Dusa McDuff | |
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![]() Dusa McDuff, Edinburgh 2009 (80th Birthday of Michael Atiyah) | |
Born | Margaret Dusa Waddington 18 October 1945 London, England |
Alma mater | University of Edinburgh Girton College, Cambridge |
Spouses | |
Parents |
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Awards | BMS Morning Speaker [1] Satter Prize (1991) Fellow of the Royal Society Corresponding Fellow of the Royal Society of Edinburgh (2008) Speaker at International Congress of Mathematicians BMC Plenary Speaker [2] Sylvester Medal (2018) |
Scientific career | |
Fields | Mathematics |
Institutions | University of Cambridge University of York University of Warwick Massachusetts Institute of Technology Institute for Advanced Study Stony Brook University Barnard College |
Doctoral advisor | George A. Reid [3] |
Doctoral students | Katrin Wehrheim |
Dusa McDuff FRS CorrFRSE (born 18 October 1945) is an English mathematician who works on symplectic geometry. She was the first recipient of the Ruth Lyttle Satter Prize in Mathematics, [4] was a Noether Lecturer, and is a Fellow of the Royal Society. She is currently the Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College. [5]
Margaret Dusa Waddington was born in London, England, on 18 October 1945 to Edinburgh architect Margaret Justin Blanco White, second wife of biologist Conrad Hal Waddington, her father. [6] Her sister is the anthropologist Caroline Humphrey, and she has an elder half-brother C. Jake Waddington by her father's first marriage. Her mother was the daughter of Amber Reeves, the noted feminist, author and lover of H. G. Wells. McDuff grew up in Scotland where her father was Professor of Genetics at the University of Edinburgh. McDuff was educated at St George's School for Girls in Edinburgh and, although the standard was lower than at the corresponding boys' school, The Edinburgh Academy, McDuff had an exceptionally good mathematics teacher. [7] She writes:
I always wanted to be a mathematician (apart from a time when I was eleven when I wanted to be a farmer's wife), and assumed that I would have a career, but I had no idea how to go about it: I didn't realize that the choices which one made about education were important and I had no idea that I might experience real difficulties and conflicts in reconciling the demands of a career with life as a woman. [8]
Turning down a scholarship to the University of Cambridge to stay with her boyfriend in Scotland, she enrolled at the University of Edinburgh. [7] She graduated with a BSc Hons in 1967, going on to Girton College, Cambridge as a doctoral student. Here, under the guidance of mathematician George A. Reid, McDuff worked on problems in functional analysis. She solved a problem on Von Neumann algebras, constructing infinitely many different factors of type II1, and published the work in the Annals of Mathematics .
After completing her doctorate in 1971 McDuff was appointed to a two-year Science Research Council Postdoctoral Fellowship at Cambridge. Following her husband, the literary translator David McDuff, she left for a six-month visit to Moscow. Her husband was studying the Russian Symbolist poet Innokenty Annensky. Though McDuff had no specific plans [9] it turned out to be a profitable visit for her mathematically. There, she met Israel Gelfand in Moscow who gave her a deeper appreciation of mathematics. [7] [8] McDuff later wrote:
[My collaboration with him]... was not planned: it happened that his was the only name which came to mind when I had to fill out a form in the Inotdel office. The first thing that Gel'fand told me was that he was much more interested in the fact that my husband was studying the Russian Symbolist poet Innokenty Annensky than that I had found infinitely many type II-sub-one factors, but then he proceeded to open my eyes to the world of mathematics. It was a wonderful education, in which reading Pushkin, Mozart and Salieri played as important a role as learning about Lie groups or reading Cartan and Eilenberg. Gel'fand amazed me by talking of mathematics as though it were poetry. He once said about a long paper bristling with formulas that it contained the vague beginnings of an idea which he could only hint at and which he had never managed to bring out more clearly. I had always thought of mathematics as being much more straightforward: a formula is a formula, and an algebra is an algebra, but Gel'fand found hedgehogs lurking in the rows of his spectral sequences!
On returning to Cambridge McDuff started attending Frank Adams's topology lectures and was soon invited to teach at the University of York. In 1975 she separated from her husband, and was divorced in 1978. [6] [10] At the University of York, she "essentially wrote a second PhD" [9] while working with Graeme Segal. At this time a position at Massachusetts Institute of Technology (MIT) opened up for her, reserved for visiting female mathematicians. Her career as a mathematician developed further while at MIT, and soon she was accepted to the Institute for Advanced Study where she worked with Segal on the Atiyah–Segal completion theorem. She then returned to England, where she took up a lectureship at the University of Warwick. [11]
Around this time she met mathematician John Milnor who was then based in Princeton University. To live closer to him she took up an untenured assistant professorship at the Stony Brook University. [9] Now an independent mathematician, she began work on the relationship between diffeomorphisms and the classifying space for foliations. She has since worked on symplectic topology. In the spring of 1985, McDuff attended the Institut des Hautes Études Scientifiques in Paris to study Mikhael Gromov's work on elliptic methods. Since 2007, she has held the Helen Lyttle Kimmel chair at Barnard College.
