Title:  Crossing numbers for tropical curves

Abstract:  In tropical geometry, curves have both an intrinic side, as metric graphs and an embedded representation in terms of so-called balanced polyhedral complexes. I will discuss the relationship between these two representations. Since most curves can't be embedded in the plane, it is often useful to relax the embedding condition by allowing transverse crossings. A tropical crossing number for a metric graph is defined to be the fewest number of crossings in a planar immersion, and I will give some results on this crossing number.