Can we compute spectral properties of (infinite-dimensional) Koopman operators?
Koopman Operator Theory Workshop — Otranto
Talks and Lectures
Invited talks, conference presentations, lecture courses, and selected recorded talks. Please get in touch if you would like me to speak at a seminar or event.
Previous Talks
2026 (? talks)
-
January 2026minicourse
A Short Course on Spectral Computations in Infinite Dimensionslecture notes available upon request -
15 January 2026Some thoughts on Koopman Operators
2025 (14 talks)
-
9 December 2025Data-Driven Spectra in Dynamical Systems
-
28 November 2025Convergent Algorithms for Infinite-Dimensional Nonlinear Spectral Problems
-
11 Sep 2025Spectral Learning for Dynamical Systems
-
9 Sep 2025Spectral Learning for Dynamical Systems Via Infinite-Dimensional Numerical Linear Algebra
-
28 Aug 2025Adversarial Dynamics and the Boundaries of Data-Driven Koopman Spectral Computability
-
2 July 2025plenary speaker
Verified Koopman Modes and an Example for Climate -
19 May 2025plenary speaker
Navigating Limits in Learning Complex Systems -
12 May 2025Adversarial Dynamics and Barriers in Operator Learning
-
8 May 2025On the Mathematical Foundations of Infinite-Dimensional Spectral Computations
-
6 May 2025Adversaries and classifying the difficulty of data-driven dynamical systems
-
24 March 2025Stable and Accurate Neural Networks: Why Existence Does Not Imply Computability
-
26 Feb 2025Learning unitary Koopman operators from trajectory data
-
19 Feb 2025Spectral Computations in Infinite Dimensions: Classifications and Applications
-
4 Feb 2025What can we learn about a dynamical system from data?
2024 (15 talks)
-
12 Dec 2024A classification theory for data-driven Koopman Spectral Computations
-
12 Nov 2024Rigorous Limits of Learning in Dynamical Systems
-
28 Oct 2024invited speaker
Towards a classification theory for data-driven dynamical systems -
21 August 2024Residual Dynamic Mode Decomposition for Stochastic Systems
-
19 August 2024minicourse
Data-driven computation of spectral properties of Koopman operators -
15 August 2024Barriers and Classifications of Robust Koopman Learning
-
10 July 2024Classifications of Data-Driven Koopman Learning
-
18 June 2024Data-Driven Spectral Measures and Generalized Eigenfunctions of Koopman Operators
-
10 June 2024Computing spectral properties of unitary Koopman Operators
-
23 May 2024The Hitchhiker's Guide to the DMD Multiverse
-
20 May 2024Can we compute spectral properties of (infinite-dimensional) Koopman operators?
-
13 May 2024An Overview of Operator Learning: Infinite-dimensional NLA
-
4 April 2024Geometric integration meets data-driven dynamical systems
-
21 March 2024Unitary Approximations of Koopman Operators
-
29 Feb 2024Polar Decompositions of Koopman Operators
2023 (17 talks)
-
20 Sep 2023Verified Koopman Spectra through Operator Folding
-
19 Sep 2023Verifying data-driven computations of Koopman spectra
-
22 Aug 2023Going beyond expectations: Stochastic ResDMD
-
17 Aug 2023Four examples of discretization issues for Nonlinear Eigenvalue Problems
-
26 July 2023Taming Discretization Challenges for Nonlinear Eigenvalue Problems
-
29 June 2023Avoiding discretization issues for nonlinear eigenvalue problems
-
26 June 2023Leslie Fox Prize Lecture
Computing semigroups with error control -
21 June 2023Avoiding discretization issues for nonlinear eigenvalue problems
-
20 June 2023semi-plenary speaker (10th Popov Prize Lecture)
The Solvability Complexity Index: A toolkit for approximation theory and the foundations of computation -
