Helen Barton Lecture

Professor Jonathan Hauenstein, University of Notre Dame

Title: Real Numerical Algebraic Geometry and Applications

Abstract: Nonlinear polynomial equations naturally arise throughout mathematics, science, and engineering with their solutions describing various phenomena including the motion of a mechanical linkage such as a robotic arm and steady states of a dynamical system arising from a biochemical reaction network.  Polynomials are central to some of the deepest mathematics and have been studied for millennia.  The advent of modern computers has ushered in a new wave of algorithms for computing solution sets to systems of polynomial equations, both from an algebraic and geometric perspective.  Since the physically-meaningful solutions in most applications are real, this talk will highlight recent developments for numerical computing and representing real solutions to systems of polynomial equations, collectively called real numerical algebraic geometry, along with demonstrating them on several applications in science and engineering.