Department of Mathematics,
California Institute of Technology
1200 East California Blvd
Pasadena, CA 91125
I am currently looking for positions. Here
is my CV.
Integrable difference equations: I specialize in discrete Painleve equations, which are discrete analogues of the much celebrated Painleve equations. These can be difference equations, q-difference equations or elliptic difference equations
Integrable lattice equations: Lattice equations are the discrete analogue of partial differential equations. There are discrete analogues of many known integrable partial differential equations. Many of the above mentioned discrete Painleve equations characterize self-similar solutions of lattice equations.
Systems of linear difference equations: Some of the above integrable systems may be solved via the compatibility of systems of difference (or differential) equations. The linear systems and their properties are of interest themselves.
Orthogonal polynomials and hypergeometric functions:Orthogonal polynomials often solve systems of differential and difference equations, which also characterize classes of special solutions of integrable systems.
Tropical geometry: My thesis was based on integrable systems defined in terms of the max-plus semiring. The geometric setting for these integrable systems is defined in terms of points of non-differentiability, which lends itself to a tropical geometric interpretation.
C. Ormerod and Y. Yamada,
From Polygons to
ultradiscrete Painleve equations, SIGMA 11 (2015), 056, 36 pages.
B. Al-Aanzi, P. Arpp, S. Gerges, C. Ormerod and K. Zinn,
Experimental and Computational Analysis of a Large Protein Network That Controls
Fat Storage Reveals the Design Principles of a Signaling Network, PLoS
Comput Biol 11.5 (2015): e1004264.
C. M. Ormerod, Spectral curves and discrete Painlevé equations, To appear, arXiv:1412.3846,
C. M. Ormerod, P.H. van der Kamp, G.R.W. Quispel, J. Hietarinta, Twisted reductions of integrable lattice equations, and their Lax representations, Nonlinearity, 27 (2014), 1367.
C. M. Ormerod, Symmetries and special solutions of reductions of the lattice potential KdV equation SIGMA 10 (2014), 002, 19 pages
C. M. Ormerod, Tropical geometric interpretation of ultradiscrete singularity confinement J. Phys. A: Math. Theor. 46, (2013) 305204
C. M. Ormerod, G.R.W. Quispel and P.H. van der Kamp, Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations, J. Phys. A: Math. Theor., Volume 46 (9) (2013) , 095204.
N.S. Witte and C.M. Ormerod, Construction of a Lax pair for the E6(1) $q$-Painlevé System, SIGMA 8 (2012), 097, 27 pages.
C. M. Ormerod, Reductions of lattice mKdV to q-PVI, Physics Letters A, Phys. Lett. A, .376 (2012) 2855–2859
P. J. Forrester, C. M. Ormerod and N. S. Witte, Connection preserving deformations and q-semi-classical orthogonal polynomials. Nonlinearity, Volume 24 (2011), Number 9, 2405.
C. M. Ormerod, Symmetries in connection preserving defomrations, SIGMA 7 (2011), 049, 13 pages.
C. M. Ormerod, The lattice structure of connection preserving deformations for q-Painleve equations I SIGMA 7 (2011), 045, 22 pages
C. M. Ormerod, A study of the associated linear problem for q-PV J. Phys. A: Math. Theor. 44 (2011) 025201
C. M. Ormerod, A Hypergeometric solutions to an ultradiscrete Painleve equation Journal of Nonlinear Mathematical Physics, Volume: 17, Issue: 1(2010) pp. 87-102
P. J. Forrester and C. M. Ormerod, Differential equations for deformed Laguerre polynomials Journal of Approximation Theory, Volume 162 (2010) no. 4
C. M. Ormerod, Associated linear theeory of ultradiscrete Painleve equations. PhD Thesis, Sydney University.
C. M. Ormerod, Connection matrices for ultradiscrete linear problems J. Phys. A 40 (2007), no. 42, 12799-12809.
C. M. Field and C. M. Ormerod, An ultradiscrete matrix version of the fourth Painleve equation Adv. Difference Equ. 2007, Art. ID 96752.
C. M. Ormerod, Connection matrices for ultradiscrete linear problems Reports of RIAM Symposium No.18ME-S5.
N. Joshi and C. M. Ormerod, The general theory of linear difference equations over the max-plus semi-ring Stud. Appl. Math. 118 (2007), no. 1, 85--97.
