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Mathematical Physics develops and applies advanced mathematical methods to enable the solution of difficult problems in physics.  It often is the work of mathematicians with a strong physics interest and intuition, or of physicists who are also highly regarded in mathematics.  Very advanced mathematical methods are applied (by individuals or collaborators) to important but difficult physics concepts to rigorously establish the behavior of theoretical systems,  resolve conundrums or find new directions.  The PHY Mathematical Physics program is dedicated to supporting such research.

Supports activities in conjunction with NSF-wide programs such as Faculty Early Career Development (CAREER), Research Experiences for Undergraduates (REU), and programs aimed at women, minorities, and persons with disabilities. Further information about all of these programs and activities is available in the Crosscutting Investment Strategies section of the NSF Guide to Programs. The program also supports activities that seek to improve the education and training of physics students (both undergraduate and graduate), such as curriculum development or physics education research directed towards upper-level or graduate physics courses, and activities that are not included in specific programs elsewhere within NSF. The program supports research at the interface between physics and other disciplines and extending to emerging areas. Broadening activities related to research at the interface with other fields, possibly not normally associated with physics, also may be considered.

Plasma Physics is a study of matter and physical systems whose intrinsic properties are governed by collective interactions of large ensembles of free charged particles. 99.9% of the visible Universe is thought to consist of plasmas. The underlying physics of the collective behavior in plasmas has applications to space physics and astrophysics, materials science, applied mathematics, fusion science, accelerator science, and many branches of engineering. The National Science Foundation (NSF), with participation of the Directorates for Engineering, Geosciences, and Mathematical and Physical Sciences, and the Department of Energy, Office of Science, Fusion Energy Sciences are continuing the joint Partnership in Basic Plasma Science and Engineering begun in FY1997 and renewed several times since. As stated in the original solicitation (NSF 97-39), which is superseded by the present solicitation, the goal of the Partnership is to enhance basic plasma science research and education in this broad, multidisciplinary field by coordinating efforts and combining resources of the two agencies. The current solicitation also encourages submission of proposals to perform basic plasma experiments at NSF and/or DOE supported user facilities, including facilities located at DOE national laboratories, designed to serve the needs of the broader plasma science and engineering community.

Plasma Physics is a study of matter and physical systems whose intrinsic properties are governed by collective interactions of large ensembles of free charged particles. 99.9% of the visible Universe is thought to consist of plasmas. The underlying physics of the collective behavior in plasmas has applications to space physics and astrophysics, materials science, applied mathematics, fusion science, accelerator science, and many branches of engineering. The National Science Foundation (NSF), with participation of the Directorates for Engineering, Geosciences, and Mathematical and Physical Sciences, and the Department of Energy, Office of Science, Fusion Energy Sciences are continuing the joint Partnership in Basic Plasma Science and Engineering begun in FY1997 and renewed several times since. As stated in the original solicitation (NSF 97-39), which is superseded by the present solicitation, the goal of the Partnership is to enhance basic plasma science research and education in this broad, multidisciplinary field by coordinating efforts and combining resources of the two agencies. The current solicitation also encourages submission of proposals to perform basic plasma experiments at NSF and/or DOE supported user facilities, including facilities located at DOE national laboratories, designed to serve the needs of the broader plasma science and engineering community.

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.

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.ConferencesPrincipal Investigators should carefully read the program solicitation "Conferences and Workshops in the Mathematical Sciences" (link below) to obtain important information regarding the substance of "conference proposals" (i.e., proposals for conferences, workshops, summer/winter schools, and similar activities). For Analysis c

Scientific advances such as genomics, quantitative structural biology, imaging techniques, and modeling of complex systems have created opportunities for exciting research careers at the interface between the physical/computational sciences and the biological sciences. Tackling key problems in biology will require scientists trained in areas such as chemistry, physics, applied mathematics, computer science, and engineering. Recognizing the vital role such cross-trained scientists will play in furthering biomedical science, the Burroughs Wellcome Fund has developed the Career Awards at the Scientific Interface. These grants are intended to foster the early career development of researchers who have transitioned or are transitioning from undergraduate and/or graduate work in the physical/mathematical/computational sciences or engineering into postdoctoral work in the biological sciences, and who are dedicated to pursuing a career in academic research. Candidates are expected to draw from their training in a scientific field other than biology to propose innovative approaches to answer important questions in the biological sciences.

