Positive curvatures, exotic manifolds and Riemannian foliations

Abstract

This postdoctoral research program lies in the area of Riemannian geometry with two main focus: in the subarea of positive/non-negative curvatures, we aim via the study of the geometry and dynamics of exotic spheres, to possibly find invariants and/or hints to the existence/obstruction to metrics with such curvature assumptions on exotic manifolds and manifolds with symmetries in the form of group actions and/or singular Riemannian foliations; in the subarea of homogeneous or locally symmetric spaces, we seek to classify Riemannian foliations on these manifolds. Proofs of concept of the expected success of this research are explicitly given through all the text.