I am continuously looking for PhD students; to work with me at the University of Birmingham, UK!1 Essential 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 the relevant mathematics.
An ideal candidate would have backgroung either in mathematics (homotopy theory, universal algebra, category theory, algebraic topology, or any related subjects), and/or in theoretical computer science (e.g., computational complexity or algorithms). Having both is not necessary as you are expected to learn the necessary tools during the course of the PhD.
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 a hope for a general theory of complexity of these problems using universal algebra, category theory, homotopy theory, and combinatorics.
The following paper, which I coauthored with Sebastian Meyer (a PhD student at TU Dresden) is a prime example of what kind of research you could be working on:
- 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.
Other possible topics include computational aspects of universal algebra and categorical perspective on homomorphism and isomorphism problems.
About the university and the group
The University of Birmingham provides an outstanding research environment (it placed third in REF 2021 in Computer Science for the quality of research).
The Theory of Computation group is one of the largest in the world, and among the top few in the UK. The group is active and open; we have two weekly seminars during term times (one internal and one external), and we are part of several collaborative networks that offer PhD students with workshops and/or summer schools (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]