Admissions PhD Programs for Mathematical Physics (Experimental Condensed Matter Physics)

[advhaver]

HI,

I am an International Student studying in the US (at a "liberal arts" small college ranked in the Top 20 as per US News Rankings). I will graduate in 2024 and intend to apply for PhD programs in Mathematical Physics starting October 2023 for admission in 2024.

GPA: I am a double major in Physics (3.9 GPA) and Mathematics (3.8 GPA), with an overall GPA of 3.85.

Research: As an international, I was not qualified for any REU. However, I have worked part-time as a research assistant with a college professor during the school year (May 2022 to now), including working full-time during the two summers (2022 and 2023). The 2021 summer was a washout due to Covid restrictions.

Recommendation Letters: I have three recommendation letters from Physics professors, including one for whom I have worked as a research assistant. I can also muster a 4th recommendation letter from a Maths professor who will be my senior thesis advisor in Maths.

GRE: I have not done any GREs. Should I focus on the subject GREs (Maths and Physics) as I will not have time to do all 3 (General, Physics and Maths)? At first glance, the requirements of most universities state that GRE is optional.

I found finding universities focusing on Mathematical Physics tough, so I tried to find professors who spend time in this area. I have managed to identify a few professors, generated a list of universities, and have no idea how to shortlist them. I haven't written to any of these professors, so I won't name them below (where two departments are listed, the same professor works in both).

1. Princeton (Mathematical Physics)
2. Chicago (Physics)
3. U Penn (Physics)
4. Duke (Physics)
5. Brown (Physics)
6. MIT (Physics and Applied Maths)
7. Columbia (APAM and Physics)
8. Harvard (Physics)
9. Stanford (Physics and SITP)
10. Cornell (Physics and Applied Maths)
11. Yale (Physics and Maths)
12. Northwestern (Maths)
13. Northwestern (ESAM and Physics)
14. Dartmouth (Physics)
15. UIUC (Physics)
16. U.C.LA (Physics)
17. Georgia Tech (Maths)
18. Georgia Tech (Physics)
19. University of Maryland - College Park (Physics)
20. University of Colorado - Boulder (Physics)

I haven't had time to research Johns Hopkins, U. Mich (Ann Arbor), Carnegie Mellon, Washington St. Louis, U.N.C Chapel Hill, U. Wisconsin (Madison), Penn State, Arizona State, Purdue, U.C Santa Barbara, U. Minn Twin Cities, N.C. State Uni, and U of Colorado Boulder.

Are there other universities I should be considering?

It has been exhausting, and I felt my list was very "dream heavy". That's partly because I started using the US News Ranking system to make this list.

Any pointers on how to reduce this list? Should I have started from colleges ranked 50-100 instead of 1-50?

And lastly, what are the opportunities in Mathematical Physics? I understand that academia is crowded, but does the industry hire PhDs in Mathematical Physics?

Thanks in advance.

 

[Vanadium 50]

Any pointers on how to reduce this list?

See if your target professors are still publishing. I can only guess who you are thinking of, but in some cases, I can't believe they are still active.

You should also discuss this with faculty where you are.

The General GRE is usually irrelevant, but required to take the PGRE. But coming from a SLAC, the GRE is an opportunity to show that you have learned as much as the candidates from Stanford,

 

[Choppy]

What specific kinds of projects are you interested in working on? So far it sounds like you've identified a specific sub-field of interest, but as you come to the end of your undergraduate education it will help to be reading as many papers as you can. Follow your nose and look into the groups that are working on and publishing research that you find really fascinating and can see yourself taking part in.

It's also worth taking the time to think about the specific skills you want to develop through your PhD. "Industry" may not specifically look for PhDs in mathematical physics, rather they're often interested in PhDs with skills that are of value to them... mathematical modeling, programming, data analysis, statistics, etc.

Don't worry too much about a university's "rank." This is based on criteria that may or may not be relevant to you. Really to narrow down your search, you have to do the research... visit campuses, speak with potential supervisors, post-docs, other graduate students. Also look at where recent graduates are ending up. And find out who has openings in the coming year. Students can sometimes set themselves up for surprising disappointment because they have amazing "stats" (high GPA, great GRE scores, glowing reference letters, etc.) but then they apply to a group that doesn't have any openings.

 

[advhaver]

See if your target professors are still publishing. You should also discuss this with faculty where you are.

The General GRE is usually irrelevant, but required to take the PGRE. But comin g from a SLAC, the GRE is an opportunity to show that you have learned as much as the candidates from Stanvard,

Thank you so much.

The process I followed, since I had to start somewhere, was to visit the university graduate school faculty site and look at those faculty who claim to have an interest in Mathematical Physics or Maths and Physics or Applied Mathematics and Physics. How would I know if the professor is still publishing? Most professors don't keep their "personal" websites updated!

I hoped that the PGRE and MGRE would be adequate. Between my two research theses (one each in Maths and Physics), research internship and preparing for the subject GREs, I will be stressed for time as it is.

What specific kinds of projects are you interested in working on? So far it sounds like you've identified a specific sub-field of interest, but as you come to the end of your undergraduate education it will help to be reading as many papers as you can. Follow your nose and look into the groups that are working on and publishing research that you find really fascinating and can see yourself taking part in.

It's also worth taking the time to think about the specific skills you want to develop through your PhD. "Industry" may not specifically look for PhDs in mathematical physics, rather they're often interested in PhDs with skills that are of value to them... mathematical modeling, programming, data analysis, statistics, etc.

Don't worry too much about a university's "rank." This is based on criteria that may or may not be relevant to you. Really to narrow down your search, you have to do the research... visit campuses, speak with potential supervisors, post-docs, other graduate students. Also look at where recent graduates are ending up. And find out who has openings in the coming year. Students can sometimes set themselves up for surprising disappointment because they have amazing "stats" (high GPA, great GRE scores, glowing reference letters, etc.) but then they apply to a group that doesn't have any openings.

When choosing colleges, I was torn between Maths or Physics as my major. Then came the pandemic (I graduated high school in 2020), and a lot changed for me. I wasn't even supposed to be in the US for college. Eventually, I chose a college that would accept me at the last minute (September 2020), permit me to take two majors (Maths and Physics) and provide a springboard for graduate school.

My primary interest lies in Physics, but my school professors said I was better at Maths. During my studies in Physics, I came across concepts like Graph Theory that made me think about studying "Applied Mathematics for Physics", and hence I started considering "Mathematical Physics". Most universities have "Mathematical Physics" as part of their Maths or Applied Maths Department. However, my Physics resume is stronger, so I am considering applying to those universities where professors in the Physics Department also work in Mathematics.

