Peter Sarnak

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Peter Sarnak

Peter Sarnak.jpg
Peter Clive Sarnak

(1953-12-18) 18 December 1953 (age 65)
Johannesburg, South Africa
NationalitySouth Africa[1]
United States[1]
Alma materUniversity of the Witwatersrand (BSc)
Stanford University (PhD)
Known forHafner–Sarnak–McCurley constant
AwardsGeorge Pólya Prize (1998)
Ostrowski Prize (2001)
Levi L. Conant Prize (2003)
Cole Prize (2005)
Wolf Prize (2014)
Scientific career
InstitutionsCourant Institute
New York University
Stanford University
Princeton University
Institute for Advanced Study
ThesisPrime geodesic theorems (1980)
Doctoral advisorPaul Cohen[1][2]
Doctoral studentsWilliam Duke
Alex Eskin
Alexandru Zaharescu
Harald Helfgott
Jacob Tsimerman
Jonathan Pila
Kannan Soundararajan
Akshay Venkatesh
Steven J. Miller
InfluencesCarl Ludwig Siegel
Juergen Moser

Peter Clive Sarnak FRS MAE[3] (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities.[1] He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. Sarnak is also on the permanent faculty at the School of Mathematics of the Institute for Advanced Study.[4] He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.


Sarnak graduated from the University of the Witwatersrand (BSc 1975, BSc(Hons) 1976) and Stanford University (PhD 1980), under the direction of Paul Cohen.[1][2] Sarnak's highly cited work (with A. Lubotzky and R. Philips) applied deep results in number theory to Ramanujan graphs, with connections to combinatorics and computer science.

Career and research[edit]

Sarnak has made major contributions to analysis and number theory.[3] He is widely recognised internationally as one of the leading analytic number theorists of his generation.[3] His early work on the existence of cusp forms led to the disproof of a conjecture of Atle Selberg.[3] He has obtained the strongest known bounds towards the Ramanujan–Petersson conjectures for sparse graphs, and he 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.[3] His work on subconvexity for Rankin–Selberg L-functions led to the resolution of Hilbert's eleventh problem.[3] During his career he has held numerous appointments including:


  • Sarnak, P. (1982). "Spectral Behavior of Quasi Periodic Potentials". Commun. Math. Phys. 84 (3): 377–401. doi:10.1007/bf01208483.
  • Some Applications of Modular Forms, 1990
  • (joint editor) Extremal Riemann Surfaces, 1997
  • (joint author) Random Matrices, Frobenius Eigenvalues and Monodromy, 1998
  • Peter Sarnak (2000). "Some problems in Number Theory, Analysis and Mathematical Physics". In V. I. Arnold, M. Atiyah, P. Lax, B. Mazur. Mathematics: frontiers and perspectives. American Mathematical Society. pp. 261–269. ISBN 978-0821826973.CS1 maint: Uses editors parameter (link)
  • (joint editor) Selected Works of Ilya Piatetski-Shapiro (Collected Works), 2000
  • (joint author) Elementary Number Theory, Group Theory and Ramanujan Graphs, 2003
  • (joint editor) Selected Papers Volume I-Peter Lax, 2005
  • (joint editor) Automorphic Forms and Applications, 2007

Awards and honours[edit]

Peter Sarnak was awarded the Polya Prize of Society of Industrial & Applied Mathematics in 1998, the Ostrowski Prize in 2001, the Levi L. Conant Prize in 2003, the Frank Nelson Cole Prize in Number Theory in 2005 and a Lester R. Ford Award in 2012.[5] He is the recipient of the 2014 Wolf Prize in Mathematics.[6] The University of the Witwatersrand conferred an honorary doctorate on Professor Peter Sarnak on 2 July 2014 for his distinguished contribution to the field of mathematics.

He was also elected as member of the National Academy of Sciences (USA) and Fellow of the Royal Society (FRS) in 2002.[3] He was awarded an honorary doctorate by the Hebrew University of Jerusalem in 2010.[7] He was also awarded an honorary doctorate by the University of Chicago in 2015.[8] He was elected to the 2018 class of fellows of the American Mathematical Society.[9]


  1. ^ a b c d e Sarnak, Peter. "CV February 2012" (PDF).
  2. ^ a b Peter Sarnak at the Mathematics Genealogy Project
  3. ^ a b c d e f g h One or more of the preceding sentences incorporates text from the website where:

    "All text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License." --Royal Society Terms, conditions and policies at the Wayback Machine (archived 2016-11-11)

  4. ^ "Faculty: School of Mathematics". Institute for Advanced Study. 2008. Retrieved 31 May 2009.
  5. ^ Sarnak, Peter (2011). "Integral Apollonian Packings". Amer. Math. Monthly. 118 (4): 291–306. doi:10.4169/amer.math.monthly.118.04.291.
  6. ^ "פרופ' פיטר סרנק". 13 February 2015. Retrieved 22 July 2015.
  7. ^ [1] Archived 19 July 2011 at the Wayback Machine
  8. ^ "University to bestow four honorary degrees at 523rd Convocation | UChicago News". Retrieved 22 July 2015.
  9. ^ 2018 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2017-11-03

 This article incorporates text available under the CC BY 4.0 license.