I get emails from students from all over India (and occasionally from other parts of Asia) asking for summer projects. Bear in mind that I work in a teaching institution. So I clearly prefer to offer projects to students at IIT Madras. If you want to work with me, kindly become a student at IIT Madras — we offer the following degrees in Physics — 5 year Dual Degree (B.S. & M.S. in Physics), 4 year B. Tech. (Engineering Physics), 2 year M. Sc. (Physics) and a Ph. D. The Institute and Department websites provide a lot of detailed information about these courses. IIT Madras also has exchange programmes with several universities worldwide — you can check to see if your university has one with IITM and if yes, you are welcome to come over as an exchange student and then work with me. I therefore do not (typically) respond to most emails (if they make it past IITM's spam filter) regarding Summer Projects.
IITM has a small number of summer fellowships which you can also apply for. Click on the URL for the current year: Summer Fellowships at IITM. I am travelling during the current summer but some of my colleagues may be available. The deadline is typically in the last week of February.
I also run the Partitions Project which you are welcome to contribute to if there is something that suits your interest. You can work on this project from anywhere and your physical presence at IITM is not necessary.