We have all heard about universities that have gamed their ranking (I remember Northeastern doing this), so University Rank is not too much of my concern as I know that most universities in the "Top 50" will offer me adequate resources. Using "rank" was just a starting point for looking for professors.

I also understand that I do not have a stellar academic record. My GPA is not 4.0/4.0, nor do I have any REUs or other fantastic research internships (I have several friends that have both). Hence I am willing to limit my expectations. This is where I need some guidance. What should my target and safety universities look like?

Visiting colleges is difficult, given time constraints, but I am talking with four of my college professors (the four from whom I expect LORs). Where would I find universities that have openings?

Thanks again.

 

[Vanadium 50]

How would I know if the professor is still publishing?

A. If you are interested in mathematical physics grad school, you should start reading the relevant journals.
B. I don't know what the relevant journals are, as that is not my subfield. Your professors may be able to help.
C. Your librarians may also be able to help.

If they publish several papers per year, they are active. If they publish one paper in several years, they are not. In between is...well, in between.

You should ask your professors where they think you would best fit.

 

[advhaver]

A. If you are interested in mathematical physics grad school, you should start reading the relevant journals.
B. I don't know what the relevant journals are, as that is not my subfield. Your professors may be able to help.
C. Your librarians may also be able to help.

If they publish several papers per year, they are active. If they publish one paper in several years, they are not. In between is...well, in between.

You should ask your professors where they think you would best fit.

Thanks, Vanadium 50.

I can show you one example.
Say we go to UCLA's Physics Department and look at all the faculty. We get a list of faculty as follows:
https://www.pa.ucla.edu/faculty.html
In this list of faculty, we look for those who have "Maths" as part of their research, and you get:
https://www.pa.ucla.edu/faculty-websites/dhoker.html
If you look at the list of publications, you get this:
https://inspirehep.net/literature?sort=mostrecent&size=25&page=1&q=find a d'hoker
Prof. D'Hoker looks quite active.

We do the same for Princeton, and we get the following:
https://phy.princeton.edu/people/faculty
If we look at "Physics and Mathematics", we get:
https://aizenman.scholar.princeton.edu/research-articles
and
https://web.math.princeton.edu/~lieb/publications.html

I still don't know if either college has any openings. Nor do I know if my resume is competitive at UCLA. I am pretty sure it's not strong enough for Princeton.

I hoped to take a list to my professors so they would be more inclined to help (since I would have done research).

1. How many colleges do I need to shortlist? Some say 6, some say 10, and some say 15. Is my list too aggressive?
2. How do I know if my resume is competitive or if I am aiming too high?

Thank you.

 

[Vanadium 50]

I still don't know if either college has any opening

And you're unlikely to.

Normally students TA while they are taking classes and are supported by their research group after that. This is two years and a bit, and the typical funding cycle is three years.

So they won't know for sure. But the university is the one making the commitment so let them assess the risk. They are in a better place for it anyway.

 

[advhaver]

And you're unlikely to.

Thanks.

How do I find universities with a greater chance of admission?

I haven't found time to research U.N.C Chapel Hill, U. Wisconsin (Madison), Penn State, Arizona State, Purdue, U.C Santa Barbara, U. Minn Twin Cities, N.C. State Uni, or U of Colorado Boulder.

Given my time limitations, I was hoping to get some direction. It's crazy trying to research so many universities.

I have found time to research the Physics department of UIUC, UCLA, UMD and some dream universities, but I need to add more practical options.

My goal is to apply to about ten universities, of which only 2-3 would be dreams, so I need to find 7-8 more universities.

Thanks.

 

[Vanadium 50]

How do I find universities with a greater chance of admission?

Apply.

I don't know your chances if you apply, but I know your chances if you don't.

 

[gwnorth]

I have managed to identify a few professors, generated a list of universities, and have no idea how to shortlist them.

Any pointers on how to reduce this list? Should I have started from colleges ranked 50-100 instead of 1-50?

How would I know if the professor is still publishing? Most professors don't keep their "personal" websites updated!

One place to start is Google Scholar. You can look up the professors you've already identified and see if they have recent publications. You can also search by topic so you can identify other additional professors engaged in research that you're interested in and then find out what universities they are associated with. Once you have your initial list of PIs you would potentially be interested in working with, you should contact them via email expressing your interest in their research, provide a brief outline of your credentials, and ask if they expect to be accepting new students in the upcoming cycle. From there you can cull your list to those where you are most likely to be a strong research fit.

Some professors may be on vacation for part of the summer or focusing on research, so you're best bet is to wait until either just before the new semester begins or just after it gets underway.

 

[advhaver]

Apply.

I don't know your chances if you apply, but I know your chances if you don't.

Yeah, but I'd rather apply to places where my chances are realistic. Building a realistic list is where I am stuck.

One place to start is Google Scholar.

Great idea.

Once you have your initial list of PIs you would potentially be interested in working with, you should contact them via email expressing your interest in their research, provide a brief outline of your credentials, and ask if they expect to be accepting new students in the upcoming cycle. From there you can cull your list to those where you are most likely to be a strong research fit.

Is it safe to approach professors without even applying to the colleges? At least one college requested prospective students not to approach professors until they are admitted. Let me see if I can find that name.

 

[gwnorth]

Is it safe to approach professors without even applying to the colleges?

This is a pretty standard practice for STEM applicants in the US, especially as you noted that PIs don't always keep their departmental or lab websites up to date. To clarify however you aren't looking to circumvent the application process by applying to professors directly, just trying to gauge whether the program would be a good fit for your goals and to ensure that the PIs you would be interested in potentially working with are anticipating accepting new students. There also maybe other PIs that you aren't aware of in the program that could also potentially be good or better fits that they can direct you to. It's a fact finding mission not a request for admission.

I did hear anecdotally of one program that discouraged potential applicants from doing so (this may be the one you are alluding to) but it's not clear if the individual was requesting information or looked to be trying to apply. How you word your email will be the difference. Even so, this one program aside, as I mentioned, it's a pretty common practice for STEM disciplines.

I'm not sure if forum guidelines would allow me to post a direct link, but there are a series of videos on YouTube from a professor in a STEM adjacent field providing advice to students wanting to apply to PhD programs in the US. I think they are highly informative. You may want to look them up. The professor who creates them is Casey Fiesler from the University of Colorado Boulder.

 

[Vanadium 50]

Google Scholar

Honestly, I've not been impressed by Google Scholar. My name is uncommon but not unusual, and it finds two orders of magnitude more papers than I have written. If I append "physics" it drops to one order of magnitude.

I use InspireHEP, which is much more accurate. It is intended for HEP; I don't know what the equivalent is in other subfields.

