Department of Mathematical Sciences
Jonathan Hauenstein, University of Notre Dame
Friday, April 10th, 2026
11:00AM-11:50AM
Stratton Hall 202
Speaker: Jonathan Hauenstein, University of Notre Dame
Title: Numerically Solving Polynomial Equations 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. This talk will highlight algorithms for numerically computing and representing solutions to systems of polynomial equations, collectively called numerical algebraic geometry. Since the physically-meaningful solutions in most applications are real, recent developments in real numerical algebraic geometry will be discussed and demonstrated on several applications in science and engineering.