Preprints, Letters, Lectures, Notes

Letters

1. 2001 - Letter to E. Bombieri on symplectic symmetry for zeta(2001)

[ BombieriLtr2002.pdf ]

2. 2002 - Letter to Z. Rudnick on multiplicities of eigenvalues for the modular surface(2002)

[ RudnickLtrSept2002.pdf ]

3. 2004 - Letter to C. Morawetz on bounds for eigenfunctions on symmetric spaces(2004)

[ Sarnak_Letter_to_Morawetz.pdf ]

4. 2005 - Letter to J. Davis on reciprocal geodesics on the modular surface(2005)

[ SarnakDavisLtr05.pdf ]

5. 2007 - Letter to J. Lagarias on integral Apollonian packings(2007)

[ AppolonianPackings.pdf ]

6. 2007 - Letter to B. Mazur on Chebyshev Bias for

$\tau(p)$ (2007)

[ MazurLtrMay08.PDF ]

7. 2008 - Letter to A. Reznikov on Restrictions of eigenfunctions(2008)

[ SarnakJun08LtrNEW.pdf ]

8. 2008 - Letter to J. Mozzochi on linking numbers of modular geodesics(2010)

[ MozzochiLtr.pdf ]

9. 2011 - Letter to E. Bachmat on positive definite L-Functions(2011)

[ positive definite Lfunctions april.pdf ]

10. 2011 - Letter to B. Gross and J. Harris on ovals of random plane curves(2011)

[ gross and harris letter updated.pdf ]

11. 2015 - Letter to Aaronson and Pollington on the Solvay-Kitaev Theorem and Golden Gates(2015)

[ Solvay-Kitaev Theorem and Golden Gates.pdf ], [ Appendix : Optimal lifting of integral points ]

12. 2023 - Letter from Sutherland (2023)

[ Sutherland Rubinstein Sarnak Letter.pdf ]

13. 2023 - Letter to Sutherland and Zubrilina(2023)

[ Nina and Drew letter.pdf ]

Lectures

14. 2004 - MAA Hedrick Lecture slides - "Ramanujan Graphs and the Ramanujan Conjectures"

[ Ramanujan_Graphs_and_the_Ramanijan_Conjectures-Hedrick-Lectures-2004.pdf ]

15. 2006 - H. Rademacher Lectures in Mathematics

[ rademacher1.pdf ]

16. 2007 - MAA Garden State Lecture - "Primes and Orbits"

[ Primes_and_Orbits.pdf ]

17. 2007 - PIMS 10th Anniversary Lecture:"Equidistribution and Primes"

[ EquidPrimes.pdf ]

18. 2009 - MAA Lecture - "Integral Apollonian Packings"

[ InternalApollonianPackings09.pdf ]

19. 2010 - Affine Sieve Lecture slides

[ Affine sieve summer 2010.pdf ]

20. 2010 - "Mobius randomness and dynamics" lecture slides

[ Mobius lectures Summer 2010.pdf ]

21. 2010 - Dartmouth Lectures slides - "Mass equidistribution and zeros/nodal domains of modular forms"

[ Dartmouth July 2010.pdf ]

22. 2011 - Clay Lecture slides - "Thin Groups and the Affine Sieve"

[ thin groups and the affine sieve 1.pdf ]

23. 2011 - Three Lectures on the Mobius function randomness and dynamics (Lecture 1)

[ MobiusFunctionsLectures(2).pdf ]

24. 2011 - Mahler Lecture Tour (Australia)

34. 2014 - King's College London & Cape Town Lectures - "Number Theory and the Circle Packings of Apollonius"

[ Johannesburg_July_2014.pdf ]

35. 2015 - ICERM lecture - "Some challenges for computing automorphic forms and their L functions"

[ ICERM Nov 2015.pdf ]

36. 2015 - Oklahoma & Stanford Lectures - "Sums of Squares and Golden Gates"

[ Sum of squares and golden gates ]

37. 2015 - Rome & Lyon/GHYS Conference - "The Affine Sieve Markoff Triples and Strong Approximation"

