Ian Lizarraga
216 Malott Hall
Email: iml32 'at' cornell 'dot' edu |
Welcome! I'm a visiting assistant professor at the Cornell University math department.
Update! Beginning in summer 2018, you can find me at the University of Sydney. I will be a postdoctoral fellow in dynamical systems, working with Martin Wechselberger.
I study applied and theoretical problems across dynamical systems, with a special emphasis on the geometric invariants of multiple timescale (slow-fast) systems and coupled oscillator systems.
My current research interests include:
- Ott-Antonsen ansatz problems and group-theoretic symmetry reduction in coupled oscillator systems
- Identification of chimeras and continuation algorithms in coupled oscillator systems
- Geometric singular perturbation theory applied to return maps of slow-fast dynamical systems, and applications to biological and chemical rhythms
Education
2011 - 2017: PhD in Applied Mathematics, Cornell University2008 - 2011: BA in Physics with Honors and Mathematics, Northwestern University
Teaching
2018 Sp, Math 1110: Calculus I (2 sections) (Instructor)2017 Fa, Math 1120: Calculus II (2 sections) (Instructor)
Past courses taught
Research
Publications
- R. Marangell, P. Cornwell, I.M.L., A. Roberts
Instability of a traveling pulse through a canard point
In prep. - I.M.L.
Modeling mixed-mode oscillations near a tangency of slow manifolds (2018)
In revision to be published in Chaos. - J. Guckenheimer and I.M.L.
Shilnikov homoclinic bifurcation of mixed-mode oscillations
SIAM Journal on Applied Dynamical Systems, 14(2), 764-786 (2015) [arXiv] - 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] - 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]