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I was wondering how PhD admissions actually work. Do we have to mention the professor we want to work with in our application? Do we reach out to them before we actually apply? And what if my research experience is in one area (theoritical computer science and coding theory) but I'd like to do my PhD in some other area (Artificial Intelligence/Machine Learning), where I haven't had any experience? Any advice would be appreciated.

Update: For context, I am an undergraduate student studying Applied Mathematics at a liberal arts college in the US. I want to apply for PhD programs in Computer Science in the US.

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    Please ask only one question per post. Aug 31 at 21:16
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Most PhD programs in the US (including CS, at least those I have any familiarity with) primarily admit students to a program; faculty advisors are chosen later.

These programs also tend to have extensive websites that explain the admissions process in detail, though you might have to dig a bit. For example the CS program at UW-Madison says about admissions decisions:

After careful review, the Graduate Admissions Committee recommends admission for the applicants they feel are most qualified for our program. The selection is made without regard to the degree goal (MS or PhD), area of interest or financial need. The department’s admissions recommendations are reviewed and approved by the Graduate School.

Nothing is mentioned about having selected an advisor or having their support ahead of time. If you dig further, they have a guidebook that mentions:

It is the responsibility of a PhD student to eventually find a dissertation advisor; the Department does not guarantee that a dissertation advisor will be provided. The dissertation advisor must be a full-time or affiliate faculty member of the Department, or have retired or resigned from such a position no more than a year ago.

"Eventually" - not before admission. Typically the first year is spent taking classes and beginning relationships with faculty members that could be potential advisors. I was not in CS, but my own grad program (neuroscience) had a more formal "rotation" structure, where new students spent the first couple of semesters in rotations with 2-4 faculty members, spending a bit of time in their labs to get to know them.

This is just one example - you will need to research individual programs to see how they do things exactly. I spent about 5 minutes finding this information for one program, though there's a lot more to read. You'll want to apply to several programs, and should plan to spend a good number of hours doing research like this into programs before you apply.

If you want to work with a specific person, I'd highly recommend reaching out to them in advance. What if you get admitted and then find out they are moving to another university? Or retiring? Or not taking students because they have too many, don't have funding, plan to go on sabbatical, etc. However, their blessing will not be required for application (unless the program says otherwise; do your homework) and may not even be particularly beneficial, depending on how admissions decisions are made.

Even if you don't have a specific person you want to work with, it can still be worthwhile to reach out, but not all faculty will be that responsive: you might just get referred to the application process if they'd prefer to not deal with prospective students until they are actually interviewed or admitted.

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There are a few questions in this post, but I will answer the title question, "For PhD admissions, do you mention who you want to work with in your application??

There is no general answer. It is different in different fields and subfields, and across countries. You should ask an advisor in your field to make sure you are doing what is expected.

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You normally need to contact the person you wish to work with before you start applying for your PhD since you need to make sure they are able to take you on as a student. You also normally need to mention it when you submit your application so the university knows everything is ready for you to start. For your last question, it depends on the area - for example, if you studied math prior to your PhD you may be able to apply for a PhD in data science, finance, etc. but it depends a lot on what the project requires and whether the specific department is willing to admit you.

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    This is not true in all countries/fields; in some places you are admitted to a program and while it may still be beneficial to be in advance contact with professors you may not choose an advisor until after the first year of study.
    – Bryan Krause
    Aug 27 at 4:33
  • Really? Wow, that is pretty weird (not that I'm doubting you, you're likely correct). At any rate it definitely would be best to contact the researcher you wish to work with beforehand because if you start a PhD program (on the condition you wish to work with a specific researcher) only to find out that the researcher is unavailable to be your supervisor then you've basically wasted a year of your life. Also, it's possible that the interests of the researcher may be focused in a different area at the time you talk to them, so it's best to make sure both your interests align.
    – user145305
    Aug 27 at 4:49
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    @user145305 Keep in mind that in some countries you start your PhD directly after completing your bachelor's degree. As far as I understand, the first year is basically just courses that in other systems would be part of the studies for a master's degree. Contacting potential advisors before being admitted to a PhD program appears to be not considered appropriate by the potential advisors.
    – Roland
    Aug 27 at 6:32
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    @Roland I'm in a country where PhDs are like that (I took two years off, but same diff, the US). However, in my field you are expected to contact advisors. There is no general answer. Even some departments are more receptive to it than others. Aug 31 at 21:12

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