## An NSF/CBMS Regional Conference in the Mathematical Sciences
## Applications of Polynomial Systems## Texas Christian University |

The principal lecturer is **David A. Cox** the William J. Walker Professor of Mathematics at Amherst College.
Professor Cox will present 10 one-hour lectures.

Professor Cox is a world-renowned master expositor and award-winning author of several popular and highly-cited books in applied algebraic geometry. While this field of mathematics dates back at least as far as the 18th century, modern 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 right 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 participants 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.

Lecture Guide (2018)

Abstracts of Professor Cox's talks (2017)

Slides of Professor Cox's talks (2018)

- Carlos D’Andrea (Universitat de Barcelona) - Carlos's talk slides
- Alicia Dickenstein (Universidad de Buenos Aires) - Alicia's talk slides
- Jonathan Hauenstein (University of Notre Dame)- Jon's talk slides
- Hal Schenck (Iowa State University)
- Jessica Sidman (Mount Holyoke College)- Jessica's talk slides

Abstracts of additional talks

Poster session abstracts

File describing the examples from Jon's Bertini demonstration

Files for Jon's examples

Jose's code

Margaret's slides

Dani's slides

David Cox Lecture 1: Elimination Theory in the 18th and 19th Centuries

David Cox Lecture 2: Elimination Theory in the 20th Century

Carlos D'Andrea: Elimination Theory in the 21st century

David Cox Lecture 3: Numerical Polynomials via Linear Algebra

David Cox Lecture 4: Homotopy Continuation and Applications

Jon Hauenstein: Applications of Sampling in Numerical Algebraic Geometry

David Cox Lecture 5: Geometric Modeling: Geometry

David Cox Lecture 6: Geometric Modeling: Algebra

Hal Schenck: Rees algebras, syzygies, and computational geometry

David Cox Lecture 7: Geometry of Rigidity

David Cox Lecture 8: Combinatorics of Rigidity

Jessica Sidman: Polynomial methods and rigidity theory

David Cox Lecture 9: The Classical Theory of Chemical Reactions

David Cox Lecture 10: Toric Dynamical Systems

Alicia Dickenstein: Algebraic methods for the study of biochemical reaction networks

The conference is supported by a grant from the National Science Foundation (DMS-1741730), by the TCU College of Science and Engineering, and by the TCU Department of Mathematics. Financial support is available to help defer the travel and living expenses of some participants. Such support can be requested on the registration form. Requests for support must be received by April 15 to be given full consideration, and funding decisions will be announced by May 1. Graduate students, recent PhDs, and members of underrepresented groups in mathematics are especially encouraged to apply.

José Carrión

Greg Friedman

Eric Hanson

Scott Nollet

Efton Park

Contact Greg Friedman (send email) if you have questions about the conference or comments on this web site.