We'll describe some of the main ideas from the papers https://arxiv.org/abs/2309.06314 and https://arxiv.org/abs/2503.12310 (joint with Yueke Hu), which establish subconvex bounds on GL(n) in some new aspects.  We'll begin by illustrating, in the setting of general linear groups over finite fields, how the methods developed in our earlier work with Venkatesh https://arxiv.org/abs/1805.07750 give rise to useful test vectors for the integral representations of L-functions furnished by known cases of the Ichino--Ikeda conjecture.  We'll then discuss the geometric problems that arise when averaging this integral representation in an amplified relative trace formula, possibly over a non-compact quotient.