Andrew V. Sutherland          Genus 1:     Genus 2:        Genus 3:         
drew@math.mit.edu

I am a Principal Research Scientist here in the math department at MIT, focusing on computational number theory.
Here is a fairly recent photograph, and a link to my Google scholar page.

Recent
    Class polynomials for nonholomorphic modular functions preprint, with Jan Bruinier and Ken Ono, has been posted, along with the partition class polynomials described therein (January 2013).
    Home page for 18.783, an introductory course on elliptic curves, is now live (Spring 2013).
    Torsion subgroups of elliptic curves over number fields, extended notes from a lecture given at the Harvard Seminar on Mazur's torsion theorem have been posted (December 2012).

Upcoming Talks/Workshops
    Algebra and Number Theory Seminar, Emory University, May 15, 2013
    Collaborative Explorations and Developments in Arithmetic Research, University of Illinois at Chicago, May 14-18, 2013
    Number Theory, Geometry, and Cryptography, University of Warwick, July 1-5, 2013
    Explicit Methods in Number Theory, Oberwolfach, July 14-20, 2013
    SIAM Conference on Applied Algebraic Geometry, Colorado State University, August 1-4, 2013
    SAC 2013 -- Selected Areas in Cryptography, Simon Fraser University, August 14-16, 2013

Publications (click title for arxiv version, journal name for journal version)
    Identifying supersingular elliptic curves, LMS Journal of Computation and Mathematics 15 (2012), 317-325.
    Accelerating the CM method, LMS Journal of Computation and Mathematics 15 (2012), 172-204.
    Isogeny volcanoes, Algorithmic Number Theory 10th International Symposium (ANTS X), 2012.
    On the evaluation of modular polynomials, Algorithmic Number Theory 10th International Symposium (ANTS X), 2012. (Selfridge Prize)
    Deterministic elliptic curve primality proving for a special sequence of numbers, with Alexander Abatzoglou, Alice Silverberg, and Angela Wong, Algorithmic Number Theory 10th International Symposium (ANTS X), 2012.
    Sato-Tate distributions and Galois endomorphism modules in genus 2, with Francesc Fité, Kiran Kedlaya, and Victor Rotger, Compositio Mathematica 148 (2012), 1390-1442.
    The probability that the number of points on the Jacobian of a genus 2 curve is prime, with Wouter Castryck, Amanda Folsom, and Hendrik Hubrechts, Proceedings of the London Mathematical Society 104 (2012), 1235-1270.
    A local-global principle for rational isogenies of prime degree, Journal de Théorie des Nombres de Bordeaux 24 (2012), 475-485.
    A low-memory algorithm for finding short product representations in finite groups, with Gaetan Bisson, Designs, Codes, and Cryptography 63 (2012), 1-13.
    Constructing elliptic curves over finite fields with prescribed torsion, Mathematics of Computation 81 (2012), 1131-1147.
    Modular polynomials via isogeny volcanoes, with Reinier Bröker and Kristin Lauter, Mathematics of Computation 81 (2012), 1201-1231.
    Computing Hilbert class polynomials with the Chinese Remainder Theorem, Mathematics of Computation 80 (2011), 501-538.
    Structure computation and discrete logarithms in finite abelian p-groups, Mathematics of Computation 80 (2011), 477-500.
    Computing the endomorphism ring of an ordinary elliptic curve over a finite field, with Gaetan Bisson, Journal of Number Theory, 113 (2011), 815-831.
    Class invariants by the CRT method, with Andreas Enge, Algorithmic Number Theory 9th International Symposium (ANTS IX), LNCS 6197, Springer, 2010, pp. 142-156.
    An explicit height bound for the classical modular polynomial, with Reinier Bröker, Ramanujan Journal 22 (2010), 293-313.
    On a theorem of Mestre and Schoof, with John E. Cremona, Journal de Théorie des Nombres de Bordeaux 22 (2010), 353-358.
    Hyperelliptic curves, L-polynomials, and random matrices, with Kiran S. Kedlaya, Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-11, 2007), Contemporary Mathematics 487, AMS, 2009, pp. 119-162.
    A generic approach to searching for Jacobians, Mathematics of Computation 78 (2009), 485-507.
    Computing L-series of hyperelliptic curves, with Kiran S. Kedlaya, Algorithmic Number Theory 8th International Symposium (ANTS VIII), LNCS 5011, Springer, 2008, pp. 312-326.
    Order computations in generic groups, PhD thesis, Massachusetts Institute of Technology, 2007 (Errata). (George M. Sprowls Award for Outstanding Thesis in Computer Science)

Preprints
    Class polynomials for nonholomorphic modular functions, with Jan Bruinier and Ken Ono, 2013.
    Sato-Tate groups of some weight 3 motives, with Francesc Fité and Kiran S. Kedlaya, 2012.
    Sato-Tate distributions of twists of y2=x5-x and y2=x6+1, with Francesc Fité, 2012.
    On the distribution of Atkin and Elkies primes, with Igor E. Shparlinski, 2011.

