Geometries by Holonomies

Wednesday, March 22, 2017 - 16:00 to 16:50
Thackeray 427
Speaker Information
Jacob Gross
University of Pittsburgh

Abstract or Additional Information

The holonomy of a connection is the group of parallel transports around loops. Berger classified all possible holonomy groups of irreducible non-symmetric Riemmanian manifolds. Some such classes are Calabi-Yau, hyper-Kähler and G2 manifolds. It turns out that Berger's theorem echoes the classification of real divison algebras. We will present the picture of geometry this paints. If time permits we'll discuss the Calabi conjectures, which specify which (1,1)-forms are the Ricci forms of a Kähler metric. They were proved by Yau, earning him the Fields Medal in 1972.