The geometry of G_2-monopoles and the Donaldson–Segal program

Abstract: G_2-monopoles are special solutions to the Yang–Mills–Higgs equation on G_2-manifolds, similar to 3-dimensional BPS monopoles.

Donaldson and Segal proposed that these gauge theoretic objects have a close relationship to the geometry of the underlying manifolds. Heuristically, G_2-monopoles with “large mass” should detect coassociative submanifolds.

In this talk, I will first introduce the conjecture in more detail. Then I will present what is known so far, which is mostly recent works of collaborators and myself. Finally, I will explain what the remaining questions are and how we plan on tackling them.

This project is joint with Gonçalo Oliveira, Daniel Fadel, Saman Habibi Esfahani, and Lorenzo Foscolo.