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Fellows Directory

Peter Sarnak

Peter Sarnak

Professor Peter Sarnak FRS


Elected: 2002


Peter Sarnak has made major contributions to analysis and number theory. He is widely recognised internationally as one of the leading analytic number theorists of his generation. His early work on the existence of cusp forms led to the disproof of a conjecture of Selberg. He has obtained the strongest known bounds towards the Ramanujan conjectures for sparse graphs, and he was one of the first to exploit connections between certain questions of theoretical physics and analytic number theory. 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. His work on subconvexity for Rankin–Selberg L-functions led to the resolution of Hilbert’s eleventh problem.

Interest and expertise

Subject groups

  • Mathematics
    • Pure mathematics


  • Sylvester Medal

    For transformational contributions across number theory, combinatorics, analysis and geometry.

  • Wolf Prize

    In the field of mathematics for his deep contributions in analysis, number theory, geometry, and combinatorics.

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