Stephen David Miller -- Curriculum Vitae

Born 1974, New York, USA

Faculty Positions Held

Professor of Mathematics, Rutgers University


Graduate Vice-Chair of Mathematics, Rutgers University


Associate Professor of Mathematics, Rutgers University


Associate Professor of Mathematics, Hebrew University


Assistant Professor of Mathematics, Rutgers University


Assistant Professor of Mathematics, Yale University



Visiting and Postdoctoral Positions

Visiting Professor, Hebrew University


Consultant, Cryptography and Anti-Piracy Group, Microsoft Research


Consultant, Theory Group, Microsoft Research


NSF Postdoctoral Fellowship, Harvard University


NSF Postdoctoral Fellowship, UC San Diego



Ph.D., Princeton University,    Advisor: Peter Sarnak
  Dissertation: Cusp Forms on SL(3,Z)\SL(3,R)/SO(3,R)


M.A., Princeton University


A.B. University of California, Berkeley



Teaching Experience

Hebrew University, 2005-6
Advanced Complex Variables ("Funktziot Merukavot Mitkadem"), included Prime number theorem and Riemann zeta function.

Rutgers University, 2001-
Courses include: Multivariable calculus, number theory, linear algebra, differential equations, cryptography, probability, topics in mathematics for liberal arts.
Graduate Courses in Automorphic Representations, Algebraic Number Theory.
Graduate (VIGRE) rotations in algebraic and analytic number theory.

Yale University, 1997-2001
Courses included: Real Analysis, Senior Seminar on Modular Forms,
Multivariable Calculus (head of course).
Graduate Courses in Number Theory and Automorphic Forms.

Co-founder of the Yale "Research Opportunities in Mathematics and Economics " (R.O.M.E.) program, through which Juniors pursue research under the direction of a faculty member.

Princeton University, Fall 1996
Instructor, Freshman Calculus

Park City/Institute for Advanced Study, July 1994
Teaching Assistant, Summer Institute on Gauge Theory

Awards and Grants

Fellow of the American Mathematical Society, 2018

National Science Foundation grant in Cryptography, CNS-1526333

National Science Foundation grant in Number Theory, DMS-1500562, 2015-2018

PI on Rutgers University GAANN grant (2014-2016)

National Science Foundation grant in Number Theory, DMS-0901594, 2009-2012.

National Science Foundation grant in Number Theory, DMS-0601009, 2006-2009.

National Science Foundation grant in Number Theory, DMS-0301172, 2003-2006.

Alfred P. Sloan Fellow, 2003-2006.

National Science Foundation grant in Number Theory, DMS-0122799, 2001-2003.

National Security Agency Young Investigators Grant for Number Theory, 1999-2000.

Yale University Hellman Fellowship for junior faculty, 1998-2001.

Initial, 3-year funding for the "Research Opportunities in Mathematics and Economics" (R.O.M.E.) program, Yale College Dean's Office, 1998-2001.

National Science Foundation Travel Grant for the 1998 International Congress of Mathematicians.

National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship,1997-2000.  Allowed two semesters without teaching while visiting U.C. San Diego (1997) and Harvard University (2000).

National Science Foundation Graduate Research Fellowship, 1994-1997.

Departmental Citation (Valedictorian), Dorothea Klumpke Roberts Award, and Highest Honors
Department of Mathematics, University of California at Berkeley, May 1993.

Publications (click here for an updated list)

Spectral and Cohomological Applications of the Rankin-Selberg Method ,
International Mathematics Research Notices, 1996, No. 1, pp. 15-26.

Level spacings for regular graphs (with D. Jakobson, I. Rivin, and Z. Rudnick), The IMA Volumes in Mathematics and its Applications, Volume 109, "Emerging Applications of Number Theory," Dennis Hejhal, Fan Chung, Joel Friedman, Martin Gutzwiller, and Andrew Odlyzko (eds.), Springer-Verlag New York, Inc. (1999), pp. 317-327.

Non-vanishing of the Central Derivative of Canonical Hecke L-functions , with Tonghai Yang, Math. Res. Letters, 7 (2000), pp. 263-278.

Landau-Siegel zeroes and black hole entropy , with Gregory Moore, and Large values of L'/L(1,-p), appendix.
Asian Journal of Mathematics, 4, No. 1, (March 2000 Kodaira volume), pp. 183-212. hep-th/9903267.

On the existence and temperedness of cusp forms for SL(3,Z) , Journal für die reine und angewandte Mathematik, 533 (2001), pp. 127.169.

The highest-lowest zero and other applications of positivity , Duke Mathematical Journal, 112, No. 1, pp. 83-116.

Summation Formulas, from Poisson and Voronoi to the Present, with Wilfried Schmid, in Noncommutative Analysis, in Honor of Jacques Carmona, Progress in Mathematics 220 (2003), Birkhäuser, pp. 419-440.

Riemann's zeta function and beyond, with Stephen Gelbart, Bull. Amer. Math. Soc. 41 (2004), 59-112.

