The Hitchhiker’s Guide to PhD Applications

What is a PhD, and why must you apply to it? What is the meaning of Life, the Universe and Everything? We will do our best to avoid such topics in our conversation here. Instead, I will give you a rough overview of how to apply for a PhD in the sciences. The document contains tips and general advice that I have gathered during my application experiences, which if followed properly will cure depression, anxiety and blindness¹. For context, I am a recently graduated 5th year Maths major from IISc, with a specialty in Geometric Analysis. I applied at the end of my 4th and 5th years. I got no offers in my 4th year, and in my 5th year I got accepted to 3 programs in the US. Out of these, I will be attending Johns Hopkins University as a Maths PhD student starting Fall 2026.

This document is a bit too long, so I have included a summary at the end of each section. Use the table of contents button on the top left to navigate to the sections most relevant to you. With this, let us begin. Do note that lots of these tips also work for people applying for a Masters program. The intended audience is people who are trying to apply for degrees abroad. NOTE: Do not read this if you aren’t intending to apply somewhere in the next 6 months or so. Firstly, it doesn’t help your current academic situation, and secondly, knowing how you can optimise your projects and courses to improve your application takes the joy out of learning and may even be counterproductive by way of analysis paralysis. That is definitely not my goal here.

Introduction

Applying for a PhD is not easy for anyone. The competition is cutthroat and the requirements stringent. Combined with perpetual funding issues in academia, this problem is likely to get worse. There are tips that will help you with your application, but it is important to note that everyone is operating on assumptions. From what I have heard, sometimes not even the admissions committee knows what kind of candidate they will be selecting. The decision depends on human bias, availability of professors, funding issues, or maybe even the weather. Who really knows. So, the most important piece of advice is:

Treat applications like a game of chance. Take inputs from a lot of qualified people, average out their advice and proceed based on that.

Why do a Phd?

This seems like a silly question to ask someone who is already reading this document, but it is important to go through the motions regardless. Why do you want to do a PhD? I have found that many of my own batchmates haven’t seriously asked themselves that question.

It is easy to go along with the flow and do what everyone else is doing. Everyone starts thinking about their major well before the 3rd semester. Everyone takes [insert name] elective once they start their major. Everyone applies for foreign internships in their 3rd year. Everyone applies for a PhD. But you don’t have to be everyone.

To be clear, it’s not bad to be generic. My own journey has been extremely typical, and I have done all of the things listed above. The majority is not misguided. However, I sincerely believe that you must look at whether these things apply to you. The point of a PhD is to gain specialisation in an area. You will contribute novel research and push the edge of human knowledge. It will also be an arduous and challenging process, where you will feel hopeless and want to quit multiple times. You will be out of the workforce for a significant portion of your adult life, and your employment prospects after a PhD will likely contract (even if the pay increases, job options won’t be as plentiful).

So you must ask yourself, does your passion for your major extend to research? Will you be satisfied with contributing new, niche ideas to your field? If you emphasize the immediate applicability of your work more, if strong financial stability is important to you or if you’re simply burnt out while doing your Bachelor’s or Master’s thesis, you should not go for a PhD without careful consideration (keep in mind this advice is from someone who hasn’t yet started their PhD, I might change my mind later).

Sometimes a PhD is not even the best way to contribute to new research in your field. If your field is volatile and projects get outdated in just a few years or even months (eg: LLM research right now), then it is not best to commit to a PhD where you have to spend 4-ish years working on a single thesis. In such cases, joining as an RA or even entering the industry straight away would give you better chances of learning more about the field and making new contributions. Some fields might not even exist by the time someone finishes their degree. I have also heard of people going into PhDs because they thought they were too far in, or they were scared of entering the corporate workforce. Research should not be driven by necessity, but by passion. Otherwise you should just switch to a corporate job where you would be equally unfulfilled but richer. Sure there will be many rough spots, but if that is all you are experiencing all of the time then maybe it is time to reconsider. And as for switching careers, it is almost never too late to do that at the student stage.

