None of these skills are actually required for any research. However, they will all make your BPO operations far easier and quicker, and are very worthwhile training if you intend to do a lot of research.
Science (1x) - reduces time required to copy a BPO by 5% per level
Advanced Industry (3x) - reduces all manufacturing and research times by 3% per level
Research (1x) - reduces time required for Time Efficiency research, by 5% per level
Metallurgy (3x) - reduces time required for Material Efficiency research, by 5% per level
Laboratory Operation (1x) - allows you to perform one additional research or copying job per level
Advanced Laboratory Operation (8x) - allows you to perform a further additional research or copying job per level
Scientific Networking (3x) - allows you to start research jobs at range, without needing to be in the same system of the BPO/facility.