Talk page
Title:
Thinness as a generic property
Speaker:
Abstract:
Are most finitely generated groups thin or arithmetic? While philosophic in nature,
this question is a natural one to ask in light of the recent surge of interest in thin
groups in the number -theoretic context. In this talk, we discuss a result joint with Rivin
which says that the generic finitely generated subgroup of SLn(Z) is thin in some sense.
The proof of this result hinges on showing that the generic such group is free, from which
thinness follows almost immediately. A key ingredient is a geometric certificate for freeness
provided by Breuillard-Gelander, and we will discuss what this certificate is and why it holds
generically.
Link: