Mervyn Tong (University of Leeds) – Where does homogeneity come from?

Everyone loves a good decomposition. How can we break down a mathematical object — a graph, a group, or a function — efficiently into well-behaved (or regular) parts? And what conditions can we place on these objects to guarantee a higher degree of regularity, such as homogeneity? It turns out an excellent source of such conditions is model-theoretic dividing lines, that is, tameness properties of (first-order) structures. This is not a coincidence. In this talk, I will dive into the deep theory of these dividing lines in search of the source of homogeneity.