Naya is a third year doctoral researcher in mathematics at The University of Oxford and The Alan Turing Institute, under the supervision of Professor Vidit Nanda and Professor Ulrike Tillmann. She holds a Masters in Mathematics from The University of Warwick and has worked as a software developer at Bank of America Merrill Lynch. Her research focuses on topological data analysis.
Naya organises the Maths in Society speaker series at Oxford, which aims to highlight how advanced mathematics is used to solve problems in areas such as healthcare, the future of energy and urban planning - many of the focus areas of the Turing.
Naya is interested in developing new algebraic-topological methods to extract information from datasets across different scientific disciplines. Topological methods offer a unique way to understand qualitative information about the structure of data, which is particularly important when the structure is not well-understood a priori. Her research seeks to provide a firm theoretical basis for techniques that can be applied in different industries.
The natural way to study data with symmetries is via group actions on the space. Given a discretised space with a group action encoding its symmetries, one can compress this in order to reduce the total quantity of data. This can be done in such a way that the original space and symmetries can be recovered. Naya is working on ways to compress data whilst maintaining the same topological structure.
Naya is also working on a collaboration led by Professor Kathryn Hess in the field of computational neuroscience. Modelling the brain as a directed graph, they are seeking to understand the space of subgraphs explored by the brain after inputting different stimuli. This project combines topological data analysis with network science and will use data from the Blue Brain Project.