**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.