Distributions and Analytic Continuation of Dirichlet Series, with Wilfried Schmid., Journal of Functional Analysis, 214 (2004), pp. 155-220.

The Highly Oscillatory Behavior of Automorphic Distributions for SL(2), with Wilfried Schmid., Letters in Mathematical Physics, 69 (2004), 265--286.

Automorphic Distributions, L-functions, and Voronoi Summation for GL(3), with Wilfried Schmid,
Annals of Mathematics 164 (2006), pp. 423-488.

Cancellation in additively twisted sums on GL(n), American Journal of Mathematics, 128 (2006), pp. 699-729.

Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?, with David Jao and Ramarathnam Venkatesan, in Advances in Cryptology - ASIACRYPT 2005: 11th International Conference on the Theory and Application of Cryptology and Information Security, Springer Verlag Lecture Notes in Computer Science, 3788 (2005), pp. 21-40.

The Rankin-Selberg method for automorphic distributions, with Wilfried Schmid, in .Representation Theory and Automorphic Forms., pp. 111-150,  Procedings of an International Symposium at Seoul National University, February 2005, Toshiyuki Kobayashi, Wilfried Schmid, and Jae-Hyun Yang, editors, Progress in Mathematics 255, Birkhauser, Boston, 2008

Spectral Analysis of Pollard Rho Collisions, with Ramarathnam Venkatesan, "Procedings of the 7th Algorithmic Number Theory Symposium" (Berlin), Springer-Verlag Lecture Notes in Computer Science  4076 (2006), pp. 573-581.

MV3: A new word based stream cipher using rapid mixing and revolving buffers, with Nathan Keller, Ilya Mironov, and Ramarathnam Venkatesan, in "Topics in Cryptology -- Procedings of CT-RSA 2007", Springer-Verlag Lecture Notes in Computer Science, 4377 (2007), pp. 1-19.

Non-degeneracy of Pollard rho collisions, with Ramarathnam Venkatesan, International Mathematics Research Notices, 2009, pp.1-10.

Expander graphs based on GRH and an application to elliptic curve cryptography, with David Jao and Ramarathnam Venkatesan, Journal of Number Theory 129 (2009), pp. 1491-1504.


Distinguishing attacks on stream ciphers based on arrays of >pseudo-random words, with Nathan Keller, Information Processing Letters 110 (2010), pp. 129-132.


A method for computing general automorphic forms on general groups, Forum Mathematicum, 22 (2010), 1207-1211.


A general Voronoi summation formula for GL(n,Z), with Wilfried Schmid, in "Geometric analysis: Present and Future", procedings of a conference held in honor of the 60th birthday of Shing-Tung Yau at Harvard, August 27-Sept 1, 2008, Advanced Lectures in Math, volume 18 (2010), 551-596.

Eisenstein series for higher-rank groups and string theory amplitudes, with Michael Green, Jorge Russo, and Pierre Vanhove, Communications in Number Theory and Physics, Volume 4, No. 3, September 2010, pp. 551-596.

Pairings of automorphic distributions, with Wilfried Schmid, Mathematische Annalen 353 (2012), 581-597.

Adelization of Automorphic Distributions and Mirabolic Eisenstein Series, with Wilfried Schmid,in Representation theory and mathematical physics, J. Adams, B. Lian, and S. Sahi, editors, Contemporary Mathematics 557 (2011), 289-334.

The Archimedean theory of the exterior square L-functions over Q, with Wilfried Schmid, Journal of the American Mathematical Society 25 (2012), 465-506.


On the rapid decay of cuspidal automorphic formswith Wilfried Schmid, Advances in Mathematics 231 (2012), 940-964.

Fourier coefficients of automorphic forms, character variety orbits, and small representations , with Siddhartha Sahi, Journal of Number Theory 132 (2012), 3070-3108.

Residual automorphic forms and spherical unitary representations of exceptional groups, Annals of Mathematics, to appear.

A p-adic integral for the reciprocal of L-functions, with Stephen Gelbart, Alexei Pantchichkine, and Freydoon Shahidi, to appear in Contemparary Mathematics, volume in memory of Ilya Piatetski-Shapiro.

Small representations, string instantons, and Fourier modes of Eisenstein series, with Michael Green and Pierre Vanhove; includes appendix "Special unipotent representations” by Dan Ciubotaru and Peter E. Trapa. To appear in the Journal of Number Theory.

Entirety of cuspidal Eisenstein series on loop groups, with Howard Garland and Manish Patnaik. To appear in the American Journal of Mathematics.

SL(2,Z)-invariance and D-instanton contributions to the D6R4 interaction, with Michael B. Green and Pierre Vanhove, Communications in Number Theory and Physics 9 (2015), pp.307-344.

Non-abelian analogs of lattice rounding, with Evgeni Begelfor and Ramarathnam Venkatesan (26 pages). To appear in Groups Complexity Cryptology.

The sphere packing problem in dimension 24, with with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska, Annals of Mathematics (2017).


Technical Notes

Summary of the Langlands-Shahidi method

A simpler way to show zeta(3) is irrational.

The eigenvalue spacings of typical large matrices.

July 9, 2008