Supports research in differential geometry; aspects of global analysis; geometric methods in modern mathematical physics; and geometry of convex sets, integral geometry and related geometric topics.

Supports the operation of national user facilities that make specialized instrumentation available to the materials research community, support research, and conduct education and public outreach.

Supports research on human language — encompassing investigations of the properties of individual human languages and natural language in general — and the intersections of linguistics with cognition, society and other areas of science.

Supports research on social life; the causes and consequences of human behavior; processes of social change; and human social organizations, including groups, institutions and societies.

Supports theoretically motivated research aimed at increasing understanding of human perception, action and cognition and their interactions.

Supports research and infrastructure to advance knowledge of human social behavior, including neural and physiological patterns; thought and emotion processes; and intentions, actions and habits that explain ways of thinking about and relating to others.

Supports research on the theory and applications of probability including discrete probability, stochastic processes, limit theory, interacting particle systems, stochastic differential and partial differential equations and Markov processes.

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

Supports research in statistical theory and methods, including research in statistical methods with applications in any domain of science and engineering.

Supports research on algebraic topology, differential topology, geometric group theory, and general topology and continua theory.

Supports research that strengthens research infrastructure across the mathematical sciences community; training projects that complement the Division of Mathematical Sciences' Workforce Program; and conference and travel requests.

Supports research in algebra, algebraic and arithmetic geometry, number theory and representation theory.

Supports research in analysis, including complex, harmonic and real analysis; dynamical systems and ergodic theory; functional analysis; mathematical physics; operator theory/algebras; partial differential equations and calculus of variations.

Supports mathematics research motivated by or having an effect on problems arising in science and engineering.

Supports research on the structure and movement of oceans, how quantities are transported, how the ocean's structure interacts with biological and chemical processes within it, and the interactions between the ocean, atmosphere, climate and ice.

Supports development of instrumentation with broad applicability to ocean science research that enhances the observational, experimental or analytical capabilities of the ocean science research community.

Supports research on ocean chemistry and the role of oceans in global geochemical cycles. Focus areas include chemical composition, speciation and transformation; internal cycling; and chemical exchanges with other Earth system components.

Supports computational mathematical research focused on developing and implementing theoretically justified and computationally efficient algorithms.

Supports the NSF Ocean Drilling Program.

Supports efforts to integrate ocean research and education via two main program areas — Research Experiences for Undergraduates Sites or Faculty Early Career Development (CAREER) awards.

Supports projects that provide research experiences to undergraduates in the research areas funded by the Division of Chemistry.

Supports research in fundamental plasma physics including study of magnetized plasmas, high-energy-density plasmas, low temperature plasmas, strongly coupled plasmas, non-neutral plasmas, and intense field-matter interaction in plasmas.

Supports computational research in artificial intelligence, machine learning, computer vision, human language technologies and computational neuroscience.

Supports computational research on the full data life cycle, from collection through archiving, analysis and discovery, to maximize the utility of information resources for science and engineering.

Supports research on the theory of algorithms focused on problems that are central to computer science and engineering, and the development of new algorithms and techniques for analyzing algorithms and computational complexity.