Welcome to my webpage. Since October 2022, I have been an assistant professor in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge and a Fellow of Trinity College, Cambridge. Email: m[dot]colbrook[at]damtp.cam.ac.uk

My research focuses on designing, analyzing, and implementing algorithms at the intersection of data science and applied mathematics. Key areas of interest include: approximation theory and spectral theory, neural networks and optimization, and inverse problems and partial differential equations. I am driven by the challenge of advancing computation and theory in infinite-dimensional settings: developing tools that not only deepen understanding but also enable practical applications for high-dimensional and data-driven problems.

I completed my PhD, titled "The Foundations of Infinite-Dimensional Spectral Computations", at the University of Cambridge in September 2020. Following that, I served as a Junior Research Fellow at Trinity College, Cambridge, for the academic years 2020-2022. During the academic year 2021-2022, I was also a FSMP Fellow at École Normale Supérieure in Paris.