Université libre de Bruxelles, 23/01/2015
“Folded hyperkähler manifolds.”
Folded hyperkähler manifolds were recently introduced by Nigel Hitchin. I shall give a construction of such metrics.
“Ricci flow, Einstein metric and the Yamabe invariant.”
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. The stability and instablity conditions are given in terms of the conformal Yamabe invariant and estimates on the smallest positive eigenvalue of the Laplacian.
“Rigidity and stability in positive scalar curvature.”
I will discuss several new stability and classification results for Riemannian and, in particular, Einstein manifolds with positive scalar curvature. This is joint work with M. Wiemeler.