38. 2015 - Waterloo & ICERM Lectures - "Solovay Kitaev Theorem and Golden Gates"

[ Waterloo lecture.pdf ]

39. 2017 - Zurich Colloquium - "Integer Points on Affine Cubic Surfaces"

[ Zurich Colloquium 2017 ]

40. 2017 - Zurich Lecture - "Topologies of the zero sets of random real projective hypersurfaces and monochromatic random waves"

[ Zurich December Lecture ]

41. 2019 - Ahlfors Lectures, Harvard University

[ Applications of points on subvarieties of tori ], [ Integer points on affine cubic surfaces ]

42. 2019 - Melrose conference MSRI/Berkeley - "Spectra of metric graphs and summation formulae"

[ berkeley Oct 19 (1).pdf ]

43. 2019 - Memorial conference for I. Piatetski-Shapiro - "An underdetermined matrix moment problem and its applications to computing zeros of L-functions"

[ israel lecture underdetermined 2019 (2).pdf ]

44. 2020 February - Localization of waves; Simon's Foundation - "The topologies of nodal sets of monochromatic random waves"

[ localization of waves simons feb 2020.pdf ]

45. 2023 - Chern Lectures Berkeley - "Prescribing the Spectra of Locally Uniform Geometries"

[ Chern Lecture 1.pdf ], [ Chern Lecture 1 Added Notes ], [ Chern Lecture 2.pdf ], [ Chern Lecture 1 - addition 2 - Minkowski ]

46. 2024 - The Four-Fold Way; Symmetries of Families of Zeta Functions Revisited

[ Symmetries Caltech Lecture April 19 2024 ]

47. 2024- ADMA Colloquium Lecture Series "Ramanujan Graphs"

[ Ramanujan graphs lecture June 22.pdf ]

2011 - Mahler Lecture Tour (Australia)

25. Public Lectures

29. Colloquium Lectures

Public Lectures

26. 1) Chaos, Quantum Mechanics and Number Theory

[ Mahler Lecture 1 -Chaos ,Quantum Mechanics and Number Theory.pdf ]

27. 2) Randomness in Number Theory

[ Mahler Lecture 2 -Randomness in number theory.pdf ]

28. 3) Number Theory and the Circle Packings of Apollonius

[ Mahler Lecture 3 -Circle packings of Apollonius and Number Theory.pdf ]

Colloquium Lectures

30. 1) Horocycle Flow at Prime Times

[ Mahler Colloquium Lecture 1- Horocycle Flows at Prime Times.pdf ]

31. 2) Thin Groups and the Affine Sieve

[ Mahler Colloquium Lecture 2 -Thin groups and the affine sieve.pdf ]

32. 3) Zeroes and Nodal Lines of Modular Forms

[ Mahler Colloquium Lecture 3- Zeros and nodal lines of modular forms .pdf ]

33. 4) Mobius Randomness and Dynamics

[ Mahler Colloquium Lecture 4 -Mobius randomness and dynamics.pdf ]

Notes and Comments

48. 1980 - Notes with P.Cohen on the trace formula Chapter 6

[ NoteswithPCohenonthetraceformulaChapter6.pdf ]

49. 1980 - Notes with P.Cohen on the trace formula Chapter 7

[ NoteswithPCohenonthetraceformulaChapter7.pdf ]

50. 2001 - Comments on Langland's Lecture "Endoscopy and Beyond"(2001)

[ SarnakLectureNotes-1.pdf ]

51. 2002 - Notes on A. Booker's Thesis
Annals of Math. . 158 (2003) 1089-1098.

[ BookerLectureNotes.pdf ]

52. 2005 - Notes on the Generalized Ramanujan Conjectures
Clay Math. Proc., 4 (2005) 639-685. .

[ FieldNotesCurrent.pdf ]

53. 2008 - Definition of Families of L-Functions

[ definition of family 2008.pdf ]

Preprints and Reprints Not Easily Accessible

54. 1982/83 - A note on the spectrum of cusp forms for congruence subgroups

[ A note on the spectrum of cusp forms for congruence subgroups ]

55. 1984 - Statistical Properties of Eigenvalues of the Hecke Operators
Proc. Conf. at Oklahoma State University . (1984) 321-331.

