Cecilia González Tokman

cecilia.gt

uq . edu . au
Address:
School of Mathematics and Physics
The University of Queensland
St Lucia, QLD 4072
Australia

Office:
67-752
Priestley Building

Welcome! I am an associate professor at the School of Mathematics and Physics at The University of Queensland.
My research interests are in Dynamical Systems and Ergodic Theory: applied, theoretical and numerical aspects.
More information, including funding and supervision, is available at my researcher profile.

News and events

Women in Dynamical Systems & Ergodic Theory Advances in Dynamics Workshop on statistical properties of chaotic dynamics in and out of equilibrium DinAmicI in Rio, Dynamics, Applications, Interactions Workshop 2+3 in Dynamics - Joint 2nd Workshop Nordestino de Sistemas Dinâmicos and 3rd Jangada Dinâmica.
Publications (Preprint versions may differ slightly from published versions.) Equilibrium states for non-transitive random open and closed dynamical systems, (joint with J. Atnip, G. Froyland and S. Vaienti). Ergodic Theory and Dynamical Systems, 2022. [ arXiv \| doi ] A patch in time saves nine: Methods for the identification of localised dynamical behaviour and lifespans of coherent structures, (joint with C. Blachut and G. Hernandez-Duenas). Journal of Nonlinear Science 33, 55 (2023). [ arXiv \| doi ] Shifts in evolutionary balance of phenotypes under environmental changes (joint with M. Kleshnina, J. McKerral, J. Filar and J. Mitchell). R. Soc. Open Sci. 9: 220744, 2022. [ bioRxiv \| doi ] Thermodynamic Formalism for Random Weighted Covering Systems, (joint with J. Atnip, G. Froyland and S. Vaienti). Communications in Mathematical Physics 386, pages 819-902 (2021). [ arXiv \| doi ] Invariant measures for random expanding on average Saussol maps, (joint with F. Batayneh). Stochastics and Dynamics Vol. 22, No. 03, 2250015 (2022) [ arXiv \| doi ] Stability and collapse of the Lyapunov spectrum for Perron-Frobenius operator cocycles, (joint with A. Quas). Journal of the European Mathematical Society (2021), no. 10, pp. 3419-3457. [ arXiv \| doi ] Lyapunov exponents for transfer operator cocycles of metastable maps: a quarantine approach, (joint with A. Quas). Transactions of the Moscow Mathematical Society 2021, V 82. (Invited paper in Oseledets and Stepin 80th birthday volume) [ arXiv \| doi ] On the number of invariant measures for random expanding maps in higher dimensions, (joint with F. Batayneh). Discrete and Continuous Dynamical Systems, 2021, 41(12): 5887-5914. [ arXiv \| doi ] A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems, (joint with C. Blachut). Journal of Computational Dynamics, Volume 7, Number 2, pp. 369-399, 2020. [ pdf \| journal ] A spectral approach for quenched limit theorems for random hyperbolic dynamical systems, (joint with D. Dragičević, G. Froyland and S. Vaienti). Transactions of the American Mathematical Society, vol. 373, no. 1, pp. 629-664, 2020. [ arXiv \| journal ] Hilbert space Lyapunov exponent stability, (joint with G. Froyland and A. Quas). Transactions of the American Mathematical Society, vol. 372, no. 4, pp. 2357-2388, 2019. [ arXiv \| journal ] Almost sure invariance principle for random piecewise expanding maps, (joint with D. Dragičević, G. Froyland and S. Vaienti). Nonlinearity, 31 5: 2252-2280 (2018). [ arXiv \| journal ] A spectral approach for quenched limit theorems for random expanding dynamical systems, (joint with D. Dragičević, G. Froyland and S. Vaienti). Communications in Mathematical Physics, 360 (3) 1121-1187 (2018). [ arXiv \| journal ] Quenched stochastic stability for eventually expanding-on-average random interval map cocycles, (joint with G. Froyland and R. Murray). Ergodic Theory and Dynamical Systems, vol. 39, no. 10, pp. 2769-2792, 2019. [ pdf \| journal ] Multiplicative ergodic theorems for transfer operators: towards the identification and analysis of coherent structures in non-autonomous dynamical systems. Contributions of Mexican mathematicians abroad in pure and applied mathematics. Guanajuato, Mexico: American Mathematical Society. Contemporary Mathematics, 709, 31-52 (2018). [ pdf \| volume ] Optimal mixing enhancement by local perturbation, (joint with G. Froyland and T. Watson). SIAM Review, 58(3): 494-513, 2016. [ pdf \| journal ] Stochastic stability of Lyapunov exponents and Oseledets splittings for semi-invertible matrix cocycles, (joint with G. Froyland and A. Quas). Communications on Pure and Applied Mathematics, 68: 2052-2081, 2015. [ pdf \| journal ] A concise proof of the Multiplicative Ergodic Theorem on Banach spaces, (joint with A. Quas). Journal of Modern Dynamics, 9: 237-255, 2015. [ pdf \| journal ] Stability and approximation of invariant measures of Markov chains in random environments, (joint with G. Froyland). Stochastics and Dynamics, 16(1):1650003, 2016. [ pdf \| journal ] Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools, (joint with A. Quas and G. Froyland). Journal of Computational Dynamics, Pages: 249 - 278, Volume 1, Issue 2, December 2014. [ pdf \| journal \| bibtex ] Ulam's method for Lasota-Yorke maps with holes, (joint with C. Bose, G. Froyland and R. Murray). SIAM Journal on Applied Dynamical Systems, 2014, 13:2, 1010-1032. [ pdf \| journal \| bibtex ] Stability and approximation of random invariant densities for Lasota-Yorke map cocycles, (joint with G. Froyland and A. Quas). Nonlinearity, 27 (2014) 647-660. [ pdf \| journal \| bibtex ] A semi-invertible operator Oseledets theorem, (joint with A. Quas). Ergodic Theory and Dynamical Systems, 34 (2014), 1230-1272. [ pdf \| journal \| bibtex ] Ensemble data assimilation for hyperbolic systems, (joint with B. Hunt). Physica D: Nonlinear Phenomena, Volume 243, Issue 1, 15 January 2013, 128-142. [ pdf \| journal \| bibtex ] Multiplicative ergodic theorems and applications. (joint with A. Quas). CMS Notes, Volume 45 No. 5, October/ November 2013, 14-15. (Canadian Mathematical Society official newsletter). [ pdf \| CMS Notes ] Approximating invariant densities for metastable systems, (joint with B. Hunt and P. Wright). Ergodic Theory and Dynamical Systems, 31 (2011), 1345-1361. [ pdf \| journal \| bibtex \| poster ] Scaling laws for bubbling bifurcations, (joint with B. Hunt). Nonlinearity 22 (2009), 2607-2631. [ pdf \| journal \| bibtex ]
Edited book Mexican Mathematicians in the World. Trends and Recent Contributions. IV Meeting Reunión de Matemáticos Mexicanos en el Mundo June 10-15, 2018. Proceedings. Edited by Fernando Galaz-García, Cecilia González-Tokman and Juan Carlos Pardo Millán. Contemporary Mathematics, 775. Aportaciones Matemáticas. [Mathematical Contributions] American Mathematical Society, [Providence], RI; Sociedad Matemática Mexicana, México, 2021. [ doi ]
Submitted work Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products, (joint with J. Atnip, G. Froyland and A. Quas). [ arXiv ] Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems, (joint with J. Atnip, G. Froyland and S. Vaienti). [ arXiv ] Prevalence of stability for smooth Blaschke product cocycles fixing the origin, (joint with J. Peters). [ arXiv ] Asymptotic limits of transient patterns in a continuous-space interacting particle system, (joint with D. Oelz). Compound Poisson statistics for dynamical systems via spectral perturbation (joint with J. Atnip, G. Froyland and S. Vaienti). [ arXiv ]

