The 2009 Graduate Student Combinatorics Conference; Spring 2009; Lexington, KY

该提案是为参加2009年研究生组合会议的75名研究生和主讲人Richard Stanley（麻省理工学院）提供部分支持。肯塔基大学主办了这次活动。24个学生的研究和说说性演讲以及25张海报是代数、几何和拓扑组合学当前趋势的代表性样本。讲座主题包括：热带定向阵、Coxeter图、k-Schur多项式、置换枚举、Hopf代数、非交叉分割格、偶发群、Rogers-Ramanujan恒等式、多图的哈密顿分解、自由和非自由超平面排列、图和有向图的能量、单调列永久猜想和k-抛物子空间排列。参与者来自美国和加拿大领先的组合学研究生项目。这些结果交叉了来自组合学各个领域的研究人员的工作，包括Ardila和Develin、Babson和Steingrimsson、Barcelo、Billera和Brenti、Bressoud、Ehrenborg和Readdy、Fukuyama、Goulden和Jackson、Haglund、Knutson和Miller以及Stanley。本次会议为组合学的年轻研究人员提供了一个受欢迎的媒介来展示他们的成果，一个建立新的专业联系的机会，一个展示组合学新成果和趋势的论坛。组合学是一个不断发展的、充满活力的、跨学科的数学领域。组合学家使用代数、拓扑、几何以及最近的调和分析和代数统计等技术来理解离散结构。组合方法应用于科学问题，包括源于遗传学、生物学和物理学的问题。GSCC将使参与者接触到组合学的许多新思想、领先发展和技术，将增强他们目前在本国机构所看到的数学，并将继续促进组合学领域的跨学科性质。此外，海报会议将鼓励参与者之间更多的网络和互动，这些新的专业联系很可能会导致未来的研究项目。

The proposal is to provide partial support for seventy-five graduate students and the keynote speaker Richard Stanley (MIT) to attend the 2009 Graduate Student Combinatorics Conference. The University of Kentucky is hosting this event. The twenty-four student research and expository talks and twenty-five posters at the poster sessions are a representative sampling of current trends in algebraic, geometric and topological combinatorics. The talk topics include: tropical oriented matroids, Coxeter graphs, k-Schur polynomials, permutation enumeration, Hopf algebras, non-crossing partition lattices, sporadic groups, the Rogers-Ramanujan identities, Hamiltonian decompositions of multigraphs, free and non-free hyperplane arrangements, energy of graphs and digraphs, the Monotone Column Permanent conjecture and k-parabolic subspace arrangments. The participants hail from leading combinatorics graduate programs in the United States and Canada. The results intersect work of researchers from a wide variety of areas of combinatorics, including Ardila and Develin, Babson and Steingrimsson, Barcelo, Billera and Brenti, Bressoud, Ehrenborg and Readdy, Fukuyama, Goulden and Jackson, Haglund, Knutson and Miller, and Stanley.This conference serves to give young researchers in combinatorics a welcoming medium to present their results, an opportunity to make new professional contacts, and a forum to showcase new results and trends in combinatorics. The field of combinatorics is a growing, vibrant and interdisciplinary area of mathematics. Combinatorialists use techniques from algebra, topology, geometry, and more recently, harmonic analysis and algebraic statistics to understand discrete structures. Combinatorial methods are applied to questions in the sciences, including those stemming from genetics, biology and physics. The GSCC will expose the participants to many of the new ideas, leading developments and techniques in combinatorics, will augment the mathematics they are currently seeing at their home institutions, and will continue to foster the interdisciplinary nature of the field of combinatorics. Additionally, the poster session will encourage greater networking and interaction among the participants and these new professional contacts may very likely result in future research projects.