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Programs: Division of Mathematical Sciences

The Division of Mathematical Sciences (DMS) supports a wide range of projects aimed at developing and exploring the properties and applications of mathematical structures. Most of these grants are awarded by the disciplinary programs to single investigators or to small groups of investigators working with graduate students and postdoctoral researchers. The Division additionally provides support for activities that differ from the research projects supported by the disciplinary programs, through special programs such as Mathematical Sciences Infrastructure.

Interdisciplinary Research

A number of areas in science and engineering have problems of great mathematical and statistical complexity or obscurity that are creating a demand for mathematical and statistical cooperation. Progress in these areas depends on close collaboration of mathematical scientists with scientists and engineers. At the same time, the problems posed often stimulate interesting, new, and deep mathematical and statistical questions that deserve attention. DMS hopes to foster interactions that require the participants to go well beyond their respective areas of expertise, to nurture young talent in the interdisciplinary mode of research, and to involve underrepresented groups whenever possible.

In the area of biosciences and biocomplexity, striking advances in biology, computer science, and the mathematical sciences are creating opportunities to collaborate on research work in fields such as molecular biology, neuroscience, and ecosystems, and offer challenging computational and analytical problems. Biological sciences interaction may extend significantly into the core areas of mathematics, such as topology, operator algebra, probability, and nonlinear dynamical systems, as well as the more traditional areas of applied mathematics and statistics.

Other opportunities include research in the areas of high-performance computing and communications; research in information technology; mathematical and statistical aspects of materials behavior and theoretical continuum mechanics; geosciences; advanced manufacturing technologies; mathematical sciences related to biotechnology; and mathematical, statistical, and computational aspects of global change research. Research in the area of materials includes interaction of thermal and mechanical effects; nanoscale science, phase transition, and formation of microstructures and crystals; foundations of nonlinear elasticity and electromagnetic materials; composite materials; and related mathematical questions such as control, optimization, and studies of differential equations arising in these contexts. Research opportunities in advanced manufacturing particularly emphasize simulation, modeling, and analysis of manufacturing processes and devices; applications for manufacturing of deterministic and stochastic quality control; and optimization. Mathematical science research related to biocomplexity, bioprocessing and bioconversion, bioelectronics and bionetworks, agricultural applications, and marine biotechnology is especially encouraged.

Environmental research supports the critical development of modeling, analysis, simulation, and prediction in the context of the total Earth system. A particular emphasis is placed on analytical and computational methods for stochastic and deterministic partial differential equations and statistical techniques that encompass the full range of temporal and spatial scales. There also are opportunities in environmental technology, including pollution prevention, monitoring, and remediation. Researchers should be aware of the implications of their efforts toward such activities.

For More Information
Write to the Division of Mathematical Sciences, National Science Foundation, 4201 Wilson Boulevard, Room 1025, Arlington, VA 22230; or contact the division by telephone, 703-292-8870; or visit the DMS home page,

Disciplinary Programs

Algebra, Number Theory, and Combinatorics

Supports research in algebra, including algebraic structures, general algebra, and linear algebra; number theory, including algebraic, analytic number theory, arithmetic geometry, quadratic forms, and automorphic forms; combinatorics, including graph theory; and algebraic geometry.

Target Date: First Tuesday in October annually.

Contact Information:

Tomek Bartoszynski
Phone: 703-292-4885
  Commutative Algebra, Group Theory
Donald James
Phone: 703-292-4877
  Number Theory
Tie Luo
Phone: 703-292-8448
  Algebraic Geometry
Kathleen O'Hara
Phone: 703-292-8491
Alvin Thaler
Phone: 703-292-8039
  Ring Theory, Vertex Algebras, Representation Theory, and other algebra


The Analysis Program supports basic research in that area of mathematics whose roots can be traced to the calculus of Newton and Leibniz. Given its centuries-old ties to physics, analysis has influenced developments from Newton’s mechanics to quantum mechanics and from Fourier’s study of heat conduction to Maxwell’s equations of electromagnetism to Witten’s theory of supersymmetry. More generally, research supported by Analysis provides the theoretical underpinning for the majority of applications of the mathematical sciences to other scientific disciplines. Current areas of significant activity include: nonlinear partial differential equations; dynamical systems and ergodic theory; real, complex and harmonic analysis; operator theory and algebras of operators on Hilbert space; mathematical physics; and representation theory of Lie groups/algebras. Emerging areas include random matrix theory and its ties to classical analysis, number theory, quantum mechanics, and coding theory; and development of noncommutative geometry with its applications to modeling physical phenomena. It should be stressed, however, that the underlying role of the Analysis Program is to provide support for research in mathematics at the most fundamental level. Although this is often done with the expectation that the research will generate a payoff in applications at some point down the road, the principal mission of the Program is to tend and replenish an important reservoir of mathematical knowledge, maintaining it as a dependable resource to be drawn upon by engineers, life and physical scientists, and other mathematical scientists, as need arises.

Target Date: First Tuesday in October annually.

Contact Information:

John Conway
Phone: 703-292-4872
Joe Jenkins
Phone: 703-292-4870
Wing Suet Li
Phone: 703-292-8104

Applied Mathematics

Supports mathematics research motivated by or having an effect on problems arising in science and engineering. Mathematical merit and novelty, as well as breadth and quality of impact on applications, are important factors. Proposals to develop critical mathematical techniques from individual investigators as well as interdisciplinary teams are encouraged.

Target Dates:
The target date for proposals submitted to the Applied Mathematics program is the first Tuesday in November each year. Unless otherwise stated in announcements or solicitations, proposals received shortly after these target dates will be reviewed if possible. (See below for the Mathematical Biology deadline date window.)

