Jason Behrstock

Title: Quasi-isometric classification of 3-manifold groups

Abstract: (Joint work with W. Neumann) Any finitely generated group
can be endowed with a metric which is unique up to maps of bounded
distortion (quasi-isometries).  A fundamental question is to classify
finitely generated groups up to quasi-isometry.  Considered from this
point of view, fundamental groups of 3-manifolds provide a rich source
of examples. Certain 3-manifolds are very robust in that the metric
structure of their fundamental group essentially encodes the
3-manifold.  Other families of 3-manifolds have fundamental groups
which all geometrically look the same.  We will survey the world of
3-manifold groups from classical results to the recent resolution of
some long standing questions.