Random Dynamical Systems

Random events occur in the physical world and throughout our everyday experiences. Taking stochastic effects into account is of central importance for the development of mathematical models of complex phenomena under uncertainty arising in applications. Macroscopic models in the form of differential equations for these systems contain randomness in many ways, such as stochastic forcing, uncertain parameters, random sources or inputs, and random initial and boundary conditions. The theory of random dynamical systems and stochastic differential equations provides fundamental ideas and tools for the modeling, analysis, and prediction of complex phenomena. Solutions to the important dynamical problems increasingly require techniques from several areas of mathematics. The research in these areas is becoming increasingly collaborative, especially crossing disciplines. In fact, rapid progress requires an organized collaborative effort like this workshop. It will serve as a venue for developing communication and establishing collaborative research among research groups.

Theoretical development in nonlinear analysis, dynamics, and stochastic differential equations has been at the forefront of science progress in a vast number of areas. Environmental fluid dynamics, geophysical flows, climate dynamics, electronic and telecommunication systems, networks of neurons, genetics, physiology, and finance are just a few of the important fields being influenced. On the other hand, these areas of science and engineering are sources of interesting mathematical problems. This workshop will focus on nonlinear and stochastic dynamics with applications to models in fluid flow, nonlinear waves, nonlinear optics, telecommunication, and related fields. Much of the analysis employed is based on the dynamical systems approach to stochastic differential equations, which is currently a very fruitful area of research and this will be a significant aspect of the purely mathematical part of the program.