Having said all this, I cannot ignore all those friends and colleagues who are perfectly suited to do a PhD, but hesitate because of imposter syndrome and financial worries. While academia may not pay handsomely on average, it will definitely sustain you. If you aren’t likely to have dependents to worry about, you will be fine. And of course if you are that good, you will get compensated well. As for those who hesitate because of a lack of belief in their abilities, imposter syndrome is extremely common in academia. Leaving higher studies because of a dwindling passion or excessive workload is common and reasonable. But to leave higher studies while being motivated and working hard is probably not the right move for most people. I am speaking out of turn here, since I have yet to start my own PhD, but most of the self doubt I have seen is due to emotional reasons. The person likely had some image of a researcher they failed to meet and have low self-confidence because of that. If your doubt comes from actual data; like noticing that you are a very low performer compared to the average in your field (and not just your cohort or immediate friends); then it is worth acting on. Keep this in mind when evaluating your decision.

Think about these things seriously at least once before you start the application process. You won’t get the time later, and it helps put your mind at ease. Even if doing a PhD is the natural choice for you (like it was for me), asking seniors and looking online for experiences of other people doing research broadens your view and helps calibrate expectations.

Summary:

• Ask yourself why you want to do a PhD, do not get swept up along with the crowd.
• Try to get an idea of what a PhD experience realistically looks like.
• A PhD is not always the best way to contribute to research in some fields.
• If you have passion and persistence, you will do well.
• Doing a PhD is a noble pursuit which makes you better than other people²

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How to begin?

Let us move on to more practical advice. The first and most important thing to do is to identify which people have the knowledge and time to help you. Make a note of your batchmates applying from the same or similar fields. Get the contact details of seniors whose profile matches yours. Find out which professors in your department are willing to guide and help you. One of the biggest advantages of being in a university is the network you have access to. These people will make your life easier every step of the way. Make sure to return the favour by helping them when they need it.

The second thing to do is to decide what sub topics you will highlight in your application. Some people are laser focussed on their specialty and don’t need to think about it. I had done some work in probability and computational geometry, but it would distract from my later courses and projects which could all be grouped under the topic of Geometric Analysis. This decision may be difficult and require a lot of deliberation, especially for people who have a decent body of work in multiple fields with little intersection.

Choosing your college list

How do you choose your list of universities? In my opinion the best thing to do is to start by identifying the countries where you want to apply to, as the timeline and rough format of applications remains the same for each country. Keep an open mind and go through the various options, especially if you aren’t one of the top performers in your college. As the academic funding in the US contracts and applications everywhere get more competitive, it is wise to look for great researchers in your field that are not necessarily in the most popular academic spots.

The next step is to find out what is important for you. Do you want a singular great advisor, even if there are no others nearby that are comparable? Do you want a strong department that has many great researchers inside and in close proximity, which makes collaboration much easier? How important is the funding amount for you? Do you want a place with good industry tie-ups just in case you change your mind later? Do you want to enter a lab that has extremely frequent research output, or a smaller but highly curated selection of papers? Many such questions can be asked, and you must pick a few that are the most important to you. For me, a dense network of researchers in my field was very important.

With your preferences in mind, you should make three categories: Aspirational, Possible and Practical (I dislike the word ‘safety school’ since it is disparaging). The classification requires calculating a rough estimate of how your application to that place would do. Do not base this on your warped view of your academic abilities, try and get data on where people with similar profiles as yourself have been placed, and ask others to evaluate you. Do NOT rely on QS or other rankings, except as a rough indicator. PhDs are far too specialised to rely on a general ranking for, even if it is a subject ranking. Also, do not place any universities that you would really not like to go to in your Practical category. It doesn’t matter even if you get in, if that is a place you would not enjoy going then there is no point applying in the first place. Each of your places should be somewhere you would be at least moderately satisfied to end up at.

I will make a note here of a sentiment that is popular amongst some people, where they apply to a lot of Aspirational places because “It doesn’t hurt to apply, and you never know what happens”. While that is technically true, applying to any place takes a lot of time, effort and in some cases even money. If you aren’t putting in efforts in your applications to these Aspirationals, then you should not be sending them anyway. And if you are putting effort into all of these, then overdoing it would only tire you out and distract you from the Possible and Practical categories where your efforts would yield more dividends. Applications are very mentally and emotionally taxing, and you will be working on your academics simultaneously. Overburdening yourself with applications that have a low chance of working is not a great idea.

