Associate Professor Cecilia Gonzalez Tokman

Associate Professor

School of Mathematics and Physics
Faculty of Science
cecilia.gt@uq.edu.au
+61 7 336 53271

Overview

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).

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.

Qualifications

  • Doctor of Philosophy, University of Maryland

Publications

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Supervision

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Available Projects

  • 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.

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Publications

Featured Publications

Book

Book Chapter

  • 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.

Journal Article

Conference Publication

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

    Other advisors:

  • Doctor Philosophy — Principal Advisor

    Other advisors:

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • 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.