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Dietmar Arno Salamon (born 7 March 1953 in Bremen) is a German mathematician.
Salamon studied mathematics at the Leibniz University Hannover. In 1982 he earned his doctorate at the University of Bremen with dissertation On control and observation of neutral systems.[1][2] He subsequently spent two years as a postdoctoral fellow at the Mathematical Research Center at the University of Wisconsin–Madison, followed by one year at the Mathematical Research Institute at ETH Zurich. In 1986 he became a lecturer at the University of Warwick, where he was appointed full professor in 1994. The summer semester 1988 he spent as a visiting professor at the University of Bremen and the winter semester 1991 at the University of Wisconsin-Madison. From 1998 to 2018 he was a full professor of mathematics at ETH Zurich, retiring as professor emeritus in 2018.[3]
Salamon's field of research is symplectic topology and related fields such as symplectic geometry. Symplectic topology is a relatively new field of mathematics that developed into an important branch of mathematics in the 1990s. Some important new techniques are Gromov's pseudoholomorphic curves, Floer homology, and Seiberg-Witten invariants on four-dimensional manifolds.
In 1994 he was an Invited Speaker with talk Lagrangian intersections, 3-manifolds with boundary and the Atiyah-Floer conjecture at the International Congress of Mathematicians (ICM) in Zurich. In 2012 he was elected a Fellow of the American Mathematical Society. In 2017 he received, with Dusa McDuff, the AMS Leroy P. Steele Prize for Mathematical Exposition for the book J-holomorphic curves and symplectic topology, which they co-authored.[4] He has been a member of Academia Europaea since 2011.
Books
- Dietmar Salamon: Funktionentheorie. Birkhauser, 2011.
- Dusa McDuff, Dietmar Salamon: J-holomorphic curves and symplectic topology. American Mathematical Society, 2004,[5] 2nd edition 2012.
- Dusa McDuff, Dietmar Salamon: Introduction to symplectic topology. Oxford University Press, 1998.[6]
- Dusa McDuff: -holomorphic curves and quantum cohomology. American Mathematical Soc. 1994. ISBN 978-0-8218-0332-5.[7]
Articles
- Dietmar Salamon: Symplectic Geometry. Cambridge University Press, 1994 (London Mathematical Society Lecture Notes), ISBN 0-521-44699-6.
- Helmut Hofer, Dietmar Salamon: Floer homology and Novikov rings. The Floer memorial volume, 483–524, Progr. Math., 133, Birkhäuser, Basel, 1995. (proof of the Arnold conjecture for ) doi:10.1007/978-3-0348-9217-9_20
- Andreas Floer, Helmut Hofer, Dietmar Salamon: Transversality in elliptic Morse theory for the symplectic action. Duke Math. J. 80 (1995), no. 1, 251–292.
- Joel Robbin, Dietmar Salamon: The spectral flow and the Maslov index. Bull. London Math. Soc. 27 (1995), no. 1, 1–33.
- Stamatis Dostoglou, Dietmar Salamon: Self-dual instantons and holomorphic curves. Ann. of Math. (2) 139 (1994), no. 3, 581–640. doi:10.2307/2118573
- Joel Robbin, Dietmar Salamon: The Maslov index for paths. Topology 32 (1993), no. 4, 827–844.
- Dietmar Salamon, Eduard Zehnder: Morse theory for periodic solutions of Hamiltonian systems and the Maslov index. Comm. Pure Appl. Math. 45 (1992), no. 10, 1303–1360. doi:10.1002/cpa.3160451004
- Dietmar Salamon: Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach. Trans. Amer. Math. Soc. 300 (1987), no. 2, 383–431. doi:10.1090/S0002-9947-1987-0876460-7
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