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

这个国家科学基金会奖提供支持CBMS区域会议在数学科学的主题“多项式系统的应用”，将在德克萨斯州沃斯堡的德克萨斯基督教大学主办，从2018年6月4日，到2018年6月8日。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，他就数学科学的一个重点领域的重要当前研究主题发表了十场演讲;讲师随后根据这些演讲编写了一本简明的专著。本次会议的主讲人是大卫A。考克斯，威廉J.步行者数学教授在阿默斯特学院。 考克斯教授是一位世界知名的数学大师，在应用代数几何的数学领域撰写了几本广受欢迎和高引用率的著作，并屡获殊荣。虽然这一数学领域的历史至少可以追溯到18世纪，但随着计算机的发展，具有大量内存和并行处理能力的计算机的可负担性已经导致了实际应用和新计算问题的现代复兴。教授考克斯的讲座将讨论该地区的历史发展，在现代的观点，导致目前的研究和应用等不同领域的计算机辅助设计，刚性的机械联系，和化学反应网络。考克斯教授的每一对讲座将发展一个选定的主题，然后由他亲自挑选的专家进一步讲座，以提供对该主题的当前研究的前沿更深入的了解。其他的会议活动将有助与会者对当前的研究问题有更广泛和深入的了解，同时也为年轻的研究人员和数学界代表性不足的团体成员提供机会，让他们与数学界的领导者交流和相互交流。考克斯教授将讲授如何通过代数几何和交换代数的方法来研究多项式系统，包括1）代数几何和交换代数中计算方法的基础结果的历史; 2）解决多项式系统的现代计算方法和最新进展; 3）当前应用的选择，着眼于帮助参与者解决他们自己的应用问题。具体的讲座主题将包括消除理论，多项式系统在真实的世界，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，旨在帮助新的研究人员通过积极参与进入该领域。会议还预计将通过加强德克萨斯州地区应用和计算代数几何研究人员之间的合作来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/.