Caroline Wormell

Caroline Wormell in Nelson Lakes National Park, New Zealand 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: ca.w****ll@gmail.com


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. In submission. Preprint

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 Response theory and its applications in geophysical fluid dynamics, Institut Henri Poincaré, Oct 2019.

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

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

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

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

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

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

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

Spectral Galerkin methods for transfer operators. Talk at AustMS (2017). Slides

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

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

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

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

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

Other talks

Numerical computing with functions in Julia. Talk for Julia Sydney Meetup group (2017). Slides (Jupyter notebook format)

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

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

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

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