PhD Scholarship in Mathematics

Modern network science is an exciting research field that has transformed the study of complex systems and led to innovations that roll over into many disciplines relating to the engineering, social, biological, and physical sciences. The network adjacency (or connectivity) matrix is at the centre of almost all research in network science. The adjacency matrix encodes the network structure and controls pervasive phenomena intrinsic to the system it represents.

Examples include epidemic outbreaks that burn through the contact network of large populations devastating vulnerable groups (e.g., elderly and indigenous communities, as dealt with shortly), the synchrony in a network of entangled neural oscillators controlling brain activities, and cascade of failure over power grid networks triggered by errors/overloads on transmission lines. Spectral graph theory directly links the properties of the eigenvalues and eigenvectors of the adjacency matrix (or Laplacian matrix) to the network's stability, spreading, resilience and percolation properties.

In this project we will build upon the rich literature in spectral graph analysis and nonlinear dynamics  to develop breakthrough theories for control and improvement of complex networked system behaviour via interventions of the link-rewiring type and their extensions. The project will deal with the areas of non-random, assortative and/or structured networks, which are not well understood and difficult to deal with, despite being the norm in the real world.  The project may also involve analysis and model building related to epidemic dynamics in human populations.