Arman Darbinyan

A quasi-isometrically diverse class of bi-orderable solvable and residually finite groups via Taut Dehn spectra

In my talk, I will discuss a new invariant, which we call Taut Dehn Spectra, that allows geometric differentiation of finitely generated groups in terms of quasi-isometry. This invariant is a generalization of several previously known quasi-isometry invariants and allows one to construct previously unknown geometrically robust classes of groups. In particular, we will discuss a construction of an uncountable class of pairwise non-quasi-isometric groups that are two-generated, solvable of derived length 3, bi-orderable, and residually finite. In particular, this provides the first example of quasi-isometrically diverse class of bi-orderable groups, and, in addition, recovers or strengthens several known results in this direction that will also be reviewed