## Geometry Seminar

**Date:** November 18, 2019

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Elise Walker, Texas A&M University

**Title:** *Toric degenerations and optimal homotopies from finite Khovanskii bases*

**Abstract:** Homotopies are useful numerical methods for solving systems of polynomial equations. I will present such a homotopy method using Khovanskii bases. Finite Khovanskii bases provide a flat degeneration to a toric variety, which consequentially gives a homotopy. The polyhedral homotopy, which is implemented in PHCPack, can be used to solve for points on a general linear section of this toric variety. These points can then be traced via the Khovanskii homotopy to points on a general linear slice of the original variety. This is joint work with Michael Burr and Frank Sottile.