Spectral computation in infinite dimensions
Algorithms for computing spectra, pseudospectra, spectral measures, semigroups, and related quantities with error control.
Matthew Colbrook
Associate Professor in DAMTP, University of Cambridge
I am an Associate Professor in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. My research lies at the intersection of data science and applied mathematics, with a particular focus on spectral computation, Koopman learning, neural networks and optimization, inverse problems, and partial differential equations.
A central theme of my work is the development of rigorous and practical algorithms for infinite-dimensional problems: methods that advance the theoretical foundations of computation while also enabling reliable high-dimensional and data-driven analysis across mathematics, physics, and engineering.
Before my current role, I was an Assistant Professor at Cambridge, a Junior Research Fellow at Trinity College, Cambridge, and a Fondation Sciences Mathématiques de Paris Fellow at École Normale Supérieure in Paris.
Email: m.colbrook@damtp.cam.ac.uk
Research Areas
Koopman learning and data-driven dynamics
Rigorous operator-theoretic methods for spectral analysis, forecasting, system identification, and model verification.
Neural networks and optimization
Foundations of stable and accurate learning, unrolled algorithms, and first-order methods for inverse problems and recovery.
PDEs, inverse problems, and scientific computing
Numerical methods for PDEs, spectral problems, scattering, and high-dimensional computational mathematics.
Background
I completed my PhD, “The Foundations of Infinite-Dimensional Spectral Computations”, at the University of Cambridge in September 2020.
My earlier degrees were also completed at the University of Cambridge, where I studied mathematics at St John’s College.
More details on positions, publications, talks, and current projects can be found via the links above.