The Geospace Section of the Division of Atmospheric and Geospace Sciences, to ensure the health and vitality of solar and space sciences on university teaching faculties, is pleased to offer awards for the creation of new tenure-track faculty positions within the intellectual disciplines which comprise the space sciences. The aim of these awards is to integrate research topics in solar and space physics into basic physics, astronomy, electrical engineering, geoscience, meteorology, computer science, and applied mathematics programs, and to develop space physics graduate programs capable of training the next generation of leaders in this field. Space Science is interdisciplinary in nature and the Faculty Development in the Space Sciences awardees will be expected to establish partnerships within the university community.

The Breakthrough Prizes were founded by Sergey Brin and Anne Wojcicki, Mark Zuckerberg and Priscilla Chan, and Yuri and Julia Milner. Selection committees for the prizes comprise previous Breakthrough Prize laureates, who choose the winners from a list of candidates obtained during the nomination period. The Breakthrough Prize Foundation currently is accepting nominations for the 2020 Breakthrough Prizes in Fundamental Physics, Life Sciences, and Mathematics. Now in its eighth year, the competition will honor top scientists with up to five prizes in life sciences, one in fundamental physics, and one in mathematics. Each prize comes with a $3 million award. In addition, up to six New Horizons Prizes, each with an award of $100,000, will be presented to promising early-career researchers in the fields of fundamental physics and mathematics.

To that end, the foundation is accepting applications for its Targeted Grants in Mathematics and Physical Sciences (MPS) program, which supports projects of exceptional promise and scientific importance in theoretical mathematics, physics, and computer science with flexible funding for up to five years. Although the emphasis of the program is theory, projects with some experimental components may be considered.  

Co-founded in New York City by Jim and Marilyn Simons, the Simons Foundation works to advance the frontiers of research in mathematics and the basic sciences. To that end, the foundation is accepting applications for its Targeted Grants in Mathematics and Physical Sciences (MPS) program, which supports projects of exceptional promise and scientific importance in theoretical mathematics, physics, and computer science with flexible funding for up to five years. Although the emphasis of the program is theory, projects with some experimental components may be considered.   Principal investigators and co-investigators must have a PhD and a tenure-track or tenured position at an established U.S. or foreign public or private educational institution or standalone research center. There are no citizenship or department requirements for principal investigators.

The Simons Foundation is inviting applications for its Collaborations in Mathematics and the Physical Sciences program. The goal of the program is to stimulate progress on fundamental scientific questions of major importance in mathematics, theoretical physics, and theoretical computer science. To that end, $2 million a year for an initial period of four years, including up to 20 percent a year for indirect costs, will be awarded in support of collaborations that address a mathematical or theoretical topic of fundamental scientific importance where a significant, new development creates a novel area for exploration or provides a new direction for progress in an established field. Questions addressed by the collaboration may be concrete or conceptual, but there should be little doubt that answering them would constitute a major scientific milestone. The project should involve outstanding researchers in a range of career stages. The foundation expects to award up to two collaborations in 2020.

Focused Research Hubs in Theoretical Physics (FRHTP) are designed to enhance significant breakthroughs at an intellectual frontier of physics by providing resources beyond those available to individual investigators, so as to promote a collaborative approach to a focused topic while promoting the preparation of scientists at the beginning of their independent scientific careers. 

MPS has long promoted efforts to recruit and retain students from underrepresented groups in all areas of the mathematical and physical sciences. AGEP-GRS introduces a new mechanism by which a current MPS research awardee is able to support one (additional) Ph.D. student in an ongoing MPS-funded research project. The goal is to create an opportunity to engage additional students in research, to develop a positive learning environment for students, and to improve diversity and retention at the doctoral level within the mathematical and physical sciences.

