Diego Artacho de Obeso (KU Leuven) will speak in the geometry seminar on 13th April, at 2pm in the Salle des Profs. Diego’s title is “Stability of Einstein metrics from the spinorial viewpoint” and his abstract is below.
Einstein metrics with non-positive scalar curvature are conjectured to be linearly stable. On spin manifolds, the existence of parallel or Killing spinors provides spinorial criteria for stability. In this talk I explain how this Bochner-type mechanism extends to non-spin manifolds using twisted spinors. In particular, we show that Einstein manifolds carrying parallel twisted pure spinors are linearly semistable. This yields stability results for a broad class of spaces, including quaternionic Kähler manifolds.