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, focused on computational number theory and arithmetic geometry.
Here is a larger photograph and links to my arXiv, MathSciNet, and Google Scholar pages. My office is in room 2-341 in the Simons Building (Building 2).

Latest News
    Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, Simons Foundation, July 13, 2017.

Recent/Upcoming Events
    Applied Mathematics, Modeling, and Computational Science (AMMCS), Waterloo (Canada), August 20-25, 2017.
    Arithmetic of Hyperelliptic Curves, ICTP Trieste (Italy), September 4-8, 2017.
    SQuaRE on Galois representations, AIM June 4-8, 2018.

Current Teaching
    Elliptic Curves (18.783), Spring 2017.

Current Editorial/Board Positions
    Mathematics of Computation, American Mathematical Society, 2014-present.
    Research in Number Theory, Springer Open Access, 2014-present.
    Number Theory Foundation, 2016-present.
    L-functions and Modular Forms Database, 2016-present.

Publications (click title for arxiv version, journal/conference name for published version)
    Modular curves of prime-power level with infinitely many rational points, with David Zywina, Algebra and Number Theory 11 (2017), 1199-1229. (related magma scripts)
    Torsion subgroups of elliptic curves over quintic and sextic number fields, with Maarten Derickx, Proceedings of the AMS, published electronically on April 12, 2017, DOI 10.1090/proc/13605, to appear in print. (related GitHub repository)
    Torsion subgroups of rational elliptic curves over the compositum of all cubic fields, with Harris B. Daniels, Alvaro Lozano-Robledo, and Filip Najman, Mathematics of Computation, to appear. (related magma scripts)
    Finding elliptic curves with a subgroup of prescribed size, with Igor E. Shparlinski, International Journal of Number Theory 13 (2017), 133-152.
    Computing L-series of geometrically hyperelliptic curves of genus three, with David Harvey and Maike Massierer, Algorithmic Number Theory 12th International Symposium (ANTS XII), LMS Journal of Computation and Mathematics 19 (2016), 220-234.
    A database of genus 2 curves over the rational numbers, with Andrew R. Booker, Jeroen Sijsling, John Voight, and Dan Yasaki, Algorithmic Number Theory 12th International Symposium (ANTS XII), LMS Journal of Computation and Mathematics 19 (2016), 235-254.
    A census of zeta functions of quartic K3 surfaces over F_2, with Kiran S. Kedlaya, Algorithmic Number Theory 12th International Symposium (ANTS XII), LMS Journal of Computation and Mathematics 19 (2016), 1-11.
    Computing images of Galois representations attached to elliptic curves, Forum of Mathematics, Sigma 4 (2016), e4 (79 pages) (related magma scripts).
    Sato-Tate groups of y2=x8+c and y2=x7-cx, with Francesc Fité, in Frobenius distributions: Lang-Trotter and Sato-Tate conjectures, Contemporary Mathematics 663 (2016), AMS, 103-126.
    Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II, with David Harvey, in Frobenius distributions: Lang-Trotter and Sato-Tate conjectures, Contemporary Mathematics 663 (2016), AMS, 127-148.
    Sato-Tate groups of some weight 3 motives, with Francesc Fité and Kiran S. Kedlaya, in Frobenius distributions: Lang-Trotter and Sato-Tate conjectures, Contemporary Mathematics 663 (2016), AMS, 57-102.
    Class polynomials for nonholomorphic modular functions, with Jan Bruinier and Ken Ono, Journal of Number Theory 161 (2016), 204-229.
    A framework for deterministic primality proving using elliptic curves with complex multiplication, with Alexander Abatzoglou, Alice Silverberg, and Angela Wong, Mathematics of Computation 85 (2016), 1461-1483.
    On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average, with Igor Shparlinski, LMS Journal of Computation and Mathematics, 18 (2015) 308-322.
    New equidistribution estimates of Zhang type, with W. Castryck, E. Fouvry, G. Harcos, E. Kowalski, P. Michel, P. Nelson, E. Paldi, J. Pintz, T. Tao, and X.-F. Xie, Algebra and Number Theory 8 (2014), 2067-2199.
    Variants of the Selberg sieve, and bounded intervals containing many primes, D.H.J. Polymath, Research in the Mathematical Sciences 1 (2014).
    Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, with David Harvey, Algorithmic Number Theory 11th International Symposium (ANTS XI), LMS Journal of Computation and Mathematics 17 (2014), 257-273.
    Sato-Tate distributions of twists of y2=x5-x and y2=x6+1, with Francesc Fité, Algebra and Number Theory 8 (2014), 543-585.
    On the distribution of Atkin and Elkies primes, with Igor E. Shparlinski, Foundations of Computational Mathematics 14 (2014), 285-297.
    Isogeny volcanoes, Algorithmic Number Theory 10th International Symposium (ANTS X), MSP Open Book Series 1 (2013), 507-530.
    On the evaluation of modular polynomials, Algorithmic Number Theory 10th International Symposium (ANTS X), MSP Open Book Series 1 (2013), 531-555. (Selfridge Prize) (errata).
    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), MSP Open Book Series 1 (2013), 1-20.
    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.
    Sato-Tate distributions and Galois endomorphism modules in genus 2, with Francesc Fité, Kiran S. Kedlaya, and Victor Rotger, Compositio Mathematica 148 (2012), 1390-1442 (errata).
    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. (related magma script)
    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, 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, in Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-11, 2007), Contemporary Mathematics 487, AMS, 2009, 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, 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
    Fast Jacobian arithmetic for hyperelliptic curves of genus 3, 2016. (related magma script)

