Georgia Institute of Technology College of Sciences

There have been many recent advances for analyzing the complex deterministic behavior of systems with discontinuous dynamics. With the identification of new types of nonlinear phenomena exploding in this realm, one gets the feeling that almost anything can happen. There are many open questions about noise-driven and noise-sensitive phenomena in the non-smooth context, including the observation that noise can facilitate or select "regular" dynamics, thus clarifying the picture within the seemingly endless sea of possibilities. Familiar concepts from smooth systems such as escapes, resonances, and bifurcations appear in unexpected forms, and we gain intuition from seemingly unrelated canonical models of biophysics, mechanics, finance, and climate dynamics. The appropriate strategy is often not immediately obvious from the area of application or model type, requiring an integration of multiple scales techniques, probabilistic models, and nonlinear methods.