Jean Bourgain’s work touches on many central topics of mathematical analysis: the geometry of Banach spaces, harmonic analysis, ergodic theory, spectral problems, and nonlinear partial differential equations from mathematical physics. His contributions have solved longstanding problems in convexity theory and harmonic analysis such as Mahler’s conjecture and the lambda-p set problem. His work has had important consequences in theoretical computer science, group expansion, spectral gaps, and the theory of exponential sums in number theory, including a complete solution of Vinogradov’s theorem in analytic number theory after more than eighty years. In Hamiltonian dynamics, he developed the theory of invariant Gibbs measures and quasi-periodicity for the Schrödinger equation.
Fields Medalist, 1994