Contact Information:

For questions concerning: Contact:
The Applied Mathematics Program in general Henry Warchall
Mathematical Geosciences Thomas Russell
Mathematics of Materials and Mechanics Michael Steuerwalt
Mathematics of Fluid Dynamics Thomas Russell
Applied Partial Differential Equations Ken Shaw
Mathematical Physics Henry Warchall
Applied Dynamical Systems Michael Steuerwalt
Mathematical Control Theory Mary Ann Horn
Mathematical Optimization Thomas Russell
Mathematical Finance Mary Ann Horn

Mary Ann Horn
Phone: 703-292-4879
  Thomas Russell
Phone: 703-292-4863
Ken Shaw
Phone: 703-292-4859
  Michael Steuerwalt
Phone: 703-292-4860
Henry Warchall
Phone: 703-292-4861

Computational Mathematics

Supports mathematical research in algorithms and numerical and symbolic methods, and research in all areas of the mathematical sciences in which computation plays a central and essential role. The prominence of computation in the research is a key distinction between the Applied Mathematics and Computational Mathematics programs.

Target Date: First week of December each year.

Contact Information:

Leland Jameson
Phone: 703-292-4883
Thomas Russell
Phone: 703-292-4863
Junping Wang
Phone: 703-292-4488

Geometric Analysis, Topology, and Foundations

Geometric Analysis

Supports research on differential geometry and its relation to partial differential equation and variational principles; aspects of global analysis including the differential geometry of complex manifolds and geometric Lie group theory; geometric methods in modern mathematical physics; and geometry of convex sets, integral geometry, discrete and combinatorial geometry, and related geometric topics.

Target Date: First Tuesday in November annually.


Supports research on algebraic topology, including homotopy theory, ordinary and extraordinary homology and cohomology, cobordism theory, and K-theory; topological manifolds and cell complexes, fiberings, knots, and links; differential topology and actions of groups of transformations; geometric group theory; and general topology and continua theory.

Target Date: First Tuesday in November annually.


Supports research in mathematical logic and the foundations of mathematics, including proof theory, recursion theory, model theory, set theory, and infinitary combinatorics.

Target Date: First Tuesday in October annually.

Contact Information:

Tomek Bartoszynski
Phone: 703-292-4885
Joanna Kania-Bartoszynska
Phone: 703-292-4881
Benjamin Mann
(on detail)
Phone: 703-292-4867
Stewart Priddy
Phone: 703-292-4878
Christopher Stark
Phone: 703-292-4869

Mathematical Biology

Supports research in areas of mathematics with relevance to the biological sciences, except statistics and probability. For research in statistics and probablility see the respective program descriptions. The Mathematical Biology program interacts with every division in the NSF Directorate of Biological Sciences, and its interests overlap those of the biology programs. Mathematical Biology regularly seeks joint reviews of proposals with biology programs.

In order to ensure both the timely handling of proposals and fairness in comparing competing requests for funding, the DMS Mathematical Biology program has established a Proposal Submission Window. The window for Fiscal Year 2005 and following years extends annually from 18 December (8:00 AM local time) to 13 January (5:00 PM local time). Except for conference and workshop proposals, which should be submitted about eight months before the requested starting date, only proposals submitted during this period will be considered for review.

Deadline Date Window: Proposals must be submitted between 18 December and 13 January.

Contact Information:

Mary Ann Horn
Phone: 703-292-4879

Statistics and Probability


Supports research on the theory and applications of probability. Subfields include discrete probability, stochastic processes, limit theory, interacting particle systems, stochastic differential and partial differential equations, and Markov processes. Research in probability that involves applications to other areas of science and engineering is especially encouraged.

Target Date: First Tuesday in November annually.

Contact Information:

Keith Crank (on detail)
Phone: 703-292-4880
Wen Masters
Phone: 703-292-4871
Robert Serfling
Phone: 703-292-4884


Supports research for developing and improving statistical theory and methods, including research in statistical methods that involve applications to any area of science and engineering. These methods are used for the collection, exploration, analysis, and interpretation of data, to enable discovery and advancement in such diverse areas as bioinformatics, biology, geosciences, astronomy, ecology, and social science. Supported areas include frequentist and Bayesian inference in parametric, semi-parametric, and nonparametric methods, time series analysis, robust methods, experimental design, spatial statistics, resampling methods, and the analysis of massive data sets.

Target Date: First Tuesday in November annually.

Contact Information:

Shulamith Gross
Phone: 703-292-4868
Xuming He
Phone: 703-292-4876
Robert Serfling
Phone: 703-292-4884

Special DMS Programs

Infrastructure Program

Provides support for activities that differ from the research projects supported by the disciplinary programs of the Division of Mathematical Sciences. These include working research sessions, such as conferences, symposia, colloquia, and special years, as well as training programs, such as grants for broadening education in the mathematical sciences or increasing the number of individuals in disciplines that are based in the mathematical sciences.

Contact Information:

John Conway
Phone: 703-292-4872
Lloyd Douglas
Phone: 703-292-4862
  Infrastructure; MCTP; MSPRF; IGMS; REU sites; MRPG; MCAA; CBMS Regional Conferences; University-Industry Cooperative Research Program
Thomas Russell
Phone: 703-292-4863
Henry Warchall
Phone: 703-292-4861

Mathematical Sciences Priority Area (MSPA)

The goal of the Mathematical Sciences Priority Area (MSPA) is to advance frontiers in three interlinked areas:

  1. fundamental mathematical and statistical sciences,
  2. interdisciplinary research involving the mathematical and statistical sciences with science and engineering, and
  3. critical investments in mathematical and statistical sciences that embed training in research activities.
Investments in the Mathematical Sciences will deepen support for fundamental research in mathematics and statistics and the integration of mathematical and statistical research across the full range of science and engineering disciplines. Initial investments in interdisciplinary research will focus primarily on three scientific themes:
  • mathematical and statistical challenges posed by large data sets,
  • managing and modeling uncertainty, and
  • modeling complex nonlinear systems.
These themes provide the basis for most of the interdisciplinary competitions that are part of the MSPA. Innovative educational activities that foster closer connections between research and education in the mathematical sciences will also be supported.

