CBMS Conference: Additive Combinatorics from a Geometric Viewpoint

CBMS 会议：几何角度的加性组合学

• 批准号: 1743625
• 负责人: Laszlo Szekely
• 金额: $ 3.5万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1743625&HistoricalAwards=false
• 关键词: CBMS; Conference; Additive; Combinatorics; Geometric

This National Science Foundation award provides support for the CBMS Conference: Additive Combinatorics from a Geometric Viewpoint, to be held at the University of South Carolina during May 21-25, 2018. The main speaker at this conference is Dr. Jozsef Solymosi from the University of British Columbia, one of the leading researchers in this area. The interaction at this event is expected to establish new partnerships and strengthen existing connections between researchers at other southeastern universities and those at the University of South Carolina. Moreover, a focused lecture series summing up current research in additive combinatorics in an accessible way substantially contributes to the professional development of the participants who will include Ph.D. students and junior researchers, as well as faculty from small colleges and teaching institutions, offering them valuable opportunities to enter collaborative networks. Recruitment from groups that are underrepresented in the mathematical sciences is a priority for the PIs. The impact of additive combinatorics in general mathematics and theoretical computer science is enormous.  The geometric viewpoint involves turning arithmetic problems into geometric problems, which can then be solved by geometric means - including discrete geometry, convex geometry, and some algebraic geometry. An archetypal example of this approach is Elekes' bound on the sum-product problem using the Szemeredi-Trotter theorem on the number of incidences between points and lines. Participants will see that arithmetic, algebra, combinatorics and geometry are intimately connected in unexpected ways. Dr. Solymosi's lectures will culminate in a monograph that will provide an accessible reference to graduate students, and fill a literature gap in an area where many results are found only in highly technical journal publications. The conference webpage is at http://imi.cas.sc.edu/events/nsf-cbms/

该国家科学基金会奖为CBMS会议提供了支持：从几何观点上的添加剂组合学，将于2018年5月21日至25日在南卡罗来纳大学举行。该会议的主要发言人是英国哥伦比亚大学的Jozsef Solymosi博士，该地区是该地区的主要研究人员之一。预计该活动的互动将建立新的伙伴关系和力量的现有联系，而其他东南大学的研究人员与南卡罗来纳大学的研究人员之间的现有联系。此外，一个重点的讲座系列以可访问的方式以添加剂组合的方式总结了当前的研究，这基本上有助于包括博士学位的参与者的专业发展。学生和初级研究人员以及小学和教学机构的教师，为他们提供了进入协作网络的宝贵机会。来自数学科学中人数不足的群体的招聘是PI的优先事项。成瘾性组合学在一般数学和理论计算机科学中的影响是巨大的。几何观点涉及将算术问题转变为几何问题，然后可以通过几何平均值来解决这些问题 - 包括离散的几何形状，凸几何和一些代数的几何形状。这种方法的原型示例是Elekes使用有关点和线之间的发动机数量的Szemeredi-Trotter定理在总和问题上的结合。参与者将看到算术，代数，组合和几何形状以意想不到的方式密切相关。 Solymosi博士的讲座将在专着中达到最终形式，该专着将为研究生提供可访问的参考，并在仅在高度技术期刊出版物中发现许多结果的领域填补文献差距。会议网页在http://imi.cas.sc.edu/events/nsf-cbms/