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Motivated by Gromov's program on the quasi-isometry classification of infinite groups, we will introduce a higher dimensional analog of Morse quasigeodesics, so-called Morse quasiflats. Just like their one dimensional versions, they are characterized by large scale hyperbolic features, such as contraction and divergence properties. After the basic definitions, we will focus on structural results, including a Morse lemma and the uniqueness of
tangent cones at infinity.

This is based on joint work with Jingyin Huang and Bruce Kleiner.