Given that thirty years has elapsed, that you know they were once students there and have finished, I think it's stretching things to use the present perfect. I would simply ask What did you study? without any need for a time reference- the context of the meeting provides it all. Even outside the context of a reunion like that, I would still use the past tense if asking an older person about their studies.
Also, your first example with the recent graduates and their certificates would also be past tense to me.
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