Suppose a student currently doing Ph.D in an institute wants to leave the institute and apply abroad for Ph.D. Should he/she mention the name of the institute he/she wants to leave? If the universities call the current PI, they will never get a positive feedback since the current institute will never want to lose their student. But the student wants to mention that he/she has work experience. What is to be done in this situation? Can the US universities reject the application based on the current PI's feedback in spite of the candidate having excellent grades and recommendations from previous PIs?