**Dusa McDuff** and **Dietmar Salamon **will receive the 2017 AMS Leroy P. Steele Prize for Exposition. They are honored for their book *J-holomorphic Curves and Symplectic Topology* (AMS Colloquium Publications, 52, 2004; second edition 2012). (Photo of Dietmar Salamon by Christina Buchmann.)

McDuff is the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College, Columbia University. Salamon is Professor of Mathematics at the Eidgenoessische Technische Hochschule (ETH) in Zurich.

Geometry and topology constitute a major area of mathematics that studies shapes. There are various kinds of geometry, such as the high-school subject of Euclidean geometry, and Riemannian geometry, which is the mathematical basis for Einstein's theories of relativity. Yet another kind is symplectic geometry, which also has profound connections to physics, as it underlies classical mechanics. Phenomena such as spinning tops, magnetism, and the propagation of water waves can be modeled using symplectic geometry.

In 1985, Mikhael Gromov published a paper introducing the notion of a "J-holomorphic curve," which intertwined symplectic topology with other areas such as algebraic geometry and string theory. Since Gromov's paper appeared, symplectic topology has undergone rapid development. His work continues to exert a tremendous influence and to stimulate some of the most exciting work in the area.

McDuff and Salamon's book *J-holomorphic Curves and Symplectic Topology* is a comprehensive introduction to Gromov's theory of J-holomorphic curves. It not only develops the topic from the basics, explaining essential notions and results in detail, but also describes many of the most spectacular results in this area. McDuff and Salamon wrote the book at the same time they themselves were making contributions at the forefront of the field. They spent nearly a decade assembling the foundations of the subject into this mammoth 700-page book. The prize citation says, "[The book] has since served as the most standard and undisputed reference in the field and as the main textbook for graduate students and others entering the field."

Born in London, Dusa McDuff received her PhD from Cambridge University (1971). After holding positions at York, Warwick, and Stony Brook universities, she is currently Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College, Columbia University. In 1991, she received the AMS Ruth Lyttle Satter Prize. She gave a plenary address at the International Congress of Mathematicians (1998), the Noether Lecture of the Association for Women in Mathematics (1998), and the AMS Colloquium Lectures (2014). She was elected a Fellow of the Royal Society of London (1994), a member of the US Academy of Sciences (1999), and a member of the American Philosophical Society (2013).

Born in Bremen, Germany, Dietmar Salamon received his PhD at the University of Bremen in 1982. After postdoctoral positions in Madison and Zurich, he took up a position at the University Warwick in 1986, and moved to ETH Zurich in 1998. He was an invited speaker at the European Congress of Mathematicians (1992) in Paris, at the International Congress of Mathematicians (1994) in Zurich, and at the ECM (2000) in Barcelona. He delivered the Andrejewski Lectures in Göttingen (1998) and at the Humboldt University Berlin (2005), and the Xth Lisbon Summer Lectures in Geometry (2009). He is a member of the Academia Europaea.

"What is Symplectic Geometry?", by Tara Holm, appears in the December 2016 issue of the *Notices of the AMS*. Also related is "What is a Pseudoholomorphic Curve?", by Simon Donaldson, in the October 2005 issue of the *Notices of the AMS*.

Presented annually, the AMS Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded Thursday, January 5, 2017, at the Joint Mathematics Meetings in Atlanta.

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