NSF/CBMS Regional Conference in the Mathematical Sciences: Combinatorial Zeta and L-functions

该奖项将支持将于2014年5月6日至10日在犹他州圣丹斯举行的关于组合Zeta和L函数的NSF-CMBS地区会议。主讲嘉宾为宾夕法尼亚州立大学数学系特聘教授李文清。这十堂课将通过Zeta函数探索数论和组合学之间的相互作用。使用代数闭包和绝对伽罗瓦群的图形类比，这些讲座探索了图的伽罗瓦理论、素数定理和Cebotarev密度定理。我们将利用数论给出Ramanujan图和扩张器的显式构造。关于阿波罗球体包装的最新结果将进一步突出组合学在数论中的应用。NSF-CBMS地区会议通过该领域领先实践者的一系列讲座，专注于重要的、前沿的研究主题，激发了人们对数学研究的兴趣和活动。这一奖项将支持大约30名与会者，包括许多处于职业生涯早期阶段的研究人员。会议出版的说明性专著将向广大受众介绍研究领域，放大会议在社会上的长期影响。

This award will support an NSF-CMBS regional conference to be held May 6-10, 2014, at Sundance, Utah on combinatorial zeta and L-functions. The principal speaker will be Wen-Ching Winnie Li, Distinguished Professor of Mathematics at Penn State University. The ten lectures will explore interactions between number theory and combinatorics via zeta functions. Using graph analogs of algebraic closure and the absolute Galois group, the lectures explore the Galois theory, prime number theorem, and Cebotarev density theorem for graphs. Number theory will be used to give explicit constructions for Ramanujan graphs and expanders. Recent results on Apollonian sphere packing will additionally highlight applications of combinatorics to number theory.NSF-CBMS regional conferences stimulate interest and activity in mathematical research by focusing on important, cutting edge-topics of research through a series of lectures by a leading practitioner in the field. This award will support approximately 30 participants in the conference, including many researchers at early stages in their careers. A published expository monograph resulting from the conference will introduce the research area to a wide audience, amplifying the long-term impact of the conference in the community.