Please get in touch (m[dot]colbrook[at]damtp.cam.ac.uk) if you would like me to present at your event or seminar.
Can we compute spectral properties of (infinite-dimensional) Koopman operators?
(recorded at the Koopman Operator Theory Workshop in Otranto)
Residual Dynamic Mode Decomposition: A very easy way to get error bounds for your DMD computations!
(recorded while visiting Steve Brunton's lab)
Measure-preserving EDMD: A 4-line structure-preserving & convergent DMD algorithm!
(recorded while visiting Steve Brunton's lab)
Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
(recorded at the Third Symposium on Machine Learning and Dynamical Systems)
Smale’s 18th Problem and the Barriers of Deep Learning
(One World Seminar Mathematics of Machine Learning Seminar)
Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators
(Communications in NLA Seminar)
Page Navigation
Lecture Courses
| 2nd Semester 2022 | Data-driven approximations of Koopman operators for dynamical systems Lecture notes (hand-written) available on request. | École Normale Supérieure |
| May - June 2022 | To infinity... and beyond!
A course on infinite-dimensional spectral computations. Lecture Notes | Gran Sasso Science Institute |
| Jan 2021 | On the barriers of AI and the trade-off between stability and accuracy in deep learning Lecture materials available on request. | 21st Geilo Winter School in eScience |
Videos of some of my talks
(recorded at the Koopman Operator Theory Workshop in Otranto)
Residual Dynamic Mode Decomposition: A very easy way to get error bounds for your DMD computations!
(recorded while visiting Steve Brunton's lab)
Measure-preserving EDMD: A 4-line structure-preserving & convergent DMD algorithm!
(recorded while visiting Steve Brunton's lab)
Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
(recorded at the Third Symposium on Machine Learning and Dynamical Systems)
Smale’s 18th Problem and the Barriers of Deep Learning
(One World Seminar Mathematics of Machine Learning Seminar)
Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators
(Communications in NLA Seminar)
Previous Talks
| 26 Feb 2025 |
Learning unitary Koopman operators from trajectory data Mini-Workshop: Geometric Integration (slides) | Cambridge |
| 12 Dec 2024 |
A classification theory for data-driven Koopman Spectral Computations Mini-Workshop: Data-driven Modeling, Analysis, and Control of Dynamical Systems (slides) | Oberwolfach |
| 12 Nov 2024 |
Rigorous Limits of Learning in Dynamical Systems Centro Euro-Mediterraneo sui Cambiamenti Climatici (slides) | Bologna |
| Oct 2024 |
Towards a classification theory for data-driven dynamical systems Signal - Image - Geometry - Modelling - Approximation (slides) | Centre International de Rencontres Mathématiques |
| 21 August 2024 |
Residual Dynamic Mode Decomposition for Stochastic Systems 26th International Symposium on Mathematical Theory of Networks and Systems (slides) | Cambridge |
| 19 August 2024 |
Data-driven computation of spectral properties of Koopman operators Minicourse on Extended Dynamic Mode Decomposition (slides) | MTNS conference, Cambridge |
| 10 July 2024 |
Classifications of Data-Driven Koopman Learning Fourth Symposium on Machine Learning and Dynamical Systems (slides) | Fields Institute |
| 18 June 2024 |
Data-Driven Spectral Measures and Generalized Eigenfunctions of Koopman Operators British Mathematical Colloquium (slides) | University of Manchester |
| 10 June 2024 |
Computing spectral properties of unitary Koopman Operators Complex Systems Seminar (slides) | Technical University of Munich |
| 23 May 2024 |
The Hitchhiker's Guide to the DMD Multiverse Machine Learning and Dynamical Systems Seminar (slides) | Alan Turing Institute |
| 20 May 2024 |
Can we compute spectral properties of (infinite-dimensional) Koopman operators? Koopman Operator Theory: Fundamentals, Approximations and Applications (slides) | Otranto (Italy) |
| 13 May 2024 |
An Overview of Operator Learning: Infinite-dimensional NLA SIAM Conference on Applied Linear Algebra (slides) | Sorbonne Université |
| 4 April 2024 |
Geometric integration meets data-driven dynamical systems Exploiting Algebraic and Geometric Structure in Time-Integration Methods (slides) | University of Pisa and Scuola Normale Superiore |
| 21 March 2024 |
Unitary Approximations of Koopman Operators
ACM Seminar (slides) | University of Edinburgh |
| 29 Feb 2024 |
