Mathematician Luis Caffarelli wins Abel prize for solving equations with geometry

Luis Caffarelli won the 2023 Abel Prize, informally called the Nobel Prize of Mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice to jet engines. bottom.

Caffarelli heard the news while having breakfast with his wife. “Breakfast just got better,” he says. “My wife was happy. I was happy. It was an emotional moment.”

Based at the University of Texas at Austin, Caffarelli began studying partial differential equations (PDEs) in the late 1970s and has contributed hundreds of papers since. He is known for connecting seemingly distant mathematical concepts, such as how to describe partial differential equations in extreme cases, using a theory that describes the smallest area a surface can occupy.

PDEs have been studied for hundreds of years and describe almost every kind of physical process, from fluids to combustion engines to financial models. Caffarelli’s most important work was on nonlinear partial differential equations that describe complex relationships between multiple variables. These equations are more difficult to solve than other partial differential equations and often produce solutions that do not make sense in the physical world.

Caffarelli helped tackle these problems with the theory of regularity, which sets out how to deal with problematic solutions by borrowing ideas from geometry. His approach has been to carefully unravel the thorny parts of the equation and solve a variety of problems in his 40+ year career.

Francesco Maggi of the University of Texas at Austin said: “But when they came out in the ’80s, these were foreign mathematics.”

Many of the nonlinear partial differential equations that Caffarelli helped write are so-called free boundary problems, where two bodies in contact share a changing surface, such as ice melting to water or water passing through a filter. Describe the physical scenario that

“He used insight combined with ingenuity, sometimes very uncomplicated, but used in ways others couldn’t see. He did it over and over again. I’ve been to Austin, Texas.

These insights have also helped other researchers transform their equations so that they can be solved on supercomputers. “He’s one of the most prominent people to take this theory to the point where it’s useful for practical applications,” he says.