Robert McLachlan
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Robert McLachlan studied at Canterbury University (BSc (Hons) 1984) and (PhD 1990), writing his thesis "Separated Viscous Flows via Multigrid" under Herb Keller. After three years at and ETH, Zurich, where he began his work on symplectic and geometric integration, he joined Massey in 1994, becoming Professor in Applied Mathematics in 2002. He won the New Zealand Association of Scientists Research Medal in 2003, the Massey University and the NZMS Research Medals in 2005, and the Germund Dahlquist Prize in 2007. He is currently the President of the New Zealand Mathematical Society and Deputy Head of the Institute of Fundamental Sciences.

Stephen Marsland
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Stephen Marsland has a BA(Hons) in Mathematics from the University of Oxford and a PhD in "Self-Organisation and Novelty Detection" from the University of Manchester, which he completed in 2002. Since then he has spent time at the Santa Fe Institute, the University of Bremen and the University of Manchester, where he was a lecturer in computer science and a researcher in the divison of Imaging Science and Biomedical Engineering. He moved to Massey in 2004, and was awarded an Early Career research award there in 2005. He is currently an associate professor and the postgraduate director of the School of Engineering and Advanced Technology at Massey.

Raziyeh Zarre (PhD student 2012 -)
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Raziyeh Zarre started her PhD project within the dynamics group in 2012. She has a Master of Science degree in Pure Mathematics, which she completed in 2009 at the Ferdowsi University of Mashhad, Iran, and a BSc in Pure Mathematics from the same university. Her MSc thesis was on Lyapanov exponents and their relation to hyperbolicity.

Matt Wilkins (PhD student 2011 -)
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Matt Wilkins received his BSc (hons) in Mathematics from the University of Canterbury in 1996, his MSc in Mathematics at the Courant Institute NYU in 2000, and his MSc in Computer Science from UBC in Canada in 2002. He worked in IT for six years in Vancouver Canada, and now is working full time at ITS Massey University while pursuing his PhD part time in the dynamics group.

Yousuf Tufail (PhD student 2012 -)
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Yousuf Tufail has a Masters degree in Mathematics from the University of Karachi, as well as an Honours degree from the same institution. He is a lecturer at the NED University of Engineering and Technology in Pakistan, currently on secondment to our group, where he is undertaking a PhD on shape analysis and diffeomorphism groups.

Former Members

Matthew Perlmutter
Matt Perlmutter was educated at Berkeley, getting a BA in Physics in 1990 and a PhD in Mathematics in 1999, writing his thesis on "Symplectic Reduction by Stages" under Jerry Marsden. This thesis grew in the telling until it became the mighty epic "Hamiltonian Reduction by Stages", published by Springer in 2007. He was a postdoc at Massey in 2000-2001, working with Robert McLachlan on geometric integration, and at the Center for Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Lisbon, 2002-2004, working on singular reduction, before returning to Massey as a lecturer. He was a plenary lecturer at MASIE (Mechanics and Symmetry in Europe) at Peyresq, France, in 2001 and a Visiting Fellow at the École Polytéchnique Fédéral de Lausanne in 2004 and 2005. Matt worked at Massey between 2006 and 2011, and is now at the Universidade Federal de Minas Gerais in Belo Horizonte, Brazil.

Fleur McDonald (PhD student 2009-)
Fleur McDonald has a BSc (Hons) in mathematics from Massey University. She joined the group in the summer of 2007-08 working as a summer research scholar on "Symmetries of elementary cellular automata". Symmetries have traditionally been required to be invertible, and the left-right and black-white symmetries of some elementary cellular automata were well known. In her project she relaxed this assumption and studied symmetries that were non-invertible, finding a surprising 2584 pairs of commuting elementary cellular automata. These were organized into a graph which revealed new structure about the space of elementary cellular automata.
She then continued on to a PhD in geometric numerical integration, writing a thesis on "Travelling Wave Solutions of Multisymplectic Discretizations of Wave Equations." She is now working in industry.

Klas Modin
Klas Modin studied mathematics and physics at Lund University in Sweden, where he also continued as a Ph. D. student supervised by Claus Führer and Gustaf Söderlind. In May 2009 he defended his thesis "Adaptive Geometric Numerical Integration of Mechanical Systems" at the Centre for Mathematical Sciences. The thesis is about the construction and analysis of variable time step geometric numerical integration algorithms. Klas was a post-doctoral fellow at Massey University, working in the Applied Dynamics Group between 2009 and 2011. He is now an Assistant Professor at Chalmers University of Technology in Goteborg, Sweden.

James Benn
(MSc Student 2010)
James Benn studied philosophy before concentrating on mathematics. His MSc thesis "The Algebraic Structure of B-series" covered geometric integration, Runge-Kutta methods and the spaces of energy-preserving and Hamiltonian B-series. He is currently studying for a PhD at Notre Dame University with Gerard Misiolek, working on geometric analysis.

