Project Grant 2601697

The National Science Foundation Division of Mathematical Sciences awarded The University of Kentucky Research Foundation $180,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop and apply mathematical tools for studying symmetry and cohomology in algebraic geometry, representation theory, and topology.

The project centers on two primary research goals: computing stable cohomology of line bundles on flag varieties in arbitrary characteristic through explicit characteristic-free resolutions by exterior powers, and exploiting newly discovered connections between mathematical areas. The work will advance understanding of the Borel-Weil-Bott theorem outside characteristic zero and clarify the failure of Green's conjecture in positive characteristic, addressing questions that have resisted solution for decades. Beyond its mathematical objectives, the project will develop and contribute rigorously tested, freely available software to Macaulay2, an open-source computer algebra system used throughout the mathematical sciences for computation and experimentation. The project supports training of mathematicians and wide dissemination of results through publications and presentations at seminars and conferences.

The award runs through July 31, 2029, with place of performance in Lexington, Kentucky.