The 1-dim groups definable in o-minimal structures has been well understood.
For example, Adam W. Strzebonski proved that every definably connected 1-dim
group definable in the field of reals is either isomorphic to (R, +) or isomorphic
to S^1 . However, up to now, there have been very few analogous results for p-adic
context. The main idea of this talk is to classify the 1-dim definably amenable
groups by using new results of Acosta, Montenegro, Onshuus and Simon.