In an ideal scenario, I’d like to do my (computer science) PhD at university U. I completely lack the credentials, and my MS work is in one of those areas where ~10 people in the world are capable of understanding/appreciating it (and it won’t be published anytime soon). Fortunately, one of those people is Professor X (they contacted me unexpectedly saying that they liked my work, having evidently seen my code-in-progress). Great, right?
Unfortunately, I don’t want to work with Professor X, I want to work with Professor Y, because I want to switch to a completely different field of CS. I have nothing against X or our field, I’ve just gotten really interested in Y’s field, and Y is arguably the best person in the world study under for these interests. So while I feel quite confident that I do want to make this switch, the fact is that currently I don’t have anything to “show” Y (in terms of credentials or research in their field).
Do I have any good angle here?