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.