Federal Project Grant Award Summary

The National Science Foundation (NSF) Division of Mathematical Sciences awarded $100,000 to the University of California, Los Angeles under the Mathematical and Physical Sciences program (CFDA 47.049) for a two-year project running from August 1, 2026 through July 31, 2028. This Project Grant supports fundamental research in algebraic topology focused on computing differentials in the Adams Spectral Sequence and advancing the understanding of the Kervaire Invariant Problem, particularly the recently resolved dimension 126 case. The research will develop and apply two novel computational techniques—the Generalized Leibniz Rule and the Generalized Mahowald Trick—to propagate differential information across broader mathematical contexts using synthetic spectra and to extend analysis to the equivariant slice spectral sequence.

Beyond the primary research objectives, the project will generate new mathematical tools and computational methods applicable to related problems in homotopy theory and algebraic topology, including identification of equivariant Hurewicz images for various ring spectra. The award includes broader impacts through student training in advanced mathematical research and active collaboration and network-building within the mathematical sciences community. The work builds directly on prior breakthroughs by the Principal Investigator and collaborators and aims to further understand the strong Kervaire Invariant Problem through rigorous computational analysis of homotopy classes detected by specific spectral sequence elements.