Mathematics Colloquia and Seminars

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In a 2009 Nature Reviews Article, Marten Scheffer and colleagues made bold claims "Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching." I will discuss early work in catastrophe theory and bifurcation theory that provided the mathematical foundations for these claims. I will also describe concrete applications to experimental systems, as well as potential applications in medicine. In particular, wearable devices can provide a rich source of data. The problem is to learn how to interpret this data in real time. Combining machine learning with theoretical and physiological insight has the potential for improving current approaches for the treatment of disorders, such as cardiac arrhythmia and epilepsy, that are characterized by striking changes in dynamics.