Title: Positive curvature conditions and Ricci flow
Abstract: Given a Riemannian manifold (M,g), it is a
fundamental problem to understand how the metric g and its curvature
properties evolve under the Ricci flow. For instance, by the celebrated
work of Hamilton, positive scalar curvature is preserved under the
Ricci flow in every dimension. Moreover, both positive sectional and
positive Ricci curvatures are preserved in dimension 3. It is then
natural to ask whether any other curvature conditions are preserved in
higher dimensions. In this talk, I will give some examples which admit
metrics with different curvature conditions and discuss the evolution
of their metrics under the Ricci flow. This is based on joint works with
David González-Álvaro.