Hidden time scales and stochastic dynamics.

Abstract: Applied problems viewed through mathematical models often pose new questions that require a combination of mathematical perspectives. This talk will cover a few applications in stochastic dynamics where dramatic noise-sensitive effects result from hidden features in the models. These examples illustrate what might be missed by using any one "classical" approach to understand the phenomena. New combined approaches reveal the hidden features behind the noise-sensitivity and suggest reduced problems which are more manageable than the original model for understanding the dynamics. Models for epidemics, chatter, and waves will be discussed, with some illustration about generalizations to other applications.