 

[gwnorth]

On Google Scholar you can search by name and institution. Once you find the relevant person you can click on them and then your search will be constrained to that specific individual.

Another potential source I came across recently is Research.com.

 

[Vanadium 50]

People switch institutions, especially in hot fields. ORCID IDs would be best, but in any event, that's why I suggested the librarians. They know (or should) what is used in a given subfield.

 

[marcusl]

I find your strategy baffling. You are looking for universities that do both "math" and "physics" and, not surprisingly, are overwhelmed at the number of choices. Why don't you look for institutions who do the kind of work that interests you? Surely you must have some preferences, some particular problems or corners of mathematical physics that excite you. Those, and the professors who do them, are the things you should pursue.

 

[Vanadium 50]

Prof. D'Hoker looks quite active.

I think you need to look more carefully.

In the past year, he's published five papers. Looks pretty good, right? One is a Snowmass summer study with hundreds of authors, so let's remove that and we get four. One is a set of lecture notes, which may be interesting and valuable, but not the sort of thing a student would work on. Finally we have two papers done in collaboration with someone at UCLA.

One is a junior faculty member, and one is a postdoc.

You can also see when he got his PhD and from that can estimate his age when you graduate - it will be around 75.

With some digging, you can find his students: the latest one graduated in 2011. This isn't always so accurate, but a picture is starting to emerge: while he may be a good choice for a potential advisor, I wouldn't put him at the top of your list.

Look at Aizenman. One paper in the last year. He was the sole author. The last time he published with anyone from Princeton was, as far as I can tell, 1994. Don't know if this was a student - just that it might have been.

He'll likely be around 82 when you graduate.

Again, he may be a good choice for a potential advisor, I wouldn't put him at the top of your list.

The thing that's hard to reconcile - and @marcusl alluded to this - is that these people do very different things. It's unclear where you are trying to go.

 

[firearmsguy]

HI,

I am an International Student studying in the US (at a "liberal arts" small college ranked in the Top 20 as per US News Rankings). I will graduate in 2024 and intend to apply for PhD programs in Mathematical Physics starting October 2023 for admission in 2024.

GPA: I am a double major in Physics (3.9 GPA) and Mathematics (3.8 GPA), with an overall GPA of 3.85.

Research: As an international, I was not qualified for any REU. However, I have worked part-time as a research assistant with a college professor during the school year (May 2022 to now), including working full-time during the two summers (2022 and 2023). The 2021 summer was a washout due to Covid restrictions.

Recommendation Letters: I have three recommendation letters from Physics professors, including one for whom I have worked as a research assistant. I can also muster a 4th recommendation letter from a Maths professor who will be my senior thesis advisor in Maths.

GRE: I have not done any GREs. Should I focus on the subject GREs (Maths and Physics) as I will not have time to do all 3 (General, Physics and Maths)? At first glance, the requirements of most universities state that GRE is optional.

I found finding universities focusing on Mathematical Physics tough, so I tried to find professors who spend time in this area. I have managed to identify a few professors, generated a list of universities, and have no idea how to shortlist them. I haven't written to any of these professors, so I won't name them below (where two departments are listed, the same professor works in both).

1. Princeton (Mathematical Physics)
2. Chicago (Physics)
3. U Penn (Physics)
4. Duke (Physics)
5. Brown (Physics)
6. MIT (Physics and Applied Maths)
7. Columbia (APAM and Physics)
8. Harvard (Physics)
9. Stanford (Physics and SITP)
10. Cornell (Physics and Applied Maths)
11. Yale (Physics and Maths)
12. Northwestern (Maths)
13. Northwestern (ESAM and Physics)
14. Dartmouth (Physics)
15. UIUC (Physics)
16. U.C.LA (Physics)
17. Georgia Tech (Maths)
18. Georgia Tech (Physics)
19. University of Maryland - College Park (Physics)
20. University of Colorado - Boulder (Physics)

I haven't had time to research Johns Hopkins, U. Mich (Ann Arbor), Carnegie Mellon, Washington St. Louis, U.N.C Chapel Hill, U. Wisconsin (Madison), Penn State, Arizona State, Purdue, U.C Santa Barbara, U. Minn Twin Cities, N.C. State Uni, and U of Colorado Boulder.

Are there other universities I should be considering?

It has been exhausting, and I felt my list was very "dream heavy". That's partly because I started using the US News Ranking system to make this list.

Any pointers on how to reduce this list? Should I have started from colleges ranked 50-100 instead of 1-50?

And lastly, what are the opportunities in Mathematical Physics? I understand that academia is crowded, but does the industry hire PhDs in Mathematical Physics?

Thanks in advance.

Does CU have mathematical physics too? I didn't notice that beforehand, anyway, I heard that for physics:

1. Princeton (Mathematical Physics)
2. Chicago (Physics)
6. MIT (Physics and Applied Maths)
7. Columbia (APAM and Physics)
8. Harvard (Physics)
9. Stanford (Physics and SITP)
10. Cornell (Physics and Applied Maths)
11. Yale (Physics and Maths)
15. UIUC (Physics)
16. UCLA (Physics)
19. University of Maryland - College Park (Physics)
20. University of Colorado - Boulder (Physics)

these are quite competitive though?

 

[advhaver]

I find your strategy baffling. You are looking for universities that do both "math" and "physics" and, not surprisingly, are overwhelmed at the number of choices. Why don't you look for institutions who do the kind of work that interests you? Surely you must have some preferences, some particular problems or corners of mathematical physics that excite you. Those, and the professors who do them, are the things you should pursue.

Let me give you a bit of background.

I started (in 2020) wanting to study Physics and Maths. I like both subjects (I was one of 3 students who took Further Maths (IB) in high school). I would have taken an Advanced Physics course, too, if it had been offered. I also enjoy working in physics laboratories and conducting experiments. My mom always thought engineering would suit me better, but I didn't want to study engineering.

I chose to major in both (Maths and Physics) in college, but when I looked for an internship, I found one in Soft Matter. The internship opportunities I got in maths involved working in a finance company (Morningstar) or a bank (Deutsche Bank), and I have little interest in finance, economics or commerce.

At my internship, I got more interested in the Mathematics (like Graph Theory) behind Physics, which is where I am now. I am not very particular about a specific area of Mathematics but more about how Mathematics can be applied to Physics.

I hope this helps.

Thanks

This isn't always so accurate, but a picture is starting to emerge: while he may be a good choice for a potential advisor, I wouldn't put him at the top of your list.

Look at Aizenman. Again, he may be a good choice for a potential advisor, I wouldn't put him at the top of your list.

The thing that's hard to reconcile - and @marcusl alluded to this - is that these people do very different things. It's unclear where you are trying to go.

