I am unable to work with you if you are a student and not a student from IITB. However,
see this page (updated around September of the year). This is a scheme designed for many people who are students, and not from IITB.
Even better, please take the IIT entrance exams (e.g. JEE, GATE, Ph.D) or whatever it takes to join IITB. It's not as difficult as you think!
If you are a Ph.D student from elsewhere, I'll be happy to talk to you in person (i.e., not via email).