On the Morgan-Shalen compactification of the SL(2,C) character varieties   of surface groups
  A gauge theoretic description of the Morgan-Shalen compactification of the $\SL$ character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space of Higgs bundles via the Hitchin map. 
Georgios Daskalopoulos (Brown Univ.), Stamatis Dostoglou (Univ.   Missouri), Richard Wentworth (UC-Irvine)