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) 93857088
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
 2015–2017: Fast algorithms for zeta functions of algebraic varieties ($325,500)
ARC Discovery Project, DP150101689
 2012–2014: Counting solutions to equations over fields of large characteristic ($375,000)
ARC Discovery Early Career Researcher Award, DE120101293
Publications and preprints
(click on the publication title for more details)

Fast polynomial multiplication over F_(2^60) (with Joris van der Hoeven and Grégoire Lecerf)

Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II (with Andrew Sutherland)

On the complexity of integer matrix multiplication (with Joris van der Hoeven)

Even faster integer multiplication (with Joris van der Hoeven and Grégoire Lecerf)
To appear in the Journal of Complexity.

Faster polynomial multiplication over finite fields (with Joris van der Hoeven and Grégoire Lecerf)

Computing zeta functions of arithmetic schemes
Proc. Lond. Math. Soc. 111 (2015), no. 6, 1379–1401.

Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time (with Andrew Sutherland)
LMS J. Comput. Math. 17 (2014), Special Issue A, 257–273.

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)
Math. Comp. 83 (2014), 3071–3091.

A subquadratic algorithm for computing the nth Bernoulli number
Math. Comp. 83 (2014), 2471–2477.

Faster arithmetic for numbertheoretic 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 inplace 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 cachefriendly truncated FFT
Theor. Comput. Sci. 410 (2009), 2649–2658.

Algorithms for padic cohomology and padic heights
Ph.D. thesis.

Efficient computation of padic 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
 Counting points on K3 surfaces: some complexity guesstimates (slides)
Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives, ICERM, Oct 2015
 Counting points on curves over finite fields
Algebraic Geometry, Arithmetic Geometry, and Commutative Algebra Seminar, University of South Carolina, Oct 2015
 Computing Lseries of hyperelliptic curves in moderate genus (slides)
Modular Forms and Curves of Low Genus: Computational Aspects, ICERM, Oct 2015
 Counting points on hypersurfaces
ICERM Research Seminar, Oct 2015
 Point counting in average polynomial time: an update
Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Jul 2015
 Some new pointcounting algorithms
Geometry & Topology Seminar, University of Sydney, Jun 2015
 Even faster integer multiplication (slides)
Optimisation Research Group Seminar, NICTA (UNSW), May 2015
 Some new pointcounting algorithms
Algebra/Geometry/Topology Seminar, University of Melbourne, May 2015
 Faster polynomial multiplication over finite fields (slides)
Australia–New Zealand Mathematics Convention, University of Melbourne, Dec 2014
 The nbody problem, Australian Mathematical Society Early Career Researcher workshop, Melbourne, Dec 2014
 Counting points on smooth plane quartics (slides)
Number Theory Down Under, University of Newcastle, Oct 2014
 Even faster integer multiplication
Algebra and Topology seminar, ANU, Sep 2014
 Computing HasseWitt matrices of hyperelliptic curves in average polynomial time (slides by copresenter Andrew Sutherland)
ANTS XI, Gyeongju, South Korea, Aug 2014
 Irregular primes to two billion
Pure Mathematics Department Seminar, UNSW, May 2014
 Counting points on curves in average polynomial time (slides by copresenter Andrew Sutherland)
Workshop on Frobenius distributions of curves, CIRM, Marseille, France, Feb 2014
 Irregular primes to two billion: progress report (slides)
CARMA, University of Newcastle, Oct 2013
 Recent progress on pointcounting algorithms (slides)
AustMS annual meeting, University of Sydney, Oct 2013
 The accumulating remainder tree and applications
Pure Mathematics Department Seminar, UNSW, Mar 2013
 Counting points on elliptic curves (slides)
MSI Colloquium, ANU, Dec 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, Nov 2012
 Old and new algorithms for computing Bernoulli numbers (slides)
AustMS annual meeting, University of Ballarat, Sep 2012
 Algorithms for Wilson primes
ACAC seminar, Macquarie University, Mar 2012
 Algorithms for Wilson primes
CCR, La Jolla, San Diego, USA, Jan 2012
 Faster deterministic integer factorization (slides)
Joint Mathematics Meetings, Boston MA, USA, Jan 2012.
 Faster arithmetic for numbertheoretic transforms (slides)
Sage/FLINT workshop, University of Warwick, UK, Dec 2011
(note: the timing data for MPIR on the last slide is wrong. The correct time is 224s.)
 Faster deterministic integer factorisation (slides)
Pure Mathematics Department Seminar, UNSW, Oct 2011
 Faster arithmetic for numbertheoretic transforms (slides)
ACAC seminar, Macquarie University, Oct 2011
 Counting points on projective hypersurfaces (slides)
Workshop on Elliptic Curve Computation, Microsoft Research, Redmond, Washington, USA, Oct 2010
 Computing zeta functions of projective surfaces in large characteristic (slides)
Workshop on Counting Points, CRM, Université de Montréal, Canada, Apr 2010
 Computing zeta functions of projective surfaces in large characteristic
Computational Algebra Seminar, University of Sydney, Apr 2010
 Computing zeta functions of certain varieties in larger characteristic (slides)
Effective methods in padic cohomology, Mathematical Institute, University of Oxford, UK, Mar 2010
 Power series arithmetic
ANU, Feb 2010
 An implementation of O(p^{1/2+ε}) pointcounting on hyperelliptic curves
AGCT12, CIRM, Marseille, France, Apr 2009
 Faster polynomial multiplication via multipoint Kronecker substitution (slides)
CS Theory Seminar, New York University, USA, Feb 2009
 zn_poly: a library for polynomial arithmetic (slides)
Joint Mathematics Meetings, Washington DC, USA, Jan 2009
 Largescale verification of Vandiver's conjecture (slides)
MIT Number Theory Seminar, Cambridge MA, USA, Dec 2008
 Polynomial arithmetic and applications in number theory (slides)
Courant Instructor Day, New York University, Sep 2008
 Linear recurrences and Kedlaya's algorithm
CCR, La Jolla, San Diego, USA, Feb 2008
Code
Teaching
2016 semester 1:
 MATH3711 Higher Algebra.
 Consultation times: TBA.
Please contact me if you are interested in doing an Honours project or postgraduate work in number theory, computational number theory, etc.
Current and past Honours students:
 Ramanan Rajkumar (2015) An extension of Kummer's proof of Fermat's Last Theorem to the Gaussian integers
 Michael Carr (2015) Elliptic curves over quadratic fields
 Dean Garden (2012) Rationality of the zeta function of a hypersurface over a finite field
 Joel Beeren (2012) Elliptic curves and factorisation
Other activities
 Web Manager
 Organiser of the Number Theory Seminar
 Member of School Computing Committee
 Member of Faculty IT Advisory Group