This solicitation describes many of the opportunities available as part of the MSPA for addressing some of the issues listed above. In FY2004, a set of focused competitions will be held; these are described or referenced in this solicitation. In future years, it is expected that some of these competitions will be broadened in scope.

  1. New activities with specific deadline dates include:
    • New Mathematical and Statistical Tools for Understanding Complex Systems in the Environment (MSPA-CSE)
    • Interactions Between the Mathematical Sciences and Computer Science (MSPA-MCS)
  2. Activities covered by existing target dates or deadlines previously announced for FY 2004 include the following. Proposals already submitted that meet the guidelines for these activities may be considered for funding:
    • Interactions Between the Mathematical Sciences and Engineering
    • Interactions Between the Mathematical Sciences and the Physical Sciences
  3. Existing activities, covered by separate solicitations and summarized in this document for information purposes, include the following:
    • Collaborations in the Mathematical Geosciences (CMG)
    • Joint DMS/BIO/NIGMS Initiative to Support Research in the Area of Mathematical Biology (DMS-NIGMS)
    • Focused Research Groups in the Mathematical Sciences (FRG)
    • Enhancing the Mathematical Sciences Workforce in the 21st Century (EMSW21)
    The existing activities are fully described in separate solicitations.
  4. Over the next few months, it is expected that competitions involving
    • undergraduate research activities on the interface between the mathematical sciences and biology and
    • interactions between the mathematical sciences and the social, behavioral, and economic sciences
    will be announced. Preliminary information about the first is provided in this document.

MSPA Program Solicitation

Approaches to Combat Terrorism

The solicitation for Approaches to Combat Terrorism (ACT) calls for proposals for Small Grants for Exploratory Research (SGER) with the potential to contribute to national security. Each of the five Divisions in the NSF Mathematical and Physical Sciences (MPS) Directorate has identified basic research opportunities. Interdisciplinary efforts are particularly encouraged, including those involving participants whose area of expertise lies outside the MPS disciplines. Such efforts must be led by a Principal Investigator from an MPS discipline and technically centered in areas supported by the MPS Directorate.

A number of possible research areas in the Mathematical Sciences are presented below. The examples provided are only meant to be illustrative and not exhaustive. Unanticipated approaches to enhancing national security are especially valuable.

Important areas of opportunity are analysis and information synthesis from multimodal large datasets such as text and speech, often in multiple languages, and imagery, including video. Key issues in every area are mathematical techniques to represent, manipulate, and analyze data, and effective models, algorithms, and implementations. Analysis and information synthesis involves problems of uncertainty, data fusion, feature extraction, data synopsis and metadata, partial disclosure, and high dimensionality. Other problems include feature detection, landmarks and registration and characterization of natural images. Data presentation is a critical issue, especially of metadata and in processes that require human mediation. Other important areas include new mathematical approaches to materials, processes, and devices such as fuel cells, miniature mass spectrometers, and other sensors; optimization problems such as the choice of placement and components in sensor arrays; mathematical epidemiology; and multiscale models of complicated diffusion and transport processes.

Especially important for Intelligence Community (IC) applications are new mathematical techniques in knowledge discovery in such areas as social network analyses traditionally done on contact graphs of transactional data (business transactions, communications between individuals, etc.) with the content contained in the transactions. A second area of particular interest is the identification (postulation) of missing data given a hypothesis or identification of data that would change an analytic conclusion. Pattern recognition algorithms that are robust to missing data, erroneous data and ambiguity are of considerable interest. Finally, incorporation of both temporal and geospatial information within text, speech and imagery pattern recognition and data mining algorithms are important in analyzing data that is widely distributed in both space and time.

An additional area of interest in imagery is the study of the effects of steganographic techniques (e.g., watermarking and fingerprinting) on image quality and on the efficiency of image retrieval, including retrieval of derived images. Both still and video imagery are of interest. In image analysis, the IC has particular interest in research that ultimately supports computational techniques that improve the speed and reliability with which images can be automatically analyzed.

ACT Program Solicitation

Focused Research Groups

The mathematical sciences thrive on sharing ideas and information from various scientific fields and disciplines. Certain research needs can only be met appropriately through the use of investigative teams. The Focused Research Groups (FRG) Program supports these teams, thereby allowing groups of researchers to respond to the scientific needs of pressing importance; take advantage of current scientific opportunities; and prepare the ground for anticipated developments in the mathematical sciences. In addition to mathematical scientists, groups may include researchers from other scientific and engineering disciplines. FRG projects are highly focused scientifically, timely, limited to 3 years' duration, and substantial in both scope and impact. Projects supported through FRG are essentially collaborative in nature, their success dependent on the interaction of a group of researchers.

FRG Award Lists
FRG Program Solicitation

Collaborations in Mathematical Geosciences

The purposes of the Collaborations in Mathematical Geosciences (CMG) activity are to enable collaborative research at the intersection of mathematical sciences and geosciences, and to encourage cross-disciplinary education through summer graduate training activities. Research projects supported under this activity are essentially collaborative in nature and include at least one mathematical scientist and at least one geoscientist.

CMG Program Solicitation

Joint DMS/BIO/NIGMS Initiative to Support Research in the Area of Mathematical Biology

Revolutionary opportunities have emerged for mathematically driven advances in biological research. These opportunities are recognized by the National Institute of General Medical Sciences (NIGMS), as well as by the National Science Foundation (NSF). Expertise of the NSF in the mathematical and biological sciences, along with its ties to both research communities, and the expertise of the NIH in biological and biomedical research make this an area where cooperation between the two agencies is appropriate.

