I am continuously looking for PhD students; to work with me at the University of Birmingham, UK! Funding is generally available, although you might wait for the next open call.1 An ideal candidate would have backgroung either in mathematics (algebraic topology, homotopy theory, abstract algebra, or related subjects), or in computational complexity theory. Having both is not necessary as you are expected to learn the necessary tools during the course of the PhD. The minimal requirements are:
- An undergraduate degree in mathematics, computer science, or any related discipline finished by the start of the PhD.
- Curiosity and motivation to study theoretical aspects of computing as well as all the relevant mathematics.
Topic: Abstract mathematics in computational complexity
You would be supervised by Jakub Opršal, i.e., myself. Currently, the main focus of my work is applications of homotopy theory in computational complexity.
I have worked extensively on classifying complexity of constraint satisfaction problems (CSPs), and their promise variants. There is a lot of interesting structure in these problems, and hence a hope for some general theories of complexity (usually using abstract tools, e.g., univeral algebra or homotopy theory). A prime example of what kind of stuff you could be working on is the following paper, I coauthored with Sebastian Meyer, a PhD student in Dresden:
- Meyer, S., & Opršal, J. (2025). A topological proof of the Hell–Nešetřil dichotomy. Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2025, (pp. 4507–4519). New Orleans, LA, USA: SIAM. arXiv:2409.12627, doi:10.1137/1.9781611978322.154.
You would be joining an active and friendly Theory of Computation group in Birmingham. We have two weekly seminars during term times (one internal and one external), and there are plenty of possibilities of visiting summer schools and/or workshops (e.g., Midlands Graduate School).
How to apply?
There are regular open calls for PhD positions, with deadlines between December and May. Application might also be considered outside of these calls. In any case, please contact me before applying, and don’t hesitate to contact me if you have any questions not answered here!
- This includes tuition fee waivers plus an annual tax-free maintenance allowance of £19,237, for eligible domestic and international students. [return]