Computational methods in arithmetic geometry

pi在计算算术几何中提出了一些研究。这些成果包括泛群算法的进一步发展和p进上同调的数值计算，低格曲线的Frobenius特征值分布的进一步研究，以及模多项式的高效计算和制表。一般来说，计算算术几何，特别是拟议的研究，与应用计算机科学的几个方面有关，包括数字数据的可靠传输和存储以及电子通信的安全。除了研究之外，拟议的活动还包括本科生参与算法和软件开发，将研究和培训活动结合起来，同时为研究界提供高价值的工具。

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.