Quasi-isometries and two-dimensional Artin groups

The talk is based on a joint work with Jingyin Huang (Ohio State U.). We show that many two-dimensional Artin groups are strongly rigid - any self quasi-isometry is close to an automorphism. In contrast, none of right-angled Artin groups have this property. The proof goes by equipping two-dimensional Artin groups with a combinatorial nonpositive-curvature-like structure - metric systolicity - and then analysing the structure of quasi-flats.