Peter Clive Sarnak (born 18 December 1953) is a South African-born mathematician with dual South-African and American nationalities. 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), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

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

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

since 2002, succeeding 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 th ...

. 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 Diri ...

. He also sits on the Board of Adjudicators and 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 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 Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is conside ...

(PhD 1980), under the direction of Paul Cohen. Sarnak's highly cited work (with A. Lubotzky and R. Phillips) applied deep results in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

to Ramanujan graphs, with connections to

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

and

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

Career and research

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

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 conjecture In mathematics, the Ramanujan conjecture, due to , states that Ramanujan's tau function given by the Fourier coefficients of the cusp form of weight :\Delta(z)= \sum_\tau(n)q^n=q\prod_\left (1-q^n \right)^ = q-24q^2+252q^3- 1472q^4 + 4830q^5-\c ...

s 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-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 giv ...

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 research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, th ...

*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–,

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 the Pólya Prize of the Society for Industrial & Applied Mathematics in 1998, the

Ostrowski Prize The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Al ...

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. He is the recipient of the 2014 Wolf Prize in Mathematics. 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 and a plenary speaker at the ICM in 1998 in Berlin. He was also elected as member of the National Academy of Sciences (USA) and

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

(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), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

in 2008. He was awarded an honorary doctorate by the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

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

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

in 2015. He was elected to the 2018 class of

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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, meeting ...

. In 2019 he became the 10th non-British citizen to ever be awarded the Sylvester Medal of the Royal Society.Sylvester Medal 2019
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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