Title: Coarse differentiation of quasi-isometries
and rigidity for solvable groups
Abstract: In the early 80's Gromov initiated a program to study finitely
generated groups up to quasi-isometry. This program was motivated by rigidity
properties of lattices in Lie groups. A lattice Γ in a group G is
a discrete subgroup where the quotient G/Γ has finite volume.
Gromov's own major theorem in this direction is a rigidity result for lattices
in nilpotent Lie groups.