Phylogenetic Algebraic Geometry

Many widely used statistical models of evolution are algebraic varieties, that is, solutions sets of polynomial equations. We discuss this algebraic representation and its implications for the construction of maximum likelihood trees in phylogenetics. The ensuing interaction between combinatorial algebraic geometry and computational biology works as a two-way street: biologists may be benefit from new mathematical tools, while mathematicians will find a rich source of open problems concerning objects reminiscent of objects familiar from classical projective geometry.