Subconvex bounds in higher rank in horizontal aspects

We'll describe some of the main ideas from the papers https://arxiv.org/abs/2309.06314 [4] and https://arxiv.org/abs/2503.12310 [5] (joint with Yueke Hu), which establish subconvex bounds on GL(n) in some new aspects, emphasizing cases where the set of ramifies places varies.  We'll indicate the challenges in extending these methods further (e.g., to the case of prime conductor twists), which would require estimates for certain bilinear forms in character sums.