PhD Studentship: Topological Methods in Computer Science
University of Birmingham - School of Mathematics
| Qualification Type: | PhD |
|---|---|
| Location: | Birmingham |
| Funding for: | UK Students, EU Students, International Students |
| Funding amount: | Funding is available to candidates with a strong background from around the world, although the competition is higher for candidates who are not UK citizens. Self-funded candidates are also welcome to apply. |
| Hours: | Full Time |
| Placed On: | 1st September 2023 |
|---|---|
| Closes: | 30th November 2023 |
The tight link between topology and computability is well-known and has been investigated extensively. Nonetheless, when the topological spaces involved do not have favorable properties (e.g, when they are not locally compact) the classical methods are not adequate for laying a computational foundation. Such spaces arise in the study of some of the most important problems of classical and modern mathematics, e.g., functional analysis, ordinary and partial differential equations, probabilistic programming, and machine learning, to name a few.
The aim of this PhD project is to develop mathematical structures that are suitable for problems of this kind. As such, a strong background in mathematics is required. In particular, a good command of topology will be highly desirable.
The University of Birmingham is well-known for its research into mathematical foundations of computer science, especially on subjects such as domain theory and category theory, where powerful tools from mathematics and computer science are brought together to address some of the fundamental conceptual and practical challenges that arise in both disciplines.
The project will be supervised by Dr. Amin Farjudian (a.farjudian@bham.ac.uk). If you wish to enquire about this project, then please explain how your background makes a PhD project in this area suitable for you.
References:
[1] Farjudian, A. and Moggi, E. “Robustness, Scott Continuity, and Computability”. In: Mathematical Structures in Computer Science (2023), 1–37. doi: 10.1017/S0960129523000233
[2] Zhou, C., Shaikh, R. A., Li, Y., and Farjudian, A. “A domain-theoretic framework for robustness analysis of neural networks”. In: Mathematical Structures in Computer Science 33.2 (2023), pp. 68–105. doi: 10.1017/ S0960129523000142
[3] Edalat, A., Farjudian, A., and Li, Y. "Recursive Solution of Initial Value Problems with Temporal Discretization". 2023. arXiv: 2301.03920 [math.NA]
[4] Moggi, E., Farjudian, A., Duracz, A., and Taha, W. “Safe & Robust Reachability Analysis of Hybrid Systems”. In: Theoretical Computer Science 747 (2018), pp. 75–99. doi: 10.1016/j.tcs.2018.06.020
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