Anna Erschler of the Institute for Advanced Study presents a research seminar talk on geometric group theory, addressing a question posed by Nowak about whether the Følner function of a group is always lossless with respect to its isodiametric function. She proves that for some groups it is not, and computes the asymptotics of the isodiametric function across several examples, including wreath products, Hall's nilpotent-by-abelian groups, and Lampshuffler groups. The talk connects this invariant to the control function governing a group's asymptotic dimension and to an invariant tied to the Universal Traveling Salesman Problem, showing equivalence for a broad class of groups with lossless Følner functions, including Brieussel-Zheng diagonal products built from expander graphs. Erschler closes by linking the isoperimetric problem to algebraic structure, showing that amenable groups of finite Assouad-Nagata dimension satisfy Shalom's property HFD and therefore cannot be simple or purely torsion, and she outlines open problems in the area.