I am flexible about studying any area of Mathematics as long as the applications are in Physics (High Energy, Quantum Field Theory, Condensed Matter, Particle Physics.., it doesn't matter too much).

I am not interested in applications related to Operations Research, Finance/Commerce/Banking, or Genetics/Biology/Biophysics. I do not mind programming and know Python and MathLab, but I don't know if I'd enjoy doing that full-time (besides, I haven't studied Data Structures, Java, C++ etc, as CompSci graduates would have).

I am just playing to my strengths which are in Physics and Maths.

Does this help?

Thanks.

 

[advhaver]

Does CU have mathematical physics too? I didn't notice that beforehand, anyway, I heard that for physics:

1. Princeton (Mathematical Physics)
2. Chicago (Physics)
6. MIT (Physics and Applied Maths)
7. Columbia (APAM and Physics)
8. Harvard (Physics)
9. Stanford (Physics and SITP)
10. Cornell (Physics and Applied Maths)
11. Yale (Physics and Maths)
15. UIUC (Physics)
16. UCLA (Physics)
19. University of Maryland - College Park (Physics)
20. University of Colorado - Boulder (Physics)

these are quite competitive though?

CU? Do you mean the University of Colorado (Boulder)?
Or do you mean CMU aka Carnegie Mellon? I am open to considering CMU, but I thought CMU would be at least as competitive as Cornell, Yale, UIUC, UMD, etc. Should I consider CMU?

I realise that my profile isn't very competitive, so I am looking for more "practical" options.

Thanks.

 

[firearmsguy]

CU? Do you mean the University of Colorado (Boulder)?
Or do you mean CMU aka Carnegie Mellon? I am open to considering CMU, but I thought CMU would be at least as competitive as Cornell, Yale, UIUC, UMD, etc. Should I consider CMU?

I realise that my profile isn't very competitive, so I am looking for more "practical" options.

Thanks.

Yeah yeah CU Boulder, not CMU

CU Boulder Would be at least as competitive as Cornell, Yale, UIUC

 

[advhaver]

Yeah yeah CU Boulder, not CMU

CU Boulder Would be at least as competitive as Cornell, Yale, UIUC

How tough is getting into CMU for a PhD (Physics)?

 

[Vanadium 50]

Morningstar

The brother-in-law of the founder is a physicist.

Where you see "flexible", I am afraid the admissions committee will see "unfocused". People who say "I want to study X, and I realize it lives at the boundary between Physics and [whatever]" tend to do better than people who say "I want to do X, or maybe Y, or possibly Z." Grad admissions committees know this. You would be well served to think about a tighter focus here.

A second, somewhat related problem is that your story sounds like "Grad school, I guess" - you have looked at what you don't want to do and what is left standing is grad school. You don't want to project this image either.

 

[marcusl]

Let me give you a bit of background.

I started (in 2020) wanting to study Physics and Maths. I like both subjects (I was one of 3 students who took Further Maths (IB) in high school). I would have taken an Advanced Physics course, too, if it had been offered. I also enjoy working in physics laboratories and conducting experiments. My mom always thought engineering would suit me better, but I didn't want to study engineering.

I chose to major in both (Maths and Physics) in college, but when I looked for an internship, I found one in Soft Matter. The internship opportunities I got in maths involved working in a finance company (Morningstar) or a bank (Deutsche Bank), and I have little interest in finance, economics or commerce.

At my internship, I got more interested in the Mathematics (like Graph Theory) behind Physics, which is where I am now. I am not very particular about a specific area of Mathematics but more about how Mathematics can be applied to Physics.

I hope this helps.

ThanksI am flexible about studying any area of Mathematics as long as the applications are in Physics (High Energy, Quantum Field Theory, Condensed Matter, Particle Physics.., it doesn't matter too much).

I am not interested in applications related to Operations Research, Finance/Commerce/Banking, or Genetics/Biology/Biophysics. I do not mind programming and know Python and MathLab, but I don't know if I'd enjoy doing that full-time (besides, I haven't studied Data Structures, Java, C++ etc, as CompSci graduates would have).

I am just playing to my strengths which are in Physics and Maths.

Does this help?

Thanks.

“Does this help?” It ‘s irrelevant to me, but it doesn’t help you. You are unfocused and that’s making your search difficult. (Vanadium 50 and I are saying similar things.)

 

[StatGuy2000]

@marcusl , @Vanadium 50 , I see that both of you are stating that the OP is unfocused in their application to graduate school programs in mathematical physics.

But as I've alluded to before in other threads, it is very difficult for any undergraduate student to have an idea of the exact field (or even sub-field) they will be interested in, especially because these students would have only been familiar with introductory courses in many physics fields.

Do you expect a student to say (as an example), "I am interested in research in experimental condensed matter physics" when such a student would have only taken at most 1 course in statistical mechanics? And likely would not have had any research experience in such a field?

My contention is that most PhD students have a general interest in research in broad disciplines (like the OP) but would not know enough to choose a dissertation field right away, which is what you are suggesting the OP do.

 

[Vanadium 50]

Do you expect a student to say (as an example), "I am interested in research in experimental condensed matter physics" when such a student would have only taken at most 1 course in statistical mechanics? And likely would not have had any research experience in such a field?

Yes.

If you want a research degree, it is reasonable to know where you want to start your research career. In addition to classes, universities have colloquia and seminars, where undergrads are encouraged to attend, as well as research projects, senior theses and the like. Every member of my entering class (and the ones on either side) knew what they wanted to do. Did some change their mind? A couple. But they came in with their ideas.

Is there a selection bias? Probably. "I want a PhD in physics, but I don't know in what field, and nothing excited me in colloquia, seminars and projects" is probably not a winning application. "I didn't attend any colloquia" probably is even less a winning application.

 

[Haborix]

Yes.

If you want a research degree, it is reasonable to know where you want to start your research career. In addition to classes, universities have colloquia and seminars, where undergrads are encouraged to attend, as well as research projects, senior theses and the like. Every member of my entering class (and the ones on either side) knew what they wanted to do. Did some change their mind? A couple. But they came in with their ideas.

Is there a selection bias? Probably. "I want a PhD in physics, but I don't know in what field, and nothing excited me in colloquia, seminars and projects" is probably not a winning application. "I didn't attend any colloquia" probably is even less a winning application.

Similarly for my entering class. And I would add that a large percentage had already done some research as an undergrad in a related field (sometimes a very closely related field).

 

[Haborix]

Imagine the person reviewing your application asks the following questions: (1) Could this person have sent this application to any other university after simply switching out the university name? (2) If no to (1), is there any evidence in the application materials that supports the reasons applicant has listed for wanting to come here? You want a "No" to (1) and a "Yes" to (2).

