I'd like someone to try a bunch of rocket fuels: check how easy synthesis is, measure cleanly the heat of formation, the density, the flash point and melting point and more, search for eutectics. From really easy (diazetidylcyclopropane, triazafarnesane) to difficult (dispiropentyl). I suggest a list in case you're interested, but it's not exactly what you asked.
Materials science: do you mean polymers, or alloys too? Because a third (!) study about alloy's galling would be really useful to mechanical engineers. You won't probably find a working theory about galling, but just more experimental data and a set of curves that show "no correlation with hardness, with pairing, but maybe with the atomic composition and with the oxide layer" would already be a progress, so you'll have something to show at the end.
Metals: in metallic form, as alloys, or any compound like catalysts? Hydrogen storage in shape memory alloys, magnetostrictive alloys and abnormally light alloys is worth a try. "Doesn't work" is just as acceptable an answer as "works" or "not interesting", so again you'll have something to tell at the end. It's a contribution to lower CO2 emissions too. Experiments with H2 under pressure are dangerous.
Vacuum insulation and electric contacts on aluminium wires look too difficult. Later maybe?
Deposit a metallic layer on lithium against corrosion in seawater, to make bathyscaphe floats. Not easy, a bit dangerous, result not guaranteed. It sound a bit exotic, but I believe it's the best possible float, and there is a real demand right now for deep-sea exploration. This can bring you to your future job.
Distill silver from recycled alloys. That would save energy over other processes, and the need exists. Needs refractory vessels. Here too, you should have something to tell at the end.
How much time do you have?