I will present a recent proof, by Kaluba, Nowak, and myself, of the fact that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n>4$. I will discuss how the same strategy gives a new proof of property (T) for $\mathrm{SL}_n(\mathbb Z)$.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/9098