Sarnak is a permanent faculty member in Mathematics at the Institute for Advanced Study (IAS). The IAS is located on 1 Einstein Drive in Princeton, New Jersey, an address inspired by Albert Einstein’s famous tenure there in the early and mid-20th century. Some of the greatest mathematical minds in modern times have called the IAS home, like John Von Neumann of early computing fame. Sarnak is thus in good company, past and present. Sarnak is also the Eugene Higgins Professor of Mathematics at Princeton University.

Sarnak received two bachelor’s degrees in mathematics from the University of the Witwatersrand in South Africa in 1975 and 1976 and his Ph.D. in Mathematics from Stanford University in 1980. He works on problems in analytic number theory, and his contributions have had important applications to other scientific areas like physics and computer science. Sarnak also invented a field known as “arithmetical quantum chaos,” and performed work leading to a solution to a famous unsolved problem in mathematics known as Hilbert’s Eleventh Problem after mathematician David Hilbert, a 19th century mathematician who issues a challenge to mathematicians at the turn of the 19th century as a list of twelve unsolved problems.

Sarnak has won numerous awards during his outstanding career in number theory, including the George Polya Prize in 1998, and most recently a Sylvester Medal in 2019.

**Featured in Top Influential Mathematicians Today**

According to Wikipedia, Peter Clive Sarnak 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 since 2007. 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. He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.

