

This document has been archived. For current NSF funding opportunities, see
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Directorate
for Mathematical and Physical Sciences
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
projects are awarded to single investigators or small groups of investigators
working with graduate students and postdoctoral researchers. Programs such
as Mathematical Sciences Infrastructure handle activities that fall outside
this mode.
Proposals for General Conferences, Workshops, Symposia, Special Years,
and Related Activities in DMS
Proposals for general conferences, workshops, symposia, special years,
and related activities should be submitted to the appropriate disciplinary
program. Proposals should be submitted 1 year before the start of the activity.
Contact the division for information on proposal requirements or see program
solicitation NSF
00109.
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 research and training, the division provides
Mathematical Sciences University/Industry Postdoctoral Research Fellowships,
Senior Research Fellowships, and IndustryBased 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.
• Disciplinary Programs
1. 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, quadratic
forms, and automorphic forms; and combinatorics, graph theory, and algebraic
geometry.
2. 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.
3. 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, reactiondiffusion
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.
4. 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. Proposals from interdisciplinary teams to develop
critical mathematical and computational techniques from modeling and algorithm
development through implementation are encouraged. Also encouraged are
proposals for innovative computational methods within the mathematical sciences.
5. 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.
6. Statistics
Supports research for developing and improving statistical
theory and methods that are used for the collection, exploration, analysis,
and interpretation of data to enable discovery and advancement in virtually
all areas of science and engineering. Subfields include parametric and
nonparametric inference, multivariate analysis, Bayesian analysis, experimental
design,
robust statistical methods, time series analysis, spatial analysis, and
resampling methods.
7. 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,
which involves applications to other areas of science and engineering,
is especially encouraged.
8. Topology
Supports research on algebraic topology, including homotopy
theory, ordinary and extraordinary homology and cohomology, cobordism theory,
and Ktheory; 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.
9. Foundations
Supports research in mathematical logic, including
proof theory, recursion theory and model theory, foundations of set theory,
and infinitary combinatorics.
• Infrastructure Programs and Other Activities
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. For additional
programs and further information, visit the DMS home page, https://www.nsf.gov/div/index.jsp?div=DMS.
1. Mathematical Sciences Research Institutes and Other Activities
The Division of Mathematical Sciences (DMS) 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 career, 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:
American Institute of Mathematics
AIM Research Conference Center
360 Portage Ave
Palo Alto, CA 943062244
Web address: http://www.aimath.org
Institute for Advanced Study
School of Mathematics
1 Einstein Drive
Princeton, NJ 08540
Email address: math@math.ias.edu
Web address: http://www.math.ias.edu
Institute for Mathematics and its Applications
University of Minnesota
400 Lind Hall, 207 Church Street SE
Minneapolis, MN 554550436
Web address: http://www.ima.umn.edu
Institute for Pure and Applied Mathematics
IPAM Building
460 Portola Plaza
Box 957121
Los Angeles, CA 900957121 (it's important to include the entire 9digit
Zip Code)
Email: ipam@ucla.edu
Web address: http://www.ipam.ucla.edu
Mathematical Biosciences Institute
The Ohio State University
231 W. 18th Avenue
Columbus, OH 43210
Tel: 6142923648
Web address: http://mbi.osu.edu
Mathematical Sciences Research Institute
17 Gauss Way
Berkeley, CA 947205070
Email: inquiries@msri.org
Web address: http://www.msri.org
Statistical and Applied Mathematical Sciences Institute
19 T. W. Alexander Drive
P.O. Box 14006
Research Triangle Park, NC 277094006
Tel: 9196859350 FAX: 9196859360
Email: info@samsi.info
Web address: http://www.samsi.info
In addition to these institutes, DMS contributes to the support of the
Banff International Research Station for Mathematical Innovation and Discovery
in Banff, Alberta, a joint venture between Canada and the United States
(visit the station’s Web site at http://www.pims.math.ca/birs). This
site is an international center for workshops, team research, and summer
schools for mathematical sciences and mathematical challenges in science
and industry.
 Regional Conferences—Operated by the conference
board of the mathematical sciences, these conferences feature a principal
speaker
who gives 10 1hour talks on a particular subject during a weeklong 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 NSFwide 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, https://www.nsf.gov/funding/pgm_list.jsp?type=xcut.
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 30 and 35 new fellows in 2004. 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, 2004; (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, 2004.
2. 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.
3. Enhancing the Mathematical Sciences Workforce in the 21^{st} Century (EMSW21)
The
longrange goal of the EMSW21 Program is to increase the number of U.S.
citizens, nationals, and permanent residents who are well prepared for
and want to pursue careers in the mathematical sciences and in other NSF
supported
disciplines. EMSW21 builds on the Vertical Integration of Research and
Education (VIGRE) Program and now includes a broadened VIGRE activity, an
additional
component for Research Training Groups in the Mathematical Sciences (RTG),
and an additional component for Mentoring through Critical Transition Points
in the Mathematical Sciences (MCTP).
 The Grants for Vertical Integration of Research and Education
(VIGRE) component focuses on 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
for the success of this program. A principal element of VIGRE is the increase
in interaction among undergraduates, graduate students, postdoctoral associates,
and faculty members. 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 Research Training Groups in the Mathematical Sciences (RTG) component provides groups of researchers who have related research goals
in the mathematical sciences with funds to foster researchbased training
and education. Although the groups may include researchers and students
from different departments and institutions, the researchbased training
and education activities must be based in the mathematical sciences. The
RTGs are expected to vary in size, scope, proposed activities, and plans
for organization, participation, and operation.
 The Mentoring Through Critical Transition Points in the Mathematical
Sciences (MCTP) component provides a system of mentoring that focuses on
points of transition critical for success in a mathematical science career
path—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 toward a specific
transition point or group of points. However, departmentwide programs that
include components for undergraduates, graduates, and postdoctorates, 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.

