Abstract: To each finitely generated group G, we associate a quasi-isometric invariant called the Dehn spectrum of G. This is the generalization of the Dehn function to the class of finitely generated, but not necessarily finitely presented groups. The invariant allows us to show that there exist uncountably many pairwise non-quasi-isometric finitely generated groups of finite exponent. We will discuss examples and properties of the Dehn spectrum, its relation to the Dehn function, and key points of the proof of the uncountability of quasi-isometry classes of Burnside groups. The talk is based on joint work with Denis Osin.