Speaker
Description
Following Benjamini-Schramm, a graph is called 'almost planar' if it can be drawn in the plane such that every edge crosses at most a bounded number of edges, and a finitely generated group is called an 'almost planar group' if its Cayley graphs are almost planar graphs. Despite being a relatively well-studied class, the only known examples of such groups are those which virtually admit a planar Cayley graph. Recently, it was conjectured by Georgakopoulos-Papasoglu that these are indeed the only examples, suggesting a robust rigidity result. In this talk, I will contextualise and report progress on this conjecture, settling it within the class of finitely presented groups. This talk is based on joint work with John Mackay and Davide Spriano.