David Harvey

Senior Lecturer at the School of Mathematics and Statistics, University of New South Wales.

Curriculum vitae.

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)

1. Statistics of different reduction types of Fermat curves (with Igor Shparlinski), to appear in Experimental Mathematics.
2. Counting points on hyperelliptic curves in average polynomial time, submitted.
3. A search for Wilson primes (with Edgar Costa and Robert Gerbicz), to appear in Mathematics of Computation.
4. A subquadratic algorithm for computing the n-th Bernoulli number, to appear in Mathematics of Computation.
5. Faster arithmetic for number-theoretic transforms, submitted.
6. Faster deterministic integer factorization (with Edgar Costa), to appear in Mathematics of Computation.
7. The Karatsuba integer middle product, J. Symb. Comp. 47 (2012), 954–967.
8. Fast computation of Bernoulli, Tangent and Secant numbers (with Richard Brent), to appear.
9. Short division of long integers (with Paul Zimmermann), proceedings of ARITH 20, 2011, 7–14.
10. 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.
11. An in-place truncated Fourier transform and applications to polynomial multiplication (with Daniel Roche), proceedings of ISSAC 2010, 325–329.
12. Irregular primes to 163 million (with Joe Buhler), Math. Comp. 80 (2011), 2435–2444.
13. Faster exponentials of power series.
14. Faster algorithms for the square root and reciprocal of power series, Math. Comp. 80 (2011), 387–394.
15. A multimodular algorithm for computing Bernoulli numbers, Math. Comp. 79 (2010), 2361–2370.
16. Faster polynomial multiplication via multipoint Kronecker substitution, J. Symb. Comp. 44 (2009), 1502–1510.
17. A cache-friendly truncated FFT, Theor. Comput. Sci. 410 (2009), 2649–2658.
18. Algorithms for p-adic cohomology and p-adic heights, Ph.D. thesis.
19. Efficient computation of p-adic heights, LMS J. Comput. Math. 11 (2008), 40–59.
20. Kedlaya's algorithm in larger characteristic, Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29.
21. Selberg's symmetry formula, Expo. Math. 22 (2004), no. 2, 185–195.

Talks

• 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.

Code

• zn_poly: a library for polynomial arithmetic in Z/nZ.
• hypellfrob: an implementation of the algorithm described in Kedlaya's algorithm in larger characteristic.
• mul_huge: a library for multiplying huge integers that don't fit into RAM.
• bernmm: an implementation of the algorithm described in A multimodular algorithm for computing Bernoulli numbers.
• ntl-fft: a more cache-friendly version of NTL's FFT routine that may speed up arithmetic on high-degree polynomials.
• Sage (external link): free, open-source mathematics software.
• GMP (external link): the GNU Multiple Precision arithmetic library.
• blahtex (external link): a program I wrote years ago to convert LaTeX into MathML, now maintained by Gilles Van Assche.