Mathematical Sciences: Ramanujan Graphs and Quaternion Algebras

该奖项支持A.Pizer教授在模形式、四元数代数和Ramanujan图之间的联系方面的研究。他打算研究通过模形式构造的Ramanujan图的极值性质。模形式起源于19世纪中叶的非欧几里德几何。另一方面，组合学代表了第一个数学活动--计数的系统化。最近发现的这两个领域之间的联系再次展示了现代数学是如何通过将看似不同的领域联系在一起而取得进步的。这项研究对通信和信息技术具有潜在的重要意义。

This award supports the research of Professor A. Pizer to work on the connections between modular forms, quaternion algebras, and Ramanujan graphs. He intends to investigate the extremal properties of Ramanujan graphs constructed via modular forms. Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Combinatorics, on the other hand, represents a systematization of the first mathematical activity, counting. The recently discovered connections between these two areas demonstrates once again how modern mathematics progresses by connecting together seemingly diverse fields. This research is potentially important in communications and information technology.