Group members Jason Atnip (UQ, Research Fellow, joint with G. Froyland) Renee Oldfield (UQ, PhD, ongoing) Joshua Peters (UQ, PhD, ongoing) Chantelle Blachut (UQ, PhD, 2021) Fawwaz Batayneh (UQ, PhD, 2021) Peter Cudmore (UQ, PhD, 2017) Tapash Alister (UQ, Honours, 2023) Renee Oldfield (UQ, Honours, 2022) Joshua Peters (UQ, Honours, 2022) Isabela Conde (UQ, Honours, 2022) Lachlan Burton (UQ, Honours, 2018) Hayden Hohns (UQ, Honours, 2016) Jeremy Nugent (UNSW, Honours, 2014, joint with G. Froyland) Georgia Tsambos (UNSW, Honours, 2013, joint with G. Froyland) Joshua Peters (UQ, Summer Research student, 2021) Lachlan Burton (UQ, Summer Research student, 2016) Cale Rankin (UQ, Summer Research student, 2016)
For potential students If you are a UQ student thinking of specialising in dynamical systems, my suggestion is to enrol in the Applied Mathematics major, taking MATH3101 (Ordinary differential equations and dynamical systems) and STAT3004 (Probability Models & Stochastic Processes) within your Level 3 Elective Courses, as well as MATH3402 (Functional Analysis) as part of the BMath Program Electives. If you are interested in discussing possible research projects (e.g. Honours, PhD) in the areas of Dynamical Systems and Ergodic Theory, feel free to send me an email, including the following: (i) a few words about your research interests and background (e.g., what math books have you read?); (ii) your CV/transcripts; and (iii) samples of your written work, such as any papers, theses and/or senior/honours projects, if applicable.

Teaching

Course material, assignments and other resources --including consultation hours-- are available to enrolled students at Learn.UQ.

