Geometry and Topology Seminar

The group G is residually finite if each nontrivial element g
lies outside some finite-index subgroup H of G.  It is natural to ask
what the minimum index of the subgroup H is, in terms of the length of g
(with respect to some word-metric on G).  The "residual finiteness
growth" of G records the answer to this question; bounds on residual
finiteness growth are known for several classes of groups.

I will define "virtually special" groups and discuss their residual
finiteness growths.  Specifically, I will describe a topological proof
that, if G is virtually special, then H can be chosen so that [G:H] is
bounded by a linear function of |g|.  Time permitting, I will also
discuss the more general issue of quantifying separability of
quasiconvex subgroups.  This is joint work with Khalid Bou-Rabee and
Priyam Patel.