Analysis

The summary for the Analysis grant is detailed below. This summary states who is eligible for the grant, how much grant money will be awarded, current and past deadlines, Catalog of Federal Domestic Assistance (CFDA) numbers, and a sampling of similar government grants. Verify the accuracy of the data FederalGrants.com provides by visiting the webpage noted in the Link to Full Announcement section or by contacting the appropriate person listed as the Grant Announcement Contact. If any section is incomplete, please visit the website for the National Science Foundation, which is the U.S. government agency offering this grant.

Analysis: 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.