Title: Helly groups
A graph is Helly if every family of pairwise intersecting (combinatorial) balls has common intersection. Groups acting geometrically - that is, properly and cocompactly - on Helly graphs are themselves called Helly. Such graphs and groups possess various non-positive-curvature-like features. Moreover, Helly graphs are closely related to injective metric spaces, whose behavior is very similar to CAT(0) spaces, and Helly groups act geometrically on injective metric spaces as well. In the talk I will overview main examples of Helly groups and their important properties.
The talk is based on works with Jeremie Chalopin, Victor Chepoi, Anthony Genevois, Hiroshi Hirai, and Jingyin Huang.