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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

1 - 20 of 29 works

Featured

2021

Journal Article

Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles

Gonzalez-Tokman, Cecilia and Quas, Anthony (2021). Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles. Journal of the European Mathematical Society, 23 (10), 3419-3457. doi: 10.4171/jems/1096

Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles

Featured

2018

Journal Article

A spectral approach for quenched limit theorems for random expanding dynamical systems

Dragičević, D., Froyland, G., González-Tokman, C. and Vaienti, S. (2018). A spectral approach for quenched limit theorems for random expanding dynamical systems. Communications in Mathematical Physics, 360 (3), 1121-1187. doi: 10.1007/s00220-017-3083-7

A spectral approach for quenched limit theorems for random expanding dynamical systems

Featured

2016

Journal Article

Optimal mixing enhancement by local perturbation

Froyland, Gary, Gonzalez-Tokman, Cecilia and Watson, Thomas M. (2016). Optimal mixing enhancement by local perturbation. SIAM Review, 58 (3), 494-513. doi: 10.1137/15M1023221

Optimal mixing enhancement by local perturbation

Featured

2015

Journal Article

Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles

Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2015). Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles. Communications on Pure and Applied Mathematics, 68 (11), 2052-2081. doi: 10.1002/cpa.21569

Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles

2024

Journal Article

Prevalence of stability for smooth Blaschke product cocycles fixing the origin

Gonzalez-Tokman, Cecilia and Peters, Joshua (2024). Prevalence of stability for smooth Blaschke product cocycles fixing the origin. Discrete and Continuous Dynamical Systems. doi: 10.3934/dcds.2024104

Prevalence of stability for smooth Blaschke product cocycles fixing the origin

2023

Journal Article

A patch in time saves nine: methods for the identification of localised dynamical behaviour and lifespans of coherent structures

Blachut, Chantelle, González-Tokman, Cecilia and Hernández-Dueñas, Gerardo (2023). A patch in time saves nine: methods for the identification of localised dynamical behaviour and lifespans of coherent structures. Journal of Nonlinear Science, 33 (4) 55. doi: 10.1007/s00332-023-09911-3

A patch in time saves nine: methods for the identification of localised dynamical behaviour and lifespans of coherent structures

2022

Journal Article

Shifts in evolutionary balance of phenotypes under environmental changes

Kleshnina, Maria, McKerral, Jody C., González-Tokman, Cecilia, Filar, Jerzy A. and Mitchell, James G. (2022). Shifts in evolutionary balance of phenotypes under environmental changes. Royal Society Open Science, 9 (11) 220744, 1-17. doi: 10.1098/rsos.220744

Shifts in evolutionary balance of phenotypes under environmental changes

2022

Journal Article

Equilibrium states for non-transitive random open and closed dynamical systems

Atnip, Jason, Froyland, Gary, Gonzalez-Tokman, Cecilia and Vaienti, Sandro (2022). Equilibrium states for non-transitive random open and closed dynamical systems. Ergodic Theory and Dynamical Systems, 43 (10) PII S0143385722000682, 3193-3215. doi: 10.1017/etds.2022.68

Equilibrium states for non-transitive random open and closed dynamical systems

2022

Journal Article

Invariant measures for random expanding on average Saussol maps

Batayneh, Fawwaz and González-Tokman, Cecilia (2022). Invariant measures for random expanding on average Saussol maps. Stochastics and Dynamics, 22 (3) 2250015, 1-18. doi: 10.1142/S0219493722500150

Invariant measures for random expanding on average Saussol maps

2022

Journal Article

Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach

González-Tokman, C. and Quas, A. (2022). Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach. Transactions of the Moscow Mathematical Society, 82 (1), 65-76. doi: 10.1090/mosc/313

Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach

2021

Book

Mexican Mathematicians in the World: Trends and Recent Contributions

Galaz-García, Fernando, González-Tokman, Cecilia and Pardo Millán, Juan eds. (2021). Mexican Mathematicians in the World: Trends and Recent Contributions. Contemporary Mathematics, Providence, Rhode Island: American Mathematical Society. doi: 10.1090/conm/775

Mexican Mathematicians in the World: Trends and Recent Contributions

2021

Journal Article

On the number of invariant measures for random expanding maps in higher dimensions

Batayneh, Fawwaz and Gonzalez-Tokman, Cecilia (2021). On the number of invariant measures for random expanding maps in higher dimensions. Discrete and Continuous Dynamical Systems- Series A, 41 (12), 5887-5914. doi: 10.3934/dcds.2021100

On the number of invariant measures for random expanding maps in higher dimensions

2021

Journal Article

Thermodynamic Formalism for Random Weighted Covering Systems

Atnip, Jason, Froyland, Gary, González-Tokman, Cecilia and Vaienti, Sandro (2021). Thermodynamic Formalism for Random Weighted Covering Systems. Communications in Mathematical Physics, 386 (2), 819-902. doi: 10.1007/s00220-021-04156-1

Thermodynamic Formalism for Random Weighted Covering Systems

2021

Book Chapter

Preface

Galaz-García, Fernando, González-Tokman, Cecilia and Millán, Juan Carlos Pardo (2021). Preface. Mexican mathematicians in the world: trends and recent contributions. (pp. vii-viii) Providence, RI, United States: American Mathematical Society.

Preface

2020

Journal Article

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems

Dragičević, D., Froyland, G., González-Tokman, C. and Vaienti, S. (2020). A spectral approach for quenched limit theorems for random hyperbolic dynamical systems. Transactions of the American Mathematical Society, 373 (1), 629-664. doi: 10.1090/tran/7943

A spectral approach for quenched limit theorems for random hyperbolic dynamical systems

2020

Journal Article

A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems

Blachut, Chantelle and González-Tokman, Cecilia (2020). A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems. Journal of Computational Dynamics, 7 (2), 369-399. doi: 10.3934/JCD.2020015

A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems

2019

Journal Article

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

Froyland, Gary, González-Tokman, Cecilia and Murray, R. U.A. (2019). Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems, 39 (10), 2769-2792. doi: 10.1017/etds.2017.143

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

2019

Journal Article

Hilbert space Lyapunov exponent stability

Froyland, Gary, Gonzalez-Tokman, Cecilia and Quas, Anthony (2019). Hilbert space Lyapunov exponent stability. Transactions of the American Mathematical Society, 372 (4), 2357-2388. doi: 10.1090/tran/7521

Hilbert space Lyapunov exponent stability

2018

Journal Article

Almost sure invariance principle for random piecewise expanding maps

Dragicevic, D., Froyland, G., Gonzalez-Tokman, C. and Vaienti, S. (2018). Almost sure invariance principle for random piecewise expanding maps. Nonlinearity, 31 (5), 2252-2280. doi: 10.1088/1361-6544/aaaf4b

Almost sure invariance principle for random piecewise expanding maps

2018

Conference Publication

Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems

González-Tokman, Cecilia (2018). Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems. Second Meeting Matemáticos Mexicanos en el Mundo [Second meeting of Mexican Mathematicians Abroad], Guanajuato, Mexico, 15-19 December 2014. Guanajuato, Mexico: American Mathematical Society. doi: 10.1090/conm/709/14290

Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems

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

Enquiries

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