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

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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.