Modulo Errors

Next week is the 25th Journées Arithmétiques, my first proper conference, conveniently held right here at the University of Edinburgh. Should be an interesting experience even if I find myself unable to follow much of the content. More at my level is Topics in Algebra, Geometry and Number Theory, a two week summerschool for beginning masters/postgraduates in Utrecht, The Netherlands. I’m hoping that’ll help me shore up the foundations in a few areas connected to my studies and allow me to finally understand what the other geometers are on about! Then I’ll be in Dublin for a few days of September, at ECC2007, the 11th Workshop on Elliptic Curve Cryptography. Again, much could be beyond me, but it’s pretty much the field I’ve settled in to and the whole area interests me, so it seems worth trying nonetheless.

Tomorrow I give my first year presentation, which determines whether I’m allowed to continue my studies. At 20-30 minutes, it’s a rather condensed version of my recent geometry club talk on the point counting problem, although this time I’m skipping more quickly through the fundamentals so that I can discuss some of the algorithms in depth, and taking a (hopefully) clearer route.

Both the report itself and the OHP slides version are available (pdf). Content covered: hyperelliptic curves, points, divisors, mumford polynomials and the Picard group/Jacobian; the discrete logarithm problem; explicit group law computation; characteristic polynomial of Frobenius and Weil theorems/interval; group-theoretic approaches; Schoof’s algorithm, SEA in genus 1, genus 2 hybrid algorithms.