Algebra, Number Theory, and Combinatorics | Apply Online

Frequently Asked Questions (FAQs)

What is the "Algebra, Number Theory, and Combinatorics" grant opportunity?

This opportunity (Funding Opportunity Number PD 04 1264) is a National Science Foundation (NSF) discretionary grant program in the Mathematical and Physical Sciences portfolio (CFDA 47.049). It is intended to support fundamental research and related research activities in core areas of pure mathematics: algebra, number theory, and combinatorics.

What type of funding instrument is used for this opportunity?

The funding instrument type is a Grant.

Is this program focused on basic research or applied/program implementation work?

The stated focus is on advancing knowledge in algebra, number theory, and combinatorics (fundamental/basic research), rather than applied development or program implementation.

Which NSF area/portfolio is this opportunity part of?

It sits within NSF's Mathematical and Physical Sciences portfolio and aligns with NSF's broader mission of funding basic research and education in science and engineering.

What algebra topics are included in the scope?

The opportunity supports research on algebraic structures and general algebra, along with linear algebra. Examples of relevant areas mentioned include groups, rings, fields, modules, representations, and other frameworks used to organize and explain mathematical systems.

What kinds of algebra research activities are described as relevant?

Examples described include developing new theoretical tools, establishing classification results, proving structural theorems, and exploring connections to neighboring areas such as geometry, topology, or computer science when those connections are grounded in algebraic questions.

How broad is the number theory scope under this opportunity?

The number theory scope is explicitly broad. It includes algebraic number theory, analytic number theory, and arithmetic geometry, and it also highlights quadratic forms and automorphic forms as targeted areas of interest.

What number theory themes are implied by the description?

The description references topics ranging from classical questions about integers, primes, and Diophantine equations to modern themes such as L-functions, modularity, Galois representations, elliptic curves, arithmetic of varieties, and geometric methods used to study number-theoretic phenomena.

Why are automorphic forms specifically mentioned?

The inclusion of automorphic forms signals interest in research at the intersection of number theory and representation theory, including themes tied to the Langlands program and related analytic and geometric techniques.

What combinatorics topics are included in the scope?

The opportunity supports combinatorics research including graph theory and connections to algebraic geometry. The description also mentions structural and extremal graph theory, enumerative and algebraic combinatorics, probabilistic methods, matroid theory, and combinatorial aspects of geometry.

What does "connections to algebraic geometry" mean in the combinatorics context here?

It indicates interest in topics where combinatorial models illuminate geometric objects (or vice versa). Examples listed include toric geometry, arrangements, tropical geometry, and combinatorial invariants arising from geometric constructions.

Is cost sharing or matching required?

No. The listing states that cost sharing or matching is not required.

Who is eligible to apply?

Eligibility is listed as unrestricted, meaning it is open to any type of applicant entity, subject to any additional eligibility clarifications that would have been included in the full program text.

When was this opportunity originally posted?

The original posting date is March 24, 2009.

What was the original proposal target date?

The original full proposal target date was October 6, 2009. It is described as the first Tuesday in October and recurring annually thereafter.

Is this specific Grants.gov listing still active?

No. The record indicates the opportunity was replaced by another listing (noted as replaced by 10 1264) and archived on August 20, 2010. That typically means applicants should consult the successor program announcement for current details.

What does it mean that the opportunity was "replaced by 10 1264"?

It means this particular entry (PD 04 1264) is not the current solicitation record. The replacement (10 1264) is the successor listing that should be used to find up-to-date solicitation details, deadlines, and submission requirements.

The listing shows ExpectedAwards as 0 and EstimatedTotalFunding as 0. Does that mean there is no funding?

Not necessarily. The information provided notes that these "0" values often reflect that the archived Grants.gov entry does not enumerate funding totals or projected award counts in that specific record, rather than indicating that the program never made awards.

Where should applicants look for authoritative, up-to-date information (award sizes, success rates, and current deadlines)?

The information provided indicates that authoritative, current details should be obtained from the NSF program description link referenced in the announcement and from the successor solicitation that replaced PD 04 1264.

Where should applicants go for current submission instructions?

Because this entry is archived, the provided guidance is to use NSF's program page and submission systems to confirm the active solicitation and the most current submission instructions.

Who should be contacted for access or technical issues?

The contact information provided points to NSF Grants.gov support at grantsgovsupport@nsf.gov for access or technical issues.

Is there a contact for issues linking to the funding announcement?

Yes. The information provided notes there was also a point of contact for problems linking to the funding announcement, in addition to the NSF Grants.gov support email.

What general category is this opportunity listed under?

It is categorized under science and technology and other research and development.

Does this program support research activities beyond a single subfield?

Yes. The scope spans algebra, number theory, and combinatorics, and it also explicitly mentions cross-connections (for example, algebra with geometry/topology/computer science when grounded in algebraic questions, and combinatorics with algebraic geometry).