Moon Duchin

 The discrete Heisenberg group H(Z) is the first example of a (non-virtually-abelian) nilpotent group, and it comes up all over mathematics.  Pansu's theorems about the asymptotic geometry of nilpotent groups give a powerful tool to study H(Z) geometrically, and with some work one can parlay large-scale information into "finer" results.  I'll discuss the growth function in H(Z) from a geometric point of view.  (including joint work with Christopher Mooney and with Mike Shapiro.)