Project Grant 2604295

The National Science Foundation Division of Mathematical Sciences awarded The Johns Hopkins University $106,400 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop new methods for studying harmonic maps into singular geometric spaces.

The project, running through August 31, 2028, and based in Baltimore, Maryland, focuses on harmonic maps whose destination spaces lack smooth structure—specifically complete metric spaces with non-positive curvature in the sense of Alexandrov (NPC metric spaces). The principal investigator will establish new regularity results for such maps, develop differential-geometric techniques applicable to non-smooth settings, and apply the resulting theory to geometric problems. Harmonic maps encode geometric, topological, and algebraic information about spaces and serve as central tools in geometric analysis, but standard calculus methods do not apply directly to spaces with sharp or irregular features.

The project supports the education and professional development of graduate students, postdoctoral researchers, and early-career mathematicians. Results will be disseminated through publications, lectures, conferences, and mentoring activities. The work serves the national interest by advancing fundamental mathematical science and creating broadly applicable tools that deepen understanding of geometric structures arising throughout mathematics and in mathematical descriptions of physical phenomena.