Algebra versus regularity for group actions on one-manifolds

JOINT WITH SIMONS SEMESTER

I will survey some results concerning the algebraic structure of finitely generated groups which admit faithful actions on compact one-manifolds. I will concentrate on continuous, C^1 , and C^2 actions, and on the various algebraic restrictions imposed by regularity requirements. Of particular interest will be nilpotent groups, right-angled Artin groups, and mapping class groups of surface. Time permitting, I will indicate some recent progress.