刘勍，南开大学数学科学学院

The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. That is, a quasi-isometry between two spaces induces a homeomorphism on their Morse boundaries. This homeomorphism satisfies a variety of metric properties including bi-h?lder, quasi-conformal, quasi-m?bius and power quasisymmetric. In this talk, we will give an introduction about Morse boundaries and investigate these structures on the Morse boundary which determine the interior space up to a quasi-isometry.