PSD - Prof Omer Bobrowski
The Topology of Hyperuniform Processes
Supervisor: Prof Omer Bobrowski and Prof Primoz Skraba
Project description:
In stochastic topology, the goal is to study the shape and structure of randomly generated spaces. Recent findings suggest that the topology of random hypergraphs exhibits a universal, distribution-independent behaviour, similar in spirit to the Central Limit Theorem (CLT) in random variables.
Hyperuniform processes are spatial particle systems that are random yet highly correlated. The range of their configurations lie between (periodic) crystals and complete randomness. Over the past decade, these processes have become central to a wide range of fields, including statistical physics, materials science, biology, and ecology.
Preliminary evidence indicates that hyperuniform processes tend to generate topological structures that differ significantly from those observed in complete random particle systems. This project aims to explore these distinctions by studying hyperuniformity through the lens of the universal topological distributions.
The first part of this project will involve experimentally uncovering how the statistical properties of hyperuniform systems influence the topological features they generate. Once these relationships are identified, the second stage will focus on developing a rigorous mathematical framework to explain them. In parallel, we will also investigate potential applications of these findings, in both statistical physics and deep neural networks.
The prospective student should have a solid background in probability and statistics, along with Python programming skills. Prior experience with particle systems or applied topology is not required, but would be advantageous.
If you wish to inquire about the project, please contact
Omer Bobrowski – o.bobrowski@qmul.ac.uk
Primoz Skraba – p.skraba@qmul.ac.uk
Funding Notes:
This project is open to candidates applying for CSC Studentships.
Further information:
How to apply
Entry requirements
Fees and funding
PhD Information Session 2026:
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