Conference abstracts

Session S01 - Computational Algebra and Applications of Algebra

July 28, 18:30 ~ 18:55

## Numerically computing Galois groups

### Jose Rodriguez

### University of Chicago, USA - joisro@uchicago.edu

The Galois/monodromy group of a family of equations (or of a geometric problem) is a subtle invariant that encodes the structure of the solutions. In this talk, we will use numerical algebraic geometry to compute Galois groups. Our algorithm computes a witness set for the critical points of our family of equations. With this witness set, we use homotopy continuation to construct a generating set for the Galois group. Examples from optimization will be stated (maximum likelihood estimation and formation shape control).

Joint work with Jonathan Hauenstein (University of Notre Dame) and Frank Sottile (Texas A&M).