How closely should my research proposal align with existing projects in the department?

Question

I am hoping to apply for a PhD in mathematics in Germany, where the most common method of pursuing a PhD is to put together a research proposal and then find a professor who will support you. This is vastly outside of my experience in the US and UK, so I am struggling to understand the norms and expectations.

So far, I have identified a university with a research group in my subfield of mathematics, and on their website, they have a list of about a dozen projects, each with 4-6 people and a smattering of papers on that topic. Most people are listed under more than one group, especially the professors.

Would I be expected to propose a topic that fits with one or more of these projects, or would I, as a prospective student, be expected to bring something more original to the table, creating a distinct project?

Answer 1

This is mostly a matter of funding, which you didn't even mention.

Many PhD students are funded through (project) grants, and they normally try to keep their PhD topics close to what they have to do for the project anyway. But even those on a "Ladesstelle" (position paid by the state) will normally be expected to work in areas in which results can later be used for applying for grants - and it is hard to know from the outside what that could be.

While you could keep your proposal close to one of the existing projects, you do not know if there is any funding for that project left. Normally, that is not the case except in very long-running projects.

Hence, the way to go is normally:

0. See if there are advertised open positions ("Wissenschaftliche Mitarbeiter"). They normally list an expected area of research.

1. If step 0 did not yield any results, reach out to a professor from an area that intersects with your research interests. Write a highly personalized e-mail, listing your demonstratable expertise. Perhaps they have an upcoming project for which they need good researchers? Make sure to keep it professional.

2. See if step 1 helped you any further.

This answer is not about mathematics in particular. And it's also not for those coming with a scholarship, which is however a rare case in Germany.

Answer 2

I could offer a general perspective from my own experience from about 8 years ago in the field of Computer Science.

Unless your mind is very strongly set on one very specific topic within your subject (which I doubt it might be at this stage), the key is to show interest in a few fields related to the department (or professor) thus showing interest as well as flexibility. The reason being that, the professor you'll be working with is very likely an expert with a much more informed perspective on the matter than you so you are very likely going to benefit from their input on the matter given your interest in something they know a lot about. In many cases, I think what is expected of you is some degree of relevant experience in the field which you could leverage in coming up with original work (unless you already have, in which case it is a big plus). I would also add that bringing up names of other professors you have worked with, who your prospective supervisors might also know, could benefit you. Not sure how things work in Germany, but it doesn't hurt to contact the professor directly expressing your interest in working with her/him.

I received a PhD grant from the university (in London) based on my proposal, which started with responding to an email from a professor (who eventually became one of my supervisors) to a mailing list seeking PhD grant applications. I was interested in one particular area, and noticed that so was the professor, so I emailed back expressing my interest in working with him. He then suggested that I put together a roughly four page long PhD proposal (as required by the university) and offered to give me feedback and a letter of support for it. He also got another professor on board who was interested not in my specific topic but a related topic that could make the proposal stronger. They sent me a few papers to read, which I did and included it in my proposal. Both of them offered strong letters of support for my application and I finally received the grant.

I know there's not any one way to go about it, but I hope this one would give you some perspective on how it could work.