What are some "hip" areas of mathematics? What are some new, hot, hip, fashionable areas of mathematics? What are some research areas that are a hotbed of research now or have some ripe, low hanging fruit? I am trying to broaden my mathematical horizons, so to say. I am in the process of applying for graduate schools & facing a mid-application crisis. I've always loved number theory and considered looking into programs with strong research focuses in it. However, being the "crown jewel" of mathematics, it seems like the very best, top notch mathematicians are the only ones who seem to cut it in the field. I consider myself a strong student, but I'm no harvard elite and probably not harvard material. After talking with some professors & mentors, I have the impression that who your advisor is, and how well known & accomplished they are greatly affects your chances of landing a post-doc, a professorship, etc... And I just don't know if I can compete with all the brilliant young people whom I have met with and heard of, and I don't know if I want to fight tooth and nail against them for every position I need (graduate school, a post-doc, a professorship [maybe, someday]). So, as I said, I would like to find some other areas I am interested in. I thought it would be a good idea to learn about some relatively new, accessible, exciting fields. As an example: I hear some interesting people are doing interesting things at Cornell, U. Chicago & elsewhere in something called geometric group theory. Neat. I'm told it has attracted several young mathematicians and since it's new, they're employable! Neater. What are some interesting new fields of mathematical research, who is researching them, and at what universities? Pure, or applied even but I don't have much undergraduate experience there. Mathematical biology sounds fascinating. Thank you!