Statistics of equilibria of large complex systems at Queen Mary University of London on FindAPhD.com

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Prof Boris Khoruzhenko No more applications being accepted Competition Funded PhD Project (Students Worldwide)

London United Kingdom Applied Mathematics Mathematics Probability

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2022.

This project concerns the development of tools for analysis of statistics of equilibria of large non-linear complex systems. In the gradient case, when the corresponding dynamics can be is visualised as the gradient descent on random surfaces, there has been considerable effort applied to understand such systems. For example, it was found that such surfaces undergo a topology de-trivialisation transition in the limit of large number of dimensions. The focus of this project will be on non-gradient systems where the topology de-trivialisation transition manifests itself in the exponential explosion of the number of unstable equilibria. The analytical part of the project is likely to involve studying various statistics of complex eigenvalues of large random matrices.

The application procedure is described on the School webpage: www.qmul.ac.uk/maths/postgraduate/postgraduate-research/application-process/. For further inquiries please contact [Email Address Removed]. Funding may be available through School of Mathematical Sciences Studentships, EPSRC DTP, and the S&E BAME Doctoral Research Studentship, in competition with all other PhD applications. Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years. Applicants interested in the full funding will have to participate in a highly competitive selection process. The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

Funding Notes

For September 2022 entry: Funding may be available through School of Mathematical Sciences Studentships, EPSRC DTP, and the S&E BAME Doctoral Research Studentship, in competition with all other PhD applications. Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years.
We welcome applications for self-funded applicants year-round, for a January, April or September start.

References

R. M. May: Will a large complex system be stable? Nature 238, 413–414 (1972).
Y. V. Fyodorov, B. A. Khoruzhenko: Nonlinear analogue of the May-Wigner instability transition. Proc. Natl. Acad. Sci. U.S.A. 113, 6827–6832 (2016).
G. Ben Arous, Y.V. Fyodorov, and B.A. Khoruzhenko: Counting equilibria of large complex systems by instability index. Proc. Natl. Acad. Sci. U.S.A., 118, No. 34, e2023719118 (2021).