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Department of Applied Mathematics and Theoretical Physics

  • 2020 - present: Junior Research Fellow, Trinity College, University of Cambridge.
  • 2016 - 2020: PhD student, DAMTP, CCA, University of Cambridge. 
  • 2015 - 2016: M.Math. (Part III), University of Cambridge.
  • 2012 - 2015: B.A. Maths, University of Cambridge.

This webpage is not kept up to date. Please visit my webpage here. 

Publications

Nyström Error Beyond $M$-Matrices: A Minimal Diagonally Dominant Obstruction
MJ Colbrook
(2026)
Adversarial dynamical systems characterize when data-driven learning succeeds or fails.
MJ Colbrook, I Mezić, A Stepanenko
– Nature communications
(2026)
17,
5397
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
G Coote, MJ Colbrook
(2026)
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
MJ Colbrook, I Mezić, A Stepanenko
(2026)
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
MJ Colbrook, M Embree, J Fillman
(2026)
Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems
MJ Colbrook
(2026)
Residual Pseudospectra Reveal a Physics-Informed Koopman Backbone for Tropical Pacific Variability and ENSO Prediction
P Lorenzo-Sanchez, MJ Colbrook, A Navarra
(2026)
Universal methods for nonlinear spectral problems
MJ Colbrook, C Drysdale
– Journal of Spectral Theory
(2026)
16,
601
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds
G Conradie, N Boullé, J-C Loiseau, SL Brunton, MJ Colbrook
(2026)
Weighted Birkhoff Averages Accelerate Data-Driven Methods
M Bou-Sakr-El-Tayar, JJ Bramburger, MJ Colbrook
(2026)
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Research Group

Mathematics of Information

Room

F0.14