A changing world raises great challenges since we need to take steps that either reduce the rate of global change or that manage resources in the face of global change. Both steps require making predictions, which requires theory. But the systems involved are truly complex, so the theory must use mathematics. Despite the long history of mathematical approaches in ecology and other environmental sciences, understanding the resilience of environmental systems in the face of global change presents substantial mathematical challenges that require novel approaches.
The mathematical issues include understanding very complex dynamical systems on appropriate time scales, with complex or stochastic forcing terms. If explicit control measures are to be designed, then issues in both control and optimal control come to the forefront. Since these are real-world problems, complex statistical issues also are present as well as computational issues. In particular, the computation and solution of partial differential equation systems (or other high dimensional systems) on irregular domains with forcing presents difficult challenges. The workshop topics will highlight both the biological and mathematical issues involved. We envision three related workshops. One workshop on fundamental mathematical issues related to the study of complex systems and two workshops focused more on two broad ranging biological issues in sustainability: rapid evolution and sustainable management of living natural resources.