Peter Clive Sarnak (born 18 December 1953) is a South African and American mathematician. Sarnak has been a member of the permanent faculty of the School of Mathematics at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

since 2007. He is also Eugene Higgins Professor of Mathematics at

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

since 2002, succeeding Sir Andrew Wiles, and is an editor of the

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...

. He is known for his work in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

. 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.

Education

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

University of the Witwatersrand The University of the Witwatersrand, Johannesburg (), commonly known as Wits University or Wits, is a multi-campus Public university, public research university situated in the northern areas of central Johannesburg, South Africa. The universit ...

( BSc 1975, BSc(Hons) 1976) and

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

(PhD 1980), under the direction of

Paul Cohen Paul Joseph Cohen (April 2, 1934 – March 23, 2007) was an American mathematician, best known for his proofs that the continuum hypothesis and the axiom of choice are independent from Zermelo–Fraenkel set theory, for which he was awarded a F ...

. Sarnak's work (with A. Lubotzky and R. Phillips) applied results in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Ramanujan graphs In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. As Murty's survey paper notes ...

, with connections to

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

Career and research

Sarnak has made contributions to analysis and number theory. He is recognised 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

Atle Selberg Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded ...

. 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. 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-function In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may gi ...

s. His work on subconvexity for Rankin–Selberg L-functions led to the resolution of Hilbert's eleventh problem. During his career he has held numerous appointments including: *Assistant Professor, 1980–83; Associate Professor, 1983; Professor, 2001–2005, Courant Institute,

New York University New York University (NYU) is a private university, private research university in New York City, New York, United States. Chartered in 1831 by the New York State Legislature, NYU was founded in 1832 by Albert Gallatin as a Nondenominational ...

*Associate Professor, 1984–87; Professor, 1987–91,

*Professor, 1991–; H. Fine Professor, 1995–96; Chairman, Dept of Mathematics, 1996–99; Eugene Higgins Professor, 2002–,

*Member, 1999–2002 and 2005–2007; Faculty, 2007–present,

Publications

* *Some Applications of Modular Forms, 1990 *(joint editor) Extremal Riemann Surfaces, 1997 * (joint author) Random Matrices, Frobenius Eigenvalues and Monodromy, 1998 * * (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: * 1988 Pólya Prize of the Society for Industrial & Applied Mathematics * 2001 Ostrowski Prize * 2003 Levi L. Conant Prize * 2005 Frank Nelson Cole Prize in Number Theory * 2012 Lester R. Ford Award * 2014

Wolf Prize in Mathematics The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. ...

* 2019

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian chair of geometry, Savilian Prof ...

of the Royal Society * 2024 Shaw Prize. 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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(ICM) in 1990 in Kyoto and a plenary speaker at the ICM in 1998 in Berlin. Sarnak has been a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

since 1991. He was also elected as member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

(USA) and

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

(FRS) in 2002.https://royalsociety.org/people/peter-sarnak-12230/ One or more of the preceding sentences incorporates text from the royalsociety.org website where: He became a member of the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

in 2008. He was awarded an honorary doctorate by the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; ) is an Israeli public university, public research university based in Jerusalem. Co-founded by Albert Einstein and Chaim Weizmann in July 1918, the public university officially opened on 1 April 1925. ...

in 2010. He was also awarded an honorary doctorate by the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

in 2015 and by

Stockholm University Stockholm University (SU) () is a public university, public research university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, social ...

in 2023. He was elected to the 2018 class of

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2019 he became the 10th non-British citizen to ever be awarded the

of the Royal Society.Sylvester Medal 2019
/ref>

References

{{DEFAULTSORT:Sarnak, Peter Clive 1953 births Living people People from Johannesburg University of the Witwatersrand alumni South African mathematicians South African emigrants to the United States 20th-century American mathematicians 21st-century American mathematicians Institute for Advanced Study faculty Courant Institute of Mathematical Sciences faculty Princeton University faculty Stanford University alumni Stanford University Department of Mathematics faculty Fellows of the American Mathematical Society Fellows of the Royal Society Members of Academia Europaea Members of the United States National Academy of Sciences Wolf Prize in Mathematics laureates Mathematical physicists Number theorists Members of the American Philosophical Society