PhD Opportunity – Applied Mathematics

Two mathematics PhD scholarships in the School of Mathematical and Computational Sciences at Massey University, Palmerston North, New Zealand. The PhD research aims to advance the mathematical theory of dynamical systems and apply the results to mathematical models of neural networks and climate. Mathematical models of systems that switch between different types of evolution suffer a curse of dimensionality. The PhD research will be part of a Marsden funded project to develop new strategies for resolving this issue by exploiting degeneracies in high-dimensional models. The scholarships are funded by the Royal Society of New Zealand Te Apārangi as part of project 25-MAU-044 led by Associate Professor David Simpson. Students will work with difference equations and ordinary differential equations, developing new theoretical results when discontinuities are present through asymptotic methods supported by numerical simulations. The results will be applied to box models of ocean circulation and/or to the internal dynamics of deep neural networks central to modern artificial intelligence.