This program is broadly concerned with fundamental challenges of modeling, analysis and computation for (mostly) incompressible fluid dynamics. Much attention will be focused on non-Newtonian fluids in which complex material constitutions produce nonlinear and/or nonlocal relationships between stresses and rates-of-strain (and sometimes strains) leading to unique and often unforeseen flow phenomena. Complex fluids are ubiquitous in engineering applications and the applied sciences from biology to geology. They serve as the focus of active areas of research within the larger fluid dynamics community.

Complex flows include those of both simple and complex fluids in simple and complex domains, in the presence of moving boundaries, and turbulent flows. Key questions for such flows include transport and mixing properties, and flow-structure interactions generating motions including swimming, flying, sliding and crawling. Recent research has revealed new connections between fluid characteristics, flow complexity and transport properties that will in part serve as a unifying theme throughout the program.

The year will be organized around specific themes highlighted by six week-long workshops encompassing the following topics:

1. Rheology of complex fluids
2. Dynamics of complex fluids
3. Microfluidics and electrokinetic and interfacial phenomena
4. Analysis and computation of simple and complex fluids
5. Transport and mixing in complex and turbulent flows
6. Fluid-structure interactions and locomotion

The mathematical scope of this program will be very broad, ranging from fundamental modeling questions through issues of computation, simulation, approximation and analysis. Program participants will include researchers from the engineering and applied sciences, including both theorists and experimentalists, numerical analysis and scientific computation, and both applied and abstract analysts. A central goal of the program will be to bring these interdisciplinary perspectives together and facilitate productive engagement. Toward this end, each focused week-long workshop will be preceded by introductory tutorials aimed at researchers from neighboring areas.