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

组合学 2010：进展、趋势

• 批准号: 1024407
• 负责人: Margaret Readdy
• 金额: $ 0.76万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-02-15 至 2011-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1024407&HistoricalAwards=false
• 关键词: Combinatorics; 2010; Advances; Trends; &amp

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.

组合数学2010：进展，趋势推测（CATS 2010研讨会）将于2010年3月26日在肯塔基州大学举行。 Sara Billey（U华盛顿）、Patricia Hersh（北卡罗来纳州）、Isabella Novik（U华盛顿）和Stephanie货车Willigenburg（U不列颠哥伦比亚省）将发表四次一小时的主旨演讲。 本次研讨会结束与特别会议“在代数几何组合学的进展”发生在美国数学学会会议在列克星敦，肯塔基州的16个讲习班与会者将给予会谈以下两天。 CATS 2010研讨会重点介绍了组合数学中的四个主要研究主题：Coxeter群、拓扑组合数学、多面体和流形以及表示论中的拟对称函数。 讨论的主题将包括了解仿射格拉斯曼（与希尔伯特方案的联系，确定其（上）同调的舒尔函数类似物），从拓扑角度的总正性（对于规则的细胞复合物，Bruhat顺序），面对向量问题的多面体和流形（查尼-戴维斯猜想，球面和流形的g-猜想，球面、流形和伪流形的下界定理），拟对称Schur函数和斜拟对称Schur函数的组合性质。 研讨会的一些参与者从事的研究跨越四个领域中的一个以上，所以他们的存在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与会者有充足的时间建立新的研究联系，讨论未决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助，并为研讨会与会者提供部分资助。 该研讨会包括研究人员在他们的职业生涯的各个阶段，包括研究生和最近的博士学位，并有一个强大的代表性的群体是在数学代表性不足。