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

这一国家科学基金会奖为将于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办的以“多项式数学系统的应用”为主题的数学科学领域的CBMS区域会议提供支持。由数学科学会议委员会主办，这一区域会议系列的每一次为期五天的会议都有一位杰出的演讲者，他就数学科学一个尖锐重点领域的当前重要研究主题发表了十场演讲；演讲者随后根据这些演讲准备了一本重要的说明性专著。本次会议的首席讲师是阿默斯特学院的威廉·J·沃克数学系教授大卫·A·考克斯。考克斯教授是世界知名的口述大师和获奖作者，著有几本在应用代数几何数学领域广受欢迎和高被引用的书籍。虽然这个数学领域至少可以追溯到18世纪，但具有大量内存和并行处理能力的计算机的负担能力的发展导致了实际应用和新的计算机计算问题的现代复兴。考克斯教授的讲座将从现代的角度讨论该领域的历史发展，并引导当前的研究和在不同领域的应用，如计算机辅助设计、机械连接的刚性和化学反应网络。考克斯教授的每两次讲座都会发展一个选定的主题，然后是他亲手挑选的一位专家的进一步演讲，以更深入地了解当前该主题研究的前沿。额外的会议活动将有助于与会者对当前的科学研究问题有一个广泛而深入的了解，同时也为年轻的研究人员和数学中代表性不足的群体的成员提供机会，与该领域的领导人以及彼此之间进行互动。考克斯教授将通过代数几何和交换代数的方法就多项式系统的研究进行讲座，包括1)代数几何和交换代数中支持计算方法的结果的历史；2)解决多项式系统的现代计算方法和最新进展；以及3)精选当前的应用程序，着眼于帮助与会者解决他们自己的应用问题。具体的讲座主题将包括消去论、现实世界中的多项式系统、几何模型、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的科学参与进入该领域。预计这次会议还将通过加强德克萨斯州地区应用和计算代数几何领域强大而集中的研究人员之间的合作，产生重大的地区影响。会议网址为：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/.