CBMS Conference: Additive Combinatorics from a Geometric Viewpoint

该国家科学基金会奖为CBMS会议提供支持：从几何角度看加性组合，将于2018年5月21日至25日在南卡罗莱纳大学举行。本次会议的主要发言人是来自英属哥伦比亚大学的Jozsef Solymosi博士，他是该领域的主要研究人员之一。本次活动的互动有望建立新的伙伴关系，并加强东南其他大学和南卡罗来纳大学研究人员之间的现有联系。此外，一个集中的系列讲座以一种易于理解的方式总结了当前在加法组合学方面的研究，这大大有助于参与者的专业发展，包括博士生和初级研究人员，以及来自小型学院和教学机构的教师，为他们提供进入合作网络的宝贵机会。从数学科学领域代表性不足的群体中招募人才是pi的首要任务。加性组合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化为几何问题，然后可以通过几何手段解决这些问题——包括离散几何、凸几何和一些代数几何。这种方法的一个典型例子是Elekes用szemeredii - trotter定理求解点与线之间的关联数的和积问题的界。参与者将看到算术、代数、组合学和几何以意想不到的方式紧密联系在一起。Solymosi博士的讲座将以专著的形式结束，这将为研究生提供一个可访问的参考，并填补了一个只有在高技术期刊出版物中才能找到许多结果的领域的文献空白。会议网页是http://imi.cas.sc.edu/events/nsf-cbms/

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/