This is a discussion of my research interests, as they have been and are currently. It's meant to be read with a copy of my c.v. handy, or better yet copies of my papers. It was written for anyone who wants to understand a bit more what this particular mathematician considers important, either as a basis for discussion, argument, or for some other reason. It is intensely personal, and should not be taken as criticism of the way any other mathematician works.
And if any of this sounds like bragging, well, I've tried not to. But I'm proud of some of the things I've done, and I hope that the correct sense comes through. Bear in mind also that much of the work I talk about below was collaborative, and part of my pride is that I took proper advantage of the chance to work with such good people.