Caroline Wormell

Caroline Wormell in Queyras region, France PhD student in the School of Mathematics and Statistics at the University of Sydney.

Postal address: Ms Caroline Wormell
School of Mathematics and Statistics F07
University of Sydney NSW 2006
Australia
Office: Room 807 Carslaw Building
Email: caroline.w****ll@sydney.edu.au


Research interests

Linear response theory of complex chaotic systems (working under Prof Georg Gottwald)

Quantitative study of statistical properties of one-dimensional chaotic systems

Backward stochastic differential equations

Publications and preprints

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 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

Computer packages

Poltergeist.jl: Julia package for adaptive calculation of statistical properties of 1D maps via spectral methods.

Research talks and posters

Forthcoming: Invited talk at Multiscale Methods for Deterministic and Stochastic Dynamics, University of Geneva, 29-30 January 2020.

Macroscopic non-hyperbolicity in chaotic dynamics. Poster at SDG Margaret River (Nov 2019).

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). Slides

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).

Linear response in weakly-coupled systems. Talk at ANZIAM (Feb 2018). Slides

Spectral Galerkin methods for transfer operators. Talk at Annual Meeting of the Australian Mathematics Society (Dec 2017). Slides

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

Spectral methods for intermittent maps using Abel functions. Poster at Foundations of Computational Mathematics conference (Jun 2017).

Fast numerical approximation of intermittent maps. Talk at ANZIAM (Feb 2017).

Fast approximation techniques for intermittent maps. Poster at Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws (Dec 2016). Prize for best poster.

Approximating 1D chaotic dynamics in a Fourier basis. Poster at Mixing Flows and Averaging Methods workshop, ESI Vienna (May 2016).

Other talks

Chaotic systems and ergodic theory. Talk for Center for Atmospheric and Oceanic Sciences graduate student lunch, NYU (Nov 2018).

Introduction to Julia. Talk for Center for Atmospheric and Oceanic Sciences graduate student lunch, NYU (Oct 2018).

Numerical computing with functions in Julia. Talk for Julia Sydney Meetup group (Dec 2017).

A user's guide to chaotic systems. Talk for USyd Mathematics Postgraduate Seminar Series (Oct 2017).

Constituent structure in Palauan. Presentation at the Australian Linguistics Society Conference, Melbourne (Dec 2016).

The mathematics of biological pattern formation, or How the Leopard Got Its Spots. Talk for Sydney University Mathematics Society (Aug 2016).

Minding your p's and q's: adventures in statistical inference. Talk for Sydney University Mathematics Society (Sep 2014).