How closely should my research proposal align with existing projects in the department? 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?
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 &quot;Ladesstelle&quot; (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:

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

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.

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.