Abstract: A rationality property of an algebraic object is a property that is valid over the field of definition of that object. For example, given a variety over the field of reals, when does it have a real point? A similar problem: given a homogeneous polynomial over a field, when does it have a non-trivial zero defined over that field?

In this talk, we will explain informally what one means by a rationality property for an algebraic group. We will illustrate the notion with examples and mention some of the tools one uses to study these.