 

[CrysPhys]

But as I've alluded to before in other threads, it is very difficult for any undergraduate student to have an idea of the exact field (or even sub-field) they will be interested in, especially because these students would have only been familiar with introductory courses in many physics fields.

Do you expect a student to say (as an example), "I am interested in research in experimental condensed matter physics" when such a student would have only taken at most 1 course in statistical mechanics? And likely would not have had any research experience in such a field?

My contention is that most PhD students have a general interest in research in broad disciplines (like the OP) but would not know enough to choose a dissertation field right away, which is what you are suggesting the OP do.

(1) As I pointed out in another thread, if a student doesn't know the general field he's interested in (e.g., experimental solid-state physics vs theoretical high-energy particle physics), how is he going to develop a candidate list of grad schools to apply to?

(2) We're talking about the US. If the student did not develop a strong interest in a particular field as an undergrad, how will he miraculously discover one in grad school? The first year will primarily be foundational courses in preparation for the qual exam. There typically is no grad lab equivalent to junior lab to permit the student to sample a variety of fields. And there typically is no opportunity for research until he gets accepted into a research group (with perhaps the exception of the first summer in some schools).

 

[StatGuy2000]

(1) As I pointed out in another thread, if a student doesn't know the general field he's interested in (e.g., experimental solid-state physics vs theoretical high-energy particle physics), how is he going to develop a candidate list of grad schools to apply to?

(2) We're talking about the US. If the student did not develop a strong interest in a particular field as an undergrad, how will he miraculously discover one in grad school? The first year will primarily be foundational courses in preparation for the qual exam. There typically is no grad lab equivalent to junior lab to permit the student to sample a variety of fields. And there typically is no opportunity for research until he gets accepted into a research group (with perhaps the exception of the first summer in some schools).

In Canada (where I am located in), it is typically the case that students complete a Masters degree prior to being admitted into a PhD program. From my observation, at the Masters level (which can take either 1 or 2 years), students typically take a selection of senior level courses and complete a research project. It's in these circumstances that students can thus be exposed to different areas of physics, from which students can then be better informed to make a decision on which research to pursue once they are admitted to a PhD program.

In the US, where students are admitted directly from an undergraduate degree, I would have expected that the foundational courses for the qual exam would give students a better feel for what research area they would ultimately pursue.

So demanding students in their third or fourth year (where they have only been exposed to introductory level courses) to decide what research field they intend to pursue (which is what is expected in their statement of purpose essay) always feels premature to me.

 

[CrysPhys]

In the US, where students are admitted directly from an undergraduate degree, I would have expected that the foundational courses for the qual exam would give students a better feel for what research area they would ultimately pursue.

No. The foundational courses are grad level versions of typical undergrad courses, such as classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics and thermodynamics, and mathematical methods. Typically no labs. There will be later grad level specialty courses in solid-state physics, nuclear physics, high-energy particle physics, .... Depending on the school, some may be required, but often a student will elect those of value to his chosen research. Typically he doesn't have the luxury of first taking a full suite of specialty grad courses and then choosing his research field.

As I've written several times, in the US, you don't want to sign onto a PhD Physics program with the expectation of finding what ignites your passion. You sign onto a PhD Physics program because some passion has already been ignited ... and a PhD Physics is the appropriate means to satisfy that passion.

For many years, I served as an industry mentor for STEM students. One was a physics undergrad in the US. When she was a senior, she wasn't sure whether she wanted to pursue a PhD physics program. I cautioned her that with only a bachelor's in physics, she would be employed as a research technician or assistant, not as a lead researcher, in industry; and she'd probably be bored to death within a year. But I also cautioned her that since she hadn't identified an area of research that ignited her passion, a PhD physics program was not a good default alternative, either. In the end, she landed a job as a research assistant for a company developing and manufacturing accelerators for medical treatment. Sure enough, within a year, she wanted out. But she now had a new found passion for medical physics. So she applied for a PhD program in medical physics and got accepted to a top program.

 

[advhaver]

Where you see "flexible", I am afraid the admissions committee will see "unfocused".

If you want a research degree, it is reasonable to know where you want to start your research career. In addition to classes, universities have colloquia and seminars, where undergrads are encouraged to attend, as well as research projects, senior theses and the like.

But as I've alluded to before in other threads, it is very difficult for any undergraduate student to have an idea of the exact field (or even sub-field) they will be interested in, especially because these students would have only been familiar with introductory courses in many physics fields.

Do you expect a student to say (as an example), "I am interested in research in experimental condensed matter physics" when such a student would have only taken at most 1 course in statistical mechanics? And likely would not have had any research experience in such a field?

Imagine the person reviewing your application asks the following questions: (1) Could this person have sent this application to any other university after simply switching out the university name? (2) If no to (1), is there any evidence in the application materials that supports the reasons applicant has listed for wanting to come here? You want a "No" to (1) and a "Yes" to (2).

(1) As I pointed out in another thread, if a student doesn't know the general field he's interested in (e.g., experimental solid-state physics vs theoretical high-energy particle physics), how is he going to develop a candidate list of grad schools to apply to?

(2) We're talking about the US. If the student did not develop a strong interest in a particular field as an undergrad, how will he miraculously discover one in grad school? The first year will primarily be foundational courses in preparation for the qual exam. There typically is no grad lab equivalent to junior lab to permit the student to sample a variety of fields. And there typically is no opportunity for research until he gets accepted into a research group (with perhaps the exception of the first summer in some schools).

No. The foundational courses are grad level versions of typical undergrad courses, such as classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics and thermodynamics, and mathematical methods. Typically no labs. There will be later grad level specialty courses in solid-state physics, nuclear physics, high-energy particle physics, .... Depending on the school, some may be required, but often a student will elect those of value to his chosen research. Typically he doesn't have the luxury of first taking a full suite of specialty grad courses and then choosing his research field.

Thanks, everyone. My dilemma is that in college, I got the opportunity to do research in ONE research laboratory. That was in experimental condensed matter physics. I did not get to work in experimental High Energy Physics or experimental Particle Physics, or Quantum Physics. I understand that Condensed Matter Physics is a vast field with several focus areas, and it would take a lot of time and effort (more than I have between now and October) to read up on each of these.

My limited exposure to Physics is why I am unsure about the area of Physics I would like to focus on. How do I know if I would like Quantum Physics more if I have never had any formal exposure to the subject?

Since my only exposure is in Condensed Matter Physics, I started looking for professors working in Experimental Condensed Matter at universities known for their condensed matter programs, even if the research being done wasn't in what I have worked on at my research assistant internship.

