
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
Fields of research
Research interests
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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
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
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
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
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
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
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
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
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
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
Supervision
Availability
- Associate Professor Cecilia Gonzalez Tokman is:
- Available for supervision
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Available projects
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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
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Doctor Philosophy
Random Dynamical Systems, Transfer Operators and Stability
Principal Advisor
Other advisors: Dr Meagan Carney
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Doctor Philosophy
Global stability of chaotic random dynamical systems
Principal Advisor
Other advisors: Dr Meagan Carney
Completed supervision
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2021
Doctor Philosophy
Existence, ergodic properties, and number of random invariant measures for multidimensional quenched random dynamical systems
Principal Advisor
Other advisors: Dr Dietmar Oelz
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2021
Doctor Philosophy
Seeking earthly measures: Algorithms for the detection, tracking and investigation of coherent structures in non-autonomous dynamical systems
Principal Advisor
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2017
Doctor Philosophy
Synchronisation of Nanomechanical Oscillators
Principal Advisor
Other advisors: Professor Joseph Grotowski
Media
Enquiries
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