Polar Decompositions of Koopman Operators Centre for Complex Systems (slides) | Queen Mary University of London |
| 19 Sep 2023 |
Verified Koopman Spectra through Operator Folding Joint Numerical Analysis and Applied Mathematics Seminar (slides) | Birmingham |
| 19 Sep 2023 |
Verifying data-driven computations of Koopman spectra PDE meets Data: Challenges and perspectives in model development and calibration (link, slides) | Warwick |
| 22 Aug 2023 |
Going beyond expectations: Stochastic ResDMD ICIAM (link, slides) | Tokyo |
| 17 Aug 2023 |
Four examples of discretization issues for Nonlinear Eigenvalue Problems Numerical Analysis in the 21st Century (link, slides) | Oxford |
| 26 July 2023 |
Taming Discretization Challenges for Nonlinear Eigenvalue Problems Complex analysis: techniques, applications and computations (link, slides) | Isaac Newton Institute |
| 29 June 2023 |
Avoiding discretization issues for nonlinear eigenvalue problems Biennial Conference on Numerical Analysis 2023 (link, slides) | University of Strathclyde |
| 26 June 2023 | Leslie Fox Prize Lecture Computing semigroups with error control (slides) | |
| 21 June 2023 |
Avoiding discretization issues for nonlinear eigenvalue problems FoCM 2023 (link, slides) | Sorbonne University, Paris |
| 20 June 2023 | Semi-Plenary Speaker (10th Popov Prize Lecture) The Solvability Complexity Index: A toolkit for approximation theory and the foundations of computation FoCM 2023 (link, slides) | Sorbonne University, Paris |
| 24 May 2023 | Avoiding discretization issues for nonlinear eigenvalue problems Imperial–UCL Numerics Seminar (slides) | Imperial College London |
| 15 May 2023 |
measure-preserving Extended Dynamic Mode Decomposition: Structure-preserving Koopmanism SIAM Conference on Applications of Dynamical Systems (link, slides) | Portland |
| 18 April 2023 | Plenary Speaker Spectral Computations in Infinite Dimensions Differential-Algebraic Equations and Operator Pencils (link, slides) | Banff International Research Station (BIRS) for Mathematical Innovation and Discovery |
| 13 March 2023 |
Residual Dynamic Mode Decomposition: A path to verified data-driven discovery of dynamics! eBrain Lab (link, slides) | Online Seminar |
| 9 March 2023 |
Residual Dynamic Mode Decomposition: Robust and verified Koopmanism for nonlinear dynamical systems Mathematical theory and applications of multiple wave scattering (link, slides) | Isaac Newton Institute |
| 2 March 2023 |
Fast Spectral Methods for Spectral Measures SIAM Conference on Computational Science and Engineering (link, slides) | Amsterdam |
| 9 Feb 2023 |
The difficulty of computing stable and accurate neural networks: On the barriers of deep learning & Smale's 18th problem G-34 Artificial Intelligence in Aviation Committee (link, slides) | Online Seminar |
| 6 Jan 2023 |
The foundations of infinite-dimensional spectral computations Joint Mathematics Meetings 2023 (link, slides) | Boston |
| 18 Dec 2022 |
Smale's 18th Problem and the Barriers of Deep Learning 15th International Conference of the ERCIM WG on Computational and Methodological Statistics (link, slides) | King's College London |
| 9 Dec 2022 |
Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems Applied and Computational Mathematics Seminar (link, slides) | University of Wisconsin–Madison |
| 16 Nov 2022 |
Measure-Preserving Extended Dynamic Mode Decomposition: Structure-preserving and rigorous Koopmanism Numerical Methods for Partial Differential Equations Seminar (link, slides, video for turbulent example won't play in pdf, but is available upon request) | MIT |
| 15 Nov 2022 |
On spectral computations in infinite dimensions: Spectral measures, Koopman operators and beyond Applied and Computational Mathematics Seminar (link, slides) | Dartmouth |
| 11 Nov 2022 |
To infinity... and beyond! The solvability complexity index and the foundations of infinite-dimensional spectral computations Mathematics Colloquium (link, slides) | Virginia Tech |
| 9 Nov 2022 |
Residual Dynamic Mode Decomposition: A path towards modal analysis of nonlinear dynamical systems Aerospace and Ocean Engineering Seminar (slides) | Virginia Tech |
| 28 Oct 2022 |
Residual Dynamic Mode Decomposition: Robust and verified Koopmanism! Data-Driven Methods for Science and Engineering Seminar (slides) | University of Washington |
| 24 Oct 2022 |
Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems Applied Mathematics Seminar (link, slides) | Berkeley |
| 20 Oct 2022 |
Measure-Preserving Extended Dynamic Mode Decomposition: Structure-preserving and rigorous Koopmanism CMX Seminar (link, slides, video for turbulent example won't play in pdf, but is available upon request) | Caltech |
| 17 Oct 2022 |
To infinity... and beyond! The solvability complexity index and the foundations of infinite-dimensional spectral computations Applied and Computational Math Seminar (link, slides) | University of Minnesota |
| 27 Sep 2022 |
Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems SIAM Conference on Mathematics of Data Science (link, slides) | San Diego |
| 27 Sep 2022 |
Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems Third Symposium on Machine Learning and Dynamical Systems (link, slides, video) | Fields Institute |
| 20 Sep 2022 |
Smale’s 18th Problem and the Barriers of Deep Learning 4th IMA conference on the mathematical challenges of big data (link, slides) | University of Oxford |
| 12 Sep 2022 |
The Solvability Complexity Index Hierarchy and Generalised Hardness of Approximation Computational mathematics in computer assisted proofs (link, slides) | AIM Workshop |
| 30 Aug 2022 |
Robust and Verified Koopmania SIAM Conference on Nonlinear Waves and Coherent Structures (link, slides) | University of Bremen |
| 23 July 2022 |
Robust and Verified Koopmania 27th Summer School on Dynamical Systems and Complexity (link, slides) | Cultural Center of Chania, Crete |
| 28 June 2022 | Plenary Speaker Numerical analysis in the age of data science through the Solvability Complexity Index hierarchy Bȩdlewo conference: Thirty years of Acta Numerica (link, slides) | Banach Center, Bȩdlewo, Poland |
| 15 June 2022 | Plenary Speaker Rigorous and data driven Koopmanism: Infinite-dimensional spectral computations for nonlinear systems XXI Householder Symposium on Numerical Linear Algebra (link, slides) | Sierra Silvana, Italy |
| 8 June 2022 | Residual DMD:
Rigorous data-driven spectral computations of Koopman operators for dynamical systems
MATHICSE seminar (link, slides) | École Polytechnique Fédérale de Lausanne |
| 7 June 2022 | Smale’s 18th Problem and the Barriers of Deep Learning AudioVisual Communications Group (slides) | École Polytechnique Fédérale de Lausanne |
| 13 May 2022 | Koopman operators and a programme on the foundations of infinite-dimensional spectral computations Numerical methods for compression and learning (link, slides) | Gran Sasso Science Institute |
| 11 May 2022 | Smale’s 18th Problem and the Barriers of Deep Learning One World Seminar Mathematics of Machine Learning Seminar (link, slides, video) | Online Seminar |
| 4 May 2022 | When can algorithms be trusted? Computational analysis in the age of data science Applied and Computational Analysis (ACA) Seminar | University of Cambridge |
| 28 March 2022 | Koopman operators and the computation of spectral properties in infinite dimensions Analysis & PDE Seminar (link, slides) | Cardiff University |
| 24 March 2022 | Koopman operators and the computation of spectral properties in infinite dimensions Numerical Analysis and Scientific Computing Seminar (link, slides) | University of Manchester |
| 18 March 2022 | Koopman operators and the computation of spectral properties in infinite dimensions Applied Mathematics Seminar (link, slides) | University of Warwick |
| 21 Feb 2022 | On the Barriers of Deep Learning, Approximate Sharpness, and Smale’s 18th Problem One World Optimization Seminar (link, slides) | Online Seminar |
| 18 Feb 2022 | Data-driven numerical analysis of Koopman operators for dynamical systems EMC2 Seminar (slides) | Ecole des Ponts |
| 7 Feb 2022 | Data-driven numerical analysis of Koopman operators for dynamical systems One World Numerical Analysis Seminar (link, slides) | Online Seminar |
| 4 Feb 2022 | Computing semigroups and solutions of time-fractional PDEs with error control Differential Equations, Numerical Analysis and Applications Seminar (link, slides) | University of Málaga |
| 15 Dec 2021 | Residual DMD: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems Mezić Group (link, slides, video) | University of California, Santa Barbara |
| 7 Dec 2021 | Can stable and accurate neural networks always be computed? QAVAS Group (slides) | University of Oxford |
