Mathematical Sciences: Ramanujan Graphs and Quaternion Algebras

该奖项支持了A教授的研究。皮泽， 研究模形式、四元数之间的联系 代数和Ramanujan图。 他打算调查 模构造的Ramanujan图的极值性质 forms. 模形式起源于非欧几何， 世纪中期。 另一方面， 手，代表了第一个数学的系统化 活动，计数。 最近发现的 这两个领域再次证明了现代数学 通过将看似不同的领域连接在一起而取得进步。 这 研究在通信领域具有潜在的重要性， 信息技术.

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.