Next year I'm going to college and would like to do undergraduate research in the second semester under the supervision of a certain professor, who I'll call Prof. M.
There are three points against me and three in my favor. They are the following
- Prof. M. works at another university, which is about 100 miles away from the one I'm going to. If he does accept to advise me, my plan is to travel to his university every week or every other week.
- I am worse than terrible when it comes to social aspects: I talk too fast, lack common sense, and I feel horribly nervous when talking to other people (specially people I don't know), often leading to awkward behavior for not knowing how to act.
- Prof. M. is a (local) bigshot. (I'm assuming he might be more selective because of this)
- I have self-studied math and physics more or less to have approximately the technical understanding a second year graduate student would have. Of course, while I know about e.g. locally ringed spaces or bosonic string theory (or insert buzzword here), I lack most of the skills and experience a real graduate student would have, such as being able to critically read research papers or having research experience. Also, this is a self-assessment, thus possibly a faulty one;
- The professor is welcoming and has a nice personality (I got this information from a friend that has a friend who was a phd student in the same university as Prof. M. and who talked to him personally);
- He has supervised* undergraduate students in the past (about five years ago);
- should I talk to Prof. M. personally or by email?
- should I mention a paper he wrote that I find particularly interesting and ask if he would accept advising me to do similar research?
In short, what is the best path to be taken here?
*Though all undergraduate students are from his university. See Professor Eldredge's comment below.