Enjoying some algebraic number theory in the shade

Floor tiling from the the Municipal Building, in Prague, the Czech Republic, illustrating wallpaper group "pmg" — 180° rotational symmetry, reflections in one axis only (license) previous/next

David Harvey

I recently received my Ph.D., working under Barry Mazur in the Harvard mathematics department.

I will be starting as a Courant Instructor at NYU in September.

Research interests

Computational aspects of number theory and arithmetic algebraic geometry.

Right now I'm working on: fast polynomial arithmetic; algorithms that use p-adic cohomology to compute zeta functions of curves over fields of large-ish characteristic; Bernoulli numbers; irregular primes.

Papers

• A multimodular algorithm for computing Bernoulli numbers
  arXiv — demo code — the 100,000,000-th Bernoulli number
  
  
• Algorithms for p-adic cohomology and p-adic heights
  Ph.D. thesis (2008)
  pdf
  
  
• Faster polynomial multiplication via multipoint Kronecker substitution
  arXiv — demo code (see the file mul_ks.c)
  
  
• Efficient computation of p-adic heights
  LMS J. Comput. Math. 11 (2008), 40–59.
  journal link — arXiv
  
  
• Kedlaya's algorithm in larger characteristic
  Int Math Res Notices 2007 (2007), no. rnm095, rnm095–29.
  journal link — arXiv — demo code
  
  
• Selberg's symmetry formula
  Expo. Math. 22 (2004), no. 2, 185–195
  pdf

Contact details

• email: dmharvey {AT} math {DOT} harvard {DOT} edu
• my PGP public key
• postal: Harvard University, Department of Mathematics, One Oxford St, Cambridge MA 02138, USA

Code

• zn_poly: an experimental library for polynomial arithmetic in Z/nZ, where n fits into an unsigned long.
• hypellfrob: a program for computing the zeta function of a hyperelliptic curve over GF(p), using the methods described in Kedlaya's algorithm in larger characteristic (see above).
• A more cache-friendly version of NTL's FFT routine that may speed up arithmetic on high-degree polynomials on some architectures.
• An ascii art frieze generator.

Other interests

• SAGE: open source mathematics software