Supervisor: Dr Amaranta Membrillo Solis
This PhD project aims to advance the mathematical framework of metric geometry for signed vector measures through an optimal transport approach. Additionally, the project will target applications to complex systems arising in scientific fields such as material science, developmental biology and meteorology.
Description: Signed measures, extending the classical concept of measures to allow positive and negative values, naturally arise in diverse scientific contexts, including the modelling of fluxes and imbalances in dynamical systems. Optimal transport theory, a powerful tool for comparing probability distributions, can be extended to handle signed measures. This project will further refine these extensions, incorporating vector-valued measures to represent multidimensional phenomena.
The theoretical aspect of the project involves developing new Wasserstein-type metrics tailored to spaces of signed vector measures. This includes exploring their geometric and topological properties, ensuring stability, and designing computationally efficient algorithms for practical implementation.
On the applied side, the project will leverage this mathematical foundation to analyse and interpret complex systems data. Optimal transport-based tools will facilitate the comparison of spatiotemporal patterns, anomaly detection and quantification of differences between observational data and simulations.
The outcomes of the project promise to bridge theoretical mathematics and practical applications, significantly enhancing our ability to interpret and predict the behaviour of complex systems dynamics.
Further information:
How to apply
Entry requirements
Fees and funding