A quasiflat in a metric space is a quasiisometric embedding of R^n. In situations that are "thick enough", such as buildings, many right-angled Artin groups, and mapping class groups, understanding the structure of quasiflats is an important ingredient in establishing rigidity results for quasiisometries. Conversely, quasiflats can also be used to show that some groups are "too thick" to be, say, cocompactly cubulated.
 
In this talk I will discuss ongoing work with Thomas Haettel and Nima Hoda, in which we prove a quasiflats theorem for the class of hyperconvex (or injective) metric spaces