Dehn functions of Solvable Lie groups

In the 2010s, Cornulier and Tessera presented an algorithm deciding whether a Lie group has exponential or polynomially bounded Dehn function. I will discuss the highlights of their work, and then focus on the following question: in case the Dehn function is polynomially bounded, what is the degree of the bounding polynomials? The heart of the matter in this context is the geometric relation between a (completely) solvable group and its largest nilpotent quotient. I will outline the basics of this geometry, and present a new method that exploits it to give (in some cases) better bounds on the degree of the bounding polynomials.

Joint with Gabriel Pallier.