Marc Hellmuth: Symbolic Ultrametrics and Beyond

Abstract

In this talk, we provide a brief introduction to symbolic ultrametrics, a concept pioneered by Andreas Dress and Sebastian Böcker in the late 1990s. Symbolic ultrametrics extend the idea of traditional metrics by using symbols instead of real-valued numbers. Similar to ultrametrics, one may ask whether there exists a dated or labeled tree (T,t) such that the label t(lca(xy)) of the least common ancestor of two leaves x and y coincides with the symbol d(x,y) determined by the underlying symbolic map d.

We will discuss how this work laid the foundation for a deeper understanding of orthologous genes. Additionally, we will explore characterizations and generalizations of symbolic ultrametrics.