Do not overfill any of three categories, keep them roughly equal unless you have a good reason for doing otherwise. Note also that your list does not have to be finally and fully prepared even very close to the application deadlines. It can fluctuate depending on how the information you have changes, how your conversations with professors at the institutes go, or many other factors. But you should definitely maintain a list on Excel or whatever software and maintain the three-tiered classification for each one.

Starting this process 3-4 months before your first deadline is more than enough time. I started much later.

Summary:

• Fully utilise your network, talk to as many people as possible.
• Start by knowing which countries you will be applying to.
• Find out what is important for you when looking for a PhD lab/institute.
• Divide each college/lab you are thinking of applying to into Aspirational, Possible and Practical.
• Don’t obsess over Aspirationals and don’t put colleges that you don’t actually want to go to in Practical.
• Rely on data from previous applicants, professors and online accounts to get a good idea of how to build these categories.

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Paperwork and Pre-requisites

1. Get your documents ready. Passports should be made well before applying. Your marksheets, transcripts, internships certificates, etc. should all be available to you. Uploading them on a cloud-based service like Google Drive is recommended.

2. Identify which exams you have to give for each application. Refer to the admissions website for each of the colleges you are interested in for that. This should also be done well before your applications. Also know the exam cutoffs each of these institutes require.

3. In some cases, admission to an institute requires passing an examination then giving an interview. In such cases most of the advice here is unnecessary.

4. Prepare well for each of the exams. In some cases they cost a lot of money to give and re-attempts also take up valuable application time. I personally know of people who were confident in their English but had to give TOEFL as many as three times to get the right cutoff. Academic writing doesn’t translate to general English skill.

5. Identify potential professors who will provide you a Letter of Recommendation (LOR). You don’t need to ask for it a long time before deadlines, a month before is more than fine. But being aware of them beforehand is an advantage, which I will elaborate on in the next section.

6. Have a vague worst case backup plan in mind, whether that be continuing for a PhD in your own institute, applying for jobs you can easily get, or even switching fields and degrees (MBA, etc.). You don’t need to start preparing for it, but having it in mind helps ease anxiety.

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Emailing Professors

This is a topic I do not have much good advice for. Emailing has an important role in networking, it’s how you connect with these professors far away from you before even beginning your application. Some people can skip this step and it will not significantly affect their acceptance chances (eg: if you are applying to a maths PhD in the US), but for most people it is vital. In some fields the entire application process consists of emailing the right people so they support your application. The type of email you will be sending will depend very much on your goal. Do you want to create an impression and be seriously considered by this professor? Or do I just want them to be aware of my existence and take a quick look at me? The first makes sense if you are looking to apply directly to this professor. The second makes sense if you are applying to a department and don’t have a specific advisor in mind. In my case, I mostly sent emails of the second kind because I was applying to departments.

In the first case, it’s better to send warm emails, i.e. where the mail is specifically tailored to the particular professor and how you can better work with them. In the second case, you should send a cold email, which is mostly generic and doesn’t change much from professor to professor. Most of my emails were cold because I did not have a specific advisor in mind as I was applying to the whole department. In case of applications to particular labs and professors, do definitely ask for a video call where you can discuss things further. Here is one of the cold mail templates I used:

Dear Professor [Name],

I am in my 5th and final year as a BS-MS student at the Indian Institute of Science (IISc) in Bengaluru, writing to enquire about potential openings in your research group for a PhD candidate.

My background is in Geometric Analysis, with courses and projects in topics like [List of project and course topics] and my current project is on [topic]. I am also eager to learn more about [topic] and [topic] in the future. These areas are deeply interconnected, and I hope to continue working on their interface during my PhD.