My first list included MIT, UC Berkeley, Harvard, Princeton, Stanford, Caltech, Columbia, Chicago, Brown, UC SB, Rice, U Penn, Penn State, UIUC, Cornell, U Mich Ann Arbor, Northwestern, Yale, UCLA, Ohio OSU, U MD College Park, UC San Diego, UT Austin, U Minn Twin Cities, Rutgers, JHU and U Colorado Boulder. Are there any others I should consider?

From this list, I narrowed it down to Chicago, Yale, U Penn, Cornell, Northwestern, UCLA, U MD College Park, UT Austin, UC San Diego, University of Minnesota Twin Cities, and Rutgers.

Currently, I am talking to 2 professors (one from my college and one from another who I am working with), and their advice has been to focus on U Penn and Cornell. They also told me not to worry too much about my (side) interest in Mathematical Physics, and I will be given the option to choose three advisors. Hence, I can work with one even if they are in another department (Mathematics) at the college.

I hope this clarifies things.

 

[StatGuy2000]

No. The foundational courses are grad level versions of typical undergrad courses, such as classical mechanics, electricity and magnetism, quantum mechanics, statistical mechanics and thermodynamics, and mathematical methods. Typically no labs. There will be later grad level specialty courses in solid-state physics, nuclear physics, high-energy particle physics, .... Depending on the school, some may be required, but often a student will elect those of value to his chosen research. Typically he doesn't have the luxury of first taking a full suite of specialty grad courses and then choosing his research field.

As I've written several times, in the US, you don't want to sign onto a PhD Physics program with the expectation of finding what ignites your passion. You sign onto a PhD Physics program because some passion has already been ignited ... and a PhD Physics is the appropriate means to satisfy that passion.

For many years, I served as an industry mentor for STEM students. One was a physics undergrad in the US. When she was a senior, she wasn't sure whether she wanted to pursue a PhD physics program. I cautioned her that with only a bachelor's in physics, she would be employed as a research technician or assistant, not as a lead researcher, in industry; and she'd probably be bored to death within a year. But I also cautioned her that since she hadn't identified an area of research that ignited her passion, a PhD physics program was not a good default alternative, either. In the end, she landed a job as a research assistant for a company developing and manufacturing accelerators for medical treatment. Sure enough, within a year, she wanted out. But she now had a new found passion for medical physics. So she applied for a PhD program in medical physics and got accepted to a top program.

The question is not about passion -- I am of course operating under the assumption that the student applying for a PhD program has passion for physics in general. So according to you, @marcusl and @Vanadium 50 , every student who has finished their bachelor's degree in physics knew exactly what precise area of physics they wanted to research after finishing one introductory course (keep in mind that all undergraduate physics courses are ultimately introductory courses), and after attending a few seminars in such a field.

But the physics field is vast -- so vast that it boggles my mind that any student (apart from a very few) would have the knowledge after completing a bachelor's degree to know the exact area they want to research in.

Let me give myself as an example. I was studying mathematics at the university. Even by the time I finished my third year of my undergraduate degree (and when I started to think about whether to apply to graduate school or not), I had no idea of the vastly different areas of research within math. After taking a full course in mathematical statistics, I became interested in wanting to study statistics in more detail and decided to essentially double major in math and statistics, and applied for a masters. But I did not have any illusion of what precise area of statistics I wanted to pursue research in until after I was accepted and enrolled in a Masters program.

 

[Vanadium 50]

@StatGuy2000 are you arguing that things are different, or that things should be different? And if the latter, should adbive be given based on how things are or how they should be?

 

[StatGuy2000]

@StatGuy2000 are you arguing that things are different, or that things should be different? And if the latter, should adbive be given based on how things are or how they should be?

I am arguing that things were different with me as an undergraduate student in math (keeping in mind that I graduated with my undergraduate degree more than 20 years ago in Canada).

At the same time, I don't think my experiences were all that unusual. Many people that I know of who ultimately completed their PhD in statistics (whether in Canada, the US, or elsewhere) frequently completed their Masters degree in statistics or some other cognate program (like mathematics, operations research, etc.) before enrolling in and being accepted to a PhD program in statistics. This would have given these students opportunities for research experience, seminar opportunities, etc. that would have given the students the chance to narrow down their research interests in just such a way that you advise.

It seems to me that physics (or mathematical physics) is different. Perhaps physics undergraduate students generally speaking know what they want to do their research on by the time they graduate.

 

[StatGuy2000]

In case I'm being especially argumentative here on this thread, my basic arguments are the following:

• You don't know what you don't know.
• You cannot be expected to be passionate about a field of research you don't know anything about.
• A single course on its own does not equip students with enough information to know whether they will be interested in it.

Can someone please point out what is wrong with my logic above?

 

[gwnorth]

I agree with @StatGuy2000. I often wonder how students graduating from undergrad are so certain as to what specific field they want to pursue for a PhD after just 4 years of study at the undergraduate level. My son will be applying to Physics grad programs this fall, but while he has identified certain fields he's not interested in pursuing, he hasn't yet narrowed his interests sufficiently to be ready to commit to a specific subdiscipline. This is why he's opted for a master's first. That'll give him more exposure to coursework and research before needing to make a firm commitment to a specific subfield for a PhD. I know that doesn't really help applicants to PhD programs in the US, but that's why he's not applying there at this time. If the OP hasn't narrowed down their area of interest sufficiently, they may want to consider applying to research master's programs first.

 

[advhaver]

@StatGuy2000 are you arguing that things are different, or that things should be different? And if the latter, should adbive be given based on how things are or how they should be?

It seems to me that physics (or mathematical physics) is different. Perhaps physics undergraduate students generally speaking know what they want to do their research on by the time they graduate.

Thanks, Vanadium and StatGuy,

I do understand what StatGuy is saying because I am in the same boat now that he was in when he was applying for grad school.

It's near impossible for someone to get the opportunity to get a research internship in 3 different areas in 4 years of college. This was more complicated because the Class of 2022, 2023, and 2024 lost a year of access to laboratories due to Covid. For example, my classmates studying Computer Science could work remotely, but Science Majors couldn't.

I do not know any of my peers who secured internships in Astro Physics, High Energy Physics, Particle Physics and Condensed Matter Physics (Quantum Materials, Mesoscopic Physics, Nanophotonics, Solid State, Soft Matter, etc..). For example, the recent advances in Ambient Temperature Super Conductors also sound exciting, but I know no research laboratory would allow me to study this subject. I am limited to what is available on Google and YouTube.

