NSF Award
1741730
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.<br/><br/><br/>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/.
