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Please get in touch (m[dot]colbrook[at]damtp.cam.ac.uk) if you would like me to present at your event or seminar.


Lecture Courses

2nd Semester 2022Data-driven approximations of Koopman operators for dynamical systems
Lecture notes (hand-written) available on request.
École Normale Supérieure
May - June 2022To infinity... and beyond! A course on infinite-dimensional spectral computations.
Lecture Notes
Gran Sasso Science Institute
Jan 2021On 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

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

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 2023Leslie 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 2023Semi-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 2023Plenary 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 2022Plenary 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 2022Plenary 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 2022Residual DMD: Rigorous data-driven spectral computations of Koopman operators for dynamical systems
MATHICSE seminar
(link, slides)
École Polytechnique Fédérale de Lausanne
7 June 2022Smale’s 18th Problem and the Barriers of Deep Learning
AudioVisual Communications Group
(slides)
École Polytechnique Fédérale de Lausanne
13 May 2022Koopman 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 2022Smale’s 18th Problem and the Barriers of Deep Learning
One World Seminar Mathematics of Machine Learning Seminar
(link, slides, video)
Online Seminar
4 May 2022When can algorithms be trusted? Computational analysis in the age of data science
Applied and Computational Analysis (ACA) Seminar
University of Cambridge
28 March 2022Koopman operators and the computation of spectral properties in infinite dimensions
Analysis & PDE Seminar
(link, slides)
Cardiff University
24 March 2022Koopman operators and the computation of spectral properties in infinite dimensions
Numerical Analysis and Scientific Computing Seminar
(link, slides)
University of Manchester
18 March 2022Koopman 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 2021Residual 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

Student prize: Selected as highly commended.
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