2008-2009 Program

This program is broadly related to computational chemistry which has reached a stage of development where many chemical properties of both simple and complex systems may now be computed more accurately, more economically, or more speedily than they can be measured. Further advances in accuracy and practicality will depend on the development of both new theory and new algorithms, and mathematical techniques will play an important role in both of these areas. The advances in chemical theory and computations have built on interfaces with a number of areas of mathematics, including differential equations, linear and nonlinear algebra, optimization theory, probability theory, stochastic analysis, sampling theory, complex analysis, geometry, group theory, and numerical analysis. Further progress in computational chemistry will require that the ties between chemistry and mathematics be strengthened. This IMA program will provide a setting for the chemistry and mathematics communities to examine some of these problems together. The year will focus on issues in electronic structure, dynamics, and statistical mechanics, including both the mathematical underpinnings of modern molecular modeling and simulation and practical issues in state-of-the-art applications. Applications areas will include organic and inorganic chemistry, biochemistry, solid-state chemistry, nanochemistry, advanced materials, photochemistry, catalysis, and environmental chemistry. Emphasis will be placed on mingling applied mathematicians with theoretical and computational chemists in each workshop. Limited financial support is available for the workshops. Detailed information about this program can be found at "Mathematics and Chemistry."

2009-2010 Program

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 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.

Opportunities for the participation in the 2009-2010 program include New Directions research professorships for established mathematicians seeking to branch into new interdisciplinary research directions, regular and industrial postdoctoral fellowships (application deadline is January 4, 2009), and general memberships (visits of a month or more, no application deadline).

The IMA actively solicits proposals for programs from members of the mathematical sciences community. Possibilities include annual programs (running September-June), summer programs (typically running two to four weeks and involving between 60-120 participants), and Hot Topics workshops (typically lasting a few days and treating a topic of exceptional contemporary interest and potential impact). Submission timelines: Preproposal for annual programs, at least four years in advance of the proposed start date; summer program proposals, roughly two to three years in advance; Hot Topics workshop proposals, a year in advance, cosponsorship by an industrial partner or institute is preferred. Additional information is available at " solicit."

Detailed information about IMA programs, as well as the online application forms for IMA workshops and memberships, can be found at " IMA."