Genome rearrangements: from biological problems to combinatorial algorithms (and back)

Recent DNA sequencing projects revealed that some classical biological theories may be incomplete or even incorrect.
I describe three controversial and hotly debated topics: Whole Genome Duplications, Random Breakage Model of Chromosome Evolution, and Mammalian Phylogenomics, and three related challenging algorithmic problems: Genome Halving Problem, Breakpoint Re-Use Problem, and Ancestral Genome Reconstruction Problem.
I further describe the "Multi-Break Rearrangements" combinatorial framework to analyzing these biological problem that, led to efficient algorithmic solutions and provided new evolutionary insights. We use these algorithmic results to reveal the fragile regions in the human genome where chromosomal rearrangements are happening over and over again. We further illustrate how this recent discovery allows one to predict how the human genome may evolve in the future.
This is a joint work with Max Alekseyev.