Masoumeh Zarei, University of Münster, Germany

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.