N. Joshi, F. Nijhoff and C. M. Ormerod, Lax pairs for ultra-discrete Painleve cellular automata, J. Phys. A 37 (2004), no. 44, L559--L565.
C. M. Ormerod, Cellular automata model of HIV infection on tilings of the plane Proceedings of the 7th Asia-Pacific Conference on Complex Systems Cairns Convention Centre, Cairns, Australia, 6-10th December 2004.
N. Bordes, C.Ormerod and B. Pailthorpe, Characterising Coupled Map Lattices. Proceedings of HPC Asia'01, Gold Coast, Australia (Sept. 24-28, 2001)
C. Ormerod and E. Rains, A
symmetric difference-differential Lax pair for Painlevé VI,
C. Ormerod and E. Rains, Commutation
relations and discrete Garnier systems, arXiv:1601.06179.Al-Anzi,
Bader, et al.
computational model captures fundamental architectural features of diverse
biological networks. bioRxiv (2016): 046813.
You can find my google scholar profile
Erdos Number : 3
University of Sydney: Bachelor of Advanced Science: Pure Mathematics, 2000-2003
University of Sydney: Doctor of Philosophy: Applied Mathematics, 2004-2008
University of Melbourne: Postdoctoral Research Fellow, 2008-2010
La Trobe University: Associate Lecturer, 2010-2011
La Trobe University, Australian Research Council, Postdoctorial Research Fellow (Promoted to Research Fellow/Lecturer in 2012), 2011-2013
California Institute of Techology, Olga-Tausky-Todd Instructor, 2013-present
ARC Discovery Project - The Sakai scheme - Askey table correspondence, analogues of isomonodromy and determinantal point processes, 2009 - 2011
ARC Discovery Project - Discrete Integrable Systems, 2011 - 2013
AMSI Workshop on Nonlinear Dynamical Systems, 2012.
I am teaching Galois Theory
and Representation Theory, Mat5c, at Caltech in Spring of 2016.
I am teaching a graduate course on Integrable systems, Mat191c Sec 7, at Caltech in Spring of 2016.
Previous lecturing experience
Caltech, 2015, Combinatorial Analysis
Caltech, 2014, Galois Theory and Representation Theory.
Caltech, 2014, Combinatorial Analysis
Caltech, 2013, q-special functions with applications to integrable systems.
Caltech, 2013, Galois Theory and Representation Theory.
La Trobe University, 2010, Calculus and Linear algebra.
La Trobe University, 2010-2012, Scientific Computing.La Trobe
University, 2012, Discrete Integrable Systems
Previous tutoring experience
Sydney University, School of Physics, 2001-2002, Scientific Computing/Scientific Visualization.
Sydney University, School of Physics, 2003-2007, Computational Science in C.
Sydney University, School of Mathematics, 2004-2007, Linear Algebra, Calculus, ODEs.
University of New South Wales, Department of Mathematics, 2007, Calculus.
La Trobe University, Department of Mathematics, 2010, Vector Calculus, Linear Algebra.
Selected conference presentations
Isaac Newton Institute for Mathematical Sciences, Discrete Integrable Systems 2009, Orthogonal polynomials and connection preserving deformations
Integrability Day 2009, La Trobe University, Australia, Groups of connection preserving deformations
The 9th conference of the Symmetries and Integrability of Difference equations (SIDE 9), Varna, Bulgaria, Symmetries of the associated linear problems for q-Painlevé equations.
Integrability Day 2010, La Trobe Unversity, Australia, Tropical geometric interpretation of singularity
The 10th conference of the Symmetries and Integrability of Difference equations (SIDE 10), Ningbo, China, Non-autonomous reductions of lattice equations
Lorentz Center for workshops in the Sciences, Leiden, The Netherlands, Special solutions of the additive discrete Painlevé equation with E(1)6 symmetry
Workshop on Nonlinear Dynamical Systems, La Trobe University, Australia, A reduction of the discrete Schwarzian Korteweg-de
Vries equation to q-P(E_6(1))
The Eighth IMACS International Conference on. Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Georgia, USA, q-Painleve equations as periodic reductions of integrable lattice equations
Joint Mathematics Meeting, Special session on Algebraic and analytic aspects of integrable systems and Painleve equations, Baltimore, USA, 2014, Twisted reductions of lattice equations