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

该奖项将支持NSF-CMBS区域会议，该会议将于2014年5月6日至10日在犹他州圣丹斯举行，讨论组合zeta和l函数。主讲嘉宾是美国宾州州立大学数学系杰出教授李文清。这十堂课将通过ζ函数探讨数论与组合学之间的相互作用。利用代数闭包的图类和绝对伽罗瓦群，本课程探讨了图的伽罗瓦理论、素数定理和Cebotarev密度定理。数论将用于给出拉马努金图和展开式的显式结构。阿波罗球填充的最新结果将进一步突出组合学在数论中的应用。NSF-CBMS区域会议通过由该领域的领先从业者通过一系列讲座关注重要的前沿研究主题，从而激发人们对数学研究的兴趣和活动。该奖项将支持大约30名会议参与者，其中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读者介绍该研究领域，扩大会议在社区中的长期影响。

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.