Suggestions for Math PhD Programs

Forum for the GRE subject test in mathematics.
J123
Posts: 7
Joined: Fri Jan 11, 2019 1:27 pm

Suggestions for Math PhD Programs

Postby J123 » Fri Jan 11, 2019 2:26 pm

Hi,

I'm currently a master's candidate in math at a middle tier university in the USA. I studied math/physics during my undergraduate outside of the USA. I'll be looking to move to a different program after picking up my master's in a years time.

My interests are inter-disciplinary. I like math being applied to solve concrete problems, and this is my main motivation of staying in academia. Philosophically, much like V. Arnold, I also think math courses should be taught with a focus on its inter-disciplinary applications. My interests, as of yet, are quite broad as well. Here are some of my interests. I am interested in Probability and PDE's within analysis, and a bit of mathematical physics. I'm also interested to dabble into such fields as machine learning, and game theory to open up more industry options.

Can someone recommend a list of good schools that has mathematicians working on inter-disciplinary areas? The type of mathematicians who inspire me are people like Barry Simon (mathematical physicist and analyst), Yuval Peres (analyst, probabilist, and a computer scientist at Microsoft), Brian Hall (mathematical physicist, probabilist, functional analyst)

I prefer the learning math first before, which is why I enrolled in a math master's program to shore up on my math background in analysis, algebra and topology. I expect to do that by the end of next year. I can never hope to learn all math that's out there, but I suppose I'll then be ready to branch out. My interests are concrete and I'd like to move to a math program where there's a fairly large number of people working on inter-disciplinary subject areas.

Any suggestions for departments which such a focus and that may be a general fit would be welcome.

J123
Posts: 7
Joined: Fri Jan 11, 2019 1:27 pm

Re: Suggestions for Math PhD Programs

Postby J123 » Tue Jan 15, 2019 1:00 am

Anyone?

djysyed
Posts: 327
Joined: Sat Oct 28, 2017 9:59 pm

Re: Suggestions for Math PhD Programs

Postby djysyed » Tue Jan 15, 2019 2:32 am

We're just undergrads, try asking in /r/math.

johanMo
Posts: 16
Joined: Tue Sep 18, 2018 1:07 pm

Re: Suggestions for Math PhD Programs

Postby johanMo » Tue Jan 15, 2019 11:26 am

Just one suggestion from my experience: the math and physics departments UT Austin seem to collaborate quite a bit. Scott Aaronson ( math-physics-cs) is also there, he's the guy to work with if you're interested in quantum computing.

finnlion
Posts: 6
Joined: Wed Oct 10, 2018 9:04 pm

Re: Suggestions for Math PhD Programs

Postby finnlion » Tue Jan 15, 2019 1:17 pm

I’ve heard Penn, Berkeley, and Minnesota have more interdisciplinary applied programs. Maryland AMSC seems very interdisciplinary as well- with faculty outside the department. What I would do is search for applied mathematics programs and look at what the research faculty are doing at that program (skim a few papers) and see if it is work that would excite you. Especially coming from a master’s, the majority of work will be in your dissertation. There definitely are interdisciplinary programs (though a lot of them are at top ranked schools, and you want matches/safeties as well). I don’t know much about physics in particular, but combing the sites of applied programs helped me find a range of schools in optimization to apply to this past year!

J123
Posts: 7
Joined: Fri Jan 11, 2019 1:27 pm

Re: Suggestions for Math PhD Programs

Postby J123 » Tue Jan 15, 2019 2:00 pm

finnlion wrote:I’ve heard Penn, Berkeley, and Minnesota have more interdisciplinary applied programs. Maryland AMSC seems very interdisciplinary as well- with faculty outside the department. What I would do is search for applied mathematics programs and look at what the research faculty are doing at that program (skim a few papers) and see if it is work that would excite you. Especially coming from a master’s, the majority of work will be in your dissertation. There definitely are interdisciplinary programs (though a lot of them are at top ranked schools, and you want matches/safeties as well). I don’t know much about physics in particular, but combing the sites of applied programs helped me find a range of schools in optimization to apply to this past year!


What do you mean when you say "especially coming from a master’s, the majority of work will be in your dissertation?"

