# Pure Maths Colloquium: David Evans

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.

 Where: Physics Theatre C When: Nov 10 2022 @ 16.00 Video: Not recorded
 Speaker: David Evans Imperial College London Title: Invariant measures on omega-categorical structures

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.