I found the spread of topics in your various publications in Geometric Analysis very appealing. With a basic understanding of many topics within this field, I think I am in a good position to dive deeper and work on new research (preferably under you!). If you anticipate openings in the upcoming cycle, I would be grateful to know whether my profile is a good fit.

I have attached my CV for your reference (with links to some of my project reports).

Thanks for your time!

[Salutations]

I had reasonable success with this template, with an average reply rate of about 15 from a total of 95 sent (I did occasionally tweak one or two lines to better suit a professor’s profile). Note that every professor I sent this to had significant work in the field of Geometric Analysis, so the email had some relevance to their work. I also sent around 10 warm emails, out of which I got 5 replies (3 of them were one line long). It’s not perfect and I would make many changes if I did it now, but it did the job. Take this as a data point and not as prescriptive advice.

You should strike your own balance between cold and hot emails, primarily because of time constraints. For your preferred professors, take some time out and write a personalised email. It might even be worth contacting their students for information if you like them a lot. For the others, send a lot out with only small variations to save your time and attention. Don’t go too cold, the professor should have something to do with what you have written to them. You can have your own standards for cold and warm, for maths it’s fine to be colder but with something like biology the average email has to be warmer. Putting too much effort into each email doesn’t guarantee more replies, you also need luck and a profile match for that.

As for when to send out the emails, I believe it best to start one month to a few days prior to the deadline of the application. For most departments, the committee will review your application months after submission, so mailing long before the deadline increases the chances of people forgetting about you. Mailing is a game of chance, so you should not compromise with quantity. I didn’t send many follow-up emails in case of no reply, but for professors I really liked, I restricted myself to two spaced follow-up emails. I scheduled all my emails to morning at the professors local time, but there is no real science to this.

Summary:

• For most people, emailing is vital to increase your chances of acceptance.
• Divide professor emails into two categories, warm and cold emails. The categorisation will depend on how much you want a response from the professor. Ask for video calls or in person meetings if you are applying to a particular professor.
• Most of your emails should be on the colder side, since emailing is a gamble the focus is on quantity. Try not to go too cold and maintain relevance. The exact mixture will depend on your field, generally more experimental fields have to be warmer.
• Don’t send out emails too early before the deadline, unless you are sure to have a regular back and forth with the professor for a while.

The Actual Application

We can finally talk about actually filling the online application form. There will be lots of mindless paperwork, uploading test scores, identity documents, transcripts, etc. This you can do, though do be careful and accurate. There will be weird edge cases and conversion issues you might face, eg: not having a last name, grades being asked for in a weird format, not having your specific degree as an option in the drop down box, etc. In such cases, almost all places should
have an application support email mentioned somewhere that you can contact.

The timeline for when to submit applications is different for different people. I am a procrastinator so I like to submit them 3-4 days before the actual deadline.

Letters of Recommendation

These are an extremely important part of your application, and also the thing you have very little control over as you get closer to applications. A good LOR means there is an established person in the community who has chosen to vouch for you (basically nepotism), a bad or even lukewarm LOR can highlight your flaws more than your achievements. So, choosing your letter writers involves balancing the quality of the recommendation and the influence of the professor.

In my opinion, you shouldn’t take a lower than neutral LOR from any professor, no matter how well known they are. It is an endorsement, and if the person writing doesn’t like you at all then it defeats the purpose. Good professors to get letters from are those that have actually seen you work, either as project supervisors, thesis advisors or course instructors for courses you actively participated in. They should be able to write at least some specific skills that you have as a researcher. For example, there was a professor I had three courses under, each with an A+ grade. However, my attendance was extremely bad for each of the courses and I very rarely interacted with him. I chose instead to get a letter from a professor I had done a 3 month internship under about 1.5 years ago. This person had actually seen me working and I had kept in touch with him via email and kept updating him about my progress in my later projects.

As mentioned earlier, you should ask professors for an LOR around a month before your first deadline. Some professors are known to be very picky about being informed early on and only writing a fixed number of LORs, you should ask around to see if that is the case for your professor. Also, keep some backup professors in mind in case any of your letter writers gets busy or refuses to write more (yes, that does happen sometimes). Though, of course, do not refer to them as backup professors.