Lecture Notes
    Torsion subgroups of elliptic curves over number fields, extended notes from a lecture given at the Harvard Seminar on Mazur's torsion theorem, December 2012.
    Elliptic curves (18.783), lecture notes for an introductory MIT course on elliptic curves, Spring 2012.

Talks
    Computing the image of Galois representations attached to elliptic curves, AMS Sectional Meeting, April 2013
    The generalized Sato-Tate conjecture, Brandeis February, 2013
    Computing the image of Galois representations attached to elliptic curves, Joint Mathematics Meetings, January 2013
    Sato-Tate distributions in genus 2, Princeton/IAS and Quebec/Vermont number theory seminars, November 2012
    On the evaluation of modular polynomials, ECC 2012 October 2012
    On the computation and evaluation of modular polynomials, Brown University, September 2012
    On the evaluation of modular polynomials, ANTS X, July 2012
    Isogeny volcanoes: a computational perspective, ANTS X, July 2012
    Computing the image of Galois, CNTA XII, June 2012
    Computing the modular equation, Barcelona-Boston-Tokyo Number Theory Seminar in Memory of Fumiyuki Momose, May 2012
    Identifying supersingular elliptic curves, Joint Mathematics Meetings, January 2012
    Sato-Tate distributions in genus 2, Boston University, November 2011
    Telescopes for mathematicians, Computational Research in Boston and Beyond (MIT), September 2011
    Hyperelliptic curves, L-polynomials, and random matrices, MSRI and Emory, February 2011
    Genus 1 point counting in quadratic space and essentially quartic time, Joint Mathematics Meetings, January 2011
    Genus 1 point counting in quadratic space and essentially quartic time, Columbia-CUNY-NYU, September 2010
    Class invariants by the CRT method, ANTS IX, July 2010
    A local-global principle for rational isogenies of prime degree, CNTA XI, July 2010
    L-polynomial distributions of genus 2 curves, ETH Zurich, May 2010
    Genus 1 point counting in quadratic space and essentially quartic time, CRM Montreal, April 2010
    Decomposing class polynomials with the CRT method, CRM Montreal, April 2010
    Modular polynomials via isogeny volcanoes, CCR Princeton, February 2010
    Computing the image of Galois representations attached to an elliptic curve, Clay Mathematics Institute, December 2009
    Computing modular polynomials with the Chinese Remainder Theorem, ECC 2009 August 2009
    Powered by volcanoes: Three new algorithms, Fields Institute, May 2009
    Computing the endomorphism ring of an ordinary elliptic curve, CCR La Jolla, April 2009
    Sato-Tate in genus 2, MIT, March 2009
    Computing class polynomials with the Chinese Remainder Theorem, Microsoft Research, November 2008
    Computing Hilbert class polynomials with the CRT method, ECC 2008, September 2008
    Computing L-series of hyperelliptic curves, ANTS VIII, May 2008
    Subexponential performance from generic group algorithms, MIT, April 2008
    Thesis defense, MIT, spring 2007
    Beating the birthday paradox, MIT, spring 2007

Data
    Partition class polynomials, as described in Class polynomials for nonholomorphic modular functions

    Elliptic curve point-counting records

    Table of factored norms of singular moduli

    Record CM constructions of elliptic curves

    Modular polynomials for the Weber ƒ function
    Modular polynomials for various modular functions used by classpoly

    Pairing-friendly Edwards curves of near-prime order with embedding degree 6
    Pairing-friendly curves of prime order with embedding degree 6
    Pairing-friendly curves of prime order with embedding degree 10

    Defining equations for X1(N) in raw form for N ≤ 101
    Alternative defining equations for X1(N) for N ≤ 190
    Optimized equations for X1(N) for N ≤ 50      (Updated October 2012 to include optimized equation for X_1(24) derived from the recent result of Jeon, Kim, and Lee)

    Sato-Tate distributions in genus 1.
    Sato-Tate distributions in genus 2.
    Standard L-polynomial coefficient distributions in genus 1, 2, and 3

    101 useful trace zero varieties
    Gallery of large Jacobians

Software
    classpoly_v1.0.1.tar, as described in Computing Hilbert class polynomials with the CRT method and Class invariants by the CRT method. Requires the ff_poly_big library.
    smoothrelation_v1.2.tar, as described in Computing the endomorphism ring of an ordinary elliptic curve over a finite field.
    smalljac_v4.0.23.tar, as described in Computing L-series of hyperelliptic curves. Requires the ff_poly library.
    ff_poly_v1.2.0.tar, fast finite field arithmetic over prime fields of size up to 261.
    ff_poly_big_v1.2.0.tar, fast finite field arithmetic over prime fields of size up to 261, uses David Harvey's zn_poly library to more efficiently handle polynomials of large degree.
    galrep_v0.tar, as described in Computing the image of Galois representations attached to an elliptic curve, preliminary version.
    galrep_ecdata_big.dat, auxiliary elliptic curve data for more extensive galrep computations (approx 104 MB)
    galrep_gl2data_big.dat, auxiliary GL(2,Z/ellZ) conjugacy class data for more extensive galrep computations (approx 4 MB)