No! You are certainly welcome to dig into an aspect of your current field of study, but you should also feel free to use this time to pursue opportunities in other fields; some of our greatest success stories have been from students who tried something different!
Yes, you need at least one sponsor, but you are not limited to only one. You may mention in your application that you intend to have a second faculty sponsor. The main faculty sponsor must be a permanent Columbia University faculty member.
