Annalisa Conversano,Massey University

O-minimal structures have been introduced in the 80s to some extent with the goal of finding generalizations of model theoretic properties of stable theories to ordered structures. Later on, numerous important applications have been found also in several areas outside logic, like algebraic geometry and number theory. In this talk we will look at how geometric invariants of definable sets in o-minimal structures can be used to understand the structure of groups in several different categories.