Arithmetic Geometry, Number Theory and Computation

The frontier of research is now studying curves of higher genus, abelian surfaces, and K3 surfaces. Here, however, the development and implementation of practical algorithms has lagged behind the theory, and we seek to correct this imbalance. Available computational resources have reached a point where algorithms are now technically feasible. In contrast to the situation with curves of low genus, brute force computation typically yields very little; to obtain practical algorithms one must exploit the theoretical infrastructure of modern arithmetic geometry. More information about the collaboration can be found on its website.