Not sure how to tag this one so feel free to edit and add tags.
When I initially started graduate school my choice for an area of study was quite nebulous. I had only figured out enough to know that I wanted to do some work involving a lot of category theory. So when I applied to schools I figured I could find some interesting topic to work on since almost anything involves category theory. Now I'm a bit more mature and I have a much better perspective and a much better idea of what I would like to do. My question then is how do I go about finding an adviser working in an area I would like to specialize in and if this person is not at my current school what are my possible courses of action?
Best Answer
I strongly recommend finding a good advisor (someone who you get along with, who has compatible understanding of how hands-on the advisor will be, who will keep you funded, who can get you a postdoc, who actually wants a student etc.) over choosing a particular subfield. There's too little correlation between what you learn about a subject as a starting graduate student and what it's like to do research in that field for you to make decisions on that basis. That said, it's reasonable to narrow your search to broad fields (say "I want to do algebra") because that still allows a huge range of subfields to work in. As long as your tastes are reasonably broad (and if they're not you should work on broadening them) you and your advisor should be able to find something that interests you both for you to work on no matter what your advisor's particular speciality.