Geometry Seminar

Date: May 1, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Jeff Sommars, Univ. of Illinois at Chicago

Title: Algorithms for Computing Tropical Prevarieties

Abstract: The computation of the tropical prevariety is the first step in the application of polyhedral methods to compute positive dimensional solution sets of polynomial systems. In particular, pretropisms are candidate leading exponents for the power series developments of the solutions. The computation of the power series may start as soon as one pretropism is available, so the parallel computation of the tropical prevariety has an application in a pipelined solver. I’ll present a parallel work-stealing implementation of a new algorithm to compute tropical prevarieties. This new software has made the first computation of the tropical prevariety of the cyclic 16-roots problem. I’ll also report on computational experiments of the n-body and n-vortex problems, as well as a tropical problem.