Equivariant Combinatorics: A Summer School and Workshop

等变组合：暑期学校和研讨会

• 批准号: 1723851
• 负责人: Jennifer Morse
• 金额: $ 2万
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1723851&HistoricalAwards=false
• 关键词: Equivariant; Combinatorics; Summer; Workshop

This award supports the participation of a diverse group of junior researchers in a summer school and workshop entitled "Equivariant Combinatorics," to be held from June 12-23, 2017 at the Centre de Recherche Mathematiques in Montreal, Quebec. Algebraic combinatorics is the underlying theme of the workshop and school; it is a vast area of mathematics concerned with the development of tools for analyzing, organizing, and arranging discrete data. The workshop and school will enhance the development of combinatorial methods essential in areas such as genomics, computer science, statistics, and physics. Emphasis is on the creation of combinatorial techniques for attacking problems in algebraic and geometric areas such as symmetric function theory, a subject with applications to probability and statistical mechanics. The program will promote the use of and training in an open-source computational symbolic algebra system, SAGE. The workshop is a forum for the communication of recent developments on a body of problems in representation theory, algebraic geometry and topology, and theoretical physics with common combinatorial underpinnings. The focus is on rectangular Catalan combinatorics, relating varied areas such as representation theory of diagonal harmonic polynomials and coinvariant spaces, flag bundles over the Hilbert scheme of points in the plane, affine Springer fibres, and Khovanov-Rozansky homology of torus knots. Three lecture series will run during the summer school preceding the workshop. The speakers, known for both their communication and academic excellence, were choosen for differing viewpoints on similar problems in equivariant combinatorics. The school will broaden participants' perspective and will enable them to more fully benefit from the subsequent workshop talks. There will also be ample opportunity to share code and gain experience with the open-source SAGE-Combinat computer algebra system. Participants will leave equipped to help colleagues at their home institutions begin mathematical experimentation in SAGE.Details of the program can be found at http://www.crm.umontreal.ca/2017/Equivariant17/index_e.php.

该奖项支持一个名为“等变组合数学”的暑期学校和研讨会的初级研究人员的多元化群体的参与，将于2017年6月12日至23日在魁北克蒙特利尔的数学研究中心举行。代数组合学是研讨会和学校的基本主题;它是一个广泛的数学领域，涉及分析，组织和安排离散数据的工具的开发。该研讨会和学校将加强在基因组学，计算机科学，统计学和物理学等领域必不可少的组合方法的发展。重点是创造组合技术，用于攻击代数和几何领域的问题，如对称函数理论，这是一个应用于概率和统计力学的主题。该计划将促进使用和培训的开放源码计算符号代数系统，SAGE。 该研讨会是一个论坛，用于交流在表示论，代数几何和拓扑学以及具有共同组合基础的理论物理学中的一系列问题的最新发展。重点是矩形加泰罗尼亚组合，涉及不同的领域，如对角调和多项式和coinvariant空间的表示理论，在平面上的点的希尔伯特计划，仿射施普林格纤维和Khovanov-Rozansky同源环面结的旗束。三个系列讲座将在研讨会之前的暑期学校举行。发言者，以他们的沟通和学术卓越而闻名，被选为对等变组合学中类似问题的不同观点。学校将扩阔参加者的视野，使他们能从随后的工作坊讲座中更全面地获益。也将有充分的机会分享代码和获得经验的开源SAGE-Combinat计算机代数系统。参加者将离开装备，以帮助同事在他们的家乡机构开始数学实验在SAGE。该计划的细节可以找到在http://www.crm.umontreal.ca/2017/Equivariant17/index_e.php。