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DMS Programs

DMS programs and activities are organized within the following:

Proposals for General Conferences, Workshops, Symposia, Special Years, and Related Activities in DMS

Proposals submitted to DMS for general conferences, workshops, symposia, special years, and related activities should be submitted to the appropriate disciplinary program. Proposals should be submitted one year before the start of the activity. Contact the division for information on proposal requirements or see program solicitation NSF 00-109 http://www.nsf.gov/cgi-bin/getpub?nsf00109.

Specific Types of Grants Supported by DMS

In addition to the usual types of research grants awarded to principal investigators and institutions, DMS supports the following:

  • University/Industry Cooperative Research - DMS feels it is important to provide more opportunities to conduct research and training in an industrial environment and for industrial scientists to return periodically to academia. To facilitate both research and training, the division provides Mathematical Sciences University/Industry Postdoctoral Research Fellowships, Senior Research Fellowships, and Industry-Based Graduate Research Assistantships and Cooperative Fellowships in the Mathematical Sciences.
  • Interdisciplinary Grants - These grants enable faculty members to expand their skills and knowledge into areas beyond their disciplinary expertise, to subsequently apply that knowledge to their research, and to enrich the educational experiences and career options for students. These grants support interdisciplinary experiences at the principal investigator's (PI's) institution (outside the PI's department), or at academic, financial, or industrial institutions, in a nonmathematical science environment.

For More Information 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

Disciplinary Programs

The Division of Mathematical Sciences supports the following disciplinary programs:

For More Information For more information about the disciplinary programs described in this section, 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.

Algebra, Number Theory, and Combinatorics

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

Analysis

Supports research on properties and behavior of solutions of differential equations; variational methods; approximations and special functions; analysis in several complex variables and singular integrals; harmonic analysis and wavelet theory; Kleinian groups and theory of functions of one complex variable; real analysis; Banach spaces, Banach algebras, and function algebras; Lie groups and their representations; harmonic analysis; ergodic theory and dynamical systems; some aspects of mathematical physics such as Schroedinger operators and quantum field theory; and operators and algebras of operators on Hilbert space.

Applied Mathematics

Supports research in any area of mathematics except probability or statistics. Research is expected to be motivated by or have an effect on problems arising in science and engineering, although intrinsic mathematical merit is the most important factor. Areas of interest include partial differential equations that model natural phenomena or that arise from problems in science and engineering, continuum mechanics, reaction-diffusion and wave propagation, dynamical systems, asymptotic methods, numerical analysis, variational methods, control theory, optimization theory, inverse problems, mathematics of biological or geological sciences, and mathematical physics.

Computational Mathematics

Supports research in algorithms, 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 Applied and Computational Mathematics

Geometric Analysis

Supports research on differential geometry and its relation to partial differential equations 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, and related geometric topics.

Statistics and Probability

Supports research on statistical theory and methods, which are used to plan scientific experiments and to understand and analyze data. Major subfields include parametric and nonparametric inference, sequential analysis, multivariate analysis, Bayesian analysis, experimental design, time series analysis, resampling methods, and robust statistics. Almost all of these subfields are computationally intensive. Probability theory is the study of mathematical structures that provide tractable models to statistics and many diverse areas, such as physics, chemistry, biology, biosciences, geosciences, and engineering. Major subfields include stochastic processes, limit theory, infinite particle systems, stochastic analysis in Banach spaces, martingles, and Markov processes.

Topology and Foundations

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; general topology and continua theory; and mathematical logic, including proof theory, recursion theory and model theory, foundations of set theory, and infinitary combinatorics.

Other Programs of Interest

In addition to support in the disciplinary programs, the Division of Mathematical Sciences (DMS) offers activities that differ from the usual type of research projects. A few examples of these programs are included here.

Mathematical Sciences Research Institutes and Other Activities

Mathematical Sciences Research Institutes - DMS currently funds three Mathematical Sciences Research Institutes. These institutes stimulate research in the mathematical sciences through thematic programs and workshops and advance the training of junior researchers in specialties related to those activities through postdoctoral fellowships of 1 to 2 year's duration. The existing sites meet only part of the Nation's need for support of communication and for collaborative work on mathematical and statistical problems. In FY 2002, DMS anticipates the establishment of new institutes that will advance research in the mathematical sciences and/or the interface of the mathematical sciences and other disciplines; address the diverse challenges and opportunities facing the Nation to which the mathematical sciences can contribute; and promote the integration of research and education.

  • Regional Conferences - Operated by the Conference Board of the Mathematical Sciences, these conferences feature a principal speaker who gives 10 one-hour talks on a particular subject during a week-long session.
  • Scientific Computing Research Environments in the Mathematical Sciences - Offers moderate grants for computing equipment that will benefit groups of outstanding researchers who are highly productive but whose work has been seriously impeded by the lack of computing facilities.
  • Undergraduate Activities-Awards are made in conjunction with NSF - wide undergraduate efforts, including Research Experiences for Undergraduates (REU), cooperative activities with the Directorate for Education and Human Resources (EHR), and other related activities. For more information on REU, visit the NSF Crosscutting Programs home page, http://www.nsf.gov/home/crssprgm. Further information about EHR programs and activities can be found in the EHR section in this Guide.
  • Mathematical Sciences Postdoctoral Research Fellowships - Fellowships will be awarded to between 25 and 30 new fellows in FY 2002. Tenure provides a research instructorship option.

Eligibility Requirements for the Mathematical Sciences Postdoctoral Research Fellowships - Each applicant will be 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 as of January 1, 2002; (2) have earned by the beginning of his or her fellowship tenure a doctoral degree in one of the mathematical sciences listed above, or had 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, 2002.

Focused Research Groups

The mathematical sciences thrive on sharing of ideas from various fields and disciplines, and certain research needs can only be met appropriately by teams of investigators. The Division of Mathematical Sciences supports such teams through the Focused Research Groups (FRG) activity. The FRG Program allows groups of researchers to respond to scientific needs of pressing importance; to take advantage of current scientific opportunities; or to 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 year's duration, and substantial in both scope and impact. Projects supported through FRG are essentially collaborative in nature, their success dependent on interaction of a group of researchers.

Grants for Vertical Integration of Research and Education

The Division of Mathematical Sciences seeks to assist universities in preparing undergraduate students, graduate students, and postdoctoral fellows for a broad range of opportunities in the mathematical sciences, and to encourage departments in the mathematical sciences to consider a spectrum of educational activities and their integration with research. Through the Grants for Vertical Integration of Research and Education (VIGRE) Program, DMS supports efforts by institutions with Ph.D.-granting departments in the mathematical sciences to carry out innovative educational programs, at all levels, that are integrated with the department's research activities. Proposals should have a core, coherent plan for integration of an undergraduate research experience; a graduate traineeship program; a postdoctoral fellowship program; and undergraduate and graduate curriculum reviews.

Cross-Disciplinary Interaction

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. The depth of the problems being raised often exceeds that of the training of the scientists and engineers currently in mathematical and statistical theory. To progress in solving these problems, mathematical scientists must be sought to work in tandem with other scientists. 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.

The following are some of these exciting research opportunities:

  • 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 with 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.


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