The PIs propose several investigations in computational arithmetic geometry. These include the further development of generic group algorithms and numerical computation of p-adic cohomology, the further investigation of the distribution of Frobenius eigenvalues of curves of low genus, and the efficient computation and tabulation of modular polynomials.
Computational arithmetic geometry in general, and the proposed research in particular, bears relevance to several aspects of applied computer science, including the reliable transmission and storage of digital data and the security of electronic communication. In addition to research, the proposed activities also include undergraduate participation in algorithm and software development, integrating research and training activities while producing tools of high value to the research community.
