Tropical Geometry, Tree Metrics and Phylogenetics

Abstract: Tropical geometry is a relatively young field in the intersection of algebra, geometry and combinatorics. It studies logarithmic deformations of algebraic and geometric objects through the lens of piecewise linear and polyhedral geometry. Many objects of interest give rise to fascinating combinatorics which can be used to study the originals and viceversa. In this talk I want to give a mild introduction to tropical geometry and focus on the example of the tropical Grassmannian, which is controlled by the combinatorics of tree metrics and is related to the study of phylogenetics.