NSF/CBMS Regional Conference in the Mathematical Sciences - Applications of Polynomial Systems - June 4-8, 2018

该国家科学基金会奖为CBMS区域会议在数学科学上的主题“多项式系统的应用”提供支持，该会议将于2018年6月4日至2018年6月8日在德克萨斯州沃斯堡的德克萨斯基督教大学举行。由数学科学会议委员会主办，在这个区域会议系列中，每个为期五天的会议都有一位杰出的讲师，他将在一个高度集中的数学科学领域就一个重要的当前研究主题发表十次演讲；讲师随后根据这些讲座准备了一篇说明性的专著。本次会议的主要讲师是David A. Cox，他是Amherst学院的William J. Walker数学教授。Cox教授是世界知名的解释大师和获奖作者，在应用代数几何的数学领域出版了几本受欢迎和被高度引用的书籍。虽然这一数学领域至少可以追溯到18世纪，但随着具有大量内存和并行处理能力的计算机的可负担性的发展，导致了实际应用和新的计算问题的现代复兴。考克斯教授的讲座将从现代观点出发，讨论该领域的历史发展，引导当前的研究和应用，如计算机辅助设计、机械连接的刚性和化学反应网络等不同领域。考克斯教授的每两节课都将发展一个选定的主题，然后由他精心挑选的一位专家进行进一步的讲座，以更深入地了解该主题的当前研究前沿。额外的会议活动将帮助与会者发展对当前研究问题的广泛和深入的理解，同时也为年轻的研究人员和数学领域代表性不足的群体的成员提供机会，与该领域的领导者以及彼此之间进行互动。Cox教授将讲授通过代数几何和交换代数方法研究多项式系统的内容，包括：1)代数几何和交换代数计算方法的基础结果历史；2)求解多项式系统的现代计算方法及其最新进展；3)选择当前的应用程序，以帮助参与者解决他们自己的应用问题。具体的对讲主题将包括消去理论、真实世界中的多项式系统、几何建模、几何约束理论和化学反应网络。补充会议活动将包括海报会议、软件演示、小组讨论和问题会议，旨在帮助新研究人员通过积极参与进入该领域。预计会议还将通过加强德克萨斯地区应用和计算代数几何研究人员之间的合作，产生重大的区域影响。会议的网址是http://faculty.tcu.edu/gfriedman/CBMS2018/。

This National Science Foundation award provides support for a CBMS Regional Conference in the Mathematical Sciences on the topic "Applications of Polynomial Systems," to be hosted at Texas Christian University in Fort Worth, TX, from June 4, 2018, to June 8, 2018. Sponsored by the Conference Board of the Mathematical Sciences, each five-day conference in this Regional Conference series features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences; the lecturer subsequently prepares an expository monograph based upon these lectures. The principal lecturer for this conference is David A. Cox, the William J. Walker Professor of Mathematics at Amherst College.  Professor Cox is a world-renowned master expositor and award-winning author of several popular and highly-cited books in the mathematical area of applied algebraic geometry. While this field of mathematics dates back at least as far as the 18th century, developments in the affordability of computers with substantial memory and parallel processing power have led to a modern renaissance in both practical applications and new computational questions. Professor Cox's lectures will discuss historical developments of the area in light of modern perspectives, leading up to current research and applications to such diverse fields as computer aided design, rigidity of mechanical linkages, and chemical reaction networks. Each pair of lectures by Professor Cox will develop a chosen topic and be followed by a further lecture by a specialist he has hand-picked to provide a deeper look at the forefront of current research on that topic. Additional conference activities will help participants develop a broad and deep understanding of current research problems while also providing opportunities for young researchers and members of underrepresented groups in mathematics to interact with leaders in the area and with each other.Professor Cox will lecture on the study of polynomial systems via methods of algebraic geometry and commutative algebra, including 1) a history of results underpinning computational methods in algebraic geometry and commutative algebra; 2) modern computational approaches to solving polynomial systems and recent advances; and 3) a selection of current applications, with an eye toward helping participants solve their own applied problems. Specific lecture pair topics will include Elimination Theory, Polynomial Systems in the Real World, Geometric Modeling, Geometric Constraint Theory, and Chemical Reaction Networks. Supplementary conference activities will include a poster session, a software demonstration, a panel discussion, and a problem session designed to help new researchers enter the field through active participation. The conference is also anticipated to have significant regional impact by bolstering collaboration among the strong concentration of researchers in applied and computational algebraic geometry in the Texas area. The conference web site can be found at http://faculty.tcu.edu/gfriedman/CBMS2018/.