I can supervise PhD students as part of the Mathematics CDT at the University of Warwick. The CDT offers full funding (fees + stipend) for four years and the programme comprises a light load (4 modules during the first 6 months) of taught courses alongside the research project. We don't expect applicants to have a polished project proposal (even though the application form asks for a "Research statement"). Instead, high-quality applications make a clear case for what area of mathematics they are interested in and who potential supervisors are.
I'm very happy to informally discuss potential projects before you apply! If you get in touch with me, please let me know what area of my work (see my research page for more infos) you are interested in. Please also attach a CV and any transcripts from previous university degrees. I can give an indication whether you are a competitive applicant (a necessary but sadly not sufficient condition!), but note that admissions decisions are made on a department-wide level.
As is common in the UK, I don't have funding for postdocs. I'm very happy to support fellowship applications, e.g., for an EPSRC postdoctoral fellowship. For fellowship applications, it's essential that the research topic is aligned with existing expertise in the department, but clearly the applicant's own idea. If you have an idea with sufficient synergies with my work (see my research page for more infos), please get in touch for an informal discussion. Any support will be conditional on wider support from the department following an appraisal process.
I'm very happy to supervise R-projects, 3rd year essays and support URSS applications provided I have expertise in the proposed project. You can find out more about my expertise on my research page. I'm also very happy to provide project ideas. Often, coming up with an interesting, yet feasible project is an iterative process between student and supervisor. However, given that you'll be spending signficant time on any project, it's important that the initial spark comes from you. I sometimes get emails along the lines of "Can you suggest a project in math biology?" and I find these very difficult to work with. Even a brief statement like "I really enjoyed learning about pattern formation in reaction-diffusion systems in MA256. I'd like to explore pattern formation in more complicated models." is an excellent starting point to discuss potential projects.
I typically get more requests (especially for URSS projects) than I can realistically support. Getting in touch early is a good idea! 😊