Data and Algebra Seminar

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 statistics, optimization, and reconstruction of 3D scenes from images.

 The talk will be on zoom (utexas.zoom.us/j/82662989237).