David González, Universidad Politécnica de Madrid

Title: Infinite families of manifolds of positive k-th intermediate Ricci curvature with k small.

Abstract: Positive k-th intermediate Ricci curvature on a manifold
of dimension n, to be denoted by Ric_k > 0, is a condition that
interpolates between positive sectional and positive Ricci curvature
(when k=1 and k=n-1 respectively). It follows from the definition
that the smaller the k, the more restrictive the condition Ric_k > 0.
In this talk we will consider various kinds of metrics on closed
homogeneous spaces, and we will discuss how to estimate the
least k for which they satisfy Ric_k >0. In particular we will look at
various infinite families of manifolds (including generalized
Aloff-Wallach spaces) that are topologically distinct and admit
metrics of Ric_k > 0 with k small. This is joint work with
Miguel Dominguez-Vázquez and Lawrence Mouillé.