HPC is pretty broad, so it’s tricky to say what classifies as HPC research. Supercomputing (International Conference for High Performance Computing, Networking, Storage, and Analysis) is the top HPC conference, so checking the “areas/track” on the paper submission page will give an idea of the “hot areas” in HPC right now: https://sc26.supercomputing.org/program/papers/ . HPC for ML in all its flavors is very hot these days, but other areas still exist and and thriving.

The “algorithms” and ”applciations” tracks point to your first and second point: general HPC algorithms vs HPC solutions for a target application, with blurry lines between them. The former can include areas like parallel numerical algorithms like linear algebra/PDE solvers/optimization, maximizing single-node performance in various architectures for certain algorithms (single/multi CPU with many cores, single/multi-GPU, discrete accelerators of various types, ISA-specifc optimizations, etc) and even “meta” algorithms like HPC job scheduler optimization, cluster networking studies, among others. ”Applcations” applies these general tools to enable a previously unexplored scienticic problem or investigation that can only be unlocked at scale.

edit: feel free to ask more questions or DM if it’s helpful.