Leonid Potyagailo: Quasiconvexity in relatively hyperbolic groups

This is a joint work with V. Gerasimov (Belo Horisonte, Brasil). We study the notion of (relative) quasiconvexity of subgroups of relatively hyperbolic groups (i.e. groups possessing a geometrically finite action by homeomorphisms on a compactum). I will state several metric and topological conditions equivalent to different types of quasiconvexity. Some applications of these results will be given.