Mathematics and Statistics Colloquium

Calvin University

Emma Schmidt
Notre Dame

February 26, 2026
3:05pm   •   North Hall 276

Real Numerical Algebraic Geometry and Kinematics

Algebraic geometry involves studying the solution sets of polynomial equations. Our goal is to numerically compute the solutions to a given polynomial system, often focusing on computing the real solutions. With the help of a path-tracking tool called homotopy continuation, we can study the structure of the real solutions and the “cells” or components that they form. Analyzing permutations of solutions gives us further insight into the structure of the real solution set. Applications will be given in robotics and kinematics, investigating how solutions to various robotic mechanisms interact with each other.