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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

Adversarial dynamical systems characterize when data-driven learning succeeds or fails.
MJ Colbrook, I Mezić, A Stepanenko
– Nat Commun
(2026)
17,
5397
Residual-Guided Dictionary Learning for Spectrally Accurate Koopman Approximation
G Coote, MJ Colbrook
(2026)
Computing Spectral Size: Rigorous Algorithms and the Limits of Computation
MJ Colbrook, M Embree, J Fillman
(2026)
Adversarial dynamical systems characterize when data-driven learning succeeds or fails
MJ Colbrook, I Mezić, A Stepanenko
(2026)
Ten Digits on a Train: AI-Assisted Verification of Two Eigenvalue Problems
MJ Colbrook
(2026)
Universal methods for nonlinear spectral problems
MJ Colbrook, C Drysdale
– CoRR
(2026)
abs/2504.17012,
601
Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds
G Conradie, N Boullé, J-C Loiseau, SL Brunton, MJ Colbrook
(2026)
Bridging the gap between koopmanism and response theory: Using natural variability to predict forced response
N Zagli, MJ Colbrook, V Lucarini, I Mezić, J Moroney
– SIAM E-Journal on Applied Dynamical Systems
(2026)
25,
196
An Introductory Guide to Koopman Learning
MJ Colbrook, Z Drmač, A Horning
(2025)
Computation and Verification of Spectra for Non-Hermitian Systems
C Drysdale, M Colbrook, MTM Woodley
– Physical review letters
(2025)
135,
170202
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