This competition is designed to support research on mathematical problems related to biological problems in areas supported by NSF and NIGMS. A direct relationship between a biological application and the mathematics is expected. Research teams, which include scientists from both the life sciences community and the mathematical sciences community, are encouraged. Both new and existing collaborations will be supported. Proposals from individual investigators will need to make the case that the individual has expertise in both areas.

Successful proposals will identify innovative mathematics or statistics needed to solve an important biological problem. Research which would apply standard mathematics or statistics to solve biological problems is not appropriate for this competition and should be submitted directly to NIH or the Directorate for Biological Sciences. Similarly, research in mathematics or statistics that is not tied to a specific biological problem should be submitted to the appropriate DMS program at NSF. Proposals designed to create new software tools based on existing models and methods will not be accepted in this competition.

Program Solicitation for the DMS/BIO/NIGMS Mathematical Biology Initiative

New Mathematical and Statistical Tools for Understanding Complex Systems in the Environment (MSPA-CSE)

This competition is aimed at developing the mathematical and statistical tools and approaches essential for the creative advancement of research in the science of complex systems. Proposals should address questions involving the fundamentals of complex systems at the interface between the mathematical sciences and the sciences related to the biotic and abiotic environment. We seek proposals that offer new mathematical and statistical approaches to the study of complex systems that are characteristic of those encountered in environmental science areas. Of particular interest are proposals that offer the possibility of new insights into the dynamical consequences of nonlinearity and high dimensionality. The most competitive proposals are likely to involve an investigator or teams of investigators with strengths in both the mathematical sciences and the applications areas.

The Program Solicitation for the MSPA-CSE activity is in Section I.1.(a) of the
Mathematical Sciences Priority Area (MSPA) program solicitation.

Interactions between the Mathematical Sciences and Computer Science (MSPA-MCS)

The NSF Divisions of Mathematical Sciences (DMS) and of Computing and Communication Foundations (CCF) plan to support research and development teams focusing on mathematical and computational innovations relevant to the following areas of specific interest:

  • Algebraic and Geometric Algorithms
  • Algorithms for Scalable Scientific Computation
  • Algorithms for Visualization
  • Statistical Learning Algorithms

As this joint funding will focus on areas of mutual interest, proposals must originate from teams involving collaborations of mathematical scientists and computer scientists. We seek proposals that offer new approaches and promise significant breakthroughs in these areas. Proposals submitted to this competition must state why the submission meets the eligibility standards of new approaches, promise of significant breakthroughs, and substantial intellectual differences from on-going work.

The Program Solicitation for the MSPA-MCS activity is in Section I.1.(b) of the
Mathematical Sciences Priority Area (MSPA) program solicitation.

Mathematical Social and Behavioral Sciences (MSBS)

This solicitation invites submission of research proposals for projects that advance the mathematical or statistical foundations of research in the social, behavioral, or economic sciences. The resulting research is expected both to further understanding of social and/or behavioral science phenomena and to address a topic of interest to the mathematical sciences. Proposals for workshops or symposia that foster the interaction of social, behavioral, and/or economic scientists with mathematicians and/or statisticians also are welcome.

MSBS Program Solicitation

NSF-Wide Research Programs

Nanoscale Science and Engineering

The goal of the Nanoscale Science and Engineering (NSE) program is to support fundamental research and catalyze synergistic science and engineering research and education in emerging areas of nanoscale science and technology, including: biosystems at the nanoscale; nanoscale structures, novel phenomena, and quantum control; nanoscale devices and system architecture; nanoscale processes in the environment; multi-scale, multi-phenomena theory, modeling and simulation at the nanoscale; manufacturing processes at the nanoscale; and studies on the societal and educational implications of scientific and technological advances on the nanoscale.

NSE Program Solicitation and Other Information

Information Technology Research

Advances in Information Technology (IT) have dramatically transformed the way in which people live, work, learn, communicate and conduct business. To insure that these transformations serve human needs, are productive for society, and sustainable over the long term, the National Science Foundation instituted the Information Technology Research (ITR) program as one of its priority areas. This program encourages innovative, high-payoff IT research and education. Fiscal year 2004 (ITR) is the fifth and last year that ITR will be an NSF priority area.

The ITR program has been enormously successful in opening up opportunities at the frontiers of IT research and education. In its first year, Fiscal Year (FY) 2000, the ITR program stressed fundamental research in IT. In the second year, FY 2001, the program was considerably broadened to include applications of IT in all scientific, engineering and educational areas. In the third year, FY 2002, the program expanded research in areas of interdisciplinary science, focusing on research at the interstices of information technology and other disciplines. In its fourth year, FY 2003, the program stimulated research on the fundamental challenges facing the continued expansion and utilization of IT across the sciences and engineering, the creation of novel uses of IT, the interaction of IT with society at large, and the use of IT to enhance security and reduce society’s vulnerabilities to catastrophic events, whether natural or man-made. In FY 2004, the focus is “ITR for National Priorities.” Particular emphasis will be placed on the distributed systems, grids and infrastructures that support the attainment of these national priorities.

