I will present the proof that $Aut(F_n)$, the automorphism group of the
free group $F_n$ on $n$ generators, has Kazhdan's property (T) for $n$ at
least 6. This is joint work with Marek Kaluba and Dawid Kielak
(https://arxiv.org/abs/1812.03456).
The case $n=5$ was settled earlier in joint work with Marek Kaluba and
Taka Ozawa (https://arxiv.org/abs/1712.07167).