[ Statistical Properties.pdf ]

56. 1988 - Torsion points on varieties and homology of abelian covers

[ Torsion points on varieties and homology of abelian covers ]

57. 1990 - Determinants of Laplacians, heights and finiteness
Volume in honor of J. Moser (1990) 601-622.

[ Determinants of Laplacians.pdf ]

58. 1993 - Arithmetic Quantum Chaos
Blythe and Schur Lectures . (May 1993)

[ Arithmetic Quantum Chaos.pdf ]

59. 1999 - Maass cusp forms with integer coefficients

[ Maass cusp forms with integer coefficients ]

60. 2000 - Perspectives on the Analytic Theory of L-Functions (with H. Iwaniec)
GAFA Geometric and Functional Analysis . Special Volume - GAFA2000 (2000) 705-741.

[ Perspectives on the Analytic Theory of L-functions.pdf ]

61. 2004 - Number variance for

$SL(2, \mathbb Z)\backslash \mathbb H$

[ SarnakNumberPaper04.pdf ]

62. 2004 - Nonvanishing of L-functions on

$\Re(s)=1$ (Shalika's 60th Birthday Conference)
Contributions to automorphic forms, geometry and number theory . (2004) 719-732.

[ ShalikaBday2002.pdf ]

63. 2007 - Remembering Paul Cohen
MAA Focus . (December 2007)

[ RememberingPaulCohen.pdf ]

64. 2010 - Generalization of Selberg's

$3/16$ Theorem and Affine Sieve

[ ArchimZ.pdf ]

65. 2011 - Three Lectures on the Mobius function randomness and dynamics (Lecture 1)

[ MobiusFunctionsLectures(2).pdf ]

66. 2011 - Real zeros of holomorphic Hecke cusp forms (with A. Ghosh)

67. 2011 - The Horocycle Flow at Prime Times (with A. Ubis)

[ The Horocycle Flow at Prime Times.pdf ]

68. 2011 - Affine Sieve (with A. Salehi Golsefidy)

[ Salehi -Sarnak S_AffineSieve7 sept 15.pdf ]

69. 2011 - Disjointness of Mobius from Horocyle Flows (with J. Bourgain and T. Ziegler)

[ disjointness b-s-z oct.pdf ]

70. 2011 - Integral Apollonian Packing
Am. Math. Monthly . (April 2011)

[ amer.math_.monthly paper as appeared.pdf ]

71. 2012 - Local statistics of lattice points on the sphere (with J. Bourgain and Z. Rudnick)

[ Local statistics of lattice points on the sphere.pdf ]

72. 2012 - Nodal domains of Maass forms I (with A. Ghosh and A. Reznikov)

[ Nodal domains of Maass forms I.pdf ]

73. 2012 - Notes on Thin Matrix Groups

[ Notes on Thin Matrix Groups.pdf ]

74. 2013 - Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions (with E. Fuchs and C. Meiri)

[ Hyperbolic monodromy groups f-m-s.pdf ]

75. 2013 - The Mobius function and distal flows (with J. Liu)

[ Mobius funcitons and distal flows.pdf ]

76. 2013 - The Quantum Variance of the Modular Surface (with P. Zhao)

[ The Quantum Variance of the Modular Surface.pdf ]

77. 2013 - Topologies of Nodal Sets of Random Band Limited Functions (with I. Wigman)

[ Topologies of Nodal Sets of Random Band Limited Functions.pdf ]

78. 2014 - Families of L-Functions and their Symmetry (with S. W. Shin and N. Templier)

[ Families of L-Functions and their Symmetry.pdf ]

79. 2024 - Strong Approximation and the Diophantine properties of Markoff triples (joint with J.Bourgain and A.Gamburd)

[ Markoff Diophantine PDF ]

Peter Sarnak

80. 2013 - Test Title

81. Number Theory and the Circle Packings of Apollonius

[ Mahler Lecture 3 -Circle packings of Apollonius and Number Theory.pdf ]