Seminar

We will discuss the relation between tropical Grassmannians and phylogenetic trees. One of the main problems in evolutionary biology is that of reconstructing a phylogenetic tree from a DNA sequence alignment of n species. This process is considerably simpli?ed if we adopt the distance based approach.
In order to really make this approach fruitful, we need to understand dissimilarity vectors of trees, which leads to the still unsolved problem of characterizing generalized m-dissimilarity vectors of n-trees. It turns out there is a natural relation between these vectors and the corresponding tropical Grassmannian G _{m,n}, and this opens the door to tropical geometry as a possible tool to solve the characterization problem. We will show what the precise relation between these two sets is and we will comment on the important open problems that are left to be solved.