Exceptional holonomy and related geometric structures: Basic theory

Marston Morse Lectures
Topic:Exceptional holonomy and related geometric structures: Basic theory
Speaker:Simon Donaldson
Affiliation:Stonybrook University
Date:Tuesday, April 3
Time/Room:2:00pm - 3:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/MarstonMorse/2018/0403-SimonDonaldson

In this lecture we will review the notion of the holonomy group of a Riemannian manifold and the Berger classification. We will discuss special algebraic structures in dimensions 6, 7 and 8, emphasising exterior algebra, and then go on to differential geometry. Here dimensions 7 and 8 correspond to the exceptional holonomy groups $G_{2}$ and Spin(7) and dimension 6 to Calabi-Yau threefolds, which also appear as an “exceptional” case from this point of view. If time allows we will also discuss calibrated geometry (i.e. special submanifolds, such as holomorphic curves, associative submanifolds) and gauge fields.