
photo by Natalie Choi (UNSW) 

David Harvey
Associate Professor and ARC Future Fellow 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
 2017–2021: Counting points on algebraic surfaces ($805,054)
ARC Future Fellowship, FT160100219
 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)

Integer multiplication in time O(n log n) (with Joris van der Hoeven)
Submitted for publication.

Polynomial multiplication over finite fields in time O(n log n) (with Joris van der Hoeven)
Submitted for publication.

Faster truncated integer multiplication
Submitted for publication.

Faster integer and polynomial multiplication using cyclotomic coefficient rings (with Joris van der Hoeven)
Unpublished manuscript.

Faster polynomial multiplication over finite fields using cyclotomic coefficient rings (with Joris van der Hoeven)
To appear in Journal of Complexity.

Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in padic cohomology (with Edgar Costa and Kiran Kedlaya)
Proceedings of ANTS XIII (2019), 221–238.

Faster integer multiplication using short lattice vectors (with Joris van der Hoeven)
Proceedings of ANTS XIII (2019), 293–310.

Faster integer multiplication using plain vanilla FFT primes (with Joris van der Hoeven)
Math. Comp. 88 (2019), 501–514.

On the complexity of integer matrix multiplication (with Joris van der Hoeven)
J. Symb. Comp. 89 (2018) 1–8.

Irregular primes to two billion (with William Hart and Wilson Ong)
Math. Comp. 86 (2017), 3031–3049.

Faster polynomial multiplication over finite fields (with Joris van der Hoeven and Grégoire Lecerf)
J. ACM 63 (2017), no. 6, Article 52

Computing Lseries of geometrically hyperelliptic curves of genus three (with Maike Massierer and Andrew Sutherland)
LMS J. Comput. Math. 19 (2016), suppl. A, 220–234.

Fast polynomial multiplication over F_(2^60) (with Joris van der Hoeven and Grégoire Lecerf)
Proceedings of ISSAC 2016, 255–262.

Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II (with Andrew Sutherland)
Contemporary Mathematics 663 (2016), “Frobenius distributions: Lang–Trotter and Sato–Tate conjectures”, 127–147, AMS.

Even faster integer multiplication (with Joris van der Hoeven and Grégoire Lecerf)
J. Complexity 36 (2016), 1–30.
2016 Journal of Complexity Best Paper Award.

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.

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
Unpublished manuscript.

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
2019
 Integer multiplication in time O(n log n) (slides)
CARMA Colloquium, University of Newcastle, May 2019
 Integer multiplication in time O(n log n) (slides)
MSI Colloquium, ANU, May 2019
 Integer multiplication in time O(n log n) (slides, video)
UNSW / University of Sydney Joint Colloquium, May 2019
2018
 Integer multiplication and the truncated product problem (slides)
Mathematics Colloquium, Macquarie University, Oct 2018
 The truncated product problem (slides)
Number Theory Down Under 6, UNSW Canberra, Sep 2018
 Integer multiplication and the truncated product problem (slides)
Number Theory Seminar, UNSW, Sep 2018
 Integer multiplication and the truncated product problem (slides)
Arithmetic Geometry, Number Theory, and Computation, MIT, Aug 2018
 Faster integer multiplication using short lattice vectors (slides)
ANTS XIII, University of Wisconsin, Madison, Jul 2018
 Counting points on curves in average polynomial time (slides)
Workshop on numerical methods for algebraic curves, Rennes, Feb 2018
2017
 Computing Bernoulli numbers (slides)
Jonathan Borwein Commemorative Conference, Newcastle, Sep 2017
 A quick survey of average polynomial time point counting for curves (slides)
PIMS Workshop on Computational Arithmetic Geometry, Simon Fraser University, June 2017
2016
 Point counting on arbitrary varieties
Second NZ Number Theory Workshop, University of Canterbury, Oct 2016
 Point counting on arbitrary varieties
Number Theory Seminar, UNSW, Oct 2016
 Fast integer multiplication and the distribution of primes
Number Theory Down Under, University of Newcastle, Sep 2016
 Computing Lseries of irrationally hyperelliptic curves
Capital Number Theory, ANU, Apr 2016
2015
 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
2014
 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
2013
 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
2012
 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.
2011
 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
2010
 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
2009
 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
2008
 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
Not currently teaching any courses.
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 students:
 Matthew Di Meglio (Honours 2019)
 Ramanan Rajkumar (Masters 2019) Searching for a counterexample to Kurepa's conjecture in average polynomial time
 Madeleine Kyng (Honours 2018) Computing zeta functions of smooth projective curves
 Dan Altman (Honours 2017) Deterministically factorising integer polynomials modulo many primes simultaneously
 Peter Bradshaw (Honours 2016) Algebraic function fields and the Riemann–Roch theorem
 Ramanan Rajkumar (Honours 2015) An extension of Kummer's proof of Fermat's Last Theorem to the Gaussian integers
 Michael Carr (Honours 2015) Elliptic curves over quadratic fields
 Dean Garden (Honours 2012) Rationality of the zeta function of a hypersurface over a finite field
 Joel Beeren (Honours 2012) Elliptic curves and factorisation
Other activities
 Coorganiser of the Number Theory Seminar
 Member of School Research Committee
 Member of School Computing Committee