ITR Program Solicitation and Other Information

Biocomplexity in the Environment

The Biocomplexity in the Environment (BE) Priority Area promotes comprehensive, integrated investigations of environmental systems using advanced scientific and engineering methods. The concept of biocomplexity stresses the richness of biological systems and their capacity for adaptation and self-organizing behavior. By placing biocomplexity studies in an environmental context, this competition emphasizes research with the following characteristics: (a) a high degree of interdisciplinarity; (b) a focus on complex environmental systems that includes non-human biota or humans; and (c) a focus on systems with high potential for exhibiting non-linear behavior. In FY 2004 and FY 2005, five topical areas are emphasized: 1. Dynamics of Coupled Natural and Human Systems (CNH); 2. Coupled Biogeochemical Cycles (CBC); 3. Genome-Enabled Environmental Science and Engineering (GEN-EN); 4. Instrumentation Development for Environmental Activities (IDEA); 5. Materials Use: Science, Engineering, & Society (MUSES).

In all areas, quantitative modeling, simulation, analysis, and visualization methods are emphasized, as well as integration of education and a global perspective. Individuals or small groups may submit proposals to conduct research projects or exploratory and planning activities. This comprehensive approach to research on biocomplexity in the environment is expected to improve science-based predictive capabilities for decision-making.

BE Program Solicitation and Other Information

Grant Opportunities for Academic Liaison with Industry

The Grant Opportunities for Academic Liaison with Industry (GOALI) initiative aims to synergize university-industry partnerships by making funds available to support an eclectic mix of industry-university linkages. Special interest is focused on affording the opportunity for: (1) faculty, postdoctoral fellows and students to conduct research and gain experience with production processes in an industrial setting, (2) industrial scientists and engineers to bring industry's perspective and integrative skills to academe, and (3) interdisciplinary university-industry teams to conduct long-term projects. This initiative targets high-risk/high-gain research with a focus on fundamental topics that would not have been undertaken by industry, new approaches to solving generic problems, development of innovative collaborative industry-university educational programs, and direct transfer of new knowledge between academe and industry.

To meet this objective, the GOALI program provides funding, for example, for faculty, postdoctoral fellows, and students to develop creative modes of collaborative interactions with industry through individual or small-group projects, and industry-based fellowships for graduate students and post-doctoral fellows.

GOALI Program Solicitation and Other Information

Human and Social Dynamics

This competition expands NSF support of the Human and Social Dynamics Priority Area, building on the FY 2003 HSD Special Competition. The HSD priority area promotes a comprehensive multi-disciplinary approach to understanding human and social dynamics that will significantly advance the scientific understanding of human action and development at the micro level, and of human adaptation and change at the organizational and societal levels. Six areas of emphasis are highlighted. Three topical areas of substantive concern are: agents of change, the dynamics of human behavior, and decision-making and risk. Three resource related areas designed to expand the nation's scientific capacity to understand the complexities of human behavior are: spatial social science, modeling, and infrastructure development. The HSD priority area will extend for five years. The FY 2004 Competition requires mandatory letters of intent.

HSD Program Solicitation and Other Information

Small Business Innovation Research

The Small Business Innovation Research and Small Business Technology Transfer Programs (SBIR/STTR) Programs stimulate technological innovation in the private sector, by strengthening the role of small business concerns in meeting Federal research and development needs, increasing the commercial application of federally supported research results, and fostering and encouraging participation by socially and economically disadvantaged persons and women-owned small businesses.

SBIR/STTR Program Solicitation

Career Development Programs

University-Industry Cooperative Research Programs in the Mathematical Sciences

The University-Industry Cooperative Research Programs in the Mathematical Sciences provide opportunities for mathematical scientists to conduct research and training in an industrial environment and for industrial scientists to return periodically to academia. To facilitate such research and training, these programs include postdoctoral research fellowships, senior research fellowships, graduate research assistantships, and graduate cooperative fellowships.

Program Solicitation

Interdisciplinary Grants in the Mathematical Sciences

The objective of the Interdisciplinary Grants in the Mathematical Sciences (IGMS) is to enable mathematical scientists to undertake research and study in another discipline so as to:

  • expand their skills and knowledge in areas other than the mathematical sciences;
  • subsequently apply this knowledge in their research, and
  • enrich the educational experiences and broaden the career options of their students.

Recipients of an IGMS award are expected to spend eleven months full time in a twelve-month period either in a non-mathematical academic science department or in an industrial, commercial or financial institution. The expected outcome is sufficient familiarity with another discipline so as to open opportunities for effective collaboration by the mathematical scientist with researchers in another discipline.

IGMS Program Solicitation

Faculty Early Career Development Program

The Faculty Early Career Development (CAREER) Program is a Foundation-wide activity that offers the National Science Foundation's most prestigious awards for new faculty members. The CAREER program recognizes and supports the early career-development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century. CAREER awardees will be selected on the basis of creative career-development plans that effectively integrate research and education within the context of the mission of their institution. NSF encourages submission of CAREER proposals from new faculty at all CAREER eligible institutions. Such plans should build a firm foundation for a lifetime of integrated contributions to research and education.

DMS CAREER Award Lists
CAREER Program Solicitation and Other Information

Research Planning Grants and Career Advancement Awards for Minority Scientists and Engineers

This Program Announcement highlights two of the special opportunities for minority scientists and engineers at the National Science Foundation: both are applicable to all NSF-supported disciplinary fields and international cooperative activities:

  • Minority Research Planning Grants (MRPG). These grants enable eligible minorities who have not had prior independent Federal research support to develop a competitive research project.
  • Minority Career Advancement Awards (MCAA). Through this effort, eligible minorities may undertake one-year enhancement projects to increase their research capability and productivity.

MRPGs and MCAAs are part of the Foundation's effort to encourage the entry and participation of highly qualified minority scientists and engineers in research careers. These opportunities are applicable to all NSF-supported disciplinary fields and to the Foundation's international cooperative activities.

