The mathematical sciences are becoming increasingly collaborative, interdisciplinary, and interactive. The vast increase in both knowledge and methods in the past decades means that the traditional funding strategies of individual investigator awards and large institutes could well be supplemented and leveraged by use of effective ways to promote connections among individual scientists and research groups.

This presents a serious challenge to the National Science Foundation in fulfilling its mission to promote the progress of science, to advance the national health, prosperity, and welfare, and to secure the national defense. Individual awards spread support widely based on merit reviews to judge the best science, while institutes concentrate support for relatively brief periods in a few areas of national importance. Currently missing is a systematic way to support innovative connections among groups of researchers that would complement and amplify the traditional support models.

Imagine a graph of nodes and edges. Consider individual researchers and institutes as nodes, but also include government laboratories, international institutions, start-up companies, and industrial research and development facilities. A program of research networks would fund supporting edges to create networked collaborations. Possible connecting edges could include:

• collaboration or interaction between researchers or groups of researchers
• travel and subsistence of researchers and experts between nodes
• exchange of graduate students
• joint supervision of postdoctoral fellows
• support for focused workshops and conferences
• shared access to facilities, equipment, and instrumentation

• Inclusive: Networks should involve significant numbers of well-qualified researchers who enjoy little or no other NSF support, increase diversity and broaden participation, and provide opportunities for entry into a research area.
• Modular: Nodes and edges can be added or deleted as required to effectively tackle the challenges which the network was formed to address.

• Addressing scientific challenges of lasting and significant importance, both internal to the area and external in impact on other fields of mathematics, science, and technology
• A clear description of the research community and research agenda at the heart of the network
• Involvement of at least three nodes, and a description of their modes of interaction
• A management plan for achieving the inclusive and modular goals mentioned above.

The addition of research networks to the DMS portfolio of research support could create new ways for mathematical scientists across a broad spectrum of organizations to interact, make possible collaborations that current programs cannot support, and provide researchers who merit support (but who, through lack of NSF funds, have not received an individual investigator award) with significant resources. Research networks could form a very cost-effective way for the DMS to further the broad goals of the NSF.

At the NSF-DMS Dialog 2004, held in Washington DC in 2004 with approximately 200 participants, the idea of research networks was specifically proposed during a panel presentation, and discussed during breakout sessions. Many supportive comments were recorded, but there were also some cautionary remarks.

The goal of this workshop is to provide DMS with community input from a wide range of professionals, discuss the pros and cons of research networks, and advise DMS about the desirability of establishing a program of networks. This discussion may also include specific issues encountered in formulating a solicitation from DMS and evaluation criteria. The outcome of the workshop will be a report from the workshop organizers to the DMS describing the discussions and giving guidance and advice based on these discussions.