In (analytic) number theory Paul Nelson's recent preprint (https://arxiv.org/abs/2109.15230) solved the subconvexity problem for a huge class of L-functions in the t-aspect.

More precisely subconvexity bounds for $L(\frac{1}{2}+it, \pi, St)$ are established for cuspidal automorphic representations of $GL_n$. 

This is a huge breakthrough and also the methods are very exciting and promising.