Ido Grayevsky

A continuum of Pairwise Non-Quasiisometric Solvable Lie Groups in Dimension 5

This talk will focus on the large scale geometry of solvable Lie groups. I will present a new method that allows one to distinguish between some quasiisometry classes of solvable Lie groups: the examples mentioned in the title are obtained by this method.
Quasiisometries are maps between metric spaces which coarsely preserve the metric. They are fundamental to geometric group theory. In particular, classifying groups up to QI classes is a prominent motivation in the field. Notably, in the class of solvable Lie groups such classification is still wide open, and seemingly still out of reach.
I have a couple of goals: first, I would like to present some of the structure theory of solvable Lie groups. This will give me a chance to play with Lie brackets on the board. In particular, I will highlight the importance of sublinear distortions to the geometry of these groups.
The second goal is to present a weaker version of quasiisometries, called sublinear biLipschitz equivalence, which capture such sublinear distortions. Our method to distinguish QI classes relies on these maps.
Joint with Gabriel Pallier (Lille)