Timothy Duff: Galois Width in Applied Algebraic Geometry

Abstract.

The Galois/monodromy group is an important invariant that can be attached to a generically zero-dimensional parametric family of polynomial systems over the complex numbers. Informally, one might feel this group controls the "complexity" of solving individual members in that family. I will recall some basic definitions before introducing a theory which provides one approach to sharpening this feeling of "complexity", utilizing an invariant I have called Galois width. Throughout the talk, I will discuss examples from computer vision and optimization which demonstrate the practicality of this theory.