The 2024 Shaw Prize in Mathematical Sciences has been awarded to Peter Sarnak, General Director of the IIAS' Advanced School in Mathematics. Sarnak has been recognized for his groundbreaking development of the arithmetic theory of thin groups and the affine sieve, which integrates number theory, analysis, combinatorics, dynamics, geometry, and spectral theory.

The Shaw Prize's Mathematical Selection Committee praised Sarnak for his "original and deep vision," highlighting his work's "profound impact" across various mathematical disciplines. Sarnak's contributions have primarily focused on number theory, an ancient and fundamental branch of pure mathematics dedicated to the study of integers and arithmetic functions.

Sarnak's pioneering research has explored the search for almost prime values of polynomials in sparse subsets derived from the orbit of a thin group. Thin groups are unique subgroups of arithmetic groups, balancing between being too large and too small. They naturally appear in both pure and applied mathematics, such as in the symmetry groups of integral Apollonian circle packings and various monodromy groups of differential equations.

Together with Prof. Jean Bourgain and Prof. Alexander Gamburd, Sarnak produced expanders from thin groups, which are highly connected sparse graphs extensively used in computer science. Their work demonstrated a crucial relationship between the minimal dimension of representations of finite linear groups and expanders.

This prestigious recognition places Sarnak among an esteemed group of IIAS-affiliated scholars who have previously received the Shaw Prize, including, Noga Alon and David Kazhdan.

For more information, please visit the Shaw Prize website: https://www.shawprize.org/laureates/2024-mathematical-sciences/