Some notions of smallness in Polish groups

In this talk we discusss some notions of small sets in Polish groups. We give some examples and applications of these notions in analysis and group theory. Moreover, we introduce a new notion of smallness which we call Haar meager sets. This notion coincides with the meager sets in locally compact groups. However, it is strictly stronger in the setting of nonlocally compact groups. We argue that this is the right topological analogue of Christian's Haar null sets. The speaker gratefully acknowledges the support of the LMS under a Scheme 2 Grant.