After talking to the professors at my college, I understand that I should focus on my primary interest (Physics) as I can still study Mathematical Physics at University as part of my PhD Prep (pre-PhD). So there is no need to select universities because they have Mathematical Physics as part of the Physics department. A college like Northwestern (for example) would permit me to study Mathematical Physics (MP) as part of (or alongside) my PhD in Experimental Condensed Matter Physics even though MP is part of their Mathematics Department. So MP is not an issue.

I would be much obliged if anyone could offer any input on the universities mentioned in my earlier post or suggest other universities known for their work in Experimental Condensed Matter Physics (E-CMP).

Thanks.

P.S. I do not know if I would be drawn towards Experimental High Energy Physics in the middle of my PhD program. Still, given my interest in materials and my fondness for tinkering (because of which my mother wanted me to study Engineering), I suspect I will find what I am looking for within "Condensed Matter".

P.P.S. Knowledge is never wasted. If, after two years of my PhD I find I am unhappy and would be happier studying Engineering, I believe I could exit with a Master in Physics and apply for a Master in Engineering. I might even follow my dad's advice and do a Master's in Computational Finance; you never know. For the moment, the dream is to do a PhD in E-CMP.

 

[Vanadium 50]

Can someone please point out what is wrong with my logic above?

It is a statement of what you think should be.

Like it or nor, some schools are better in some areas than others. Knowing what you want to research helps steer your application.
Schools ask for a statement of purpose. They expect to know "why us".
About 2000 students a year somehow manage to come up with an area they are interested in.

Is the system perfect? I don't think anyone would say it is. Is it unfair? Probably to some degree, but I am not sure you'd get unanimity on what fairness is. But in any event, it's the system in place, and our advice should be geared to guiding the people through the system as it is, and not as some of us wish it would be.

 

[advhaver]

I agree with @StatGuy2000. I often wonder how students graduating from undergrad are so certain as to what specific field they want to pursue for a PhD after just 4 years of study at the undergraduate level. My son will be applying to Physics grad programs this fall, but while he has identified certain fields he's not interested in pursuing, he hasn't yet narrowed his interests sufficiently to be ready to commit to a specific subdiscipline. This is why he's opted for a master's first. That'll give him more exposure to coursework and research before needing to make a firm commitment to a specific subfield for a PhD. I know that doesn't really help applicants to PhD programs in the US, but that's why he's not applying there at this time. If the OP hasn't narrowed down their area of interest sufficiently, they may want to consider applying to research master's programs first.

Most programs in the US permit the student to exit the PhD with a Master's in Physics after completing the exams. Given the investment made by the university, I expect there to be riders, and this is only offered as an exception, but there is the option of an exit if you can justify it.

 

[advhaver]

Like it or nor, some schools are better in some areas than others. Knowing what you want to research helps steer your application.

Fair enough. Let's assume that my area of interest is Experimental Condensed Matter Physics. My research for the past 15 months (part-time and full-time) has been on Soft Matter.

Could anyone provide a "sanity check" on the university lists I suggested in post #32?

 

[StatGuy2000]

It is a statement of what you think should be.

Like it or nor, some schools are better in some areas than others. Knowing what you want to research helps steer your application.
Schools ask for a statement of purpose. They expect to know "why us".
About 2000 students a year somehow manage to come up with an area they are interested in.

Is the system perfect? I don't think anyone would say it is. Is it unfair? Probably to some degree, but I am not sure you'd get unanimity on what fairness is. But in any event, it's the system in place, and our advice should be geared to guiding the people through the system as it is, and not as some of us wish it would be.

If you are asking me what I think should be the way to apply to PhD programs in general, my view is that students should complete a Masters degree first (preferably with a thesis or project option), then apply for a PhD program (as is required for PhD programs in Canada and several other countries).

But I get it -- direct admissions is the system American universities employ.

What I question is how the 2000 students a year you quote somehow manage to "know" what exact research field within physics they intend to pursue research in (as expressed in their statement of purpose), given their relative lack of knowledge/experience of said field.

You seem to be implying that physics programs in universities in the US do a good job of making their students aware of the vast research fields available, and thus graduates know exactly what research field they want to pursue.

 

[CrysPhys]

If you are asking me what I think should be the way to apply to PhD programs in general, my view is that students should complete a Masters degree first (preferably with a thesis or project option), then apply for a PhD program (as is required for PhD programs in Canada and several other countries).

Ideally for a master's program to accomplish your goals, a physics student would need at least 1 yr of graduate level foundational courses [e.g., mechanics (classical and relativistic), electricity and magnetism, quantum mechanics, statistical mechanics and thermodynamics, advanced math], followed by at least 1 yr of graduate level specialty courses across a spectrum of fields (e.g., solid-state, high-energy particle, astro, plasma, nuclear, fluids, AMO (atomic, molecular, and optical) ...), and followed by at least X yrs of research projects in at least Y specialties. Then (a) the student can decide whether he wants to do a PhD program at all, or pack it in and (b) assuming he wants to do a PhD program, he now has enough advanced knowledge and direct research experience to determine (i) what specialty and (ii) what methodology (e.g., experimental, theoretical, or computational). Given the large number of combinations, does this sound realistic?

If we limit a master's to 2 yrs, including a 1 yr research project, then that means the student would need to choose the research project after 1 yr of foundational courses. So maybe he is slightly better off than after 4 yrs of undergrad courses (if that comprises his entire basis for selection), but not much. And there is time to complete only ONE research project, correct? If that ignites his passion, he's all set for a PhD program. But if it doesn't????

 

[CrysPhys]

Most programs in the US permit the student to exit the PhD with a Master's in Physics after completing the exams. Given the investment made by the university, I expect there to be riders, and this is only offered as an exception, but there is the option of an exit if you can justify it.

A grad student is not an indentured servant. If you want to quit, you quit. [Depending on your funding sources, there may be some fine print attached.] To get the master's, you need to fulfill the requirements for a master's (typically completing a required set of courses with a minimum required grade in each). But that's also why a master's in physics (specifically in physics, not in all majors) in the US doesn't have much value. For most of the top schools, you can't apply for a terminal master's. The only way you get a terminal master's from those schools is to (a) apply for and be accepted into a PhD program, (b) complete the requirements for a master's, and (c) not complete the requirements for a PhD.

 

[CrysPhys]

In case I'm being especially argumentative here on this thread, my basic arguments are the following:

• You don't know what you don't know.
• You cannot be expected to be passionate about a field of research you don't know anything about.
• A single course on its own does not equip students with enough information to know whether they will be interested in it.

Can someone please point out what is wrong with my logic above?

Yes, but:

* You do know what you do know.

* You can be passionate about a single field of research that you do know something about.

