Alberto Rodríguez Vázquez has just started a Marie-Curie postdoc here at the ULB. He will talk in the differential geometry seminar on 7th October so we can all hear about his research. The talk will be at 2pm in the Salle des Profs. Alberto’s title is “Positive Curvature and Totally Geodesic Submanifolds from a Symmetry Viewpoint” and his abstract is below.

*First, 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 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.*

*Second, I will discuss work with Juan Manuel Lorenzo Naveiro, where we classify totally geodesic submanifolds of homogeneous nearly Kähler 6-manifolds and their G2-cones. For this, we develop algebraic tools to study totally geodesic submanifolds in naturally reductive homogeneous spaces and Riemannian cones.*