Program Solicitation

Increasing the Participation and Advancement of Women in Academic Science and Engineering Careers (ADVANCE)

The goal of the ADVANCE program is to increase the participation of women in the scientific and engineering workforce through the increased representation and advancement of women in academic science and engineering careers. To meet this goal, the ADVANCE program provides award opportunities for both individuals and organizations: Fellows Awards, Institutional Transformation Awards, and Leadership Awards. With each of the three types of ADVANCE awards, NSF seeks to support new approaches to improving the climate for women in U.S. academic institutions and to facilitate women's advancement to the highest ranks of academic leadership. Creative approaches to realize the goal of this program are sought from men and women. Members of underrepresented minority groups and individuals with disabilities are encouraged to apply.

ADVANCE Program Solicitation and Other Information

Training Programs

Enhancing the Mathematical Sciences Workforce in the 21st Century

The long-range goal of the Enhancing the Mathematical Sciences Workforce in the 21st Century (EMSW21) program is to increase the number of U.S. citizens, nationals, and permanent residents who are well-prepared in the mathematical sciences and who pursue careers in the mathematical sciences and in other NSF-supported disciplines. EMSW21 builds on the VIGRE program and now includes a broadened VIGRE activity, an additional component for Research Training Groups (RTG) in the Mathematical Sciences, and an additional component for Mentoring through Critical Transition Points (MCTP) in the Mathematical Sciences.

For more detailed information, see the EMSW21 Program Solicitation.

The three components of the EMSW21 program are:

  • Grants for Vertical Integration of Research and Education (VIGRE)
    The focus of this component is enhancing the educational experience of all students and postdoctoral associates in a department (or departments). Broad faculty commitment and a team approach to enhancing learning are necessary. A principal element of VIGRE activity is increasing the interaction among undergraduates, graduate students, postdoctoral associates, and faculty members, whether pair-wise or collectively. Integrating research and education for graduate students and postdoctoral associates, involving undergraduates in substantial learning by discovery, and developing a team approach are keys to successful VIGRE projects. These goals can be accomplished in many ways and proposers should develop creative approaches that suit their circumstances.

    The enhancement of educational experiences of all students should stem from an understanding of current patterns of student participation in the life of the department(s). All VIGRE proposals are required to include the outcome of a curriculum review and at least five years of data on past performance in attracting and retaining well-qualified U.S. citizens, nationals, and permanent residents as graduate students and postdoctoral associates in the mathematical sciences, including women and those from underrepresented groups. Those departments who have had previous VIGRE awards should present data through the period of the award. Departments can use this information to describe its capacity to host a VIGRE project that will create a significant improvement in the educational experiences of their students and postdoctoral associates. These data may also inform recruitment and retention plans and mechanisms for assessment of the project.

    VIGRE Award List

  • Research Training Groups (RTG)
    This component will provide groups of researchers with related research goals in the mathematical sciences with funds to foster research-based training and education. The groups may include researchers and students from different departments and institutions, but the research-based training and education activities must be based in the mathematical sciences. The RTGs are expected to vary in size, scope, proposed activities and in their plans for organization, participation, and operation, but will all have the following characteristics: they are based in a U.S. academic institution that grants the Ph.D. in the mathematical sciences; are focused on a major research theme in the mathematical sciences; have a convincing plan showing how the proposed activity would create new or enhanced research-based training and education experiences in the mathematical sciences for the students and post-doctoral investigators; have a significant collective mentoring component.

  • Mentoring through Critical Transition Points (MCTP)
    This component will provide a system of mentoring devoted to points of transitions in a mathematical sciences career path that are critical for success from undergraduate studies to the early years in a tenure track position. The program may be a comprehensive department effort or a more focused endeavor involving a few faculty mentors and aimed towards a specific transition point or group of points. However, department-wide programs that include components for undergraduates, graduates, and postdocs, may be more appropriate for the VIGRE component. Successful proposals will be those that provide ways to increase the number and the quality of training of U.S. citizens, nationals, or permanent residents entering the scientific workforce with strong mathematical training including the number of degrees awarded in the mathematical sciences.

Mathematical Sciences Postdoctoral Research Fellowships

The purpose of the Mathematical Sciences Postdoctoral Research Fellowships (MSPRF) is to permit participants to choose research environments that will have maximal impact on their future scientific development. Awards are made for appropriate research in areas of the mathematical sciences, including applications to other disciplines. The MSPRF award provides a stipend support for two nine-month academic years and six summer months, for a total of 24 months' support, within a 48-month period. Each applicant is required to submit a research plan for the tenure period requested. The fellowships are not intended to support the preparation of prior research results for publication or the writing of textbooks. To be eligible for one of these fellowships, an individual must (1) be a citizen, national, or lawfully admitted permanent resident alien of the United States; (2) have earned by the beginning of his or her fellowship tenure a doctoral degree in one of the mathematical sciences listed above, or have research training and experience equivalent to that represented by a Ph.D. in one of those fields; and (3) have held the doctorate for no more than 2 years, as of January 1 of the year of the award.

MSPRF Program Solicitation

Distinguished International Postdoctoral Research Fellowships

The Directorate for Mathematical and Physical Sciences (MPS) of the National Science Foundation announces a special opportunity for postdoctoral investigators to conduct research projects abroad as MPS Distinguished International Postdoctoral Research Fellows (MPS-DRF). The objective of this activity is to provide talented recent doctoral recipients in the mathematical and physical sciences an effective means of establishing international collaborations in the early stages of their careers, thereby facilitating and enhancing connections between the U.S. science and engineering community and its international counterparts. By providing the resources needed to establish collaborations with potential for long-term impact, this activity is aimed at recognizing and supporting future leaders. As the scientific enterprise becomes increasingly global, there is a growing need for scientists who will excel and provide leadership in such an environment. MPS encourages applicants whose research would especially benefit from international collaboration to apply for an MPS-DRF award.

