Part of ERC research group SOS, led by Viviane Baladi.

Office: | Room 25-26.129, Jussieu |
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Email: | w****ll@lpsm.paris |

Numerics for statistical properties of chaotic systems

Diffusion maps

Wormell, C.L. and Reich, S., Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation. To appear in *SIAM Numerical Analysis* (2021). Preprint

Wormell, C.L. and Gottwald, G.A., Linear response for macroscopic observables in high-dimensional systems. *Chaos* **29** (2019) 113127. Preprint, DOI

Wormell, C.L., Spectral Galerkin methods for transfer operators in uniformly expanding dynamics. *Numerische Mathematik* **142** (2019) 421–463.
Preprint, DOI

Wormell, C.L. and Gottwald, G.A., On the validity of linear response theory in high-dimensional deterministic dynamical systems. *Journal of Statistical Physics* **172** (2018) 1479–1498. Preprint, DOI

Gottwald, G.A., Wormell, C.L., and Wouters, J.,
On spurious detection of linear response and misuse of the fluctuation-dissipation theorem in finite time series.
*Physica D*
**331** (2016) 89–101. Preprint, DOI

* Forthcoming: Linear response for hyperbolic maps with singularities*. Talk at Dynamics Days 2021, hopefully Nice (23-27 Aug 2021).

* Forthcoming: Emergence and breakdown of linear response in globally coupled systems*. Talk at International Conference on Mathematical Physics, hopefully Geneva (2-7 Aug 2021).

* Forthcoming: Linear response for the Lozi map and mixing of SRB measure cross-sections*. Talk at École d'été finistérienne en systèmes dynamiques, Brest (22 Jun 2021).

*Operator convergence of diffusion maps and the bistochastic normalisation*. Talk at SIAM Conference on Applications of Dynamical Systems, online (May 2021). Slides

*Linear response in high-dimensional globally coupled chaotic dynamics*. Seminar at Courant Networks and Dynamical Systems, online (April 2021).

*Rigorously validated estimation of statistical properties of expanding
maps*. Talk at AMS Spring Southeastern Sectional Meeting, online (Mar 2021).

*Linear response in high-dimensional globally coupled systems*. Invited talk at Linear Response: Rigorous Results and Applications, online (Jan 2021). Slides, video

*Rigorously validated estimation of statistical properties of expanding maps*. Seminar at CRM-CAMP, online (Aug 2020). Slides

*Spectral convergence of diffusion maps.* Seminar at Sydney Dynamics Group, online (Jun 2020). Slides

*Spectral Galerkin transfer operator methods in uniformly-expanding dynamics.* Seminar at Georgia Tech CDSNS Colloquium, online (Jun 2020). Slides

*Linear response for macroscopic observables in high-dimensional systems.*
Invited talk at Multiscale Methods for Deterministic and Stochastic Dynamics, Geneva (Jan 2020). Slides

*Linear response for macroscopic observables in high-dimensional systems.*
Invited talk at Response theory and its applications in geophysical fluid dynamics, Institut Henri Poincaré (Oct 2019). Slides

*Emergence of linear response at macroscopic scales.* Poster at Nonlinear and stochastic methods in climate and geophysical fluid dynamics, Institut Henri Poincaré (Oct 2019). Poster

*Linear response for macroscopic observables in complex chaotic systems.*
Seminar at Sydney Dynamics Group (Sep 2019).

*Spectral Galerkin transfer operator methods in uniformly-expanding dynamics.*
Invited talk at
Thermodynamic Formalism: Ergodic Theory and Validated Numerics, CIRM Luminy (Jul 2019). Slides

*Mesh-free solving of nonlinear PDEs via forward-backward SDEs.*
Talk at ANZIAM (Feb 2019).

*Validity of linear response theory in high-dimensional deterministic dynamical systems.*
Seminar at University of Potsdam (Dec 2018).

*Chebyshev Galerkin methods for transfer operators in uniformly-expanding dynamics.*
Seminar at Centro di Giorgi, Pisa (Nov 2018).

*Rigorous and accurate numerical computation for intermittent maps.*
Talk at Dynamics Days Europe (Sep 2018).

*Tight coupling bounds on decay of correlations in Markovian uniformly expanding dynamics.*
Seminar at Sydney Dynamics Group (Jul 2018).

*On spurious detection of linear response in chaotic systems with finite time series.*
Talk at Emerging Aspirations in Complex Systems Mini-Workshop (Oct 2017). Slides