24 May 2023Avoiding discretization issues for nonlinear eigenvalue problems
-
15 May 2023Measure-Preserving Extended Dynamic Mode Decomposition: Structure-preserving Koopmanism
-
18 April 2023plenary speaker
Spectral Computations in Infinite Dimensions -
13 March 2023Residual Dynamic Mode Decomposition: A path to verified data-driven discovery of dynamics!
-
9 March 2023Residual Dynamic Mode Decomposition: Robust and verified Koopmanism for nonlinear dynamical systems
-
2 March 2023Fast Spectral Methods for Spectral Measures
-
9 Feb 2023The difficulty of computing stable and accurate neural networks: On the barriers of deep learning & Smale's 18th problem
-
6 Jan 2023The foundations of infinite-dimensional spectral computations
2022 (30 talks)
-
18 Dec 2022Smale's 18th Problem and the Barriers of Deep Learning
-
9 Dec 2022Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems
-
16 Nov 2022Measure-Preserving Extended Dynamic Mode Decomposition: Structure-preserving and rigorous Koopmanism
-
15 Nov 2022On spectral computations in infinite dimensions: Spectral measures, Koopman operators and beyond
-
11 Nov 2022To infinity... and beyond! The solvability complexity index and the foundations of infinite-dimensional spectral computations
-
9 Nov 2022Residual Dynamic Mode Decomposition: A path towards modal analysis of nonlinear dynamical systems
-
28 Oct 2022Residual Dynamic Mode Decomposition: Robust and verified Koopmanism!
-
24 Oct 2022Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems
-
20 Oct 2022Measure-Preserving Extended Dynamic Mode Decomposition: Structure-preserving and rigorous Koopmanism
-
17 Oct 2022To infinity... and beyond! The solvability complexity index and the foundations of infinite-dimensional spectral computations
-
27 Sep 2022Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
-
27 Sep 2022Residual Dynamic Mode Decomposition: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
-
20 Sep 2022Smale’s 18th Problem and the Barriers of Deep Learning
-
12 Sep 2022The Solvability Complexity Index Hierarchy and Generalised Hardness of Approximation
-
30 Aug 2022Robust and Verified Koopmania
-
23 July 2022Robust and Verified Koopmania
-
28 June 2022plenary speaker
Numerical analysis in the age of data science through the Solvability Complexity Index hierarchy -
15 June 2022plenary speaker
Rigorous and data driven Koopmanism: Infinite-dimensional spectral computations for nonlinear systems -
8 June 2022Residual DMD: Rigorous data-driven spectral computations of Koopman operators for dynamical systems
-
7 June 2022Smale’s 18th Problem and the Barriers of Deep Learning
-
13 May 2022Koopman operators and a programme on the foundations of infinite-dimensional spectral computations
-
11 May 2022Smale’s 18th Problem and the Barriers of Deep Learning
-
4 May 2022When can algorithms be trusted? Computational analysis in the age of data science
-
28 March 2022Koopman operators and the computation of spectral properties in infinite dimensions
-
24 March 2022Koopman operators and the computation of spectral properties in infinite dimensions
-
18 March 2022Koopman operators and the computation of spectral properties in infinite dimensions
-
21 Feb 2022On the Barriers of Deep Learning, Approximate Sharpness, and Smale’s 18th Problem
-
18 Feb 2022Data-driven numerical analysis of Koopman operators for dynamical systems
-
7 Feb 2022Data-driven numerical analysis of Koopman operators for dynamical systems
-
4 Feb 2022Computing semigroups and solutions of time-fractional PDEs with error control
2021 (21 talks)
