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Karen Keskulla Uhlenbeck

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24 Aug 1942

Cleveland, Ohio, USA

Karen Uhlenbeck's father was an engineer and her mother was an artist. She grew up in the country, the eldest of four children. Many mathematicians know from early age that mathematics will be their life but this was not so with Karen Uhlenbeck. As a child she was interested in books and this led her to an interest in science. She writes:

As a child I read a lot, and I read everything. I'd go to the library and then stay up all night reading. I used to read under the desk in school. ... we lived in the country so there wasn't a whole lot to do. I was particularly interested in reading about science. I was about twelve years old when my father began bringing home Fred Hoyle's books on astrophysics. I found them very interesting. I also remember a little paperback book called "One, Two, Three, (and, in?) Infinity" by George Gamow, and I remember the excitement of understanding this very sophisticated argument that there were two different kinds of infinities.

Uhlenbeck entered the University of Michigan with the intention of studying physics but a combination of studying exciting mathematics courses and finding that physics practicals were not a strong point lead her to change to mathematics. She was awarded a B.S. in mathematics in 1964.

After graduating from the University of Michigan, Uhlenbeck continued her studies at the Courant Institute in New York. However at this time she married and decided to follow her husband when he went to Harvard. She entered Brandeis University and was awarded a Master's Degree in 1966. She remained at Brandeis to study for her doctorate under Richard Palais' supervision, and was awarded a Ph.D. in 1968.

Her first appointment was a one year post in 1968-69 at Massachusetts Institute of Technology. Then another temporary post, this time a two year one as a lecturer at the University of California, Berkeley during 1989-71. She describes her search for a permanent position:

I was told, when looking for jobs after my year at MIT and two years at Berkeley, that people did not hire women, that women were supposed to go home and have babies. So the places interested in my husband - MIT, Stanford, and Princeton - were not interested in hiring me. I remember that I was told that there were nepotism rules and that they could not hire me for this reason, although when I called them on this issue years later they did not remember saying these things ... I ended up at the University of Illinois, Champaign-Urbana because they hired me, and my husband came along. In retrospect I realized how remarkably generous he was because he could have been at MIT, Stanford, or Princeton. I hated Champaign-Urbana - I felt out of place mathematically and socially, and it was ugly, bourgeois and flat.

After being on the faculty at Urbana-Champaign from 1971 to 1976, she moved to the University of Illinois at Chicago where she was promoted to full professor. At this time she:

... became friends with S T Yau , whom I credit with generously establishing my finally and definitively as a mathematician.

In 1983 she was awarded a MacArthur Prize Fellowship and moved to a professorship at the University of Chicago. In 1988 Uhlenbeck was appointed Professor in the University of Texas at Austin where she also holds the Sid W Richardson Foundation Regents Chair in Mathematics.

Uhlenbeck is a leading expert on partial differential equations and describes her mathematical interests as follows:

I work on partial differential equations which were originally derived from the need to describe things like electromagnetism, but have undergone a century of change in which they are used in a much more technical fashion to look at the shapes of space. Mathematicians look at imaginary spaces constructed by scientists examining other problems. I started out my mathematics career by working on Palais' modern formulation of a very useful classical theory, the calculus of variations . I decided Einstein 's general relativity was too hard, but managed to learn a lot about geometry of space time. I did some very technical work in partial differential equations, made an unsuccessful pass at shock waves, worked in scale invariant variational problems, made a poor stab at three dimensional manifold topology , learned gauge field theory and then some about applications to four dimensional manifolds, and have recently been working n equations with algebraic infinite symmetries.

Uhlenbeck's work provided analytic tools to use instantons as an effective geometric tool. In Simon Donaldson reminisces about the work on the applications of instantons that led him to receive a Fields Medal in 1986. He describes the "bubbling" phenomenon saying:

In fact the papers of Uhlenbeck which appeared about that time [1982] contained essentially all the analysis required to put this picture on a firm footing. The papers do not discuss "bubbling" explicitly - perhaps the arguments were supposed to be obvious to experts by analogy with the work of Sacks and Uhlenbeck in the harmonic maps case.

In 1988 Uhlenbeck lectured on Instantons and Their Relatives at the Centennial Celebration of the American Mathematical Society . Witten , who gave the next talk on Geometry and quantum field theory at the symposium said:

In the talk just before mine, Karen Uhlenbeck described some purely mathematical developments that at least roughly might be classified in this area. She described advances in geometry that have been achieved through the study of systems of nonlinear partial differential equations. Among other things, she sketched some aspects of Simon Donaldson 's work on the geometry of four-dimensional manifolds, instantons - solutions, that is, of a certain nonlinear system of partial differential equations, the self-dual Yang-Mills equations, which were originally introduced by physicists in the context of quantum field theory.

Two years later, in 1990, Witten received a Fields Medal for his work on topological quantum field theories. At the same International Congress of Mathematicians in Kyoto, Karen Uhlenbeck was a Plenary Speaker.

Among the many honours that Uhlenbeck has received for her work one should mention in particular that she was elected a Member of the American Academy of Arts and Science in 1985 and a Member of the National Academy of Sciences the following year.

She has also served on the editorial boards of many journals; a complete list to date is Journal of Differential Geometry (1979-81), Illinois Journal of Mathematics (1980-86), Communications in Partial Differential Equations (1983- ), Journal of the American Mathematical Society (1986-91), Ergebnisse der Mathematik (1987-90), Journal of Differential Geometry (1988-91), Journal of Mathematical Physics (1989- ), Houston Journal of Mathematics (1991- ), Journal of Knot Theory (1991- ), Calculus of Variations and Partial Differential Equations (1991- ), Communications in Analysis and Geometry (1992- ).

Source:School of Mathematics and Statistics University of St Andrews, Scotland