Maurice Rojas (Texas A&M University)

Abstract

Growing up, we learn about certain simple equations we can solve or understand within class time, e.g., small linear systems and conic sections. However, there is a whole family of high degree equations which are just as easy to handle. The key is to make use of tropical geometry and to know a little real algebraic geometry.

We'll introduce some of these tropical methods for looking at real zero sets. In particular, we'll see dramatic speed-ups of some older algorithms for counting connected components of real zero sets. We'll also see an unusual connection to the abc-Conjecture.

We assume no background in algebraic geometry.