Pure Maths Colloquium: David Evans

An omega-categorical structure \(M\) is a countably-infinite first-order structure (such as a graph) whose automorphism group \(G\) has finitely many orbits on \(M^n\), for all finite \(n\). Such structures can arise as limits of classes of finite structures in various ways. We are interested in \(G\)-invariant, finitely-additive probability measures on the definable subsets of \(M\) (or \(M^n\)). The questions we are looking at are partly motivated by questions of Elwes and Macpherson on MS-measurability of omega-categorical structures. In this talk I will focus on some tools from representation theory (work of Tsankov and Jahel-Tsankov) and applications of these by my PhD student Paolo Marimon to proving non-existence of invariant measures on certain `sparse’ graphs which are key examples in the questions of Elwes and Macpherson.