- Random matrices, Frobenius eigenvalues, and monodromy
- Zeros of principal $L$-functions and random matrix theory
- Extremals of determinants of Laplacians
- Zeroes of zeta functions and symmetry
- FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2
- Low lying zeros of families of L-functions
- The behaviour of eigenstates of arithmetic hyperbolic manifolds
- Some Applications of Modular Forms
- Elementary number theory, group theory, and Ramanujan graphs
- Ramanujan graphs
- Density of integer points on affine homogeneous varieties
- Perspectives on the Analytic Theory of L-Functions
- Chebyshev's Bias
- Explicit expanders and the Ramanujan conjectures
- Quantum ergodicity of Eigenfunctions on PSL2(Z)/H2
- On the period matrix of a Riemann surface of large genus (with an Appendix by J.H. Conway and N.J.A. Sloane)
- Affine linear sieve, expanders, and sum-product
- $L^\infty$ norms of eigenfunctions of arithmetic surfaces
- Compact isospectral sets of surfaces
- On Selberg's eigenvalue conjecture
- Hecke operators and distributing points on the sphere I
- Determinants of Laplacians
- Bounds for multiplicities of automorphic representations
- The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros
- Estimates for Rankin–Selberg L-Functions and Quantum Unique Ergodicity
- Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series
- On cusp forms for co-finite subgroups ofPSL(2,ℝ)
- Heegner points, cycles and Maass forms
- The Pair Correlation Function of Fractional Parts of Polynomials
- Class numbers of indefinite binary quadratic forms II
- Sums of Kloosterman sums
- Spectra of hyperbolic surfaces
- The arithmetic and geometry of some hyperbolic three manifolds
- Three Lectures on the Mobius Function Randomness and Dynamics
- Ramanujan duals II
- The distribution of spacings between the fractional parts of n2α
- Minima of Epstein’s Zeta function and heights of flat tori
- Geodesics in homology classes
- Integrals of products of eigenfunctions
- Hecke operators and distributing points on S2. II
- Statistical Properties of Eigenvalues of the Hecke Operators
- Notes on the Generalized Ramanujan Conjectures
- Generalization of Selberg's 3/16 Theorem and Affine Sieve
- Classical and Multilinear Harmonic Analysis
- Mobius Randomness and Dynamics
- Disjointness of Moebius from Horocycle Flows
- What is . . . An expander
- Recent progress on the quantum unique ergodicity conjecture
- Spectra of elements in the group ring of SU(2)
- Topologies of nodal sets of random band limited functions.
- The Möbius function and distal flows
- Notes on Thin Matrix Groups
- Dirichlet L-functions at the central point
- Nodal Domains of Maass Forms I
- Moduli space, heights and isospectral sets of plane domains*
- Diophantine Problems and Linear Groups
- Number variance for arithmetic hyperbolic surfaces
- Prime Geodesic Theorems
- Ramanujan duals and automorphic spectrum
- Quantum variance for Hecke eigenforms
- Integral Apollonian Packings
- Sector Estimates for Hyperbolic Isometries
- Perturbation theory for the Laplacian on automorphic functions
- Sieving and expanders
- Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve
- The laplacian for domains in hyperbolic space and limit sets of Kleinian groups
- The weyl theorem and the deformation of discrete groups
- Betti numbers of congruence groups
- Additive number theory and maass forms
- Families of L -Functions and Their Symmetry
- Determinants of Laplacians; Heights and Finiteness
- Prime and almost prime integral points on principal homogeneous spaces
- Spectral behavior of quasi periodic potentials
- The horocycle flow at prime times
- Real zeros of holomorphic Hecke cusp forms
- A new curvature invariant and entropy of geodesic flows
- Mass equidistribution for Hecke eigenforms
- Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
- The spectrum of fermat curves
- Fourth moments of grossencharakteren zeta functions
- Elementary Number Theory, Group Theory, and Ramanujan Graphs: Graph Theory
- The affine sieve
- On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums
- The n-level correlations of zeros of the zeta function
- Super-Golden-Gates for PU(2)
- Equidistribution of holonomy about closed geodesics
- ON SELBERG'S EIGENVALUE CONJECTURE
- Integral points on quadrics in three variables whose coordinates have few prime factors
- Some hypersurfaces in P4 and the Hasse-principle
- Local Statistics of Lattice Points on the Sphere
- A new method for lower bounds of L-functions
- Markoff Triples and Strong Approximation
- Cusp forms for character varieties
- Zeros ofL-functions attached to Maass forms
- Topology and nesting of the zero set components of monochromatic random waves
- Strong spectral gaps for compact quotients of products of PSL(2,R)
- A proof of Siegel's weight formula
- Arithmetic and Equidistribution of Measures on the Sphere
- Quantum unique ergodicity for SL 2(O)\ H32(O)∖ and estimates for L-functions
- Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
- Maass cusp forms.
- The determinant of the Eisenstein matrix and Hilbert class fields
- Automorphic forms and applications
- Poincaré series forSO(n, 1)
- Spatial statistics for lattice points on the sphere I: Individual results
- Automorphic spectrum and Fermi’s Golden Rule
- Spectra of singular measures as multipliers on Lp
- A celebration of John F. Nash, Jr.
- Quantum Chaos, Symmetry, and Zeta functions, I: Quantum Chaos
- Quantum unique ergodicity for SL $ _2({\cal O})\!\setminus\! {\bf H}^3 $ and estimates for L-functions
- On the topology of the zero sets of monochromatic random waves
- Extremal Riemann Surfaces
- Compact isospectral sets of plane domains.
- The Selberg Trace Formula and Related Topics
- Distjointness of Mobius from horocycle flows