Summary:

• A bad or neutral LOR can be very harmful to your application.
• Preferably reach out to professors that have interacted and worked with you personally. They should be able to confidently write about specific skills you have as a researcher by seeing you work.
• Most professors are fine with a month’s notice to write their LORs. There are some that are notorious for demanding too much time, only writing a fixed number of letters. Ask other people and gather information.
• Your letter writers can always suddenly get busy, always have one or two backups in mind.

CVs

I won’t speak much on the topic of writing a good CV here, because if you are applying for a Masters or a PhD program you have almost surely made a CV many times by now. Your CV must be a summary of all your relevant work. Include everything you think is strong and relevant to your profile. It is my personal opinion that going beyond 2 pages is not necessary unless you have been exceptionally productive during your UG/Masters degree. Since most CVs will only be viewed online, you can also include hyperlinks to project reports in the CV.

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Statement of Purpose (or Cover Letter, etc.)

As with all the things in the document, the best thing to do is to ask everyone. Make many people review your SOP and, as always, average their advice. As with the other application-related things, there isn’t much science to writing an SOP. In the hierarchy of importance, I would rank the components of an application like this:

1) Academics (GPA, Projects, Academic fit, etc.)
2) Letters of Recommendation
3) Statement of Purpose/Cover Letter, etc.
4) Personal Statement (if one is required)

An SOP is usually the last thing reviewers look at. If you don’t meet the university’s criteria for academics from the first two things, then even Shakespeare himself writing your SOP wouldn’t help you get in. However, since in the final days before your applications this is the only thing you can control, people tend to give undue importance to it. At most it functions as a tiebreaker between perfectly qualified candidates. Many people with good profiles get in with even the laziest of SOPs, because not letting in an amazing candidate because they weren’t good at English literature is an insane thing to do for a university. Having said that, I do have some tips to make your SOP better.

The biggest mistake I have seen while reviewing other people’s SOPs is that they treat them like an extended CV. There will be paragraph upon paragraph listing each of their projects, the techniques they learnt, the courses they took and the books they read. You have already supplied this information in your application through your transcripts, CV, and other information you enter into the admission portal. Your aim should be to sell yourself as a good employee and PhD student. Think about why people would choose you over someone else with similar qualifications. Do you have a collaborative nature? Are you extremely punctual, systematic and diligent? Are you one of the most ambitious people in your batch? Find out things like this about yourself which make you stand out, and highlight using your work.

As an example, I saw a Cover Letter written by my friend that was the standard list of achievements and projects. He had mentioned a computational project where the job was to model gravitational waves. He gave a fair account of what models he made and the technical skills gained during the project. However, since I knew him personally I knew it was an extremely challenging task because none of the code written by other researchers had been made public. Additionally, the professor with which he had started the modelling project had essentially abandoned this approach and told him to work on other things. He had worked for around 1.5 years independently to make the final models and was writing a comprehensive guide on the process to help others in the field. This project shows immense commitment, long-term planning and initiative. Yet none of it showed up in his own description of the project, replaced by a list of skills and topics learned. A more involved description of his involvement in the project and how it changed his attitude towards research occupied roughly the same amount of space but conveyed the extent of his effort much more effectively.90

It is also important to have an overarching theme for the SOP. Mine was showing the process of how I got an interest in my field. I could talk about all the projects and courses I took while highlighting how they led me to have an interest in the subject. If you haven’t changed fields much, a good narrative might be showing how your interests and thoughts have changed as you learnt more about the field. If you transitioned from one field to another, focussing on the reasons for your change might be very important. From what I have seen, a theme of change is the most effective because you get to talk about various projects and courses over the years while highlighting your strengths at the same time. Having a theme and narrative also helps you remove unnecessary material and prevents the SOP from turning into a list of academic achievements. Not mentioning tangential or weak projects/courses can be a good thing. In all cases, your theme should highlight that you are ready to start a PhD using your project and course experiences as evidence.

