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.
Here are my stats in case it is relevant:
School: Unknown Midwest state school  doesn't grant math PhDs
Major: Math
Minor: Physics
Overall GPA: 3.75 Major GPA: 4.0
GRE Verbal: 168, Quant: 162, Writing: 4.0
MGRE: ??
Research: Currently working on project in knot theory.
Courses: No grad courses since we don't offer PhD. Typical undergrad prep (e.g. blue Rudin, Hoffman & Kunze Linear Algebra, etc).
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.
Good departments for topology/geometry
Re: Good departments for topology/geometry
UC Irvine will be a good fit for you.
Re: Good departments for topology/geometry
You might want to look at these schools.
http://gradschools.usnews.rankingsandr ... yrankings
and
http://gradschools.usnews.rankingsandr ... yrankings
http://gradschools.usnews.rankingsandr ... yrankings
and
http://gradschools.usnews.rankingsandr ... yrankings
Re: Good departments for topology/geometry
Given your interests, I'd say definitely apply to Stony Brook. They are very strong in differential geometry. They recently hired Simon Donaldson, who along with xiuxiong Chen and song sun (also both at sb) recently proved a big result relating existence of Kahler Einstein Metrics on Fano manifolds to k stability (known in field as ytd conjecture). They also have a lot.of interaction between their math and physics departments, if that interests you. Most topology has to do with stuff like 4 manifolds as well as symplectic topology, not sure if they have many people in knot theory
Last edited by dh363 on Wed Jul 09, 2014 8:04 pm, edited 1 time in total.
Re: Good departments for topology/geometry
dh363 that is awesome. Exactly what I was looking for. It is too bad that it is so difficult to get accepted at Stony Brook! I'm still going to apply though, you never know what might happen. Do you know of any other schools that are similar to SB in terms of their research interests?

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 Joined: Mon Apr 15, 2013 4:18 pm
Re: Good departments for topology/geometry
University of Texas also has lots of good topology, especially in low dimensional topology. There are also quite a few professors who work close to physics, especially string theory.
Also dh363...do you mean symplectic topology?
Also dh363...do you mean symplectic topology?