Deciding where to go for a PhD

 Posts: 6
 Joined: Sat Dec 09, 2017 4:54 pm
Deciding where to go for a PhD
I was admitted into the PhD programs at Stanford, Chicago and Columbia. I am somewhat undecided about an area I will work in, but I've done some number theory and enjoyed it. I know that Stanford is a very good place to study analytic number theory, while the analytic number theorists at Columbia are quite old. Chicago seems to have a larger department and people working in Langlands.
The pay is sufficient at all three. I also know that the culture at the three places is different, but I'm uncertain as to how much importance this is to be given. I'd prefer to live in a city, and I don't think I'll really like the 'techieentrepreneur' vibe at Stanford.
I've been told by some that Stanford and Chicago have a much stronger reputation than Columbia, so much so that I should not even consider going to Columbia (given I have no preference to work with some particular person there). Is this true? What other factors should I consider before making a decision?
The pay is sufficient at all three. I also know that the culture at the three places is different, but I'm uncertain as to how much importance this is to be given. I'd prefer to live in a city, and I don't think I'll really like the 'techieentrepreneur' vibe at Stanford.
I've been told by some that Stanford and Chicago have a much stronger reputation than Columbia, so much so that I should not even consider going to Columbia (given I have no preference to work with some particular person there). Is this true? What other factors should I consider before making a decision?

 Posts: 38
 Joined: Tue Nov 08, 2016 3:19 pm
Re: Deciding where to go for a PhD
All three schools are great IMO. Stanford is the strongest for analytic number theory and Chicago is (probably) the strongest for algebraic number theory / Langlands stuff.
Are you planning to go to their open houses? I'm sure seeing what their departments are like will give you a much better sense of which one is the best fit for you.
Are you planning to go to their open houses? I'm sure seeing what their departments are like will give you a much better sense of which one is the best fit for you.

 Posts: 6
 Joined: Sat Dec 09, 2017 4:54 pm
Re: Deciding where to go for a PhD
I have not yet decided whether I should. I'm an international student.
Re: Deciding where to go for a PhD
You should visit during the open houses or some other time if you can't make the specific open house dates. If you combine the visits together, the total travel reimbursement (generally they stack) from those 3 schools should be enough or close to enough, if you make plane flights early/now. If you are still short a decent amount of money for travel, you should talk to those departments asap since they are pretty wellfunded and might be able to give you more money if you show there are no cheaper plane tickets. I don't know that you'll get a 'techieentrpreneur' vibe at Stanford (all 3 have business schools anyway), since you'll probably mainly talk to people in the math department and you don't have to socialize with undergrads or business grad students if you don't want to. Stanford and UChicago are considered top 6 and Columbia top 10. I would say it's still worth visiting Columbia if it's not too big a hassle, but given that you said there's no one in particular you want to work with and that the people you would work with are very old there, I would be leaning towards one of the other two more.
Re: Deciding where to go for a PhD
Chicago has Frank Calegari, Matt Emerton, and Alex Eskin (though he's more of an ergodic theorist). The first two are both true algebraic number theorists.
Columbia has Johan de Jong (more of an algebraic geometer), Eric Urban, Michael Harris (both algebraic number theory), and Dorian Goldfeld (analytic number theory).
Stanford has Daniel Bump (more automorphic representations), Brian Conrad (arithmetic geometry), Kannan Soundararajan (analytic number theory), and Akshay Venkatesh (automorphic representations, algebraic number theory).
For analytic number theory/automorphic forms, Chicago isn't really the right place; Columbia has Goldfeld, who may not be young but is still very active and has advised many excellent students; Stanford is clearly the top with Sound and Venkatesh.
Columbia has Johan de Jong (more of an algebraic geometer), Eric Urban, Michael Harris (both algebraic number theory), and Dorian Goldfeld (analytic number theory).
Stanford has Daniel Bump (more automorphic representations), Brian Conrad (arithmetic geometry), Kannan Soundararajan (analytic number theory), and Akshay Venkatesh (automorphic representations, algebraic number theory).
For analytic number theory/automorphic forms, Chicago isn't really the right place; Columbia has Goldfeld, who may not be young but is still very active and has advised many excellent students; Stanford is clearly the top with Sound and Venkatesh.

