Speaker: Anders Jensen (Aarhus)

Title: Sampling a tropical variety

Abstract: The tropical variety of a polynomial ideal I is (the support of) a d-dimensional polyhedral fan. We discuss the problem of finding a non-zero vector in this fan, given I. In other words, we seek a monomial-free initial ideal of I. For prime ideals this is an important problem, since finding a monomial-free initial ideal is the first step in computing the whole tropical variety of I by fan traversal. One algorithm already appeared in [Bogart, J.,Speyer, Sturmfels, Thomas]. This time however, our tools will be Groebner bases and projections combined with the new tropical curve algorithm by Chan and Maclagan and various characterisations of stable intersections of tropical varieties which will appear in a joint paper with Josephine Yu.