Mathematical modeling of spatial evolution with applications to cancer

Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in life sciences. In this talk I will discuss how spatial interactions may change the laws of evolution, giving rise to a system of scaling laws that describe the growth of disadvantageous, neutral, and advantageous mutants in growing populations. Applications of these laws to bacterial growth and carcinogenesis will be discussed.