Ian Lizarraga



Coordinates:

489 Carslaw Building
School of Mathematics and Statistics
University of Sydney

Email: ian.lizarraga 'at' sydney 'dot' edu 'dot' au



Welcome! I'm a postdoctoral fellow working with Robby Marangell and Martin Wechselberger at the University of Sydney. I work on multiple-timescale dynamical systems.

I was a PhD student at Cornell University, advised by John Guckenheimer and Steven Strogatz.

My citation count (and other statistics) can be viewed on my ResearchGate profile.



Education and Work

2018 - 2023: Postdoctoral Fellow in Dynamical Systems, University of Sydney
2017 - 2018: Visiting Assistant Professor, Cornell Math Department
2011 - 2017: PhD, Applied Mathematics, Cornell University
2008 - 2011: BA, Physics with Honors, Mathematics, Northwestern University

Publications and preprints

  1. T. Kaper, I.M.L., R. Marangell, and T. Vo
    Geometric construction of trigger waves in reaction-diffusion systems
    In progress.
  2. I.M.L. and M. Wechselberger
    Delayed and singular Hopf bifurcations in nonstandard slow-fast systems
    In progress.
  3. Bronwyn Bradshaw-Hajek, I.M.L., R. Marangell, and M. Wechselberger
    A geometric singular perturbation analysis of generalised shock selection rules in reaction-nonlinear diffusion models
    Submitted (2023), 43 pages. [arXiv]
  4. I.M.L. and R. Marangell
    Nonlinear stability of shock-fronted travelling waves under nonlocal regularization
    Submitted (2022), 26 pages. [arXiv]
  5. I.M.L. and R. Marangell
    Spectral stability of shock-fronted travelling waves under viscous relaxation
    J Nonlinear Sci 33, 82 (2023). [arXiv]
  6. Bronwyn Bradshaw-Hajek, I.M.L., R. Marangell, and M. Wechselberger
    A geometric singular perturbation analysis of regularised reaction-nonlinear diffusion models including shocks
    Proceedings of 47th Sapporo Symposium on Partial Differential Equations (2022), pp. 53--64.
  7. I.M.L., B. Rink, and M. Wechselberger
    Multiple timescales and the parametrisation method in geometric singular perturbation theory
    Nonlinearity 34 4163 (2021). [arXiv]
  8. I.M.L., R. Marangell, and M. Wechselberger
    Slow unfoldings of contact singularities in singularly perturbed systems beyond the standard form
    J Nonlinear Sci 30, 3161--3198 (2020). [arXiv]
  9. I.M.L. and M. Wechselberger
    Computational singular perturbation method for nonstandard slow-fast systems
    SIADS 19(2), 994–1028 (2020). [arXiv]
  10. I.M.L.
    Tangency bifurcation of invariant manifolds in a slow-fast system
    Chaos (accepted pending minor revisions). [Preprint].
  11. J. Guckenheimer and I.M.L.
    Shilnikov homoclinic bifurcation of mixed-mode oscillations
    SIADS 14(2), 764-786 (2015) [arXiv]
  12. I.M. Kloumann, I.M.L., and S.H. Strogatz
    Phase diagram for the Kuramoto model with van Hemmen interactions
    Physical Review E 89, 012904 (2014) [arXiv]
  13. J. Teyssandier, S. Naoz, I.M.L., and F. Rasio
    Extreme orbital evolution from hierarchical secular coupling of two giant planets
    ApJ 779 166 (2013) [arXiv]

Talks

2023 May: SIAM Conference on Dynamical Systems, Portland, Oregon, USA
2022 Dec: AustMS Special Session on Dynamical Systems and Ergodic Theory, UNSW, Australia
2022 Nov: Sydney Dynamics Group Workshop, New Zealand
2022 Aug: SIAM Conference on Nonlinear Waves and Coherent Structures, Germany
2022 Apr: Dynamics Seminar, Boston University
2021 May: SIAM Conference on Dynamical Systems, Online
2021 May: Applied Maths Seminar, UNSW, Australia
2020 Dec: AustMS, Dynamical systems special session
2020 Mar: VIC-ANZIAM Lecture, University of Melbourne, Australia
2020 Mar: Applied Maths Seminar, Monash University, Melbourne, Australia
2020 Feb: ANZIAM, Hunter Valley, Australia
2019 Dec: Applied Maths Seminar, University of New South Wales, Sydney, Australia
2019 Nov: Sydney Dynamics Group Workshop, Margaret River, Australia
2019 Jul: Equadiff, Universiteit Leiden, Netherlands
2019 Jul: Slow-Fast-Ival Workshop, University of Edinburgh, UK
2019 May: SIAM Conference on Dynamical Systems, Snowbird, UT, USA
2019 Feb: ANZIAM, Nelson, New Zealand
2018 Nov: Sydney Dynamics Group Workshop, Blackheath, Australia
2018 Oct: Sydney Dynamics Group Seminar, Sydney, Australia
2017 Aug: Cornell Applied Math Seminar, Ithaca, NY, USA
2015 May: SIAM Conference on Dynamical Systems, Snowbird, UT, USA
2015 Mar: Cornell Dynamical Systems Seminar, Ithaca, NY, USA
2014 July: SIAM Annual Meeting, Chicago, IL, USA
2013 Nov: Cornell Scientific Computing and Numerics Seminar, Ithaca, NY, USA

Refereeing

I have served as a referee for the following journals:

Teaching

Non-teaching semester (2011--2017): supported by a Cornell Sage Fellowship (2011-2012) and otherwise through NSF Grant No. 1006272 (PI: John Guckenheimer).

CV

Available upon request.
Last updated: July 2023