Biography
Matthew Burfitt received his Ph.D. in mathematics from the University of Southampton, where he studied the cohomology of free loop spaces of certain homogeneous spaces. He has previously held positions as part of the Topological Data Analysis group at the University of Southampton, the Neuro-Topology group at the University of Aberdeen, and the Beijing Institute of Mathematical Sciences and Applications (BIMSA), where the central focus of his work was on homology theories of digraphs and quivers with a view towards computation and their use with large directed complex networks. He joined the Hetao Institute of Mathematics and Interdisciplinary Sciences (HIMIS) as an Assistant Professor in 2026 and his current research is focused within algebraic topology and applications with artificial intelligence.
Research Interest
Algebraic topology
Topological data analysis
Homologies of digraphs and quivers
Machine learning and deep learning
Seeing concrete application gives me a strong motivation for the direction of my work. In turn, advancements in applied topology provide new questions within the existing theory, bringing together previously unrelated concepts and establishing the development of new mathematical ideas. My research interests lie primarily within topological data analysis at the interface between theory and applications. I enjoy working on mathematics that improves our understanding and can be used to obtain more efficient algorithms for computations of homologies of directed complex systems. More broadly, I am very interested in how geometric methods can used to understand the structure of data and the mechanisms behind the success of machine learning, and deep neural networks.
Education
2013-2017, University of Southampton, PhD in Mathemaics
2008-2012, University of Warwick, MMath
Employment
2026-present, Herao Institute of Mathematics and Interdisciplinary Sciences (HIMIS) Assistant Professor
2022-2026, Beijing Institute of Mathematical Sciences and Applications (BIMSA), Postdoctoral researcher
2021-2022, University of Aberdeen, Research fellow
2018-2020, University of Southampton, Postdoctoral researcher in topological data analysis
Awards
Beijing postdoctoral international exchange and training
Publications
[1] M. Burfitt, J. Brodzki, and P. Dłotko, Understanding the geometry of deep learning with decision boundary volume (2026) arXiv:2603.14768
[2] M. Burfitt, J. Wu, S. Yau, and S.-T. Yau, Computing singular simplicial homologies of digraphs and quivers, (2025) Accepted by the Beijing journal of pure and applied mathematics
[3] M. Burfitt and T. Cutler, Inductive construction of path homology chains, (2025) arXiv:2411.09501
[4] M. Burfitt, N. Senn, L. Broche, R. Levi, N. Oren, G. Waiter, and M. MacLeod, Assessment of cerebral small vessel disease burden at ultra-low field using dimensionality reduction of field-cycling imaging (2025)
[5] M. Burfitt, and J. Grbić, The cohomology of free loop spaces of rank 2 flag manifolds, Homology, Homotopy and Applications, 25 (2) 343-371 (2023).
[6] M. Burfitt, A projective model for fast field cycling MRI images, 2022 Proceedings of the 4th International Conference on Trauma Surgery Technology (2022)
[7] M. Burfitt, and J. Grbić, The cohomology of free loop spaces of SU(n+1)/T^n (2022) arXiv:2106.03440
[8] J. Brodzki, M. Burfitt, and M. Pirashvili, On the complexity of zero-dimensional multiparameter persistence (2020) arXiv:2008.11532
[9] F. Belchí, J. Brodzki, M. Burfitt, and M. Niranjan, A numerical measure for the instability of Mapper-type algorithms, Journal of Machine Learning Research 21 (2020) 1-45.