David Harvey
Senior Lecturer at the School of Mathematics and Statistics, University of New South Wales.
Contact details
email: d DOT harvey AT unsw DOT edu DOT au (PGP public key)
phone: +61 (2) 9385-7088
office: 6108 Red Centre
postal: School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia
Research interests
Computational number theory and arithmetic geometry, polynomial and integer arithmetic
Grants and awards
- ARC DECRA grant “Counting solutions to equations over fields of large characteristic”, 2012–2014.
Publications and preprints
(click on the publication title for more details)
- Even faster integer multiplication (with Joris van der Hoeven and Grégoire Lecerf).
- Faster polynomial multiplication over finite fields (with Joris van der Hoeven and Grégoire Lecerf).
- Computing zeta functions of arithmetic schemes.
- Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time (with Andrew Sutherland).
- An incomplete variant of Wilson's congruence (with Joel Beeren and Tim Trudgian).
- Counting points on hyperelliptic curves in average polynomial time, Ann. of Math. (2) 179 (2014), no. 2, 783–803.
- A search for Wilson primes (with Edgar Costa and Robert Gerbicz), to appear in Mathematics of Computation.
- A subquadratic algorithm for computing the n-th Bernoulli number, Math. Comp. 83 (2014), 2471–2477.
- Faster arithmetic for number-theoretic transforms, J. Symb. Comp. 60 (2014) 113–119.
- Faster deterministic integer factorization (with Edgar Costa), Math. Comp. 83 (2014), 339–345.
- Statistics of different reduction types of Fermat curves (with Igor Shparlinski), Exper. Math. 22 (2013), no. 3, 243–249.
- The Karatsuba integer middle product, J. Symb. Comp. 47 (2012), 954–967.
- Fast computation of Bernoulli, Tangent and Secant numbers (with Richard Brent), Springer Proceedings in Mathematics & Statistics, Vol. 50, 2013, 127–142.
- Short division of long integers (with Paul Zimmermann), proceedings of ARITH 20, 2011, 7–14.
- Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces (with Brendan Hassett and Yuri Tschinkel), Comm. Pure Appl. Math. 65 (2012), no. 2, 264–286.
- An in-place truncated Fourier transform and applications to polynomial multiplication (with Daniel Roche), proceedings of ISSAC 2010, 325–329.
- Irregular primes to 163 million (with Joe Buhler), Math. Comp. 80 (2011), 2435–2444.
- Faster exponentials of power series.
- Faster algorithms for the square root and reciprocal of power series, Math. Comp. 80 (2011), 387–394.
- A multimodular algorithm for computing Bernoulli numbers, Math. Comp. 79 (2010), 2361–2370.
- Faster polynomial multiplication via multipoint Kronecker substitution, J. Symb. Comp. 44 (2009), 1502–1510.
- A cache-friendly truncated FFT, Theor. Comput. Sci. 410 (2009), 2649–2658.
- Algorithms for p-adic cohomology and p-adic heights, Ph.D. thesis.
- Efficient computation of p-adic heights, LMS J. Comput. Math. 11 (2008), 40–59.
- Kedlaya's algorithm in larger characteristic, Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29.
- Selberg's symmetry formula, Expo. Math. 22 (2004), no. 2, 185–195.
Talks
- May 2014: Irregular primes to two billion, Pure Mathematics Department Seminar, University of New South Wales.
- Feb 2014: Counting points on curves in average polynomial time (slides by co-presenter Andrew Sutherland), CIRM, Marseille.
- Oct 2013: Irregular primes to two billion: progress report (slides), CARMA, University of Newcastle.
- Oct 2013: Recent progress on point-counting algorithms (slides), Australian Mathematics Society annual meeting, University of Sydney.
- Mar 2013: The accumulating remainder tree and applications, Pure Mathematics Department Seminar, University of New South Wales.
- Dec 2012: Counting points on elliptic curves (slides), Mathematical Sciences Institute Colloquium, Australian National University.
- Nov 2012: Counting points on elliptic curves (slides), Computational Algebra Seminar, University of Sydney.
- Nov 2012: Counting points on hyperelliptic curves (slides), CARMA, University of Newcastle.
- Sep 2012: Old and new algorithms for computing Bernoulli numbers (slides), Australian Mathematics Society annual meeting, University of Ballarat.
- Mar 2012: Algorithms for Wilson primes, Centre for Advanced Computing - Algorithms and Cryptography, Macquarie University.
- Jan 2012: Algorithms for Wilson primes, Center for Communications Research, La Jolla, San Diego.
- Jan 2012: Faster deterministic integer factorization (slides), AMS Special Session on the Mathematics of Computation: Algebra and Number Theory, Joint Mathematics Meetings, Boston MA.
- Dec 2011: Faster arithmetic for number-theoretic transforms (slides), Sage/FLINT workshop, University of Warwick.
(note: the timing data for MPIR on the last slide is wrong. The correct time is 224s.)
- Oct 2011: Faster deterministic integer factorisation (slides), Pure Mathematics Department Seminar, University of New South Wales.
- Oct 2011: Faster arithmetic for number-theoretic transforms (slides), Centre for Advanced Computing - Algorithms and Cryptography, Macquarie University.
- Oct 2010: Counting points on projective hypersurfaces (slides), Workshop on Elliptic Curve Computation, Microsoft Research.
- Apr 2010: Computing zeta functions of projective surfaces in large characteristic (slides), Workshop on Counting Points, Centre de recherches mathématique (CRM), Université de Montréal.
- Apr 2010: Computing zeta functions of projective surfaces in large characteristic, Computational Algebra Seminar, University of Sydney.
- Mar 2010: Computing zeta functions of certain varieties in larger characteristic (slides), Effective methods in p-adic cohomology, Mathematical Institute, University of Oxford.
- Feb 2010: Power series arithmetic, Australian National University.
- Apr 2009: An implementation of O(p^{1/2+ε}) point-counting on hyperelliptic curves, Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-12), CIRM, Marseille.
- Feb 2009: Faster polynomial multiplication via multipoint Kronecker substitution (slides), CS Theory Seminar, CIMS.
- Jan 2009: zn_poly: a library for polynomial arithmetic (slides), Joint Mathematics Meetings, Washington DC.
- Dec 2008: Large-scale verification of Vandiver's conjecture (slides),
MIT Number Theory Seminar.
- Sep 2008: Polynomial arithmetic and applications in number theory (slides),
Courant Instructor Day, NYU.
- Feb 2008: Linear recurrences and Kedlaya's algorithm,
Center for Communications Research, La Jolla, San Diego.
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