Title:     Numerical Methods for Solving Polynomial Systems

Speaker:     Dr. Dan Bates, United States Naval Academy.

Abstract:     Polynomial systems show up all over the place, both within mathematics (especially algebraic geometry) and in other STEM disciplines (including with chemical reaction networks, kinematics, and more).  We even encounter them in multivariable calculus when we seek to find critical points.  While there have been symbolic, algebraic methods for solving polynomial systems since the 1960s, an entirely different numerical, geometric approach has been developed since the 1990s.  This approach has allowed users to solve significantly larger polynomial systems at the cost of moving from exact solutions to approximations.  In this talk, we'll go through some of the basic ideas of the field of numerical algebraic geometry (e.g., homotopies, witness sets), tour some of its greatest hits, and end up with a couple of open problems.  No prior knowledge of algebraic geometry or numerical methods will be necessary.