Kristin McLeod
(Honours Student and Summer Research Student 2006)
Kristen McLeod is studying for a BSc (Hons) in mathematics. In the summer of 2006-07 she worked as a summer research scholar on "A method for computing exact Poincare maps of Hamiltonian systems". Standard methods for calculating Poincaré maps involve an interpolation step which (especially at the large time steps often used in symplectic integration) leads to smearing of the phase portrait. In her project she developed new symplectic integrators that can be used to calculate Poincaré maps with no interpolation error. She spent a semester abroad at the University of Exeter in 2007. With the group she researched the dynamical behaviour of the leapfrog method applied to systems of atoms under Lennard-Jones forces. From 2010-2013 she did a PhD at INRIA-Sophia Antipolis in the south of France, after which she moved to a postdoc at Simula in Oslo, modelling the heart.

Philip Zhang
(PhD student 2005-2007)

Xing-You (Philip) Zhang originally studied and was a lecturer at Chongqing University before emigrating to New Zealand in 2004. He has published extensively on PDEs, especially on homogenization and the structure of global strange attractors. In early 2008 he submitted his PhD thesis on "Dynamics and Numerics of Generalized Euler Equations". Many PDEs of mathematical physics, eg those arising in fluid mechanics, micromagnetics, and image registration, have the structure of an Euler equation, ie they describe geodesics on an infinite-dimensional group. They can be integrable or non-integrable. Philip studied nonintegrable generalizations of the Camassa-Holm shallow water equation, proving results on existence and well-posedness of solutions. A unique blow-up process by which solitary waves (solitons) are created was studied analytically and numerically. He is now a Research Scientist at Callaghan Innovation (formerly IRL) postdoc, working on PDEs arising in nanotechnology and medical devices.

Dion O'Neale
(PhD 2009)

Dion completed a conjoint degree in arts and science at the University of Auckland in 2002, majoring in mathematics and physics. His B.Sc. Honours degree in Mathematics, also at Auckland, involved projects with Philip Sharp and John Butcher on the restricted three-body problem with photo-gravitational effects and on stability of linear multi-step methods respectively. He wrote his M.Sc. thesis in Germany at the Heinrich Heine Universitaet in Duesseldorf under the supervision of Marlis Hochbruck. This was titled "Split-step Methods for Highly Oscillatory, Non-linear Problems" and developed numerical integrators for solving differential equations which describe relativistic laser-plasma interaction. This research lead him to articles by Robert McLachlan, under whose supervision at Massey University Dion began his Ph.D. in 2005. His Ph.D. thesis is on geometric numerical integration and focuses on highly oscillatory Hamiltonian systems and preservation of period orbits.
He is now a Research Fellow in the Department of Physics at the University of Auckland.

Brett Ryland (PhD 2007) Thesis: Multisymplectic Integration
Brett Ryland hails from the minute hamlet of Maxwell—a placename that perhaps created his destiny to work in numerical PDEs. He was on the New Zealand Mathematical Olympiad team in 1996 and earned a record three degrees from Massey: BSc (Hons) in 2001, MSc in 2002, and PhD in 2007. In his Master's research he studied the dynamical of mechanical systems subjected to nonholonomic constraints on their velocities, such as rolling wheels. Although these conserve energy and are time-reversible, they are not, strictly speaking, conservative. Brett explored various 6-dimensional nonholonomic systems for signs of dissipative behaviour. In his PhD on "Multisymplectic Integration", he studied Runge-Kutta and Partitioned Runge-Kutta methods for Hamiltonian PDEs such as nonlinear wave equations. A crucial result was that the widely-studied Gauss Runge-Kutta method is not, in fact, well-defined in general, but that the Lobatto IIIA-IIIB PRK method can be well-defined, explicit, and stable. In 2008 he joined the University of Bergen, Norway, on a postdoc with Hans Munthe-Kaas. The photo shows Brett and Robert making a few last-minute adjustments to a paper at SciCADE 2007, St Malo.

Anna Mills (PhD, 2006) Thesis: Image Registration Based on the Geodesic Interpolating Spline

Luke Fullard (Summer Research Student 2005)
Luke Fullard got a BSc (Hons) in mathematics in 2007. In the summer of 2005-06 he worked as a summer research scholar on "Smooth Switching Poincare Transformation of the 2-Body Kepler Problem", studying variable time step methods for the Newtonian 2-body problem. While several such methods were already known, he combined their best features to create a simple, unified method that did not require a "smooth switch" and gave errors independent of the orbit's eccentricity. In 2008 he began a PhD at Massey on modelling of hydrothermal eruptions, supported by a scholarship from the New Zealand Institute of Mathematics and its Applications.

Patrick Rynhart (PhD, 2004) Thesis: Mathematical Modelling of Granulation Processes
Patrick completed BSc (Hons) and PhD degrees in Mathematical Physics at Massey University and later worked as a Postdoctoral Fellow in the Applied Mathematics Group of the Institute of Fundamental Sciences. He is now the Team Leader (Information Technology) within the Technical Services Group of the School of Engineering and Advanced Technology.

Seung-Hee Joo (PhD, 2003) Thesis: Contact Systems and Contact Integrators