Marc Hellmuth: Exploring 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 \(t(\operatorname{lca}(x,y))\) 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.