I recently finished applying to several Ph.D. programs in Computer Science, and as part of the application process I had to select one or two subfields of CS that I was interested in. For many of them I selected specialties like Artificial Intelligence and Machine Learning, and I've already started receiving emails from professors in those fields who would be interested in advising me.
My statements of purpose mentioned that I was "particularly interested" in AI and Machine Learning, and whenever possible I checked those boxes on the application forms. However, I'm also interested in other specialties (e.g. Theory), and although my statements of purpose do mention that I have varied interests in CS, I never specifically selected Theory as one of my desired specialties.
Have I painted myself into a corner here? If I'm accepted to a Ph.D. program in Computer Science and I selected specialty X on my application, can I still conduct research in specialty Y?