Also, is it not the case that (pure) math departments house such research groups? For example, Columbia's math department seems to great groups in probability and mathematical physics. Quite a lot of applied math/applied physics groups work on such topics as computational fluid dynamics, earth sciences, inverse/medical imaging. I'm not awfully interested in these areas. I'm more inclined towards probability, machine learning, quantum computing etc. as inter-disciplinary applications of math. Maybe same theoretical/mathematical physics, but I don't see pursuing it as a full time thing.

finnlion
Posts: 6
Joined: Wed Oct 10, 2018 9:04 pm

Re: Suggestions for Math PhD Programs

Postby finnlion » Tue Jan 15, 2019 8:48 pm

I mean that you’ll have a lot of graduate coursework before you start your PhD. Hopefully some of it can be applied to your PhD degree and you will more quickly move toward the dissertation/research phase of your PhD. Potential dissertation advisors are even more important as you consider PhD programs coming from a master’s than a bachelors.

I don’t know about the topics you’re interested in, in particular. I just know that for optimization as well I had to comb through a lot of department websites to find the ones that were working in it. I also searched journals that were related to optimization, and looked at where the authors of articles I liked worked.

J123
Posts: 7
Joined: Fri Jan 11, 2019 1:27 pm

Re: Suggestions for Math PhD Programs

Postby J123 » Wed Jan 16, 2019 5:53 am

finnlion wrote:I mean that you’ll have a lot of graduate coursework before you start your PhD. Hopefully some of it can be applied to your PhD degree and you will more quickly move toward the dissertation/research phase of your PhD. Potential dissertation advisors are even more important as you consider PhD programs coming from a master’s than a bachelors.

I don’t know about the topics you’re interested in, in particular. I just know that for optimization as well I had to comb through a lot of department websites to find the ones that were working in it. I also searched journals that were related to optimization, and looked at where the authors of articles I liked worked.


Make sense.

I don't have specific research interests in particular, but, as I said, I'm leaning towards the topics I mentioned in my earlier post. I'd like to keep primary/secondary areas, which is why I was looking for a suggestions of schools where I will have enough opportunities to explore diff. topics.

basically_trash
Posts: 5
Joined: Thu Jan 31, 2019 12:12 am

Re: Suggestions for Math PhD Programs

Postby basically_trash » Fri Feb 01, 2019 1:09 am

There's a documentary out there called "The Most Unknown". It traces 9 researchers/professors around the world to explore consciousness. Many of them are physicists of some type. While enjoying the movie, you can see if any of those scientists' universities are interesting to you.

That said, University of Colorado at Boulder is publishing NASA's data for the recent JUNO mission to Jupiter. I think there's also the guy who's working on the strontium clock stuff. Their math physics program may be of interest. My colleague is finishing her masters now in Math and has applied there for the current time cohort.

When you say "interdisciplinary", you can look to see if anyone offers or is working on the Langlands Program. Langlands is working on his Grand Unified Theory in Math, so is working on making connections across the sub-topics within Math. I think University of Toronto has a Langlands Program group. Not sure about U.S. Universities.

J123
Posts: 7
Joined: Fri Jan 11, 2019 1:27 pm

Re: Suggestions for Math PhD Programs

Postby J123 » Sun Feb 03, 2019 1:35 am

basically_trash wrote:There's a documentary out there called "The Most Unknown". It traces 9 researchers/professors around the world to explore consciousness. Many of them are physicists of some type. While enjoying the movie, you can see if any of those scientists' universities are interesting to you.

That said, University of Colorado at Boulder is publishing NASA's data for the recent JUNO mission to Jupiter. I think there's also the guy who's working on the strontium clock stuff. Their math physics program may be of interest. My colleague is finishing her masters now in Math and has applied there for the current time cohort.

When you say "interdisciplinary", you can look to see if anyone offers or is working on the Langlands Program. Langlands is working on his Grand Unified Theory in Math, so is working on making connections across the sub-topics within Math. I think University of Toronto has a Langlands Program group. Not sure about U.S. Universities.


Thanks for your response. I looked at UC Boulder's program, and I seemed to like it. I'll keep it in mind for when I apply.

Not sure I am cut out to even think about working on the Langlands program. :p




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