In 1984 McDuff married Milnor, now a professor at Stony Brook University, and a Fields medallist, Wolf Prize winner and Abel Prize Laureate. [6] [10] [12]
For the past 30 years McDuff has been a contributor to the development of the field of symplectic geometry and topology. She gave the first example of symplectic forms on a closed manifold that are cohomologous but not diffeomorphic and also classified the rational and ruled symplectic four-manifolds, completed with François Lalonde. [13] More recently, partly in collaboration with Susan Tolman, [14] she has studied applications of methods of symplectic topology to the theory of Hamiltonian torus actions. She has also worked on embedding capacities of 4-dimensional symplectic ellipsoids with Felix Schlenk, [15] which gives rise to some very interesting number-theoretical questions. It also indicates a connection between the combinatorics of J-holomorphic curves in the blow up of the projective plane and the numbers that appear as indices in embedded contact homology. [10] [12] With Katrin Wehrheim, she has challenged the foundational rigor of a classic proof in symplectic geometry. [16]
With Dietmar Salamon, she co-authored two textbooks Introduction to Symplectic Topology [17] and J-Holomorphic Curves and Symplectic Topology. [18] [19]
McDuff was the first to be awarded the Satter Prize, in 1991, for her work on symplectic geometry; she is a Fellow of the Royal Society (1994), a Noether Lecturer (1998) and a member of both the United States National Academy of Sciences (1999) and the American Philosophical Society (2013). [20] In 2008 she was elected a Corresponding Fellow of the Royal Society of Edinburgh. [21] She was a Plenary Lecturer at the 1998 International Congress of Mathematicians (ICM) [22] and an Invited Speaker at the 1990 ICM. [23] In 2012 she became a fellow of the American Mathematical Society. [24] In 1999, she was the first female Hardy Lecturer, an award from the London Mathematical Society. [25] She is also a member of the Academia Europaea, [26] and is part of the 2019 class of fellows of the Association for Women in Mathematics. [27]
In 2010, she was awarded the Senior Berwick Prize of the London Mathematical Society. [28] For 2017 she received, jointly with Dietmar Salamon, the AMS Leroy P. Steele Prize for Mathematical Exposition. [29] In 2018 she received the Sylvester Medal by the Royal Society. [30]
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.
In mathematics, specifically in topology and geometry, a pseudoholomorphic curve is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation. Introduced in 1985 by Mikhail Gromov, pseudoholomorphic curves have since revolutionized the study of symplectic manifolds. In particular, they lead to the Gromov–Witten invariants and Floer homology, and play a prominent role in string theory.
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable. They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten.
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang–Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as (smooth) three- and four-dimensional manifolds.
In mathematics, specifically in symplectic geometry, the symplectic sum is a geometric modification on symplectic manifolds, which glues two given manifolds into a single new one. It is a symplectic version of connected summation along a submanifold, often called a fiber sum.
Tian Gang is a Chinese mathematician. He is a professor of mathematics at Peking University and Higgins Professor Emeritus at Princeton University. He is known for contributions to the mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis.
Joan Sylvia Lyttle Birman is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.
Katrin Wehrheim is an associate professor of mathematics at the University of California, Berkeley. Wehrheim's research centers around symplectic topology and gauge theory, and they are known for work on pseudoholomorphic quilts. With Dusa McDuff, they have challenged the foundational rigor of a classic proof in symplectic geometry.
In mathematics, the Reeb vector field, named after the French mathematician Georges Reeb, is a notion that appears in various domains of contact geometry including:
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In mathematics, more precisely in symplectic geometry, a hypersurface of a symplectic manifold is said to be of contact type if there is 1-form such that and is a contact manifold, where is the natural inclusion. The terminology was first coined by Alan Weinstein.
Paul Ian Biran is an Israeli mathematician. He holds a chair at ETH Zurich. His research interests include symplectic geometry and algebraic geometry.
Helmut Hermann W. Hofer is a German-American mathematician, one of the founders of the area of symplectic topology.
The Ruth Lyttle Satter Prize in Mathematics, also called the Satter Prize, is one of twenty-one prizes given out by the American Mathematical Society (AMS). It is presented biennially in recognition of an outstanding contribution to mathematics research by a woman in the previous six years. The award was funded in 1990 using a donation from Joan Birman, in memory of her sister, Ruth Lyttle Satter, who worked primarily in biological sciences, and was a proponent for equal opportunities for women in science. First awarded in 1991, the award is intended to "honor [Satter's] commitment to research and to encourage women in science". The winner is selected by the council of the AMS, based on the recommendation of a selection committee. The prize is awarded at the Joint Mathematics Meetings during odd numbered years, and has always carried a modest cash reward. Since 2003, the prize has been $5,000, while from 1997 to 2001, the prize came with $1,200, and prior to that it was $4,000. If a joint award is made, the prize money is split between the recipients.
Laura Grace DeMarco is a professor of mathematics at Harvard University, whose research concerns dynamical systems and complex analysis.
Megumi Harada is a mathematician who works as a professor in the department of mathematics and statistics at McMaster University, where she holds a tier-two Canada Research Chair in Equivariant Symplectic and Algebraic Geometry.
Emmy Murphy is an American mathematician and a professor at Princeton University who works in the area of symplectic topology, contact geometry and geometric topology.
François Lalonde is a Canadian mathematician, specializing in symplectic geometry and symplectic topology.
Kaoru Ono is a Japanese mathematician, specializing in symplectic geometry. He is a professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University.
Dietmar Arno Salamon is a German mathematician.
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