Strong shortcut groups and asymptotic cones
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The study of discrete groups acting nicely on spaces satisfying various nonpositive curvature conditions is an active area of research in geometric group theory. Diverse families of groups have been studied in this context, including CAT(0) groups, cubical groups, hierarchically hyperbolic groups, Helly groups, systolic groups, quadric groups, etc. In this talk I will discuss the strong shortcut property, a weak nonpositive curvature condition of rough geodesic metric spaces that unifies all of these families of groups and which also includes the Heisenberg group. I will discuss group theoretic consequences of nice actions on strong shortcut spaces and I will give an asymptotic cone characterization of the strong shortcut property.