Combinatorics 2010: Advances, Trends & Speculations (CATS 2010 Workshop)

2010年组合数学：进展、趋势和推测(CATS 2010研讨会)将于2010年3月26日在肯塔基大学举行。萨拉·比利(华盛顿大学)、帕特里夏·赫什(北卡罗来纳州)、伊莎贝拉·诺维克(华盛顿大学)和斯蒂芬妮·范·威利根伯格(不列颠哥伦比亚省大学)将发表四次一小时的主旨演讲。本次研讨会与随后两天在肯塔基州列克星敦举行的美国数学学会会议上举行的特别会议“代数与几何组合学的进展”相吻合，届时将有16名研讨会参与者发表演讲。除了四位演讲者外，预计至少还有25名研究人员将参加研讨会。CATS 2010研讨会重点介绍了组合学中的四个主要研究主题：Coxeter群、拓扑组合学、多面体和流形，以及表示理论中的准对称函数。讨论的主题将包括理解仿射Grassmannians(与Hilbert格式的联系，确定Schur函数的(上)同调)，从拓扑角度的全正性(对于正则细胞复形，Bruhat阶)，多面体和流形的面向量问题(Charney-Davis猜想，球面和流形的g-猜想，球面和流形的下界定理)，以及拟对称Schur函数和斜拟对称Schur函数的组合性质。许多研讨会参与者从事的研究涉及四个领域中的一个以上领域，因此他们的出席将有助于促进研讨会的跨学科目标。研讨会的日程安排包括让研讨会参与者有充足的时间建立新的研究联系，讨论尚未解决的问题，并确定可能的新研究途径。该奖项为受邀演讲者提供全额资金，为研讨会参与者提供部分资金。研讨会包括处于其职业生涯所有阶段的研究人员，包括研究生和新近的博士，并且有很强的代表性，这些群体在数学中的代表性不足。

Combinatorics 2010: Advances, Trends & Speculations (CATS 2010 Workshop) will be held at the University of Kentucky on March 26, 2010. Four one-hour keynote addresses will be given by Sara Billey (U Washington), Patricia Hersh North Carolina State), Isabella Novik (U Washington) and Stephanie van Willigenburg (U British Columbia). This workshop dovetails with the special session "Advances in Algebraic & Geometric Combinatorics" occurring at the American Mathematical Society meeting the following two days in Lexington, KY where sixteen of the workshop participants will be giving talks. Besides the four speakers, at least twenty-five additional researchers are expected to participate in the workshop.The CATS 2010 Workshop highlights four of the major research themes in combinatorics: Coxeter groups, topological combinatorics, polytopes and manifolds, and quasisymmetric functions in representation theory. Topics of discussion will include understanding affine Grassmannians (connections with Hilbert schemes, determining a Schur function analogue for its (co)homology), total positivity from a topological perspective (for regular cell complexes, Bruhat order), face vector questions for polytopes and manifolds (the Charney-Davis conjecture, the g-conjecture for spheres and manifolds, lower bound theorem for spheres, manifolds and pseudomanifolds), and combinatorial properties of quasisymmetric Schur and skew-quasisymmetric Schur functions. A number of the workshop participants are engaged in research spanning more than one of the four areas, so their presence will help foster the interdisciplinary goals of the workshop. The workshop schedule includes ample time for workshop participants to establish new research contacts, discuss open problems and determine possible new avenues of research.The award provides full funding for the invited speakers and partial funding for the workshop participants. The workshop includes researchers at all stages of their careers, including graduate students and recent PhDs, and has a strong representation of groups which are underrepresented in mathematics.