Karen Keskulla Uhlenbeck is an American mathematician and a founder of modern geometric analysis. She is a professor emeritus of mathematics at the University of Texas at Austin, where she held the Sid W. Richardson Foundation Regents Chair. She is currently a visiting associate at the Institute for Advanced Study and a visiting senior research scholar at Princeton University.Uhlenbeck won the 2019 Abel Prize for “her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” She is the first woman to win the prize since its inception in 2003.Uhlenbeck is one of the founders of the field of geometric analysis, a discipline that uses differential geometry to study the solutions to differential equations and vice versa. She has also contributed to topological quantum field theory and integrable systems.
Together with Jonathan Sacks in the early 1980s, Uhlenbeck established regularity estimates that have found applications to studies of the singularities of harmonic maps and the existence of smooth local solutions to the Yang–Mills–Higgs equations in gauge theory.In particular, Donaldson describes their joint 1981 paper The existence of minimal immersions of 2-spheres as a “landmark paper… which showed that, with a deeper analysis, variational arguments can still be used to give general existence results” for harmonic map equations.Building on these ideas, Uhlenbeck initiated a systematic study of the moduli theory of minimal surfaces in hyperbolic 3-manifolds (also called minimal submanifold theory) in her 1983 paper, Closed minimal surfaces in hyperbolic 3-manifolds.
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