U.S. mathematician Karen Keskulla Uhlenbeck has won the 2019 Abel Prize—one of the field’s most prestigious awardscfor her wide-ranging work in analysis, geometry and mathematical physics. Uhlenbeck is the first woman to win the 6-million-kroner (U.S.$702,500) prize, which is given out by the Norwegian Academy of Science and Letters, since it was first awarded in 2003.

Uhlenbeck learnt that she had won on 17 March, after a friend called and told her that the academy was trying to contact her. “I was completely amazed,” she told Nature. “It was totally out of the blue.” The academy announced the award on 19 March.

Uhlenbeck is legendary for her skill with partial differential equations, which link variable quantities and their rates of change, and are at the heart of most physical laws. But her long career has stretched across many fields, and she has used the equations to solve problems in geometry and topology.

One of her most influential results—and the one that she says she’s most proud of—is the discovery of a phenomenon called bubbling, as part of seminal work she did with mathematician Jonathan Sacks. Sacks and Uhlenbeck were studying ‘minimal surfaces’, the mathematical theory of how soap films arrange themselves into shapes that minimize their energy. But the theory had been marred by the appearance of points at which energy appeared to become infinitely concentrated. Uhlenbeck’s insight was to ‘zoom in’ on those points to that this were caused by a new bubble splitting off the surface.

She applied similar techniques to do foundational work in the mathematical theory of gauge fields, a generalization of the theory of classical electromagnetic fields, which underlies the standard model of particle physics.

Source & further reading:
https://www.scientificamerican.com/article/soap-bubble-pioneer-is-first-woman-to-win-prestigious-math-prize/