* A single course taught by the right professor can spark interest (even passion) in a subject; a single course taught by the wrong professor can kill passion (even interest) in a subject. [Not physics related, but have you seen the movie Dead Poets Society?] Regardless, you do have further resources to explore your interests other than a single course [e.g., prior innate interests going back to high school (and, in my own personal instance, elementary school), including science fair projects; inspiration by specific professors; junior-level specialty courses (e.g., solid-state or nuclear); survey lab courses (e.g. junior lab at MIT); undergrad research (during the semester and, more particularly, summer internships; senior thesis comes too late as a deciding factor, since grad school applications are generally due by end of first semester senior year); attending presentations in different fields given by professors or guest speakers; reading articles in different fields (not necessarily in advanced academic journals, but e.g. in Physics Today); talking to researchers in different fields (besides professors, researchers in government labs, industry, and business); participating in formal mentoring programs].

 

[CrysPhys]

But I get it -- direct admissions is the system American universities employ.

What I question is how the 2000 students a year you quote somehow manage to "know" what exact research field within physics they intend to pursue research in (as expressed in their statement of purpose), given their relative lack of knowledge/experience of said field.

You seem to be implying that physics programs in universities in the US do a good job of making their students aware of the vast research fields available, and thus graduates know exactly what research field they want to pursue.

It's a self-fulfilling protocol, isn't it? If students know what research field they want to pursue, and if they have evidence to support that (along with requisite grades and test scores), they will have a strong application and be admitted. If they don't know what they want, and if they apply to find out what they might want (if any), they will have a weak application and be rejected.

As it should be. We've been round the block on this many times. A PhD in physics is not a guarantee of a career, either in the specific research field, or in physics per se at all. So the PhD program needs to have value in and of itself. Given the long years (and attendant personal and financial trade-offs), it has value in and of itself only if it satisfies an innate passion for research. And you generally do not have a passion for "research in physics", but a passion for "research in X". If you don't, why do it?

 

[advhaver]

You seem to be implying that physics programs in universities in the US do a good job of making their students aware of the vast research fields available, and thus graduates know exactly what research field they want to pursue.

In my limited experience, I suspect their success is partial.

Take my mom and dad, for example. They both graduated in the 80s. Mom in economics, Dad in engineering. Mom found her true interests lie in art, and Dad self-studied macroeconomics (after his BS).

My ONLY experience is in Soft Matter. I do not know enough about the other avenues in Physics to know if I would enjoy them more or less. It was during my research internship in soft matter I came across Graph Theory and enjoyed that enough to consider studying Mathematics while doing my PhD in Physics. I know I have no interest in Astronomy, but I don't know enough about Quantum, Particle, High Energy etc.

The US education system exposes you to several courses outside your core subjects. It also means you are limited to 4-6 classes each in your core subjects (such as Mathematics and Physics). That is too limiting to decide on a PhD. But it is what it is. We can't change the system, we have to live with it's limitations.

If that ignites his passion, he's all set for a PhD program. But if it doesn't????

Or what if it ignites a passion for the one area he/she has experience in, only for him/her to find out later that there are other subjects that are more exciting?

A grad student is not an indentured servant.

That's the worst-case scenario I am willing to consider. If I am unhappy, I will complete a master's (in Physics) and choose another avenue. Since my interests have always been related to maths and physics, there are plenty of other options (within these subjects).

* A single course taught by the right professor can spark interest (even passion) in a subject; a single course taught by the wrong professor can kill passion (even interest) in a subject. [Not physics related, but have you seen the movie Dead Poets Society?] Regardless, you do have further resources to explore your interests other than a single course [e.g., prior innate interests going back to high school (and, in my own personal instance, elementary school), including science fair projects; inspiration by specific professors; junior-level specialty courses (e.g., solid-state or nuclear); survey lab courses (e.g. junior lab at MIT); undergrad research (during the semester and, more particularly, summer internships; senior thesis comes too late as a deciding factor, since grad school applications are generally due by end of first semester senior year); attending presentations in different fields given by professors or guest speakers; reading articles in different fields (not necessarily in advanced academic journals, but e.g. in Physics Today); talking to researchers in different fields (besides professors, researchers in government labs, industry, and business); participating in formal mentoring programs].

Agreed. A good professor can make a world of difference.

I have always been drawn towards Mathematics and Physics. As a high schooler, I used to tinker with springs, capacitors, inductors, Peltier elements, piezo-electric sensors, etc. I built several projects, including an umbrella gun (inspired by The Kingsman), Wolverine claws, Taser rings (inspired by Superman), etc. I am pretty clear whatever I end up doing, it will involve Mathematics or Physics or both.

As of now, I am relying primarily on my college classes, undergrad research and senior theses (I have 2 - one each in Maths and Physics). I am unsure if that's enough, but I am ploughing ahead.

Meanwhile, the question I was hoping to find an answer to remains unanswered.
"Could anyone provide a "sanity check" on the university lists I suggested in post #32?"

Thanks, everyone.

 

[CrysPhys]

Or what if it ignites a passion for the one area he/she has experience in, only for him/her to find out later that there are other subjects that are more exciting?

That's always the case. It's necessary and sufficient to have passion in one area of research. If later on you find other areas that ignite your passion even more, you can switch (if opportunities arise, circumstances permit, and you're willing to do what it takes to retrench). I've known some researchers who have stayed in the same narrow niche for their entire careers; and others who have made radical shifts.

That's like a guy falling in love with a girl, but refusing to make a commitment ... because he might meet another girl that he finds even more exciting.

 

[advhaver]

That's always the case. It's necessary and sufficient to have passion in one area of research. If later on you find other areas that ignite your passion even more, you can switch (if opportunities arise, circumstances permit, and you're willing to do what it takes to retrench).

Exactly, that's what I meant when I said, "I am ploughing ahead", with the limited knowledge at my disposal.

I could use that "sanity check", though. Have I missed including any university in my long list? Is my short list too "dream heavy"? Should I switch any from my shortlist and long list?

The shortlist: Chicago, Yale, U Penn, Cornell, Northwestern, UCLA, U MD College Park, UT Austin, UC San Diego, University of Minnesota Twin Cities, and Rutgers.

The long list: MIT, UC Berkeley, Harvard, Princeton, Stanford, Caltech, Columbia, Chicago, Brown, UC SB, Rice, U Penn, Penn State, UIUC, Cornell, U Mich Ann Arbor, Northwestern, Yale, UCLA, Ohio OSU, U MD College Park, UC San Diego, UT Austin, U Minn Twin Cities, Rutgers, JHU and U Colorado Boulder.

 

[Vanadium 50]

My advice hasn't changed - you need to go through the list of people with whom you might want to work and see if they still active. Yes, that's a lot of work. But it is your future.