Study of problems on discrete groups by geometric methods

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We proved that Gromov's group containing quasi-isometric image of expanders has fixed-point property for a large class of CAT(0) spaces. In relation to the possible geometric proof of the Margulis superrigidity theorem, we studied a certain geometric invariant of the 2-dimensional Euclidean building associated to PGL(3,Q_p). In the case p=2, we made progress on the related deformation problem of polyhedral. Motivated by a certain rigidity problem on discrete groups, we studied conformal-geometric structures such as strongly pseudoconvex CR structures and quaternionic CR structures, and obtained some results.