Topological-based numerical methods for real-world problems

This project proposes to use numerical methods, specifically methods incorporating topological techniques, to investigate a range of complex interdisciplinary research problems. This will involve working with existing partners and creating new partnerships with research groups and industries to create innovative solutions to real-world problems.

There are three key existing collaborations which this project will continue:

The institute of Cardiovascular Sciences - Advancing photoacoustic imaging technologies within the biomedical optics sector by employing topological numerical methods.

Renishaw plc. - Improving the sensitivity of spectrometers using topological machine learning.

6 Bit Education Ltd. - Improbing the similarity measures in student assignments using machine learning on topological trees.

Additionally, this project will seek a new collaboration with the Computation and Theory of Soft Materials department within the School of Chemistry, where numerical and mathematical methods will be implemented to study soft materials.

The main goal of this PhD is to create numerical toolkits and libraries based on topological methods to solve a variety of research problems. The solutions to these problems will have a real-world impact and could be implement in the near future. The approach of running several mini projects along with industry placements allows for hands-on learning and opportunities to learn from other groups of people with different areas of expertise. This project offers great chances for groundbreaking advancements in many fields.