CS - Prof Ginestra Bianconi
1. Topological Synchronization of Higher-order Networks
Supervisor: Prof Ginestra Bianconi
Project description:
Synchronisation phenomena are ubiquitous in complex interacting systems. Traditionally these dynamical models are defined on networks. However, recently, it has been shown that in complex systems interactions are often higher-order and they involve two or more nodes. In higher-order networks dynamical variables can be associated to higher-order simplices, i.e. edges, triangles, tetrahedra and so on leading to Topological Synchronization demonstrating how topology shapes dynamics and how dynamical processes learn topology [1].
This project will investigate the mathematical foundation of Topological Synchronization and .tackle the problem of designing and controlling topological synchronization patterns using the tools of dynamical systems combined with algebraic topology and discrete geometry.
We are looking for highly motivated applicants with excellent academic record, and a MSc either in mathematics or in physics. Knowledge of either dynamical systems or algebraic topology will be beneficial but is not strictly required.
References:
[1] Millán, A.P., Sun, H., Giambagli, L., Muolo, R., Carletti, T., Torres, J.J., Radicchi, F., Kurths, J. and Bianconi, G., 2025. Topology shapes dynamics of higher-order networks. Nature Physics, pp.1-9.
Funding Notes:
This project is open to candidates applying for CSC/Underrepresented Studentships and self-funded candidates.
Further information:
How to apply
Entry requirements
Fees and funding
PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/
As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.
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.
2. Statistical mechanics and information theory of geometry and its applications
Supervisor: Prof Ginestra Bianconi
Project description:
The interplay between geometry and dynamics is a fundamental mathematical problem of wide relevance in a variety of fields ranging from theoretical physics to the study of complex systems and networks.. Geometry is encoded in the metric degree of freedom both for continuous manifolds and for discrete networks where they can be though as a generalization of edge weights.
Characterizing the joint evolution of the metric degree of freedom and the dynamical state of the network is a key problem in brain research, artificial intelligence and machine learning.
This project will investigate the information content of continuous and discrete structures coupled with dynamical processes starting from the recently proposed geometric quantum relative entropy [1,2] and will explore applications of this approach to complex systems and AI.
We are looking for highly motivated applicants with excellent academic record, and a MSc either in mathematics or in physics. Knowledge of statistical mechanics and network theory is highly desirable.
References:
[1] Bianconi, G., 2025. Gravity from entropy. Physical Review D, 111(6), p.066001.
[2] Bianconi, G., 2025. Beyond holography: the entropic quantum gravity foundations of image processing. arXiv preprint arXiv:2503.14048.
Funding Notes:
This project is open to candidates applying for CSC/Underrepresented Studentships and self-funded candidates.
Further information:
How to apply
Entry requirements
Fees and funding
PhD Information Session 2026:
On Wednesday 14 January, we will be holding a short information session about PhD studies in Mathematics at QMUL. For full details about the event, please visit: https://www.qmul.ac.uk/maths/postgraduate/postgraduate-research/phd-information-session-2026/
As one of the UK’s most diverse universities, QMUL fosters an inclusive and supportive academic community.
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.