Colloquium

The life sciences are pushing the boundaries of stochastic processes theory. In this talk, I will illustrate this point through three diverse problems. The first problem comes from pharmacology. What should you do if you accidentally miss a dose of medication? Skip the dose? Double your next dose? I will formulate a mathematical model to answer this question and show that it requires generalizing an exotic random variable studied by Erdos and others in the 1930s. The results of this analysis challenge current medical recommendations on this question. Second, in a very different biological and mathematical problem, I will show how a longstanding question about insect respiration leads to a new class of stochastic PDEs that provides significant physiological insight. Finally, in another disparate problem, I will address a question from human fertilization. Why do 300 million sperm cells search for the egg when only a single sperm cell is necessary? I will show how the apparent redundancy in this and other systems in cell biology can be understood in terms of recent results in extreme statistics that modify traditional timescale calculations.