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

微分方程是我们在日常生活中经历的几乎每一种物理现象的数学模型。我的研究项目包括研究这些类型的方程，揭示其解的基本性质，从而提供对正在建模的物理现象的洞察。我对控制电波传播的微分方程式模型感兴趣，电波使人的心脏收缩并泵血，或通过神经系统传输信号。我在这个领域的研究项目包括从数学上研究缺陷(例如病变组织)对这些波传播的影响。例如，在心脏中，这些缺陷的影响可能会导致严重的情况，如心动过速和室颤(通过折返波)，这可能会导致死亡。

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.