When and how to apply for a winter internship at the IIT IISC and IISER?

If you haven’t already worked with a research group or under a professor during your summertime, IISc would be a little difficult for you. 

There are a lot of professors and postdoctoral fellows who are enrolled in a subdiscipline at IISc. So any kind of internship will give you a little edge over others to be selected for winter internship. 

If you are a scholar at KVPY or INSPIRE or NIUS, you might have better chances but the statement of purpose matters as well. Usually, you will have to send a mail with your CV and the statement of purpose along with a list of courses that you have completed to any of the professors who are related to that sub-discipline. You must also remember to apply early in September and if it is feasible for you, you must decide on a topic, duration, accommodation before October.

IISER - For IISERs, it would be advisable to go for Mohali or Bhopal. The application process is quite similar. September end to October is considered to be the best time to decide on a date and duration.

IITs - a few of them conduct sponsored winter programs but there is no logic in going to an IIT to study theoretical mathematics. You can rather go to Kanpur and Powai and the application procedure for both of them is the same as above.

If you wish to pursue cryptology, cryptanalysis, economical models, number theory, ISI and CMI would be considered better when it comes to exposure and experience. For complex analysis, and astrostatistics, you can go to IMSc, ISI, IISc, and CMI. You can opt for mathematical biology at IISERs and IISc.