Should I send a follow up email to a prospective PhD advisor? I was in contact with the professor in late September and had talked to home about applying to the school. I have since submitted an application. 
Should I send an email to touch base with him and let him know I look forward to hearing from him?
There is nothing wrong to write an email to inquire about your application status, but I will suggest first contact the admission office. Remember it varies from school to school that how much a supervisor can play a role in admission process.