thanks for all the positive and encouraging comments. I'm indeed lucky to have gotten in. I should also correct myself in saying I can get into any school I want -- that's nonsense -- at best, I have a reasonable shot.
I am at a top institution in my country, not the UK, in a strong math program. If I stayed for my master's, I would be doing specific research with a specific person who is known in his field -- though how well-known, I don't know. The purpose of this would be specifically to get a publication.
For those wanting to know about my profile, here it is:
I had low subject GRE (740 math) [I was sick the two weeks before and was on antibiotics during the exam], which I've been told kept me out of a lot of schools.
I have no putnam, no competitions. I've never been into that stuff.
On the other hand, I have a near-perfect GPA, started taking grad courses in geometry and topology in my second year, three scholarships which cover my tuition, have spoken at several conferences, and have written two articles for undergrad magazines. I have a joint publication in preparation and I've written about a dozen small documents on various topics ranging from compact operators on hilbert spaces, to harmonic function theory, to spectral theory and Riemannian manifolds. I also got a stipend to teach a few tutorials in measure theory for one of my supervisors' classes. I've worked at the school's math help centre for two years now and graded, lots of private tutoring.
I think what really did it was research experience. I've gotten two REU-type scholarships and I stuck with them, so about eight months of research at a time on a single project. Most importantly, I impressed a prof who got his PhD at Brown during my summer work: I worked consistently, independently, found my own resources / papers / books to read from, was always ready to present ideas, and from the 2 projects I have nearly 100 pages of personal work.
I've heard Brown is very good from everyone, but again I have to visit first. What are my options for talking to profs and checking their research?