The next important piece of advice is that you should use your SOP to fill in the gaps in the rest of your application. Did you get abnormally low marks in an important course? This is the perfect time to talk about why that might have happened and what you did to overcome this deficiency. Anything that doesn’t show up in your CV, transcripts and other documents but is still important to painting a picture of you as a researcher should find its way into your SOP.

Finally, be extremely aware of the word limit. Have multiple versions of the SOP going into different levels of detail according to the word/page limit. Since there is no consensus among universities of how long it should be, this is very important. Start with the longest version first (around 2 pages), and keep cutting down. Things to cut down first include elements of unnecessary storytelling, but never let go of the theme. Your aim should always be to market yourself as a good PhD student.

Now we must talk about customising the SOP. Of course it must change for each university and professor you apply to, but to what extent? This is similar to the classification of cold vs. warm emails we talked about earlier. Is it important for the place you are applying to to know that you want to go there specifically? In most cases the answer should be no, because both universities and students understand that they have to apply to multiple other universities no matter how much they like a particular one. For me this meant including a paragraph that contained the professors I wanted to work with at the university with a few words about why I like the university. This was the only thing that changed between my applications. If you have a particularly good reason for liking a professor or university that goes beyond “They have a good ranking/are good researchers”, then it wouldn’t harm to mention that. Otherwise, telling a university or professor how good they are serves no purpose; it will not help your application.

Finally, to put my money where my mouth is, I am including a link to a Google Doc containing two examples of SOPs, one that I used during my first application cycle and one that I used in the second one that finally got me an acceptance. It might be instructive to see what changed between the two versions, though I can find fault with both in hindsight.

2024 SOP

2025 SOP

Summary:

• An SOP carries much less importance in your application compared to your Academic Record and Recommendation Letters. At most, it serves as a tiebreaker between equally qualified candidates.
• Your aim should be to sell yourself as a good employee and researcher. Use your experiences in your projects and courses as evidence for your research qualities, don’t just state things.
• Find a theme for your SOP, good choices might be to focus on your changing interests throughout your degree. It allows you to talk about all of your experiences while highlighting the unique skills and perspectives that make you stand out.
• Use your SOP to compensate for the weak points in your applications. You can use them to explain bad grades, short projects and long gaps in the CV provided the explanations are reasonable.
• Customising your SOP for a particular university should only be done if you have a good anecdote/unusually strong reason for preferring them in particular. Telling a professor or university how good they are serves no purpose; they already know.

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Personal Statements and Personality questions

Some places will ask you questions like “How do you think you can become a valuable member of the community at [X University]?”, or ask for Personal Statements where you can share your own story. Personally I have no reason to believe this is an important part of the hiring process. However, when I was forced to write Personal Statements, I wrote about my experiences coordinating the mathematics club in my institute and how that has influenced me to be community-driven.

I have also seen questions that ask about leadership skills/community outreach, etc. and I mostly used the same script everywhere. I haven’t heard from any of the people I have interacted with that such entries have any meaningful impact on a STEM admission. However if you do have time to spare, then it doesn’t hurt to try.

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How to continue the cycle

It is not like all your deadlines will be on the same date, after which you will be free to work on other things. Application season lasts for months, with people applying all the way from November to April just for the Fall intake. Take into account rolling admissions, and you might end up applying the whole year round! Applications will be a major distraction and energy sink during this period of time. To stay on top of your work, proper pacing and scheduling becomes important.

Firstly, to continue the cycle it is very important to realise that applications are a stochastic game. You can almost never guarantee admission into a particular institution no matter how “safe” it might be. What you can say with good confidence is that you will definitely get into the “Practical” institutions if you keep applying consistently. This is because rejections can happen for too many reasons, and many of them relate to politics outside of our control. The department might have had a bit too much hiring in your field in the previous cycle, which means they won’t take anyone with your background no matter how good they are. There might be funding cuts right around the corner. Someone in the committee might have a grudge against the potential advisor you listed.

