Damian Osajda (Universitat Wien) Fixed point theorem for systolic complexes (Joint with Victor Chepoi from Marseille) We prove that any finite group acting on a (weakly) systolic (i.e. simplicially non-positively curved) complex fixes a point. This is a systolic counterpart of a similar CAT(0) result. As consequences we show the following results. A (weakly) systolic group contains only finitely many conjugacy classes of finite subgroups. A free product of systolic groups amalgamated over a finite group is systolic. (Weakly) Systolic complexes are classifying spaces for finite subgroups of (weakly) systolic groups.