The mission of the Institute for Pure and Applied Mathematics (IPAM) is to make connections between a broad spectrum of mathematicians and scientists, to launch new collaborations, to better inform mathematicians and scientists about interdisciplinary problems, and to broaden the range of applications in which mathematics is used. Funding from this proposal will support IPAM's mission through programs that bring together researchers from many different fields for periods ranging from 1 day to 3 months, as well as a activities aimed at education and at increasing diversity in mathematics and science. Almost every program combines mathematics and a field of science or engineering; most programs include both pure and applied mathematics; IPAM has focused on important emerging topics, such as proteomics, internet search engines, compressed sensing, nanosystems, virtual surgery, and document space. In programs where there is an emphasis on pure mathematics, IPAM works to create ties between different groups of researchers working on related problems.
IPAM's research programs enhance the vitality of mathematics by promoting interactions between different fields of mathematics and between mathematics and science; they promote new research collaborations; they help the career development of graduate students, postdocs and junior faculty; and they launch both junior and senior scientists on new research directions. The net effect is to build new scientific communities that can address the complex scientific challenges of our time. IPAM's education and diversity activities increase the flow of students into the scientific workforce and encourage the full participation of women and underrepresented minorities in mathematics and science. This is of tremendous importance for the vitality of mathematics and science in the broader community.
