I second this. I worked for several professors over 20 years as a software programmer at an ivy league college, mostly working alongside grad students. The gr

I second this. I worked for several professors over 20 years as a software programmer at an ivy league college, mostly working alongside grad students. The grad students had to fight to get to work on their own projects or do them in secret. Collaborating with someone without getting the approval of your advisor was often considered a betrayal and would get shut down as soon as discovered. If you weren't interested in the advisors projects they would not take you on. Post docs were treated even worse. This isn't true of all advisors, but many of them are like this because they are trying to build their own reputations using your work (their name goes on all your papers). If you really want to work on your own thing be up front about it; otherwise you'll spend the entire time doing things you're not interested in and which will define the kinds of jobs you can get afterwards.