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

该提案将为75名研究生和主讲人理查德·斯坦利(麻省理工学院)参加2009年研究生组合学会议提供部分支持。肯塔基大学将主办这一活动。24个学生研究和说明性演讲和25张海报在海报会议上是代数、几何和拓扑组合学当前趋势的代表性样本。讨论的主题包括：热带定向拟阵，Coxeter图，k-Schur多项式，置换计数，Hopf代数，非交叉划分格，零星群，Rogers-Ramanujan恒等式，多重图的哈密顿分解，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。这些研究结果涉及了来自组合学各个领域的研究人员的工作，包括Ardia和Develin，Babson和Steingrimsson，巴塞罗，Billera和Brenti，BresSoud，Ehrenborg和Readdy，Fukuyama，Goulden和Jackson，Haglund，Knutson和Miller，以及Stanle.这次会议为组合学的年轻研究人员提供了一个展示他们的结果的受欢迎的媒介，一个建立新的专业联系的机会，以及一个展示组合学新结果和趋势的论坛。组合数学领域是一个不断发展、充满活力和跨学科的数学领域。组合学家使用代数、拓扑学、几何学，以及最近的调和分析和代数统计学的技术来理解离散结构。组合方法被应用于科学中的问题，包括那些源于遗传学、生物学和物理学的问题。GSCC将使参与者接触到组合数学中的许多新思想、领先发展和技术，将增强他们目前在本国机构看到的数学知识，并将继续促进组合数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联系和互动，这些新的专业联系很可能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.