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The Norwegian Academy of Science and Letters today announced that Karen Uhlenbeck has won the 2019 Abel Prize, a Nobel-level honor in math. Uhlenbeck won for her foundational work in geometric analysis, which combines the technical power of analysis—a branch of math that extends and generalizes calculus—with the more conceptual areas of geometry and topology. She is the first woman to receive the prize since the award of 6 million Norwegian kroner (approximately $700,000) was first given in 2003.
Caroline Series, a math professor at the University of Warwick in Coventry, U.K., and president of the London Mathematical Society, says, “To see a woman right up there, honored for a lifetime of distinguished work in math, who has made a huge difference to the development of the field in the last 40 years—that is hugely important.”
Uhlenbeck - Career - University - Texas - Austin
Uhlenbeck, 76, spent much of her career at the University of Texas in Austin and is now a visitor at the Institute for Advanced Study (IAS) in Princeton, New Jersey. Her work stands at the heart of several important advances in math, including the revolutionary work in 4D topology by Simon Donaldson of the Simons Center at the State University of New York in Stony Brook. It has also fertilized interactions between math and theoretical physics, including string theory.
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An example of the kind of object studied in geometric analysis is a minimal surface. Analogous to a geodesic, a curve that minimizes path length, a minimal surface minimizes area; think of a soap film, a minimal surface that minimizes energy. Analysis focuses on the differential equations governing variations of surface area, whereas geometry and topology focus on the minimal surface representing a solution to the equations. Geometric analysis weaves together both approaches, resulting...
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