-
15 Dec 2021Residual DMD: Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems
-
7 Dec 2021Can stable and accurate neural networks always be computed?
-
1 Dec 2021Computing semigroups and solutions of time-fractional PDEs with error control
-
18 Nov 2021Infinite-Dimensional Spectral Computations
-
8 Nov 2021Infinite-Dimensional Spectral Computations
-
26 Oct 2021Can stable and accurate neural networks always be computed?
-
20 Aug 2021Computing spectral measures and a programme on the foundations of infinite-dimensional spectral computations
-
6 Aug 2021Non-linear Forchheimer corrections in acoustic scattering
-
5 Aug 2021Modelling chordwise-varying porosity to reduce aerofoil-turbulence interaction noise
-
23 July 2021Can stable and accurate neural networks always be computed?
-
22 July 2021Can stable and accurate neural networks always be computed?
-
19 July 2021Computing Spectral Measures
-
14 July 2021Computing spectral measures of self-adjoint operators
-
12 July 2021Computing semigroups with error control
-
11 June 2021Can stable and accurate neural networks always be computed?
-
26 May 2021Can stable and accurate neural networks always be computed?
-
12 May 2021Computing semigroups with error control and a framework for infinite-dimensional computations
-
6 April 2021Lighthill–Thwaites Prize Lecture
Diagonalising the infinite: How to compute spectra with error control -
26 March 2021Infinite-Dimensional Spectral Computations
-
22 March 2021Probing the infinite: Computing spectral & transport properties in infinite dimensions
-
18 March 2021Diagonalising the infinite: How to compute spectra with error control
2020 (10 talks)
-
10 Dec 2020Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators
-
6 Dec 2020A Mathieu function boundary spectral method for acoustic scattering
-
26 Oct 2020Diagonalising Infinite-Dimensional Operators: Computing spectral measures of self-adjoint operators
-
30 Aug - 2 Sep 2020selected as highly commended
How To Compute Spectra With Error Control -
14-15 July 2020The Foundations of Infinite-Dimensional Spectral Computations
-
23 June 2020How to compute spectral properties of operators on Hilbert spaces with error control
-
3 June 2020How to compute spectral properties of operators on Hilbert spaces with error control
-
26 May 2020Scattering, Acoustic Black Holes and Mathieu Functions: A boundary spectral method for diffraction by multiple variable poro-elastic plates
-
5 May 2020The Foundations of Infinite-Dimensional Spectral Computations: Can we compute spectral properties?
-
15 April 2020The Foundations of Infinite-Dimensional Spectral Computations
2019 (14 talks)
-
9-13 Dec 2019The Foundations of Infinite-Dimensional Spectral Computations
-
5-30 Aug 2019Solving Wiener-Hopf type problems numerically: a spectral method approach
-
8-12 Jul 2019Do stable networks with recovery guarantees exist?
-
25-28 Jun 2019Spectral problems and new resolvent based methods
-
14 June 2019Resolving the resolvent: How to "diagonalise" infinite matrices
-
23 May 2019On Instabilities of Deep Learning in Image Reconstruction
-
22 May 2019Spectral resolvent based methods
-
10 May 2019Can neural networks always be trained? On the boundaries of deep learning
-
6 May 2019Can neural networks always be trained? On the boundaries of deep learning
-
2 May 2019Spectral analysis and new resolvent based methods
-
1 May 2019Can neural networks always be trained? On the boundaries of deep learning
-
24 Apr 2019The Unified Transform: A New Tool for Scattering Problems
-
10 Apr 2019The Unified Transform: A New Tool for Scattering Problems
-
12 Feb 2019Using the Unified Transform (Fokas method) for acoustic scattering problems
2018 (6 talks)
-
19 Nov 2018The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs
-
16 Nov 2018The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs
-
12 Nov 2018The Computational Spectral Problem and a New Classification Theory; Novel Algorithms, Impossibility Results and Computer Assisted Proofs
-
24 Oct 2018The Computational Spectral Problem and a New Classification Theory: Novel Algorithms, Impossibility Results and Computer Assisted Proofs
-
2-7 Sep 2018On the solvability complexity index hierarchy, the computational spectral problem and computer assisted proofs
-
30 May 2018Infinite dimensional spectral computations and linear algebra: Extending the QR algorithm to infinite dimensions
Videos of Some Talks
Residual Dynamic Mode Decomposition
Recorded while visiting Steve Brunton’s lab
Measure-preserving EDMD: A 4-line structure-preserving DMD algorithm
Recorded while visiting Steve Brunton’s lab
Residual Dynamic Mode Decomposition
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
Diagonalising Infinite-Dimensional Operators
Communications in Numerical Linear Algebra Seminar
Lecture Courses
Spectral Computations in Infinite Dimensions
Part III Mathematical Tripos — University of Cambridge (Lent Term, 2022–present).
Lecture notes available on request — a book on this topic will appear later this year.
IB Mathematical Methods I
Natural Sciences Tripos — University of Cambridge (Michaelmas Term, 2022–present).
Lecture notes and example sheets are available on Moodle.
Data-Driven Approximations of Koopman Operators for Dynamical Systems
École Normale Supérieure (Spring 2022).
Lecture notes (hand-written) available on request.
To Infinity… and Beyond! A Course on Infinite-Dimensional Spectral Computations
Gran Sasso Science Institute (May–June 2022).
Lecture notes.
On the Barriers of AI and the Trade-off Between Stability and Accuracy in Deep Learning
21st Geilo Winter School in eScience (Jan 2021).
Lecture materials available on request.