Chomskys not in fashion at the moment; most modern students of linguistics have only been taught enough (often a caricature of what he actually wrote) to dismiss him out of hand, and get on with the Real Stuff advanced by Pinker or Halliday. I'd like to see Chomsky rehabilitated (!), but unless your supervisor is about 60 I doubt if they'll be keen.
An interesting source book on this subject is Bach and Harms (eds): Universals in Linguistic Theory. - not sure of the date, but it's probably before the '70s.
Student or Learner