NSE's official site http://web.mit.edu/nse/education/grad/phd.html contains the most up-to-date information concerning curriculum and exams.

Core requirement ("the modules"):

Pass the modules with satisfactory grades. Refer to the "Threshold Requirements for Undertaking Doctoral Research" session of the above link for details about the GPA requirement.

Oral exam:

Reference: http://web.mit.edu/nse/pdf/education/Procedures_for_the_Oral_Exam.pdf

• Starting 2015 offered twice a year (beginning of Feb, end of May). In 2014 oral exams were scheduled Feb 3-12, 2014.
• Roughly one hour for answering the 1st question (prepared question), another hour for the 2nd (mandatory question).