Helmut Hofer

This article is about the mathematician. For the zoologist, see Helmut Otto Hofer.

Helmut Hofer
Hofer at Oberwolfach in 2015
Born	(1956-02-28)February 28, 1956
Nationality	Germany United States
Alma mater	Universität Zürich
Known for	Symplectic capacities Hofer geometry Symplectic homology Finite energy foliations Symplectic field theory Polyfold theory
Awards	Ostrowski Prize (1999) Heinz Hopf Prize (2013)
Scientific career
Fields	Mathematics
Thesis	A Variational Approach to a Class of Resonance Problems with Application to a Wave Equation Problem  (1981)
Doctoral advisor	Peter Hess

Helmut Hermann W. Hofer (born February 28, 1956) ^[1] is a German-American mathematician, one of the founders of the area of symplectic topology. ^[2]

He is a member of the National Academy of Sciences, ^[3] and the recipient of the 1999 Ostrowski Prize ^[4] and the 2013 Heinz Hopf Prize. Since 2009, he is a faculty member at the Institute for Advanced Study in Princeton, New Jersey. ^[2] He currently works on symplectic geometry, dynamical systems, and partial differential equations. His contributions to the field include Hofer geometry. Hofer was elected to the American Academy of Arts and Sciences in 2020. ^[5]

He was an invited speaker at the International Congress of Mathematicians (ICM) in 1990 in Kyoto ^[6] and a plenary speaker at the ICM in 1998 in Berlin. ^[7]

He is currently an editor of Annals of Mathematics. ^[8]

Selected publications

• Ekeland, Ivar; Hofer, Helmut (1985). "Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems". Inventiones Mathematicae . 81 (1): 155–188. Bibcode:1985InMat..81..155E. doi:10.1007/BF01388776. MR   0796195. S2CID   120891372.
• Hofer, Helmut; Zehnder, Eduard (1987). "Periodic solutions on hypersurfaces and a result by C. Viterbo". Inventiones Mathematicae . 90 (1): 1–9. Bibcode:1987InMat..90....1H. doi:10.1007/BF01389030. MR   0906578. S2CID   121157240.
• Ekeland, Ivar; Hofer, Helmut (1989). "Symplectic topology and Hamiltonian dynamics". Mathematische Zeitschrift . 200 (3): 355–378. doi:10.1007/BF01215653. MR   0978597. S2CID   123600347.
• Hofer, Helmut (1990). "On the topological properties of symplectic maps". Proceedings of the Royal Society of Edinburgh, Section A. 115 (1–2): 25–38. doi:10.1017/S0308210500024549. MR   1059642. S2CID   121426158.
• Hofer, Helmut (1993). "Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three". Inventiones Mathematicae . 114 (3): 515–563. Bibcode:1993InMat.114..515H. doi:10.1007/BF01232679. MR   1244912. S2CID   123618375.
• Hofer, Helmut; Zehnder, Eduard (2011). Symplectic invariants and Hamiltonian dynamics. Modern Birkhäuser Classics. Basel: Birkhäuser Verlag. doi:10.1007/978-3-0348-0104-1. ISBN   978-3-0348-0103-4. MR   2797558.
• Hofer, Helmut; Wysocki, Krzysztof; Zehnder, Eduard (1998). "The dynamics on three-dimensional strictly convex energy surfaces". Annals of Mathematics . 148 (1): 197–289. doi:10.2307/120994. JSTOR   120994. MR   1652928.
• Hofer, Helmut; Wysocki, Krzysztof; Zehnder, Eduard (2003). "Finite energy foliations of tight three-spheres and Hamiltonian dynamics". Annals of Mathematics . 157 (1): 125–255. doi: 10.4007/annals.2003.157.125 . MR   1954266.

Notes

1. "Curriculum Vitae Prof. Dr. Helmut Hofer" (PDF). Leopoldina Nationale Akademie der Wissenschaften.
2. "IAS press release". IAS. Archived from the original on August 5, 2016. Retrieved February 29, 2012.
3. "2 NYU faculty elected to National Academy of Sciences". NYU.
4. "Beilinson and Hofer share Ostrowski Prize" (PDF). Notices Amer. Math. Soc. 47 (8): 885. 2000. MR   1776106.
5. "New Members". American Academy of Arts & Sciences. Retrieved April 23, 2020.
6. Hofer, Helmut (1991). "Symplectic invariants". Proceedings of the International Congress of Mathematicians (1990, Kyoto). Vol. 1. pp. 521–528.
7. Hofer, Helmut H. W. (1998). "Dynamics, topology, and holomorphic curves". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 255–280.
8. "Editorial Board | Annals of Mathematics" . Retrieved March 25, 2024.

External links

• Helmut Hofer at the Mathematics Genealogy Project
• Oberwolfach photos of Helmut Hofer