We present a brilliant proof due to Matomäki-Radziwiłł of the asymptotic behaviour of Liouville function in short intervals. We also sketch a proof of a more general result concerning a similar problem for a real-valued multiplicative function.
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/7671