Abstract:
Phylogenetic trees are models for evolution of species on macro or
micro (genetic) level in biology. A tree is, like in graph theory, a
connected graph without loops.
Together with species data for each node and matrices on each edge
that describe the change in data between the species, the tree form a
phylogenetic model. The tree has a finite set of leaves, the nodes with
only one incident edge.
To find a model that best fits a give set of species data at the leaves
is a basic problem in phylogeny. Which tree, and which matrices?
I will present an algebraic geometric approach to this problem, when the
matrix elements are random variables.