Math 2100, Math 7100: Applied Mathematical Analysis, (UQ).
Math 2010: Analysis of Ordinary Differential Equations (UQ).
Math 3101/7131: Ordinary differential equations and dynamical systems (UQ).
Math 1052: Multivariate Calculus & Ordinary Differential Equations (UQ).
Math 3101: Bifurcations and Chaos (UQ).
Math 4104/Math 7144: Advanced Hamiltonian Dynamics and Chaos (UQ).
Math 1051: Calculus and Linear Algebra (UQ).
Math 5175: Ergodic Theory, Dynamical Systems and Applications (UNSW).
Math 1031: Mathematics for Life Sciences (UNSW).
Math 300: Advanced Calculus (University of Victoria).
Math 151: Finite Mathematics (University of Victoria).

Selected service roles

Member of the Scientific Committee of MATRIX (2019-present).
Chair of ANZIAM 2024 Invited Speakers committee. Committee member in 2019 and 2022.
Member of the Program Advisory Board. Australian Mathematical Society Annual Meeting 2022.
Chair of the TM Cherry prize committee for best student presentation at the 2021 ANZIAM annual conference.
Ordinary member of the Australian Mathematical Society council (2018-2021).
Queensland representative at the ANZIAM Executive Committee (2019-2021).
Faculty of Science LCPC, UQ (2018-2020).
School of Mathematics and Physics Research Committee, UQ (2017-present). Director of Research since 2022.

Selected recent presentations

ANZIAM Conference 2023 Plenary lecture. Cairns, Australia (02/23)
Mexican Mathematical Society Colloquium. Mexico [V] (12/22)
Dynamical systems in NZ. Castaways, New Zealand (11/22)
Probabilistic techniques for random and time-varying dynamical systems, CIRM, France (10/22)
Dynamical Systems Seminar. Centro de Matematica Universidade do Porto. Porto, Portugal (09/22)
International Workshop on Dynamics, Optimization, and Computation Paderborn, Germany (09/22)
27th International Conference on Difference Equations and Applications (ICDEA). Paris, France/[V] (07/22)
7th International Conference on Random Dynamical Systems. Vietnam [V], (06/22)
65 Annual Meeting of the Australian Mathematical Society. U Newcastle, Australia [V] (12/21)
3 Encuentro de Mujeres Matemáticas Mexicanas. Sociedad Matemática Mexicana. Mexico [V] (11/21)
Coloquio Oaxaqueño. Instituto de Matemáticas UNAM. Oaxaca, Mexico [V] (10/21)
10th International Workshop on Set Oriented Numerics. Dynamics, Optimization, Computation. Germany [V] (09/21)
Dynamics Days Europe. France [V] (08/21)
One World Dynamics Seminar. [V]=virtual seminar (07/21)
SIAM Conference on Applications of Dynamical Systems (DS21). USA [V] (05/21)
Sydney Dynamics Group. University of Sydney. Australia [V] (05/21)
New Trends in Dynamics. Southern University of Science and Technology. China [V] (05/21)
ANZIAM Conference 2021. Australia [V] (02/21)

Events co-organised

	Advances in random dynamical systems and ergodic theory, ICIAM 2023, August 20-25, 2023, Tokyo, Japan.		Thermodynamic Formalism for Random Dynamical Systems, January 9 - 20, 2023, MATRIX, Creswick, Australia.
	Minisymposium on Transfer Operators and Geophysical Flows at the SIAM Conference on Mathematics of Planet Earth (MPE20), August 3-14, 2020, virtual event.		Dynamical Systems and Ergodic Theory Special Session at the AustMS Conference, 4-7 Dec 2018, University of Adelaide.
	Mexican Mathematicians in the World (Matemáticos Mexicanos en el Mundo), 10-15 Jun 2018, Casa Matemática Oaxaca.		Dynamical Systems and Fluid Dynamics Special Session at the WIMSIG Conference, 24-26 Sep 2017, University of South Australia.
	Mathsfest Workshop "Advances in Ergodic Theory, Hyperbolic Dynamics and Statistical Laws", Nov-Dec 2016, The Australian National University.		3rd meeting of Mexican mathematicians (Tercera Reunión de Matemáticos Mexicanos en el Mundo), 15-19 August 2016, CIMAT, Mexico.

	Workshop on Random Dynamical Systems and Multiplicative Ergodic Theorems, 18-23 January 2015, BIRS, Banff, Canada.		Dynamical Systems Special Session at the 59th Annual Meeting of the Australian Mathematical Society, September 28 - October 1st, 2015, Flinders University, Adelaide.

	Focused Research Group on Ergodic Theory and Transfer Operators, 12-16 August 2013, CIMAT, Guanajuato, Mexico.		International Workshop on Set-Oriented Numerics in Dynamical Systems, 3-6 September 2012, UNSW, Sydney.