Peter Sarnak

I work in the mathematical fields of number theory and analysis and their applications. In recent years I have been interested in the spectral problems at the center of the modern theory of automorphic forms and harmonic analysis. These have applications to classical number theory, for example, to the theory of zeta functions and Hilbert's problem on the arithmetic of quadratic forms as well as to combinatorics and computer science using constructions of highly connected but sparse networks. These spectral problems also give one of the few instances of quantizations of classically chaotic Hamiltonians than can be studied mathematically in the semiclassical limit.