Nationality British Role Mathematician Doctoral advisor George A. Reid Fields Mathematics | Awards Noether Lecture Name Dusa McDuff | |

Born Margaret Dusa Waddington
18 October 1945 (age 70)
London, England (1945-10-18) Institutions University of Cambridge University of York University of Warwick Massachusetts Institute of Technology Institute for Advanced Study Stony Brook University Barnard College Alma mater University of Edinburgh Girton College, Cambridge Notable awards BMS Morning Speaker Satter Prize Fellow of the Royal Society Speaker at International Congress of Mathematicians BMC Plenary Speaker Residence Stony Brook, New York, United States Books Introduction to symplectic topology, J-holomorphic Curves and Symplectic Topology Education University of Edinburgh, University of Cambridge Similar People Dietmar Arno Salamon, Mikhail Leonidovich Gromov, Katrin Wehrheim, Yakov Eliashberg, John Milnor | ||

Doctoral students Katrin Wehrheim |

## Interview at cirm dusa mcduff

**Dusa McDuff**, FRS (born 18 October 1945) is an English mathematician who works on symplectic geometry. She has been awarded the first Satter Prize and become a Noether Lecturer and a Fellow of the Royal Society.

## Contents

- Interview at cirm dusa mcduff
- Dusa mcduff thinking in four dimensions
- Early life and education
- Work and research
- Honors and recognition
- References

## Dusa mcduff thinking in four dimensions

## Early life and education

Margaret Dusa Waddington was born in London, England, on 18 October 1945 to biologist Conrad Hal Waddington and his second wife, Edinburgh architect Margaret Justin Blanco White. 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 and lover of H. G. Wells and an author in her own right. Though born in London, McDuff grew up in Scotland, where her father was appointed 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. 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.

Turning down a scholarship to the University of Cambridge to stay with her boyfriend in Scotland, she enrolled at the University of Edinburgh. Awarded a BSc in 1967, McDuff eventually matriculated as a doctoral student at Girton College, Cambridge. 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 II_{1}, 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 (literary translator David McDuff), McDuff left for a six-month visit to Moscow. Her husband was studying the Russian Symbolist poet Innokenty Annensky and Dusa had no specific plans, yet it turned out to be a very profitable visit for her mathematically. There, she met Israel Gelfand in Moscow who gave her a deeper appreciation of mathematics. 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. At around this time, in 1975, she separated from her first husband. At York, she "essentially wrote a second PhD" while working with Graeme Segal. At this time a position at MIT opened up for her, reserved for visiting female mathematicians. Her career as a mathematician started picking up after her stint 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 was given lectureship at the University of Warwick.

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. Now an independent mathematician, she started working on the relationship between diffeomorphisms and the classifying space for foliations. She has since taken up 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.

McDuff is married to Fields medallist, Wolf Prize winner and Abel Prize Laureate John Milnor, a mathematician at Stony Brook University.

## Work and research

For the last 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 of rational and ruled symplectic four-manifolds, completed with Francois Lalonde. More recently, partly in collaboration with Susan Tolman, 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, 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. With Katrin Wehrheim, she has challenged the foundational rigor of a classic proof in symplectic geometry.

With Dietmar Salamon, she co-authored two textbooks *Introduction to Symplectic Topology* and *J-Holomorphic Curves and Symplectic Topology*.

## Honors and recognition

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 the United States National Academy of Sciences (1999). She was a Plenary Lecturer at the 1998 International Congress of Mathematicians. In 2012 she became a fellow of the American Mathematical Society. In 1999, she was the first female Hardy Lecturer, an award from the London Mathematical Society. She is also a member of the Academia Europaea.

In 2010, she was awarded the Senior Berwick Prize of the London Mathematical Society. For 2017 she will receive the AMS Leroy P. Steele Prize for Mathematical Exposition.