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Abstract: In this talk, I will introduce the ancestral recombination graph (ARG): a powerful way to encode the ancestry of a species through its DNA. ARGs have enabled us to simulate and study evolution on a massive scale, while also providing an extremely efficient method to compress human genomic data for further study. I will discuss how ARGs are used in modern genetic research, and how they might be generalised to handle more complex biology. Bio: My interest lies in developing mathematical and computational tools to address important problems in genetics. After completing a BSc at UCT on a variety of mathematical subjects, I proceeded to do my honours in applied maths, focusing on topological data analysis. I then transitioned into medical genetics with a research assistanceship and MSc in Bioinformatics at Stellenbosch University. I'm now in the 2nd year of my DPhil in Genomic Medicine and Statistics at Oxford University, in which I'm developing a new method to simulate genetic evolution.