All of these arbitrary reasons that we cannot control can cause rejection. It is not always that you weren’t “good enough”. Despite this knowledge, continuing to apply despite multiple rejections is extremely hard. I did not manage to do it in my first application cycle, I just accepted that I wasn’t good enough. However, in hindsight I can see that I had one of the better profiles in my batch, and I would have surely gotten in if I had continued applying. While there may be a certain part of the population that is delusional about their chances and keeps on applying, from what I have seen of academia most people tend to be underconfident and suffer from imposter syndrome.

Have a good support system around you. Do not neglect your friends and family during this period. They will help you remain objective and motivated throughout this process. Keep talking to batchmates, friends, seniors and professors. Also, having dedicated time slots for working on applications is extremely important. It prevents procrastination, but more importantly it prevents application work from taking over your life. I have seen a few too many friends lose their minds by checking their application portals again and again, and spending most of their time on application discussion forums.

The best way to gauge how many applications to send before giving up is again, to ask people with similar backgrounds and look at the data. Try to be as objective as possible. If you cannot source such information, make your best possible guess before you get any of your results, add 7 to it and write it down. Try and hit that number of applications irrespective of how many applications you fail. While it is possible that your initial guess might be an underestimate, again with the prevalence of imposter syndrome in academia I think most people would be fine with this strategy.

Summary:

• Applications take a lot of time and energy to complete. And for most people, the deadlines span over multiple months. Maintaining a balanced approach to the amount of effort put in becomes important.
• Applications are dependent on a lot of factors beyond your control. Getting rejected from your favourite places can be hard but one should not draw too many conclusions from it.
• Continuing to apply to places is extremely important, do not cut your cycle short because of one or two disappointments. Rely on your friends, family and peer network to remain objective and motivated.
• Have dedicated time slots to working on applications, it helps keep everything contained.

Interviews

I only had one interview in my application process, which I did not pass. So it is not my place to be giving interview advice to people. What I have heard is that if the professor didn’t really want to interview you in the first place, the interview will likely not change their mind.

This on-site visit preparation guide from the IMPRS (International Max Planck Research Schools) website containing potential questions and tips on presentations, etc. may be helpful. You can also check the List of Sources at the end for more information.

List of Sources

This is my perspective on applications and how to do them well. It is obviously very heavily influenced by my particular specialisation and circumstances. I hope you will be able to apply them to your situation. As always, the most important advice is to ask every qualified person you can think of for advice and averaging it out. To at least slightly rectify the situation, I have asked some of my friends to contribute some videos, blogs, websites, etc. they found particularly helpful during their own application process.

General Links:

1. Grad Cafe: Forum for viewing admission results for graduate applications around the world, you can also submit your own. For your own sanity, do not check it too often after submitting an application.
2. https://lucylai.com/blog/gradapps.html: A general guide much more concise than my own. The interview section seems particularly useful.
3. Concise Application Tips for US mathematics PhD applicants

SOP/Cover Letter tips:

1. https://www.findaphd.com/guides/academic-cover-letters
2. https://drive.google.com/drive/folders/1LMYk6zJBRMo1sHFHK7aAbz-bSBWvHnKD?usp=sharing: Drive link containing ~25 SOPs of various IISc senior batches (‘24 and earlier) applying to the US
3. LMU Application Tips: Tips and pointers on what to include in your CV, Motivation letter, etc. by LMU in Germany.
4. YouTube video by channel Lucy Lai (neuroscience focussed)

Interview tips:

1. YouTube video by channel All ‘Bout Research (Chemistry focussed)
2. On-site visit preparation guide: Guide by the IMPRS institute in Germany on how to prepare for their on-site visit and interviews, contains good potential questions.

Finding Universities:

1. Chatbots are pretty good at finding places you wouldn’t normally look at, though they can have weird biases at times.
2. https://hyperspace.uni-frankfurt.de/category/jobs/: Compiled list of job openings in Relativity and Cosmology (roughly).
3. https://inspirehep.net/jobs?sort=mostrecent\&size=25\&page=1\&status=open\&q=: Job openings in High Energy Physics
4. https://crc326gaus.de/projects/: Job openings in Europe for PhD in Algebraic geometry and Number theory.
5. https://cvgmt.sns.it/positions/: Job openings in Europe for Calculus of Variations and Geometric Measure Theory.