Logic Colloquium 12 de Março 2009, 18h00 Abstract: Starting with the work of Pillay (1988) the main line of research on definable groups has been guided by the analogy with real Lie groups. However there are also some striking differences: the correspondence between Lie groups and Lie algebras works well in the simple and semisimple case, but fails in the abelian case. To remedy this, there have been two lines of attack in the study of definable groups. One through the study of generic subsets, a kind of substitute for the Haar measure, the other through the study of the Euler characteristic and other homotopy invariants of a definable group. The two lines of research are highly intertwined and advances in each side have been possible through the advances on the other side. I will give an overwiew of the work of several authors on these topics and if time permits I will present some new results in collaboration with M. Mamino and M. Otero. The prerequisites will be kept to a minimum. | back |