Intermediate Quasiflats

In the early 80s, Gromov initiated a far reaching program to study
groups as geometric objects.
He asks to identify an infinite group up to a natural geometric equivalence.
In my talk I will concentrate on Gromov's program in the realm of nonpositive curvature
and highlight the role of quasiflats, i.e. spaces/groups which are  equivalent to  Euclidean spaces.
I will present new structural results on quasiflats, explain their relevance to the classification
program and provide applications.

Part of the talk is based on joint work with Jingyin Huang and Bruce Kleiner.