Bifurcations: traveling waves in reaction-diffusion systems, and realizability for delay differential equations

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Differential equations are mathematical models for almost every physical phenomenon we experience in everyday life. My research program involves studying these types of equations, uncovering basic properties about their solutions, and thus providing insight into the physical phenomenon which is being modelled. I am interested in differential equation models governing the propagation of electrical waves which make the human heart contract and pump blood, or transmit signals through the nervous system. My research projects in this area involve studying mathematically the effects of imperfections (e.g. diseased tissue) on the propagation of these waves. For example, in the heart, the effects of these imperfections can lead to serious conditions such as tachycardia and ventricular fibrillation (via re-entrant waves) which can cause death.