Arnaud Beauville
UC Davis
To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric. A famous theorem of Berger gives a complete (and rather small) list of the groups which can appear. Surprisingly, the compact manifolds with holonomy smaller than SO(n) are all related in some way to Algebraic Geometry. I will explain how this occurs and how this gives rise to deep problems in Algebraic Geometry.