Simon is Professor of Mathematical Genomics at the University of Oxford's Department of Statistics. His group’s research interests focus on the area of population genetics, specifically the use of stochastic models to understand patterns of variation in samples drawn from a population. Work is also ongoing on methods to map disease genes in admixed populations, and methods for fine-mapping association signals. He spends part of his time in the Department of Statistics, and part of his time at the Wellcome Trust Centre for Human Genetics (WTCHG).

His research spans population and evolutionary genetics, bioinformatics, stochastic methods, reproductive biology.