People often think of Galois theory as a tool for showing the intractability of univariate polynomial equations. This talk presents the opposite perspective: how Galois theory can be used to analyze the unexpected tractability of highly structured systems of multivariate polynomial equations. Numerical monodromy heuristics based on homotopy continuation methods are a key tool, allowing in many cases the analysis of an appropriate Galois group. I will give an overview of these methods, how they motivate a proposed complexity measure for solving systems (the "Galois width"), and various applications where these methods are useful, such as reconstruction of 3D scenes from images.

About the speaker

Timothy Duff is an Assistant Professor in the Department of Mathematics at the University of Missouri. He is interested in applied/computational algebraic geometry and its applications to problems such as 3D reconstruction in computer vision.