Growth rate of braid groups

I will explain how to apply a braid version of celebrated Tait conjectures to estimate the growth rate of braid groups with respect to the Artin generators. Also, I will present some techniques to find the crossing number of a braid. At the end of the talk, we will discuss relations between the growth rate and Stallings' conjecture. This is joint work with Geidar Mamedov, https://arxiv.org/abs/1905.03210.