Peter Sarnak Awarded 2024 Shaw Prize in Mathematical Sciences

The 2024 Shaw Prize in Mathematical Sciences has been awarded to Peter Sarnak, Gopal Prasad Professor in the School of Mathematics, for his "development of the arithmetic theory of thin groups and the affine sieve, by bringing together number theory, analysis, combinatorics, dynamics, geometry, and spectral theory."

In their citation, the Shaw Prize's Mathematical Selection Committee extolled Sarnak's "original and deep vision" which has had a "profound impact" on numerous areas of study. Although his interest in mathematics is indeed wide-ranging, many of Sarnak's major contributions have been motivated by number theory. Number theory is a branch of pure mathematics devoted primarily to the study of integers (e.g., whole numbers) and arithmetic functions. It is one of the oldest and most fundamental areas of mathematics, with its origins dating back to ancient civilizations. Number theory has been described as the "queen of mathematics" due to its fundamental nature, beauty, and ability to inspire groundbreaking work. While initially considered a purely theoretical field, number theory has found numerous modern applications in cryptography, computer science, communications, physics, and more.

Within this field, Sarnak's pioneering work on "the search for almost prime values of polynomials in sparse subsets arising as the orbit of a thin group," and his efforts to produce "expanders out of some thin groups," conducted alongside Jean Bourgain, Faculty (1994–2018), and Alexander Gamburd, Member (2005–06, 2007–08, 2022), both in the School of Mathematics, were praised.

With his receipt of the Shaw Prize in Mathematical Sciences, Sarnak joins an illustrious group of IAS affiliated scholars who have received the award. In recent years, this includes Shing-Tung Yau, Faculty (1980–84) in the School of Mathematics, and Vladimir Drinfeld, Member (1990, 1996–97, 1998) and Visiting Professor (2019–20) in the School, who were presented with the 2023 Shaw Prize for their contributions to the fields of mathematical physics, arithmetic geometry, differential geometry, and Kähler geometry. Noga Alon, frequent Visiting Professor in the School of Mathematics, won the 2022 Shaw Prize for his contributions to discrete mathematics and theoretical computer science. In 2021, the Prize was awarded to Jean-Michel Bismut, Member (1984, 1994) in the School of Mathematics, and Jeff Cheeger, Member (1972, 1977–78, 1995) in the School, for their work on modern geometry.