The goal of the CPS program is to develop the core system science needed to engineer complex cyber-physical systems that people can use or interact with and depend upon. Some of these may require high-confidence or provable behaviors. The program aims to foster a research community committed to advancing research and education in CPS and to transitioning CPS science and technology into engineering practice. By abstracting from the particulars of specific systems and application domains, the CPS program seeks to reveal cross-cutting fundamental scientific and engineering principles that underpin the integration of cyber and physical elements across all application sectors.

The mission of the Simons Foundation is to advance the frontiers of research in mathematics and the basic sciences. To that end, the foundation is inviting applications for the 2015 Simons Fellows Programs in both mathematics and theoretical physics. Through the two programs, the foundation will award grants of up to $100,000 to university faculty for a research leave from classroom teaching and administrative obligations of up to a semester in order to help boost their creativity and/or provide intellectual stimulation. The goal of the program is to make it easier to take such leaves, or to extend sabbatical leaves by an extra half year.

The Mathematics and Physical Sciences division at the Simons Foundation is inviting Letters of Intent for the Simons Collaborations in MPS program, the aim of which is to stimulate progress on fundamental scientific questions of major importance in mathematics, theoretical physics, and theoretical computer science. To that end, grants of up to $2 million per year for up to four years will be awarded in support of collaborative projects that address a mathematical or theoretical topic of fundamental scientific importance and where a significant new development has the potential to create a novel area for exploration or provides a new direction for progress in an established field. The questions addressed by the collaboration may be concrete or conceptual, but there should be little doubt that answering them would constitute a major scientific milestone. The project also should have clearly defined initial activities and goals by which its progress and success can be measured.

The goal of the program is to stimulate progress on fundamental scientific questions of major importance in mathematics, theoretical physics, and theoretical computer science. To that end, $2 million a year for an initial period of four years, including up to 20 percent a year for indirect costs, will be awarded in support of collaborations that address a mathematical or theoretical topic of fundamental scientific importance where a significant, new development creates a novel area for exploration or provides a new direction for progress in an established field. Questions addressed by the collaboration may be concrete or conceptual, but there should be little doubt that answering them would constitute a major scientific milestone. The project should involve outstanding researchers in a range of career stages. The foundation expects to award up to two collaborations in 2020.

The National Science Foundation Directorates for Mathematical and Physical Sciences (MPS), Computer and Information Science and Engineering (CISE), Engineering (ENG), and the Simons Foundation Division of Mathematics and Physical Sciences will jointly sponsor up to two new research collaborations consisting of mathematicians, statisticians, electrical engineers, and theoretical computer scientists. Research activities will be focused on explicit topics involving some of the most challenging questions in the general area of Mathematical and Scientific Foundations of Deep Learning. Each collaboration will conduct training through research involvement of recent doctoral degree recipients, graduate students, and/or undergraduate students from across this multi-disciplinary spectrum. Annual meetings of the Principal Investigators ("PIs") and other principal researchers involved in the collaborations will be held at the Simons Foundation in New York City. This program complements NSF's National Artificial Intelligence Research Institutes program by supporting collaborative research focused on the mathematical and scientific foundations of Deep Learning through a different modality and at a different scale.

The National Science Foundation Directorates for Mathematical and Physical Sciences (MPS), Computer and Information Science and Engineering (CISE), Engineering (ENG), and the Simons Foundation Division of Mathematics and Physical Sciences will jointly sponsor up to two new research collaborations consisting of mathematicians, statisticians, electrical engineers, and theoretical computer scientists. Research activities will be focused on explicit topics involving some of the most challenging questions in the general area of Mathematical and Scientific Foundations of Deep Learning. Each collaboration will conduct training through research involvement of recent doctoral degree recipients, graduate students, and/or undergraduate students from across this multi-disciplinary spectrum. Annual meetings of the Principal Investigators ("PIs") and other principal researchers involved in the collaborations will be held at the Simons Foundation in New York City. This program complements NSF's National Artificial Intelligence Research Institutes program by supporting collaborative research focused on the mathematical and scientific foundations of Deep Learning through a different modality and at a different scale.