# PhD projects

### University of Auckland Marsden Grant Scholarship in Applied Mathematics

Two PhD positions are available from 1 October 2018 on the Marsden grant *Understanding the geometry of dynamics: invariant manifolds and their interactions*. Interested candidates are encouraged to apply.

The scholarship provides student fees and support for a PhD student to investigate the geometry of dynamical systems, which will be supervised by Professors Bernd Krauskopf and Hinke Osinga. Specifically, the goal is to explain novel kinds of chaotic dynamics and intricate oscillatory patterns formed by a mix of large and small amplitudes. Such dynamics are found, for example, in cell models, pulsating lasers, chemical reactions, and bursting neurons. The emphasis is on generic phenomena that capture the essence of the dynamical behaviour. The student will consider representative model systems and investigate how the phase space is organised by smooth surfaces known as invariant manifolds: their interactions are the key to understanding the overall behaviour in this context.

Students from all nationalities with a suitable higher degree in Mathematics or Applied Mathematics are eligible for these PhD positions. We are particularly interested in students with demonstrable skills in some of the following:

- dynamical systems theory;
- numerical analysis with emphasis on bifurcation theory and path following;
- differential geometry;
- topology;
- computer graphics and visualisation;
- programming in Fortran or C-related language (Python);

Informal inquiries are welcome by email.

**Contact:** Professor Hinke Osinga:
(H.M.Osinga@auckland.ac.nz)

Hinke Osinga

Last modified: Sat May 12 16:25:16 NZST 2018