|Location:||MSRI: Simons Auditorium|
Let G be a classical Schottky group of discrete isometries of the three dimensional Poincare upper half space, and let L= L(G) denote the limit set in the boundary, represented by the complex plane, say. We will discuss some results regarding Hausdorff dimension and the limit set. In particular, one defines the difference set D(L) to be the subset of the reals consisting of ||x-y||, where x,y are in L. We show that if L has Hausdorff dimension at least 1 then D(L) has Hausdorff dimension 1 (i.e., the "Falconer distance set conjecture" holds in this context).
This is joint work with Jonathan Fraser (Manchester, UK)