[4] He was member of the Board of Adjudicators and for one period chairman of the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.

[1][2] Sarnak's work (with A. Lubotzky and R. Phillips) applied results in number theory to Ramanujan graphs, with connections to combinatorics and computer science.

[3] He has obtained the strongest known bounds towards the Ramanujan–Petersson conjectures for sparse graphs, and was one of the first to exploit connections between certain questions of theoretical physics and analytic number theory.

[3] There are fundamental contributions to arithmetical quantum chaos, a term which he introduced, and to the relationship between random matrix theory and the zeros of L-functions.

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