### Abstract

In the first talk Pillay will discuss various notions of "connected component" for definable groups in arbitrary structures, formulate p-adic versions of the conjectures relating definably compact groups in o-minimal structures to compact Lie groups, and discuss other "good" theories of genericity which generalize stable group theory. In the second talk Onshuus will consider the case of definably compact groups definable in ordered vector spaces over ordered division rings . In the third talk, Onshuus will consider the case of definably compact groups definable in a p-adically closed field K and defined over Q_p. In the fourth talk Pillay will consider the case of elliptic curves defined over a p-adically closed field.