Videos

New Four-Dimensional Gauge Theories Workshop: On the Geometry of $G_2$-Monopoles and the Donaldson--Segal Program

Presenter
October 27, 2022
Keywords:
  • $G_2$-monopoles
MSC:
  • 58D27
  • 53C07
  • 58E15
Abstract
$G_2$-monopoles are special solutions to the Yang--Mills--Higgs equation on (noncompact) $G_2$-manifolds, similar to the 3-dimensional BPS monopoles. Donaldson and Segal conjectured that these gauge theoretic objects have a close relationship to the geometry of the underlying $G_2$-structure. Intuitively, $G_2$-monopoles with “large mass” are predicted to concentrate around coassociative submanifolds. In this talk, I will introduce the relevant concepts to this conjecture, in particular, $G_2$-monopoles and coassociative submanifolds, in more detail. Then I will explain what the state-of-art is, with an emphasis on the work I have done (or planning on doing) with my collaborators. This is a joint project with Gonçalo Oliveira, Daniel Fadel, Saman Habibi Esfahani, and Lorenzo Foscolo.