MPS-DRF awards are available for research abroad in the mathematical and physical sciences. Science centers in all foreign geographical regions are eligible as host institutions. Appropriate establishments include institutions of higher education; industrial research institutions and laboratories; government research institutes, laboratories, and centers; and non-profit research organizations.

There are some similarities between this program and the International Research Fellowship Program (IRFP) managed by the National Science Foundation's Division of International Programs. (See the IRFP Solicitation and other information.) Since the objectives and the guidelines of the two programs differ somewhat, prospective applicants should examine both programs to determine the best match.

A unique feature of this program is that resources are available during the fellowship period for awardees to travel in order to establish and to further international contacts and collaborations and to maintain a viable presence in the Fellow's research community in the United States. Thus, Fellows will be provided resources to visit other foreign sites as well as to return to the U.S. for short visits.

MPS-DRF Program Solicitation

Graduate Research Fellowship Program

NSF Graduate Fellowships offer recognition and three years of support for advanced study to approximately 900 outstanding graduate students in the mathematical, physical, biological, engineering, and behavioral and social sciences, including the history of science and the philosophy of science, and to research-based Ph.D. degrees in science education. Approximately 90 awards will be in the Women in Engineering (WENG) and Women in Computer and Information Science (WICS) components. Fellowships are awarded for graduate study leading to research-based master's or doctoral degrees in the fields of science, mathematics, and engineering supported by the National Science Foundation. NSF Graduate Research Fellowships are open only to individuals who are, at the time of application, citizens or nationals of the United States or permanent resident aliens of the United States. Fellowships are intended for individuals in the early stages of their graduate study. In most cases, an individual has three opportunities to apply: during the senior year of college, prior to or during the first year of graduate school, and the beginning of the second year of graduate school.

GRFP Program Solicitation and Other Information

Integrative Graduate Education and Research Traineeship Program

The Integrative Graduate Education and Research Traineeship (IGERT) program has been developed to meet the challenges of educating U.S. Ph.D. scientists, engineers, and educators with the interdisciplinary backgrounds, deep knowledge in chosen disciplines, and technical, professional, and personal skills to become in their own careers the leaders and creative agents for change. The program is intended to catalyze a cultural change in graduate education, for students, faculty, and institutions, by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. It is also intended to facilitate greater diversity in student participation and preparation, and to contribute to the development of a diverse, globally-engaged science and engineering workforce.

IGERT is an NSF-wide endeavor involving the Directorates for Biological Sciences (BIO), Computer and Information Science and Engineering (CISE), Education and Human Resources (EHR), Engineering (ENG), Geosciences (GEO), Mathematical and Physical Sciences (MPS), Social, Behavioral, and Economic Sciences (SBE), the Office of Polar Programs (OPP), and the Office of International Science and Engineering (INT).

IGERT Program Solicitation and Other Information

Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences

The goal of the Undergraduate Biology and Mathematics (UBM) activity is to enhance undergraduate education and training at the intersection of the biological and mathematical sciences and to better prepare undergraduate biology or mathematics students to pursue graduate study and careers in fields that integrate the mathematical and biological sciences. The core of the activity is long-term research experiences for interdisciplinarily balanced cohorts of at least four undergraduates. Projects should focus on research at the intersection of the mathematical and biological sciences. Projects should provide students exposure to contemporary mathematics and biology, addressed with modern research tools and methods. That is, projects must be genuine research experiences rather than rehearsals of research methods. Projects must involve students from both areas in collaborative research experiences and include joint mentorship by faculty in both fields. In addition, it is expected that projects will strengthen the research and education capacity, infrastructure, and culture of the participating institutions. To this end, projects should create models for education in the mathematical and biological sciences and influence the direction of academic programs for a broad range of students. UBM is a joint effort of the Education and Human Resources (EHR), Biological Sciences (BIO), and Mathematical and Physical Sciences (MPS) directorates at the National Science Foundation (NSF).

UBM Program Solicitation

Research Experiences for Undergraduates (REU)

For Students

NSF funds a large number of research opportunities for undergraduate students through its REU Sites program. An REU Site consists of a group of ten or so undergraduates who work in the research programs of the host institution. Each student is associated with a specific research project, where he/she works closely with the faculty and other researchers. Students are granted stipends and, in many cases, assistance with housing and travel. Undergraduate students supported with NSF funds must be citizens or permanent residents of the United States or its possessions. An REU Site may be at either a US or foreign location.

By using the web page, Search for an REU Site, you may examine opportunities in the subject areas supported by various NSF units. In addition, you may search by keywords to identify sites in particular research areas or with certain features, such as a particular location.

Students must contact the individual sites for information and application materials. NSF does not have application materials and does not select student participants. A contact person and contact information is listed for each site.

For Faculty

The REU Program Announcement provides guidance on how to apply for an REU Supplement or for an REU Site. The REU program seeks to expand student participation in all kinds of research - whether disciplinary, interdisciplinary, or educational in focus - encompassing efforts by individual investigators, groups, centers, national facilities, and others. The program seeks to attract a diversified pool of talented students into careers in science and engineering and to help ensure that they receive the best education possible.

A request for an REU Supplement may be included within a proposal for a new or renewal NSF grant or cooperative agreement or as a supplement to an ongoing NSF-funded project. An REU Supplement request is handled by the NSF program officer for the underlying research grant.

For an REU Site, a formal proposal is submitted by the annual deadline of September 15. REU Sites are funded by research divisions/directorates throughout the Foundation, with the point-of-contact for each given on the web page, REU Points of Contact at NSF.

REU Program Solicitation and Other Information

Math and Science Partnership

The Math and Science Partnership (MSP) program addresses a portion of the President's challenge ­ enunciated in No Child Left Behind ­ to strengthen K-12 science and mathematics education. The MSP program promotes a vision of education as a continuum that begins with our youngest learners and progresses through adulthood. The program supports partnerships that unite K-12 schools, institutions of higher education, and other stakeholders in activities that ensure that no child is left behind.

