BRIDGES Lectures: G2 in action, and a mathematical theory of exceptions

TL;DR

This paper presents notes from a lecture series on the geometry of G2 and exceptional complex Lie groups, connecting gauge theory, extremal structures, and a new mathematical theory of exceptions.

Contribution

It offers a detailed mathematical framework for understanding G2 and related exceptional Lie groups, integrating recent theories of exceptions.

Findings

Develops a mathematical theory of exceptions.

Provides geometric insights into G2 and exceptional Lie groups.

Connects gauge theory with extremal structures.

Abstract

The BRIDGES meeting in gauge theory, extremal structures, and stability was held in June 2024 at l'Institut d'\'Etudes Scientifiques de Carg\`ese in Corsica, organized by Daniele Faenzi, Eveline Legendre, Eric Loubeau, and Henrique S\'a Earp. The first week was a summer school consisting of four independent but related lecture series by Oscar Garc\'ia-Prada, Spiro Karigiannis, Laurent Manivel, and Ruxandra Moraru. The present document consists of notes for the lecture series by Laurent Manivel on the geometry of G2 and the other exceptional complex Lie groups. Some assistance in the preparation of these notes by the author was provided by several participants of the summer school. See the Comments field for more information.