Abstract: An important invariant of a riemannian manifold is its holonomy group. Work of Cartan, Berger and others classified the Lie groups that can occur as a holonomy group. Among these groups, there are certain special cases whose geometry has been extensively studied. Examples include Calabi-Yau manifolds, (Hyper-)kahler manifolds, G2 and Spin(7) manifolds. Furthermore, special holonomy has particularly gained popularity after physicists started applying special holonomy manifolds to their models in String and M-theory.
This talk will be a gentle introduction into this exciting area of mathematics that draws ideas from many fields such as differential geometry, representation theory, algebraic geometry, PDE theory and theoretical physics.