International Conference and Workshop on Cluster Algebras and Related Topics

该提案旨在支持将于2008年12月在墨西哥（莫雷利亚和墨西哥城）举行的聚类代数及相关主题国际会议和研讨会。这些活动将由代数、数论与组合学项目和国际科学与工程办公室共同资助。簇代数为令人印象深刻的各种现象提供了一个统一的代数和组合框架，这些现象包括颤振表示、Teichmuller理论、经典和非交换代数几何、热带微积分、泊松几何、李理论以及扇形和多面体的组合学。会议和研讨会将年轻和成熟的研究人员聚集在一起，研究涉及簇代数及其衍生对象的所有主要研究方向（簇类别，簇品种，具有潜力的颤振等），目的是在不同的应用领域之间进行交叉受精和思想交流。会议和研讨会吸引了大约100名与会者，其中包括大量年轻研究人员，其中大多数来自美国和拉丁美洲。该活动的形式——一周的介绍性迷你课程，随后是另一周的研究讲座——旨在将年轻数学家介绍到这个令人兴奋的领域，并促进具有不同数学背景的成熟研究人员之间的思想交流。

This proposal aims to support the International Conference and Workshop on Cluster Algebras and Related Topics, to be held in Mexico (Morelia and Mexico City) in December 2008. These activities will be cofunded by the Algebra, Number Theory, and Combinatorics Program and the Office of International Science and Engineering.Cluster algebras provide a unifying algebraic and combinatorial framework for an impressive variety of phenomena in settings as diverse as quiver representations, Teichmuller theory, classical and non-commutative algebraic geometry, tropical calculus, Poisson geometry, Lie theory, and combinatorics of fans and polytopes. The conference and workshop bring together both young and established researchers working on all major lines of inquiry involving cluster algebras and objects derived from them (cluster categories, cluster varieties, quivers with potentials, etc.), with the goal of cross-fertilization and exchange of ideas between the different domains of application. The conference and workshop attracted approximately 100 participants, including a large number of young researchers, most of them from the US and Latin America. The format of the event---a week of introductory mini-courses followed by another week of research talks---is designed to introduce young mathematicians into this exciting field, and facilitate exchange of ideas between established researchers with different mathematical backgrounds.