Explore a 50-minute lecture on the Fredrickson-Andersen $2$-spin facilitated model (FA-$2$f) on $\mathbb Z^d$, a key interacting particle system with kinetic constraints exhibiting cooperative and glassy dynamics. Delve into sharp results for the first time, $\tau$, at which the origin is emptied for the stationary process when the density of empty sites is small. Examine the dominant relaxation mechanism, proof techniques, and additional results for more general kinetic constraints models, including full universality results in two dimensions. Learn about the model's behavior in dimensions $d\geq 2$ and its relationship to the threshold constant for $2$-neighbour bootstrap percolation on $\mathbb Z^d$. Gain insights from this joint work presented by Cristina Toninelli from CNRS & Université Paris Dauphine – PSL at the Institut des Hautes Etudes Scientifiques (IHES).