Melody Chan
(UC Berkeley) Tropical ranks for symmetric matrices
ABSTRACT. We introduce and study three different notions of tropical rank
for symmetric and dissimilarity matrices in terms of minimal decompositions into rank 1 symmetric matrices, star tree
matrices, and tree matrices. Our results provide a close study of the tropical secant sets of certain nice tropical
varieties, including the tropical Grassmannian. In particular, we determine the dimension of each secant set, the convex
hull of the variety, and in most cases, the smallest secant set which is equal to the convex hull. Joint work with Dustin
Cartwright.