safety schools

Arsenic&Lace

The concept of safety school does still exist in the sense that places like Stanford are popular and fill up their quota pretty quickly with lots of strong applicants since lots of people apply; a school like ASU actually can't get enough good graduate students so they probably accept people with less stellar applications. Even still none of the grad students at ASU I've met are dummies or lousy students, from what I've gathered/talked about they all had pretty good apps.

EDIT: And a school like ASU sort of winds up funneling graduates into industry, presumably because none of the faculty are networked enough to get them into academic positions, although I have found one ASU PhD working at UT Austin when I googled around for it. So the wisdom goes that if you want an academic job, particularly in something like theory, you ought to find a place with a famous advisor to have a shot at it.

Dens

So say I am really interested in PDEs and Diff geometry; obvious PDEs is much more popular. If I do my Ph.D on PDEs, can I do research later in Diff Geometry? Should I still apply to universities that don't offer either? That's what I meant as "safety"

Takuza

I'll again state that I am just an undergraduate, and there are people more qualified to answer this than me. With that said, obviously you can research something different than your PhD topic post PhD. To use your example, of course a Ph.D in PDE's can do Diff Geo work after graduation. The practical question (and perhaps what you were really asking) is, who will hire you to do so when it doesn't seem to be your area of expertise? That is something I can't comment on.

As far as if you should apply to universities that don't offer your research interests, that seems like the type of life-choice-analysis that only you are qualified to make for yourself. If you simply cannot imagine life without a PhD and you are desperate to start as soon as possible, applying to "safety" places certainly sounds like a good decision.