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Associate Professor Cecilia Gonzalez Tokman
Associate Professor

Cecilia Gonzalez Tokman

Email: 
Phone: 
+61 7 336 53271

Overview

Background

Cecilia is an associate professor in the School of Mathematics and Physics at the University of Queensland. After completing undergraduate studies at Universidad de Guanajuato / CIMAT and PhD at the University of Maryland, College Park, she held research fellowships from the Pacific Institute for the Mathematical Sciences (PIMS) and the Australian Research Council (ARC). She has also held a Promoting Women Fellowship by UQ.

Cecilia is an expert in the field of random dynamical systems (RDS). Along with collaborators, she has developed a framework for the study of transport in RDS, relying on the so-called Lyapunov–Oseledets spectrum. Her key contributions include the development of tools and algorithms to (i) approximate coherent structures and Lyapunov exponents, (ii) establish limit laws and quantify fluctuations, (iii) develop a thermodynamic formalism and (iv) optimise mixing. Her work also includes significant advances on data assimilation, metastable and dynamical systems.

Cecilia has received significant research funding from the Australian Research Council, including a 2016 Discovery Early Career Researcher Award (DECRA) a 2018 ARC DP and a 2022 ARC DP as lead CI. She has led or co-led competitive applications for conference funding (20-60 participants), including a 2023 MATRIX Workshop, co-funded by the MATRIX-Simons Collaborative Fund, an Australian Mathematical Sciences Institute (AMSI) funded Mathsfest Workshop (ANU, 2016), a Banff International Research Station Workshop (Canada, 2015) and a BIRS-CMO Workshop (Mexico, 2018).

Cecilia has delivered over a hundred invited lectures, seminars and colloquia in almost twenty countries, including invited/keynote addresses at the ANZIAM 2023 annual conference, 2014 International Workshop Set Oriented Numerics (U Canterbury, NZ), 2017 Workshop Ergodic Theory, Algorithms & Rigorous Computations (U Warwick, UK), 2017 EMALCA (Latin-American & Caribbean Math School, Mexico) and participation at invitation-only workshops at AIM (USA), BIRS (Canada), Bernoulli Center (Switzerland), CMO (Mexico), CIRM (France), Centro De Giorgi (Italy), Lorentz Center (Netherlands) and MATRIX (Australia).

Cecilia's service roles include: MATRIX Scientific Committee (2019-), Australian Mathematical Society council (2018-2021) and Queensland representative at the ANZIAM Executive Committee (2019-2021).

Availability

Associate Professor Cecilia Gonzalez Tokman is:
Available for supervision

Research interests

  • Dynamical Systems and Ergodic Theory

    Cecilia’s research interests include dynamical systems, ergodic theory and related areas. Her recent work focuses on random dynamical systems, transfer operators, Lyapunov exponents and coherent structures.

Works

Search Professor Cecilia Gonzalez Tokman’s works on UQ eSpace

29 works between 2009 and 2024

21 - 29 of 29 works

2016

Journal Article

Stability and approximation of invariant measures of Markov chains in random environments

Froyland, Gary and Gonzalez-Tokman, Cecilia (2016). Stability and approximation of invariant measures of Markov chains in random environments. Stochastics and Dynamics, 16 (1) 1650003, 1650003.1-1650003.23. doi: 10.1142/S0219493716500039

Stability and approximation of invariant measures of Markov chains in random environments

2015

Journal Article

A concise proof of the multiplicative ergodic theorem on banach spaces

González-Tokman, Cecilia and Quas, Anthony (2015). A concise proof of the multiplicative ergodic theorem on banach spaces. Journal of Modern Dynamics, 9 (01), 237-255. doi: 10.3934/jmd.2015.9.237

A concise proof of the multiplicative ergodic theorem on banach spaces

2014

Journal Article

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools

Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 1 (2), 249-278. doi: 10.3934/jcd.2014.1.249

Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools

2014

Journal Article

A semi-invertible operator Oseledets theorem

Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). A semi-invertible operator Oseledets theorem. Ergodic Theory and Dynamical Systems, 34 (4), 1230-1272. doi: 10.1017/etds.2012.189

A semi-invertible operator Oseledets theorem

2014

Journal Article

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles

Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2014). Stability and approximation of random invariant densities for Lasota-Yorke map cocycles. Nonlinearity, 27 (4), 647-660. doi: 10.1088/0951-7715/27/4/647

Stability and approximation of random invariant densities for Lasota-Yorke map cocycles

2014

Journal Article

Ulam's method for Lasota-Yorke maps with holes

Bose, Christopher, Froyland, Gary, Gonzalez-Tokman, Cecilia and Murray, Rua (2014). Ulam's method for Lasota-Yorke maps with holes. SIAM Journal on Applied Dynamical Systems, 13 (2), 1010-1032. doi: 10.1137/130917533

Ulam's method for Lasota-Yorke maps with holes

2013

Journal Article

Ensemble data assimilation for hyperbolic systems

Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2013). Ensemble data assimilation for hyperbolic systems. Physica D: Nonlinear Phenomena, 243 (1), 128-142. doi: 10.1016/j.physd.2012.10.005

Ensemble data assimilation for hyperbolic systems

2011

Journal Article

Approximating invariant densities for metastable systems

Gonzalez Tokman, Cecilia, Hunt, Brian R. and Wright, Paul (2011). Approximating invariant densities for metastable systems. Ergodic Theory and Dynamical Systems, 31 (5), 1345-1361. doi: 10.1017/S0143385710000337

Approximating invariant densities for metastable systems

2009

Journal Article

Scaling laws for bubbling bifurcations

Gonzalez-Tokman, Cecilia and Hunt, Brian R. (2009). Scaling laws for bubbling bifurcations. Nonlinearity, 22 (11), 2607-2631. doi: 10.1088/0951-7715/22/11/002

Scaling laws for bubbling bifurcations

Funding

Current funding

  • 2022 - 2025
    What predictions can I trust? Stability of chaotic random dynamical systems
    ARC Discovery Projects
    Open grant

Past funding

  • 2018 - 2021
    New mathematics to quantify fluctuations and extremes in dynamical systems (ARC Discovery Project administered by the University of New South Wales)
    University of New South Wales
    Open grant
  • 2016 - 2020
    Coherent structures in chaotic dynamical systems
    ARC Discovery Early Career Researcher Award
    Open grant

Supervision

Availability

Associate Professor Cecilia Gonzalez Tokman is:
Available for supervision

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Available projects

  • Dynamical Systems and Ergodic Theory

    Topics available for student projects at PhD/Masters/Honours level include:

    (i) Non-autonomous or random dynamical systems. These systems model the evolution of phenomena affected by external influences, such as deterministic forcing or stationary noise. Topics under investigation include Lyapunov exponents, multiplicative ergodic theory, statistical behaviour and stability.

    (ii) Theoretical and computational analysis of metastable and coherent structures in dynamical systems. Such structures encode important information of the long term evolution and transport phenomena in the underlying system. For example, they are useful to identify, analyse and quantify features of natural phenomena such as oceanic eddies and atmospheric vortices.

Supervision history

Current supervision

  • Doctor Philosophy

    Random Dynamical Systems, Transfer Operators and Stability

    Principal Advisor

    Other advisors: Dr Meagan Carney

  • Doctor Philosophy

    Global stability of chaotic random dynamical systems

    Principal Advisor

    Other advisors: Dr Meagan Carney

Completed supervision

Media

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