|Karen Uhlenbeck is a distinguished mathematician of the highest international stature, specializing in differential geometry, non-linear partial differential equations, and mathematical physics. At the same time, Uhlenbeck’s efforts across the educational spectrum, especially her role as a founder of Park City-IAS Mathematical Institute, have added vitality to the mathematical scene. Uhlenbeck’s mentoring, both formal (she co-founded the Annual Women in Mathematics Program at the IAS) and informal, of women mathematicians is legendary.
Uhlenbeck’s most famous work is in gauge theory and in harmonic maps. The fundamental importance of “bubbling” and its role in establishing compactness results in a wide range of non-linear geometric partial differential equations was first recognized in her work on gauge theory and harmonic maps. In gauge theory, her work in the early 1980s laid the analytic foundations for the application of gauge theory to geometry and topology. In particular, her work underpins the striking applications of gauge theory to 4-dimensional smooth topology pioneered by Donaldson in his Fields medal winning work. She and her collaborators have produced some of the most influential, foundational papers in mathematical gauge theory, stability theory of holomorphic bundles, and harmonic mappings.
Uhlenbeck has worked in many other areas, always at the interface of geometry and analysis. In harmonic maps, she introduced fundamental new methods into integrable systems in her study of harmonic maps to Lie groups. In recent years, she has turned her attention to the theory of integrable systems, and with her coauthor Chuu-Lian Terng, introduced new ways to think of classical KdV flows and their tau functions and virasoro symmetries.
Uhlenbeck graduated from the University of Michigan with a BS in mathematics in 1964. After continuing her studies at the Courant Institute and Brandeis, she received her Masters in 1966, and PhD (with Richard Palais as supervisor) in 1968, both from Brandeis. Following appointments at MIT, the University of California at Berkeley, the University of Illinois, and the University of Chicago, she has held since 1987 the Sid W. Richardson Foundations Regents Chair III in Mathematics at the University of Texas at Austin. She has served as Vice-President of the American Mathematical Society (1987– 90).
She has been awarded a MacArthur “Genius” Fellowship, the Steele Prize of the American Mathematical Society, and the U.S. National Medal of Science. In 1990, she became the second woman (after Emmy Noether in 1932) to present a plenary lecture at an International Congress of Mathematicians. She is a fellow of the American Academy of Arts and Sciences and the U.S. National Academy of Sciences. Professor Uhlenbeck is the recipient of six honorary degrees, most recently from Harvard and Brandeis Universities; she received her seventh from Princeton University in June 2012.