| 1 Dec 2021 | Computing semigroups and solutions of time-fractional PDEs with error control NOMADS Seminar (link, slides) | Gran Sasso Science Institute |
| 18 Nov 2021 | Infinite-Dimensional Spectral Computations Computational Mathematics and Applications Seminar (link, slides) | University of Oxford |
| 8 Nov 2021 | Infinite-Dimensional Spectral Computations Scientific Computing and Numerics (slides) | Cornell University |
| 26 Oct 2021 | Can stable and accurate neural networks always be computed? Mathematics of deep learning (link, slides) | Isaac Newton Institute |
| 20 Aug 2021 | Computing spectral measures and a programme on the foundations of infinite-dimensional spectral computations IWOTA 2021 (link, slides) | Lancaster |
| 6 Aug 2021 | Non-linear Forchheimer corrections in acoustic scattering AIAA Aviation 2021 (link, slides) | Online |
| 5 Aug 2021 | Modelling chordwise-varying porosity to reduce aerofoil-turbulence interaction noise AIAA Aviation 2021 (link, slides) | Online |
| 23 July 2021 | Can stable and accurate neural networks always be computed? SIAM annual meeting 2021 (link, slides) | Online |
| 22 July 2021 | Can stable and accurate neural networks always be computed? Pop-up numerical analysis conference 2021 (slides) | Bickleigh |
| 19 July 2021 | Computing Spectral Measures Pop-up numerical analysis conference 2021 (slides) | Bickleigh |
| 14 July 2021 | Computing spectral measures of self-adjoint operators ICOSAHOM 2021 (link, slides) | Vienna |
| 12 July 2021 | Computing semigroups with error control ICOSAHOM 2021 (link, slides) | Vienna |
| 11 June 2021 | Can stable and accurate neural networks always be computed? Machine Learning + X Seminar (link, slides) | Brown University |
| 26 May 2021 | Can stable and accurate neural networks always be computed? Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence (link, slides) | Ludwig-Maximilians-Universität München |
| 12 May 2021 | Computing semigroups with error control and a framework for infinite-dimensional computations Groupe de Travail du LJLL (link, slides) | Jacques-Louis Lions Lab (Sorbonne University, University of Paris, National Center for Scientific Research) |
| 6 April 2021 | Diagonalising the infinite:
How to compute spectra with error control BMC-BAMC 2021 (link, slides) | University of Glasgow |
| 26 March 2021 | Infinite-Dimensional Spectral Computations Mechanics Seminar (slides) | Cornell University |
| 22 March 2021 | Probing the infinite: Computing spectral & transport
properties in infinite dimensions Quantum Optics and Quantum Many-body Systems Seminar (link, slides) | University of Strathclyde |
| 18 March 2021 | Diagonalising the infinite:
How to compute spectra with error control Early Career Applied Mathematics Meeting (link, slides) | Online Seminar |
| 10 Dec 2020 | Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators Annual Meeting of the Australian Mathematical Society (link, slides) | Online Seminar |
| 6 Dec 2020 | A Mathieu function boundary spectral method for acoustic scattering Canadian Mathematical Society Winter Meeting (link, slides) | Online Seminar |
| 26 Oct 2020 | Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators Communications in NLA (link, slides, video) | Online Seminar |
| 30 Aug - 2 Sep 2020 | How To Compute Spectra
With Error Control On The Foundations of Infinite-Dimensional Spectral Computations Computational Techniques & Applications Conference (link, slides) | University of New South Wales |
| 14-15 July 2020 | The Foundations of Infinite-Dimensional Spectral Computations British Early Career Mathematicians' Colloquium (link, slides) | University of Birmingham |
| 23 June 2020 | How to compute spectral properties of operators on Hilbert spaces with error control Collective Phenomena Group (link, slides) | TCM, Cavendish Laboratory University of Cambridge |
| 3 June 2020 | How to compute spectral properties of operators on Hilbert spaces with error control Electronic Structure Group (link, slides) | TCM, Cavendish Laboratory University of Cambridge |
| 26 May 2020 | Scattering, Acoustic Black Holes and Mathieu Functions: A boundary spectral method for diffraction by multiple variable poro-elastic plates Waves in Complex Continua (Wavinar) See the design logo computed using methods in this talk (link, slides, video) | International Centre for Mathematical Sciences |
