Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry. One note on expectations - each of the domains you men

Great suggestions. I would add that Calculus on Manifolds might be sufficient for differential geometry. One note on expectations - each of the domains you mentioned is typically an upper level undergraduate course (except for the first three). These courses usually progress at a rate of maybe 10 - 15 pages per week (~200 pages of a textbook covered in 16 weeks). It's genuinely hard to absorb this material in that amount of time, and unless you're exceptionally capable you should assume it will take you even longer under self-study. If you proceed with doing this, make sure you work through at least a few of the exercises at the end of each chapter of each book, and try to compare your solutions against solutions you find online. This is not to discourage anyone - studying all of this will probably be very rewarding! It's just a lot of work. It takes a massive amount of effort to get to the point where you can understand all the prerequisites needed to follow a research paper in modern math or physics.