Laureation address – Professor Dusa McDuff

Professor Dusa McDuff
Laureation Address
Laureator: Professor Lars Olsen
Friday 27 June 2014

Chancellor, it is my privilege to present Professor Dusa McDuff for the degree of Doctor of Science, honoris causa.

Dusa McDuff is a mathematician who has produced seminal and ground-breaking work on symplectic geometry. Dusa has received numerous prizes and recognitions for her work. For example, she was the first person to be awarded the Satter Prize is 1991; she became a Fellow of the Royal Society in 1994; a Noether Lecturer in 1998, and a member of the United States National Academy of Sciences in 1999. She was also a Plenary Lecturer at the 1998 International Congress of Mathematicians, and in 2012 she became a Fellow of the American Mathematical Society.

Margaret Dusa McDuff was born in London. However, she grew up in Edinburgh, where her father was a professor who taught genetics and wrote books about such diverse topics as art and philosophy. Unlike the mothers of her friends, Dusa’s mother also worked as an architect, and perhaps it was through her that Dusa got a first glimpse of the difficulties of being a professional woman: her mother worked with the civil service in Edinburgh (taking part in the building of Council houses after the war) because she had no connections that enabled her to get a job in a private architectural practice.

In 1967, she earned her bachelor’s degree in mathematics from the University of Edinburgh and entered graduate school at Cambridge. Here, under the guidance of George Reid, Dusa worked on problems in functional analysis. She solved a difficult and noteworthy problem on von Neumann algebras (namely, constructing infinitely many different factors of type II₁).

While still a research student, Dusa followed her husband for a six-month visit to Moscow in 1969. There, she met the great Russian mathematician Israel Gel’fand. About this meeting Dusa says:

‘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 II₁ factors, but then he proceeded to open my eyes to the world of mathematics. It was a wonderful education, in which reading Pushkin, Mozart, or Salieri played as important a role as learning about Lie groups or reading about Cartan and Eilenberg. Gel’fand amazed me by talking of mathematics as though it were poetry’.

This is a beautiful quote because it shows that mathematics is an art. The difference between mathematics and the other arts, such as music and painting, is that our culture does not recognise it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. There is no question that if the world had to be divided into the poetic dreamers and the rational thinkers most people would place mathematicians in the latter category. Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind-blowing as cosmology or physics, and allows more freedom of expression than poetry, art, or music. Mathematics is the purest of arts.

However, I digress. After Moscow, Dusa returned to Cambridge for a two-year Science Research Council Fellowship, working with Frank Adams and later Graeme Segal. She was appointed Lecturer first at the University of York (1972-76) and then at the University of Warwick (1976-78). This was the time during which Dusa struggled most to find her voice in mathematics. However, it was also during that time that Dusa’s career took a major turn. Why the changes? In 1974, Dusa was invited to spend a year on the faculty at MIT. One position was open for a visiting professor and the space had been reserved specifically for a woman. During that year, a whole new world opened up to Dusa, showing her what she was capable of doing as a mathematician.

Dusa was on the faculty of the State University of New York at Stony Brook from 1978-2008, starting as an Assistant Professor and ending as a Distinguished Professor, along the way serving two years as Department Chair. She retired from SUNY in 2008 and has, since 2007, held the Helen Lyttle Kimmel ’42 Chair in Mathematics at Barnard College.

Dusa’s mathematical work centres around differential geometry and, in particular, symplectic geometry. What is symplectic geometry? It is the branch of geometry that studies symplectic manifolds; that is, differential manifolds equipped with a closed, non-degenerate 2-form. While this explanation certainly is correct, it does not tell a non-expert much. So let me try with another explanation.

A differential manifold is simply a smooth surface, such as the surface of a sphere, or the surface of an ellipsoid. It is a slightly more difficult to explain what a closed, non-degenerate 2-form is. In order to explain this, let me start by recalling that the concept of symplectic geometry arose in the study of classical mechanical systems, such as a falling apple, an oscillating pendulum, or a planet orbiting the sun. Let us, for example, consider an oscillating pendulum. To fully describe the motion of such a pendulum we need to know two pieces of information, namely, the angle between a vertical line and the string of the pendulum, and the rate at which this angle changes. These two pieces of information are collectively called a state. Once the state is known, the trajectory of the system can be determined by Newton’s laws. It turns out that the states of a physical system (such as the pendulum) cannot take on arbitrary values, but are constrained to lie on a certain smooth surface, or manifold. As time progresses the states of the system move around on the surface according to the laws of nature and, loosely speaking, the closed, non-degenerate 2-form that I mentioned before is the mechanism that describes how the system evolves in time.

It is natural to ask how abstractly this can be set up. Can we axiomatise the properties of this example, and then just deal with it abstractly (without worrying about the precise classical mechanical setup that led to it)? In fact, we can, and symplectic manifolds are the appropriate abstraction.

However, I am confident that you did not come here to listen to a lecture in mathematics; in particular, not our Mathematics students who are graduating today. You, the graduating Mathematics students, are, in a very real sense, my students: we studied complex numbers in first year; we struggled with epsilons and deltas in second year; we learnt about the Riemann integral in third year and we marvelled at the beauty of the Lebesgue integral in fourth year.

Yes, you are my students. It has been an absolute delight to teach you and I will miss all of you now that you are moving on. Thank you for all your hard work and many congratulations on your great success. Your parents, your friends, and the Dean, will wish all of you good luck and happy lives ever after. If you achieve this you will indeed be blessed and fortunate. I, on the other hand, wish you this: may you all have fulfilling and rewarding lives.

But I digress once again. Throughout her career, Dusa has been concerned with educational issues at both undergraduate and graduate levels, as well as being active in encouraging more women to study mathematics. A few years ago, I attended a conference in Texas where I met a young colleague who attended SUNY as an undergraduate. I was curious and asked her about Dusa’s teaching, and she said, ‘Dusa is great. She’s one of the best teachers’. She then added, ‘I loved her British accent, and she wears hippie skirts like no other!’

Chancellor, in recognition of her major contribution to mathematics, and especially her work on symplectic geometry, I invite you to confer on Professor Dusa McDuff the degree of Doctor of Science, honoris causa.