Computing amoebas using semidefinite programming

Jan Foniok

Abstract

An amoeba is a (logarithmic) real image of an algebraic variety generated by a complex polynomial. I will talk about an attempt to solve the following problem: Given a point in the Euclidean space, is it a member of an amoeba generated by a single Laurent polynomial? The attempt consists in using Laserre's method for approximating the minimum of a polynomial by semidefinite programming. I will show both this method and how it applies to the problem of amoeba membership problem. The approach works in the case of a linear amoeba, but the general case remains to be examined thoroughly. Based on joint work with Daniel Johansen and Thorsten Theobald.