Abstract: I will present joint work with Miguel Domínguez Vázquez, David González-Álvaro, and Jason DeVito, focused on constructing examples of compact Riemannian manifolds with Ric2>0 curvature in dimensions 10, 11, 12, 13, and 14. The condition Ric2>0 is an intermediate curvature condition that interpolates between positive sectional curvature (sec>0) and positive Ricci curvature (Ric>0). We achieve this using a generalization of the fat bundle notion.