Timothy Roberts

My research interests lie in applying geometric ideas to dynamical systems problems. My past work has centered on two main themes: classical ODES, where I used geometric singular perturbation theory to analyze a model a thermoregulation in the brain; and linear spectral theory of traveling fronts and pulses, where I helped develop a new numerical scheme for detecting the stability of fronts and pulses (in one spatial dimension) using geometric ideas (the Riccati transformation).

My current work focusses on using rigorous, geometric techniques to understand pattern formation in different physical and biological applications. My PhD work centered on building a rigorous mathematical framework for the existence and bifurcation analysis of spatiotemporal patterns in reaction-diffusion equations. In that work, I have proved that defect solutions undergo a process called homoclinic snaking, and have been able to make strong qualitative predictions about the nature of their bifurcation diagrams. I have also been working on proving the existence of radially symmetric structures in nonlocal models of amphiphilic copolymers which have industrial and biomedical applications.

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