MSP Program Solicitation and Other Information

Institutes and Support for Conferences and Travel

Mathematical Sciences Research Institutes

The Division of Mathematical Sciences currently funds seven awards given to different mathematical sciences research institutes. These projects stimulate research in all of the mathematical sciences through thematic and residential programs, workshops, and access to distinctive resources. All of the institutes offer visiting opportunities for researchers in every stage of their careers, and most offer postdoctoral fellowships for one or more years, with mentoring provided by outstanding scientists. Many of these centers involve new researchers, graduate students, and undergraduates through tutorials related to current programs, mathematical research experiences based on industrial or other problems, and summer schools. Interested parties are encouraged to contact the institutes directly for information on current and future programs, visiting opportunities, and other activities. The seven institutes and their web sites are:

In addition to these institutes, DMS contributes to the support of the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, Alberta, a joint venture between Canada and the United States (visit the station's website at This site is an international center for workshops, team research, and summer schools for mathematical sciences and mathematical challenges in science and industry.

Conferences, International Travel, Workshops and Special Years in Mathematical Sciences

The Division of Mathematical Sciences supports a variety of conferences, workshops, and related activities that are submitted as proposals from principal investigators to the appropriate disciplinary program.

Conferences will be supported only if equivalent results cannot be obtained at regular meetings of the professional societies. Requests for support of activities at regular professional society meetings ordinarily originate with educational institutions or professional scientific societies.

For conferences, workshops, or related activities, the criterion of overall impact on the U.S. mathematical sciences community will be paramount in making decisions among otherwise equally meritorious proposals.

The Division of Mathematical Sciences funding priorities are the following:

  • Participation in research conferences is one way for mathematical scientists to remain involved in research activities. Those conference proposals that dedicate a substantial portion of the budget to ensure the participation of individuals who have no other source of federal support will have a high priority.
  • Conference proposals that contribute to the Foundation's effort to enlarge the science personnel base of the nation by including students and recent doctoral recipients, women, minorities, and persons with disabilities among the invited speakers and/or participants will have a high priority.
  • Conference proposals that are linked to National Science Foundation research priorities, Federal initiatives, or strategic areas, especially by providing opportunities for mathematical scientists to learn how they may contribute to these activities and/or to participate in multidisciplinary projects, will have a high priority.
  • In general, funding to support participation in conferences held abroad has been very limited.

Program Solicitation

Regional Conferences of the Conference Board of the Mathematical Sciences

Each five-day Regional Conference of the Conference Board of the Mathematical Sciences (CBMS) features a distinguished lecturer who delivers ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences. The lecturer subsequently prepares an expository monograph based upon these lectures, which is normally published as a part of a regional conference series. Depending upon the conference topic, the monograph is published by the American Mathematical Society, the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Support is provided for about 30 participants at each conference and the conference organizer invites both established researchers and interested newcomers, including postdoctoral fellows and graduate students, to attend.

Call for Proposals and Other Information

International Opportunities for Scientists and Engineers

The National Science Foundation recognizes the importance of enabling U.S. researchers and educators to advance their work through international collaboration, and of helping to ensure that future generations of U.S. scientists and engineers gain professional experience beyond this nation's borders early in their careers. The Office of International Science and Engineering (INT) contributes to NSF's mission by promoting new partnerships between U.S. investigators and their colleagues in other countries, or new cooperative projects between established collaborators. Such activities may be in any field of science and engineering research and education supported by NSF.

The Office of International Science and Engineering also supports an array of activities designed to provide opportunities for junior investigators. Graduate and undergraduate students and postdoctoral researchers can receive travel and living expenses to participate in the overseas aspects of collaborative research projects proposed to NSF by senior U.S. investigators. Graduate students can also be supported through INT's dissertation enhancement awards, or for participation in the East Asia Summer Institutes (EASI) in Japan, Korea, Taiwan, or China. Principal Investigators of existing grants from other parts of NSF may request supplemental support to include junior faculty members, postdoctoral investigators, graduate students, and qualified undergraduates who are conducting collaborative research in foreign countries.

Program Solicitation

Grants for Computational Resources

Scientific Computing Research Environments in the Mathematical Sciences

The Scientific Computing Research Environments in the Mathematical Sciences (SCREMS) program supports computing environments dedicated to research in the mathematical sciences. Proposals may request support for the purchase of computing equipment and limited support for professional systems administrators or programmer personnel for research computing needs. These grants are intended to support research projects of high quality that require access to advanced computing resources. Awards are made to provide support for specific research projects rather than to provide general computing capacity. Proposers are encouraged to include projects involving symbolic and algebraic computations, numerical computations and simulations, as well graphical representations (visualization) in aid of the research.

SCREMS Program Solicitation

Major Research Instrumentation Program

The Major Research Instrumentation Program (MRI) is designed to improve the quality and expand the scope of research and research training in science and engineering, and to foster the integration of research and education, by providing instrumentation for research-intensive learning environments. The MRI Program assists in the acquisition or development of major research instrumentation by U.S. institutions that is, in general, too costly for support through other NSF programs. The maintenance and technical support associated with these instruments are also supported. Proposals may be for a single instrument, a large system of instruments, or multiple instruments that share a common research focus. Computer systems, clusters of advanced workstations, networks, and other information infrastructure components necessary for research are encouraged.

Awards for instrumentation range from $100,000 to $2 million. Lesser amounts are considered in proposals from non-Ph.D. granting institutions, from mathematical sciences, or from the social, behavioral and economic science communities.

MRI Program Solicitation and Other Information

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