Карен Уленбек: Геометриялық анализдің негізін қалаушы математик ғалым

American mathematician

Karen Keskulla Uhlenbeck ForMemRS (born August 24, 1942) is an American mathematician and one of the founders 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 distinguished visiting professor at the Institute for Advanced Study and a visiting senior research scholar at Princeton University. She 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, and so far only, woman to win the prize since its inception in 2003. She donated half of the prize money to organizations which promote more engagement of women in research mathematics.

Uhlenbeck was born in Cleveland, Ohio, to engineer Arnold Keskulla and schoolteacher and artist Carolyn Windeler Keskulla. While she was a child, the family moved to New Jersey. Uhlenbeck's maiden name, Keskulla, comes from Keskküla and from her grandfather who was Estonian, while her current surname is Dutch. Uhlenbeck received her B. A. (1964) from the University of Michigan. After temporary jobs at the Massachusetts Institute of Technology and University of California, Berkeley, and having difficulty finding a permanent position with her husband because of the "anti nepotism" rules then in place that prevented hiring both a husband and wife even in distinct departments of a university, she took a faculty position at the University of Illinois at Urbana–Champaign in 1971. However, she disliked Urbana and moved to the University of Illinois at Chicago in 1976 as well as separating from her first husband Olke Uhlenbeck in the same year. She moved again to the University of Chicago in 1983. a visiting associate at the Institute for Advanced Study and a visiting senior research scholar at Princeton University.

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, Simon 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. In particular, her work is described by Simon Donaldson in a survey of Yang–Mills geometry as foundational in the analytic aspects of the calculus of variations associated with the Yang–Mills functional. A wider survey of her contributions to the field of calculus of variations was published by Simon Donaldson in the March 2019 issue of Notices of the American Mathematical Society; Donaldson describes the work of Uhlenbeck, along with Shing Tung Yau, Richard Schoen and several others, as developing a whole circle of ideas and techniques involving the dimension of singular sets, monotonicity, 'small energy' results, tangent cones, etc. [that] has had a wide ranging impact in many branches of differential geometry over the past few decades and forms the focus of much current research activity.

In 1991, Uhlenbeck co founded, with Herbert Clemens and Dan Freed, the Park City Mathematics Institute (PCMI) with the mission to "provide an immersive educational and professional development opportunity for several parallel communities from across the larger umbrella of the mathematics profession."