Project Grant 2316659

This National Science Foundation (NSF) Project Grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $125,000 in funding to Wichita State University from August 2023 to July 2025. The research objectives are to investigate the classification of four and higher-dimensional spaces, including compact Riemannian manifolds, Einstein manifolds, and shrinking gradient Ricci solitons, whose curvature satisfies a positivity condition. Key strategies involve analyzing solutions to the Ricci flow, applying the maximum principle to partial differential equations, and understanding the relationship between various notions of positive curvature. The project aims to extend the Gauss-Bonnet theorem in dimension two and Hamilton and Perelman's work on geometrization in dimension three to higher dimensions. In addition, the grant supports educational outreach activities for middle and high school students in the local Wichita area, as well as mentoring programs for undergraduate and graduate students at Wichita State University to broaden participation, especially among underrepresented minority students.