Lecture Notes
    Number Theory (18.785), Fall 2016.
    Primes is in P (18.095 lecture), January 2017.
    Sato-Tate Distributions, notes from lectures given at the Arizona Winter School, March 2016.
    Perfect Forward Secrecy (18.095 lecture), January 2016.
    Number Theory (18.785), Fall 2015 (OCW link ).
    
Elliptic curves (18.783), Spring 2015 (OCW link).
    
Arithmetic geometry(18.782), lecture notes for an introductory course on arithmetic geometry, Fall 2013 (OCW link).
    
Torsion subgroups of elliptic curves over number fields, notes from a lecture given at the Harvard Seminar on Mazur's torsion theorem, December 2012.

Talks (selected)
    A database of genus 3 curves over Q, Rational Points 2017, Franken-Akademie Schloss Schney (Germany), July 2017
    Computing L-series of genus 3 curves, Workshop on Arithmetic Geometry and Computer Algebra, University of Oldenburg (Germany), June 2017
    Strong arithmetic equivalence, AGCT-16, CIRM Luminy (France), June 2017
    Modular curves of prime-power level with infinitely many rational points, Arithmetic Aspects of Explicit Moduli Problems, BIRS Banff (Canada), May 2017
    Sato-Tate in dimension 3, Harvard Number Theory Seminar, Harvard, December 2016
    Torsion subgroups of rational elliptic curves over the compositum of all cubic fields, Explicit Methods in Number Theory: Conference in Honour of John Cremona's 60th Birthday, Warwick University (UK), April 2016
    Modular curves of prime-power level with infinitely many rational points, AMS Southeast Sectional Meeting, University of Georgia, Athens, March 2016
    Sato-Tate distributions, Columbia-CUNY-NYU Number Theory Seminar, CUNY Graduate Center, February 2016
    Sato-Tate distributions of abelian varieties, Abelian Varieties Multi-Site Seminar Series, University of Washington, January 2016
    Computing the image of Galois representations attached to elliptic curves, Computational representation theory in number theory, Oregon State University, July 2015
    Sieve theory and small gaps between primes: Introduction (talk 1), A variational problem (talk 4), Narrow admissible tuples (talk 5), Oberwolfach (Germany), July 2015
    Computing the image of Galois representations attached to elliptic curves, AGCT-15, CIRM Luminy (France), May 2015
    Computing the image of Galois, Dartmouth Mathematics Colloquium, October 2014
    Sato-Tate groups of abelian varieties of dimension g ≤ 3, Workshop on statistics and number theory, CRM Montreal (Canada), September 2014
    Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, ANTS XI (Korea), August 2014
    Telescopes for mathematicians, Conference on the Impact of Computation in Number Theory, NCTS (Taiwan), July 2014
    The refined Sato-Tate conjecture, CNTA XIII (Canada), June 2014
    The Sato-Tate conjecture for abelian varieties, Heilbronn Seminar, Bristol University (UK), February 2014 (also at Yale, Amherst, and Boston College March/April 2014)
    Counting points on curves in average polynomial time, Frobenius Distributions on Curves, CIRM (France), February 2014
    The Sato-Tate conjecture for abelian varieties, University of Chicago, January 2014
    New bounds on gaps between primes, Brandeis-Harvard-MIT-Northeastern Joint Colloquium, October 2013
