Naya is a final 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 previously worked as a software developer at an investment bank. Her research focuses on topological data analysis.
Naya is a Tutor at St. Catherine's College, Oxford in pure and applied mathematics. She has also been a Teaching Assistant for Category Theory and Topology & Groups.
She organised 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.
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.
Fewer that 1% of know protein structures listed in the Protein Data Bank are known to be knotted, and understanding their folding mechanisms and the functional advantages of the occurrence of knots is an open question in biology. One stream of Naya's research, led by Agnese Barbensi, is applying tools from knot theory to provide topological shape descriptors of these proteins, and to study the topological untangling of such structures.
Naya has also worked with Daniele Celoria on developing a link between discrete Morse theory, combinatorics and knot theory. The main output of this research is a generalisation of two results, one from combinatorics and one from knot theory, captured in a single result called the generalised Clock Theorem.
Naya worked 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 was motivated by data and simulations from the Blue Brain Project.