New examples with positive \(\text{Ric}_2\) curvature.

I will present joint work with Miguel Domínguez Vázquez, David González-Álvaro, and Jason DeVito, focused on constructing the first examples of compact Riemannian manifolds with \(\text{Ric}_2>0\) curvature in dimensions 10, 11, 12, 13, and 14. The condition \(\text{Ric}_2 > 0\) is an intermediate curvature condition that interpolates between positive sectional curvature (\(\text{sec}> 0\)) and positive Ricci curvature (\(\text{Ric}> 0\)). We achieve this using a generalization of the fat bundle notion.