Enjoying some algebraic number theory in the shade
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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)
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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
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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
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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