    Isogeny volcanoes, Palmetto Number Theory Series (PANTS XX), September 2013
    Computing L-series of low genus curves, SIAM Conference on Applied Algebraic Geometry, August 2013
    Computing the image of Galois, Workshop on Number Theory, Geometry, and Cryptography, University of Warwick (UK), June 2013
    Sato-Tate distributions, Emory University and CEDAR Workshop at UIC, May 2013
    Computing the image of Galois representations attached to elliptic curves, University of Connecticut and AMS East 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 (video) and Quebec/Vermont Number Theory Seminar, 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 (Canada), 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 University, 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 (France), July 2010
    A local-global principle for rational isogenies of prime degree, CNTA XI (Canada), July 2010
    L-polynomial distributions of genus 2 curves, Rational Points, ETH (Switzerland), May 2010
    Genus 1 point counting in quadratic space and essentially quartic time, CRM Montreal (Canada), April 2010
    Decomposing class polynomials with the CRT method, CRM Montreal (Canada), 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 (Canada), August 2009
    Powered by volcanoes: Three new algorithms, Fields Institute (Canada), 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 (Netherlands), September 2008
    Computing L-series of hyperelliptic curves, ANTS VIII (Canada), May 2008
    Subexponential performance from generic group algorithms, MIT, April 2008
    Thesis defense, MIT, May 2007
    Beating the birthday paradox, MIT, April 2007

Data
    Narrow admissible tuples database, part of the bounded gaps between primes polymath project.

    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 of all levels up to 300 for the j-function
    Modular polynomials of prime level up to 5000 for the Weber ƒ function
    Modular polynomials of prime level up to 200 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

    Optimized equations for X1(m,mn) for m ≥ 2 and mn^2 ≤ 120
    Optimized equations for X1(N) for N ≤ 100      (Updated and extended February 2014 based on joint work with Mark van Hoeij))
    Alternative defining equations for X1(N) for N ≤ 190
    Defining equations for X1(N) in raw form for N ≤ 101

    Sato-Tate distributions in genus 1.
    Sato-Tate distributions in genus 2.
    Sato-Tate distributions in genus 3 (a few examples).

    101 useful trace zero varieties
    Gallery of large Jacobians

Software
    classpoly_v1.0.2.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_v1.3.tar, as described in Computing the endomorphism ring of an ordinary elliptic curve over a finite field.
    smalljac_v4.1.3.tar, as described in Computing L-series of hyperelliptic curves. Requires the ff_poly library.
    ff_poly_v1.2.7.tar, fast finite field arithmetic over word size prime fields (up to 61 bits).
    ff_poly_big_v1.2.7.tar, fast finite field arithmetic over word size prime fields (up to 61 bits), uses David Harvey's zn_poly library to more efficiently handle polynomials of large degree.

Acknowledgements
    Many of the research products (publications/data/software) listed above were supported by NSF Grants DMS-1115455 and DMS-1522526.