The Algebra and Number Theory program supports fundamental research in algebra, algebraic and arithmetic geometry, number theory, and representation theory. These mathematical fields are interconnected, with algebra providing the structural foundation for studying equations, symmetry, and abstract mathematical systems. Algebraic geometry focuses on solutions to systems of polynomial equations and their geometric properties, while arithmetic geometry explores number-theoretic properties through geometric techniques. Number theory investigates the properties and relationships of integers and other number systems, and representation theory studies abstract algebraic structures by representing their elements as linear transformations of vector spaces.

The program also supports conferences, workshops, and similar events that foster collaboration, share recent advancements, and build research communities within these mathematical areas. These events play a critical role in disseminating knowledge, training early-career researchers, and fostering connections among mathematicians across different institutions and geographic regions. Researchers planning to organize conferences or workshops are encouraged to review the specific NSF solicitation for "Conferences and Workshops in the Mathematical Sciences" for detailed guidance on proposal preparation and requirements.

For conference proposals with budget requests not exceeding $50,000, organizers should submit their proposals six to twelve months in advance of the planned event. For those with budget requests exceeding $50,000, proposals should be submitted nine to twelve months before the event date. Proposals must clearly articulate the goals, expected outcomes, and broader impacts of the conference or workshop, including plans for inclusivity and diversity in participation. They should also provide details on the event structure, topics to be covered, key participants, and mechanisms for disseminating results.

In addition to supporting individual and collaborative research projects, the Algebra and Number Theory program seeks to advance the mathematical sciences community by encouraging activities that bridge disciplines, mentor early-career researchers, and promote innovation. Applicants are expected to align their proposals with NSF's broader goals, including intellectual merit and broader societal impacts, as part of the merit review criteria.

Prospective principal investigators are encouraged to carefully review relevant NSF guidelines and consult with program officers as needed to ensure their proposals meet the expectations and requirements for funding consideration.