Starting an REU late because of quarter system?
I was an undergraduate at an institution on the quarter system and the three math REUs that I attended allowed me and others in the same position to start late. In my experience, math REUs are very accomodating with these sorts of things. I also saw other students leave slightly early or travel somewhere in the middle of the program for a week for various reasons. You should inform whoever is running the REU about your situation once you are accepted to check if starting late will be OK, however. There are also several REUs that start reasonably late, maybe the first or second week of June, so that a student on the quarter system should not have to miss more than a week.