Workshop on Graphs and Arithmetic

数论和组合学之间的相互作用有着悠久的历史。在过去的二十年里，自守形式和数论的深入结果被用来构造（最优）扩展器，这是众所周知的，在计算机科学和通信网络中有广泛的应用。这些技术被推广到构建更高维的类似物。最近，图的zeta函数已经扩展到复形。它们包含了组合对象的拓扑和谱信息，使得当且仅当该对象是谱极值时，黎曼假设成立。此外，近年来算术组合学的令人兴奋的发展提供了新的工具来构建良好的扩展器，这反过来又被用来获得深数论结果的家庭。与此同时，扩展的概念在群论和计算机科学中扩展到一个不同的新context.A研讨会上的图形和算术将于2010年3月8日至12日，在CRM，蒙特利尔，加拿大，审查最近令人兴奋的发展在扩展和数论。重点将放在组合学，群论和数论之间的相互联系。理论和应用都将得到重视。17位受邀演讲者来自美国。为了支付受邀演讲者的费用，并部分支持研究生和最近的博士学位，寻求NSF的支持，以补充CRM承诺的资金。

There is a long history of interaction between number theory and combinatorics. In the past two decades, deep results in automorphic forms and number theory were used to construct (optimal) expanders, which are known to have wide applications in computer science and communication networks. These techniques were generalized to construct higher dimensional analogues. Very recently, zeta functions for graphs have been extended to complexes. They contain topological and spectral information of the combinatorial objects so that the Riemann hypothesis is satisfied if and only if the object is spectrally extremal. Furthermore, exciting developments in arithmetic combinatorics in recent years provide new tools to construct families of good expanders, which in turn are used to obtain deep number theoretic results. At the same time, the concept of expansion is extended in group theory and computer science to a different new context.A workshop on graphs and arithmetic will take place March 8-12, 2010, at CRM,Montreal, Canada, to review recent exciting developments in expanders and number theory. The focus will be on the interconnections between combinatorics, group theory and number theory. Both theories and applications will be emphasized. Seventeen invited speakers are from the US. To cover the expenses of the invited speakers and partially support graduate students and recent doctorates, support from the NSF is sought to supplement the fundscommitted by the CRM.