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In every dimension d, there are several infinite families of convex cocompact Coxeter groups of isometries of hyperbolic d-space: the superideal reflection groups. Danny Calegari of the University of Chicago shows that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of any such family, with overwhelming probability, June 25, 2014 at the Bill Thurston Legacy Conference.
The conference, "What's Next? The mathematical legacy of Bill Thurston," held at Cornell June 23-27, 2014, brought together mathematicians from a broad spectrum of areas to describe recent advances and explore future directions motivated by Thurston's transformative ideas.