 Posts: 6
 Joined: Sat Dec 09, 2017 4:54 pm
Re: Deciding where to go for a PhD
I know this, and I indeed think that from a mathematical perspective, Stanford would be the best place to go to given my interests. But I have no idea as to how much weight I should give to nonacademic factors, and how well these other factors can be judged in a 2 day visit.
By the way, the page: http://www.math.columbia.edu/~thaddeus/theses.html seems to indicate that Michael Harris has not had a student graduate in the last 7 years.
By the way, the page: http://www.math.columbia.edu/~thaddeus/theses.html seems to indicate that Michael Harris has not had a student graduate in the last 7 years.
Re: Deciding where to go for a PhD
Michael Harris has had plenty of students lately, but in Paris, not at Columbia (check his math genealogy).Grothaltric wrote:I know this, and I indeed think that from a mathematical perspective, Stanford would be the best place to go to given my interests. But I have no idea as to how much weight I should give to nonacademic factors, and how well these other factors can be judged in a 2 day visit.
By the way, the page: http://www.math.columbia.edu/~thaddeus/theses.html seems to indicate that Michael Harris has not had a student graduate in the last 7 years.
In any case, it's important to work out what's best for you, both in the short term (how happy you'll be during your PhD, based on location and other factors) and long term (career prospects in academia).
I will say that unless you have a strong algebraic background, Chicago probably isn't the right place for you (and it has the smallest number theory group regardless). Goldfeld at Columbia is an excellent advisor (and New York has an active number theory community).

 Posts: 38
 Joined: Tue Nov 08, 2016 3:19 pm
Re: Deciding where to go for a PhD
Do you have any insight on how these three compare for someone looking to work on algebraic number theory / the Langlands program? I know all three have at least some people working on such subjects (or related ones).kuz wrote:Michael Harris has had plenty of students lately, but in Paris, not at Columbia (check his math genealogy).Grothaltric wrote:I know this, and I indeed think that from a mathematical perspective, Stanford would be the best place to go to given my interests. But I have no idea as to how much weight I should give to nonacademic factors, and how well these other factors can be judged in a 2 day visit.
By the way, the page: http://www.math.columbia.edu/~thaddeus/theses.html seems to indicate that Michael Harris has not had a student graduate in the last 7 years.
In any case, it's important to work out what's best for you, both in the short term (how happy you'll be during your PhD, based on location and other factors) and long term (career prospects in academia).
I will say that unless you have a strong algebraic background, Chicago probably isn't the right place for you (and it has the smallest number theory group regardless). Goldfeld at Columbia is an excellent advisor (and New York has an active number theory community).

 Posts: 6
 Joined: Sat Dec 09, 2017 4:54 pm
Re: Deciding where to go for a PhD
Chicago also has Kazuya Kato.kuz wrote:Chicago has Frank Calegari, Matt Emerton, and Alex Eskin (though he's more of an ergodic theorist). The first two are both true algebraic number theorists.
Re: Deciding where to go for a PhD
For algebraic number theory/Langlands, they're all pretty excellent, and I'm not sure if any one is much better than another. Chicago is very strong  Emerton and Calegari are younger guys who are very active in the algebraic number theory community (I don't know much about Kato).korobeiniki wrote:Do you have any insight on how these three compare for someone looking to work on algebraic number theory / the Langlands program? I know all three have at least some people working on such subjects (or related ones).kuz wrote:Michael Harris has had plenty of students lately, but in Paris, not at Columbia (check his math genealogy).Grothaltric wrote:I know this, and I indeed think that from a mathematical perspective, Stanford would be the best place to go to given my interests. But I have no idea as to how much weight I should give to nonacademic factors, and how well these other factors can be judged in a 2 day visit.
By the way, the page: http://www.math.columbia.edu/~thaddeus/theses.html seems to indicate that Michael Harris has not had a student graduate in the last 7 years.
In any case, it's important to work out what's best for you, both in the short term (how happy you'll be during your PhD, based on location and other factors) and long term (career prospects in academia).
I will say that unless you have a strong algebraic background, Chicago probably isn't the right place for you (and it has the smallest number theory group regardless). Goldfeld at Columbia is an excellent advisor (and New York has an active number theory community).

 Posts: 1
 Joined: Thu Feb 15, 2018 7:21 pm
Re: Deciding where to go for a PhD
As far as number theory / automorphic forms / Langlands goes, Richard Taylor is moving to Stanford from IAS effective September 1, 2018. Arguably this makes it the strongest department in the world in this area, except when Peter Scholze dines alone.
I know grad students who chose Stanford over comparable schools after attending the open houses, specifically because they felt the grad students at Stanford were happier and had healthier and more balanced priorities in life. So if department atmosphere is something you weight heavily, I'd strongly encourage you to attend the open houses.
The techie/entrepreneur atmosphere is definitely present among the undergraduates at Stanford, and in departments like CS / EE / ICME, but not among the grad students or faculty in the math department. (This is something else you can ask about at the open house.)
I know grad students who chose Stanford over comparable schools after attending the open houses, specifically because they felt the grad students at Stanford were happier and had healthier and more balanced priorities in life. So if department atmosphere is something you weight heavily, I'd strongly encourage you to attend the open houses.
The techie/entrepreneur atmosphere is definitely present among the undergraduates at Stanford, and in departments like CS / EE / ICME, but not among the grad students or faculty in the math department. (This is something else you can ask about at the open house.)