Phylogenetic combinatorics: A mathematical theory for the analysis of phylogenetic trees and networks

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According to Charles Darwin's theory of evolution, the present day species can be related by an evolutionary tree, much in the same way as members of a family can be related by a family tree. One of the central problems in biology is to work out what this tree is (or, usually small parts of this tree), since this can be helpful, for example, in understanding how organisms work. The flourishing area of phylogenetics is concerned with solving this problem. However, since it is by no means an easy problem, advanced mathematical theories are required to help discover its solution. The main aim of this project is to investigate and develop such mathematical theories. We expect that these theories will not only enable biologists to better understand their data, but that they will almost certainly lead to new research directions in pure mathematics, much in the same way that physics inspired new mathematics in the 20th century.