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Despite the remarkable unity of the basic components of the living world (DNA, RNA, the genetic code), we are probably still not aware of the diversity of genome structures nor of the diversity of means genomes use to evolve. Rearrangements, gene transfers, duplications, hybridization, transposable elements, single nucleotide substitutions, repetitions, insertions, deletions, have been successively discovered and modeled in the XXth century. They are used to document the evolutionary history of life on earth and to understand adaptation processes. Indeed, by comparing complete or partial genomes it is possible to infer a great amount of new biological information concerning gene function, evolutionary relationship between species, ancestral genome organization, mechanisms of evolution and variation in rearrangement, duplication and loss rates among the different branches of a tree. This has important consequences such as variations on the genetic and physiological specificities of species, with far-reaching applications ranging from evolutionary theory right through to drug discovery and personal medicine.

Each problem, each type of mutation, has its own model and set of algorithmic and statistical tools to accurately predict the deep past of our molecules. The research activity around the mathematics and computer science of molecular evolution, thanks to high impact researchers, has reached a certain maturity. It is able to handle most of the known mutations in various kingdoms of life, with a common background of mathematical, combinatorial, probabilistic, statistical, optimization and algorithmic problems. Yet challenges are still overwhelmingly more numerous than accomplishments. There is still place for pioneering work: integrative models, mixing single nucleotide substitutions and rearrangements, are still almost non-existent ; models are often too simple and unrealistic to yield trustworthy biological hypotheses ; new data generated by next generation sequencing hides a quantity of information which is probably more abundant than what we can use ; regularly the sequencing of new species increases the modes of organization and evolution we know and we have to model. The goal of this conference will be to discuss about future directions and goals in light of past accomplishments.