I am a recent PhD specializing in algebraic geometry. But I also want to do research in some other areas of math (e.g. quantum computation, compressed sensing, and PDE's). What would be a good way of learning these so that they can become a research interest?

I have very little background in physics. My plan/goal is to begin research in one of these areas by next February. I do not want to be limited in the areas in which I do my research (e.g. only doing research in algebraic geometry).