CBMS Regional Conference in the Mathematical Sciences - Algebraic and Topological Combinatorics of Ordered Sets - 18 - 22 July, 2005

代数组合学的枚举方面与表示理论和代数几何有着密切的联系，几十年来一直是一个非常活跃的研究领域。自70年代中期以来，与多面体、单纯复合体、三角球和同调球、超平面和子空间排列有关的其他枚举问题有了爆炸式的增长。我们建议组织一个CBMS系列讲座，展示这一发展的拓扑和代数方面，由安德斯·比约纳（Anders Bjorner）主讲，他从早期开始就是这场革命的先锋。拟议的会议将集中讨论集发挥重要作用的主题。Anders Bjorner是与部分有序集相关的代数和拓扑组合学的主要专家。他的讲座将全面总结与部分有序集有关的当代拓扑组合学。这将对参与者和当地组合学界未来的研究产生重大影响。

The enumerative aspects of algebraic combinatorics with its strong connections to representation theory and algebraic geometry has been a very active area of research for decades. Other enumerative questions related to the number of faces of polytopes, simplical complexes, triangulated and homology spheres, and hyperplane and subspace arrangements had an explosive growth since the mid-70's. We propose to organize a CBMS lecture series that will showcase the topological and algebraic aspects of this development by ten lectures given by Anders Bjorner who has been at the vanguard of this revolution from its early days. The proposed conference will focus on topics where posets have played an important role. Anders Bjorner is the leading expert on algebraic and topological combinatorics that is relevant to partially ordered sets. His lectures will be a comprehensive summary of the contemporary topological combinatorics related to partially ordered sets. This will have a strong influence on the future research of the participants and local combinatorics community.