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Peter Sarnak

## Summary

Peter Clive Sarnak [3] (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities.[1] Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007.[4] He is also 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.[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.

Peter Sarnak

Born
Peter Clive Sarnak

18 December 1953 (age 68)
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)
Sylvester Medal (2019)
Scientific career
FieldsMathematics
InstitutionsCourant Institute
New York University
Stanford University
Princeton University
ThesisPrime geodesic theorems (1980)
Doctoral students
InfluencesCarl Ludwig Siegel
Juergen Moser
Websitewww.math.ias.edu/people/faculty/sarnak

## Education

Sarnak is the grandson of one of Johannesburg's leading rabbis and lived in Israel for three years as a child. He 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

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:

### Publications

• Sarnak, P. (1982). "Spectral Behavior of Quasi Periodic Potentials". Commun. Math. Phys. 84 (3): 377–401. Bibcode:1982CMaPh..84..377S. doi:10.1007/bf01208483. S2CID 123319103.
• 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 (eds.). Mathematics: frontiers and perspectives. American Mathematical Society. pp. 261–269. ISBN 978-0-8218-2697-3.
• (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

Peter Sarnak was awarded the Pólya 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 an invited speaker at the International Congress of Mathematicians (ICM) in 1990 in Kyoto[7] and a plenary speaker at the ICM in 1998 in Berlin.[8]

He was also elected as member of the National Academy of Sciences (USA) and Fellow of the Royal Society (FRS) in 2002.[3] He became a member of the American Philosophical Society in 2008.[9] He was awarded an honorary doctorate by the Hebrew University of Jerusalem in 2010.[10] He was also awarded an honorary doctorate by the University of Chicago in 2015.[11] He was elected to the 2018 class of fellows of the American Mathematical Society.[12] In 2019 he became the 10th non-British citizen to ever be awarded the Sylvester Medal of the Royal Society.[13]

## References

1. Sarnak, Peter. "CV February 2012" (PDF).
2. ^ a b Peter Sarnak at the Mathematics Genealogy Project
3. https://royalsociety.org/people/peter-sarnak-12230/ One or more of the preceding sentences incorporates text from the royalsociety.org 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. ^ a b "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. S2CID 590695.
6. ^ "פרופ' פיטר סרנק". Wolffund.org.il. 13 February 2015. Retrieved 22 July 2015.
7. ^ Sarnak, Peter (1990). "Diophantine problems and linear groups". Proceedings of the International Congress of Mathematicians, 1990, Kyoto. Vol. 1. pp. 459–471.
8. ^ Sarnak, Peter (1998). "${\displaystyle L}$ -functions". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 453–465.
9. ^ "APS Member History". search.amphilsoc.org. Retrieved 28 April 2021.
10. ^ [1] Archived 19 July 2011 at the Wayback Machine
11. ^ "University to bestow four honorary degrees at 523rd Convocation | UChicago News". News.uchicago.edu. Retrieved 22 July 2015.
12. ^ 2018 Class of the Fellows of the AMS, American Mathematical Society, retrieved 3 November 2017
13. ^ Sylvester Medal 2019