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Quasi-isometric rigidity of warped cones and expanders

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Thang Nguyen (NYU)

Warped cone was defined by Roe, and can be used to get an geometric object that carries the information of the action of a group. In the case of actions with spectral gap, we obtain a family of expanders from this construction. We are looking for situations where coarse geometry of warped cone and expanders determines the action. In the talk, I will explain the construction warped cones, expanders together with ideas why we get rigidity results when the spaces that groups acting on are nice enough. Joint work with David Fisher and Wouter van Limbeek.