- Entropy estimates for geodesic flows
- Nonvanishing of L-functions on (s) = 1
- Markoff Surfaces and Strong Approximation: 1
- Hecke Operators and Distributing Points on S 2 . I 1
- Advances in random matrix theory, zeta functions, and sphere packing.
- Poincaré series forSO(n, 1)
- Equidistribution and primes
- Explicit solutions of $\square u = 0$ on the Friedmann-Robertson-Walker space-times
- The variance of arithmetic measures associated to closed geodesics on the modular surface
- On the spectrum of the Hecke groups
- Integral points on Markoff type cubic surfaces
- Linking Numbers of Modular Knots
- The Quantum Variance of the Modular Surface
- Non-vanishing of periods of automorphic functions
- Irregular distribution of {nβ}, n=1,2,3,…, quadrature of singular integrands, and curious basic hypergeometric series
- Quantum unique ergodicity for SL2.O/nH3 and estimates forL-functions
- Recent Progress on QUE
- Quantum Chaos, Symmetry, and Zeta functions, II: Zeta Functions
- A Panorama in Number Theory or The View from Baker's Garden: Maass Cusp Forms with Integer Coefficients
- Some remarks on Landau-Siegel zeros
- Selected Works of Ilya Piatetski-Shapiro
- Stable polynomials and crystalline measures
- Spectra and eigenfunctions of laplacians
- Kloosterman, quadratic forms and modular forms
- Kloosterman, quadratic forms and modular forms
- Special Values of Selberg's Zeta-function
- Spectral gap for products of $\PSL(2,\bbR)$
- Gap Sets for the Spectra of Cubic Graphs
- Comments on Robert Langland ’ s Lecture : “ Endoscopy and Beyond ”
- The Mobius disjointness conjecture for distal flows
- The Schur lectures (1992)
- Restriction Theorems and Appendix 1 & 2
- Randomness in Number Theory
- ON THE FREY-MAZUR CONJECTURE OVER LOW GENUS CURVES
- Monodromy of families of curves
- Determinants of Laplacians on Surfaces
- Problems of the Millennium : The Riemann Hypothesis ( 2004 ) by Peter Sarnak
- On the number of points on certain curves and an uncertainty principle
- Remembering Paul Cohen (1934-2007)
- Some commentary on Atle Selberg’s mathematics
- Extremal Riemann surfaces : from the proceedings of the AMS special session with related papers January 4-5, 1995, San Francisco, California
- Some applications of modular forms: Introduction
- Remembering Jean Bourgain (1954–2018)
- Class Numbers of Indefinite Binary Quadratic Forms *
- Special issue on the occasion of Fritz Grunewald’s 60th birthday
- Domains in Hyperbolic Space and Limit Sets of Kleinian Groups
- Derivation of the reflection integral equation of the zeta function by the quaternionic analysis
- Arithmeticity ( or not ) of Monodromy Peter Sarnak April 23 , 2013
- Appendix 4-Regular Graphs with Large Girth
- 153 Abelian Varieties , Theta Functions and the Fourier Transform
- Some applications of modular forms: Modular Forms
- Maass cusp forms ( L function / Teichmfiller space )
- Papers in analysis, number theory and automorphic L-functions
- 978-0-521-51918-2-Random Walk : A Modern Introduction
- Kloosterman Centennial Celebration Kloosterman , quadratic forms and modular forms
- ISOSPECTRAL MANIFOLDS WITH DIFFERENT LOCAL GEOMETRIES 3
- Ratner's Work on Unipotent Flows and Its Impact
- Book Review: Prime numbers and the Riemann hypothesis
- Book Review: The Riemann zeta function
- Cambridge Studies in Advanced Mathematics 121 Representation Theory of the Symmetric Groups Cambridge Studies in Advanced Mathematics Representation Theory of the Symmetric Groups Central Projection Formulas 22 1.4 Permutation Representations 27 1.4.1 Wielandt's Lemma 27 1.4.2 Symmetric Actions and
- The Graphs Xp, q
- Reduction steps in proving the main theorems
- GUE discrepancies in various families
- SPECTRAL THEORY OF AUTOMORPHIC FORMS LECTURES BY PETER SARNAK, NOTES BY TONY FENG
- Band Engineering for Quantum Simulation in Circuit QED
- Maryam Mirzakhani: 1977–2017
- Additive Combinatorics
- A Survey of Peter D. Lax’s Contributions to Mathematics
- Monodromy of some other families
- Schedule of talks
- Communications in Mathematical Physics: Preface
- On the occasion of Robert Osserman ’ s retirement
- Factorization estimates for abelian varieties . Homogénéité de certaines distributions sur les groupes p-adiques . Concentration of measure and isoperimetric inequalities in product spaces . Quantum ergodicity of eigenfunctions on PSL[2](Z)\H[2]
- Lectures on Lyapunov Exponents
- Some applications of modular forms: Preface
- Coffee Coffee Coffee Coffee Coffee 1100-1200
- On the work of Akshay Venkatesh
- The Grand Riemann Hypothesis
- Title : Ergodic Properties of Square-Free Numbers
- Papers in representation theory
- The Selberg trace formula and related topics : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 22-28, 1984, with support from the National Science Foundation
- In Memory of Marina Ratner 1938–2017
- Distribution of low-lying Frobenius eigenvalues in various families
- Reformulation of the main results
- Elementary Number Theory, Group Theory, and Ramanujan Graphs: Bibliography
- Bounded cutoff window for the non-backtracking random walk on Ramanujan Graphs
- RECENT PROGRESS ON THE QUANTUM UNIQUE ERGODICITY
- Analytic Number Theory: Spectral Theory and L-functions
- Compact lsospectral Sets of Surfaces *
- Invariant Means on L∞(Sn )
- An appreciation of Jean Bourgain’s work
- Bounds for Fourier coefficients of 1/2–integral weight
- Statements of the main results
- Large N limits and Fredholm determinants

This paper list is powered by the following services:

Peter Sarnak is affiliated with the following schools:

This website uses cookies to enhance the user experience. Privacy Policy

Want to be an Academic Influence Insider?

Sign up to get the latest news, information, and rankings in our upcoming newsletter.