Dirac operators and the stability of Einstein metrics

The stability of Einstein metrics refers to the stability of Einstein metrics as critical points of the total scalar curvature functional (Hilbert-Einstein action). It is fundamental in understanding the variational structure of Einstein metrics as well as in convergence issues in the Ricci flow. After discussing the background and previous work, we will talk about our work with Xiaodong Wang and Guofang Wei using the Dirac operator in the study of stability problem for Einstein metrics as well as some applications.