PhD Opportunity – Applied Mathematics

Mathematical models of systems that switch between different types of evolution suffer a curse of dimensionality. Their dynamical behaviour cannot be faithfully reproduced with fewer equations. Researchers currently persist with low-dimensional models, or suffice with numerical computations and observations. The PhD research will be part of a Marsden funded project to develop new strategies for resolving this issue by exploiting the poorly recognised but common occurrence of degeneracies in high-dimensional models. The degeneracies arise for diverse reasons, including energy conservation, optimisation, and physical constraints, and are often obscured until the model is viewed abstractly. The over-arching idea is that the degeneracies provide a novel and over-looked avenue by which dimensionality can be reduced and the models can be analysed thoroughly.

The scholarships will be funded by the Royal Society of New Zealand Te Apārangi as part of project 25-MAU-044 led by Assoc. Prof. David Simpson who will be the primary PhD supervisor. The students will work with difference equations and ordinary differential equations. They will develop new theoretical results when discontinuities are present in the equations through asymptotic methods supported by numerical simulations. The students will apply the results to box models of ocean circulation and/or to the internal dynamics of deep neural networks central to the functioning of modern artificial intelligence.

Who we're looking for

Application checklist

Include the following with your application:

• your CV
• a copy of your complete academic transcripts
• a cover letter introducing yourself and your interest in applying