| 5 May 2020 | The Foundations of Infinite-Dimensional Spectral Computations: Can we compute spectral properties? Applied and Interdisciplinary Mathematics Seminar & Numerical Analysis Seminar (link, slides) | University of Bath |
| 15 April 2020 | The Foundations of Infinite-Dimensional Spectral Computations Applied Mathematics Seminar (link, slides) | UC Berkeley |
| 9-13 Dec 2019 | The Foundations of Infinite-Dimensional Spectral Computations Complex analysis: techniques, applications and computations (link, slides, video) | Isaac Newton Institute |
| 5-30 Aug 2019 | Solving Wiener-Hopf type problems numerically: a spectral method approach Isaac Newton Institute Workshop on Wiener-Hopf technique (link, slides, video) | Isaac Newton Institute |
| 8-12 Jul 2019 | Do stable networks with recovery guarantees exist? Applied Inverse Problems Conference (link, slides) | Universite Grenoble-Alpes |
| 25-28 Jun 2019 | Spectral problems and new resolvent based methods 28th Biennial Numerical Analysis Conference (link, slides) | University of Strathclyde |
| 14 June 2019 | Resolving the resolvent: How to "diagonalise" infinite matrices Oxford-Cambridge Applied Mathematics Meeting (link, slides) | University of Oxford |
| 23 May 2019 | On Instabilities of Deep Learning in Image Reconstruction The Mathematics of Deep Learning and Data Science (link, slides, video) | Isaac Newton Institute |
| 22 May 2019 | Spectral resolvent based methods Imperial–UCL Numerics Seminar | Imperial College London |
| 10 May 2019 | Can neural networks always be trained? On the boundaries of deep learning Département de mathématiques et applications de l’ENS (link, slides) | École Normale Supérieure |
| 6 May 2019 | Can neural networks always be trained? On the boundaries of deep learning Biomedical Imaging Seminar (link, slides) | École Polytechnique Fédérale de Lausanne |
| 2 May 2019 | Spectral analysis and new resolvent based methods Applied Partial Differential Equations Seminar (link, slides) | University of Washington |
| 1 May 2019 | Can neural networks always be trained? On the boundaries of deep learning Cambridge Analysts' Knowledge Exchange (link, slides) | University of Cambridge |
| 24 Apr 2019 | The Unified Transform: A New Tool for Scattering Problems British Applied Mathematics Colloquium 2019 (link, slides) | University of Bath |
| 10 Apr 2019 | The Unified Transform: A New Tool for Scattering Problems Cambridge Analysts' Knowledge Exchange (link, slides) | University of Cambridge |
| 12 Feb 2019 | Using the Unified Transform (Fokas method) for acoustic scattering problems Waves Group Seminar (link, slides) | University of Cambridge |
| 19 Nov 2018 | The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs Applied and Computational Mathematics Seminar (link, slides) | UC Irvine |
| 16 Nov 2018 | The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs Analysis and Applied Math Seminar (link, slides) | UC Berkeley |
| 12 Nov 2018 | The Computational Spectral Problem and a New Classification Theory; Novel Algorithms, Impossibility Results and Computer Assisted Proofs Scientific Computing and Numerics (SCAN) Seminar (link, slides) | Cornell University |
| 24 Oct 2018 | The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs Cambridge Analysts' Knowledge Exchange (link, slides) | University of Cambridge |
| 2-7 Sep 2018 | On the solvability complexity index hierarchy, the computational spectral problem and computer assisted proofs Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis (link, slides) | Dagstuhl, Germany |
| 30 May 2018 | Infinite dimensional spectral computations and linear algebra: Extending the QR algorithm to infinite dimensions Cambridge Analysts' Knowledge Exchange (link, slides) | University of Cambridge |
| 3 May 2017 | A new class of algorithms for computing spectra with error control SIAM-IMA Cambridge Student Chapter (link, slides) | University of Cambridge |
| 23 Nov 2016 | Scaling laws of passive-scalar diffusion in the interstellar medium and links to pseudo-differential equations and levy flights Cambridge Analysts' Knowledge Exchange (link) | University of Cambridge |
| Aug 2015 | A Study of Passive Tracers in the Turbulent Interstellar Medium Caltech SURF scholar program | Caltech |
| Sep 2014 | A numerical model for past ocean circulation and mixing CSRIM Programme | University of Cambridge |
| Sep 2014 | A numerical model for past ocean circulation and mixing Investigating Past Ocean Dynamics | University of Bern |