David Simpson

This PhD opportunity at Massey University focuses on piecewise-smooth dynamical systems, particularly those that switch between different types of evolution and suffer from the curse of dimensionality. The project is part of a Marsden funded initiative aiming to develop innovative strategies for dimensionality reduction by leveraging degeneracies commonly found in high-dimensional models. These degeneracies, arising from energy conservation, optimisation, and physical constraints, often remain hidden until the model is viewed abstractly. The research seeks to exploit these features to enable thorough analysis and reduction of complex systems. Successful candidates will work with difference equations and ordinary differential equations, developing new theoretical results for systems with discontinuities using asymptotic methods and numerical simulations. Applications of the research include box models of ocean circulation and the internal dynamics of deep neural networks, which are central to modern artificial intelligence. The position is based in the School of Mathematical and Computational Sciences at Massey University, under the supervision of Associate Professor David Simpson. Two Marsden scholarships are available, each covering all tuition fees for both international and domestic students and providing a tax-free stipend of NZ$35,000 per year for up to three years. The funding is provided by the Royal Society of New Zealand (Marsden grant 25-MAU-044). Applicants should have a strong academic background in mathematics or a related discipline, with experience in difference equations, ordinary differential equations, asymptotic methods, and numerical simulations being advantageous. To apply, candidates should email their CV, academic transcript, and cover letter to Associate Professor David Simpson. Applications are accepted year round. For further information and to apply, visit the project page: Piecewise-smooth dynamical systems PhD project .