About the project
Objective
This project aims to build mathematical foundations and design efficient algorithms for problems on metric graphs. The research will proceed in two stages. First, the focus will be on developing geometric and topological methods to construct or reconstruct metric graphs from real-world data. Second, the project will address the extraction of statistical information and the solution of applied problems on metric graphs through optimization-based approaches.
Background
Metric graphs offer a powerful way to model real-world data that has an underlying network structure together with spatial attributes. Examples of metric graphs include road networks, brain connectivity networks, and social networks. Unlike tabular data which is well-structured, metric graphs are inherently complex and nonlinear. Existing methods are ill-suited for computational and practical analysis of metric graphs, which limits their utility as models for real data. My research aims to provide an essential framework for applications of metric graphs in machine learning and data science.
About the Digital Futures Postdoc Fellow
Yueqi Cao completed his PhD in mathematics at Imperial College London in 2025. He works on applied and computational mathematics and statistics, with a particular interest in geometric and topological data analysis. Prior to that, he obtained master’s degree and bachelor’s degree in mathematics from Beijing Institute of Technology.
Main supervisor
Johan Karlsson
Co-supervisor
Sandra Di Rocco
