Research interests
I am interested in problems at the interface of dynamical systems, network theory, and geometry. In particular, I have been working on higher-order and adaptive networks, where the structure co-evolves with the dynamics. One direction involves fast-slow systems: using geometric singular perturbation theory, one can ask whether fast-slow adaptive networks give rise to genuinely higher-order effective dynamics, even when the underlying system is pairwise. Another direction concerns when adaptive networks on directed hypergraphs admit simplicial or semi-simplicial descriptions, which bears on the question of when homological tools can be justified for such systems.
Invariant Polynomials and Equiaffine Invariant Measures for Certain Two-Surfaces
→ Open thesis Bachelor's thesis — Queen's University BelfastOperators on Hilbert Space
Undergraduate project covering bounded and unbounded operators on Hilbert space, building to the spectral theorem for non-compact self-adjoint operators.
→ Read PDF