

Regarding his appointment, Dr. Hofer said, "The Institute is a unique place and I am thrilled to join its Faculty. During my professional life, I spent two years at different stages of my career at IAS. The opportunity to meet and interact with extraordinary people had a significant impact on my professional development. I consider it as an extraordinary privilege to be part of the Institute and to further its mission to encourage and support fundamental research. "

Dr. Hofer has worked in a number of fields including variational problems in Hamiltonian dynamics and symplectic and contact geometry/topology. His work with Ivar Ekeland in the late 1980s introduced new invariants of symplectic domains called symplectic capacities, which were used to establish a number of the foundational results in symplectic topology.  The Arnold Conjecture, perhaps the most striking result in symplectic topology to date, relates the number of fixed points of a Hamiltonian symplectomorphism to the topology of the underlying manifold. Hofer, together with Dietmar Salamon, made a major contribution towards the solution of this conjecture.  Their work, like all others, built on the work of Andreas Floer and in particular, Floer homology.  Hofer worked with Floer on several papers on the subject, some of which were published jointly after Floer's premature death in 1991.

Following his work on the Arnold Conjecture, Hofer introduced the method of holomorphic curves in contact geometry.  This led to a wealth of new results in Hamiltonian dynamics and in particular to a proof of the Weinstein Conjecture, which is concerned with the existence of periodic orbits of contact type Hamiltonian systems, in many cases.  This work led him, together with Yakov Eliashberg, to the concept of contact homology.  In recent works, Hofer and his collaborators Kris Wysocki and Eduard Zehnder have introduced new analytic tools to study the geometry of moduli spaces, which provides the foundations for his ongoing work with Eliashberg on symplectic field theory.

Dr. Hofer studied at the University of Zurich, where he earned an undergraduate degree in 1979 and a Ph.D. in 1981.  He taught at Zurich from 1979 to 1982, and the following year he joined the University of Bath as a Lecturer in Pure Mathematics.  From there, he went to Rutgers, The State University of New Jersey, where he served as Assistant Professor (1985-87), Associate Professor (1987-88), and then as Professor (1988-89).  Dr. Hofer then went to Germany and became a C-4 Professor at Ruhr-Universität Bochum, a position he held from 1989 to 1993. From 1993 to 1997, he was Professor at Eidgenössische Technische Hochschule (ETH) in Zurich. He joined the Courant Institute of Mathematical Sciences of New York University as Professor in 1997 and was named Silver Professor in 2006.

Dr. Hofer is the recipient of the 1999 Ostrowski Prize.  He was elected to the National Academy of Sciences and Academia Europaea in 2008.  He serves as Chairman of the Scientific Advisory Board of the

Max Planck Institute for Mathematics in the Sciences

at Leipzig, Germany, and as co-chair of the Scientific Advisory Committee of the

Mathematics Science Research Institute

(MSRI) in Berkeley. Dr. Hofer also serves on the editorial boards of

Communications in Pure and Applied Mathematics

and

EMS Monographs in Mathematics

, is Associate Editor of

Monographs in Mathematics

and was recently named Managing Editor of

Inventiones Mathematicae

.


About the Institute for Advanced Study

The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. The Institute exists to encourage and support curiosity-driven research in the sciences and humanities—the original, often speculative thinking that produces advances in knowledge that change the way we understand the world. Work at the Institute takes place in four Schools: Historical Studies, Mathematics, Natural Sciences and Social Science. It provides for the mentoring of scholars by a permanent Faculty of no more than 28, and it ensures the freedom to undertake research that will make significant contributions in any of the broad range of fields in the sciences and humanities studied at the Institute.

The Institute, founded in 1930, is a private, independent academic institution located in Princeton, New Jersey. Its more than 6,000 former Members hold positions of intellectual and scientific leadership throughout the academic world. Thirty-three Nobel Laureates and 40 out of 56 Fields Medalists, as well as many winners of the Wolf or MacArthur prizes, have been affiliated with the Institute.