Suggestions for grad schools to apply to

[deekin]

I'm starting to do some research into what grad schools I should apply to this fall for a pure math PhD. I'll be finishing my undergrad in May 2015 with a major in math and minor in physics. I'm not 100% sure what area I want to go in to, but I'm leaning more towards the topology and geometry side of things. I'm currently doing some work in topology (knot theory) and really enjoy it. I am also interested in geometry/topology research that is related to physics. As an example, I think UCSB may be a good fit because they have a research training group in geometry, topology, and physics and they have that connection with Microsoft Research Station Q. Stony Brook is another school I've been looking at.

I'd like to know if any of you have some suggestions of math departments to check out. I'm having a hard time finding places that are a good fit mainly because I don't really know how to tell if a dept's faculty in this area are very strong or not. Thanks.

 

[homeomorphic]

Maybe have a look at UC Davis (Greg Kuperberg), Indiana University (Vladimir Turaev, Dylan Thurston, Michael Larsen, Charles Livingston, Paul Kirk), Columbia (Brian Greene, Mikhael Khovanov), Stanford (Eliashberg), UC Irvine (Ronald Stern), Michigan State (Ronald Fintushel, Matt Hedden), University of Illinois, Chicago (Louis Kauffman), UCLA (Ko Honda), Georgia Tech (John Etnyre). All the parentheses people have a pretty good reputation. It's not an exhaustive list by any means. Just some ideas. You can always look at the rankings, but they don't tell the whole story.

I came into math from that same topology/physics direction in my undergrad. A general warning is that you might be pulled too far in a pure math direction if you get a math PhD. Some people are okay with that. I wasn't too happy with it. I can handle pure math, but as someone with more of a scientist's curiosity to understand nature, it wasn't quite what I was looking for. Generally, it's very hard to do both math and physics on a deep level, especially as a graduate student, where you are forced to specialize to a large degree in order to finish in a reasonable time period. Some people can pull it off, but it's not easy.

 

[deekin]

Awesome! Thank you so much homeomorphic, I was hoping you'd chime in. The list of people to pay attention to is especially helpful. Georgia Tech also has this guy Stavros Garoufalidis that looks like he does some cool stuff and his students seem to get good post-doc positions afterwards. Once again, thank you.