Finally, after almost a year, my PhD diploma is in a proper frame and is hanging on the wall!
The frame came with some interesting mounting hardware. The plastic hangers have a pointy part on the wall side. Insert those into the key hole hangers on the frame side, put the frame up against the wall where you want to hang it, and press against the wall. The pointy part leaves a little dimple in the drywall right where the plastic hangers need to be nailed. Take the plastic hangers off the frame, nail it to the wall where the dimple is, and then hang the frame.
Pretty clever.
Now I have it hanging on the wall above my computer. Looks pretty good there.