# Mathematician Nahmod Receives Coveted Simons Foundation Grant [1]

Mathematics professor Andrea R. Nahmod has been named a principal investigator for a Simons Foundation Collaboration in Mathematical and Physical Sciences that will involve leading mathematics and physics researchers in the United States and Europe in a systematic, coordinated study of wave turbulence.

The four-year, $8 million grant with possibility of extension is a collaboration directed by Jalal Shatah [2] at the Courant Institute at New York University (NYU).

Nahmod says of the recognition, “It is a huge honor to have been awarded the most prestigious and coveted of the collaborations grant awards given by the Simons Foundation. I am very proud that UMass has been chosen to receive it and that I am a principal investigator on it.”

The researchers explain that waves are found everywhere in nature and are central in describing fundamental physical phenomena at all scales, from quantum mechanics to general relativity. When a number of interacting waves are present in a system, such as low- or high-pressure waves moving as weather across a continent, “the description of an individual wave is neither possible nor relevant.What becomes of physical importance and practical use is the density and statistics of the interacting waves.”

This illustrates the need for wave turbulence theory, what Nahmod calls a fundamental question in physics and mathematics. In spite of the fact that illustrious mathematicians including giants such as Leonardo da Vinci and the Russian mathematician Andrey Kolmogorov have contributed to scientists’ understanding of it, she adds, “to this day wave turbulence theory is still lacking robust mathematical foundations. This is what we’ll be working on.”

The mathematics of wave turbulence theory offers scientists the ability to predict the evolution of the wave action spectral density of interacting wave systemsin practical, useful terms. Nahmod’s team’s website states that “a perfect example to illustrate the importance of wave turbulence theory is that of forecasting surface gravity waves in the oceans,” which are important for navigation and safe operations at sea and on offshore platforms. Forecasters using equations derived with wave turbulence theory release models every three hours every day to mariners and those who rely on the information.

But, they point out, “Although the wave kinetic equation has been widely used, its range of applicability has never been put on a rigorous mathematical foundation. Its predictions of the energy spectrum are not always in agreement with empirical data. This discrepancy could, in part, be explained by the lack of a rigorous mathematical theory. This collaboration is the first attempt for a systematic coordinated study of wave turbulence theory in a large-scale project, bringing together state-of-the-art skills in the areas of mathematics and physics, with theoretical, experimental and numerical expertise.”

Nahmod received her Ph.D. degree in mathematics from Yale University and took postdoctoral positions at Macquarie University, Sydney, Australia, and at the University of Texas at Austin and was twice member of the Institute for Advanced Study at Princeton. She came to campus in 1998. She is a fellow of the American Mathematical Society, and a recipient of the Sargent-Faull Fellowship at Harvard’s Radcliffe Institute for Advanced Study and of a Simons Fellowship and of a Simons Professorship (Fall 2015). She was named UMass’s Spotlight Scholar and received the campus’s Award for Outstanding Accomplishments in Research and Creative Activity in 2016.